:Dlnéx... It»! . :3 . .4 (In; ‘I Gl’Ihrziuul v . 95.53.11: .- . 0| .bx1alg . . II. (It'tl‘ ,431 71.1.3.5? . . ‘.v\o..o.il. 3‘ C41. 'nivlpcg Ina-lb... ‘ t9... 22.....{11' 3' "r I’-7‘I~. y i A x.¢..‘I:r..i . .A’x..ll3‘ XII. iv}: Elvilyg .IO...:¢.0 J... . . v . , ‘ o. ,i r , :2? . . ‘. L .5 gas-7: . 37:5'Dsn2CE} 1.... 9.3% .5; .2l littrurxt. 91:1 5,: u...\v.. .7 i 700"- an: .5. 3'5 ‘ IIIIIIIIIIIIIII IIIIIIIIIIIIIIIIIIIII 247 This is to certify that the dissertation entitled NEW DESIGN METHOD FOR FROZEN EARTH STRUCTURES WITH REINFORCEMENT presented by JOSEPH A . SOPKO , JR . has been accepted towards fulfillment of the requirements for Ph.D. Civil Engineering degree in 6.3.WM Major professor Date fiuqqsl’ 3 .l‘i‘lo MS U is an Affirmative Action/Equal Opportunity Institution 0-12771 I LIBRARY Michigan State , University PLACE IN RETURN BOX to remove this checkout from your record. TO AVOID FINES return on or before date due. DATE DUE DATE DUE DATE DUE I fl ; JIM I II _I MSU to An Affirmative Action/Equal Opportunity Institution cMma-m NEW DESIGN METHOD FOR FROZEN EARTH STRUCTURES WITH REINFORCEMENT BY Joseph A. Sopko, Jr. 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 1990 ABSTRACT Difficult soil conditions and earlier failures using more conventional construction methods on deep shafts and approach structures at a construction site showed the need for a frozen ground support system. Ground freezing was particularly suitable for the project because it did not require lowering of the water table, thus avoiding potential problems for existing nearby structures. Preliminary design methods showed the potential for large tensile stresses around openings in the shaft wall, hence the need for reinforced frozen wall sections. Irregular wall geometry of the proposed frozen earth structure and poor soil conditions required specialized computational methods for design and evaluation of structural stability. Conventional design methods were found to be too conservative and would result in frozen earth structures that were excessively large and cost prohibitive. Also, conventional analysis techniques were unable to account for the complex frozen wall geometry required for construction. A.laboratory testing program was conducted to determine elastic and time-dependent material properties of the weaker soils in both uniaxial compression and tension. The finite element method was used to evaluate stresses and displacements at critical locations which would lead to unstable and unsafe conditions during construction. Composite steel—concrete reinforcement members were designed and placed so as to transfer loads to less critical wall areas. These reinforcement members were installed prior to ground freezing. Stress and deformation changes within the reinforced frozen wall were evaluated for the excavation and construction phase using frozen soil creep parameters and a nonlinear finite element analysis. Field measurements during construction showed agreement with predicted wall movements. The use of measured elastic and time-dependent soil properties with the finite element method for evaluation of the frozen wall structural behavior was considered a significant success. This approach can deal with complex frozen wall geometry and should be suitable for a variety of design requirements. This Dissertation is Dedicated to Fred P. ”GO GREEEN - GO WHITE” Adolph ii ACKNOWLEDGMENTS The writer wishes to express his appreciation to his major professor, Dr. Orlando B. Andersland, Professor of Civil Engineering, for his guidance and numerous suggestions during the research, laboratory, and field investigations, as well as the preparation of this dissertation. The writer also expresses thanks to members of the doctoral committee, Dr. Robert K. Wen, Professor of Civil Engineering, and Dr. Grahame J. Larson, Professor of Geology. .Gratitude is extended to John.A. Schuster, for supporting this work. iii TABLE OF CONTENTS LIST OF TELES O O O O O O O O O O O O O 0 LIST OF FIGURES O O O O O O I O O O O O O 0 LIST OF SMOLS I O O O O O O O O O O O O CHAPTER I 1.1 1.2 CHAPTER II 2.1 2.2 2.3 2.5 CHAPTER III 3.1 3.2 INTRODUCTION . . . . . . . General. . . . . . . . . . . Objectives and Scope . . . . REVIEW OF LITERATURE . . . . Conventional Frozen Wall Design. Finite Element Method. . . . Material Properties. . . . . 2.3.1 Soil Description . . 2.3.2 Mechanical Behavior. Soil Parameter Measurements. 2.4.1 Deformation and Strength 2.4.2 Tensile Behavior . . Standardized Developments. . PROJECT DESIGN PARAMETERS. . Site Description . . . . . . 3.1.1 Geologic Profile . . 3.1.2 Soil Profile . . . . 3.1.3 Ground water Profile Required Excavation Limits . iv . vii .viii . xii O O ~l ~4 u: ha .E . .13 . .20 . .20 . .20 . .37 3.3 CHAPTER IV 4.1 402 CHAPTER V 5.1 5.2 5.3 5.4 5.5 CHAPTER VI 6.1 6.2 Frozen Earth Wall Geometry . . . . . . MATERIAL PROPERTIES. . . . . . . . . . Uniaxial Compression Tests . . . . . . 4.1.1 Compression Sample Preparation 4.1.2 Equipment and Test Procedures. 4.1.3 Time-dependent Compression Tests Uniaxial Tension Tests . . . . . . . . 4.2.1 Tension Tests. . . . . . . . . 4.2.2 Tension Sample Preparation . . 4.2.3 Equipment Test Procedure . . . 4.2.4 Time-dependent Tension Tests . THEORETICAL ANALYSIS . . . . . . . . . Conventional Design Approximations . . Elastic Finite Element Analysis. . . . 5.2.1 Elastic Finite Element Models of IndiVidual Cells 0 O O O O I 0 5.2.2 Elastic Finite Element Models for the Buttress Sections . . . . Analysis of the Reinforced Section . . 5.3.1 Elastic Finite Element Models Analysis of the Reinforced Section . . . . . . . . . . . Time-dependent Nonlinear Finite Element Analysis. . . . . . . . . . . . . . . Structural Analysis Summary . . . . . FIELD PERFORMANCE. . . . . . . . . . . Field Instrumentation. . . . . . . . . Wall Movement Observations . . . . . . .67 .76 .76 .77 .78 .80 .81 .82 .84 .86 .86 105 106 110 111 115 118 119 120 123 141 142 143 6.3 Comparison with Predicted Deformations . . 144 CHAPTER VII DISCUSSIONS AND RECOMMENDED DESIGN . . . . 150 7.1 Clarification of Site Conditions . . . . . 150 7.2 Stability and Deformation Analysis . . . . 150 7.2.1 Recommended Laboratory Testing Procedures. . . . . . . . . . . . 156 7.3 Structural Design. . . . . . . . . . . . . 161 7.4 Reinforcing Methods and Selection. . . . . 163 7.5 Creep Effects and Factor of Safety . . . . 167 CHAPTER VIII CONCLUSIONS. . . . . . . . . . . . . . . . 170 LIST OF REFERENCES O O O O O O O O O O O O O O O O O O O 174 APPENDIX A, LABORATORY TEST DATA . . . . . . . . . . . . 178 vi Table 2.1. 2.2. 2.3. 5.1. 5.2. 5.3. 504O SOSO LIST OF TABLES Constants for vylov's Deformation Equation .41 Creep Parameters from Pullout Tests. . . . .41 n Values for Different Pile Types at -6%2. .41 Internal Stresses from Elastic Analysis. . 127 Predicted Structural Life Based on Elastic Analysis and Compression Creep Test . . . 127 Summary of Force and Moment Reaction, Cell 1 Acting on Buttress Between Cell 1 and cell 2 O O O O O O O O O O O O O O O O 127 Summary of Force and Moment Reaction, Cell 2 Acting on Buttress Between Cell 1 and Cell 2. . . . . . . . . . . . . . . . 128 Summary of Force and Moment Reaction, Cell 3 Acting on Buttress Between Cell 2 and Cell 3. . . . . . . . . . . . . . . . 128 Material Properties Used in Elastic malYSi-S O O O O O O O O O O O O O O O O O 128 Material Properties Required for Frozen Soil in Nonlinear Analysis. . . . . . . . 129 Material Properties for Bond Link Elements 129 Time-dependent Parameters of Frozen Soil . 129 vii Figure 201O 2.2. 2.3. 2.4A. 204BO 2.5. 2.6. 2.8A. 2.83. 2.8C. 209O 2.10. LIST OF FIGURES Initial Tangent Modulus vs. Degrees Below Freezing (Jessberger, 1981) . . . . . . . .42 Initial Tangent Modulus vs. Temperature for Fairbanks Silt (Haynes, 1978) . . . . . .. 43 Initial Tangent Modulus vs. Axial Strain Rate (Bragg and Andersland, 1981) . . . . .44 Young's Modulus vs. True Axial Strain for Ice and Coarse Sand-Ice Samples (Goughnour and Andersland, (1968). . . . . . . . . . .45 Young's Modulus vs. True Axial Strain for Fine Sand-Ice Samples (Goughnour and Andersland, 1968) . . . . . . . . . . . . .46 Comparison Numerical Results Based on the Power Creep Law with Different values of Moduli Ratio (800, 1983). ... . . . . . . .47 Tangent Poisson's Ratio vs. Axial Strain, Constant Strain Rate Compression Test at .20C (Bragg, 1982) O O O O O O O O O O O O O 48 Tangent Poisson's Ratio vs. Axial Strain, Constant Strain Rate Compression Test (Bragg, 1980) O O O O O O O O O O O O O O O49 Stress-Strain Curves on Selected Sample (Akagawa' 1980) O O O O O O O O O O O O O O50 Stress-Strain Curves on Selected Sample (Akagawa,1980). . . . . . . . . . . . . . .51 Stress-Strain Curves on Selected Sample (Megawa’ 1980) O O O O O O O O O O O O O O52 Tangent Poisson's Ratio vs. Time Constant Stress Compression (Creep) Test (Bragg,1980). . . . . . . . . . . . . . . .53 Applied Stress vs. m Parameter of Constant Stress Experiments (Sego and Morgenstern, 1983) O O O O O O O O O O O O O O O O O O O54 viii 2.14 2017 301O 3.1. 3.2. 3.3. 3.4. 401O 4.2. 4.3. Applied Stress vs. a Parameter of Constant Stress Experiments (Sego and Morgenstern, 1983) O O O O O O O O O O O O O O O O O O O55 Parameter a vs. Time (Klein and Jessberger, 1976) . . . . . . . . . . . . .56 Comparison of Numerical Results Based on the Power Creep Law with Creep Parameters from Eckardt (1981) and varying Parameter n (300, 1983) . . . . . . . . . . . . . . .57 Comparison of Numerical Results Based on the Power Creep Law with Creep Parameters from Eckardt (1981) and Varying Parameter b (300, 1983) . . . . . . . . . . . . . . .58 Comparison of Numerical Results Based on the Power Creep Law with Creep Parameters from Eckardt (1981) and varying Parameter °C. (500, 1983) . . . . . . . . . . . . . .59 Comparison of Numerical Results Based on the Power Creep Law with Pagameters from Eckardt (1981) and Varying ’ (Soc, 1983) .60 Comparison of Numerical Results for the Power Creep Law with Average Creep Parameters of Tension and Compression Compared with Experimental Results (SOC, 1983)O O O O O O O O O O O O O O O O61 Generalized Soil Profile . . . . . . . . . .71 Generalized Soil Profile (Continued) . . . .72 Lateral Earth Pressure Diagram as Presented in the Project Specifications . . . . . . .73 Proposed Underground Structure as Shown in the Contract Documents. . . . . . . . . . .74 Three-dimensional Illustration of Proposed Frozen Earth Structure(s) . . . . . . . . . .75 Cross Section of Sample Freezing Apparatus .87 Load Frame for Compression Tests . . . . . .88 Lever Arm Scenario for Compression Tests . .89 ix 4.4. 