LIBRARY W Michigan State University TO AVOID FINES return on or before date due. F—__—————__———————T DATEDUE DATE DUE \DATE DUE l PLACE IN RETURN BOX to remove this checkout from your record. i i } FEB 33 2001 “I _________ MSU is An Affirmative Action/Equal Opportunity Institution cMmMuM—o.‘ AN EXPERT SYSTEM FOR THE PRELIMINARY DESIGN OF CANTILEVER RETAINING WALLS BY NASRULLAH ABEER A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Civil and Environmental Engineering 1991 ABSTRACT AN EXPERT SYSTEM FOR THE PRELIMINARY DESIGN OF CANTILEVER RETAINING WALLS BY NASRULLAH ABEER An application of knowledge-based expert systems (KBES) in the domain of geotechnical engineering design was devel- oped and evaluated. The KBES, named TWALL, performs the pre- liminary design of cantilever retaining walls, including the proportioning of wall dimensions to ensure external stabili- ty (i.e., wall stability against overturning, sliding and bearing failures) and provision of sufficient steel to ensure internal stability of the wall. TWALL is structured to design for either external stability only or both exter- nal stability and internal stability. In TWALL, a hierarchical decomposition of the task of wall design is used as a basis for system organization. The knowledge base of TWALL is developed in production rule lan- guage provided by the LEVELS expert system shell. There are a total of 297 rules used in the knowledge base. The devel- oped system is semi-automated with a user-friendly interface and contains proportioning algorithms developed to obtain a design with only few trials. The design of a cantilever retaining wall is influenced by a large number of parameters including wall height, engineering properties of foundation soil and backfill material, and water levels. A parametric sensitivity analy- sis was performed to assess the effect of these parameters on the wall design. The wall design is also influenced by the assumed lateral earth pressure conditions (at-rest or active) behind the wall. The effect of earth pressure as- sumptions on wall dimensions and overall cost has also been studied for different wall heights and other parameters. At the present state of geotechnical knowledge, it is difficult to relate parameters affecting wall design in a purely algorithmic way to the proportioning of the wall. Engineering judgement and experience is required for the selection of required design parameters. Some heuristics are written to help novice designers in the selection of soil parameters and wall dimensions. To my parents, wife Sumera and children Umar, Aisha and Hamzah iv ACKNOWLEDGEMENTS I would like to express my sincere gratitude and appre- ciation to my thesis advisor Dr. Thomas F. Wolff for his guidance and encouragement during the course of this re- search. Appreciation is also expressed to Dr. Orlando Andersland, Dr. Perviz Soroushian and Dr. Grahame J. Larson for their moral support and helpful suggestions as members of my guidance committee. I wish to express my sincere thanks and appreciation to Dr. Wayne Bergstrom and Messrs; Mark Alvey, Scott Gleason, Kevin Miller and his colleagues and Ralph Strom for their help in knowledge elicitation. I also thank the students of Michigan State's CE 818, CE 419 and CE 499 courses for their participation in the validation of TWALL. Finally, I am indebted to the Pakistan Army, Corps of Engineers for providing financial support without which it 'would have been impossible to complete this study. TABLE OF CONTENTS LIST OF TABLES . ........... . ........... ....... ........ xii LIST OF FIGURES ............................... ........ xiv CHAPTER 1. INTRODUCTION 1.1 General ........... ............................. 1 1.2 Problem Statement ... ........ . ........ . ...... ... 3 1.3 Objectives of the Study ........................ 5 1.3.1 Main Objectives ...... .......... ............ 5 1.3.2 Sub-Efforts ................................ 6 1.3.2.1 Literature Review ........................ 6 1.3.2.2 Knowledge Elicitation .................... 6 1.3.2.3 Parametric Sensitivity Analysis .......... 6 1.3.2.4 Active Versus At-Rest Analysis ........... 7 1.3.2.5 Synthesis of Knowledge-New Recommendations for Design ............... 8 CHAPTER 2. CURRENT PRACTICE IN CANTILEVER RETAINING WALL DESIGN 2.1 General ................. ........ ............... 9 2.2 Wall Proportions ........ ....... ................ 9 2.3 Forces Acting on the Wall ...................... 10 2.4 Lateral Earth Pressure ........ ......... . ...... . 12 2.4.1 Brief Historical Background . ..... .......... 14 2.4.2 Active and Passive Earth pressure: Classical Theories ................................... 15 2.4.2.1 Coulomb’s Theory .......... ............ 16 2.4.2.1 Rankine’s Theory .. ................. ... 20 2.4.3 At-Rest Earth Pressure .................... 25 2.4.4 Earth Pressure at Intermediate Active State 26 2.4.5 Factors Affecting Earth Pressure Predictions 27 2.4.5.1 Wall Movement . ........ ...... ...... .... 27 2.4.5.2 Wall Friction ......................... 28 2.4.5.3 Water .... .................. ........... 29 vi 2.4.5.5 Surcharges ... ......................... 2.4.5.6 Seasonal Variation .................... 2.4.6 Field Measurement of Lateral Earth Pressure 2.4.7 Location of Resultant Earth Force ..... .... 2.5 Foundation Pressure .... ..... . ........ ......... 2.6 wall stability 0 O O. O O. O OOOOOOOOOOOOOOOOOOOOOOO 2.6.1 External Stability ......OOOOOOOOOOOOOOOOOO 2.6.1.1 Stability Against Overturning .. ....... 2.6.1.2 Stability Against Sliding ............ 2.6.1.3 Bearing CapaCj-ty ......OOOOOOOOOOOOOOOO 2.6.1.4 Settlements ..... ........ .... .......... 2.6.2 Structural Design ........ ................. 2.6.2.1 Basis for Structural Design ........... 2.6.2.2 Stem DeSign ....OOOOOOOOOOCOO ......... 0 2.6.2.3 Heel Design .... .................. ..... 2.6.2.4 Toe Design .. .............. .. .......... 2.6.2.5 Moment Capacity . ...................... 2.6.2.6 Checks for Shear ...................... 2.7 Soil Properties ............................... CHAPTER 3. EXPERT SYSTEMS AND THE DEVELOPMENT OF TWALL 3.1 Introduction .......................... ..... . 3.2 Historical Perspective ......OOOOOOOOOOOIOOOOOO 3.3 Architecture of an Expert System ..... . ........ 3.4 Knowledge Representation in Expert Systems .... 3.5 Problem-Solving Strategies in Expert Systems .. 3.5.1 Forward Chaining ......... ....... .......... 3.5.2 BaCRward Chaining 0 ........ ......OOOOOOOOOC 3.5.3 Hybrid Approach ..... ...................... 3.6 Expert System Building Tools ...... ............ 3.6.1 General-Purpose Programming Languages .... 3.6.2 General-Purpose Representation Languages .. 3.6.3 Expert System Shells ...................... 3.6.3.1 Domain-Specific Shells ................ 3.6.3.2 Domain-Independent Shells ..... ........ 3.7 Previous Geotechnical Applications ........... 3.7.1 RETWALL ................................... 3.7.2 CONE O... 00.... ....... O O. O O 000000000000 vii 3O 31 32 32 33 36 36 36 4O 41 43 44 44 48 5O 53 54 55 56 57 58 59 62 63 63 64 64 65 65 66 67 67 68 71 3.7.3 RETAIN ......O...............OOO.......... 73 3.8 Background on Present Research ........... ..... 74 3.9 Development of TWALL ............... ....... .... 76 3.9.1 General................. ............ ....... 76 3.9.2 Problem Identification .. ..... ............. 78 3.9.3 Collection of Knowledge ................... 81 3.9.4 Problem Conceptualization ................. 82 3.9.5 Selection of Expert System Building Tool .. 83 3.9.6 Knowledge Representation .................. 86 3.9.7 Selection of Control Strategy ............. 87 3.9.8 Knowledge Formalization ................... 88 3.9.9 Prototype Implementation .................. 88 3.9.10 Testing, Validation and Expansion ......... 89 3.10 Architecture of TWALL ....... . ........ ........ 94 3.10.1 Knowledge Base . .................... ...... 94 3.10.1.1 Goal Statements ......... ...... ...... . 94 3.10.1.2 Production Rules ................. .... 96 3.10.1.3 Procedural Rules . ................... . 96 3.10.2 Inference Mechanism . ............... . ..... 97 3.10.3 Session Context ............... ......... .. 98 3.10.4 User Interface ................ ...... .... 98 3.10.5 Explanation Facility ...... ............... 98 3.10.6 External Graphics Program ........... ..... 99 CHAPTER 4. TWALL: KNOWLEDGE BASE 4.1 General ...000......00000000000000.....OOOOOOOO 100 4.2 Building Blocks of TWALL ..................... . 102 4.2.1 881: General Information ................ 102 4.2.2 332: Wall Suitability ................... 102 4.2.3 BBB: Parameters Evaluation .............. 104 4.2.4 BB4: Trial Wall Dimensions .............. 107 4.2.5 BBS: Forces on Wall ..................... 109 4.2.6 BB6: Overturning Stability .............. 110 4.2.7 BB7: Sliding Stability .................. 114 4.2.8 BBB: Conservative Design ................ 116 4.2.9 BB9: Bearing Capacity ................... 118 4.2.10 BB10: Parameters for Structural Design ... 121 4.2.11 8811: Stem Design ........................ 121 4.2.12 8812: Base Design ........................ 122 4.2.14 BB13: Cost Analysis ...................... 125 4.2.15 8814: Graphic Interface ... ...... ......... 125 4.3 Examples of Design Process ............. ....... 128 viii CHAPTER UIUIU'I I. UNH 5 5. 5.4 5. 5. 5 CHAPTER 6. 000‘ .0 UNH 3 3 U'IU'IU'IU'IUiU'IUI 4 4 4 General PARANETRIC SENSITIVITY ANALYSIS Assumptions . . . . . . O O O O O I O . O . O . . . . O O O O O . O C . O O . . . Effect of Changes in Variables on Wall stability 0 O O O O O O O O O O ...... O O O O O O O O O O O O O O O O O O O O .1 Method of Analysis ............. .... Results .2 to e \lmUinFUNH O. UUUUUUU O. . O O NNNNNNN 0. Effect Wall Height ...... .............. ....... Base Length . ....... . ..... ............. Heel Length ........................... Backfill Slope ........................ Soil Friction Angle .... Soil Unit Weight .. ..... ............... Wall Friction Angle ..... .............. Distribution on Heel Gene .1 .2 3 WALL General ral Wall Friction of Change in Heel length on Method of Analysis ................ .... Results Pressure Backfill Slope ......... ............... Water Table Summary DESIGN EFFECT OF EARTH PRESSURE ASSUMPTIONS ON Method of Analysis ............. ............... Results 6.3.1 Part 1: Effect of Wall Height ............. 6.3.2 O\O\O\ .3 .3. 3 .1.1 1.2 1 3 Cost 3 2.1 .3.2.2 3 2.3 Base Length Backfill and Concrete .. Wall cost Effect of Overload Factors ............................. Part II: other Factors Affecting Wall Effect of Wall Friction Effect of Sloping Backfill ............ ix 132 133 134 134 136 136 140 141 145 146 146 147 150 150 151 152 155 155 158 158 161 162 165 165 165 167 170 170 170 173 173 CHAPTER 7. KNOWLEDGE ELICITATION AND HEURISTICS DEVELOPMENT 7.1 General ........................... ..... 0...... 177 7.2 Knowledge Elicitation .......... ....... ........ 177 7.3 Heuristics Development ........................ 179 CHAPTER 8. DETAILED SUMMARY AND CRITICAL ASSESSMENT general ................. ..... ................. 189 Design procedure .............................. 189 Lateral Earth Pressure ........ ....... ......... 191 Active versus At-Rest Pressures . ........ ...... 192 Wall Stability ................................ 194 O... UlchUNH oooooooooo Overturning Stability ..................... 195 Sliding Stability ......................... 196 Bearing Capacity .......................... 197 What Governs Design? ......... . ..... ....... 198 e e PUMP common UIUIUiU'I Development of TWALL ......... .............. ... 199 TWALL Design Process ... ............. .. ...... .. 202 TWALL Versus Algorithmic Programs ..... ...... .. 203 Expert Systems in Education .................. . 205 00000000 \Dmdm 8.9.1 Educational features of TWALL ........ ..... 206 CHAPTER 9. SUMMARY, CONCLUSIONS AND RECOMMENDATIONS 9.1 Summary .... ............... . ...... ............. 208 9.2 Conclusions ................................... 209 9.2.1 Conclusions Regarding Application of Expert System Technology ..... .............. ...... 209 9.2.2 Conclusions Regarding Wall Design ....... .. 210 9.3 Recommendations for Future Research ... ..... ... 212 LIST OF REFERENCES ........................... ......... 214 APPENDIX A. QUESTIONNAIRE ON CANTILEVER WALL DESIGN ... 222 APPENDIXB. EMPLERUN...........................O... 229 B1. TWALL Solution of Example 1, Appendix N, The U.S. Corps of Engineers Manual (EM 1110-2-2502) .... 229 82. TWALL Solution of Example 12.4 (Bowles 1982) .. 241 APPENDIX C. TWALL: SAMPLE RULES AND PROCEDURES ....... C1. C2. Sample Rules .................................. sample Procedures ......OOOOO0......00000000000 APPENDUX D. COMPARATIVE STUDY D1. D2. D3. General ..... ............................... ... Results 0.... ..... O00.000000000000000....00.... Summary ....................................... xi 244 244 250 254 254 255 Table LIST OF TABLES Recommended trial dimensions for cantilever walls ..........................O.............. Movements required to achieve active conditions Overload factors . ............. ................ Comparison of PC-Based expert system shells ... Comparison of TWALL results with Example 1, Appendix N, The U.S. Army Corps of Engineers, (EM 1110-2-2502 1989) ............ . ......... ... Comparison of TWALL results with Example 12.4 (Bowles 1982) . ................ . ........... .... Range of variables .............. . ............. Base safety factors . ........ . ..... ............ Effect of toe length on net pressure on heel at different wall heights ..................... Effect of toe length on net pressure at different wall friction angles .... ..... ....... Range of parameters ....... ..... ... ..... ....... Trail wall dimensions based on expert’s opinion ........ ......... .............. ..... ... Expert opinion on design values of soil parameters ............................ ..... ... Expert's opinion on earth pressure prediction .................................... xii Page 11 20 47 7O 91 92 135 135 154 154 164 180 181 182 Expert’s opinion on cantilever wall stability ......... ...... ...................... 183 Expert's opinion on various aspects of Structural deSign. ..... ....................... 184 Comparison of TWALL designs with students (CE 419) designs (backfill slope = 10 degrees) 258 Comparison of TWALL designs with students (CE 419) designs (backfill slope = 15 degrees) 259 Comparison of TWALL designs with students (CE 419) designs (backfill slope = 20 degrees) 260 xiii LIST OF FIGURES Parts of cantilever retaining wall ............ Force system: cantilever retaining wall ....... Coulomb failure wedge .. ......... .............. Assumed conditions for failure:Coulomb ...... .. Rankine's active state of stress ... ........ ... Failure of cohesionless soils behind cantilever retaining walls . ....... . ....... .... Pressure distribution under base .............. Force system: External stability analysis ..... Effect of eccentricity on distribution of soil pressure under the base .......... ............. Forces considered for the structural design of stem, heel and toe . ...... ................. Architecture of an expert system . ............ . Hierarchy of TWALL knowledge base ...... ...... . Architecture of TWALL ..... . ................... Structure of building blocks in TWALL ......... Inference network for wall suitability ........ Inference network for parameters evaluation ... Inference network for wall stability against overturning ................................... Inference network for wall sliding stability... xiv Page 13 17 17 23 23 35 38 46 50 61 84 101 103 104 111 115 4.8 4.9 4.10 4.11 Inference network for wall stability against bearing capacity failures ..................... Inference Inference Inference Structure TWALL design process when trial dimensions network for stem design ............. network for base design . ..... . ...... network for cost analysis ........... of external program GTWALL .......... recommended by TWALL are used ................. TWALL design process with bad guess of soil parameters and Percent change versus percent Percent change versus percent Percent percent Percent bearing change change change safety trial wall dimensions in overturning safety factor change in parameter values ..... in sliding safety factor change in parameter values ..... in bearing safety factor versus in values of parameters ........ in overturning, sliding and factors versus percent change in AXmax of wall height ................ Effect of change in base length on overturning safety factor ....... ............. . Effect of change in heel length on overturning safety factor ........ . ....... Effect safety Effect safety Effect safety Effect safety Effect of change in base length on sliding factor .. ......... .. of change in heel length on sliding factor .... of change in base length on bearing factor ............ ...... ......O........ of change in heel length on bearing factor ................................. of change in wall friction on overturning safety factor ..................... Effect of change in wall friction on sliding safety factor ....... .......................... XV 119 123 123 126 127 131 131 137 137 138 139 142 142 143 143 144 144 148 148 6.10 Effect of wall height on eccentricity at different wall friction angles ................ Effect of wall friction on bearing safety factor ............... ....... .................. Effect of heel length on net downward pressure on heel at different wall heights ............. Effect of wall height on permissible heel length ........................................ Effect of heel length on net pressure on heel at different wall friction angles ........ Effect of wall friction on permissible heel length ............... . .......... . ...... . ..... . Effect of heel length on net pressure on heel at different backfill slopes ............. Effect of heel length on net pressure on heel at different water levels in backfill ......... Effect of water table on permissible heel length ........ ..... ............... ..... ....... A typical cantilever retaining wall ........... Effect of wall height on base length ....... ... Effect of wall height on required backfill .... Effect of wall height on required concrete .... Effect of wall height on earth force on stem... Effect of wall height on wall cost ............ Difference in required materials and wall cost under active and at-rest conditions ...... Effect of overload factors on wall cost assuming active conditions .................... Effect of overload factors on wall cost assuming at-rest conditions ................... Effect of wall friction on wall cost for different wall heights ........................ Effect of wall friction on wall cost assuming active and at-rest conditions ........ xvi 149 149 153 153 156 156 158 158 159 163 167 167 168 168 171 171 172 172 174 174 6.12 0-1 Effect of sloping backfill on wall cost ....... Comparative study: base lengths designed by students (CE 419) versus TWALL ...... . ......... . Comparative study: heel lengths students (CE 419) versus TWALL . ..... ................. Comparative study: sliding safety factors obtained by students (CE 419) versus TWALL .... Comparative study: overturning safety factors obtained by students (CE 419) versus TWALL .. xvii 175 256 256 257 257 CHAPTER 1 INTRODUCTION 1.1 Cantilever Retaining Walls A retaining wall is a structure that provides lateral resistance necessary to prevent horizontal movement of a retained soil mass (Newman 1976). There are several types of retaining walls that can perform this function including gravity walls, cantilever walls and crib walls. The wall type (considered under study) here is the cantilever retain- ing wall. The terms associated with a cantilever retaining wall cross section are shown in Figure 1.1. The stem acts as a cantilever beam which must resist lateral pressure caused by the backfill material. The base is the structural component that must transmit vertical forces and to some extent, horizontal forces, to the foundation soil. The heel is the portion of the base on the back side of the wall and the toe is the base portion on the front side of the wall. A base key may be provided to increase lateral resistance in case “the foundation soil is weak. The key can be at different Ibocations along the base. The backfill is material placed to éfix zfl§' A§_—7KT“ZK—fzfif Front Face —> ‘—— Back Face Backfill ‘"— Stem 55T:35*’6K' Backfill Toe ‘ Heel Base Kev Foundation Soil Figure 1.1 Parts of cantilever retaining wall 3 elevate the ground surface to the design elevation. 1.2 Problem statement Cantilever retaining walls are designed by trial and error. Trial section dimensions are assumed and earth pres- sures acting on that section are computed based on some earth pressure theory. The stability of the wall is checked against overturning, sliding and bearing capacity failures and against excessive settlements. The section dimensions are revised until the wall is externally stable against these failure modes with a reasonable safety margin and rea- sonable economy. Then computations for bending moments, shears and required reinforcement are performed to ensure internal stability of the wall. For the safe and economical design of a cantilever retaining wall, a geotechnical engineer is required to make use of his experience and judgment besides using theoretical and empirical methods. The design process also involves certain heuristics (rules of thumb) that can only be applied efficiently by an engineer experienced in wall design. This study critically assessed heuristic rules required to implement the design of a cantilever retaining wall. Indeed it was found and will be shown that the design task Inay require consideration of hundreds of "rules". Manual computational methods available for the design (Df'cantilever retaining walls are tedious and time consuming 4 and can be viewed as things of past in this age of comput- ers. Conventional computer programs such as TWDA (Price et al., 1980) and B-24 (Bowles 1988) are being used for the design of retaining structures. But it is difficult for a novice user to understand their workings and there are prob- lems associated with altering such programs to suit new requirements. The algorithmic nature of traditional conventional pro- gramming languages such as BASIC and FORTRAN limits informa- tion representation to numerical and graphical means. Design problems such as cantilever wall design require professional expertise, knowledge and experience for decision making, rather than simply an analysis of numerical problems. Thus, there is some advantage developing design tools that can handle rules and experience than that provided by the algo- rithmic solutions. Researchers in the area of artificial intelligence, (a branch of computer science) have recently invented tech- niques to create programs that are more interactive, knowl- edge intensive, user-friendly and easily modifiable than earlier FORTRAN (or BASIC) computer programs (e.g., CBEAR and TWDA). These programs are called knowledge-based expert systems (KBES) or expert systems (ES). KBES are essentially attempts to model the performance of human experts within their respective domains (Fenves et al., 1984). Knowledge in KBES is more explicit, accessible and expandable than the knowledge embedded in the codes of a 5 conventional program. KBES uses a systematic approach for finding the answer to the problem and explaining its behav- ior through an explanation facility (Rychener 1988). Over the past few years, a number of KBES have been developed for some selected problems in civil engineering. Some of the areas in which the KBES are developed include structural design (Maher 1988), interpretation and geotechn- ical characterization of data from cone penetrometers (Mullarkey 1985), management and architectural design (Flemming 1988), selection and preliminary design of earth retaining structures (Hutchinson et al., 1987) and reha- bilitation of earth retaining walls (Adams et al., 1990). The few developed KBES related to retaining structures are limited either to selection of the appropriate type of wall for a given situation or to use for diagnostic purposes only. No published literature was found where an attempt has been made to use an expert system technology for the struc- tural design of cantilever retaining walls by combining heuristics with analytical methods being used for the design. 1.3 Objectives of the study 1.3.1 Main Objectives The two primary objectives of this study were to devel- o$> a semi-automated knowledge-based expert system for the 6 preliminary design of cantilever retaining walls and to assess the suitability of such an approach to this class of problems. Supporting the main objective are several sub-efforts which are summarized in the following sections. 1.3.2.1 Literature Review This effort consisted of reviewing previous research on earth pressure, current design procedures for cantilever retaining walls and capabilities of knowledge-based expert systems for the development of present system. 1.3.2.2 Knowledge Elicitation This effort involved heuristic knowledge elicitation from engineers experienced in the design of retaining struc- tures. Knowledge elicited from such experts was mostly used to verify the heuristics developed from parametric sensitiv- ity analysis. This effort is described in Chapter 7. 1.3.2.3 Parametric Sensitivity Analysis The stability of a cantilever wall is affected by a ruimber of variables including wall height, base and heel 7 length, backfill and foundation soil parameters, wall fric- tion, backfill slope and water table. By understanding clearly how these variables (independently and in combina- tion) affect wall stability, one can better proportion the wall dimensions for safe and economical design with fewer trials. This analysis also helped to develop heuristics to guide novice program users. An example of sensitivity analysis would be the effect of toe length. A change in toe length effects the distribu- tion of upward soil pressure under the base. With a short toe, the upward soil pressure may exceed the downward pres- sure at the intersection of heel and stem and the point of maximum shear and moment shifts from the intersection point toward the free end of the heel. In this situation, a common assumption used for the structural design of heel (i.e., the point of maximum shear and moment is at the intersection of heel and stem) is violated. A parametric sensitivity analy- sis can help to determine a minimum toe length so that this assumption is not violated. This analysis is described in Chapter 5. 1.3.2.4 Active Versus At-Rest Analysis The assumption regarding state of stress in the backf- ill for computing lateral earth pressure behind cantilever retaining walls is somewhat controversial. Many references (e.g., Das 1984, Bowles 1988) recommend assuming an active state of stress in the backfill for earth pressure predic- 8 tions. On the other hand, recently some agencies (e.g., the U.S. Army Corps of Engineers, 1989) have recommended design- ing for at-rest conditions. These assumptions affect the magnitude of lateral earth pressure which ultimately affect wall dimensions and overall cost of the wall. A design tool such as TWALL provides a convenient way to study the quantitative effect of active and at-rest assumptions on required quantity of materials and cost of the wall. This analysis also helped in writing some heuris- tic rules. Chapter 6 describes this analysis. 1.3.2.5 Synthesis of Knowledge - New Recommendations for Design The development of TWALL necessitated a critical look at a variety of design recommendations and required generat- ing numerous designs for the developments of heuristics. It is useful after this experience to reflect on findings and make one’s own recommendations regarding prediction of earth pressure behind cantilever retaining walls and proportioning of wall dimensions. Chapter 8 summarizes this effort. CHAPTER 2 CURRENT PRACTICE IN CANTILEVER RETAINING WALL DESIGN 2 o 1 Genera 1 The general approach to the design of a cantilever re- taining wall is to analyze conditions that would exist at the time of impending collapse and to apply suitable factors of safety to prevent such a collapse. This approach is known as limit design and requires limiting equilibrium mechanics (Lambe and Whitman 1969). The design must ensure external and internal stability of the wall. External stability refers to wall stability against overturning, sliding and bearing capacity failures. The wall is considered internally stable when all its parts have sufficient flexural and shear strength to resist applied bending moments and shears. 2.2 Wall Proportions Site conditions impose certain constraints on wall proportions. The height of wall depends on the elevation difference across the wall and the depth of required cover on the toe side of the wall. The stem thickness and 10 reinforcement must be sufficient to resist shears and moments due to earth pressure against the wall. The stem thickness at the top of the wall should be sufficient to permit easy placement of concrete. The dimensions of the base, heel and toe are a function of result from the stability and strength requirements established in the design procedure. The required base width is a function of strength properties of backfill and founda- tion soils and the slope of backfill. The thickness of the base depends on shears and moments at sections located at the front and the back faces of the stem. The base in front of the wall should be placed below the depth of frost ac- tion, zone of seasonal variation and the depth of scour. The toe and heel lengths are governed by overturning and sliding stability requirements. Recommended trial wall dimensions given by various references are shown in Table 2.1. 2.3 Forces Acting on the Wall The forces considered for the stability analysis of a unit width of a cantilever retaining wall are shown in Figure 2.1 (a). These include the driving-side soil force Pfl,and water force PWD against the vertical section AB at the end of the heel, the resisting-side soil force Pfl_and water force Pkm against the vertical section CD at the end of toe, the effective soil force N’ and uplift force U that act vertically on the base DB, shear S along DB and the Table 2.1 Recommended trial dimensions for cantilever walls Top thickness Bottom thickness sufficient for placement of concrete increase thickness with depth by 1/4 to 3/4 in/ft minimum 30 cm 0.1 H (same as base thickness) Parts of wall Peck (1974) Das (1984) Bowles (1988) Base Width (8) 0.4 to 0.65 H 0.5 to 0.7 H 0.4 to 0.7 H H/12 to H/8 Thickness 0.1 H H/12 to H/10 8/3 Toe length 0.1 H 8/3 Ste- minimum 20 cm prefer 30 cm H/12 to H/10 (same as base thickness) 12 total weight the wall components and the soil masses above the base. The principal structural elements of the wall are the stem, heel and toe. The forces considered for the structural design of these elements are shown in Figure 2.1 (b). The forces acting on the stem are different from those acting on the wall due to difference in height (Figure 2.1) 2.4 Lateral Earth Pressure The magnitude of lateral earth pressure is determined by the physical properties of the soil, the physical inter- action between the soil and the structure and the value of displacements and deformations (Kedzi 1987) To simplify lateral earth pressure predictions, many designers assume an active state of stress on the driving side (heel side) of the wall (Bowles 1988, Das 1984). Howev- er some engineers (e.g., Matsuo et al., 1978) and agencies (e.g., U.S. Army, 1989) recommend assuming an at-rest state of stress. The active state corresponds to the minimum lateral pressure that can develop and at-rest state implies that no deformations or displacements occur. In reality an intermediate state of stress (a state of stress between active state and at-rest state) may exist on the driving side but it is difficult to predict earth pressure under this state of stress. The passive state of stress is the ”‘4 13 A El < ) a a I we - Weight of soil Ic - weight of concrete Ws P80 dc'_' 1!! '- 5 I V7 C 1 "s P ... i F "” Pl! —_ D LWLLi U’ V ' "'4' 0 Water pressure under base (13) PM 5 4/”/' A 2g M 9': 8 Per V , K/ M STEF‘ Due to NC, We, and Pst Due to we, and We irf1ki VV n L) (1 l l M iii—Ml 1 j v Soil and enter Soil and water pressure pressure under toe under heel go; HEEL Figure 2.1 Pressure system:cantilever retaining wall: (a) Pressures considered for external stability (b) Pressures considered for internal stability 14 greatest stress that may exist on the resisting side (toe side) of the wall (Lambe and Whitman 1969) and corresponds to lateral compression to failure. The reliability of lateral earth pressure predictions is an important factor for safe and economical design of cantilever retaining walls. Although significant research has been carried out on methods for earth pressure predic- tions (Terzaghi 1920, 1934 1936 and 1940, Rowe 1969, Clough and Duncan 1971, Bang and Hwang 1986, Seed and Duncan 1986); the same old classical earth pressure theories (Coulomb’s and Rankine) continue to be used by designers for estimating earth pressure. To understand the difficulties associated with earth pressure prediction, the subject is discussed in the following sections. 