4.5A. 4OSBO 405CO 4.6. 4.7. 4.8. 4.9. 4.10. 4.11. 4 O 12A. 4.128. 4.12C. 4013. Axial Strain vs. Compressive Stress for Modified Constant Strain Rate Compression Test. . . . . . . . . . . . . .90 Time vs. Axial Strain for Compression Creep Tests at Various Applied Stresses . . . . .91 Logarithmic Plot of Time vs. Strain for Compression Creep Tests Where the Tangent of the Angle of Plotted Data is the Creep Parameter b . . . . . . . . . . . . . . . .92 Logarithmic Plot of Compressive Deviator Stress vs. Strain Rate Where the Tangent of the Resulting Line is the Creep Parameter n . . . . . . . . . . . . . . . .93 Logarithmic Plot of Time vs. Reciprocal of Applied Compressive Stress. Extrapolation of the Plotted Line is Used to Determine the Maximum Allowable Compressive Stresses for a Given Length of Time (for Factor of Safety Equal to 1). . . . . . . . . . . . .94 Tension Test Sample Showing End Cap Assembly. . . . . . . . . . . . . . . . . .95 Dimensions of Tension Test Samples . . . . .96 Trimming Lathe for Tension Test Samples. . .97 Tension Test Load Frame. . . . . . . . . . .98 Axial Strain vs. Tension Stress for Constant Strain Rate Tension Test . . . . .99 Time vs. Axial Strain for Tension Creep Tests at Various Applied Stresses . . . . 100 Logarithmic Plot of Time vs. Strain for Tension Creep Tests Where the Tangent of the Angle of Plotted Data is the Creep Parameter b . . . . . . . . . . . . . . . 101 Logarithmic Plot of Compressive Deviator Stress vs. Strain Rate Where the Tangent of the Resulting Line is the Creep Parameter n . . . . . . . . . . . . . . . 102 Logarithmic Plot of Time vs. Reciprocal of Applied Tensile Stress. Extrapolation of the Plotted Line is Used to Determine the X 5.8. 5.9. 5.10. 5.11. 6.1A. 6.2. 6.3. Maximum Allowable Tensile Stresses for a Given Length of Time (for Factor of Safety Equal to 1). . . . . . . . . . . . Conventional Approximation for a Circular Shaft O O O O O O O O O O O O O O O O O O Conventional Method for Elliptical cafferdam O O O O O O O O O O O O O O O O Typical Three-Dimensional Grid Used in Elastic Analysis. . . . . . . . . . . . . Boundary Conditions Imposed on Grids Used in Figure 5 O 3 O O O O O O O O O O O O O O Three-Dimensional Finite Element Method Grid of Buttress Between Adjacent Cells . Regions of Excessive Tensile Stresses as Computed by Elastic Finite Element Method Two-Dimensional Grid Used in Elastic Model of Buttress Section . . . . . . . . . . . Two-Dimensional Nonlinear Finite Element Method Grid of Buttress Section . . . . . Exaggerated Nodal Deformation at Time = 0. Exaggerated Nodal Deformation at Seven Days O O O O O O O O O O O O O O O O O O O Exaggerated Nodal Deformation at 30 Days . Location of Strain Gauges on Reinforcing Elements O O O O O O O O O O O O O O O O O Detail of Strain Gauges Used on Reinforcing Elements . . . . . . . . . . Angles Measured to Monitor Reinforcement Deformation . . . . . . . . . . . . . . . Detail of Tape Measurement Scheme on Reinforcing Elements. . . . . . . . . . . xi 103 130 131 132 133 134 135 136 137 138 139 140 146 147 148 149 5‘; actasc'n'b Ekvex Ecoacl nob: 5:,Og'ne'be égvag.n9.b° €§,Og,nt.bt X'Yo 2 LIST OF SYMBOLS relative displacement rate on the bond interface of two materials; relative creep displacement on the bond interface of two materials; creep parameters for the creep law of the bond interface element; elastic modulus or initial tangent modulus; respectively, instantaneous and creep strain; effective creep strain rate; respectively, proof strain and proof stress for plastic deformation; creep parameters for power creep law; effective creep parameters for power creep law; compressive creep parameters for power creep law tensile creep parameters for power creep law; stress; local coordinates for three-dimensional finite elements. xii area; a constant; moduli of nonlinear deformation in vyalov's equation; cohesion intercept; load; unconfined compressive strength; absolute value of negative temperature; arbitrary temperature, positive; exponentin vyalov's equation; Poisson's ratio; shear stress; angle of internal friction; soil parameter in vyalov's creep equation. xiii I. INTR D TI N 1-1 W The use of frozen ground support systems for construction, as it is known today, was initially developed in Germany by F.H. Poetsch in 1883. Numerous improvements, both in technique and equipment, have since made ground freezing a competitive construction option. This process involves the circulation of a refrigerated coolant through a series of freeze pipes for the purpose of extracting heat and converting the soil water to ice. This frozen soil forms a relatively strong, watertight construction material. The layout of freeze pipes may vary, but their primary purpose is to form retaining and/or watertight structures composed of frozen earth. Artificial ground freezing is used to provide frozen walls for support of open excavations, deep shafts, tunnels, and may also be used to form supports for structural underpinning. This dissertation will be limited to analysis and design of frozen soil support systems for open excavations. The concepts presented may also be applied to other construction applications. The concept of providing a frozen wall for support of an open excavation during construction involves installation 1 2 of a series of refrigeration pipes along the perimeter of the proposed excavation. The diameter and spacing of these refrigeration pipes will vary depending on excavation limits. For most projects the freeze pipes must extend to a relatively impervious subsurface stratum so as to avoid seepage below the wall with possible thaw damage. Within each freeze pipe, a smaller diameter down pipe is installed. The coolant circulates down through the inner pipe and then up the annulus between the two pipes. This may be reversed in some specific applications. Both pipes are connected to larger diameter pressure and return manifolds which lead to the refrigeration plant. A common refrigeration source consists of one or more trailer mounted refrigeration plants. The typical plant is electric or diesel driven, employing ammonia or freon as the primary coolant. The refrigeration plant serves to extract heat from a secondary coolant, typically a calcium chloride water mixture (brine). This secondary coolant is circulated through the manifold to the freeze pipes and back to the refrigeration plant. The coolant circulating through the freeze pipes removes heat from the adjacent ground, converting soil pore water to ice. The frozen soil walls formed by this process provide temporary ground support and a water barrier around an excavation during construction. In most cases the excavation will be vertical and 3 immediately adjacent to the frozen wall, relying totally upon frozen soil strength to provide support for the adjacent unfrozen soil. In certain cases it is necessary to reinforce the frozen wall with steel or concrete structural elements which can take tensile stresses that may develop in wall sections subjected to bending. The basic intent of the ground freezing contractor is to provide a structurally safe and watertight frozen earth barrier suitable for construction involving large and deep excavations. To accomplish this, detailed analyses are required which relate to thermal design, wall structural behavior, bottom stability, refrigeration plant capacity, and the closed-circuit pumping system. 1.2 ijectives and Scope The thesis has been directed to the formulation of procedures needed for structural design of frozen earth cofferdams with reinforcing elements. Emphasis was given to the use of two- and three-dimensional finite element models (FEM) in the analysis. Field measurements used to verify predicted behavior were obtained from an actual cofferdam located in Milwaukee, Wisconsin. Material parameters needed for the analysis were determined from laboratory tests conducted on soil samples taken in the vicinity of the proposed excavation. After design, the structure was built and field performance was monitored. Field behavior 4 indicated that the design methods used were valid and that they would appear to be appropriate for design and construction of other frozen earth structures. The laboratory test procedures used may be suitable for development into standardized frozen soil test methods, particularly for frozen earth structural design problems. Subsurface soil conditions at the Milwaukee area site presented problems relative to the use of normal earth support methods during construction. Earlier failures with slurry diaphragm walls made ground freezing an attractive alternative construction method. Preliminary designs were prepared by Geocentric Engineering and Geofreeze, Inc., with the author's participation in all phases. These frozen earth structures included three cylindrical dropshafts. Analytical solutions, based on elastic theory with approximate material parameters, were used in the preliminary design phase for frozen walls surrounding the cylindrical shafts. .A connecting transition structure between the dropshaft and a trash rack required more complex wall geometry to allow for required excavation limits. Numerical methods were utilized for analysis of the more complex wall structure. More importantly, certain areas within the frozen earth wall would be subjected to tensile stresses. The frozen soil, having a much lower strength in tension than in compression, raised major design questions as to the effects and/or consequences of tensile stresses on 5 wall stability. If these tensile stresses were too excessive, the soil areas in question would require reinforcement with a material capable of absorbing these stresses so as to give acceptable levels of deformation. Before a design could be developed, laboratory tests were conducted to determine the soil material properties in tension and compression. Parameters required for this analysis included elastic moduli and time-temperature-stress creep constants for prediction of long term frozen soil deformation. .A three-dimensional elastic FEM model was used to determine stress states and initial internal stresses within the structure. After selecting a wall geometry which minimized tensile stress areas and distributed compression stresses to acceptable levels, a final wall geometry and analysis model were developed. This final elastic model was used to determine stresses acting on those areas which would require reinforcement. Stress zones in tension were considered critical areas and subsequently were analyzed using a two-dimensional time-dependent FEM program. This program permitted the use of material parameters which included bond stresses at interfaces with the potential for slip failure, as well as different moduli for tension and compression. Long term wall deformation at critical locations could then be computed. 6 After design, construction commenced, and various monitoring systems were used to evaluate performance of the frozen earth wall. Based on wall movement (very small) and stress computations, it was possible to show that the design procedure was acceptable and that the methods could be applied to future ground freezing projects requiring complex wall geometry and use of reinforcing elements to augment the frozen soil strength in tension. II. EVIEW QF LITERATURE 2.1 Conventional Frozen Wall Design Conventional design methods have been used for many years and have worked well on many projects. Their success can be largely attributed to the type of structure involved and the skill and expertise of the contractor, and not the structural design method used. Frozen earth walls may be classified as either straight walls, curved walls, or complex structures. While there may be many variations of walls within each category, the design method used is essentially the same. Loads which act on a frozen earth structure must be determined prior to the design. These loads may be estimated on the basis of local soil conditions. Quite often the soils to be frozen may have a very low shear strength, permitting the earth pressures to be considered hydrostatic. There are times, however, when the "active" or ”at rest” condition may apply (Sanger, 1968). During the freezing process, soil expansion can create additional pressures. Methods have been developed for computing these pressures (Ladanyi, 1982; Shuster, 1972). They can sometimes be neglected in coarse grained soils, but must be accounted for in clays or silts. These forces are 8 considered initial forces and are usually neglected once excavation has taken place (Klein, 1981). After determining the loads which will be acting on the structure and other considerations such as project geometry constraints, the frozen earth structure can be designed. The structural analysis of frozen earth walls is usually based on soil parameters obtained from unconfined compression tests, triaxial compression tests, and/or unconfined compression creep tests. The shear strength is then determined using the parameter c and.¢ (Jessberger, 1982). Prediction of deformation rate and total deformation for frozen earth structures requires a complex analysis. This analysis is based on creep parameters which describe the time- and temperature-dependent mechanical properties of frozen soil. These parameters can be obtained by conducting a series of creep tests (vyalov, 1962) which are discussed in later sections. Curved walls or circular shafts are the most common frozen earth structures. Their popularity is due largely to the compressive stress state in the structure. Since frozen soil has a much higher compressive than tensile strength, curved walls are structurally more efficient. Curved walls may vary somewhat in cross section, including circular shafts and circular or elliptical arches. Elliptical shapes require a length to width ratio no greater than two, so as to avoid the development of tensile stresses (Shuster, et al., 1978). Design of a curved frozen earth wall includes concepts based on the Mohr/Coloumb failure criterion. The shear strength can be determined for representative frozen samples using the unconfined or triaxial compression tests. For relatively long loading periods, the friction angle will approach a value representative of the unfrozen soil. vyalov (1962) and Jessberger and Nussbaumer (1973) used this parameter in Eq (1) to determine wall thickness (rfag) for vertical shafts: ta ‘ N¢_1+11/(N¢-1) ...... . P I" 8 2C JNO (1) (1+ 81nd) ). (l - sin¢ )' where N (p . 4 is the angle of internal friction, P; is the horizontal earth and water pressure, r‘I and r1 are, respectively, the inner and outer frozen wall radii. When conventional methods are used, Sanger (1968) recommends that a factor of safety of 3 to 5 be included on either earth pressures or wall thickness. This is in addition to compensating for free standing time for the frozen wall system. Another method, proposed by Domke (1915), for determining wall thickness of a frozen shaft involves computation of the ratio - 2 1.2-J9 3+5: (2) r1 K K 10 where K is the uniaxial compressive strength, and other symbols are defined in Eq (1). This formula assumes that the frozen soil is in a partially rigid plastic, and linear elastic condition (Jessberger, 1982). If the frozen soil behavior were assumed to be totally plastic, the following equations (Jessberger and Nussbaumer, 1973) can be used for computation of wall thickness (r; - rt). Tresca criterion: P .3." ex? — (3a) 1' Rises criterion: (3b) r1 2 0c Mohr/Coloumb criterion: :3 ' exp 3.“. for IV 0. (3c) r1 2c Eq's (3a) and (3b) are applicable for vertical strain (5:) equal to zero, and Eq. (3c) for the angle of internal soil friction (¢) equal to zero. Equations (1), (2), and (3) involve relatively simple methods for determining the frozen shaft thickness. These methods require strengths that represent field conditions immediately after freezing and excavation. If the structure were to remain in place for some period of time, the design must be based on the long term frozen soil strength 11 corresponding to the service life of the structure. An expression for this strength (VYalov, 1962) is: 1‘1 (t/to) (4) where t is time, and 0.0 and to are temperature- and soil- dependent properties. In many cases, intolerable deformations may occur long before the failure stage. This behavior is common in frozen walls which are not braced for a period of several months after excavation. vyalov's (1962) method for computing the deformation of the interior wall of a frozen shaft is based on three assumptions: 1. The frozen soil creep behavior under uniaxial stresses is represented by: O " Aum (5a) where A.is both time- and temperature-dependent, and can be expressed as A -- w(0 +1)k c'A (5b) 6 is the absolute temperature below freezing, ( m ), ( A), and k are frozen soil creep parameters. Typical values for these parameters are listed in Table I. 2. The cylinder is very long in proportion to its diameter. 3. VOn Mises' criterion for plastic flow is used. For these conditions vyalov's equation for the inner wall 12 deflection is: A: om A A (1 - (a/b)2m (6a) a 2 where A =- 3'((m + ”/2.“ A (6b) The terms a and b are, respectively, the inner and outer frozen wall radii, n is a soil parameter (see Table I), and is defined in Eq (5b). A major problem with this equation, along with elastic solutions for design, is that their results, while safe, are very conservative, resulting in the construction of structures which are much more expensive than needed (Shuster, et al., 1978). The geometry of many projects dictates that a straight wall be employed. Straight walls usually fall into one of three types: gravity, braced, or anchored walls. The massive form of the straight gravity wall is more commonly used. Generally two to five times more soil volume must be frozen for a gravity wall as compared to a curved wall serving the same purpose (Shuster, et al., 1978). When designing a gravity wall, the conventional retaining wall analysis is used in relation to overturning and sliding. Safety in terms of overturning and sliding are the major design criteria and are used in lieu of any structural analysis. The effectiveness of these walls is related to the large amount of soil that must be frozen, and consequently they are extremely expensive. A third form, the straight anchored wall, requires a 13 highly sophisticated anchor design along with extremely careful field control (Shuster, et al., 1978). Shuster notes that the wall may be damaged or destroyed by water inflow during drilling for anchors and indicates that anchored walls are too sensitive to be used for most projects. The braced wall, an alternative to an anchored wall, serves the same purpose, but does not require such delicate and detailed construction techniques. Due to the nature of installing a braced wall, the procedures can be more labor intensive and can involve a complex bracing system compared to installing a gravity or curved wall. Complex structures can be defined as those incorporating combinations of curved and straight walls. They generally have unusual shapes to allow for obstructions such as underground utilities. Analysis of these geometric configurations can be complicated. Current design of complex structures is based on elastic material properties and rigid design concepts. These results are generally very conservative. Since most current design methods are conservative, and in some cases inaccurate, especially when irregular shapes are used, there is a clear need for alternative design methods. Several approaches, based on the FEM, have been presented in the literature. These methods incorporate techniques of analyzing frozen soil structures which allow for extended periods of time and handle the nonlinear 14 properties associated with these frozen soil materials. 