2.4.1 Brief Historical Background The methods currently being used in practice for earth pressure computation can be traced back to either Coulomb’s or Rankine's theory of earth pressure. Coulomb obtained a minimum value of force against a wall by considering force equilibrium of a rigid failure wedge bounded by a planar failure surface, a rough frictional planar wall back face and the ground surface (Bowles 1982). Rankine considered a semi-infinite soil mass in a state of plastic equilibrium and solved for minimum and maximum stress. Both Coulomb and Rankine assumed straight rupture 15 planes for estimating earth pressure. Kotter in 1903 derived a differential equation governing stresses along a curved rupture-plane. Fellenius in 1927 made earth pressure calcu- lations assuming a circular rupture-plane and Rendulic in 1935 assumed a logarithmic spiral as rupture-plane for computing earth pressure (Feld 1940, Hansen 1953) Terzaghi (1920) was first to point out that the deform- ations in the soil mass must be compatible with wall move- ments. Ohde in 1938 investigated in detail the behavior of wall rotating about its top and bottom (Hansen 1953). The above mentioned works were mainly theoretical. Regarding experimental work, a considerable number of researchers con- tributed toward active earth pressure (Terzaghi 1934, Jakobson 1958, Clough and Duncan., 1971, Lee et al., 1972, Broms et al., 1972, Coyle et al., 1974, Ingold 1979, Sherif et al., 1984, Fang and Ishibashi 1986). Only a few research- ers have studied passive earth pressure (Rowe et al., 1965, Rowe 1969, James et al., 1970, Shields et al., 1973). 2.4.2 Active and Passive Earth Pressure: Classical Theories The classical earth pressure theories of Coulomb and Rankine were developed in 1776 and 1857 respectively. In one way or the other, these theories are still in use for the :prediction of lateral earth pressure behind retaining struc- ‘tures. To check if these theories are applicable for earth Ixressure prediction against cantilever retaining walls, a 16 brief review is presented in the following sections. 2.4.2.1 Coulomb's Theory (1776) The basic approach of Coulomb’s theory is to determine the minimum and maximum earth force consistent with limiting equilibrium of homogeneous and isotropic soil mass. For cohesionless soils, Coulomb assumed that a wedge of soil is formed behind walls with planar back face at minimum lateral force (Figure. 2.2). Coulomb assumed that the failure wedge acts as a rigid body and friction is developed between the back face of the wall and the failure wedge (Huntington 1957). Coulomb’s theory solves for the total lateral earth force assuming that the rupture surface is a plane (Figure 2.2) and that the shear resistance is fully mobilized along this plane. For the active case, shear on the failure plane acts against gravity and the largest total lateral earth force computed for any orientation 0 represents the smallest value of lateral earth force on the back of a retaining wall. Coulomb's theory yields only the resultant force; the state of stress within the soil mass is not obtained. As moment equilibrium is not considered, the location of resul- tant with respect to wall height is unknown. A linear pressure distribution increasing with depth is usually assumed behind a wall increasing with depth for the czase of a level or uniformly sloping ground without 17 Planar Wall Back Face Failure wedge Failure Surfaces Figure 2.2 Coulomb failure wedge l «7‘ R l Pressure Distribution Figure 2.3 Assumed conditions for failures: Coulomb 18 surcharge or water table provided the soil mass is in a state of failure throughout the wedge (Wu 1975). This solu- tion places the point of application of the resultant later- al earth force at one-third of wall height. The magnitude of the active earth force against the wall is obtained by considering the equilibrium of the failure wedge (Figure 2.3). W is the weight of soil within the failure wedge. PA is the resultant active force acting at the wall friction angle 6 from the normal. R is the resultant of the normal and shear stresses along the rupture surface and acts at an angle of shear resistance o from the normal. The analytical solution of forces acting on failure wedge yields: R5575?2 Pk= 2 (2.1) where 7 is unit weight of the backfill, H is the wall height, K is a coefficient of active earth pressure and is given as: K3: Sin2(a+¢) (2.2) Sin9asin(a-6)P+JSin<¢+6)5in(¢'9) ]2 sin(a-6)sin(a+B) ‘where a, B, o and 6 are angles as shown in Figure 2.3. The (derivation of these equations can be found in Huntington (1957) and Bowles (1982). Similarly, the expression for the passive earth force Pp is written as: 19 2 Pffl (2.3) 2 where Kp is a coefficient of passive earth pressure and is given as: K'= sin’(a-¢) 2 (2.4) P sin?asin(a+5)1-J sin(¢+6)sin(¢+p) Sin(a+6)sin(a+fl) For horizontal backfill, vertical wall backface (a=90 deg) and no wall friction, the coefficients of active and passive earth pressure reduce to K,=tan2(45-¢/2) and Kp=tan2(45+¢/2) respectively. The main deficiencies in Coulomb's theory are in the assumptions involving the ideal soil and a plane rupture surface. The assumption of a plane rupture surface has a minor effect in the active case but it can lead to large errors for the passive case where wall friction is present. The validity of Coulomb’s theory for estimating lateral earth pressure behind retaining wall is limited to the case in which lateral deformation of the wall exceeds certain minimum limits sufficient to yield the backfill (Table 2.2). The deformation required to reduce the total lateral pres— sure of cohesionless soils to Coulomb’s active state of stress is about 5 times smaller than the deformation :required to establish a linear distribution of lateral pressure (Terzaghi 1934, Duncan et a1. 1990). Also, the assumption of a planar wall back face is violated for canti- lever retaining wall. 2() Table 2.2 Movements required to achieve active conditons (modified from Duncan et a1. 1990) Hall Backfill Mode of Required Investigators Height Compacted Movement Movement at (ft) Hall Top Terzaghi (1934a) 4.9 Sand Rotation 0.0011H Terzaghi (1934a) 4.9 Sand Translation 0.0011H Terzaghi (1934a) 4.9 Sand“) Rotation 0.0020H Broms & Ingelson 9.0 Sand Rotation 0.0003H (1971) Sherif & Fang 4.0 Sand Rotation 0.0005H (1984) Sherif & Fang 4.0 Sand“) Rotation 0.0005H (1984) Fang & Ishibashi 3.33 Sand Rotation 0.0003H (1986) Fang & Ishibashi 3.33 Sand Translation 0.0003H (1986) Hatsuo et al., 32.8 silty Rotation 0.0006H to (1878) Sand 0.0008H 0.0003H to Slag Rotation 0.0005H (1) Uncompacted sand 21 Water in the backfill results in a bilinear pressure distribution behind the wall. In this situation, Coulomb’s K should be used with effective vertical stresses 0", to compute effective horizontal stress (i.e., o'H=Ka',) and additional stress caused by the water should be added to the horizontal stress to compute the total stress on the wall. Experimental results (Fang and Ishibashi 1986) have shown that Coulomb’s theory underestimates the total active force behinds walls rotating about top and bottom. However, the experimental values of total active force behind walls With translational movements is in close agreement with the Values predicted by Coulomb's theory. 2.5.2.2 Rankine's Theory (1857) Rankine considered a semi-infinite cohesionless soil mass that can develop a state of failure with the slightest deformation (Tschebatarioff 1951) . He examined the effect of lateral expansion and compression of such a soil mass. The s‘tate of stress under active and passive conditions are c=alled Rankine's states and require that there be no shear- ing stresses on vertical planes in a soil mass with a hori- ZOntal ground surface (Peck et a1. 1974) . In reality no semi-infinite mass of cohesionless soil exists. Even if it ‘33ws that even under active conditions, the earth pressure 33 distribution is not hydrostatic and the resultant is expect- ed to act above the lower third point. Sherif et al., (1982), Sherif et al., (1984) and Fang and Ishibasi (1986) also observed the similar range of locations of resultant earth force. Handy (1985) reports the effect of soil arching on earth pressure behind retaining walls. According to him, initially the magnitude of earth pressure exceeds the at-rest values and the resultant of lateral earth pressures acts at 0.33H because of triangular pressure distribution. But with the wall movement, the pressure distribution becomes parabolic and the pressure falls below the active values but the point of application of the resultant rises to 0.42H. For walls with foundation restraints, the resultant is expected to act below 0.33H. Wright et al., (1975) recommend point of application of resultant earth force at 0.265H for walls founded on piles. 2.5 Foundation Pressure Lateral earth pressure causes an eccentric loading on the base of retaining structures. The soil pressure distri- bution along the bottom of the wall base can be computed by assuming a linear variation and using mechanics formulas for combined bending and axial stresses. Taking moments about an axis perpendicular to the wall base of width B and of unit lemmgth, the minimum and maximum base pressures are given 34 as (Bowles 1982): 22 V --— 1i ‘1 B( B (2.12) in which e=(B/2)-x and x=(M;+g)/V where V is the sum of vertical forces at the bottom of the base, e is eccentricity or a horizontal distance from the middle of the base to a point where V acts, x is the dis- tance from the free toe end to the point of action of V (Figure 2.6) , Mr and Mo are resisting moment and overturning moment respectively. The above is easily extended below the water table by taking separate pressure distributions for N’ and U where N’=( V-U). The wall base is sized such that e is less than or equal to B/6 so that the resultant of vertical forces re- mains within the middle third of the base. This assures compressive contact pressure across the entire base. This solution is applicable when the resultant acts on the toe side of the wall from base mid point. The pressure distribu- tion is assumed to be linear and the area of pressure dia- gram should equal the total vertical load. 2.6 Wall Stability To ensure external stability, a cantilever retaining “Hall must be found safe against overturning, sliding, and 35 uLi i 1111‘ i toe lU uheel A 1 <11... qmax N qmin =(V/B) (l-6e/B) // qmax =(V/B) (1+6e/B) Figure 2.6 Pressure distribution under the base 36 bearing capacity failures and excessive base settlements should not be expected. The steel reinforcement of stem, heel and toe should be sufficient to ensure internal stabil— ity against applied bending moments and shears. 2.6.1 External Stability 2.6.1.1 Stability Against Overturning Stability against overturning is obtained by ensuring that the moments available to resist wall overturning are greater than the moments tending to overturn the wall (Wu 1975). The force system on the wall is shown in Figure 2.7. Overturning is checked by summing moments about point 0 on the toe side of the wall. Neglecting any vertical components on the toe side, the sum of vertical forces is: 2w = w, + wc + PSDV (2.13) where W, and We are weights of backfill and wall concrete (base and stem) respectively and PSDV is a driving-side vertical friction component resisting overturning and taken as me=Pfi,sin6. Then, the resisting moment is given as: M,='2:WLW+PWRLWR (2-14) :Ln.which PWR is a horizontal water force on resisting side 37 of the wall, [W and IMm are moment arms as shown in Figure 2.7. The development of full passive earth force Pp on the toe side of the wall requires large wall deformations which may not be desirable in a real structure. For a wall in equilibrium the mobilized resisting force PSR on the toe side can be almost equal to the passive earth force. Base shear S is developed at much smaller wall movements than Pap Thus, the passive resistance in front of the wall is developed only after the full mobilization of base shear. The resisting force PSR is neglected in TWALL because a fill may be placed behind the wall before it is placed in front of the wall or cut may be made in front of the wall during its service life. If PSR is to be included in the analysis, the U.S. Army Corps of Engineers recommends limiting its value to half theifi,(U§S. Army, 1989). The weight of soil above the toe is also neglected because of its small contri- bution toward the wall stability and uncertainty that it will remain present during the life of the structure. The forces tending to overturn the wall include a driving-side earth force PSDH acting at a distance Lfl,from the wall base, an uplift force U acting vertically beneath the base at distance 1% from the toe, the resisting-side water force PWD acting at a distance IMD from the base. Then the overturning moment is given as: Mo = PSDH LSD + U Lu + Pwn LWD (2-15) 38 W3 2: <— '6 8 <1 Figure 2.7 Force system: external stability r). as ‘L. .3" 39 in which PM = Ps1) cos6. where 6 is a wall friction angle. For Rankine analysis 6 is taken as the backfill slope angle B and for Coulomb analy- sis, it can be taken as B<6<¢ for overturning analysis. The factor of safety against overturning is the ratio of resisting moments to the overturning moments and is computed as: 1='..<.;'.(o)-—1E (2.16) M O A safety factor of 1.5 to 2.0 depending on wall importance, is considered adequate for safety against overturning (Wu 1975, Bowles 1988). The concept of resultant ratio is used by the Corps of Engineers for evaluating wall stability against overturning (U.S. Army, 1989). The resultant ratio is the ratio of the distance x to the base width B as shown in Figure 2.7. The wall founded on soil is considered safe against overturning if the resultant ratio is between 1/3 to 2/3. In other words, if the resultant force on the foundation passes through the middle third of the wall base. From the previous discussion on lateral earth pressure, it can be concluded that total earth forceP,SD may vary between active and at-rest values depending on wall move- nmmts. Compaction and other such factors can cause pressures even higher than at-rest pressure. For active conditions, 4O Coulomb’s or Rankine’s theory can be used for predicting 15D. For at-rest conditions, Jaky’s equation with some modi- fication for sloping backfill as suggested in Danish Code may be used for estimating Pfiy 2.6.1.2 Stability Against Sliding The horizontal earth force PSDH and net horizontal water force (PWD-PWR) on vertical plane AB (Figure 2.7) cause the wall to tend to slide forward. The forces that resist sliding are the friction force S beneath the base and the resisting-side soil force PSR in front of the wall. In TWALL, P“_is also neglected in sliding stability analysis for the same reasons as mentioned earlier. The resisting force against sliding is computed as: FR= N’tan6b (2.17) where N’ is effective vertical force beneath wall base and given as N'=V-U, &,is friction angle between the wall base and foundation soil. The friction angle between wall base and foundation &,nmy'be taken as equal to soil friction angle ¢ because wet concrete adheres sufficiently to the foundation soil and the effective developed resistance can Ibe considered between soil to soil (Bowles 1982). The factor of safety against sliding is a ratio of fcmces that resist sliding to driving forces and may be 41 computed as: F.S. (sh—1:5 (2.18) P H A safety factor of 1.5 is considered adequate for safety against sliding failures (Wu 1975, Bowles 1988) The friction between wall base and foundation soil depends on the shear strength of foundation soil. If the resistance to wall sliding is not sufficient to offset the driving forces, the base length may be increased or a key can be added to the base. The shear surface may follow different shapes depending on the location and length of the key. 2.6.1.3 Bearing Capacity The base of the wall should be sized to ensure that the actual contact pressure does not exceed the bearing capacity of the foundation soil. The wall is considered safe against bearing capacity if the ultimate bearing force Quh exceeds the actual effective soil force N’ by a sufficient factor of safety. The embedment depth for cantilever retaining walls is ‘usually less than the base width and the wall length is «considerably larger than the base width. Assuming the base 42 sand is reasonably dense, the mode of bearing capacity failure of a cantilever retaining wall can be considered as general shear failure of a shallow strip footing. Thus, the ultimate bearing force of foundation soil may be computed using Meyerhof’s bearing capacity equation (Bowles 1982). The shape factors are neglected since the base is considered as strip footing and depth factors can be ignored being slightly conservative. Then, the equation for bearing capac- ity can be written as: Q“, = B’[chic + qui(l + 0.5'ycB’N,i,] (2.19) where B’= effective foundation width = B-2e cohesion of foundation soil 0 q = effective overburden stress ‘h = effective unit weight of foundation soil taking into account the variation of water table below the wall base to a depth He (Bowles 1982) 'n = (2He-dw)dw/(He2'nm) + (vy’/He)(He-dw)2 in which He 0.5Btan(45+¢/2) dw = depth of water table below wall base 'hm = wet unit weight of soil in depth dw 7’ = submerged unit weight = ymeyw N N,l and N, are bearing capacity factors for a hori- cl zontal strip footing under vertical loading and are given as: \a.‘ h‘.‘ g e“‘\ § 43 N = [em] tan2(45+¢/2) N = (Nq-1)cot¢ N = (Nq-1)tan(1.4¢) ic, iq and i, are inclination factors that account for the shear resistance along the foundation slip plane on the toe side of the wall and are given as: ic = iq = [149/9012 i. [Him2 0 = tan" (PAH/V) where 0 is an angle of resultant measured from the vertical axis. The factor of safety is a ratio of ultimate bearing capacity of foundation soil Qw to the actual effective soil force N’ under the base. A minimum safety factor of 2 for cohesionless soils and 3 for cohesive soils is considered adequate for safety against bearing capacity failures (Bowles 1988). The Corps recommends a minimum safety factor of 3 for all type of soils (U.S. Army, 1989). The factor of safety against bearing capacity failure may be computed as: F.S. (mags: (2.20) NI 2 . 6. 1.4 Settlements For walls founded on granular soils, most of the ex- pected settlement occurs during the construction period and 44 settlement is not a serious problem (Bowles 1988). But for walls founded on or underlain by cohesive soils, a settle- ment analysis is required if the applied pressure exceeds the preconsolidation pressure of the foundation soil. The analysis is based on the computed pressure distribution along the bottom of the base. Walls on compressible soils may settle toward the backfill and significantly increase the earth pressure on the back face of the wall (Terzaghi and Pack 1967). To keep the settlement relatively uniform in such soils, the resul- tant force should be kept near the middle of the base (Bowles 1982). Excessive differential settlements also contribute toward the instability of the wall. Settlement computations are beyond the scope of this study. However, heuristics incorporated in TWALL minimize differential settlement by keeping the base resultant near the middle of the base. 2.6.2 Structural Design 2.6.2.1 Basis The structural design of a cantilever wall is based on factored service loads in recognition of the possibility of an increase above service load conditions. The American Concrete Institute (ACI) Code 318-89 specifies that cantile- ‘ver walls should be designed according to flexural design 45 provisions of the Code but the application of overload factors is not directly apparent. An overload factor is a number from 0.9 to 1.7 that is to be multiplied with the structural loads to satisfy the safety provisions of ACT Code. The overload factors given in ACI 9.2.4 for the design of members to resist earth pressure cannot be applied as easily to retaining walls as to the members in building. There can be many different combinations of factored dead load D and live load L and the earth pressure. The ACI Code interpretation are: (1) the dead load that increases design moments should be multiplied by 1.4, such as for heel, (2) the dead load such as earth over heel that reduces the effect of earth pressure should be multiplied by 0.9, (3) the effect of earth pressure such as soil pressure under heel should be multiplied by 1.7 (ACI 318-89). Obviously, these factored load states seem to be quite confusing to the designer and perhaps contradictory. To simplify the Code interpretation, many engineers (Wang et al., 1985, Ferguson et al., 1988, Nilson et al., 1986) neglect soil pressure under the heel and use an over- load factor 1.4 for dead loads over the heel. The other reasons given for this neglect are that the actual soil pressure under the heel is very small and its distribution is non-linear. This reasoning has been generally based on a pressure distribution as shown in Figure 2.8 (a). There is also a possibility that the upward soil pres- sure under the heel is distributed as shown in Figure 2.8 (b). This distribution results when the resultant of forces 46 (a) When e>0 -_4,... R Toe Heel l Base 1 “1111111 qheel- (V/B) (1-6e/B) qtoea (v/a) (1+6e/B) ‘3’; Q”) When e < 0 Toe Heel ‘/// Base / I qtoe I U] \ N Figure 2.8 Effect of eccentricity on distribution of soil pressure under the base 47 R acts on the heel side from mid point of the base. In this case, neglect of soil pressure under the heel can lead to very conservative heel thickness. The overload factors commonly recommended by the structural engineers for the design of cantilever retaining walls are given in Table 2.3 (Wang et al., 1985, McCormac 1986). Many engineers (e.g., Newman 1976, Bowles 1988) recommend not to neglect soil pressure under the heel for heel design and subtract it from loads over the heel before applying overload factors. Similarly, for toe design, the loads over the toe are subtracted from the upward soil pressure before applying load factors. Generally, the same load factors are used for the design of stem, heel and toe. The overload factors can vary between 1.7 to 1.9, depending on importance of retaining structure and assumptions, such as active or at-rest, made for earth pressure computations. Table 2.3. Overload factors Wall Part Type of loading load factor Stem Earth pressure 1.7 Heel Soil and water over heel 1.4 Weight of heel 1.4 Surcharges 1.7 Toe Weight of toe 0.9 Soil pressure under toe 1.7 The structural design of stem, heel and stem is disc- uSsed in the following sections. The design is restricted to 48 the calculation of pressures, shears, moments and required area of steel. The discussion on development length, splic- ing and other minor details is beyond the scope of this study. 2.6.2.2 Stem Design The stem is considered as a cantilever beam of unit width for computing steel area and treated as a cantilever slab while making checks for shear (Nilson et al., 1986). The shear and moment at the base of stem due to lateral earth pressure are computed and are used to determine the stem thickness and required steel reinforcement. The criti- cal section for bending moment is taken at the bottom of stem and critical section for shear can be taken at distance d from the bottom of stem (ACI-11.1.3.1), where d is a dis- tance from mid of reinforcement to the front face of the stem where stem joins the base. To make the calculations simple, many engineers usually take critical section for both shear and moment at the bottom of stem (McCormac 1986, Bowles 1988). The critical section for shear taken at stem bottom results in a slightly thicker stem which helps the stability of the wall but may :reduce wall movement essential to develop active conditions behind the wall . The earth pressure on the stem due to backfill is assumed to vary bilinearly in the presence of water with 49 depth from wall top and attains maximum value at a depth equal to the height of stem Hr The pressure due to water varies linearly in proportion to the depth of water above the base. The weight of stem causes some axial compression which can be neglected being very small. Then, the maximum pressure that acts at the bottom of the stem is given as: p- [Y (HS—Hwb) +? (HwD_ tb) 1K+Yw(HwD— tb) —YW(HWR- tb) (2 . 21) where K is coefficient of earth pressure which can vary between active and at-rest values and y and 7’ are effective and submerged unit weights of backfill soil respectively. H“, and H“,R are water table heights from the bottom of wall base on driving and resisting side respectively, t5 is base thickness and 7w is unit of weight of water. The shears and moments at the bottom of stem can be given as: V = P3‘! cos6 + PM,- P (2.22) WY 3 l - P“l cos6 L8d + PW,1 Lwd + Pwr LWt (2.23) where P,d is lateral earth force on driving side of the stem, 6 is wall friction angle, Pm,and Pm.are horizontal water forces on heel and toe side of the wall respectively. L“ de and Lm are moment arms as shown in Figure 2.9. Lateral earth force P8r on toe side is neglected because of uncertainties associated with its presence. The bending moment requires the use of vertical 50 13 l T . F— l | Hs-HwD p.9v We Psd s 5 L. _V’_ __ _ '1' as I E I! V I Ls d f "I I PM [1100 P" No i lwd HwR LEE ! i __ .. tb V ’ J. i. i ‘ _§_ W I L( B STIR! ’1 Due to We, We and PsDV Due to We and Wc 1 qsr q.1 . 31 3 u ATT AL): {1:111 qtoe 1 $2 QM Soil and water Soil and water pressure pressure under toe under heel k—L‘L—H I‘ Lh ’1 TO! m Figure 2.9 Forces considered for the structural design of stem heel and toe 51 reinforcement on the backfill side of the stem. In addition, temperature and shrinkage reinforcement must be provided according to ACI-14.3.3. Two-third of temperature and shrin- kage steel may be used on the front face because of higher temperature variation. There should be just enough vertical steel on front face to support the horizontal reinforcement 2.6.2.3 Heel Design The heel is designed as a cantilever beam for the down- ward forces acting over the heel and upward soil pressure which acts under the heel. The forces that are considered over the heel include the weight of backfill, weight of the heel itself, vertical component of lateral earth force and weight of water. The forces acting over the heel tend to push the heel downward into the foundation soil. The neces- sary upward reaction to hold it attached with the stem is provided by the upward soil and water pressures under the heel and a shear force at the intersection with the stem. The critical section for bending moment is taken at the center of the stem steel because the plane of weakness is likely to occur at stem steel rather than at the back face of stem where it joins heel (Wang et al., 1985). The Code (ACI-11.1.3) allows the critical section for shear to be taken at distance d from the face only when compression is induced in the end region due to support reaction. In the jpresent case, tension is induced in the concrete where heel joins the stem. Therefore, many designers consider the 52 critical section for shear at a point where heel joins the stem. The shear usually controls the heel thickness (Wang et al., 1985, McCormac 1986). The shear and moment at the critical sections are computed to determine heel thickness and steel reinforce- ment. The expressions for computing pressure q, shear V and moment M, at the critical sections are given as: q.qsr-qheel-(Sl+SZ)Lh (2.24) L2 2 25 V-(qsr—qhee1)Lh'(Sl+32)-—h' ( ° ) iii—(gleam (2.26) M- (qsr-qheel) 2 6 where qst is pressure over the free end of heel due to down- ward acting loads, qheel is upward soil pressure at the end of heel, sl and s2 are slopes of pressure distribution over and below the heel respectively,ih,is the heel length and Lhl is the distance from stem face to the center vertical tensile steel of the stem (Figure 2.9). The base is not subjected to extreme temperature as it is well below the ground surface. Therefore, the requirement of temperature and shrinkage steel is very small and mainly this steel acts as spacers bars for the main flexural steel. (McCormac 1986, Nilson et al., 1986) 53 2.6.2.4 Toe Design The toe is also designed as a cantilever beam for the weight of soil, water over the toe and the weight of toe itself all acting downward and the soil pressure under the toe acting upward. The critical section for moment is taken at a point where toe joins the stem and the critical section for shear can be taken at a distance d from the face of the stem (Wang et al., 1985). It is convenient to take the critical section at the face of support because usually the toe length is small. The thickness of toe need not be same as the thickness of heel but most designers make it same (McCormac 1986, Bowles 1988) for ease of construction. The shear and moment at the critical section are com- puted to determine toe thickness and reinforcement. The pressure q, shear V and moment M, at the face of stem where toe and stem join can be computed as: q-che-qsl-S2Lt (2.27) 2 L V-(qtoe-qsl)Lt-SZ—2—c (2'28) L2 L3 2.29 M-(qtoe—qsl) 32-82—62 ( ) where q” is pressure over the toe, gm,is upward soil and ‘water pressures at far end of the toe, 52 is slope of upward 54 soil pressure distribution under the base, L,is the toe length (Figure 2.9). 2.6.2.5 Moment Capacity In this study, the cantilever retaining wall is de- signed for shear and bending in accordance with strength design method of the ACI Code. For computing nominal moment capacity (oMn), the stem, heel and toe are treated as canti- lever beams of unit width and steel area is calculated according to the provisions of the ACI Code. The wall is considered safe against bending if the nominal moment capac- ity of each component of the wall exceeds the factored maximum moment (Mu) on that component. The expression for computing nominal moment capacity is given as: (an-tbAsfy(d-§) (2.30) a _A_s£z_ (2.31) 'o.85f;.b where A, = steel area H II yield strength of steel :fg = allowable compressive strength of concrete d = distance from extreme fiber to the mid of steel b = unit width 55 The derivation of above equations can be found in many books on design of reinforced concrete (e.g., McCormac 1986, Hassoun 1985). 2.6.2.6 Checks for Shear Stirrups are not commonly used in the design of canti- lever retaining walls. Therefore, each part of the wall must have enough strength to stand against shear without using shear reinforcement. While making checks for shear, the stem, heel and toe are treated as a cantilever slab (Nilson et al., 1986). The wall is considered safe against shear if nominal shear strength (¢Vc) of each part of the wall is greater than the maximum factored shear (Vu) acting on that part. The expression for computing nominal shear strength of concrete is given as: ¢VC'2¢(/7Zbd (2.32) where o is strength reduction factor and is taken as 0.85 for shear design. ffi” b and d are same as already defined. 