2.2 Finite Element Method Use of the Finite Element Method (FEM) for designing frozen earth structures has been described by Klein (1981), 500 (1983), 500, et al. (1985), Jessberger (1982), Klein and Jessberger (1979), and Thompson and Sayles (1972). While the FEM has been widely incorporated into structural engineering design, its use for analyzing frozen earth structures is now in the preliminary stages. This is because most commercial FEM programs are not designed to handle the time-dependent creep behavior unique to frozen. soil materials. These problems include time-dependent deformation under load, and material properties that vary ‘with temperature, stress state, and time. While FEM programs are not readily available to handle these problems, several methods have been proposed in the literature which, when coupled with standard FEM design, should be able to analyze frozen earth structures. The review of current methods and proposals for using the FEM is centered around four major topics. These topics include a brief summary of the standard FEM analysis, time- dependent creep analysis, methods of handling materials with nonlinear or varying properties, and methods of analyzing frozen earth structures reinforced with different material (plastics, timber, or steel). A discussion of the current 15 literature on each individual topic will be presented, and then it will be shown how they can be combined in the analysis of frozen earth structures. The standard FEM analysis consists of dividing the structure into a set of simple subregions called finite elements. For each element, displacements are assumed to be linear functions which maintain continuity along the edges of adjacent elements. These functions are related to the displacement of particular points of the element called nodes. The internal strain energy for each element is then expressed in terms of the nodal displacements. By summing the strain energy for all elements, and subtracting the work done by external forces, the potential energy for the entire body is determined. By minimizing the potential energy with respect to the nodal displacements, a system of equations is developed to determine the unknown displacements. These equations are then modified to account for known displacements at the boundaries. After this modification, the total system of equations for the unknown displacements is solved. The element strains and stresses are then computed from the nodal displacements. While this is a gross simplification of the FEM, its procedure is generally used to analyze elastic structures where time is not a factor. When the behavior of a structure changes with time, the basic FEM.must be altered. Greenbaum and Rubinstein (1968) and Krause (1980) have shown ways of modifying the 16 standard FEM to compensate the time dependent deformation of pressurized thick-walled cylinders at high temperatures. This method was originally proposed by Mendelson, et a1. (1959). It consists of performing the analysis using the five following steps: Step 1: At time t=0, the elastic solution is determined using the conventional FEM. This will give the nodal displacements and stresses at the start of the problem. Step 2: Assume that the stresses computed in Step 1 remain constant over a very small increment of time, t. Calculate a creep strain over this time increment using a predetermined function. This function is perhaps the most critical step in the procedure. Several functions have been proposed for use with frozen soils and will be discussed later. Step 3: Add the new creep strain from Step 2 to the previously computed strain. (During the first iteration the previous strain will equal 0.) Treat the creep strain as an initial strain in the standard FEM and solve the resulting stresses. Step 4: Test the stresses against their existing values at the beginning of the time increment. If they are larger than a preset fraction of the existing stresses, repeat Steps 2 and 3 with a smaller time increment. If the stresses are less than or equal to the preset fraction of the existing stresses, go to Step 5. Step 5: Add another time increment and repeat Steps 2, 3 and 4. Continue in this manner until the desired time interval has been reached or until a steady state condition has been achieved. These five steps are common to most time-dependent FEM programs. Note that the function needed in Step 2 is critical. This is particularly true in frozen soils where a ‘variety of functions are required for different stress states, temperatures, and time increments. Functions of 17 this type have been recently proposed in the literature. A major problem in using the FEM to analyze time- dependent creep problems associated with frozen soil is that the material behaves differently when exposed to different states of stress. The most pronounced variation of these properties is the obvious difference between the stress- strain relationships in compression versus those in tension. This problem can be approached in different ways; the tensile value can be used for all stress states, giving a conservative value; a checking procedure can analyze each stress state and use the appropriate parameter; or an effective value can be used which is a function of both the compressive and tensile values. Regardless of the method used, its implementation occurs in a predetermined function in Step 2 of the given algorithm. As previously stated, this function is of extreme importance. One of the simplest approaches to selecting a function to compute the creep strain rate vector was proposed by Klein (1981). This method assumes that the frozen soil exhibits the same stress-strain relationships in tension as in compression. While this assumption is contrary to experimental results presented in the literature, it can be used in certain applications. For instance, in circular structures or arches where most elements are in compression, this assumption may yield satisfactory results. With this assumption, Klein has introduced a time hardening law which 18 can be used to compute the creep rate vector: (76) g; =- ACcC-loeB-l (01 - L; (02 + 03)) fig, - ACcC-loeB-l (o3 - A; (02 + 03)) (7b) ég - ACtC"10eB'1 (O3 - 3 (01 + 02)) (7c) cgys ACcC‘loeB‘1 (3/2) 012 (7d) where A, B, and C are material creep properties and o = 1/3 (01 +02 + 03), and (01), (q), and (03) are the major, intermediate, and minor principal stresses, respectively. 500, et al. (1985) proposed the use of three different functions for computing the creep rate vector. One of these is the Von Mises Yield Function. This function can model an element separately in compression or tension, using appropriate parameters from compression or tensile creep tests. However, in the FEM analysis, an element may be exposed to both tensile and compressive stresses. In this case, the VOn Mises Function cannot be used directly. Another method involves the Drucker-Prager Yield function which is capable of representing the multiaxial stress states. Creep parameters are needed from both tension and compression tests. A third function proposed by $00, the Modified Von Muses Function, introduces a set of weighting functions to compensate for the varying stress states. .After the initial procedure (Step 1) in the FEM, the stress state of each element is checked individually. Depending on the different stress states, a different modified function is used to 19 determine the creep rate for a particular element using effective creep parameters. A major advantage of this method is that the frozen soil creep parameters needed in the Modified functions can be obtained from uniaxial tests and effectively describe the displacements occurring at each node in the multiaxial stress state for all elements. OE_2<01P0.> p=f£ 0" (8a) 5 01 p ‘_ e 2 ( O ‘qec) CC 0C a i q I —S- (81)) X. 01 q Ct ’ z ( 0 Sb) bt be a 1 s a _ (8C) 2 01 S bC ne.£(°irn) {-11:- (8d) 2 01 r “C where (qf)=(o.t°), (e°)=(et), n=(nt), b=(bt) if (01) is tensile, . and b=(b°) if to.) is compressive. The creep parameters include (5:), (etc), (nt), and (bf) for the tensile state. For the compressive state they include (0:), (e °°), (n°) (b°) .nd represent the effective creep parameters. Thus far, the analysis of structures composed entirely of frozen soil has been discussed. It was noted that frozen soil is much weaker in tension than in compression. The design and construction of straight walls, particularly cantilevered walls, would result in a structure with close to half of the elements in tension. Reinforcing these tensile sections with steel or some other material would not only increase the stability of 20 the structure, but could greatly reduce the amount of soil that must be frozen. 