2.7 Soil Properties The soil properties of the foundation soil and the backfill must be defined for design in order to obtain an efficient and safe design. Lateral earth pressure depends on unit weight and friction angle of backfill. Although, 56 probably stronger, the friction angle of typical clean granular backfill materials used in retaining wall problems is often taken between 30 to 36 degrees and unit weights are often in the range 100 to 115 pcf. The shear strength and compressibility of foundation soil must be known to design against bearing capacity fail- ures or excessive settlements. The parameters required for the foundation soil are the friction angle, unit weight and cohesion. These parameters can best be estimated using direct shear test since retaining wall is plane strain case. However, these parameters are often inferred from N value of SPT results or from the designer’s experience. CHAPTER 3 EXPERT SYSTEMS AND THE DEVELOPMENT OF TWALL 3.1 Introduction A brief review of techniques and tools for building an knowledge-based expert system (KBES) or expert system (ES) is presented in this chapter. The application of these techniques and tools to the development of TWALL is also discussed. Some of the recently developed KBES in the domain of geotechical engineering are also described. Artificial intelligence (AI) is a branch of computer science that deals with the study of how to make computers do things for which, at the moment, people are better (Rich 1983). Expert systems are practical applications of AI re- search programs involved in problem-solving (Adeli 1988). An expert system can be defined as an interactive computer program incorporating judgment, experience, rules of thumb and intuition to provide knowledgeable advice about various tasks (Gasching et al., 1981). The reaction of many professionals involved in comput- er-aided engineering design to the above definition was both uneasiness and impatience. In the opinion of these 57 58 professionals, present conventional computer programs for engineering applications have become increasingly interac- tive and perhaps judgment might be best left to the practi- tioner in this interaction. Fenves (1986) describes the main features of KBES that clearly separate them from algorithmic programs: 1. The knowledge base in KBES can be manipulated indepen- dently from the control mechanism. 2. The inference process used in KBES can be conveyed to the user through some form of an explanation facility. 3. To some degree, the domain-dependant knowledge in- corporated in the program is readable and understand- able. 4. An algorithmic program uses a small amount of knowledge over many cycles, where as KBES typically has to search a large amount of knowledge at each cycle and a partic- ular piece of knowledge may apply only once. 5. The knowledge base can be extended incremently over a period of use without major (or any) restructuring. 3.2 Historical Perspective In the first 15 years after the birth of artificial intelligence at Dartmouth college in 1956, researchers :mostly relied on domain-independent search strategies (e.g., problem reduction, means-end-analysis) to obtain a 59 solution to a problem (Samuel 1963). These search strategies were successful for the solution of some simple or very well structured problems such as games. However, for real complex problems where the search space tend to expand exponentially with the number of parameters involved, these early strate- gies proved to be inadequate (Rich 1983). AI researchers then in the early 1970’s adopted a new approach that combined the domain knowledge with the prob- lem-solving strategies (Fenves 1986). This marked the first generation of expert systems. As an example, MYCIN, an expert system that diagnoses infectious diseases (Shortliffe 1976) was developed that combined domain specific knowledge and problem-solving strategies. The second generation of expert systems emphasized knowledge rather than search techniques and lead to the field of knowledge engineering. The problem-solving tech- niques and the domain-dependent knowledge were separated. This approach permits the combination of new domain knowl- edge with the existing problem-solving environment (Fenves 1986). Thus, at present the developer of a new expert system has to concentrate on only obtaining, compiling and formal- izing the domain—specific knowledge rather than building a problem solving environment (Mullarkey 1985). 3.3 Architecture of an Expert System The architecture of an expert system refers to the components of the expert system and the way they are 60 'connected to each other. The basic components of an expert system are a knowledge base (static memory), a context (dynamic memory or working memory) and an inference mecha- nism. Additional components including a knowledge acqui- sition facility, an explanation facility, a help facility and a user interface are also needed to enhance the extensi- bility of an expert system and to make it more user friendly (Adeli 1988). The interrelationship among these components is illustrated in Figure 3.1. The knowledge base is a collection of facts and heuris- tics containing information available in a particular do- main. The context is a temporary storage facility for the current state of the specific problem being solved and it expands continuously as the reasoning of the solution pro— gresses. The inference mechanism is a control strategy that specifies the order in which the rules will be compared and applied or "fired" in the working memory. The knowledge acquisition facility provides a means for entering or revising knowledge in the knowledge base. The explanation facility provides reasons why particular ques- tions are being asked and justifies inferences. The help facility guides the user for using the system more effec- tively. The user interface provides a means for user inter- action with the expert system. The interface can be in the form of menus, windows or graphics. A detailed discussion on the architecture of an expert system can be found in Boose (1986) and Nebendahl (1988). The architecture of TWALL 61 USER USER INTERFACE HELP CONTEXT . . EXPLANATION FACILITY FACILITY INFEREN CE I I KNOWLEDGE MECHANISM BASE KNOWLEDGE ACQUISITION FACILITY Figure 3.1 Architecture of an expert system 62 essentially contains all the components discussed above and these components are discussed in Section 3.10. 3.4 Knowledge Representation in Expert Systems The knowledge representation method selected for the domain has a significant impact on the selection of the tool used to build an expert system. Some of the actively used forms of knowledge representation are logic-based represen- tation, rule-based representation and network-based repre- sentation (Mullarkey 1987). For detailed discussion on these methods, see Barr et al., (1981), McGee (1990) and Dym et al., (1991) Most of the developed knowledge-based expert systems are based on the rule-based representation (Adeli 1988). The rule-based systems are also referred to as production sys- tems (Maher et al., 1987). The rule-based systems have an advantage in that they can explain how and why they perform certain action and one can evaluate their outcome and re- sults. The domain knowledge in rule-based systems is repre- sented in the form of "IF...THEN" rules. The general form of the rule is: RULE 1 IF [(premise 1). .................. ...(premise n)] THEN [(conclusion 1 ................. (conclusion m] The IF part of the rule is generally referred to as left- hand-side (LHS) while THEN part of the rule is called as 63 right-hand-side (RHS). A single production rule is under- stood to be a smallest unit of information in the entire system. In contrast to algorithmic programs, an important feature of rule-based KBES is that the rules of the knowl- edge base need not be in a specified order in which they are to be considered. 3.5 Problem Solving Strategies in Expert Systems Problem solving generally involves the search for a solution. The solution path consists of all states that lead from the initial state to the goal state (Maher et al., 1986). Problem solving strategies (also referred to as control strategies or inference mechanisms) commonly used in rule-based systems are: forward chaining, backward chaining and the hybrid approach (Adeli 1988). In these strategies, the goal state represents a potential solution and the initial solution state represents the input data. These strategies are currently implemented in a variety of rule- based expert system building tools commercially available in the market (e.g., LEVELS, M.1 and Ist-CLASS) 3.5.1 Forward chaining Forward chaining strategy (also referred to as bottom- up, data driven or antecedent driven) is a problem-solving strategy that starts from an initial state of known facts 64 and proceeds forward to infer their immediate conclusion. The conclusions are added to known facts in the context and further inferences are made. This process continues until the goal state is achieved or no useable rule is found. This strategy is useful where there are few input data and many solutions (Maher et al., 1987). As an example, DIPMETER ADVISOR (Davis et al., 1981) uses forward chaining control strategy for inferring subsurface geological structure. 3.5.2 Backward Chaining Backward chaining is a problem-solving strategy that starts with the goal of the problem and works backwards, looking for evidence that supports or contradicts the goal. The process involves looking at the THEN part (conclusion) of the rules that would conclude the goal and then examining the IF parts (premises) of these rules to determine what situation will cause them to fire. Backward chaining is also referred to as goal-driven, antecedent driven or top-down strategy. This strategy is suitable where there is large input data and few goals. Backward chaining is often em- ployed in diagnostic problems such as MYCIN (Shortliffe 1976) for diagnosing infectious diseases and WASTE INCINERA- TION (Huang et al., 1986) for diagnosing malfunction in hazardous waste incineration facilities. 65 3.5.3 Hybrid Approach The hybrid approach is a combination of backward chain- ing and forward chaining. This approach utilizes a "blac- kboard" environment. The blackboard will keep track of the simultaneous application of forward and backward reasoning chains (Adeli 1988). A good discussion on use of the black- board model for problem-solving is given by (Nii 1986). The LEVELS expert system shell (LEVELS, 1989) can be used to develop expert systems using hybrid approach. 3.6 Expert System Building Tools Basically, there are three types of tools available for building KBES (Hayes-Roth et al., 1983, Harmon and King 1985, Mullarkey 1987): general-purpose programming languages (GPPL) such as LISP and PROLOG, general-purpose represen- tation languages (GPRL) such as OPSS3 (Adeli 1988) and expert system building frameworks or shells (e.g., LEVELS). These tools are briefly discussed as below: 3.6.1 General-Purpose Programming Languages Presently, KBES can be implemented in AI languages such as LISP and PROLOG as well as in procedural languages such as C and PASCAL (Adeli 1988). LISP is an acronym for LISt Processing. It was invented by McCarty in 1960 for 66 nonnumeric computations (Adeli 1988). This language is the choice of many AI researchers in United States and is most suitable for symbolic representation and list processing (Harmon and King 1985). PROLOG is an acronym for PROgramming in LOGics. It is based on formal logic and a simplified version of first- order predicate logic (Clocksin et al., 1981). PROLOG is popular in Europe and Japan (Nebendahl 1988). It is a versa- tile language for database type applications but has limita- tions for numeric data manipulation (Adeli 1988). The development of many engineering KBES involves a considerable number of algorithmic computations in addi- tion to symbolic manipulations. Therefore, AI languages may not be preferred for engineering applications. Among the popular algorithmic languages, PASCAL and C might be better candidates in these cases (Adeli 1988). System develoPers that use general programming languag- es as a tool to build KBES have complete flexibility in designing the system but they have to implement the entire structure including the knowledge base, inference mechanism and other components of the system. The cost of this app- roach is very high in term of time and efforts. This app- :roach is suitable for those interested in more basic issues of expert system building techniques (Mullarkey 1987). An important approach that is becoming increasingly popular for developing new expert systems is the use of "shells" to be described in 3 . 6 . 4 . *1 (D 19 67 3.6.2 General-Purpose Representation Languages These languages are generally classified by the form in which the knowledge base is represented e.g., as a produc- tion system (Newell 1977) or as a frame-based system (Stefik 1979). These tools such as OPS83 (Adeli 1988), UNIT (Stefik 1979) provide maximum flexibility to the developer in de- signing a system for a specific application. The difficulty with these tools is that a significant portion of the code necessary to produce a working KBES must be written and manipulated by the program developer (Mullarkey 1987). 3.6.3 Expert System Shells Expert system shells, also referred to as frameworks and environments, have been recently developed to facilitate the development of KBES. These are expert systems without the knowledge base and usually provide one or more knowledge representation methods and inference mechanisms. They are easier to use but less flexible than an GPPL and GPRL (Adeli 1988). There are two main categories of these shells; domain driven-shells and domain-independent shells (Mullarkey 87). 3.6.3.1 Domain-Specific Shells Domain-specific shells are those developed from specif- ic parent expert systems by separating knowledge base from 68 the control mechanism. They can only deal with same class of problem as the original system because of control strategy incorporated in the inference mechanism. These tools are developed for either diagonistic tasks such as EMYCIN (vanM- elle 1979) and EXPERT (Weiss et al., 1979) or interpretation tasks such as HEARSAY (Balzer et al., 1980). These tools are not suitable for problems involving extensive mathematical computations. 3.6.3.2 Domain-Independent Shells Domain independent shells are those developed indepen- dently of a application domain. Usually, multiple forms of knowledge representation and control strategies are avail- able in these shells (Mullarkey 1987). The KBES developer chooses the type of knowledge representation and control mechanism and adds domain-specific knowledge within the constraints imposed by the particular representation. Expert system building shells are ideal tools for developing KBES for those not expert in computer science. Incorporation of the rules in such a package is far simpler than building a complete system including an inference mechanism. Few civil engineering problems can be solved by a purely heuristic approach. Numerical algorithmic routines must usually be combined with heuristics (Kostem 1986). Thus, an ES shell for civil engineering application should be able to handle scientific numerical computations within 69 the system. The ideal tools for building KBES in civil engineering applications would allow for the following (Ludvigsen et al., 1986, Adeli 1988): 1. Extensive mathematical manipulation within the system. 2. Different forms of knowledge representations. 3. Various control strategies. 4. Interfacing ability with other programs written in any languages. 5. Natural language interface. 6. Explanation of static queries of knowledge and dynamic queries about the line of reasoning. 7. Programming aid (e.g., editor and debugger). 8. Reasonable Cost. ES shells available in the market at the time of this effort have been analyzed in some detail by Ludvigsen 1986, Mullarkey 1987 and Adeli 1988. Table 3.1 shows the compara- tive capabilities of PC-based expert system shells. Only PC- Based shells are considered because the developed system is expected to be used on personal computers which are easily accessible. The LEVELS expert system shell (LEVELS 1989) met all criteria discussed above except that it allows only one form of knowledge representation i.e., rule-based represen- tation. The characteristics of LEVELS are discussed briefly as follows: LEVELS is an "advanced development environment and 70 Table 3.1 Comparison of PC-Based expert system shells (Modified from Ludvigsen et al., 1986) ATTRIBUTE EXPERT-EASE LEVELS ".1 ISt-CLASS Proprietary Human Edge LEVELS Teknowledge interest Software Research Inc. List price $695 S 495 S 5000 $495 (1987) (IBM-PC) (IBM-PC) (IBM-PC) (IBM-PC) Ability to handle NO YES YES YES complex math Directly Indirectly Indirectly Ability to NO YES YES YES interface with other Directly Directly directly software Explanation NONE Extensive Limited NONE Overall Buddies A Friend A Friend A Friend friendliness Documentation Outstanding Sufficient Sufficient Limited User Support Limited Available Available Available Inference mechanism Forward Forward and Backward Backward Chaining Backward and Limited and Forward Chaining Forward Chaining Chaining '71 delivery vehicle for expert system" (LEVELS 1989). It was developed by Level Five Research in PASCAL in 1986 and uses a ruled-based knowledge representation. LEVELS can handle complex mathematical tasks and uses both backward chaining and forward chaining control strategies. LEVELS is entirely menu and function key driven and is easy to use. It allows easy integration with algorithmic programs written in TURBO PASCAL, FORTRAN and C or any other program that is a .BAT, .COM or .EXE file. It also permits installation of up to three external programs on its main menu that can be run form within LEVELS. The ACTIVATE facil- ity of LEVELS can execute dBASE-II programs from within LEVELS. Its facilities include a help facility, explanation facility and text editor. LEVELS has the capability to explain both the static queries of knowledge and dynamic queries about the line of reasoning. LEVELS can be used on an IBM PC with as little as 256 K of RAM. However, to use all its features, 512 K RAM is required. The knowledge bases of LEVELS can be chained and compiled. It has the ability to address 4000 rules and is available at relatively modest price. Looking at the price and the capabilities, LEVELS seemed to be one of the best commercial ES shells available in the market for developing engineering KBES on microcom- puters (Adeli 1988) and was selected for the development of TWALL. 72 3.7 Previous Geotechnical Applications Some previous applications of expert system technology to geotechnical engineering problems are briefly described in the following sections. 3.7.1 RETWALL RETWALL (Hutchinson et al., 1987) is an expert system for selecting and sizing earth retaining walls. RETWALL was implemented on SUN2 Microsystems using the expert system shell BUILD, a backward-chaining production rule system. The system also employs graphical procedures written in C. The user interface is through multiple windows and graphics. RETWALL provides extensive explanations in the form of ’Why', ’note list’ and ’explain’ predicates. The knowledge-base of RETWALL contains knowledge of various prototype retaining wall cross sections and how to select among them. This knowledge is not well documented in literature so it was obtained from specialist engineers in the field through survey. The selection of the most appro- priate type of retaining wall is based on type of applica- 'tion, soil and topographical conditions and designer prefer— ences . The system has two main modules, the high level and low .level. The purpose of high level is the selection of the particular retaining structure for a given application. At 73 present, the system can choose among 10 available wall types. The lower level module is designed to perform the preliminary design of the selected retaining structure. Presently, the only lower level routine available is that which designs blockwork walls. 3.7.2 CONE CONE (Mullarkey 1985) is a knowledge-based system that classifies soils based on cone penetrometer data and infers shear strength of the soil. The knowledge incorporated into CONE is embodied in a series of production rules using the OPSS programming language and LISP functions. The knowledge base of CONE consists of three main modules: information gathering, soil classification and shear strength estimation. Both backward and forward chain- ing control strategies are used in CONE. The information gathering process uses backward chaining strategy and the soil classification and shear strength estimation uses a forward chaining strategy. CONE uses fuzzy logic to repre- sent the uncertainty in the empirical interpretation of the data. 3.7.3 RETAIN RETAIN (Adams et al., 1988 and Adam et., al 1990) is a KBES for retaining wall failure diagnosis and rehabilitation 74 design synthesis. RETAIN consists of a database implemented in DBMS INFORMIX and series of modules including site iden- tification, failure diagnosis, design synthesis, cost esti- mation and evaluate/consistency. The database integrates OPS83 production rules, C language algorithmic functions and INFORMIX ESQL database queries. The RETAIN system uses DIGR inference engine to traverse the network. RETAIN system was developed on a Microwaves workstation but the entire system has also been transported to a PC. The knowledge base for retaining wall failure diagnosis contains possible failure modes of all possible wall types as well as possible evidence associated with each failure mode. The heuristic knowledge base for design synthesis is represented as relational database tables. For problem- solving, the RETAIN system uses the derivation approach for retaining wall failure diagnosis and the formation approach for the synthesis of rehabilitation design (In the deri- vation approach, a solution of the problem at hand is de- rived from a list of predefined solution stored in the knowledge base; In the formation approach, a solution is formed from the eligible solution components stored in the knowledge base). 3.8 Background on Present Research Numerous procedural computer programs have been used in the past for the design of cantilever retaining walls. 75 Newman (1976) used a procedural program to produce a struc- tural design of cantilever wall for various loading condi- tions and heights. A computer program was used by Rhomberg and Street (1981) to compile a design aid for concrete cantilever retaining wall design within 5% of absolute minimum cost. The U.S. Army Corps of Engineers (U.S. Army, 1989) makes extensive use of computer programs for the design of retaining structures. In these programs, most if not all of the decision- making process is left to the user or alternatively, proce- dural programs (e.g., TWDA by Price et al., 1980) use numer- ous iterations for optimum design. In addition, they have a limited knowledge base and can’t explain their working and justify their answers. Recently developed knowledge-based expert systems have overcome some of the limitations of procedural programs. The main characteristics of KBES are discussed in section 3.1 and these include the separation of knowledge base from the control mechanism, use of heuristic knowledge and the explanation facility. An extensive literature review revealed that no attempt has been made to develop KBES for the structural design of cantilever retaining walls. Thus, the decision was made to develop a system for the design of cantilever walls that would guide the user through iterative design process by using heuristic rules incorporated in the knowledge base. The other aspects of cantilever retaining wall design that were investigated are: (1) a comprehensive parametric 76 sensitivity analysis was made to understand the behavior of the wall under different loading conditions, develop heuris- tics and test the program and (2) a study was made to see the effect of active and at-rest conditions on the cost of the wall. 3.9 Development of TWALL 3.9.1 General Traditionally, a knowledge engineer, (AI specialist) cooperates with a team of domain experts (specialists of a particular domain) for developing a KBES. Since the human experts may not be knowledgeable about KBES programming, the knowledge engineer translates the expert’s knowledge into the system. With the recent invention of expert system building shells, the domain expert can also act as knowledge engineer with a little programming background. The knowledge engineer must first acquaint himself or herself with the application domain and then obtain domain experts’s knowl- edge through interviews, literature, experimentation and (questionnaires. For techniques of knowledge elicitation, see Greewell (1988) and Cordingely (1989). Some of the basic steps involved in the development of an expert system include problem identification, analysis axui acquisition of knowledge, selection of expert system Iniilding tool and inference mechanism and formalization of 77 the knowledge base. The next step is to develop a prototype system using the knowledge base and AI techniques. The subsequent step is the evaluation, review and expansion of the developed system, refinement of the user interface and the addition of user facilities. For a detailed discussion see Harmoon and King (1985) and Kulikowski (1989). The knowledge-based expert system TWALL for the design of cantilever retaining walls was developed as follows: 1. Preliminary design tasks were performed after reviewing the literature on the design of cantilever walls and expert systems. These included problem identification, problem conceptualization, selection of expert system building tool, method of knowledge representation and inference mechanism. 2. A prototype knowledge-based system was developed based on knowledge obtained from the literature for propor- tioning wall dimensions to ensure internal and external wall stability. Some heuristics were developed by running the program with different wall dimensions and observing their effect on wall stability i.e., simula- tion and experimentation. See Chapter 4 for details. 3. Parametric sensitivity analysis was performed by vary- ing input variables that affect wall design within a practical range and computing the safety factor against overturning, sliding and bearing capacity failures. The analysis was also performed to see the effect of change 78 in heel length on upward soil pressure beneath the base under different loading conditions. The analyses are discussed in detail in Chapter 5. Some heuristics were deduced from this analysis for incorporating in the system during its expansion. The effect of active and at-rest conditions on the cost of the wall was studied (see Chapter 6). A questionnaire was sent to experts associated with the design of retaining walls to further define heuristic knowledge. Some of the previous heuristics were re- vised. A specimen questionnaire is shown in Appendix A. The knowledge obtained form the experts and the devel- opment of heuristic are discussed in Chapter 7. The developed prototype was expanded by incorporating heuristics deduced from previous work. The major stages of TWALL development are discussed in detail in the following sections. 3.9.2 Problem Identification Identification of an appropriate problem is an extreme- ly important first step in developing an expert system. There are several guidelines that can help to determine whether a certain task is appropriate as a basis for KBES development. Some of the yardsticks of a good domain are (Fenves et al., 1984, Mullarkey 1985 and Prerau 1989): 79 The use of expert knowledge, judgement and experience is the key element in the performance of the task being considered. There is a need for non-conventional programming ap- proach. The task is decomposable and the development of the expert system can be phased. Major components of the domain knowledge are available from books and publications. Domain experts are available and can be debriefed for heuristic knowledge. It takes several hours to several days for an expert to complete a typical task. Basic skills required for the task are routinely taught to the novices but expertise is gained through experi- ence. The need for the task is expected to continue for several years. 3.9.2.1 TWALL Implementation The domain characteristics of cantilever retaining walls design are discussed below in the context of the eight criteria above to see whether the domain is suitable for using expert system technology: 1. The design values of shear strength parameters of 80 backfill and foundation soil that are used for the wall design are not reliable. The uncertainty is due to random variability of properties and insufficient sampling. The value of wall friction angle to be used in the design is also highly uncertain. Intuition, judgement and previous experience have to be used to select right value of design parameters. Heuristic rules deduced from designers experienced in the wall design can be incorporated in the expert system to guide novice users. The design of a cantilever wall itself is a trial and error procedure. To reduce the number of trials and computational time, the designer is required to assume reasonable trial dimensions (e.g., base length, heel length, and stem thickness). Further experience is necessary regarding how to change the trial design based on the results of one iteration of analysis. Novice users can be guided through heuristics incorpo- rated in an expert system. The design of a cantilever wall requires both symbolic reasoning and numerical calculations. Thus, a non- conventional approach is desirable. The task of cantilever retaining wall design can be decomposed in to sub-tasks such as external stability and external stability and so on. Also, the expert system can be developed in phases according to the sub- tasks. The major components of the domain knowledge of the 81 wall design are available form books, journals and publications. 5. There is a need to capture expertise from the experts on the wall design and experts are available from whom the heuristic knowledge can be obtained. 6. Wall design is a time consuming job and may take many hours to complete the design. 7. The design procedures of cantilever retaining wall are routinely taught but expertise is only gained after a considerable experience. 8. Cantilever retaining walls are being used to retain soil and their use is expected to continue in future for long time to come. From the above discussion, it is evident that the design of cantilever walls is an appropriate domain for using expert system technology. 3.9.3 Collection of Knowledge The domain knowledge of a cantilever wall design con- sists of heuristic knowledge and descriptive knowledge. The heuristic knowledge expresses surface relationships which an expert has observed to be of some use when tackling problems in the domain. The descriptive knowledge represents the formally expressed laws and relationships which make up the theory of problem domain (McGee 1990). 82 There are two main sources of knowledge; literature and human experts. The descriptive knowledge for the design of cantilever wall was mostly obtained for books, journals, specifications and magazines. However, these sources lack heuristic knowledge. To obtained heuristic knowledge, a questionnaire was sent to several experts associated with the design of retaining walls. See Chapter 7 for discussion on knowledge obtained from the experts. Dr. Thomas F. Wolff (Associate Professor, Michigan State University) has been involved in design and construc- tion of retaining structures, revision of design manuals and the development of computer programs for retaining walls during his long association with the U.S. Army Corps of Engineers. He acted as domain expert throughout the devel- opment of TWALL and was consulted as and when required. 3.9.4 Problem Conceptualization In this phase of knowledge base development, an initial study of the problem is carried out to define the goal and identify the key concepts and relationships that form the basis for expert’s decision (McGee 1990). The problem is decomposed into sub-problems until the knowledge engineer has produced a complete top-down hierarchical view of the problem-solving process. Clear distinctions are also made between evidence and hypothesis and action to be taken at each step is carefully specified (Kulikowski 1989). 83 In this phase of TWALL development, the goal and sub- goals were defined and key concepts and relationships were identified for making various decisions. As an example, the main goal in the present case is "safe cantilever wall design" and sub-goals are "external stability and internal stability". The problem was decomposed into sub-problems and a complete top-down hierarchical view of the problem-solving process was produced as shown in Figure 3.2. The figure reads from left to right. 