800, et al. (1984) used the FEM to demonstrate the deflection of frozen sand beams reinforced with steel. The bond interface element was a modification of that proposed by Goodman, et al. (1968) for jointed rock analysis. Analysis of these beams showed that, up to certain critical stresses, the reinforcement can accept a large portion of the tensile load. When stresses reached this critical point, the bond failed and load was then transferred from the reinforcement to the frozen soil. Creep parameters needed to model load transfer at the steel/frozen soil interface in these beams were studied by Alwahhab (1983). Several variations of finite element analysis methods have been outlined. Using the FEM, structures with complex shapes and different materials can be accurately analyzed. For each elastic method, material properties needed include Young's modulus and Poisson's ratio. Programs modeling the time-dependent deformation of frozen soil must have a series of creep parameters to permit computation of the strain rate vector. Regardless of the computational method, the results can only be as accurate as the parameters used. This review will now focus on what parameters are needed and the current methods being used to determine them. 21 2.3 Material Properties To perform a design analysis prior to construction of a frozen earth structure, it is necessary to determine the material properties of the soil. These properties are required to predict the performance of the structure, and also to determine the loads which will act on the structure. This section will review the material properties needed, with attention directed to identification, mechanical properties, and test methods used to determine the mechanical properties of frozen soil. 2.3.1 Soil Description Assume that a series of borings have been drilled, samples recovered, and a summary exploration report has been prepared for the site. The most important factors in this report are the site geology and hydrology (Shuster et al, 1978). Soil stratigraphy should be evaluated so as to determine any possible problems such as aquifers or obstructions which could interfere with the placement of refrigeration pipes. Soil conditions at the bottom of the excavation should be closely evaluated. .An impervious bottom is desired to tie in with the frozen wall and eliminate the need for pumping water out of the excavation. The site exploration report can also be a quick reference as to what types of soil laboratory tests should be conducted. Site hydrology is often the deciding factor in the 22 design of a frozen earth structure. Sites containing coarse grained soils near a large body of water may have lateral ground water flow. This flow can be measured using a fluorine ion or radioactive solutions (Shuster, et al., 1978). Shuster, et al. (1978) further states that if ground water flows were greater than 1.5 meters/day, special provisions, such as additional refrigeration pipes, or closer pipe spacings, must be made prior to construction of the frozen earth structure. Conventional soil tests should be performed on samples recovered from the initial boring. These include unit weight, water content, mechanical grain size analysis, Atterberg limits, and unconfined or triaxial compression tests (Shuster, et al., 1978; Sanger, 1968). The unit weight and water content provide information on the degree of saturation of the in situ soil. Complete saturation is desired so that soil particles will be bonded on freezing, thus providing sufficient strength. Successful freezing projects have been completed, however, with soil saturation as low as 10% (Shuster, 1982). A grain size analysis indicates whether clean free draining sands are present along with the potential problem involving lateral ground water flow. Another complication, determined from.grain size distribution, is frost heave expansion potential. Frost expansion is generally negligible in coarse grained, free draining soils. As the 23 percentage of fine grained soils increases, frost heave will occur if the freezing rate exceeds the rate at which excess pore water can drain at the freezing front. Pressures created by frost expansion can create large forces which must be considered in design. .As mentioned in Section II, design loads can be determined using a conventional earth pressure analysis. This analysis is dependent on the soil strength parameters c andq». These parameters can be determined with standard, unconfined or triaxial compression tests. If deformation computations are required, values of Young's modulus, Poisson's ratio, and time/temperature-dependent creep parameters are required. These parameters can be obtained from unconfined or triaxial compression tests and creep tests on the frozen soil. As noted earlier, results of these tests are used in the conventional structural design of frozen earth structures. A.classification system suitable for both frozen and unfrozen soil conditions must be used for consistent description. The Unified Classification System (U.S. Army Corps of Engineers), the most common method of classifying unfrozen soils, is based on the results of a grain size analysis and Atterberg limits. An expansion of this system for frozen soils was introduced by Linnel and Kaplar (1966). This system divides the frozen soil into three major divisions. Each division has several subdivisions which can 24 be used to accurately classify the frozen soil. These subdivisions include: 1. Coarse grained, fine grained or highly organic soils, 2. soils having segregated ice not visible to the unaided eye, or soils having segregated ice visible to the unaided eye, and 3. soil, with ice inclusions greater than 25 mm in thickness. These soils are then classified as ice. Based on this initial site and soil information, a preliminary design can be conceptualized. In order to perform a more detailed and accurate analysis, the mechanical prOperties of the frozen soil must be investigated. 2.3.2 Mechanical Behavior Several material parameters, including Young's modulus, Poisson's ratio, and various creep parameters, are required for the FEM.in the analysis of frozen earth structures. The mechanical properties of frozen soil vary considerably with temperature, time and stress state. It is important to know which properties are critical in the FEM, and what effect time, temperature, and stress state have on these properties. One material property common to all FEM analysis is the elastic or Young's modulus. This parameter can be easily determined in the laboratory as described in Section 4.3 25 using a constant strain rate test. While determining a value for the elastic modulus is not difficult, it should be noted that test variables such as temperature, strain rate and total strain can affect the value. The effects of temperature on Young's modulus have been shown by Bragg and Andersland (1981), Haynes (1978), and Akagawa (1980). These studies all indicate values of Young's modulus increasing with decreasing temperatures, as summarized in Figures 2.1 and 2.2. The effect of the strain rate on the modulus can also be observed in Figures 1 and 2, and more specifically in Figure 3. All results show that values for the modulus tend to increase with increasing strain rate. Goughnour and Andersland (1968) showed the effect of true plastic strain on Young's modulus. .As shown in Figure 2.4, the modulus decreased with increasing strain. It can also be observed that temperature effects are consistent with previous results. Klein (1981) neglected these changes and used a constant value for Young's modulus. 800 (1983) adjusted the values of Young's modulus to correspond to the increased strain. The values of Young's modulus used were approximately two thirds of those determined under elastic test conditions. 800 noted that values of Young's modulus have less effect on deflections computed in FEM analysis when finer grids are used. While these test procedures have an effect on the value of the modulus, it is of greater concern what effect the 26 modulus has on the results of the FEM analysis. 800 (1983) has shown how variations of the modulus in tension and compression affect numerical results and has compared these variations with experimental data. Comparisons were made by comparing the ratio of the tensile modulus to the compressive modulus. Varying the ratio as much as ten times did not show a marked difference as shown in Figure 2.5. The reason for this slight effect is that the primary function of the modulus is for determining the deformation prior to a steady state stress distribution. Once this state is reached, the creep behavior is independent of the modulus. Another parameter needed in the FEM analysis is Poisson's ratio. Various methods for determining Poisson's ratio are discussed in Section 2.4.1. Poisson's ratio has been shown to vary with temperature, strain, strain rate, and time. The most pronounced variation of Poisson's ratio occurs with strain. Both Bragg and Andersland (1982) and Akagawa (1980) reported increases in Poisson's ratio with increasing strain. This trend is shown in Figures 2.6, 2.7 and 2.8. These figures also show an increase in Poisson's ratio with increasing strain rate and decreasing temperature. The effects of temperature are not as noticeable as are those caused by changes in the strain rate. Bragg and Andersland (1982) also noted that Poisson's ratio changed during constant stress creep tests. The ratio 27 increased during the first 100 to 200 hours and then stabilized. Higher constant stresses yielded higher values of Poisson's ratio, as shown in Figure 2.9. Changes in Poisson's ratio are influenced largely by dilation of the soil particles. Bragg (1980) noted that dilatency contributed to the creep resistance during all three phases of creep and accounted for values of Poisson's ratio greater than 0.5. Dilatency is more common in relatively dense coarser grained soils than fine grained soils. No information was found showing the effects of varying Poisson's ratio in FEM analysis. Poisson's ratio, however, is used in the same steps as Young's modulus and, therefore, effects of its variation would not be observed once the steady state creep deformation begins. As noted in Step 2 of Section 2.2, a function must be used to determine the creep strain during a particular time increment. The functions used by Klein (Eq 7) and 500 (Eq 8) both contain parameters which describe the creep properties of the frozen soil. These parameters are directly related to the soil parameters used by vyalov (1962) in his equation: c = null) (9) .A where A.is defined in E0 (5b), (9), (A );k and m are constants representative of the frozen soil. 800, et al. (1985) based his incremental function on a 28 power creep law described by Andersland, et al. (1978): n E : 5 0 ch (10) where ( g) is an arbitrary. strain rate, (ac) is a temperature-dependent proof stress. When the exponential parameter b is less than 1, soil behavior corresponds to primary creep, while b equal to 1 corresponds to secondary creep. The parameters for Eq (9) and Eq (10) are related as shown by Eq (11): Eml). c 3 ° (11a) tref A . O c 3 ....T... (Gkoo) (11b) A ‘ l. 9. - (11c) Am ' b " —- (11d) The equation used by Klein (1981) to develop the functions used in his analysis were based on vyalov's Eq (9)- 1/m 6‘ O + -2 ' son“) A (12) where sour) isthe elastic modulus at a particular temperature and other terms are as defined in Eq (5). As with the other material properties, the creep parameters are very sensitive to the test procedures used. 29 The most common test used to determine these parameters is the constant stress uniaxial creep test. Sego and Morgenstern (1983) show that the creep parameter A, as defined in Eq (5), increased with increasing axial stress, as shown in Figures 2.10 and 2.11. Klein and Jessberger (1979) showed that the parameter a decreased steadily with time during their tests. 