3.9.5 Selection of Expert System Building Tool Artificial intelligence (AI) languages such as LISP and PROLOG offer definite advantage over procedural languages (e.g., PASCAL, FORTRAN and BASIC) with regard to represent- ing heuristic knowledge. But these languages have limita- tions for descriptive knowledge that needs extensive numeric data manipulation. AI languages are also considered memory intensive and slow as compared to procedural languages. The KBES for the design of a cantilever walls could have been developed using one of the following approaches. 1. The heuristic knowledge could be coded in LISP or PROLOG and the descriptive knowledge could be coded in some high level language (e.g., PASCAL and FORTRAN). An interface would then be developed to maintain the inte- grated environment. 84 CANTILEVER RETAINING WALL DESIGN r l CHECK WALL DETERMINE DESIGN 1m WALL WALL COST SUI'I‘ABMI'Y PARAMEI'ERS DIMENSIONS SIABILITY ANALYSIS ._ 6 < H< 30 | _. Non-Compressible Foundation Soil Base Heel Stern r [ I I _ Cohesionless Backfill Backfill Concrete Excavation Total _ Tedmicel Know-how Volume Volume Cost I l l Backfill Foundation Water Table Earth Pressure Soil Soil Coefficient EXTERNAL INTERNAL Forces on Wall _ Required Parameters for Structural Design I l OVERI'URNIING SLIDING BEARING STABILITY 5113;1er CAPACITY Total Overntrning Forces Causing — Eccemricity Moment. Mo Wall Sliding. PD” __ Efl’ective vertical Total Resisting Forces Resisting Force. N Moment. MR Wall Sliding. PR __ Ultimate bearing S‘fuy Fun°'=MO’MR Safely Factor: PR/P DH Capacity, Quk —- Safety Factor: Quit/N STEM DESIGN BASE DESIGN Pressures on Stern _ Shears and Moments on Heel Forces on Stan __ Shears and Moments on Toe Shears and Moments on Stern __ Wide Beam Shear Steel Reinforcement ,._. Steel Reinforcement for Heel _ Steel Reinforcement for Toe Figure 3.2 Hierarchy of cantilever retaining walls design '1 85 2. A complete system could be developed in some procedural language such as PASCAL which is fairly good at symbol- ic reasoning as well as numeric data manipulation. 3. A commercially available expert system building envi- ronments or shells could be used to develop a new system. Building a KBES using the first two approaches amounts to building a complete system including inference mechanism, explanation facility, help facility and knowledge acqui- sition facility. The development of these facilities is a specialist job and mostly performed by AI specialists. In addition, the AI languages are not compatible with other languages (Finn et al., 1986) and the development of an interface is tedious. To build a complete system demands enormous time and efforts and may take five to ten man years to build such a system (Fenves et al., 1984). Also, due to availability of expert system building environments in the market, building a complete system is not innovative except for those involved in AI research. The invention of expert system shells has facilitated the development of KBES. Here, a builder of new KBES is required to select the type of knowledge representation, inference mechanism and add the domain-specific knowledge into the existing framework within constraints imposed by a selected representation. Presently, it is not very difficult to find suitable shell for a given domain. 86 3.9.5.1 TWALL Implementation The third approach as discussed above was followed for the development of TWALL. The LEVELS expert system shell developed by Information Builders (LEVELS 1989) was selected for the present application because it meets all the re- quirements to develop a KBES for the design of cantilever retaining walls. 3.9.6 Knowledge Representation Methods of knowledge representation in expert systems were briefly discussed in section 3.4. The framework of organizing information and knowledge into a knowledge base of TWALL is provided by a knowledge engineering language known as Production Rule Language (PRL). PRL is a versatile environment for the formulation of an expert’s knowledge into LEVELS expert system shell with a wide range of data types and functions. PRL knowledge bases are compiled before being executed and take less memory and time than symbolic languages-based systems. They allow development of sophisti- cated and interactive program in much less time and with much less effort than the conventional programming languages. The production rule is used as basic construct of knowledge representation in PRL knowledge base. Ordering of rules within the knowledge base is not important and new 87 rules can be added any time. PRL is capable of representing several different types of information in a single knowledge base including simple factual statements, numeric data, mathematical expressions, attribute-value associations and strings. A simple fact data type is defined as any phrase or statement which can be asserted to be either true or false. A numeric fact is a fact with numeric value. PRL supports integers and floating point decimal as numeric data. PRL also supports assignment, basic algebraic operations and exponential and trigonometric expressions. Attribute-value facts represent objects with common states or conditions. The string fact type can be any combination of ASCII charac- ters with a maximum length of 80 characters. 3.9.7 Selection of Control Strategy Control strategies in expert system were discussed in section 3.5. The LEVELS expert system shell has both back- ward and forward chaining control strategies. Basically, the inference engine of LEVELS follows backward chaining control strategy by default but forward chaining can also be simu- lated. For the present design, the backward chaining control strategy was followed because it is was found convenient to follow this strategy in LEVELS. Backward chaining control strategy is considered appro- priate for diagnostic type problems instead of design 88 problems (Adeli 1988). For the design of cantilever walls, the knowledge base was structured such that the use of backward chaining control strategy did not pose any problem. It shows that the backward chaining can be used for design problems with carefully structured knowledge base. 3.9.8 Knowledge Formalization In this phase, the concepts and relations identified in the conceptualization phase are mapped onto the formal representation which can be interpreted by the computer program (McGee 1990). If the expert system building tool has already been selected, the purpose of this phase is to find an apprOpriate mapping from a semi-formal domain knowledge into a formal representation mechanism provided by the tool. Else, the formalization phase can provide a valuable input for the selection of an appropriate tool for building the expert system. For the development of TWALL, the concepts and relations identified in the conceptualization stage were mapped on to PRL provided by LEVELS. 3.9.9 Prototype Implementation The prototype knowledge base is built up in this phase. The ES builder must select the scope of sub-programs to be covered by the prototype. Once the sub-programs have been formalized and represented within the chosen building tool, 89 the changes in the formalization will inevitably appear. Thus, the conceptualized and formalized knowledge is modified to build a working prototype (Kulikowski 1989). The knowledge for the prototype is mostly obtained from the published literature on the subject (Fenves et al., 1984). 3.9.9.1 TWALL Implementation A prototype working knowledge base was developed in this phase of TWALL development. Formalized knowledge was compiled using the LEVELS compiler and modifications and corrections were made in the formalized knowledge to build a working prototype. The knowledge for the prototype was obtained mostly from the literature. 3.9.10 Testing, Validation and Expansion In this phase, the developed prototype is tested for programming errors and validated for the intended tasks. According to the test results, the knowledge base is modi- fied and expanded by incorporating heuristic knowledge obtained from the domain experts. 3.9.10.1 TWALL Implementation The developed prototype was tested for any bugs in the tmogram and validated for the reliability of results. For 90 validation, two approaches were used; comparison to student designs and comparison to published designs. In the first approach, a problem of cantilever retaining wall design with different design parameter was given to students in an advanced foundation design course (CE 818) at MSU and the class was asked to design the wall using the developed prototype and check the results manually. Also, the students in an earth retaining structure design course (CE 419) were asked to design cantilever walls for 34 different sets of parameters and then these 34 walls were designed on TWALL for comparison. In the second approach, examples on cantile- ver walls design in different text books and design manuals were solved using the developed prototype and results were compared. The results of first approach compared well. However, there were slight differences and the system was modified accordingly. The system was also modified to improve the user interface as suggested by the CE 818 Class. Appendix D shows the comparison of TWALL designs with that of CE 419 Class. The results of the second approach are shown in Table 3.2 and 3.3. TWALL output is given in appendix B. Table 3.2 shows the comparison of TWALL wall results ‘with Example 1, Appendix N, The US Corps of Engineers Manual (EM 1110-2- 2502). The results of external stability compare fairly well but there are significant differences in inter- rual stability results. The reasons for this difference are: 91 Table 3.2 Comparison of TWALL results with Exapmle 1, Appendix N, The US Army Corps of Engineers Manual (EM 1110-2-2502 1989). ITEM TWALL Corps of Percent Engineers Difference (1989) Hall Dielnsions Hall heigth ft 25.00 25.00 0.00 Base length ft 18.78 20.00 ~6.49 Base Thickness ft 3.00 3.00 0.00 Heel length ft 9.62 12.00 -24.70 Toe length ft 6.67 5.00 25.03 Stem top thickness ft 1.50 1.50 0.00 Stem bottom thickness ft 2.49 3.00 -20.48 Earth Pressure Method for earth pressure Jaky General prediction (at-rest) wedge Earth pressure coefficient K 0.561 0.547 2.49 Earth force on stem kips 16.29 24.06 ~47.70 Earth force on wall kips 26.79 27.62 -3.09 Hell Stability Overturning stability Xr ft 8.61 7.34 14.75 Eccentricity ft 0.78 2.66 -241.00 8/6 ft 3.13 3.33 6.38 Safety factor 2.83 2.43 14.13 Sliding safety factor 1.68 1.71 -1.78 Bearing safety factor 8.08 6.38 21.03 Structural Design Steel for stem (sq-in/ft) Top of Stem 0.58 - - Middle of Stem 0.82 - ' Bottom of Stem 1.96 3.14 -60.20 Steel for heel (sq-in/ft) 1.88 3.13 -66.49 Steel for toe (sq-in/ft) 1.30 0.90 30.77 92 Table 3.3 Comparison of TWALL results with Example 12.4 Bowles (1982) ITEM TWALL BONLES Percent (1982) Difference Wall Dimensions Hall heigth ft 28.40 28.40 0.00 Base length ft 14.64 14.42 1.50 Base thickness ft 2.42 2.42 0.00 Heel length ft 9.00 9.50 -5.50 Toe length ft 3.74 3.00 19.78 Stem top thickness ft 1.25 1.30 -4.00 Stem bottom thickness ft 1.89 1.92 -1.58 Earth Pressure Method for earth pressure prediction Coulomb Rankine Earth pressure coefficient K (6=B) Earth force on stem kips 0.294 0.294 0.00 Earth force on wall kips 11.42 11.43 0.08 15.22 15.33 -0.72 Hall Stability Overturning safety factor 2.60 2.54 2.30 Sliding safety factor Considering passive pressure - 2.45 - Neglecting passive pressure 2.02 2.05 -1.49 Bearing capacity Eccentricity ft 1.59 1.84 -15.72 Safety factor 5.17 4.30 16.82 Structural Design Steel for stem (sq-in/ft) Top of Stem 0.46 0.50 -8.68 Middle of Stem 0.61 0.64 -4.91 Bottom of Stem 2.30 2.26 1.73 Steel for heel (sq-in/ft) 1.62 1.81 -11.73 Steel for toe (sq-in/ft) 1.02 1.02 0.00 93 1. For the structural design of the stem, the Corps con- siders a section at the end of heel for computing earth force on stem which is justified only if the surface of the top of the heel is perfectly smooth. In reality, the top heel surface is rough and taking section at the end of the heel with sloping backfill results in very high earth force on the stem. 2. For the structural design of the heel, the Corps uses a longer heel than TWALL that results in large moments at the intersection of heel and stem. Consequently, the requirement of steel for Corps design is more than the TWALL. 3. For the toe design, TWALL uses a longer toe than the Corps. Therefore, required steel for TWALL design is more than the Corps design but its overall effect would be insignificant because toe length is much shorter than the heel length. In summary, the Corps design seems to be conservative because the Corps assumed a section at the end of the heel for computing earth force on the stem that resulted in very high earth force on stem. TWALL results compared very close- ly with Bowles, Example 12.4 (Bowles 1982) as shown in Table 3.3 In this phase of TWALL development, the developed jprototype was also expanded by incorporating the heuristic :rules. These heuristic rules were derived from literature 94 review, parametric sensitivity analysis, simulation and experimentation and knowledge obtained from the experts on wall design (see chapter 4 for detailed discussion). 3.10 Architecture of TWALL A schematic representation of TWALL is shown in Figure 3.3. The various components of TWALL are described briefly in the following sections. 3.10.1 Knowledge base The knowledge base of TWALL consists of the domain- specific knowledge and the control knowledge. The domain specific knowledge consists of goal statements and produc- tion rules. The control knowledge consists of procedural rules and control commands (e.g., DISPLAY, FORGET CYCLE). There are a total of 297 rules in the knowledge base of TWALL. The knowledge base of TWALL is discussed in detail in Chapter 4. 3.10.1.1 Goal Statements The goal statements are simple or object attribute facts which describe a conclusion that can be reached by the Iknowledge base. For each goal statement there should be at least one rule in the knowledge base that has the same 95 USER INTERFACE Y HELP FACILITY H SESSION CONTEXT H EXPLANATION (working memory) FACILITY \ / INFEREN CE MECHANI Backward Chaining EXTERNAL GRAPHICS PROGRAM SM KNOWLEDGE BASE Hr GOALS PRODUCTION RULES ‘——> PROCEDURAL RULES Figure 3.3 Archimcturc of TWALL 96 conclusion as that of the goal statement. Each goal state- ment must be preceded by a goal number. As an example, one of the goal statement used in TWALL is: 2.1 Cantilever wall design is safe 3.10.1.2 Production Rules A production rule is a basic building block of the knowledge base and consists of a rule statement, premise and a conclusion. The rule statement is a name given to the rule; it can be a simple fact or a string. The premise part of the production rule consists of IF, AND, and OR state- ments and the conclusion part consists of THEN, AND and ELSE statements. If all statements of premise part are TRUE, then the state of the fact of the THEN statement is added to session context. The ELSE statement is invoked only when the premise part of the rule is FALSE. An example of a produc- tion rule used in TWALL is: RULE wall suitability IF wall suitabilityl OR user preference _THEN cantilever wall suitable for present application ELSE cantilever wall is unsuitable AND DISPLAY wall unsuitable AND FORGET ALL AND CYCLE 97 3.10.1.3 Procedural Rules The main function of the procedural rules is to inter- act with an external programs. The procedural rule can be used to read data from the disk file or write data on an external device. They can also be used to activate the external programs. An example of a procedural rule used in TWALL to call an external graphics program and to pass parameters through a disk file is: RULE activate ACTIVATE GTWALL.EXE DISK GDATA.PRL SEND H SEND HS SEND B SEND tb SEND heel SEND toe THEN know activate external program 3.10.2 Inference Mechanism The inference mechanism in TWALL follows backward chaining control strategy as already discussed in section 3.9.7. 3.10.3 Session Context (working memory) The session context is a scratch pad where facts ob- tained during consultation session are stored in the memory. The current value of any fact of the context of the session 98 can be incorporated into a TEXT, DISPLAY or EXPAND displays. See the LEVELS user manual for more details (LEVELS 1989). 3.10.4 User Interface The communication between the user and TWALL is through the keyboard and CRT screen. Input data for wall design are provided by the user either by giving appropriate values of the design parameters or answering the queries made by TWALL. The values calculated by rules in TWALL can be changed at any time using CHNG and RUN function keys pro- vided by LEVELS. The help facility in LEVELS is a context- sensitive on-line help system that is available from most points within the system. The information about all aspects of LEVELS can be obtained after entering the help system. 3.10.5 Explanation Facility TWALL assists the user to respond to the queries by providing various explanations. As an example, TWALL renders the following explanation of embedment depth when the user fails to understand the query about embedment depth. EMBEDMENT DEPTH .A vertical distance to which the base in front of a retain- .ing wall is laid below ground surface is called embedment depth. The base should be placed below the depth of frost action, zone of seasonal variation and depth of scour. The embedment depth may not exceed half the base length so that the assumption of shallow foundation is not violated. 99 The explanation facility of LEVELS is through the "re- port" system. The user can enter the system by pressing the "WHY" function key. The information about reasoning process can be obtained through four menus: 1. Using the Fact Menu, the user can see the answer to the question and conclusions drawn or can change, add or delete the facts. 2. From the Rule Menu, the user can review the rules of the knowledge base and trace the line of reasoning. 3. From the Option Menu, the user can save or retrieve the context of the knowledge base. 4. From the Report Menu, the user can generate the knowl- edge tree showing the logical sequence of rule fired. 3.10.6 External Graphics Program An external graphics program called GTWALL was coded in Microsoft FORTRAN to draw the final design sketch of the wall. The design parameters are passed from the expert system to GTWALL through a disk file. After displaying the design sketch, the external program returns the control back to the expert system. CHAPTER 4 TWALL: KNOWLEDGE BASE 4.1 General The knowledge base of TWALL is developed in Production Rule Language PRL (i.e., IF, THEN, ELSE type rules). There are a total of 297 rules used in the development of this knowledge base. The rules are further classified into 14 building blocks (38’s) as shown in Figure 4.1. The main idea of using 88’s is to classify all the required rules accord- ing to their intended uses. For example, rules that check the suitability of a cantilever retaining wall for a given application can represent a building block. The division of knowledge base into building blocks has also helped to understand and explain the key concepts and relations used in the development of the knowledge base. The control knowledge needed for solving a problem is {developed in 38's and is represented by means of control commands. For example, the SEND command can be used to pass jparameters to an external program through a disk file. A Ibujlding block may be executed once or many times depending upon its function . 100 101 LEVELS EXPERT SYSTEM SHELL i KNOWLEDGE BASE BB 1: GENERAL INFORMATION i BBZ: WALL SUITABILITY I BB3: PARAMETER EVALUATION >1 BB4:TR.IALWALLDIMENSIONS ‘ A EXTERNAL STABILITY INTERNAL STABILITY 335‘ FORCES ON WALL 3310: PARAMETERS FOR I STRUCTURAL DESIGN + 336: OVERTURNING STABILITY i or I +— 337: SLIDING STABILITY 3311: STEM DESIGN + 338: CONSERVATIVE DESIGN A * 3312: BASE DESIGN « 339: BEARING CAPACITY / BB13: COST ANALYSIS i 3314: GRAPHICS Figure 4.1 Structure of building blocks in TWALL 102 4.2 Building Blocks of TWALL The BB's of TWALL are described briefly in the follow- ing sections. 4.2.1 BB1: General Information BBl contains rules that interactively acquaint the user with the purpose, capabilities and limitations of the expert system TWALL. It also gathers the basic information whether the user wishes to design the wall for external stability only or both external and internal stability. The heuristics that guided the design of this BB dealt mostly with develop- ing a comfortable interface for the user. 4.2.2 BB2: Wall Suitability BBZ contains rules to check the suitability of a canti- lever retaining wall for a given application. The user has an option to over-ride the recommendations made by the system and continue with the design. The main purpose of this BB to show the capabilities of expert systems for solving the deductive type of problems. The inference net- ‘work of this BB is shown in Figure 4.2. 4.2.3 BB3: Parameters Evaluation The inference network of BB3 is shown in Figure 4.3. 13118 BB contains rules that query the user for the required 103 $ WALL SUITABILITY 6 < H < 30 NON COMPRESSIBLE PLANT AND FOUNDATION SOIL EQUIPMENT GRANULAR BACKFILD TECHNICAL KNOW-HOW Figure 4.2 Inference network for wall suitability 104 I . (PARAll/fliTERS EVALUATION SOIL PARAMETE19 (WATER TABLD REQUIRED SAFETY FACTORS EARTH PRESSURE COEFFICIENT OVERTURNING SLIDING ACTIVE AT-REST B = backfill slope MISC BEARING 8 = wall friction angle Df = embedment depth qo = uniform surcharge Figure 4.3 Inference network for parameters evaluation 105 design parameters. These parameters include soil friction angle and unit weight, backfill slope angle, wall friction angle, surcharge, water table and required safety factors for wall stability against overturning, sliding and bearing capacity failures. Making use of heuristics incorporated in the knowledge base, the system displays permissible limits and recommended values of the parameters for guiding the user when queried. See Chapter 7 for heuristics development. The system provides default values for some of the parameters including wall friction angle and required safety factors. The default values used by the system are displayed with the query and the user has an option to either use the default values or make changes according to the guidelines provided in the query. See example run (Appendix B) for sample queries. As an example, a sample query for wall friction angle and user response is illustrated below: Do you want to enter wall friction angle of your choice? Enter "TRUE" If "FALSE" the system will assume default wall friction angle i.e., 6=(B+¢)/2=26.7 Press function key to know more about wall friction. ........................... THREE FALSE Wall friction angle (6) ? Permissible values: 10.0 <6< 35.0 deg ............................ The system calculates default wall friction angle 6 based on heuristic (i.e., 6=(B+¢)/2) developed in this study. The rules of this building block also query the user regarding the assumption to be made for computing earth 106 pressure coefficient (active or at-rest). For the active choice, the system assumes Coulomb's active conditions and computes the earth pressure coefficient K using equation 2.2. The user can also use Rankine's equation assuming 6=B because Coulomb's and Rankine's equations yields the same results for 6=B. For the at-rest choice, the system computes earth pressure coefficient using Jaky's equation or modified Jaky's equation for sloping backfill (equation 2.9 and 2.10) 0 4.2.3.1 Data Screening The input data enters TWALL through queries to the user. It is important to scan the incoming data so that user mistakes in responses to the query can be detected and rectified there and then. Heuristic rules are used to speci- fy the reasonable and practical limits for the input parame- ters. If any error is detected by the system in the input data, a message "out of range" is displayed to the user and the system queries the user again with the same question. This format allows immediate correction of any mistake in the incoming data. In the following sample rule if the user makes some Inistake in entering the data, the DISPLAY statement displays ‘the message "out of range" to the user, the FORGET statement removes all facts pertaining to base length B from the session context, the CYCLE statement moves control again to 107 the top of the rule and the user is again queried with the same question. RULE backfill internal friction angle IF Ql>=20 AND 91<=45 THEN know 41 ELSE DISPLAY out of range AND FORGET 91 AND CYCLE 4.2.4 384: Trial Wall Dimensions The rules in BB4 queries the user for base, heel and top stem thickness. The heuristics incorporated in these rules not only recommend an appropriate range for the de- sired parameter but also guide the user to a reasonable re- sponse by limiting the maximum and minimum ranges of the parameter being queried. A sample rule below demonstrates this ability. RULE IF AND AND AND AND AND AND THEN base width HwD>O Ba.=0.4*H Bb:=H Ba1:=0.6*H Bb1:=0.7*H B >=O.4*H B <=H know B The above rule queries the user about base length which is a function of wall height H. This rule applies when water level on heel side of the wall is above the base. "Ba" and "Bb" are maximum allowable base lengths (maximum expect- ed.range) and "Bal" and "Bbl" are recommended base lengths 108 (based on experience of TWALL development). These recom- mended and maximum base lengths are displayed when user is queried about the base length. In this way, the user is guided to respond to a query by making use of experience of the experts on the design of retaining walls. The last two facts before THEN part of the rule impose minimum and maxi- mum limits for B on the user for his or her response. See example run for sample query (Appendix B). Shear reinforcement (i.e., stirrups) is not commonly used in the design of cantilever retaining walls. Therefore, the stem thickness should be sufficient to resist critical shear without any steel reinforcement. The system computes bottom stem thickness where shear is maximum by equating total horizontal force on stem (equation 2.22) to the shear strength of concrete (equation 2.32). Finally, the system computes initial toe length by subtracting heel and stem bottom thickness from the base length. The heel is designed as cantilever beam where steel reinforcement is provided at the top of the heel to carry tensile stresses. A short toe may result in a situation ‘where upward soil pressure exceeds the downward soil pres- sure at the intersection of heel and stem which is not desirable from structural design point of view (see Chapter 5 for a detailed discussion). Using heuristics derived from gparametric sensitivity analysis, the rules in the building Iilock limit toe length to not less than 24 to 30 percent of base length depending on wall angle friction and wall height. Thus, a situation as mentioned above is avoided. As 109 an example, the following rule recomputes toe and base lengths when computed toe length is less than minimum required toe length. RULE toe length IF toeF.S.0T>3.0 DO IF Es.OT < 2.0 ELSE IF INCREASE TOE LENGTH F-S-or > 3-0 THEN KNOW FORCES 0“ WALL DECREASE TOE LENGTH KNOW Mo KNOW FORCES ON WALL KNOW Mo KNOW MR KNOW MR F.S.m= MR/MO F'S‘OT=MRIMO CANTILEVER WALL IS SAFE AGAINST WALL OVERTU RNING Figure 4.4 Inference network for wall stability against overturning 112 different values of design parameters (within the practical range) and studying their effects on wall stability against overturning. B 8 (CF)B+B(I)(F.S.otReq-F.S.otAval)/F.S.otAval ............ (4.1) heel a (CF)heel+heel(l)(F.S.otReq-F.S.otAval)/F.S.otAval) ....... (4.2) where CF is a convergence factor, I is an index value which is 1.00 for this equation, F.S.otReq is required safety factor and F.S.otAval is available safety factor. The CF used with B and heel are 1.15 and 1.10 respectively. The first term in the above equations provide a con- stant percent increase in B and heel and the second term provides an increase related to degree which the design lacks the required safety factor. The second term governs equations 4.1 and 4.2 when the difference between the re- quired and the available safety factors is large. But when the difference in required and available safety factors becomes very small the calculated base and heel lengths by the second term also become very small and the system keeps doing unnecessary iterations. To avoid such a situation, a convergence factor was introduced in equation 4.1 and 4.2. The convergence factors reduces the number of iterations by increasing the base length 15 percent and the heel length 10 percent during each iteration. A higher CF is used with B so that net effect of increasing in the base and heel lengths is a lengthened toe. The following rule shows the use of equations 4.1 and 4.2. 113 RULE safety against overturning IF F.S.otAval=F.S.otReq THEN wall is safe against overturning moments This rule is activated when the trial wall design fails in overturning. To achieve the goal, (i.e., wall is safe against overturning moments) the inference mechanism of TWALL tries to establish all facts in the rule starting from the top. "Br" and "heelr" are recommended percent increase in base and heel length that are displayed to the user when the trial design fails in overturning. The FORGET statements removes all undesirable facts from the session context because these need to be re-estab- lished for after base and heel length are modified. If these facts are not removed from the session context, the infer- ence mechanism will not pursue the goals that need to be re- established with modified wall dimensions. The facts with "B" and "heel" compute the required increase in the base and Iheel lengths. The user has an option to either accept the «default percent increase in base and heel length or change ‘these values by using CHNG function of LEVELS. The CYCLE statement makes the system recompute all removed facts from session context with increased base and heel lengths. 114 Finally, the available safety factor is recomputed and com- pared with the required. This iterative process continues until the available safety factor exceeds the required safety factor. See Appendix B for a sample interaction of the system with the user. 4.2.7 BB7: Sliding Stability The inference network of stability of the wall against sliding failures is shown in Figure 4.5. The rules in BB7 are structured first to query the user whether to design the wall with or without a base key and then to compute the safety factor against wall sliding. For walls designed with base key, the system considers passive resistance only in front of the key. The system limits key depth between 1 feet to 0.58. To simplify calcu- lation of shear resistance under the base with the key, TWALL assumes rupture surface passing through the bottom of the key and parallel to the wall base. The passive resis- tance in front of the wall above the bottom of the base is neglected for all cases. Heuristic rules derived from parametric sensitivity analysis and knowledge obtained from the experts on retaining wall design were used to improve the design algo- rithms for wall stability against sliding. It is known from parametric sensitivity analysis that increasing base and heel length improve wall stability against sliding but an increase in heel length improves wall stability more 115 SLIDING STABILITY KNOW TOTAL HORIZONTAL FORCE ON WALL, PDH KNOW TOTAL RESISTING FORCE, PR ES. S = PR/PDH WHILE 1.5 > FMS S > 2.0 DC IF THEN ES. 5 < 1.5 ELSE INCREASE PEEL. AND B IF ES. 8 > 2.0 DECREASE HEEL AND B B<2H THEN ELSE IMPROVE DOUNDATION KNOW PDH SOIL KNOW PDH KNOW PDH KNOW PR KNOW PR KNOW PR PS 5: PR/PDH ES. 5: PR/PDH E's S= PR/PDH CANTILEVER WALL IS SAFE AGAINST WALL SLIDING Figure 4.5 Inference network for wall Sliding stability 116 effectively than an increase in base length. The developed expressions to increase base and heel length are given below. These expression were developed by running the program with different values of design parame- ters and studying the effect of change in these parameters on wall stability against sliding failures. 8 . (CF)B+B(I)(F.S.sReq-F.S.sAval)/F.S.sAval ................. (4.3) heel= (CF)heel+heel(I)(F.S.sReq-F.S.sAval)/F.S.sAval ........... (4.4) where F.S.sReq is required safety factor and F.S.sAval is available safety factor against sliding failures. The CF used with B and heel are 1.03 and 1.07 respectively. It is to be noted that higher CF is used with the heel so that net effect of increase in base and heel lengths is a lengthened heel. The index value I for these equation is also unity. These above expressions use the same logic as those previ- ously described for overturning stability in 886. In weak foundation soils, the required base length becomes excessively large to meet the sliding stability requirements and wall dimensions fall out of proportions. If such a situation arises in TWALL, the rules in this BB temporary halt the design process and advise the user to consider improving the foundation soil parameters i.e., the ‘unit weight and the soil friction angle. Then the design is :repeated with new foundation soil parameters. This interac- ‘tive process continues until wall dimensions with reasonable jprcportions are Obtained. In this knowledge base, the base 117 length is considered excessively large when it exceeds twice the wall height. 4.2.8 388: Conservative Design According to the knowledge base of TWALL, the design of a cantilever retaining wall is considered as conservative when safety factors against wall sliding and overturning exceed 2 and 3.0 respectively. These limits are upper bound values that could be found in literature on the design of retaining structures (Das 1984, Bowles 1988). The safety factor against sliding usually controls the wall design as known from the parametric sensitivity analy- sis. Therefore, the expressions developed in this study to make the design economical are based on sliding stability requirements. The developed expressions as given below reduce the base and the heel lengths according to the dif- ference between the available and required safety factors against sliding failures. The system recalculates all forces and moments on wall with modified B and heel and then re- check overturning and sliding safety factors. B = (CF)B-B(I)(F.S.sAval-F.S.sReq)/F.S.sAval ................. (4.5) heel= (CF)heel-heel(I)(F.S.sAval-F.S.sReq)/F.S.sAval ............ (4.6) *where CF is a convergence factor and I is an index value. frhe convergence factor for both B and heel is 0.95 and index ‘values are 0.35 and 0.4 for B and heel respectively. Small 118 index values are used in the above expressions to reduce the effect of second term when the difference between the re- quired and available safety factor is large. These expres- sions were also developed in a similar fashion as discussed earlier. The heuristic developed from parametric sensitivity analysis is that the decrease in heel length substantially reduces the safety factor against wall sliding. The higher index factor used in equation 4.6 with heel reduces heel length five percent more than the base length in each itera- tion during the trial design process. Thus, the net effect is decreased heel that reduces safety factor against wall sliding to required value in a fewer iterations. 4.2.9 BBS: Bearing Capacity The inference network Of bearing capacity is shown in Figure 4.6. The rules in BB9 compute bearing capacity of the foundation soil and safety factor against bearing capacity failures using equations 2.19 and 2.20 respectively. making use of heuristics, the rules Of this BB also ensure that point of application of resultant of forces acts be- 'tween the middle third of the base (i.e., eccentricity =0 AND e>B/6 AND DISPLAY eccentricity out of limits AND heel:=1.05*heel AND B:=l.02*B AND CYCLE AND x:=(Mr-Mo)/N AND e:=0.5*B-x AND e<=B/6 THEN know eccentricity within limits The rules in BB9 also advise the user to improve fou- ndation soil or increase embedment depth when its fails in bearing. The specimen rule is: RULE safety factor against bearing IF F.S.bAval=F.S.bReq THEN wall is safe against bearing capacity failures The above rule is activated when the available safety factor falls below that required. The DISPLAY statement in the rule displays the message to the user regarding wall the failure due to weak foundation soil and renders advice to improve foundation soil. The FORGET statement removes the 121 facts that need to be modified in the session context and the CYCLE statement makes the program re-establish the for- gotten facts either through computations Or through queries from the user. In this case, the system queries the user for embedment depth Df, foundation soil friction angle ¢2 and cohesion c2 and recomputes the safety factor against bearing capacity failures. However, the user also has an option to modify wall dimensions (e.g., base and heel) through "WHY" function of LEVELS. This interactive process continues until the available safety factor exceeds the required. 4.2.10 BBlo: Parameters for structural Design The rules in BB10 are structured to query the user for the design parameters required for the structural design of stem and the base. These parameters include the compressive strength of concrete f'“ yield strength of steel:fi,and overload factors. The allowable ranges of fy and f’c are displayed to the user when queried. Default values of overload factors for stem, heel and toe design are provided but the user has an option to change the default values. The user also has an option to either consider or neglect upward soil pressure under the base for the heel design. 4.2.11 3311: stem Design The rules in this BB are structured to compute pres- sures, shears and moments at five different locations along 122 stem height (i.e., stem top, 1/4, 1/2 and 3/4 of stem height and stem bottom). Pressures, shears and moments are computed using equation 2.21, 2.22 and 2.23 respectively. The forces considered for the structural design Of stem are shown in Figure 2.9. The strength design method of ACI Code (ACI 318-89) is followed for computing required steel reinforcement at top, middle and bottom of the stem. The computed steel is then checked for minimum and maximum allowable limits as speci- fied in the Code. The system uses the default top stem thickness (i.e., 12 inches) or any value as preferred by the user. The bottom stem thickness is computed by equating the compressive strength of concrete to the shear at stem bottom as discussed earlier. See Figure 4.7 for the inference network of stem design. 4.2.12 3312: Base Design The inference network Of this 33 is shown in Figure 4.8. The rules in 3312 compute pressures, shears and moments on the heel and toe using equations 2.24 through 2.29 and Figure 2.9. These pressures, shears and moments are computed at.five different locations along the heel and toe (i.e., free ends, 1/4, 1/2 and 3/4 of heel or toe and points where heel and toe join stem) . The user has an Option to either Linclude or neglect upward soil pressure under the heel to compute shear and moments on heel. Shear usually controls the design of the heel and toe. 123 STEM DESIGN KNOW EARTH PRESSURE ON STEM KNOW EARTH FORCES ON STEM KNOW SHEARS ON STEM KNOW MOMENTS ON STEM KNOW STEM STEEL REINFORCEMENT Figure 4.7 Inference network for stem design BASE DESIGN KNOW SHEARS AND MOMENTS ON HEEL KNOW SHEARS AND MOMENTS ON TOE KNOW WIDE BEAM SHEAR KNOW ALLOWABLE SHEAR WHILE WIDE BEAM SHEAR > ALLOWABLE SHEAR DO INCEASE BASE THICKNESS KNOW SHEARS AND MOMENTS ON HEEL KNOW SHEARS AND MOMENTS ON TOE KNOW WIDE BEAM SHEAR KNOW ALLOWABLE SHEAR KNOW HEEL STEEL REINFORCEMENT KNOW TOE STEEL REINFORCEMENT Figure 4.8 Inference network for base design 124 Therefore, the rule in this 33 are design to first check the heel and toe for wide beam shear before computing required steel reinforcements. The larger of shears computed on heel and toe is taken as the critical shear and the base is checked for this shear so that the critical shear does not exceed the compressive strength of base concrete. When wide beam shear exceeds the compressive strength of concrete, the system recommends an increase in base thickness to the user and waits for his or her response. Then the system recomputes shear strength of the base with increased base thickness and compares it again with the critical shear. This interactive process continues until the shear strength of the base concrete exceeds the wide beam shear. The expression developed for increasing the base thickness in each iteration is given below: tb=1.1tb+0.45tb(Vwidebeam-QVC)/¢Vc ..... ........ ..... (4.7) where tb is a base thickness, Vwidebeam is a critical shear on the base and QVC is a allowable compressive strength of concrete. The convergence factor of 1.1 and index factor of 0.45 were developed through a trial and correction process. The rest of the rules in this 33 compute required steel reinforcement for heel and toe and check for their allowable minimum and maximum limits. The steel requirement is computed at three different locations along heel and toe namely, at free ends, middle and at the points where heel and toe joins stem. Heel and toe are also designed according 125 to the ultimate strength method of the ACI Code. 4.2.13 3313: Cost Analysis The rules in 3313 compute required quantities of exca- vation, backfill and concrete and cost per lineal feet of the wall. The default cost of materials is based on Means Construction Cost Data 1991. The user has an option to change the default cost Of materials during design process. The inference network of 3313 is shown in Figure. 4.9. 4.2.14 3314: Graphic Interface The structure of the external graphics program GTWALL coded in Microsoft FORTRAN is shown in Figure 4.10. A procedural rule in 3314 interacts with GTWALL. The control commands in this 33 activate and send final design dimen- sions of the wall to GTWALL through a disk file. GTWALL receives incoming data from TWALL in a specific format, checks for current video configuration, draws the wall design sketch with all its dimensions and waits for user response. On the user response, the program control is shifted back to LEVELS and the inference mechanism termi- nates the current session and activates various function keys that can be used by the user to perform various task (e.g., save the current session context, check the reasoning process of wall design, restart the program or exit the program). 126 l > C COST ANALYSIS ) Y Required Volume l Required Total Cost Of Backfill Excavation Required Volume Material Cost of Concrete Figure 4.9 Inference network for cost analysis 127 KNOWLEDGE BASE EXTERNAL PROGRAM : GTWALL MAIN PROGRAM GRAPHIC MODE XY GRAPH END PROGRAM VARROW HARROW Figure 4.10 Structure of external program GTWALL 128 4.3 Examples of the Design Process In the process of development and expansion of TWALL, over a hundred cantilever wall designs were made using TWALL (e.g., 34 walls were designed for a class on retaining structures (CE 419), see appendix D). From these designs, it was found that, TWALL typically makes 3 to 4 iterations to obtain the design. The number of iterations in TWALL have been minimized by incorporating the heuristics as discussed in the previous sections. The reduction in iterations have reduced the computational time to less than a minute on XT computers. A complete design process of TWALL and its interaction with the user is shown in appendix 3. In general, the design process of the cantilever wall on TWALL is summarized in Figures 4.11. The Figure shows changes in base length, heel length and overturning and sliding safety factors after each iteration when lower limits of trial dimensions recommended by TWALL were used. As can be seen from the figure that TWALL reaches the optimal design in 3 iterations. A few sample TWALL interactions with the user are shown below. The user responses are hatched for clarity. Base width (3) ? Recommended width: 12.50 and it will recalculate the safety factor against overturning. However, you have an option to increase base and heel lengths of your choice using "WHY" and "FACTS MENU". 3 = 12.68 ft Heel = 6.90 ft Toe = 3.25 ft ........................................... Please press ggngerg to continue S L I D I N G F A I L R E The wall design is unsafe against sliding forces as the safety factor 1.44 is less than 1.5. The system will increase 11.1 % heel and 7.1 % base length as you press and it will recalculate safety factor. However, you have an option to increase heel and base lengths of your choice using "WHY" and "FACTS MENU". F.S.overturning = 2.81 B = 18.34 ft Heel = 9.63 ft Toe = 3.25 ft Please press ggfifiéfg to continue I N S U F F I C I E N T B A S E T H I C K N E S S The wall design is unsafe due to insufficient base thickness for wide beam shear. The system will increase 17.78 % base thickness as you press and will again check the base for vide beam shear. tb = 1.80 ft OVC = 20224 Ibs Vwidebeam = 23771 lbs D E S I G N S U M M A R Y Safety factor against wall overturning = 3.21 Safety factor against sliding failures = 1.54 Safety factor against bearing failures = 4.55 Wall height ft = 25.0 Wall height above ground surface ft = 22.00 Stem height ft = 22.88 Top stem thickness ft = 1.00 Bottom stem thickness ft = 2.53 Base width ft = 19.64 Heel length ft = 10.70 Toe length ft = 6.41 Base thickness ft = 2.12 Stem steel sq-in/ft = 1.83 Heel steel sq-in/ft = 1.98 Toe steel sq-in/ft = 0.88 Cost $/ft = 937.38 The design process of TWALL with a bad guess of soil parameters and trial wall dimensions are shown in Figure 4.12. The figure shows changes in base length, heel length and overturning and sliding safety factors with the number of iterations. As can be seen from this figure that even with the bad guess of input parameters, TWALL reaches the safe design in 6 iterations. This number is small as com- pared to the numerous iterations made by procedural programs developed for problems having open-form solution such as the design of cantilever retaining wall. 131 25 20 1: cm : E. - 15 e g: *< .3 -: 3 -§ 10 8 = '1 a g 5 t: O ' ' 0 0 1 2 3 Number of Iterations Figure 4.11 TWALL design process when trial wall dimensions recommended by TWALL are used 50 .10 45 .......................................... . ................................. . ......... . .............................. i9 40 .......................... . ............................................. .. ............................ .I c i _ V F.S.Wm. :8 m I: 35 .............................. ....................... f, ........................................................ ‘17 9 a, : F? = 30.. .................................. ....- ............ . ..................... . ....... ..... . ....... . .......... .6 Q E 25 .................................... "' ..... , ..... . ........................................................ .25 :1 ° ' Hut ’ a Q ...................... . ......... .. ............ . .................................................. 1' = 20 ,4 2 \ Q . m fl :3 0 1 1 1 1 4 O 0 1 2 3 4 5 6 7 8 Number of Iterations Figure 4.12 TWALL design process with bad guess of soil parameters and trial wall dimensions CHAPTER 5 PARAMETRIC SENSITIVITY ANALYSIS 5.1 General The proportions of a well-designed cantilever retaining wall are influenced by a number of variables. These include wall height, backfill strength and density, foundation soil strength, wall friction, backfill slope and water table. This chapter summarizes the results of a series of para- metric sensitivity analyses performed to study the interre- lationships among these variables, wall proportions and safety factors. The results of these analyses were used for writing heuristics (rules of thumb). These heuristics were then incorporated in the expert system TWALL during its expansion. The analyses were carried out in two parts. In the first part, a sensitivity analyses were performed to evalu- ate the effect of change in these variables on safety factor against wall overturning, sliding failures and bearing failures. The analysis was performed by varying each vari- able within a typical range and computing the safety factor 132 133 while keeping the other variables constant. This method reveals not only the sensitivity but also the direction of the change in safety factor to a change in any variable. In the second part, a specific study was made of the effect of change in heel length on the distribution of net downward pressure on the heel. The analysis was first per- formed assuming horizontal backfill, neglecting wall fric— tion and considering the water table at wall base. Then, the effects of backfill slope, wall friction and water table on the distribution of pressure on the heel were studied. 5.2 Assumptions The following assumptions were made for the present parametric sensitivity analyses: a. The backfill soil is cohesionless and characterized by an internal friction angle, ¢1 and unit weight, 71. b. The foundation soil is either cohesionless or cohesive and characterized by an internal friction angle, ¢2, cohesion, c2 and unit weight, 72. c. Coulomb’s active conditions were assumed behind the wall and passive resistance in front of wall was ne- glected. 5.3 134 Effect of Changes in Variables on Wall stability 5.3.1 Method of Analysis The expert system TWALL (Chapter 3 and 4) was used for the parametric sensitivity analysis. The analysis was per- formed as follows: A realistic range for each variable (X) was selected that brackets most commonly-encountered design situa- tions. The midpoint value (Xmid) and the maximum dif- ference (AXmax) between the midpoint value and extreme values was computed for each variable (Table 5.1). The change index (AX) for each variable (X) was comput- ed as the ratio of deviation of X from Xmid to AXmax X - Xmid AX(%) = 100 ........... ......OOOOOOOO (5.1) AXmax where AXmax = Xmax - Xmid A "midpoint" base safety factor (F0) was computed using the median value of all variables and wall proportions (Table 5.2). A safety factor (Fx) was computed as each variable was varied across the range. The relative change in safety factor (AF) as a percent of F0 was calculated as: 135 Fx - Fo AF(%) 100 ......................... (5.2) Fo Table 5.1 Range of variables Parameter (X) Unit Xmin Xmid Xmax 5Xmax Wall height H ft 10 20 30 10 Base Length 8 ft 11 15 19 4 Heel length heel ft 6 10 14 4 Backfill unit weight 11 pcf 90 110 130 20 Backfill friction angle ¢1 deg 25 35 45 10 End. soil unit weight 72 pcf 100 120 140 20 End. soil friction angle ¢2 deg 25 35 45 10 Fnd. soil cohesion c2 psf - C) 2000 2000 Wall friction/¢l(mid) 0 0.5 1 0.5 Backfill slope/¢1(mid) -0.5 0 0.5 0.5 Water table height/H(mid) -l 0 1 l Table 5.2 Base safety factors Safety factor against overturning, F.S. (ot) 7.77 Safety factor against sliding failures, F.S.(s) 3.63 Safety factor against bearing capacity failure, 8.78 F.S.(b) The base safety factors shown in Table 5.2 appear to be higher than required for an economical design. These safety factors corresponds to active conditions in the backfill. If the wall is designed for at-rest conditions and the other 136 factors like compaction and pore water pressure are also considered, the present design barely meets stability requirements against sliding failures. For example, the base safety factor against sliding failures reduces from 3.63 to 1.48 when considering at-rest conditions with a water table at H/2 from wall base. Also, these base safety factors were kept high so that all parameters could be varied within the specified ranges without reducing actual safety factors below allowable limits. 5.3.2 Results The effects of change in variables on safety factor against overturning F.S.(ot), sliding F.S.(s) and bearing capacity F.S.(b) failures are shown in Figure 5.1 through Figure 5.4. The effects of changes in the variables on wall design are discussed briefly in the following sections. 5.3.2.1 Wall height The effects of change in wall height H on three safety fac- tors are shown in Figure 5.4. The factor of safety against wall overturning is more sensitive to change in wall height than to changes in other variables. The reason is that the force causing overturning (leaving aside common variables) is a function of the square of wall height whereas the re- sisting force is a function of wall height and heel length. Range 01 = 35 :10 A 4o ()2 = 351 10 ~ o 71 =110:20 V 12 =12oizo (Q 20 Blel = .53; .5 u. BI¢1 = 0:.5 .E 0 a -15 :L 4 0 heel -10 i 4 U) Ev/n - o i 1 E g -2o (J 3g 4w Hw/H -60 -150 -100 -so 0 50 100. 150 Xmln Xmld Xmax % Change in AXmax Figure 5.1 Percent change in overturning safety factor versus percent change parameter values 60 Range 40 $1 = 35: 10 a =fi¢m '07 11 =110+2o V 20 _ ‘ (5 y). -120: 20 IL' 61M =515 : 0 film = 03.5 ._ n in 1 4 0 heel -10 i 4 a -20 aw/n - o _+_ 1 c a .c 0 -4o e\° -60 Hw/H -80 -150 -100 -so 0 so 100 150 Xmln Xmld Xmax % Change in AXmax Figure 5.2 Percent change in sliding safety factor versus 60 percent change in parameter values 138 600 Range A 500 41 =35110 £ ¢2 =35110 (I; 400 11 =1101-20 I]: :4, =120i20 : .mm 1 - 5;:5 ._ W01 = 0 1.5 g, a -as;g4 c 200 11.01 .10 i I a null: - o + 1 z _ 0 100 a! 0 «(:2 -100 -150 -100 -50 0 so 100 150 so A 25 .o V 0? IL 0 .E 8. c -25 e 1: <9 39 .50 (b) Hw/H -75 -150 -100 -50 o 50 100 150 Xmll'l Xmid Xm.x % Change in AXmax Figure 5.3 (a) and (b) Percent change in bearing safety factor versus percent change in parameter values (Table 5.1) 300 200 100 % Change In Satety Factor -100 139 F.S.(b) F.S.(s) -150 -100 ~50 O 50 100 150 Xmln Xmid Xmax % Change in AXmax Figure 5.4 Percent change in overturning, sliding and bearing safety factors versus percent change in ASXmax of wall height (Table 5.1) 140 As wall height is increased at a fixed value of heel length, the increase in overturning forces and moments is more rapid than the increase in forces resisting overturning. Thus, the overturning safety factor decreases rapidly and the decrease is more pronounced at low values of H. The rise in wall height also decreases the sliding safety factor because of increase in the magnitude of horizontal forces and decreases bearing capacity safety factor because of increase in the magnitude of vertical forces acting on wall base. 5.3.2.2 Base length Increasing the base length at a fixed value of heel en- larges toe length, which improves overturning safety factor by increasing the moment arms of resisting forces (Figure 5.1). The effect of change in overturning safety factor with the change in base length is independent of type of founda- tion soils (Figure 5.5). Sliding safety factor also increas- es slightly with the increase in base length (Figure 5.2). For cohesionless foundation soils, the effect of changing base length (holding heel constant) on the safety factor against wall sliding is not very significant as the raise in total vertical force (2V) is due to increase in weight of wall base only, which is small (Figure 5.7). Some very interesting observations were made when studying the effect of change in base length on safety factor against bearing capacity failures. Lengthening the 141 toe shifts the point of application of the resultant of forces acting on the wall base and alters eccentricity. The alteration in eccentricity affects the safety factor against bearing capacity failure. As can be seen from Figure 5.9 that the bearing capacity safety factor initially increases with the increase in base length because of a decrease in eccentricity and it attains maximum value at zero eccentric- ity. A further increase in base length reduces bearing capacity safety factor because of an increase in eccentrici- ty. But when the base length becomes very large, the safety factor again increases because of large bearing area that diminishes the effect of eccentricity. The percent change in bearing capacity safety factor in cohesionless soils is almost twice as compared to the change in cohesive soils. 5.3.2.3 Heel length Increasing the heel length at a constant base length improves safety factors against overturning and sliding because it increases the magnitude of resisting forces (Figure 5.6 and 5.8). The effect on the overturning safety factor is not as significant as on the sliding factor. The effect of increased heel on sliding safety factor is signif- icant because of increase in soil weight over the heel which enhances the forces that resist wall sliding. The increase in soil weight over the heel also increases the magnitude of forces resisting overturning but the overall effect is 142 .mm J z: - ¢eso ' 0 3 150 ”=4 05 j c2=1 ksf .5 100 / o I / a e c . a £3 50‘ ’//// ag . 1 q 0 . . . . . 0.55 0.65 0.75 0.85 0.95 1.05 B/H Figure 5.5 Effect of change in base length on overturning safety factor. i I 0250 2? ; ¢$fi0 O . v . u— as : 62:1 ka ‘ e at I .. // 3, 15 c 2 L1 0 10 a? _7 0 . . 1 a . . . 0.5 0.6 0.7 0.8 0.9 1.0 1.1 heel/B ...1 1.11.4111 1.1 P a. Figure 5.6 Effect of change in heel length on overturning safety factor 143 80 ' 0281 ksf j c2=2 ksf ? d ... 60 / a? . l I .5 40 / ¢ 4 u I c . to z 1 (J 20 v o 1 + “‘ 44,0235 -I 027-40 0 . . r 0.55 0.65 0.75 0.85 0.95 1.05 BIH Figure 5.7 Effect of change in base length on sliding safety factor 100 ‘ 0250 ,‘ 0130 3 ‘02 [L E O a C '6 .: C) 32 02.1 ksf 02-2 ksf '20 U l ' I V 1 ' I ' I ' I ' 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 heeUB Figure 5.8 Effect of change in heel length on sliding safety factor 144 100 ' <fi=w é . 02:35 ”2 ‘ IL 02:30- E 0 a C G .2 (J 32 02-1 ka- C282 ksf 0.55 0.65 0.75 0.85 0.95 1.05 B/H Figure 5.9 Effect of change in base length on bearing safety factor 40 §:3°j "n\\\ m ‘ 16;?” 02% u. 20‘ I /\ \, '5 i 7/ W o I A’,// . g’10 1’ g . shunt “‘0 (J 1 02-2 ksf $2 0 ._i '10] v v v r u u 04 as 06 07 08 09 L0 heeUB Figure 5.10 Effect of change in heel length on bearing safety factor 145 reduced because of reduction in the moment arm of resisting forces with decreased toe (toe length decreases when heel, length is increased at constant base length). The change in heel length has no effect on the sliding safety factor in purely cohesive soils but it has a significant effect in cohesionless soils (Figure 5.8). The effect of change in heel length on bearing capacity safety factor also resulted in some interesting observa- tions. The variation of the bearing capacity safety factor with the change in heel length is shown in Figure 5.10. A change in heel length affects the location of the resultant of forces acting on the wall base and eccentricity, which in turn influences bearing capacity safety factor. The maximum safety factor was found to occur when the heel length is about 80 percent of the base length; and eccentricity corre- sponds to minimum value. The results suggest that in weak foundation soils, a large heel can help to improve bearing as well as sliding stability of the wall. But a large heel will also result in large bending moments at the intersec- tion of heel stem which in turn will increase the require- ment of steel. Thus, the designer has to keep in mind the economics of the design. 5.3.2.4 Backfill slope Increasing the backfill slope angle B increases the coefficient of earth pressure and the height of vertical 146 section at the end of the base. Therefore, the magnitude of the driving force Pfl,is increased substantially. The effect of increase in vertical component ofP:3D on wall stability due to increase in backfill slope is not sufficient to neutralize the effect of overall increase in Pg" Thus, safety factors against overturning, sliding and bearing capacity failures decrease with the increase in backfill slope (Figure 5.1 to 5.3). 5.3.2.5 Soil Friction Angle Increasing the backfill soil friction angle ¢1 improves the safety factor against overturning, sliding and bearing capacity failures by reducing the driving forces (Figures 5.1 to 5.3). The increase in foundation soil friction angle has no effect on overturning safety factor (Figure 5.1) but it has significant effect on sliding safety factor (Figure 5.2). The foundation soil friction angle has marked influ- ence on bearing capacity safety factor and the most signifi- cant change was observed when it was varied from 35 to 45 degrees (Figure 5.3). 5.3.2.6 Soil Unit Weight The unit weight of backfill soil 71 has only a minimal effect and foundation soil unit weight 72 has no effect on safety factor against wall overturning and sliding. However, 147 the increase in backfill unit weight decreases the safety factor against bearing capacity failure and the increase in unit weight of foundation soil increases the bearing capaci- ty safety factor to some extent. 5.3.2.7 Wall Friction Angle Increasing the assumed wall friction angle 6 reduces the coefficient of earth pressure and horizontal forces and increases vertical forces on the wall. An increase in the 6/¢1 ratio increases the safety factor against overturning and sliding and decreases the bearing capacity safety factor as shown in Figure 5.1, 5.2 and 5.3 respectively. The in- crease in overturning safety factor with the increase in wall friction angle is more pronounced at higher wall heights (Figure 5.11). The increase in sliding safety factor with the increase in wall friction angle is more pronounced at wall heights below 20 feet (Figure 5.12). For a given wall height, the effect of wall friction on bearing capacity safety factor depends on eccentricity and the maximum safety factor is obtained when eccentricity is minimum. The effect of wall height on eccentricity at different values of wall friction angle is shown in Figure 5.13. The effect of wall friction on bearing safety factor at different wall heights is shown in Figure 5.14. 148 100 80 ‘ H-40 - 60 // H.20 H310 L \\\\ \ 0.6 0.0 1.0 1.2 8I01 Figure 5.11 Effect of change in wall friction on overturning safety factor : H.10 30 ..., H820 .... 1 H.30 : // H.40 /" 10d / / \\ % Change In ES. (5) 0.0 0.2 0.4 0.6 0.8 1.0 1.2 8101 Figure 5.12 Effect of change in wall friction on sliding safety factor 149 6 Z awho 4‘ I, g: .. I 8101:05 ‘ / ,/ 3 _/7/// Eccentricity O 0'10'20 30 40'50 Wall Height ft Figure 5.13 Effect of wall height on eccentricity at different wall friction angles 150 A I .9 V 100 /‘ IL H-30 5 50 1 0 a 5 o - 3 H220 o .l \\ °\0 .50 H310 -100 f . . f . . 0.0 0.2 0.4 0.6 0.8 1.0 1.2 8/¢l Figure 5.14 The effect of wall friction on bearing safety factor 150 5.4. Effect of Change in Heel Length on Pressure Distribution on Heel 5.4.1 General Many references (Das 1984, Bowles, 1988) recommend a toe length of one-third of base length ( i.e., heel length 40 to 50 percent of base length) but the reasons for this recommendation have not been well documented in the liter- ature. A systematic approach has been followed in the pres- ent analysis to determine a maximum heel length or minimum toe length that can be used in the wall design without developing a net negative pressure on the heel (i.e., a case where the upward pressure beneath the heel at the intersec- tion of heel and stem exceeds the downward pressure on the heel at that point). An increase in heel length or decrease in toe length causes the point of application of resultant of forces on base to shift toward the free end of the heel; that increas- es the upward soil pressure at the intersection of heel and stem. The upward soil pressure at the point of intersection of heel and stem may become larger than the downward pressure at that point with an excessively long heel. Under such situations, a common assumption made for the structural design of heel (i.e., heel acts as cantilever beam and the point of maximum shear and moment is at the intersection of heel and stem) is violated. The wall design for moments and 151 shears at the intersection of heel and stem may be unsafe under these conditions. 5.4.2 nethod of analysis Realistic values of backfill and foundation soil param- eters were selected for this analysis (Figure 5.15). In this analysis, for a given wall height, the base length was established after optimizing the design. Then, the net down- ward pressure at the intersection of the heel and stem was computed for varying heel lengths between 50 to 70 percent of the base length. The analysis was performed by varying heel length because TWALL is structured to accept heel rather than toe as a trial dimension. The analysis was first performed assuming horizontal backfill, neglecting wall friction and considering the water table at the wall base. Then, the effects of backfill slope, wall friction and water table on the distribution of pres- sure on heel were studied. 5.4.3 Results In the present analysis, net downward pressure at the intersection of heel and stem was obtained by subtracting the upward soil pressure from the downward pressure at that point. The effect of change in heel length on net downward pressure at different wall heights is shown in Figure 5.15. 