800 (1983) varied the parameters used in his analysis and compared the results to experimental beam deflection data. Equations (9) and (11) relate the parameter A to the parameters n and b used by $00. A variation in these parameters can drastically affect the numerical analysis as illustrated in Figures 2.14 and 2.15. 50018 results showed that the computed beam deflection increased with a decrease in.03 and n, and an increase of (ti) and b, and vice versa. Soo's comparisons indicate that the parameters n and (ac) were the most sensitive in altering numerical results. In some frozen earth walls, structural reinforcement may be added for transfer and distribution of loads, particularly tensile loads. The adfreeze bond between frozen soil and a structural member anchors the reinforcement to the earth structure. This adfreeze bond is a function of ice adhesion to the structural member, mechanical interaction between the frozen soil and roughness of the structural element (Andersland and Alwahhab, 1982). As noted earlier, this interface was modeled by See (1983) 30 in the FEM using an element similar to that used in modeling jointed rock. The mechanical properties needed to model the frozen soil/steel interface are the initial bond modulus Cs, and the creep parameters (fig, (oug, n and b. These properties are related to relative displacement of a steel bar in a frozen sand sample (Alwahhab, 1983). The displacement of the bar was described by 0s “ (13) a; =cc t °sc where (g;) is an arbitrary displacement responding to a proof bond stress (on), and n and b are creep parameters for the bond interface. This model was used by Soo, et al. (1984) for determining deflection in a reinforced sand beam. Parameter values used are listed in Table 2. Andersland and Alwahhab (1984) reported that while temperature had virtually little effect on the creep parameters, it did affect the ultimate load of the system. The creep factor n was greatly influenced by the reinforcement materials used, as reported by Parameswaram and Jones (1981). A.summary of the different n values are listed in Table 2.3. 2.4 Soil Parameter Measurements The parameters needed to perform an FEM analysis have been described in Section 2.2. Before an analysis of a 31 particular structure can be performed, values of these parameters must be known for the soils involved. .A laboratory testing program.must be conducted to determine these mechanical properties. Test methods available for frozen soil are quite varied. The current methods used to determine these mechanical properties can be divided into four major categories: uniaxial compression, uniaxial tension, multiaxial compression, and multiaxial tension. Multiaxial tests will not be discussed as they were not required for the design of the current project. 2.4.1 Deformation and Strength The uniaxial compression test is the most common test used for determining mechanical properties of frozen soil. Its simplicity, compared to other tests, makes it available to most laboratories. The mechanical properties of frozen soil in compression, including Young's modulus, Poisson's ratio and creep parameters, can be determined using the uniaxial compression test. One form of the uniaxial compression test is the constant strain rate test. Strain rate, test temperature, and sample size and shape contribute to variations in the results from this test. These effects on the values of the material properties for frozen soil will be reviewed in this section. Strain rates used in the constant strain rate uniaxial compression test have ranged from as low as 8.1X10-7/sec 32 (Bragg and Andersland, 1981) to as high as 3.0/sec (Haynes, et al., 1981). Both Bragg and Andersland, and Haynes conducted tests on several samples to determine the effects of strain rates on test results. Both observed consistent increases in Young's modulus, with increasing strain rate. Bragg and Andersland (1981), using a burette, measured volume changes during the test by placing the sample in a triaxial cell filled with fluid. Using the volumetric strain, they calculated values for Poisson's ratio at various strain rates. Their results showed a scatter of data with no correlation between strain rate and Poisson's ratio. Studies to determine temperature effect on frozen soil properties using the constant strain rate uniaxial compression tests have been conducted by Bragg (1980) and Akagawa (1980). Results from both studies showed the effects of temperature on Young's modulus and found an increase in Young's modulus was consistent with a decrease in temperature. Akagawa (1980) and Bragg and.Andersland (1982) both used cylindrical samples with diameters of 5.0 cm and 2.89 cm and lengths of 10.0 cm and 5.78 cm, respectively. Axial deformation was measured directly using displacement transducers. Haynes, et al. (1975) and Haynes (1978) used dog bone or dumbbell shaped samples and based their results on behavior of the cylindrical portion of the samples. The 33 cylinder had a diameter of 2.54 cm and a length of 3.8 cm. Deformation of the total sample was measured using displacement transducers, and an analytical method was used to calculate the elastic deformation of the cylindrical portion. Bragg and Andersland (1981) reported that uniaxial compressive strength decreased slightly and the initial tangent modulus increased with increasing sample diameter (constant length to diameter ratio). Due to the expense of testing equipment, most researchers have only one test apparatus, designed for a particular sample shape and size, and results of this variation on the values of material properties are limited. The constant strain rate uniaxial compression test is an efficient method for determining the unconfined compressive strength, Young's modulus and Poisson's ratio. Bragg and Andersland (1982) and Haynes (1978) have also used this method to determine various creep parameters needed to model the time-dependent behavior of frozen soil. A more direct approach to determining these parameters is the constant stress uniaxial compression test. The constant stress uniaxial compression test involves placing the sample under a continuous state of uniaxial stress and measuring the corresponding deformation with time. Extensive studies using this test were conducted by Bragg and Andersland (1982), Eckardt (1981, 1979), Alkire (1971), and Andersland and Akili (1967). While this test is 34 primarily used to determine creep parameters, it has also been used to determine Young's modulus and Poisson's ratio (Bragg and Andersland, 1982; Akagawa, 1980). Variables which should be considered when conducting constant stress tests are the stress levels, time increments, test temperatures, and sample shape and size. One of the difficulties encountered when conducting this test is keeping the stress level constant. .As the sample deforms axially, the cross-sectional area increases. This must be compensated for by increasing the load. Bragg and Andersland (1982) measured the volumetric strain, determined the increase in area, and added small weights to maintain a constant stress level. Eckardt (1981) measured the lateral deformation with a series of displacement transducers and used a loading device which automatically increased the load with increasing cross-sectional area. Akagawa (1980) placed an electronic ”clip gauge” around the circumference of the sample and.measured the radial deformation, computed the increase in cross-sectional area, and increased the load accordingly. Different researchers have conducted constant stress tests at varying stress levels. Bragg and Andersland (1982) conducted their tests at stresses from 1140 to 1296 psi; Eckardt (1981) varied stresses from 574 to 8609 psi; Akagawa's (1980) stresses were from 65 to 1573 psi; and Andersland and Akili (1967) used stress levels from 36 to 35 675 psi. Bragg and Akagawa both investigated the effects of stress levels on Poisson's ratio. Their conclusions were identical, showing that Poisson's ratio was proportional to stress at low stress levels and stabilized initially at higher stress levels, but increased linearly with time. The duration of load used in testing varies considerably in the literature. Most tests are conducted until tertiary creep begins and the sample fails. Eckardt (1979) and Andersland and Akili (1967), however, used a step loading system and increased the load with time. Eckardt notes that creep rate during the secondary phase was not influenced by stress and strain history. Therefore, once enough data was