152 The figure shows that higher the wall height, the longer the heel that can be used without the upward pressure exceeding the downward pressure on the heel. Thus, varying heel (or toe) according to wall height will not only improve wall stability but also reduce the cost of the wall by reducing wall dimensions. The permis- sible heel length (a heel length that can be used in the wall design such that upward pressure under the heel does not exceeds the downward pressure) as a function of wall height is shown in Fig. 5.16. The figure shows that the permissible heel length increases from 60 % to 64 % when wall height increase from 10 to 25 feet. The effect of change in toe length on pressure dis- tribution on heel is shown in Table 5.3. The required mini- mum toe length also increased from 0.188 to 0.23B when wall height was increased from 10 to 25 feet. Figure 5.16 and Table 5.3 is applicable to walls with cohesionless horizontal backfills, frictionless backface and water table at the base level. Necessary adjustment are required to be made for wall friction, sloping backfills and water table as discussed in the sections below. 5.4.3.1 Wall friction ' The effect of wall friction on pressure distribution beneath the heel of a 15 feet high wall is shown in Figure 5.17. The figure shows upward pressure exceeds the 153 2000 ‘ l i '7: values 1. I s ‘ 7, I 02: 34 m : \ 0:: 1:3 I 1000-; \ 6 = 0 C a “.15 \ \ B = 0 o ‘ \\\ m 500 .. 5 H210 \'\.\‘\ u \ o- \.\. E. : \ 3'5 '500‘. z : -1000 ‘ . 0.45 0.50 0.55 0.60 0.65 0.70 0.75 heel/B Figure 5.15 Effect of heel length on net downward pre- ssure on heel at different wall heights 0.65 0.64 l 0.63 Heel/B \ 0.62 / 0.61 0.60 E 0.59 I ' I 0 5 10 15 20 25 30 Wall Height it Figure 5.16 Effect of wall height on permissible heel length, 154 Table 5.3 Effect of toe length on net pressure on heel at different wall heights H Toe Toe/B Toe/H Net Pressure on Heel ft ft (psf 1.56 0.280 0.16 433 1.31 0.240 0.13 253 10 1.01 0.183 0.10 10 0.74 0.134 0.07 -257 0.46 0.080 0.05 -575 2.46 0.328 0.16 810 2.09 0.279 0.14 488 15 1.71 0.228 0.11 123 1.34 0.178 0.09 -229 0.97 0.129 0.05 -775 4.35 0.334 0.17 1554 3.70 0.284 0.15 1083 3.05 0.234 0.12 548 25 2.40 0.184 0.09 -71 1.75 0.134 0.07 -795 Table 5.4 Effect of toe length on net pressure on heel at different wall friction angles (H=15 ft) 6 Toe Toe/B Toe/H Net Pressure on Heel deg. ft psf 2.56 0.328 0.16 810 2.09 0.279 0.14 488 6:0 1.71 0.228 0.11 123 1.34 0.178 0.09 -229 0.97 0.129 0.05 ~775 2.01 0.335 0.134 737 1.71 0.285 0.114 398 6:6/2 1.41 0.235 0.094 19 1.11 0.185 0.074 -413 0.81 0.135 0.054 -908 2.01 0.335 0.134 418 1.71 0.285 0.114 180 1.41 0.235 0.094 -80 6:4 1.11 0.185 0.074 -401 0.80 0.135 0.054 -786 155 downward pressure at the intersection of heel at heel/B=0.62 when 6=0 and at heel/B=0.53 when 6=¢. Thus, the wall friction significantly affects pressure distribution on the heel and reduces the heel length that can be used with- out developing a negative pressure on the heel. In the present case, the required reduction in heel length is about 14 percent when wall friction increases from 6=0 to 6=¢. The permissible heel with the increase in wall friction angle is shown in Figure 5.18. The effect of wall friction on toe length is shown in Table 5.4. The minimum required toe length increased from 0.233 to 0.298 when wall friction angle was increased from zero to soil friction angle. These limitations on toe gener- ally agree with the recommendations (i.e., toe=0.338) by Das (1984), Bowles (1988) but are based on observations. 5.4.3.2 Backfill Slope In the present design, the total earth force is assumed to act parallel to the backfill slope. Therefore, backfill slope has a similar effect to that of wall friction (Figure 5.19). 5.4.3.3 Water Table The effect of heel length on net pressure distribution at the intersection of heel and stem with different water 156 *‘1um‘ I His :1 g, 1 5=0 x _ 500 “ 71:115 5: = 8 1 w \ \ {1:128 I . l5 \ I =¢ g 0 ‘ \\ \\ g I \ \ m . §\\\ 0’ u e -500- \ g I 0 . \ z 4000 0.45 0.50 0.55 0.60 0.65 0.70 heel/B Figure 5.17 Effect of heel length on net pressure on heel at different wall friction angles 0.64 H315 1‘1 0.62 0.60 . \ length \ 056 \~ 054. \\\\\-§“%~ heeUbase 0.52 . . . . . 0.0 0.2 0.4 0.6 0.8 1.0 5/¢ Figure 5.18 Effect of wall friction on permissible heel length 157 levels in the backfill behind a 15 feet high wall is shown in Figure 5.20. The water table on toe side was assumed at base level and the distribution of water and soil pressure under the base was assumed linear. The presence of water in the backfill increases downward pressure on the heel. The increase in upward pressure (soil and uplift) under the heel is not the same because of eccentric loading on the wall base. Therefore, net downward pressure on heel increases with the increase in water level in the backfill. Thus, a longer heel can be used for a given wall height with the presence of water in the backfill as compared to the heel length which can be used in the absence of water in the backfill (Figure 5.21). 6.4.4 Summary The parametric sensitivity analyses discussed in this Chapter helped to understand the effects of different design parameters and wall proportions on the stability of the wall. Some useful heuristics were deduced from these analy- ses and were incorporated in TWALL to shorten the trial design process. It was found from the second part of this analysis that the maximum heel length that can be used for the wall design without developing a situation when upward pressure under the heel exceeds the downward pressure may vary between 50 percent to 60 percent of base length. In other words, 158 1000 J l * a 5:0 1. " \ H715 it _ - ¢2= 34 3 50° . B=¢12 \ \ 71.1115 ,5 . 12 = 120 5 = c . \ \ O o . \ \ 2 ‘ \ \ a - \\\\ fl . 3 . h I a -500 4 \ u I o z 1 4000 0.45 0.50 0.55 ‘ 0.60 0.65 0.70 heel/B Figure 5.19 Effect of heel length on net pressure on heel at different backfill slopes. 1000-— ‘ T .1 i .5 ‘ \\\ H 15 n o. . \\\ 01: 33 - 500- \\\ i(if-£115 Q ‘ \ \ fl =120 g " \ \ 5 = 0 c . \\ B = o o 0‘ \ \\\ 2 ‘ \ a 'l \\ HWIH/Z an ,0 -5..- \ i HW-H/4 a : HW‘IO 2: . i -1 , . 0033.45 0.50 0.55 0.60 0.65 0.70 0.75 heel/B Figure 5.20 Effect of heel length on net pressure on heel at different water levels in backfill 159 0.70 1 i ""HI15 11 0.68 .= “ c: c 2 0.66 / / o m / 3 0.64 2 o 0 // “g 0.62-/ 0.60 0.0 0.1 0.2 0.3 0.4 0.5 0.6 leH Figure 5.21 Effect of water table on permissible heel length 160 allowing 10 percent to 15 percent of the base length for stem, the minimum required toe length generally should not be less than 25 to 30 percent of the base length depending on wall height, backfill slope, wall friction and water table for a typical design of cantilever retaining walls. CHAPTER 6 EFFECT OF EARTH PRESSURE ASSUMPTIONS ON WALL DESIGN 6.1 General This chapter summarizes the results of an analysis per- formed to assess the difference between the assumptions of active and at-rest states of stress in the backfill on the design of cantilever retaining walls. The design criteria for computing lateral earth pres- sures behind cantilever retaining walls are somewhat con- troversial. Some references (e.g., Das 1984, Bowles 1988) recommend assuming an active state of stress in the backfill for computing lateral earth pressures. On the other hand, some researchers (e.g., Matsuo et at., 1978) recommend assuming an at-rest state of stress in the backfill. U.S. Army, Corps of Engineer recommends assuming at-rest condi- tions in the backfill for overturning and bearing capacity analysis and active conditions for sliding stability analy- sis of the wall (U.S. Army 1989). The design assumptions regarding the state of stress in the backfill affect the magnitude of lateral earth force which ultimately affect recommended wall dimensions. 161 162 It was found from the literature review on cantilever wall design that no attempt has been made to quantify the effect of the assumed earth pressure conditions on wall dimensions, required quantities of materials and cost. The expert system TWALL provides a convenient and expedient means to investigate such questions. This analysis also helped in writing some heuristics. A typical cantilever retaining wall (Figure 6.1) was analyzed to assess the effect of the earth pressure assump- tion on recommended base length, required quantity of back- fill and concrete and cost per unit length of the wall. The effects of overload factors, wall friction, backfill slope and water table on overall cost of the wall under active and at-rest conditions were also studied. Coulomb and Jaky's equations were used for computing earth pressures for active and at-rest states respectively. The analysis is limited to cohesionless backfills and foundation soils not having settlement problems. 6.2 Method of Analysis Realistic values of backfill and foundation soil param- eters were selected as shown in Table 6.1. Means Building Construction Cost Data 1990 (Mahoney 1990) was used for calculating costs of cast-in-place concrete and compacted backfills. The analysis was performed in two parts. In the first set of analyses, the wall height was 163 Backfill ‘1'_ Stem 7m— Toe Heel I (Ease I Foundation Soil Figure 6.1 A typical cantilever retaining wall 164 varied from 10 to 30 feet for each assumption i.e., the active and at-rest. Using recommended base length from the expert system, required quantities of backfill, concrete and cost per lineal foot were computed. For these comparative analyses, the backfill was assumed horizontal, the water table was assumed at the base of the wall, wall friction was neglected and an overload factor of 1.7 was used for the structural design of stem, heel and toe. In the second set of analyses, the effects of variation in parameters including overload factors, backfill slope and wall friction on wall design for active and at-rest assump- tions were studied. These parameters were varied within the ranges shown in Table 6.1. Table 6.1. Range of parameters Parameters Unit Values Backfill friction Angle ¢l deg 34 Foundation soil friction angle 62 deg 35 Backfill unit weight yl pcf 115 Foundation soil unit weight 72 pcf 120 Backfill slope angle 8 deg' 0 - 0.75 ¢1 Wall friction angle 6 deg 0 - ¢l Load factor 1.4 - 2.0 6.3 Results The results of the analyses are discussed in the following sections: 165 6.3.1 Part 1: Effect of Wall Height The effects of wall height under different earth pres- sure conditions on required base length B, required quanti- ties of material and overall cost per foot of wall were studied in this part. The results are shown first in terms of actual wall dimensions and quantities of construction materials (Figure 6.2 through 6.6) and then these results are summarized in term of percentages (Figure 6.7). 6.3.1.1 Base Length The effect of wall height on required base length B for active and at-rest assumptions is shown in Figure 6.2. As would be expected, at-rest conditions result in greater recommended base lengths than the active conditions and the difference in required base lengths under these conditions increases with the increase in wall height. The required base length for at-rest conditions is about 39 percent higher than the required base length for active conditions (Figure 6.7). The variation of wall height does not affect this difference significantly. 6.3.1.2 Backfill and Concrete The variation of required quantities of backfill and concrete per foot of wall as a function of wall height is 166 shown in Figure 6.3 and 6.4 respectively. Backfill was calculated considering a unit wall length for the area above the heel to the ground level and the area of Coulomb’s wedge at the end of the heel. The required quantities of backfill and concrete for both assumptions obviously increase with the increase in wall height. The increase is more rapid for high walls because the total earth force which is a function of the square of the wall height. The difference in the required quantities of materials for wall heights below 10 feet is negligible but the differ- ence increases with the increase in wall height. Possible (likely) reasons for this behavior are: 1. There are some minimum limits on wall dimensions for low walls (e.g., top stem thickness may not be less than 8 inches), which are not strength re- quirements but are rather for ease of construction (Bowles 1988). These restrictions on wall dimen- sions result in almost the same stem and base thicknesses for wall heights below 10 feet. There— fore, for low walls, the material requirements for both pressure are almost the same. 2. The increase in lateral earth force on the stem with increasing wall height is more rapid for an at-rest state of stress than for an active state of stress (Figure 6.5). The requirement of bottom stem thickness increases more rapidly with the 167 1.41 .111 At -Rest Active 0 15 a // E // 10 Base Length tt o V'V' "I‘ "V‘ " U"' 'I“ i'j‘ VI 0 5 10 15 20 25 30 35 40 Wall Height it Figure 6.2 Effect of wall height on base length 700 ‘ i ‘ At -Rest 200 3: l / Active o 4001 /// E 3003 // o : // cc . m . V .00 A : V 0 5 10 15 20 25 30 35 40 Wall Height 11 Figure 6.3 Effect of wall height on required backfill 168 120 . ' // AbRefl .. 100: '8 I // Active 80‘ o . a 2 - / g 60 5 ‘ / o 40 / 3 // 20‘ é : V 0‘.... .... .... .... .... .... .... ...T 0 5 10 15 20 25 80 35 40 Wall Height it Figure 6.4 Effect wall height on required concrete 20 ; At-Rest \ / / Active . /' // : / 3 ;/ 5'20 25'30'35'40 Wall Height ft Force on Stem Kips 3 f 5 1 Figure 6.5 Effect of wall height on earth force on stem 169 increase in wall height for at-rest state than for active state. Thus, the required quantity of con- crete increases more rapidly. The ratio of required quantity of backfill for at-rest to that for active conditions decreases from 1.4 for H=10 feet to 1.34 for H=30 feet (Figure 6.7). This decrease is mainly due to variation in ratios of heel/B for different wall heights (i.e., same ratio of heel/B under active and at-rest conditions could not be used for all wall heights because of stability requirements). Thus, the required backfill for at-rest conditions is about 30 to 40 percent more than the active conditions. The ratio of concrete required for at-rest versus active states increases with wall height (Figure 6.7). This increase can be attributed to a higher increase in the stem thickness under the at-rest state than the active state. As concrete is a more expensive construction material than the backfill, the effect of cost of concrete on total cost is more pronounced than the effect of backfill cost. 6.3.1.3 Wall Cost The cost per linear foot of the wall increases with the increase in wall height for both active and at-rest condi- tions (Figure 6.6). The difference in the cost for the two assumptions is small for wall heights below 10 feet but the 170 difference increases with increasing wall height. The cost per unit length of wall for at-rest assumption was observed to be about 17 percent to 34 percent higher than the active assumption when wall height was changed from 10 to 30 feet (Figure 6.7). 6.3.2 Part II: Other Factors Affecting Wall Cost The effects of overload factors, wall friction assump- tion and backfill slope on cost per unit length of the wall were analyzed in this part of the analysis. The results are discussed in the following sections. 6.3.2.1 Effect of Overload Factors The effect of overload factors on the cost at different wall heights for active conditions is shown in Figure 6.8. The effect is negligible for wall heights below 15 feet because of restrictions on minimum wall dimensions as dis- cussed earlier. For wall heights between 20 to 25 feet, the cost per unit length of wall increased 9 to 15 percent when overload factors were increased from 1.4 to 2.0. The effect of overload factors on wall heights for at-rest conditions is shown in Figure 6.9. The results are almost identical to that discussed above. 171 1400 ‘ I 1 / At- Rest 1200 I I / Active a» 8m): /// a; 5 // O 600 q ‘yv L) : ///>//r ‘wo: :;,/l 3 // 200 I / 0: O 5 1O 15 20 25 30 35 40 Wall Height tt Figure 6.6 Effect of wall height on wall cost 1A5. 3 Backfill 1.40 ‘ I I \\ Base Length 2 135 ‘ “K .1 : 7 o I .g 130‘ 2 1 / m I / 0 125 c: 1 //' J. 1 A// “ 1.20 q , : Cost i// 135 I Concrete / fl 1.10 V"' 'V'ff‘t' flit fit! '1'! VIVY iii! 0 s 10 15 20 25 30 35 40 Wall Height it Figure 6.7 Difference in required materials and wall cost under active and at-rest conditions 1— 172 20 7 [.___—Fl : i Actlve ‘ 01: u $2: 35 151 71:115 [4.25 ‘°‘ /// H-ZO 5 //j'// ’4/ _______. 11.1. .6 1.3 2.0 2.2 Overload Factor % Increase in Wall Cost Figure 6-8 Effect of overload factors on wall cost assuming active conditions 20 l : lAt-Rost 15 Fla-25 10 r \\ 5 : //1/ I / 1.6 1.3 2.0 2.2 Overload Factor % Increase in Wall Cost Figure 5-9 Effect of overload factors on wall cost assuming at-rest conditions 173 6.3.2.2 Effect of Wall Friction An increase in wall friction angle decreases the cost of the wall (Figure 6.10). As can be seen from the figure, the decrease in wall cost as 6 is varied from 0 to ¢ is about 10 percent for H=1O feet and 19 percent for H=30 feet. Thus, for high walls, the effect of wall friction on the cost of the wall is quite significant. The effect of wall friction on a 20 feet high wall for active and at-rest assumptions is shown in Figure 6.11. The figure shows that the decrease in the cost for the at-rest state is more rapid than the decrease for the active state. 6.3.2.3 Effect of Sloping Backfill The effect of an upward sloping backfill behind a 20 feet high wall under active and at-rest states is shown in Figure 6.12. The upward sloping backfill substantially increases the cost of the wall. The increase in the cost is even more pronounced for the at-rest state of stress than the active state. The factors which contribute toward this significant increase in the cost include: 1. A high value of earth pressure coefficient which in turn increases lateral earth force on the wall. This results in larger wall dimensions which in turn increase quantity of backfill. 2. An additional quantity of backfill material for the 174 10 ‘ i on ' ""-"" $1: 34 o 5 71:115- I 72 =120 :: . B = O G ' E 3 o \ c I \ - -5 ‘ N\\\ a u m d \ \ \ - a a ‘10 ‘ \ \ H-lO d) : ~\\\\\~ 2g 45: \\\\\\ 2 11.30 -20 , . , v f , 0.0 0.2 0.4 0.6 0.8 1.0 1.2 filo Figure 6.10 Effect of wall friction on wall cost for different wall heights 10 r, o— : H820 " 3 : o 5 . 76 I 3 ° 1 fl 0: -5 1 \ g: 1 \\‘\\\N 93 .10 ‘ \ o 1 ‘\ lg : \\\\\\~ ‘ Acflve ‘9 ‘15- \\\‘\\\ a I At-Rest J -20 , . , , . . OJ) (L2 0u4 0J5 (L8 1.0 1.2 file Figure 6.11 Effect of wall friction on wall cost assuming active and at-rest conditions 175 50 . dawn-H- 0 .5 45 1 2; At-Rest as 405 01: 34 /’ : ¢2= 35 = 35 1 71 = 115 / c E““12= 120 g: 30: 5 = ‘JVI : i / Active "" 25 , r 3 20 i / a : l 0 1 / / 5 15 . I g : _ 10 2 7/ .\° 5 1 / i/ 0 I O O 0.2 0.4 0.6 0.8 1.0 B/¢ Figure 6.12 Effect of sloping backfill on wall cost 176 sloping part of the backfill. The weight of sloping backfill on the heel which results in a thicker base thus increasing the require- ment of concrete. CHAPTER 7 KNOWLEDGE ELICITATION AND HEURISTIC DEVELOPMENT 7 e 1 6.30:8]. The literature and human experts are the main sources of knowledge for the design of retaining structures. The knowledge obtained from the literature has been discussed in Chapter 2. The knowledge elicited from experts on the design of retaining structures is briefly discussed in this chap- ter. Some of the heuristic rules derived from literature review, experts knowledge, parametric sensitivity analysis and active versus at-rest analysis are also described. The heuristics developed through simulation and experimentation during the development of TWALL and discussed in Chapter 4 are also briefly repeated to complete the list. 7.2 Knowledge Elicitation A detailed review of literature on earth retaining structures in general and cantilever retaining walls in particular was conducted. Standard textbooks, research papers and design manuals give sufficiently detailed 177 178 information that can be used for the design of retaining structures. However, the information obtained from the literature lacks heuristic knowledge (e.g., what to do when a trial design fails in sliding) which is an essential requirement for building an expert system. Therefore, it was decided to consult human experts experienced in the design of retaining structures (engineers having geotechnical background and few years of experience in the design of retaining structures are considered experts in the present context). A questionnaire was prepared for this purpose addressing the following areas: 1. Heights for which cantilever walls are most suitable. 2. Initial trial dimensions of the wall. 3. Realistic ranges of design parameters. 4. Method to be used for earth pressure prediction. 5. Wall stability. 6. Structural design of stem, heel and toe. Engineers involved with the design of earth retaining structures from both the public and private sectors were then invited to complete the questionnaire. Knowledge thus elicited was then organized and some heuristics were derived from this knowledge. The knowledge obtained was not quite agreeable among experts. Thus, a "middle" approach was used when writing heuristics. The results of the survey are 179 summarized in Table 7.1 through 7.5. 7.3 Heuristic Development The heuristics developed in this study are given below: Cantilever retaining walls are most suitable for wall heights between 5 to 30 feet. Maximum base length should not exceed twice the wall height. Either the Coulomb or Rankine theory of earth pressure can be used for earth pressure prediction behind cantilever retaining walls. Provided a reasonable safety factor is used the earth pressure distribution behind the wall can be assumed as hydrostatics and the point of applica- tion resultant earth force can be taken at 33 percent of wall height for the bottom of wall base. The total horizontal force on the wall can be computed assuming active conditions behind the wall only when large wall movements are accept- able. The effect of compaction can be incorporated in the design either by limiting the weight of roller or by taking the point of application of resultant of forces at 40 to 50 percent of wall height from 180 Table 7.1 Trial wall dimensions based on expert's opinion Hall Parts Miller et al. Alvey Gleason Strom (1991) (1991) (1991) (1991) Base Width (8) 0.67M 0.8H 0.75H 0.6SH Hax=2H Hax=1.5H Hax=no limit Max=H Min=12 in 0.1H Thickness 0.1 H 0.15H 0.15M Min: 12 in 0.68 Heel length 0.5 8 0.58 0.458 Min=12 in Ste- Top thickness H < 10 ft 8 in 18 in 10 in 8 in 10 20 ft 0.1H 30 in 18+ in 12 in Bottom 0.1H 0.1SH 0.1H 0.1H thickness H=wall height 181 Table 7.2 Expert's opinion on design values of soil parameters base and foundation soil Item Miller et al. Alvey Strom Bergstrom (1991) (1991) (1991) (1991) Soil Friction Angle (degrees) 1. Compacted Soil cu, SH 38 41 3s 35 GP, SP 36 37 30 33 0v, 5? 34 33 - 33 GC, SC 32 25 - 30 2. Loose Soil cu, SH 34 34 - 33 GP, SP 32 30 - 31 cu, SP 30 30 - 30 GC, SC 28 23 - 30 Soil Unit Height (Pcf) 1. Compacted Soil GU, SH 115-120 125 120 130 GP, SP 110-115 125 110 130 GU, SP 120-125 115 - 135 GC, SC 125-130 120 - 135 2. 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E eonuumnom Eonum comuuonu 0>~¢ .H0 00 noannx Bonn h in i >unannoum Ham: n0>0nwucmo co 20wcndo m.un0me 0.5 CHQMB Table 7. 5 l Overload Fact: 7 when base ccrlsidered ' Stem Heel ice 2. When base not consider-e Stem Heel ice 1\ Critical Sect 1. Pic-ments Stem Heel 184 Table 7.5 Expert's opinion on various aspects of structural design Item Miller et al. Gleasson Strom (1991) (1991) (1991) Overload Factors 1. When base pressure is considered Stem Active 1.7 Active 1.9 1.9 At-rest 1.4 At-rest 1.7 Heel DL 1.4 Active 1.9 1.9 LL 1.7 At-rest 1.7 Toe DL 1.4 Active 1.9 1.9 Pressure 1.6 At-rest 1.7 2. When base pressure is not considered Stem 1.7 same as above - Heel 1.7 - Toe 1.7 - Critical Sections 1. Moments Stem Base top Base top Base top Heel Face of Stem (heel At center line of At stem steel side) stem steel Face of stem (toe Face of stem (toe Toe Face of Stem (toe side) side) side) 2. Shears Distance “d" from Base top Stem Base top base top Face of stem Distance "d" from Heel Face of stem stem face Distance "d" from Distance "d" from stem face stem face Toe Face of stem Provisions of ACI 318-83 Adequate Adequate except some load factors Adequate but dif- ficult to apply. Use constant load factors 10. 11. 12. 185 the bottom of the base. The passive resistance in front of the wall should be neglected in wall design. The friction angle of good granular backfill used in retaining wall problems is often between 30 to 36 degrees and unit weight is often in the range of 100 to 115 pound per cubic foot. The wall friction angle can be assumed between 0 to 66 percent of the backfill soil friction angle but may not be less than backfill slope. The friction angle between the wall base and foun- dation soil can be taken same as foundation soil friction angle. Wall stability can be ensured by providing the following safety factors: Overturning = 1.5 to 3 or keeping the resultant within the middle third of wall base Sliding = 1.3 to 2 Bearing = 2.0 to 3.0 Lengthening the heel and toe improves wall sta- bility against overturning failures but lengthen- ing the toe improves overturning stability more effectively than the heel. The expressions given below can help to compute the required increase in base B and heel lengths when a trial design fails in overturning: 13. 14. 186 01 ll (1.15)B+B(F.S.otReq-F.S.otAval)/F.S.otAval heel (1.10)heel+heel(F.S.otReq-F.S.otAval)/ F.S.otAval where F.S. otReq is required overturning safety factor and F.S.otAval is available safety factor. Wall stability against sliding can be improved by increasing the heel length or by adding a base key. The expressions below can be used to compute the required increase in base B and heel lengths when a trial wall design fails in sliding. (D II (1.03)B+B(F.S.sReq-F.S.sAval)/F.S.sAval heel (1.07)heel+heel(F.S.sReq-F.S.sAval)/ F.S.sAval where F.S.sReq is the required safety factor and F.S.sAval is the available safety factor against sliding failure. The following expressions can help compute the required decrease in base and heel lengths to make the design economical when a trial wall design is conservative: B = 0.958-0.358(F.S.sAval-F.S.sReq)/F.S.sAval heel = 0.9SB-O.40heel(F.S.sAval-F.S.sReq)/ F.S.sAval 15. 16. 17. 18. 19. 20. 187 A base key should not be used routinely in wall design but should only be used when required to satisfy the stability requirements which otherwise are difficult to achieve with reasonable wall dimensions. To improve safety against bearing capacity fail- ure, the following action can taken: 0 Lengthen wall base. 0 Densify the foundation soil or replace it with better soil. 0 Increase embedment depth. 0 Use piles. For computing safety factor against bearing capac- ity failure use an average base pressure over a base width reduced for eccentricity as suggested by Meyerhof. If eccentricity is sufficiently great as to put part of the base in tension (i.e., e>B/6) and the base resultant acts on the toe side of the base, an increase in heel length can reduce eccent- ricity. If eccentricity is excessive as above, but the resultant acts on the heel side of the wall, de- crease in heel length can reduce eccentricity. Upward soil pressure under the base should not be neglected for the structural design of heel. Doing so is unnecessarily conservative. 21. 22. 188 As known from active versus at-rest analysis that varying overload factors does not greatly affect wall cost. Thus, it is reasonable to use a uniform overload factor of 1.9 for the structural design of stem, heel and toe when wall is designed for active conditions and 1.7 when wall is design for at-rest conditions. The critical section for shears and moments for the structural design of stem, heel and toe can be taken at the intersection of stem and base, stem and heel, and stem and toe respectively. CHAPTER 8 DETAILED SUMMARY AND CRITICAL ASSESSMENT 8.1 General The development and testing of the knowledge-base system TWALL and the numerous parametric analyses performed in this study provided an opportunity to critically assess the philosophy and procedure of cantilever retaining wall design. This chapter critically assesses various design assumptions and discusses the effect of variations in design parameters on wall stability. The failure criteria that govern the design of the wall and the salient features of TWALL are also discussed. 8.2 Design Procedure The design of a cantilever retaining wall involves recommending the base size and the position of stem on the base as well as thickness and reinforcing of stem, heel and toe such that a number of criteria are satisfied. At present no closed-form solutions exist to directly obtain design proportions for cantilever retaining walls; as such the 189 190 design is a trial and error procedure. This trial and error procedure can be expedited by assuming reasonable trial dimensions (i.e., base, heel and toe) and intelligently revising successive trial designs based on the results of the preceding trials. There are various guidelines available in the literature on trial dimensions as presented in Chapter 2. During the development and validation process, TWALL was used for the analyses summarized in Chapters 5 and 6 as well as for solving design problems given to undergraduate and graduate classes (Appen- dix D). From these experiences the preliminary trial wall dimensions given below were found to work well and are the writer’s recommendations. 1. Base length B a. B = 0.5 to 0.6H when water is below base b. B = 0.6 to 0.7H when water is above base 2. Base thickness tb a. tb== 1 ft. when H<1O ft b. tb== 1 to 2 ft. 'when 1015 ft 191 4. Minimum toe length a. toe = 0.248 when H<15 0=<6<0.5¢ b. toe = 0.268 when 1520 ft The guidelines given above are consistent with pub- lished recommendations but have been further refined through parametric studies and knowledge elicited from experts on the wall design. The recommended trial base and heel lengths are based entirely on the experience of the writer during TWALL development. 8.3 Lateral Earth Pressure (Considerations and Assumptions) The pressures and forces acting on a cantilever retain- ing wall are indeterminate to a significant degree because the available static equilibrium equations are not suffi- cient to solve for unknowns. To obtain a solution, some additional assumptions need to be made. For nonlinear mate- rials such as soil, it is commonly assumed that a failure state exists along some surface and that the shear strength of the soil is fully mobilized along that surface. Then the 192 equilibrium equations are solved with these assumptions. This approach is known as limit-equilibrium analysis. The Coulomb and Rankine theories are examples of limit equilibrium methods. For the prediction of earth pressure behind a cantilever retaining wall neither Coulomb’s nor Rankine's equations apply exactly because the back of this type of wall departs greatly from a plane surface. However, Rankine’s theory can be used without significant error as the wall interference with the outer rupture surface is usually very small (see Figures 2.4 and 2.5). The use of Coulomb's theory is clearly justifiable when inclination of resultant lateral earth force is paral- lel to the backfill slope. For this special case (and a vertical wall) Coulomb’s formula yields the same solution as Rankine’s. To the extent that the wall friction differs from the slope angle, the error in Coulomb theory lies in the assumption that the failure surface is a plane. Either the Coulomb or the Rankine equation can be used for earth pressure prediction in TWALL. By default TWALL uses Coulomb's equation but the user has an option to change to Rankine’s equation by assuming the wall friction angle equal to the backfill slope angle. 8.4 Active Versus At-Rest Pressures There is a controversy over the appropriate assumptions (i.e., active or at-rest) for computing lateral earth 193 pressure behind cantilever retaining walls. The justifica- tion usually given for assuming active conditions is that the wall yields sufficiently for active pressure conditions to develop before any failure takes place. The consider- ations to support designing for at-rest are: (1) higher pressures have been observed in the past during most of the experimental work and field tests, (2) the wall may not yield to meet the required deformations for active condi- tions because of its rigidity, and (3) even after active conditions are achieved (i.e., shear strength of the soil is fully mobilized), the pressures may increase with time to at-rest due to relaxation of the soil particles. In the light of above controversy, it was considered of interest to study the effect of active versus at-rest assumptions on wall dimensions, required quantities of mate- rials and the cost of the wall. In the past, it was diffi- cult to perform such an analysis because there was no tool available such as TWALL that would provide consistent (and thus comparable) design and also be easy to use. The results of the analysis showed that for at-rest conditions, the required base length and quantities of backfill were about 40% greater and required concrete was 13 to 35 % greater depending on the wall height (10 to 30 ft). The additional overall cost varied from 17 % for a 10 feet high wall to about 35 % for a 30 feet high wall. Concrete is an expensive construction material as compared to the back- fill soils. Thus, variations in the cost of the wall closely follow variations in the required quantities of concrete. 194 The effect of overload factors, wall friction and backfill slope angle on the overall cost of the wall under active and at-rest conditions were also studied. The maximum difference in costs due to the effect of overload factors and wall friction angles varied between 3 to 5 % which is insignificant. But a notable difference in wall cost (about 17 % at B=0.75¢) was observed with the variation of backfill slope angle (see Chapter 6 for details). Classical earth pressure theories (i.e., Coulomb and Rankine’s) do not account for the numerous uncertainties associated with the prediction of earth pressure. Although designing for at-rest conditions costs about 20 to 30 per- cent more than designing for active conditions, it still would appear justified to design yielding walls for at-rest conditions to ensure wall stability and good performance under adverse conditions. For non-yielding walls, in addi- tion to designing for at-rest, a surficial surcharge of few hundred pounds per square foot might be assumed when calcu- lating earth pressure or higher safety factors should be used to compensate for the uncertainties. TWALL provides an option to the user to a design wall for at-rest conditions and uses Jaky's equation to calculate earth pressure. 8.5 Wall Stability The stability of a cantilever retaining wall is affect- ed by a number of variables including wall height, backfill and foundation soil parameters, wall friction, backfill 195 slope and water table. A designer with some experience in the design of earth retaining structures can easily guess the individual effect of any of these variables but it is difficult to predict the relative magnitude of effect of these variables on the stability of the wall. A parametric sensitivity analyses were performed (see Chapter 5) to study the effect of these variables on over- turning, sliding and bearing capacity safety factors. Some important results of this analysis are briefly discussed in the following sections. 8.5.1 Overturning Stability The overturning safety factor is most sensitive to the wall height and least sensitive to the unit weight of the backfill soil. An upward sloping backfill adversely affects overturning stability because it increases the earth pres- sure on the wall. Wall friction helps to improve overturning stability by reducing overturning moments and increasing the resisting moments. The reduction in overturning moments is due to a decrease in earth pressure coefficient, reflecting the earth force acting at an inclination to the wall. The increase in resisting moments is due to the downward vertical component of the lateral earth force. The effect of wall friction is more pronounced for higher wall because the vertical fric- tional component is greater and acts at the end of a longer heel. 196 Increasing the base length at a fixed heel length results in a lengthened toe which improves overturning sta- bility due to an increase in the moment arm of the resisting forces. Increasing the heel length at a fixed base length has little effect on overturning stability because weights over the heel increase as toe length decreases and these effects tend to compensate. 8.5.2 Sliding Stability The sliding safety factor is most sensitive to backfill and foundation soil friction angles and least sensitive to the backfill soil unit weight. Increasing the base length at a fixed heel length has an insignificant effect on sliding stability in cohesionless foundation soils because an in- crease in base length adds only a small dead weight to the effective vertical force. Increasing the heel length at a fixed base length in cohesionless foundation soil has a more pronounced effect on sliding safety than on overturning stability. This is be- cause the increase in heel length significantly increases dead weights over the heel which directly improves sliding stability but has little effect on overturning. The effect of wall friction on sliding stability is similar to that on overturning stability as discussed earli- er. Increasing the wall height decreases the effect of wall friction on sliding stability. For a constant wall friction angle, an increase in wall height increases the vertical 197 component of the lateral earth force which can be a small pnertion of the total vertical force. Therefore, the overall increase in resisting force is not significant but the horizontal component of the lateral earth force increases with the square of the increase in wall height. Thus, the effect of wall friction decreases with the increase in wall height. From the above discussion, it can be concluded that the effects of wall friction are more significant for low walls than for high walls. 8.5.3 Bearing Capacity The bearing capacity of a foundation soil is most sensitive to the friction angle of the foundation soil and least sensitive to the change in heel length. Sloping backf- ill and the location of water table also significantly effect the safety factor. Some important observations were made when studying the effect of changes in base and heel lengths on bearing capac- ity safety factor. It is generally understood that the increase in base length should improve bearing capacity safety factor but it was found from the present analysis that a change in base length at a fixed heel length affects the point of application of resultant of forces acting on the base. In other words, eccentricity significantly affects the bearing capacity of the foundation soil. The safety factor attains a maximum value at minimum leccentricity (i.e., the resultant acts close to the middle 198 of the base) and decreases with further increase in base length. However, when base length becomes very large, the effect of eccentricity is nullified due to increase in bearing area. It was found that minimum eccentricity can be obtained by keeping the base length equal to about 65 per- cent of the wall height using approximately the same range of parameters as used in this study (Table 5.1). When studying the effect of change in heel length at constant base length on the bearing capacity safety factor, it was found that increasing the heel length increased the bearing capacity safety factor until the heel length was about 80 percent of the base. Then the safety factor dropped off with further increase in heel length as the eccentricity become excessively negative. Here again the maximum safety factor was obtained when eccentricity was a minimum. A study conducted by Peck et al., (1948) showed that, with a few exceptions, most walls failed due to misjudgment of foundation conditions rather than to incorrect assumption regarding the backfill pressure. Thus, the potential bearing capacity failure should also be given due importance in the wall design especially as optimization leads to narrower base and heel lengths. 8.5.4 What Governs Design? What failure mode (overturning, sliding or bearing capacity failure) should govern the design of cantilever re- taining wall and under what conditions? The exact answer to 199 this question could not be found in the literature because there can be no mathematical solution for such an ill-de- fined problem that is influenced by a large number of vari- ables. It has been generally said that wall sliding usually governs the design. From the experience of TWALL development, some of the observations regarding the failure modes may prove to be a step forward in better understanding the interrelationship of design variables for cantilever retaining walls. Over- turning was found to govern the design only when backfill soil is very weak as compared to the foundation soil. A wall may fail in overturning with a short toe or heavy surcharges because a short toe reduces the resisting moments and a heavy surcharge increases overturning moments due to the point of application of lateral earth force that acts higher than one-third of the wall height. The bearing capacity may govern when a combination of adverse conditions (e.g., dense and steeply sloping upward backfill and presence of water) occur simultaneously. Such conditions can occur adjacent to dam spillways and other hydraulic structures. In all other cases, wall sliding mostly governs the design. 8.6 Development of TWALL TWALL was developed for IBM-compatible personal comput- ers in production rule language provided by the LEVELS expert system shell. The LEVELS is an expert system building 200 environment with both forward and backward chaining control strategies. The backward chaining control strategy was used in TWALL because it was found convenient to work with such control strategy in LEVELS. Backward chaining is considered appropriate for prob- lems with large input data and few goals (e.g., diagonistic problems and interpretation tasks). Design problems are con- sidered open-ended problems because there can be many solu- tions of the same problem. Thus, the backward chaining has not heretofore been considered appropriate for design prob- lems such as the design of cantilever retaining walls. The knowledge base of TWALL was structured such that the goals were kept minimum and a large number of unknown facts (e.g., pressures and forces on wall) were made known. This could be accomplished through computations within the rules as the LEVELS supports all types of mathematical computations. Thus, the use of backward chaining control strategy did not pose any serious problem in the development of TWALL. From this experience, it can be said that backward chaining can be used for design problems by carefully struc- turing the knowledge base and using appropriate expert system building tool. The knowledge base of TWALL consists of a total of 297 rules and these rules are further classified into 14 build- ing blocks for ease of programming and understanding the logic. A building block performs a specific task and con- tains rules required to implement the intended task. 201 TWALL was developed in stages. Initially, a prototype was developed based on knowledge mostly obtained from the literature. Parametric sensitivity analysis was then per- formed to understand the behavior of the wall under differ- ent loading conditions and for writing of heuristic rules. A questionnaire was also sent to experts on the design of retaining structures to obtain heuristic knowledge and further verify the heuristics deduced from the parametric sensitivity analysis. Some of the heuristics deduced from the parametric sensitivity analyses were further refined and quantified through experimentation during the expansion stage of TWALL development (see Chapter 4 for details). The prototype was then expanded by incorporating these heuris- tics in the rules of TWALL. In the testing, verification and validation stage of TWALL development, the system was first tested and verified to check that the inference process is executing exactly as it was intended to. For this purpose, the system was run with simple examples to observe any crash or malfunctioning. Then for the validation of TWALL, some solved examples were selected from textbooks and design manuals and TWALL results were compared with these solutions. These results compared closely (see Chapter 3 for details). Walls designed by students of undergraduate and gradu- ate classes (CE 419 and CE 818) were also designed on TWALL and results were compared. The results also compared closely (see Appendix D). 202 8.7 TWALL Design Process The knowledge base of TWALL is structured to design the wall for external stability only or for both external sta- bility and internal stability. When designing a wall for external stability, TWALL ensures that the wall is stable against overturning, sliding and bearing capacity failures. TWALL also controls rotational settlements by keeping the resultant as close as possible to the middle of the base. When designing a wall for both external and internal stability, TWALL first ensures external stability and then calculates shears and moments at five different points (free end, 1/4, 1/2, 3/4 and fixed end) along the stem, heel and toe. The stem, heel and toe are commonly designed as canti- lever beams which implies that maximum shears and moments occur at the intersection points of stem, heel and toe. Thus, TWALL calculates steel requirements assuming that maximum moments occur at the intersection points. This approach is correct for the stem and toe because TWALL ensures that maximum shears and moments always occur at their intersection points. Where the heel is relatively long (typically>0.78), the upward pressure under the heel at the intersection with the stem exceeds the downward pressure at that point. This shifts the points of maximum shear and moment from the intersection toward the middle of heel. Under these condi- tions a heel designed for shear and moment at the 203 intersection with the stem may be unconservative. The heuristics incorporated in TWALL limit heel length such that the upward pressures do not exceed the downward pressures at the intersection of stem and heel. Thus, TWALL ensures that the points of maximum shear and moment always occur where heel joins the stem. It is not difficult in practice to design the heel for a maximum moment that occurs at a point other than the intersection point. But is not done in TWALL for two reasons: (1) the assumption that the heel acts as a cantilever beam is violated, and (2) a sig- nificant number of rules would need to be added to the knowledge base to calculate the maximum shears and moments on heel at a point other than the intersection point which would have made the knowledge base unnecessarily large. TWALL is a prototype expert system where an effort has been made to replicate an "expert" but the program still cannot be regarded as an "expert" who would have to anticipate every thing about the wall design. 8.8 TWALL Versus Algorithmic Programs The main five features of an expert system that sepa- rates it from a conventional or algorithmic program were de- scribed in section 3.1. TWALL incorporates these features as discussed below: 1. The LEVELS expert system shell was used for the 204 development of TWALL. The knowledge base regarding cantilever wall design was incorporated in a set of LEVELS production rules to make a working expert sys- tem. Thus, the knowledge base (or rules) of TWALL can be manipulated independently from the control mechanism provided by LEVELS. The inference process of TWALL can be conveyed to the user through an explanation facility. Explanations of static queries (queries regarding the technical con- tents of the knowledge base) were incorporated during the development process of TWALL. For dynamic queries (queries regarding inference process) LEVELS provides explanations through "REPORT" system. The knowledge base of TWALL is developed in production rule language which is very close to natural language. Therefore, the knowledge base of TWALL is more readable and understandable. The inference mechanism of TWALL looks at the conclu- sions of all rules of the knowledge base in perusal of each goal and selects the applicable rule whose conclu- sion matches the goal. In this way TWALL searches a large amount of knowledge at each cycle rather than applying small amount of knowledge over many cycles. The knowledge base of TWALL can be extended simply by adding a goal in the main rule. The additional rules can be added anywhere in the knowledge base because rules need not be in any order as statements in procedural programs. 205 Conventional computer programs (e.g., the Corps of Engineers TWDA) for cantilever retaining wall design having an open-form solution method and may make numerous itera- tions to automate the design. Therefore, these programs are calculation intensive and time consuming. The heuristics incorporated in TWALL reduce the number of iterations to a very few and thus, saves substantial computational time. On average, TWALL makes 3 to 4 iterations and takes less than a minute on XT microcomputers (8 MHz) to automate the design which is a significant step forward in software engineering. The heuristics used in TWALL can also be used in existing algorithmic cantilever retaining wall design programs with some minor modifications. 8.9 Expert Systems in Education Computers have been used in the educational environment as a problem solving tool for over twenty years. Students have been taught to program in various programming languages or to use application programs. Good educational applica- tions software should have a friendly interface, interactive features and graphic displays. Using conventional approach- es, it requires a considerable time to develop such a software. Recently, expert system technology has become a new tool in solving problems in various disciplines. In the past, the development of an expert system was difficult 206 because AI specialists were often needed. The cost to devel- op a system for educational uses was not justified to many institutions. At present, expert system building tools (shells) are available commercially and run on low-cost microcomputers. Thus, using expert system in the educational environments is now justified for both the software develop- ment cost and the hardware cost. As an example, expert system technology is being used for teaching concrete mix design (Malasri et al., 1989). 8.9.1 Educational Features of TWALL Programs such as TWALL appear to have application in teaching design, explaining design process or acting as a surrogate consultant. The knowledge base of TWALL is struc- tured such that the user is first queried for the required design parameters and then the system proceeds with the design process. During the consultation session, the user can ask "WHY" a certain piece of information is required, and the system explains the logic by displaying the rule that is being pursued. If the user is not clear about the content of the query being made, the system provides an elaborate explanation of the query through the "EXPAND" statement. The ability to answer "WHY" questions and ex- plaining the queries makes the logic used by the system apparent. The student can learn by asking the system ques- tions as he or she would ask the teacher. 207 The design process of TWALL is interactive i.e., it keeps the user informed through various displays during the design process. For example, if the trial wall fails in overturning, it recommends the increase in wall dimensions, displays them to the user (see Appendix B) and gives an option to the user to either accept these recommended dimen- sions or change them if not satisfied. In this fashion, the user remains involved in the design process. Once the design process is complete, the user can check the reasoning pro- cess of the design through the "REPORT" system of LEVELS. CHAPTER 9 SUMMARY, CONCLUSIONS AND RECOMMENDATIONS 9.1 Summary This dissertation has presented the development of TWALL, a knowledge-based expert system for the preliminary design of cantilever retaining walls. The design of a canti- lever retaining wall includes proportioning the wall dimen- sions to ensure external stability and providing sufficient steel and concrete area to ensure internal stability. The developed system is structured to ensure external stability and, at the user's option, internal stability of the wall. The development stages of TWALL included knowledge collec- tion from the literature, development of a prototype, para- metric sensitivity analysis, knowledge elicitation from experts on wall design, development of heuristics, expansion of the developed prototype and testing and validation of the program. The present program is limited to cohesionless backfills and foundation soils not having significant set- tlement problems. The system was developed for IBM-compatible personal computers in production rule language provided by the LEVELS 208 209 expert system shell. There are a total of 297 rules used in the development of TWALL. These rules are further classified into 14 building blocks. The idea of using building blocks was to classify all the rules according to their intended uses. The developed system has a user-friendly interface and is semi-automated such that it can obtain a design within 3 to 4 trials. Its computational time is less than a minute on XT class microcomputers. 9.2 Conclusions The objectives of the study have been achieved with the development of the knowledge based expert system TWALL and the following conclusions are drawn from this experience: 9.2.1 Conclusions Regarding Application of Expert System Technology 1. The development of TWALL demonstrates the viability of knowledge-based techniques as an effective problem solving tool for design tasks that combine heuristic knowledge and extensive computations such as the design of cantilever retaining walls. 2. In the process of developing TWALL, the approaches used for the collection and formalization of the knowledge, development of the prototype and finally the expansion of the developed prototype by incorporating heuristics 210 have proven successful. The same approach appears fruitful for similar design problems in civil engineering. 3. Carefully-selected expert system building tools such as LEVELS can be used to represent both heuristic knowl- edge and knowledge expressed as extensive mathematical formulas and algorithms. 4. Backward chaining control strategy can be used for design problems by carefully structuring the knowledge base and using an appropriate expert system building shell. 5. Knowledge collection and formalization is the lengthi- est part of building an expert system. The collection of heuristic knowledge from domain experts is even more difficult because experts are reluctant to share their hard-earned knowledge with the developer of an expert system. 6. TWALL can be used in educational environments to check the reasonableness of cantilever retaining walls pro- portioned by students. Students can also learn about the design process of cantilever retaining wall using explanation facility of TWALL. 9.2.2 Conclusions Regarding Wall Design 1. Based on various parametric studies and testing and validation results, it can be concluded that TWALL 211 efficiently obtains designs consistent with published examples, experienced designers and students solutions. Parametric sensitivity analyses helped to understand the effect of various design parameters on the stabili- ty of a cantilever retaining wall. It was found that a toe length less than 30 percent of the base length may result in a situation where the upward pressure under the base exceeds the downward pressure on heel at the intersection of heel and stem. For this case, the assumption that the heel acts as a cantilever beam is violated. This situation can be avoided by providing an adequate toe. The cost of a wall designed for at-rest conditions was greater than one designed for the active state by 17 to 34 percent as wall height was varied from 10 to 30 feet. The effect of change in overload factors from 1.4 to 2 on the cost of the wall was negligible for walls below 15 feet because of constructibility requirements. For walls between 20 to 30 feet, the additional cost varied between 9 to 15 percent. Wall sliding usually governs the design of a cantilever retaining wall when typical safety factors of 2, 1.5 and 3 are used to ensure wall stability against over- turning, sliding and bearing capacity failures respec- tively. Overturning governs the design only when the wall is designed with very weak backfills and a strong 212 foundation soil. The bearing capacity of the foundation soil may govern the design when the wall is designed with a dense and steep upward sloping backfill, when there is a weak foundation soil and/or the water table is near the ground surface. 6. The point of application of the resultant on the base significantly affects the bearing capacity of the foundation soil. Increasing base and heel lengths im- prove bearing capacity and the peak bearing value is obtained at minimum eccentricity. Further increasing the base and heel lengths decreases the bearing capaci- ty safety factor but as the base becomes very long (B>0.7SH), the bearing safety factor again increases due to large bearing area. 9.3 Recommendations for Future Research The interdisciplinary nature of this research has raised many questions; some of them remained unanswered and become required avenues for future research. These include the study of models to represent uncertainty in KBES, fuzzy logic and its application to design problems in geotechnical engineering and the development of knowledge-based systems for a variety of tasks in geotechnical engineering. The following areas appear to offer the greatest potential for further research: 1. Further extension of the developed system to other 213 types of retaining structures including gravity retain- ing walls and reinforced earth walls. Expansion of TWALL knowledge base to estimate shear strength parameters of backfill and foundation soil from standard penetration test (SPT) or cone penetrome- ter test results. Development of a reliability-based design procedure for cantilever retaining walls implemented using an appro- priate expert system building tool. 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Winterkorn and H-Y Fang, Van Nostrand Reinhold, New York. Wu, T.H. (1976). Soil Mechanics, Allyn and Bacon, Boston. APPENDICES APPENDIX A QUESTIONNAIRE ON CANTILEVER WALL DESIGN APPENDIX A QUESTIONNAIRE ON CANTILEVER WALL DESIGN The purpose of this questionnaire is to elicit knowl- edge from experts familiar with the design and construction of retaining structures. The knowledge thus elicited will be used to write heuristics (rules and "rules of thumb") for an expert system being developed for the preliminary design of cantilever retaining walls. PART 1 Wall Proportions and External Stability Q1. Q2. Q3. Q4. Cantilever retaining walls are most appropriate for wall heights of to feet. The design of cantilever retaining walls is a trial and error process. What initial trial dimensions should be assumed to minimize the number of trials? a. Stem bottom thickness as % of wall height b. Base thickness as % of wall height c. Base width as % of wall height d. Heel length as % of base width What should be the minimum top stem thickness for various wall heights? a. less than 10 feet in b. 10 to 20 feet in c. over 20 feet in Cohesionless backfills are generally recommended for retaining walls. The angle of internal friction (0) of cohesionless soils may vary between about 28 and 45 222 Q5. Q6. Q7. Q8. 223 degrees depending on soil type and degree of compac- tion. What friction angles do you recommend for the soils given below? The soils are classified according to Unified Soil Classification System. Soil type Angle to be used Expected in actual design angle (degrees) (degrees) 1. Well compacted a. GW, sw b. GP, SP c. GM, SM d. GC, sc 2. Loose a. GW, SW b. GP, SP c. GM, SM d. GC, SC What unit weights do you recommend for the following soils if used as wall backfill? Soil type Unit weight pcf 1. Well compacted a. cw, sw b. GP, SP c. GM, SM d. GC, SC 2. Loose a. GW, SW b. GP, SP c. GM, SM d. GC, SC Which theory do you prefer for computing lateral earth pressure behind cantilever retaining walls? a. Coulomb’s theory. b. Rankine’s theory. c. Either theory can be used. Coulomb’s theory assumes a planar wall back face for predicting lateral earth pressure behind retaining structures but cantilever retaining walls have vertical back face (i.e., vertical stem and horizontal heel). How does this assumption affect earth pressure predic- tions behind cantilever retaining walls? Rankine's theory neglects wall friction for earth Q9. 224 pressure computations but experimental and full-scale , tests show that friction does develop between wall back face and the backfill. How does the neglect of wall friction affect wall design? (e.g., effect on wall dimensions and overall cost) Both Coulomb and Rankine,s theories can be used for predicting earth pressure behind a wall with dry or fully saturated backfills. How is the earth pressure effected when these theories are used for earth pressure prediction behind a wall where water table is present. Q10. Q11. Q12. Q13. Q14. What value of wall friction angle (6) do you consider most appropriate when Coulomb's theory is used for earth pressure prediction with sloping backfills? a. 6:0 b. 6:8 c. 6:0 d. 6=(B+0)/2 e. 6:2/3 0 f. other Should the same wall friction angle (6) be used for computing earth pressure on stem and wall? In not, what different values do you recommend? In earth pressure computations generally, a hydrostatic pressure distribution is assumed behind retaining walls and the total earth force is assumed to act at one third of wall height from wall base. Experimental and full-scale tests show that the resultant of forces may act higher than the one-third of wall height from base and pressure distribution depend on amount and type of wall movements. In your opinion what pressure distribu- tion should be assumed behind the wall and where would the point of application of total force to be consid- ered to act? Compaction may induce higher pressures than active behind the wall. How can the compaction effects can be incorporated in the design. a. By considering point of application of resultant of forces to act at 0.4 to D.SH instead of 0.33H. b. By limiting the weight of roller so that compac- tion does not induce residual pressures. c. By neglecting compaction effects. d. Any other method Some designers and agencies recommend to assume at-rest Q15. Q16. Q17. Q18. Q19. Q20. 225 conditions behind cantilever retaining walls for com- puting lateral earth pressure irrespective of walls rigidity. Is it appropriate in your opinion? Why and why not? Many designers neglect passive resistance on toe side of the wall for stability checks. Which of the follow- ing is appropriate? a. Neglect the passive resistance completely. b. Consider passive resistance at most equal to half the value of passive earth pressure. c. Consider passive resistance equal to the passive earth pressure and use higher safety factors against wall overturning and sliding. What minimum safety factors do you recommend to ensure wall safety against overturning, sliding and bearing capacity failures? a. Overturning failures b. Sliding failures c. Bearing capacity failures Which of the following criterion is more appropriate to ensure stability against wall overturning? a. Incorporate adequate safety in the design. b. Ensure resultant of forces remain within middle third of wall base. c. Either "a" or "b" is appropriate d. Others. What possible measures can improve the stability of a cantilever retaining wall if it fails in overturning during stability checks. How wall stability against sliding failures can be improved? If passive resistance in front of the wall is to be considered. Which of the equation given below is more appropriate for computing safety factor against sliding failures? a. F.S.(s) b. F.S.(s) c. Others (Vtan0+cB+PRH/PDH where V =total effective vertical force acting under the base Q21. Q22. Q23. Q24. Q25. Q26. Q27. Q28. 