acquired in the secondary phase to compute the creep parameters, additional loads can be applied, provided the sample is still in a state of secondary creep. By doing this, Eckardt (1979) states that the number of samples needed to accurately describe creep behavior can be reduced from 10 or 12 to 4 or 5. The effects of time on Poisson's ratio were noted by Akagawa (1980) and Bragg and Andersland (1982). Both reported that, at low stress levels, Poisson's ratio was independent of time, but at high stress levels it increased linearly with time. The test temperatures used during constant strain creep tests were not as varied among researchers as the stress levels. Akagawa (1980) used test temperatures as low as -30°C, while Bragg and Andersland (1982), Eckardt (1981, 36 1979), Akagawa (1980) and Andersland and Akili (1967) all used temperatures in the range of -15°C. This temperature appears to be the most common in the literature for constant stress tests. vyalov (1962) has shown that by lowering the temperature the creep rate was substantially reduced. In laboratory testing, however, the creep parameters obtained in the constant stress test are temperature dependent. Because of this, the type of construction freezing method should be determined prior to testing, as different methods result in different soil temperatures. The laboratory testing temperature should be as close to the expected field temperature as possible. The uniaxial compression test can be used to determine all the compression properties of a frozen soil needed in an FEM analysis. The constant strain rate test provides a quick and accurate way to determine Young's modulus. Poisson's ratio can also be determined, provided there is a method to measure either radial or volumetric strain. The uniaxial constant stress creep test is a convenient, but somewhat lengthy, method for determining these properties. 2.4.2 Tensile Behavior Frozen soil behavior in tension is very different from that in compression; hence, tensile tests are required to determine frozen soil tensile properties. The constant strain rate uniaxial tension tests are the simplest; 37’ however, load application requires special consideration. Many investigators have used the dog bone or dumbbell shaped sample. Loading platens are attached to the sample ends by screws or end caps frozen onto the specimen with load and deformation measurements taken on the cylindrical (gauged) center portion of the sample. The constant stress uniaxial tension test is less common. The most detailed work reported (Eckardt, 1981) used dog bone shaped samples, with screws used to transfer load to loading platens. The cylindrical portion had a diameter of 5 cm and a length of 15 cm. Two bands with dial gauges attached were mounted to the upper and lower ends of the cylindrical portion of the sample for measurement of axial deformation. Tensile stresses, ranging from 108 to 435 psi, were applied by a step loading system with tests conducted at several temperatures. Results of these tests showed failure strains in tension of less than one percent, compared to much larger strains at the same stress level in compression. Tests results showed that long term failure strengths ranged from one-third to one-fourth of the comparable long term strengths in compression. The constant stress tension test is an efficient method for determining the frozen soil creep parameters. Table 1 summarizes average values of these parameters from Eckardt's work. While published literature is scarce regarding the 38 constant stress uniaxial tension tests, the results obtained are extremely important in analyzing multiaxial stress conditions in frozen earth structures. 2.5 Standardized Developments Several test methods for determining the mechanical properties of frozen soil were reviewed in Section III. The effect of test procedure variations on material properties have been summarized. The test procedural variations normally include: 1. Strain rate (if applicable), 2. Load increments (if applicable), 3. Test temperature, 4. Confining pressure (if applicable), 5. Sample size, 6. Sample shape, and 7. Test machine stiffness. While no standard test method for frozen soils has been adopted by organizations such as the American Society for Testing and Materials, or the American Association of State Highway and Transportation.Officials, many trends are appearing in the literature. While these trends are not designated as official standards, they appear to be "generally" accepted. The International Symposium on Ground Freezing (ISGF) working group has proposed some test procedure recommendations in an effort to begin the development of standardization. Its recommendations will be outlined in this section. 39 With no standard strain rate for compression or tensile testing, it was observed that strain rates in the range of 1x10T/sec to 1X104/sec are quite common in the literature for constant strain rate uniaxial tests. Triaxial test strain rates appear to be on the lower end of this range. The ISGF working group recommends a strain rate of 1.66X104/sec be used for uniaxial compression tests. Sanger (1968) advised that a rate of 5.5X104/sec be used on uniaxial compression tests to determine design parameters for frozen earth structures. Load increments used in the constant stress creep test vary in the literature. Most researchers used applied stresses varying from 1000 to 2000 psi. .Although some studies had values on both sides of this range, all used at least one load within this range. Bragg and Andersland (1982) cite the need for common test procedures for determining long term strength. This would permit realistic comparisons between material properties of different soils. The ISGF working group recommends that load increments be functions of the uniaxial compressive strength q. For tests lasting less than 100 hours, it is advised that the loads be 0.7q, 0.5g, 0.4q and 0.3q. If the tests are to be run longer, it recommends loads of 0.5g, 0.3g, 0.2g and 0.1g. Variation of test temperatures is not as common as other procedures. As mentioned in Section III C, most tests are conducted between -10°C and -15°C. Since greater 40 deformation occurs near the freezing point, tests conducted in this range would give a lower strength limit for design criteria. The ISGF working group suggests that tests be conducted at temperatures of -10°C and -2°C. They note that temperature variations should be limited to 0.2°C for samples tested at -10°C. One of the few test procedures that appears to be common in most compression tests is the use of cylindrical shapes. Convenience and the fact that most commercially available test equipment is designed for cylindrical samples is the reason. Tension tests were run exclusively on dumbbell or dog bone shaped samples. This shape is the most practical for load application. It also reduces stress concentrations which may occur in testing (Mellor et al., 1984; Hawkes and Mellor, 1970). These sample shapes were also endorsed by the ISGF working group (Sayles, et al., 1987). Sample size is also limited by test equipment. .All procedures reviewed used samples with diameters ranging from 2.5 to 10.0 cm and lengths generally two times the sample diameter. The ISGF working group concurs, but stipulates that sample size be a function of grain size. It advises that the minimum diameter should be at least ten times the maximum particle size, and either 5.0 or 10.0 cm.diameters be used when the soil particle size is not a controlling factor. 41 The need for standardization continues to increase as more engineers conduct tests in this field. The National Research Council of Canada is in the process of developing standard test procedures for laboratory testing of permafrost. This guide is not expected to be complete for several years (Heginbottom, 1985). As controlled ground freezing in construction continues to grow in popularity, and the exchange of information continues, the demand for standardized test procedures will increase. Table 2.1 Constants for vyalov's deformation equation (from Andersland, et al., 1978) m for e =10°C Soil m A MPa'h/°C‘ Suffield clay 0.42 0.14 0.73 Bat-Baioss clay 0.40 0.18 1.25 Hanover silt 0.49 0.07 4.58 Callovian sandy loam 0.27 0.10 0.88 Ottawa sand 0.78 0.35 44.72 Manchester fine sand 0.38 0.24 2.29 Table 2.2 Creep parameters from pullout tests (from Alwahhab, 1983) Temp. Eu (cm/min) a” (kg/cmz) n -1o°c 2.54x10“ 1.82 2.75 Table 2.3 n Values for different pile types at -6%: (from 800, et al., 1985) Material n B.C. Fir 4.48 Concrete 4.63 Painted Steel 6.02 Creosoted B.C. Fir 5.36 Unpainted Steel 10.23 H-Section 10.08 R 1.20 0.97 0.87 0.89 1.00 1.00 mnw. TANGENT uoouws (ON/M2) 10 10" 42 I I T I I F I I r “I I I T I F I Tj 1 1 4 , E-txtOE-J/SEC .. .I " E-ixios—i/‘ssc d E-iuios-slscc v? E-ixios-a/szc .I 1 hence-7m / —i -—< ‘ 1 I J - I J ‘ I i 3 “I l - .1 I I I I T r1 I I I r I I I I IWI 2 1 1 0 10 DEGREES BELOW FREEZING Figure 2.1 Initial tangent modulus vs. degrees below freezing (Jessberger 1981) was TANODIT uoomus (ON/m2) 43 am A I 22.”:- 2 zone: 1 37.531 —( 1w: 0 .1 II ’1 Iw-n .. 3m”) ‘ 1 T t q Ell-r ‘ fl . t Mum/0(Q 1 O mun/0(8) “-1 1 * O Wan/0(6) "I “Sq/0(0) inn-31 n wintuit”I)”IIrlrrunrllnll[WHITHI[Tllurlltrrlnnnl m 10.00 zone seen «an M use WM(C) Figure 2.2 Initial tangent modulus vs. temperature for Fairbanks silt (Haynes 1978). INITIAL TANGENT MODULUS (ON/m) 44 10 W I ITIIIII I I IIIIIII I I IIIIIII I I IIIIII] I I ITIIII -I -I -( a-I -( -I q c! --i -i 1 j j Z . .. -I ‘0‘. I I I IIIIII I I I IIIIII I I IIIIII] l l IIIIII| I I IIIIII 10" 10" 10" 10" 10" 10 AXIAL STRAIN RATE (t/SEC) Figure 2.3 Initial tangent modulus vs. axial strain rate (Bragg and Andersland 1981). 45 10'_ I I I IITTII I I TIIIIII I T IIITI Z 1 -I -I 3 I I I d -1 £210 a : m 1 d D - d S .- 8 ~ -+ 2 .J . .m d o -I 2 £32 ‘ - 10'- \‘K I 3 . q - 'l "l fl - 10‘ I I IIIIIII I I llllII] r I IIIIII 10“ 10". 