226 Pm=horizontal passive resistance on toe side of the wall F5“: horizontal driving force on heel side of the wall c =cohesion of foundation soil Large wall movements are required for a cantilever wall to fail in sliding and active condition are expected to be induced in the backfill due to these movements. Therefore, some designers recommend thatPDH for slid- ing analysis should always be computed assuming active conditions behind the wall. What do you recommend? When undrained shear strength parameters (c and 0) of foundation soil are used, what reduction factor should be used with cohesion term "c" as given in sliding stability equation of 020? For sliding stability analysis, many designer believe that the wet concrete adhere sufficiently to the foun- dation soil and friction angle between wall base and foundation soil as same as internal friction angle of foundation soil. Is it appropriate in your opinion? The presence of water on heel on toe side of the wall induces uplift pressure beneath the wall. How does uplift pressure affect wall stability against sliding and bearing capacity failures and how its effects can be incorporated in the design? How can the stability of a cantilever retaining wall be improved if the wall fails in bearing capacity during stability checks? If the eccentricity exceeds limits in the design pro- cess (i.e., resultant of forces acts out of middle third of wall base). What measures can help to bring eccentricity within limits in cases given below? a. When the resultant acts out of middle third on toe side of the wall from middle of base. b. When the resultant acts out of middle third on heel side of the wall from base mid point. Do you recommend the use of base key in routine design of cantilever retaining walls? or should the base key be only used to avoid base length becoming excessively long because of sliding stability requirement in week foundation soils. What can be the maximum base length (8) in term of wall Q29. Q30. 227 height (H)? a. B = H b. B = 1.5H C. B = 2H d. No limits For computing safety factor against bearing capacity failures, which of the following is more appropriate? a. Use average soil pressure under the base b. Use maximum soil pressure under the base (If (a), neglect the next question) Non-uniform pressure distribution under the base is caused by eccentric loading on the wall. The effect of eccentricity is already incorporated in the design by reducing the base length in bearing capacity equations recommended by Meyerhof and Hansen. If this approach is used, will not, the use of maximum soil pressure under the base for computing safety factor against bearing capacity make the design conservative? PART 2 Structural Design of Cantilever Retaining Wall Q31. Q32. Are the provision of ACI code 318-83 adequate for the design of cantilever retaining wall? If not, what modification do you recommend? The following approaches are commonly used for heel design: Approach 1:- Neglect soil pressure under the heel and apply load factors to dead loads and live load over the heel. Approach 2:- Consider soil pressure under the heel and subtract it from the loads over the heel before applying the load factors. Which approach do you consider more appropriate 1. Approach 1 2. Approach 2 (If the answer is 2 , go to Q34) Q33. Q34. Q35. Q36. 228 The application of load factors is not apparent from the ACI Code. What load factor do you recommend for the structural design of the wall parts when base soil pressure is neglected for heel design. Stem Under active conditions Under at-rest condition Heel Dead load over heel Live load over heel Toe Dead load over toe Soil pressure under toe What load factor do you recommend for the structural design of the wall parts when base soil pressure is considered for heel design Stem Under active conditions Under at-rest conditions Heel Net load on heel Toe Net load on toe Where the critical sections be taken for the flexural and shear design of stem, heel and toe? Moment Stem Heel Toe Shear Stem Heel Toe What can be the approximate difference in cost per foot of wall under active and at-rest conditions? APPENDIX B EXAMPLE RUN APPENDIX B EXAMPLE RUN 81. TWALL Solution of Example 1, Appendix N, The 0.8. Army Corps of Engineers (EM 1110-2-2502 1989) This section contains a transcript of a sample run of TWALL and demonstrates the interaction between TWALL and the program user. The user responses are hatched for clarity. W E L C O M E T O AN EXPERT SYSTEM FOR THE PRELIMINARY DESIGN OF CANTILEVER RETAINING WALLS BY NASRULLAH ABEER AND DR. THOMAS F. WOLFF MICHIGAN STATE UNIVERSITY ........................... 229 230 I N T R O D U C T I O N TWALL is an expert system for the preliminary design of cantilever retaining walls. In TWALL, you have an option to design the wall for external stability only or for both external stability and internal stability. For the present design, the system will first check the suitability of the wall for a given application by asking you few questions. Then you will also be asked required design parameters during consultation session. For external stability, the system will check wall stability against overturning, sliding, and bearing capacity failures. For both external and internal stability, system will first ensure external stability and then will calculate required steel for stem heel and toe and perform cost analysis. The wall design has implemented in Foot-Pound System of units. The function keys at the bottom of screen are available for use when illuminated. Press to continue rigeg gang F9 - Help ................................................. ts / I—IIB s backfill t e m water table H HS -—— I HwD toe heel ——— Df | base tb B I Press i to see notations Using keyboard arrows, place the arrow ===> beside your area of interest and press to make selection. After making your selection, press to continue. Press to know more about external and internal stability External Stability ................................................................ .................................................... Wall height (H) ? 6 tO 30 ft Permissible range: H TRUE FALSE ............................ TRUE FALSE A cantilever retaining wall is not suitable for present application according to criteria laid in this knowledge base. However, if you still have the option to continue with the design. Use horizontal arrow keys to move cursor between and and Press to continue ................... TRUE FALSE Internal friction angle of backfill soil (01) ? 30 to 36 deg 20 to 45 deg Recommended values: 01 Permissible values: 01 ....................... Internal friction angle of foundation soil (02) ? Recommended values: 232 Cohesionless soils 02 = 30 to 36 deg Cohesive soils 02 = O to 20 deg Permissible values: 02 = 0 to 45 deg Cohesion of foundation soil (c2) ? Recommended values: when 02>20 c2 = 0 to 1500 psf when §2<20 c2 = 500 to 4000 psf Permissible values: c2 = 0 to 4000 psf 0 Unit weight of backfill soil (F1)? Recommended values: F1 Permissible values: F1 100 to 125 pcf 80 to 150 pcf Note:- The required unit weight is moist. In case of water presence, the system will increase this weight according to the heuristics incorporated in the system to make it saturated. Unit weight of foundation soil (F2) ? Recommended values: F2 Permissible values: F2 100 to 130 pcf 80 to 150 pcf .................................... ................... Note: The soil weight being asked is moist. Backfill slope angle (8)? Permissible values: 0 function key to know more about wall friction. ................... TRUE FALSE Wall friction angle (6) ? Permissible values: 10.0 <6< 35.0 deg ....................... Uniform surcharge (qo)? Permissible values: qo = 0 to 3000 psf Press function key to know about surcharge Embedment depth (Df) ? Recommended values: 2 function key to know more about embedment depth Is the water table at or above the bottom of wall base? If "FALSE", the system will assume water table 234 below the base. TRUE Depth of water table below wall base, (dw)? Permissible range: dw>=0 (Water has no effect if water table is below 26.8 ft. from wall base) ................................ E A R T H P R E S S U R E Do you assume active conditions behind the wall for earth pressure computations? If "TRUE", the system will assume Coulomb’s active conditions. If the wall will be design for at-rest conditions. Coulomb and Rankine’s theories yields the same results for 6:8. TRUE FALSE 0 V E R T U R N I N G S T A B I L I T Y Safety factor for wall stability against overturning? Enter to use default value (i.e., F.S.otReq=2). Enter , to change the default value. TRUE Safety factor against overturning? Recommended values: 1.50 to use default value (F.S.sReq=1.S). Enter , to change the default value. .................................. T8888 FALSE ............................. ...................................... 235 B E A R I N G C A P A C I T Y Safety factor to ensure adequate bearing capacity of the foundation soil? Enter to use default value (F.S.bReq=3). Enter , to change the default value. FALSE W A L L S T A B I L I T Y After obtaining the required parameters, now we will evaluate the stability of the wall assuming trial dimensions. The wall is considered safe against overturning, sliding and bearing capacity failures if calculated safety factors are larger than the safety factors given below: Safety factor against wall overturning >=2.25 Safety factor against sliding failures >=1.50 Safety factor against bearing failures >=3.00 Please press gfififififfi to continue Base width (8) ? Recommended width: 12.50 , the system will assume default value. Else, enter , to change the default value. TRUE Top stem thickness? Permissible values: 1 20 ft 15 O V E R T U R N I N G F A I L U R E The wall design is unsafe as the safety factor against overturning moments 2.04 is less than 2.25. The system will increase 20.2 % heel length and 25.2 % base length, as you press and it will recalculate the safety factor against overturning. However, you have an option to change these dimensions using "WHY" and "FACTS MENU". 8 = 15.00 ft Heel = 8.00 ft toe = 4.51 ft Please press B A S E K E Y Do you want to design cantilever wall with base key? If "FALSE", the system will design the wall without base key. TRUE 237 Yield strength of steel, fy? Permissible range: 30. Else enter . Press , the system will use the default values. Else enter to change the default values. TRUE Overload factor? Recommended range: 1.7 , the system will assume the default values. If , Press to change the default values. TRUE FALSE D E S I G N S U M M A R Y Safety factor against wall overturning = 2.83 Safety factor against sliding failures = 1.68 Safety factor against bearing failures = 8.03 Wall height ft = 25.0 Wall height above ground surface ft = 22.00 Stem height ft = 22.00 Top stem thickness ft = 1.50 Bottom stem thickness ft = 2.49 Base width ft = 18.78 Heel length ft = 9.62 Toe length ft = 6.67 Base thickness ft = 3.00 Stem steel sq-in/ft = 1.96 Heel steel sq-in/ft = 1.88 Toe steel sq-in/ft = 1.30 Cost $/ft = 1100.82 SUMMARY OF COMPUTATIONS 1. INPUT DATA Backfill soil friction angle 01 = 35.00 deg Foundation soil friction angle 02 = 40.00 deg Foundation soil cohesion c2 = 0.00 psf Unit weight of backfill soil F1 = 120.00 pcf Unit weight of foundation soil F2 = 135.00 pcf Backfill slope angle 8 = 18.43 deg Wall friction angle 6 = 18.43 deg Uniform surcharge qo = 0.00 psf Embedment depth Df = 3.00 ft 239 2. EXTERNAL STABILITY Coefficient of earth pressure K =0.S61 Lateral earth force on stem P =16298 Ibs Horizontal force on stem Ph =1S463 Ibs Lateral earth force on wall PsD=26788 Ibs Total net horizontal force PH=25414 Ibs Total downward vertical force V=SO744 Ibs Effective vertical force N'=50744 Ibs Safety factor against overturning = 2.83 Safety factor against wall sliding = 1.68 Eccentricity e=0.78 ft Safety factor against bearing capacity failures Qult/N’ = 8.03 3. STRUCTURAL DESIGN PRESSURES SHEARS AND MOMENTS a. Stem Distance Pressures Shears Moments from top psf Ibs Ib-ft of stem 0.0 0 0 0 5.5 704 1836 3366 11.0 1408 7345 26931 16.5 2399 18779 103286 22.0 2815 29379 215446 b. Heel Distance Pressures Shears Moments from free psf Ibs Ib-ft end of heel 0.0 2717 0 0 2.4 2215 22020 47658 4.8 1712 26740 68956 7.2 1209 30252 184574 9.9 707 32555 258884 c. Toe Distance Pressures Shears Moments 240 from free psf Ibs Ib-ft end of toe 0.0 5565 0 0 1.7 5336 9094 7640 3.3 5108 17807 30134 5.0 4879 26138 66847 6.7 4650 34088 117143 STEEL REINFORCEMENT a. Stem Steel at stem top sq-in/ft = 0.58 Steel at stem middle sq-in/ft = 0.82 Steel at stem bottom sq-in/ft = 1.96 b. Heel Steel at heel free end sq-in/ft = 1.30 Steel at mid heel sq-in/ft = 1.30 Steel at heel near end sq-in/ft = 1.88 c. Toe Steel at toe free end sq-in/ft = 1.30 Steel at mid toe sq-in/ft = 1.30 Steel at toe near end sq-in/ft = 1.30 4. COST ANALYSIS Backfill cost = 193.02 $/ft of wall Concrete cost = 891.10 S/ft of wall Excavation cost = 16.70 $/ft of wall Total =1100.82 $/ft of wall 82. TWALL Solution of Example 12.4 (Bowles 1982) DESIGN SUMMARY Safety factor against wall overturning Safety factor against sliding failures II II N 01 O 241 Safety factor against bearing failures = 5. Wall height ft = Wall height above ground surface ft = Stem height ft = Top stem thickness ft = Bottom stem thickness ft = Base width ft = Heel length ft = Toe length ft = Base thickness ft = Stem steel sq-in/ft = Heel steel sq-in/ft = Toe steel sq-in/ft = Cost $/ft = SUMMARY OF COMPUTATIONS 1. INPUT DATA Backfill soil friction angle 01 = 34. Foundation soil friction angle 02 = 32. Foundation soil cohesion c2 = 400 Unit weight of backfill soil F1 = 115 Unit weight of foundation soil F2 = 112 Backfill slope angle 8 = 10. Wall friction angle 6 = 10. Uniform surcharge qo = 0.0 Embedment depth Df = 5.0 2. EXTERNAL STABILITY Coefficient of earth pressure K =0.294 Lateral earth force on stem P =11425 Horizontal force on stem Ph =11251 Lateral earth force on wall PsD=15220 Total net horizontal force PH=14889 Total downward vertical force V=41794 Effective vertical force N'=41794 Safety factor against overturning = 2.60 Safety factor against wall sliding = 2.02 Eccentricity e=1.S9 17 28.4 23.4 25.9 1.25 1.89 14.6 9.00 3.74 2.42 2.30 1.62 1.02 905. 00 00 .00 .00 .00 00 00 0 0 Ibs Ibs Ibs Ibs Ibs Ibs ft Safety factor against bearing capacity failures Qult/N’ 5.17 0 0 8 4 05 deg deg psf pcf pcf deg deg psf ft 3. STRUCTURAL DESIGN 242 PRESSURES SHEARS AND MOMENTS a. Distance from top of stem b. Distance from free Stem 0.0 6.5 13.0 19.5 26.0 Heel end of heel C. Distance from free Toe end of toe Pressures psf 396 792 1298 1583 Pressures psf 4558 3449 2341 1233 125 Pressures psf 7308 6880 6453 6026 5598 STEEL REINFORCEMENT a. Stem Shears Ibs 1266 5063 12453 20252 Shears Ibs 13765 20280 24301 25828 Shears Ibs 6640 12880 18720 24160 Moments Ib-ft 0 2740 21923 80882 175383 Moments Ib-ft 0 22313 51990 118704 175049 Moments Ib-ft 3139 12305 27126 47225 Steel at stem top Steel at stem middle Steel b. Heel Steel Steel Steel 0. Toe Steel Steel Steel at at at at at at at 4. COST Backfill stem bottom heel free end mid heel heel near end toe free end mid toe toe near end ANALYSIS cost Concrete cost Excavation cost Total 243 sq-in/ft sq-in/ft sq-in/ft sq-in/ft sq-in/ft sq-in/ft sq-in/ft sq-in/ft sq-in/ft 205.42 677.95 21.69 905.09 0.46 0.61 2.30 1.02 1.02 1.62 1.02 1.02 1.02 $/ft of wall $/ft of wall $/ft of wall S/ft of wall APPENDIX C TWALL: SAMPLE RULES AND PROCEDURES APPENDIX C TWALL: SAMPLE RULES AND PROCEDURES C1. Sample Rules ! Rules that give an option to the program user to 1 design the wall for external or internal stability 1 and specifies the facts required to be proved before 1 the system reaches a conclusion of safe design. RULE IF THEN AND RULE IF THEN AND RULE IF AND AND AND AND AND AND THEN ELSE RULE IF AND AND AND AND AND AND AND evaluate external stability required IS external stability Evaluate for external stability stability:="external stability" evaluate internal stability required IS internal stability Evaluate for internal stability stability:="internal stability" external stability stability:="external stability" cantilever wall is suitable for present: application know parameters know trial wall dimensions wall is externally stable DISPLAY design summaryl know activate external program External wall design is safe DISPLAY design unsafe internal stability stability:="internal stability" cantilever wall is suitable for present: application know parameters know trial wall dimensions wall is externally stable wall is internally stable know cost analysis DISPLAY design summary2 244 AND know 245 activate external program THEN cantilever wall design is safe ELSE DISPLAY design unsafe ! Rules to check the suitability of a cantilever wall 1 for a given application. RULE IF AND AND AND AND AND THEN RULE IF OR THEN ELSE AND AND AND wall H<=30 H>=6 suitability Granular backfill Foundation soil is not highly compressible Have Have wall wall wall wall user technical know_how required plant and equipment for: construction suitabilityl suitability suitabilityl preference cantilever wall is suitable for present: application cantilever wall is unsuitable DISPLAY wall unsuitable FORGET ALL CYCLE ! Rules to query the user for required overturning ! safety factor or to assign default value RULE IF THEN AND RULE IF AND AND THEN default safety factor F.S.ot preference know required F.S.ot F.S.otReq:=2 optional safety factor NOT F.S.ot preference F.S.otReq>=1.25 F.S.otReq<=3.5 know required F.S.ot Rule to query the user for trial base width. "Ba" and "Bb" are ranges of recommended base widths and "Bal" and "Bbl" are maximum base widths which are displayed to the user when queried. RULE base width Ba:=0.4*H Bb:=H Ba1:=0.5*H IF AND AND AND AND AND THEN ELSE AND AND AND AND AND AND 246 Bb1:=0.8*H B>=0.4*H B<=H know 8 DISPLAY out of FORGET B FORGET Ba FORGET Bb FORGET Ba1 FORGET Bb1 CYCLE range ! Rules to determine toe length. RULE IF AND AND AND THEN RULE IF AND AND AND AND THEN RULE IF AND AND AND THEN RULE IF THEN AND AND toe length 6=0 toe:=B-(heel+tsb) toeMin:=0.24*B toe>=toeMin know toe toe length 6>0 6<=0.5*01 to :=B-(heel+tsb) toeMin:=O.26*B toe>=toeMin know toe toe length 6>0.S*01 toe:=B-(heel+tsb) toeMin:=0.30*B toe>=toeMin know toe toe length toe=F.S.otReq wall is safe against overturning forces safety against overturning F.S.otAval =F.S.otReq wall is safe against overturning forces 1 Rule that shows the facts for stem design RULE IF AND AND AND AND THEN RULE IF AND AND AND AND AND AND AND THEN RULE IF AND AND stem know know know know know know design earth pressures on stem earth forces on stem shear on stem moments on stem stem reinforcement stem is safe against shear and bending earth pressure at 0.25Hs from top HwD>0.75*Hs+tb HwR>0.7S*Hs+tb p2a:=qo*K*LF p2b:=K*F1*(H-HwD)*LF p2c:=K*(1.05*F1-62.4)*(0.25*Hs-(H-HwD))*LF p2d:=62.4*(0.25*Hs-(H-HwD))*LF ' p2e:=62.4*(0.25*Hs-(H-HwR))*LF p25 know . WT on heel side l WT on toe side =p2a+p2b+p2c+p2d-p2e p25 earth force at 0.25Hs from top HwD<= HwR<= O.75*H+tb 0.75*H+tb PsZa:=p2a*(Hs/4) AND AND AND THEN RULE IF AND AND AND AND AND THEN RULE IF AND AND AND AND THEN RULE IF AND AND AND THEN 249 Pst.=0.5*p2b*(Hs/4) Ps2:=PsZa+Pst Y2.=(P52a*(Hs/8)+Ps2b*(Hs/12))/PsZ know P52 shear on stem 6=0 Vs1:=Psl Vs :=Psz Vs3:=PsB Vs4.=Ps4 VsS:=PsS wall friction angle shear shear shear shear shear know shear on stem moments on stem Msl:=0 MsZ:=VsZ*Y2 Ms3.=Vs3*Y3 Ms4:=Vs4*Y4 MsS:=VsS*YS know moments on at at at at at stem top 0.25Hs from top stem middle 0.75Hs from top stem bottom moment at stem top moment at 0.25Hs from stem top moment at stem middle moment at stem bottom tem ! l l ! moment at 0.75Hs from top 1 s stem bottom reinforcement Know stem bottom max and min steel Know possible stem bottom steel Know required stem bottom steel know stem bottom steel within limits know stem bottom reinforcement 1 Rule to calculate cost per foot of wall RULE IF AND AND AND THEN wall cost/ft Cexca:=CostExca*Vexca/27 lexcavation cost/ft Cfill:=CostFill*Vfill/27 lbackfill cost/ft Ccon :=CostConc*Vconc/27 lconcretecost/ft cost:=Cfill+Cconc+Cexca know total cost 1 Rule to activate external graphics program RULE activate ACTIVATE GTWALL.EXE DISK GDATA.PRL SEND H SEND HS SEND tst SEND tsb SEND B SEND tb SEND heel SEND toe THEN know activate external program 250 C2. Sample Procedures c************************ GTWALL ************************* C C C C Program GTWALL receive data from KBES TWALL through disk file and draws final design sketch of cantilever retaining wall. The program has been implemented in Microsoft FORTRAN. C********************************************************* C INCLUDE ’FGRAPH.FI’ COMMON /GRAPH/H,HS,TST,TSB,B,TB,HEEL,TOE OPEN(3,FILE=’GDATA.PRL’,STATUS=’UNKNOWN’) READ(3,*) NuVar READ(3,1) H READ(3,1) HS READ(3,1) TST READ(3,1) TSB READ(3,1) B READ(3,1) TB READ(3,1) HEEL READ(3,1) TOE FORMAT(1X,E13.7) IF (B.GT.H) THEN XYMAX = B ELSE XYMAX = H ENDIF CALL graphicsmode(ASPECT, SCR) XMIN = -xymax/2.3 XMAX = (XYMAX+xymax/2.30)*ASPECT/SCRt YMIN = -xymax/2.3O YMAX = XYMAX+xymax/2.30 CALL XYGRAPH(XMIN,XMAX,YMIN,YMAX) CALL endprogram() END C********************************************************** C C XYGRAPH - Subroutine to draw design sketch of the cantilever retaining wall C********************************************************** SUBROUTINE xygraph(XMIN,XMAX,YMIN,YMAX) INCLUDE ’FGRAPH.FD' COMMON /GRAPH/H,HS,TST,TSB,B,TB,HEEL,TOE INTEGER*2 dummy, newx, newy, locx, locy,i INTEGER*2 maxx, maxy EXTERNAL newx, newy RECORD /xycoord/ xy RECORD /wxycoord/ xy1 RECORD /rccoord/ curpos COMMON maxx, maxy character*(10 ) fonnam/"t'courier’"/ character*33 str 00000 251 Calculate each position and display it on the screen. Draw a rectangular border CALL moveto(1,1,xy) DUMMY = lineto(maxx-1,1) DUMMY = lineto(maxx-1,maxy-1) DUMMY = lineto(1,maxy-1) DUMMY = lineto(1,1) CALL moveto(2,2,xy) DUMMY = lineto(maxx-2,2) DUMMY = lineto(maxx-2,maxy-2) DUMMY = lineto(2,maxy-2) DUMMY = lineto(2,2) DUMMY = SETWINDOW(.FALSE.,XMIN,YMIN,XMAX,YMAX) CALL SETVIEWORG(50,0,xy) XC = 0.0 YC = CALL moveto_w(XC,YC,xy1) YC = H - TB DUMMY = lineto_w(XC,YC) XC = TOE DUMMY = lineto_w(XC,YC) XC TOE + TSB - TST YC 0.0 DUMMY = lineto_w(XC,YC) XC = TOE + TSB DUMMY = lineto_w(XC,YC) YC = H - TB DUMMY = lineto_w(XC,YC) XC = B DUMMY = lineto_w(XC,YC) YC = H DUMMY = lineto_w(XC,YC) XC = 0.0 DUMMY = lineto_w(XC,YC) CALL VARROW(0.0,H,-B/S.0,l) ' registerfonts('*.fon’) setfont(fonnam // ’h5w4b’) xc = -B/5.0 1 i 252 YC = H/2.0 CALL GETVIEWCOORD_W(XC,YC,XY) locx = xy.xcoord - 21 locy = xy.ycoord - 3 CALL MOVETO(LOCX,LOCY,xy) WRITE(STR,'(FS.2)’) H9 call outgtext(STR) CALL VARROW(0.0,H-TB,B+B/5.0,1) XC = B+B/5.0 YC = (H-TB)/2.0 CALL GETVIEWCOORD_W(XC,YC,XY) locx = xy.xcoord - 21 locy = xy.ycoord - 3 CALL MOVETO(LOCX,LOCY,xy) WRITE(STR,'(FS.2)’) H-TB call outgtext(STR) CALL VARROW(H-TB,H,B+B/5.0,0) XC = B+B/5.0 YC = (H-TB+H)/2.0 CALL GETVIEWCOORD_W(XC,YC,XY) locx = xy.xcoord locy = xy.ycoord - 3 CALL MOVETO(LOCX,LOCY,xy) WRITE(STR,’(FS.2)’) TB call outgtext(STR) CALL HARROW(0.0,B,H+H/8.0,l) XC = B/2.0 YC = H + H/8.0 CALL GETVIEWCOORD_W(XC,YC,XY) locx = xy.xcoord - 16 locy = xy.ycoord - 5 CALL MOVETO(LOCX,LOCY,xy) WRITE(STR,’(FS.2)’) 8 call outgtext(STR) CALL HARROW(0.0,TOE,H-TB-TB/2.0,0) XC = TOE/2.0 YC = H-TB-TB/2.0 CALL GETVIEWCOORD_W(XC,YC,XY) locx = xy.xcoord - 30 locy = xy.ycoord - 15 CALL MOVETO(LOCX,LOCY,xy) WRITE(STR,’(FS.2)') TOE call outgtext(STR) CALL HARROW(TOE+TSB,B,H-TB-TB/2.0,1) XC = (TOE+TSB+B)/2.0 YC = H-TB-TB/2.0 CALL GETVIEWCOORD_W(XC,YC,XY) locx = xy.xcoord - 16 locy = xy.ycoord - 5 CALL MOVETO(LOCX,LOCY,xy) WRITE(STR,'(FS.2)’) HEEL call outgtext(STR) 253 xc = (TOE+TSB-TST+TOE+TSB)[2.0 YC = -H/13.0 CALL GETVIEWCOORD_W(XC,YC,XY) locx = xy.xcoord - 25 locy = xy.ycoord - 5 CALL MOVETO(LOCX,LOCY,xy) WRITE(STR,’(FS.2)’) TST call outgtext(STR) XC -B/4 YC H + H/6 CALL GETVIEWCOORD_W(XC,YC,XY) locx = xy.xcoord - 20 locy = xy.ycoord + 10 CALL MOVETO(LOCX,LOCY,xy) WRITE(STR, '(A33)') ’Press to End session’ call outgtext(STR) XC 0.0 YC 0.0 CALL GETVIEWCOORD_W(XC,YC,XY) locx = xy.xcoord - 7O locy = xy.ycoord - 43 CALL MOVETO(LOCX,LOCY,xy) WRITE(STR, '(A33)') ’CANTILEVER WALL: DESIGN SKETCH’ call outgtext(STR) END APPENDIX D COMPARATIVE STUDY APPENDIX D COMPARATIVE STUDY D1. General This section contains the results of a comparative study conducted to compare TWALL designs of cantilever re- taining walls with the designs done manually by students of earth retaining structures design course (CE 419). The class consisting 34 students was asked to design 34 different cantilever retaining walls. Basically, three variables i.e., wall height, backfill soil friction angle 0 and slope angle 8 were changed within the economical and practical range. The design included checks for wall sliding and overturning only. The students were not asked to check for bearing capacity failures because it was beyond the scope of CE 419 course. Then the same 34 cantilever walls were designed on TWALL. D2. Results A comparison of students and TWALL design is shown in Figures D-1 to D-4 and Tables D-l to D-3. In general the results compare well. The comparison of recommended base lengths by TWALL and students are shown in Figure D-1. For walls below 15 feet, the recommended base lengths by TWALL and students compare very closely and the variation is within one feet. For walls above 15 feet TWALL recommends longer base as compared to that recommended by the students. For these walls, the students designs were safe for wall sliding and overturning but their designs failed in bearing capacity. TWALL recommended long base to ensure wall stabil- ity against bearing capacity failures. The comparison of recommended heel lengths is shown in Figure D-2. The results are similar to that discussed above. Some of the students used longer heel than TWALL but their design resulted in a situation where upward pressure at the intersection of heel and stem exceeded the downward pressure on the heel and the point of maximum shear and moment 254 255 shifted away from the intersection point toward the free end of the heel. Heuristics incorporated in TWALL limits heel length to avoid such situation and ensures that point of maximum shear and moment always remains the intersection point. Thus, the assumption that heel is designed as a cantilever beam remains valid. Figures D-3 and D-4 show the comparison of TWALL and students sliding and overturning safety factors respective- ly. The results compared generally well. Small scatter of sliding safety factors show that wall sliding mostly gov- erned the design. But for walls 20 feet and above, the bearing capacity governs the design as can be seen from Tables D-1 to D-3. 03 . Summary Generally, TWALL designs of cantilever retaining walls compared well with the students designs. For walls below 15 feet sliding mostly governed the design but for walls above 20 feet, bearing capacity governed the design. In the pres- ent study, wall overturning was not critical because high wall friction was used that substantially reduces the horizontal force on the wall. Overturning can possibly governs the design when foundation soil is very strong as compared to the backfill or the wall is acted upon by a very high surcharge load. Very short toe can also result in overturning failures. TWALL can be used as a design tool for the preliminary design of cantilever retaining walls and for checking the existing designs with confidence and reliability. TWALL can also be used as an educational software to demonstrate the capabilities of knowledge based expert systems for designs problem in geotechnical engineering. 256 22 l .1: 20* 1 x m 18 . ‘é ‘ I 4i 2/ 0 1 f 2* '2 6 ‘ i "f 1F/ 44 14 s— /4-a’ . 1 1 I 17/ / 1 V 12 ‘ C—r—fi' ‘fi at! . v a .c: 1 1 ’ AA? if a a 3-25 ‘6 10 I. // H F 1 l 1’ 4’ s 8 ’E/J/ a n H-ZO '4 AME/ABE £1-15 0 6--------da J 3 ‘ /’ 6 m 4 I1 l/ 4'10 / / 1 / i 2 ' I fil ' r ' T fil fi f r Ifii r 2 4 6 8 10 12 14 16 18 20 22 Base Length (TWALL) ft Figure D-l Comparative study: base lengths designed by students (CE 419) versus TWALL 14 «U 1 I / m / 12 / a. / . , a 1 4r / .u 10 / /1 c ’ / 0 ‘ . / ‘,/ g a/ / 1.1 8 111- -——a-25 23' 1 A'/ ' / .a / I: / a a“ 6 5 / /a ‘61 ‘ fi/i‘a ' x “‘20 == 4.7—9 4’ o 4' Z-i-lS A / ‘ 3 l / '3 fl/i / 2 2‘ / / a-lo g 4/ / l 0 v/ r ‘, 1 A . . . 0 2 4 6 8 10 12 14 Seal Length (TWALL) ft Figure D-2 Comparative study: heel lengths students (CE 419) versus TWALL 257 3.00 A. J / n u 275 I S a ’ x “g 2501 // ,’ 4., d a / ' / m 1/ ’ ~' 225 “ , //F ’ a. 3a a a / a 200 . '" 'd . / file 9 'U / Ep/ 2: 1.75 .a r? m . / l/m . / / E m 1.50 B! . ‘ / / h / / i 125 . / . / i 1.00 . .1- , . , . , - , . T . 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00 F.S.sliding (TWALL) Figure D-3 Comparative study: sliding safety factors obtained by students (CE 419) versus TWALL 4.5 4.0 (Students) H-20 F.S.overturning 1.5 2.0 2.5 3.0 3.5 4.0 4.5 F.S.overturning (TWALL) FiGure D-4 Comparative study: overturning safety factors obtained by students (CE 419) versus TWALL degrees). 258 Table D-l Comparison of TWALL designs with Students (CE419) designs (backfill slope=10 Wall Parameters Students Design TWALL Design Wall Soil Friction Angle Soil Friction Angle Height fl Misc. 30 33 36 30 33 36 Base Length 5.00 5.00 4.50 5.19 5.05 4.79 Heel Length 3.00 3.00 2.00 2.50 2.50 2.00 10 Toe Length 1.00 1.00 1.25 1.50 1.35 1.35 F.S.sliding 1.81 2.36 2.00 1.74 1.98 2.14 F.S.overturning 2.00 2.27 2.21 2.03 2.15 2.21 Base Length 7.00 - 7.00 8.50 - 7.00 Heel Length 3.50 - 3.00 4.50 - 3.50 15 Too Length 1.50 - 3.00 2.75 - 2.22 F.S.sliding 1.67 - 1.80 1.81 - 2.03 F.S.overturning 1.96 - 2.20 2.43 - 2.30 Base Length 12.00 14.00 12.00 12.00 11.00 10.00 Heel Length 8.00 9.00 8.00 6.50 6.50 5.50 20 Toe Length 2.00 3.00 2.00 4.32 3.43 3.12 F.S.sliding 2.13 1.88 2.68 1.83 2.05 2.14 F.S.overturning 2.86 3.19 2.50 2.71 2.72 2.64 F.S.bean'ng - - - 3.06 3.07 3.14 Base Length 12.70 9.75 9.00 16.00 14.50 13.00 Heel Length 8.00 6.50 6.00 9.00 6.50 7.25 25 Too Length 2.00 1.50 1.5 5.26 6.45 4.34 F.S.sliding 1.77 1.98 2.09 1.95 1.81 2.15 F.S.overturning 2.34 2.14 2.09 3.08 2.82 2.85 F.S.bearing - - - 3.11 3.06 3.07 259 Table D-2 Comparison of TWALL designs with Students (CE419) designs (backfill slope= 15 degrees). Students Design Wall Parameters Wall Soil Friction Angle Soil Friction Angle Hetitght Misc. 30 33 36 30 33 36 Base Length ft 6.00 6.00 4.50 5.50 5.19 5.04 Heel Length ft 3.00 4.00 2.50 2.50 2.50 2.50 10 Toe Length ft 2.00 1.00 1.00 1.81 1.50 1.35 F.S.sliding 1.70 2.08 1.94 1.63 1.86 2.15 F.S.overturning 2.3 2.52 2.04 2.06 2.13 2.26 Base Length 7.00 8.00 7.50 9.00 8.19 7.00 Heel Length 4.00 5.00 5.00 4.50 4.50 3.50 15 Toe length 2.00 1.5 1.5 3.20 2.40 2.21 F.S.sliding 1.77 1.89 2.08 1.68 1.90 1.93 F.S.overturning 1.99 2.39 3.00 2.43 2.44 2.21 Base Length 11.00 11.75 8.50 13.19 12.00 10.50 Heel Length 7.66 8.00 6.00 8.00 7.00 6.00 20 Toe length 2.00 2.00 1.50 3.90 3.84 3.46 F.S.sliding 1.90 1.98 1.99 1.90 1.99 2.06 F.S.Overturning 2.70 2.41 2.04 2.90 2.84 2.65 F.S.bearing - - - 3.07 3.24 3.05 Base Length 11.75 10.25 12.50 17.50 16.00 14.00 Heel Length 7.25 7.50 8.50 10.00 8.50 7.00 25 Toe Length 3.00 1.50 2.50 5.66 5.87 5.55 F.S.sliding 2.28 1.82 2.20 1.93 1.98 2.01 F.S.overturning 2.04 2.06 2.00 3.22 3.15 2.93 F.S.bearing - - - 3.08 3.08 3.15 h I =é 260 Table D-3 Comparison of TWALL designs with Students (CE 419) designs (backfill slope=20 degrees). ll Wall Parameters Students Design TWALL Design 1| I Wall Soil Friction Angle Soil Friction Angle Height Misc. 30 33 36 30 33 36 Base Length ft 5.00 5.00 5.00 6.40 5.19 5.04 Heel Length ft 3.00 3.00 2.00 2.96 2.50 2.50 10 Toe Length ft 1.00 1.00 2.00 2.25 1.50 1.35 F.S.sliding 1.77 2.00 1.80 1.61 1.72 1.98 F .S.overtuming 2.19 2.60 2.30 2.28 2.04 2.17 Base Length - 9.00 - - 9.00 - I Heel Length - 5.00 - - 4.50 - 15 Toe Length - 2.00 - - 3.21 - F.S.sliding - 1.94 - - 1.77 - F.S.overturning - 2.88 - - 2.53 - Base Length 14.00 8.50 - -15.00 13.00 - Heel Length 9.00 5.50 - 8.00 7.00 - 20 Toe length 3.50 2.00 - 5.60 4.77 - F.S.sliding 2.00 2.00 - 1.74 1.84 - F.S.Overturning 4.10 2.20 - 3.06 2.89 - F.S. bearing - - - 3.07 3.11 - Base Length 12.76 11.00 13.00 21.00 18.00 15.50 Heel Length 6.70 7.00 8.00 12.76 9.50 7.50 25 Toe Length 3.70 2.00 3.00 6.50 6.76 6.47 F.S.sliding 1.50 1.90 1.67 1.97 1.96 1.97 F.S.overturning 2.00 2.27 2.11 3.66 3.37 3.10 F.S.bearing - - - 3.01 3.02 3.10 IC QRIES IlfllllflljfllflfllflfllifilfllfllllHI 6