10" 1 TRUE PLASTIC AXIAL STRAIN In/In Figure 2.4 Young's modulus vs. true axial strain for ice and coarse sand—ice samples (Goughnour and Andersland 1968). YOUNG'S MODULUS (PSI) 46 10. 1 I I rTIII] I I I lTlll] I I I IIIII 7 - + C1 0‘ O 54.6% F Sand 0 T=-705C n 9 57.92 F gand + q a T=-7.5C 0 n O 10. I I I IIITI] I I I ll1Il]-‘ I I I IIrr 104 10" 1O 1 TRUE PLASTIC AXIAL STRAIN in/in Figure 2.48 Young's modulus vs. true axial strain for fine sand-ice samples (Goughnour and Andersland (1968). wucmu AT Mia-SPAN 0N.) liiijiunllIIIJJlIiJlJiIIJIInilljnjllnii E 5 0.0100 47 R = Moduli Ratio (tension/compression) m 2.00 Figure 2.5 ITIIIIjlllilllIF1UWIIIIIIIITI[leIIIYITIIITIIIlrI 400 can can Ida: ms (HOURS) Comparison numerical results based on the power creep law with different values of moduli ratio (800 1983). TANGENT POISSON 'S RATIO 48 ‘010..II'lllllljllTTlI['1III—IIIlljfirrifirrllIlIlTillllllll1.1 d an I IOE-S/noc : = : 1,00: 108-6/00: _ 030-5 2 E .1 '4 1 : 10E-7/uc : I . 0.80: .. d .1 5 : 2 -1 q : 0.70-3 . “I -1 g : 0.50: 2 2 I z : 0.50:1 : -I 0.40 I 0'” [IIIIIIIT1TIII1I7FITTIIlTrlTIIIFrllUIrI—TIUIITFTII 0.00 2.00 4.00 6.00 8.00 10.00 AXIAL STRAIN (s) Figure 2.6 Tangent Poisson's ratio vs. axial stain, constant strain rate compression test at -2 (Bragg 1982). TANGENT POISSON'S RATIO 49 1.20 dfi I I I1 Fl I I I I I T I I I 1f I I I I I I I I I‘ I I I I I ... 3 l I 3 1.00 1 I - -1 3 A : 1 * : .1 ..4 .. (180 j 2 "I _ .1 I-i 1 3 i 1 CL60 j 1 -I -4 I 3 _, II (L40 1 i ‘ Nominal Strain Rate « En = 1.19 x 10'4/3 I 0.20 I “-1 .4 q 0.00 [IT I I I I II I [I‘IfiI I I I I I F] FI’I I I I rrrrl I I Ij I I I I 0.00 2.00 4.00 5.00 8.00 AXIAL STRAIN (as) Figure 2.7 Tangent Poisson's ratio vs. axial strain, constant strain rate compression test (Bragg 1980). 50 sample (Akagawa 1980). an q fi u-I " “30(3) zoo-1 3 -I&(c) fi q no— d —I .I : -mwm I q «n- I d .1 I ”-4 I oIrTIIII—IIIIIIIIIIIIIIIIIIIIIII[IIIIIIIII up u» u» u» nuismmuu) FlGure 2.8A Stress-strain curves on selected POISSON'S RATIO 0.00 0.00 mm 030 0.00 51 in11111111111441141111111111IIIJIIIJIIJIIIIIIIII -JOC ~15 C -7.5 C 00m Figure 2.88 Stress-strain curves on selected 4.00 AXIAL STRAIN (s) “Om sample (Akagawa 1980). IIIIIIIIIrrrTIIIIIT1IIIIII—lITjIIrljfillT wmmnmcswmw) 52 .1 IO r -30c 1 .4 -I 4’ J : .705°C 1 fi 1 -15°c .1 4 fl and fi q .I -I IIIIII IIIIIIIIIIIIIIIIIIIIIIIIIIIII «will uh an um um Anmsmuma) Figure 2.8C Stress-strain curves on selected sample (Akagawa 1980). TANGENT POISSON'S RATIO 53 0-9 I I I I I I I I I I I I T I I I I I j r I I I’j I I I I r I I I I I .. 1 1 -I 2 a % O = 0.893 MN/m O = 0.857MN/m2: 1 . _I -I - -I 0.7 ~ I ‘ 2 I ‘I 0.785 MN/m _1 I . 0.5 l j j I :1 — —- — —Computed A .1 d ‘ 1 j 4 - I 0.3 a I _1 '4 I I Z A I 1 .1 d 001 q I I I T I I I I I I I I I IT I I I I I I I I I_I I I I I I r1 I I 0 200 400 600 TIME. t(min.) Figure 2.9 Tangent Poisson's ratio vs. time, constant stress compression (creep) test (Bragg 1980). 0.10 54 LJIILLLILLLJ4IIIII[lllllllLlLILi1J__LlJll m-0.052-0.00033 IIIIIIII Figure 2.10 IIIIIIIIIIIIIIIIIIIIIIIIIIIIIII I“ moo M M Wan-(I'D) Applied stress vs. m parameter of constant stress experiments (Sego and Morgenstern 1983). 55 am a . a A = 0.00210 uni; / 21 /. 1 ’1/ 1‘ /" uni: , A(Z/h) 2 //i' I / 2 / NM- 1 I . A ./ . m1 , 2 / , - / d / 3 m rIIllII‘IIIIIIIIII‘IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII mm) Figure 2.11 Applied stress vs. a parameter of constant stress experiments (Sego and Morgenstern 1983). PARAMETER A 56 10-‘: I l I I I I I I] I I I I I r1: ‘ 2 1 A 1 1 10 -53 '5 2 1 - ’I 3 A = 22/03 = (mmZ/Nh) 1 I 1 10"“: ":1 1 3 3 I -I -I 10 '73 1 : 3 I 1 IO .. I . I I I I I I II— I I r I I I 3 10 1 2 10 'HME t (h) Figure 2.12 Parameter A vs. time (Klein and Jessberger 1976). nuuwmcnuwauxh) 57 11111111111141111111111411111 610 WufiI- mmm M MIC!) ”an“ m IIIIIIIIII]IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII Figure 2.13 1m am an M qumu» Comparison of numerical results based on the power creep law with creep parameters from Eckardt (1981) and varying parameter n (500 1983). ummmnunwnkswamq 58 can q uno~ : “by” _ manhunt-n _ «nu-no.1) q .I «no— q d . munc- q .1 0.100- .“ lllllIIlII'lIllllIII[IIIIIIIFIIIIIIIIIIIIIIIIIIIII um {um mun mun Inn awn nuzmanw Figure 2.14 Comparison of numerical results based on the power creep law with creep parameters from Eckardt (1981) and varying parameter b (800 1983). 59 m m Decrease OC by 15% a i a gun With Creep Parameters g from Echardt (1981) DAN Increase 0c by 502 m 'IITIIIIII]IIIIIIIIIIIIIIIIIIIlIIjIIIIIIIIIIIIIIII on 10.00 M m M nuimunn Figure 2.15 Comparison of numerical results based on the power creep law with creep parameters from Eckardt (1981) and varying parameter 0c (500 1983). m KI ”-9014 (h) LIJJIIIJJJJ[LllJJlLlullllJlJlllll'llllJllllI p 5 60 Figure 2.16 Increase éc by 507 With Creep Parameters from Echardt (1981) Decrease BC by 50% M am an an “IEOQUID Comparison of numerical results based on the power creep law with parameters from Eckardt (1981) and varying EC (800 1983). unsmunmwnbswuaq 11111111l11111114414441144111114441111 61 Experimental Results P=148 leo’ -60C Experimental P=153 lbs., -10°C Average Creep Parameters 153 lbs., -10°C r 148 lbs. , -6°C m IIIIIIIIITIIIIIIrII[IIIIIIIIIIII1IIfiIIIIIIIIIFIII m an an no no M 1‘ M) Figure 2.17 Comparison of numerical results for the power creep law with average creep parameters of tension and compression compared with experimental results (800 1983). III. PRQQEQT DE§I§N PARAMETER§ The project discussed in this dissertation is referred to as the Cross Town (CT) 8 dropshaft and approach structures. These structures represent a portion of the entire Cross Town Interceptor System and Inline Pump Station which are components of the Milwaukee Metropolitan Sewer District's Incline Storage System. This system, when completed, will be capable of providing a combined storage volume of approximately 650 acre-feet of storm water, eliminating sewage overflow into Lake Michigan. The Cross Town Interceptor consists of approximately four miles of a 30-foot diameter tunnel and 2.5 miles of a 17-foot diameter tunnel. The invert elevation of the tunnels vary between 275 and 345 feet below ground surface. 3.1 Site Description The CT-B dropshaft and approach structures were constructed on a 12 acre site on the south bank of the Menomonee River in the proximity of the Menomonee and Milwaukee River junction. The entire Milwaukee area is in the Eastern Lakes section of the central lowland 62 63 physiographic province. Within Milwaukee County, ground level elevations range from 580 to 830 feet (MSL). The area is essentially flat with gently rolling hills. Topography of the area is composed of a variety of bedrock, glacial land forms, and changes caused by lake deposits, erosion by streams and rivers, and man-made alterations. 3.1.1 o c P ile Glacial till is the most abundant soil strata reported on all boring logs for this project. The tills show no consistent stratification and are composed of a dominant clay matrix with varying quantities of silt, sand, gravel and boulders. The geologic report presented with the MMSD Contract Documents indicates that the till is presumed to be mainly a basal deposit of the last stage of the continental glaciation. The tills are reported to contain many small to large bodies of more granular soil that apparently formed near the margin of the ice sheet with some overlain and, in some cases, interbedded with fine-grained and stratified soil deposits that formed in melt-water lakes near the ice front. The thickest of these lacustrine deposits are found in the lowland areas. Most of the river valleys in the area contain Holocene deposits which overlie glacial deposits. The report states that these deposits include alluvium along most streams and a thick deposit of estuarine materials formed in the 64 Menomonee and Milwaukee River valleys during a higher Lake Michigan water level. Thickness of the various strata range from several to more than 200 feet. The average strata thickness is less than 100 feet in the area away from Lake Michigan, to more than 100 feet in areas closer to Lake Michigan. This would indicate submerged preglacial or glacially deepened valleys or end moraines at the construction site. The bedrock in Milwaukee is composed of a thick sequence of uniform dolomite in the Niagaran series. This rock is overlaid by Devonian rock. Ordovician and Cambrian rocks range from a few hundred to more than 1,000 feet deep in the Milwaukee area. The Bedrock surface in the area exhibits details of glacial erosion with east-west trending valley with a steeply sloping north side. The valley floor slopes gently to the east, and apparent depressions are visible at two locations where coring was done in preparation of the contract documents. Coring conducted for the exploration phase showed that the uppermost rock levels included extremely small amounts of weathering. Rock discontinuities were more evident in rock near the soil interface, and exhibited relatively higher permeabilities. 65 3.1.2 Soil Profile For design of this project, several borings and related geotechnical data were provided by the contract documents. The possibility of borings not being representative of actual conditions existed since considerable ground disturbance may have occurred as a result of previous construction, earlier failure of the dropshaft, and extensive grouting operations in the area. Though the geologic strata and related properties vary, several borings were analyzed, and for design purposes were incorporated into a generalized soil profile as shown in Figure 3.1. While geotechnical properties were the key factor in selection of ground freezing for construction, the economic feasibility gained by using ground freezing to provide temporary support was also considered. The geotechnical properties were used to determine lateral earth pressures acting on the proposed frozen earth structure(s). The lateral pressure diagram furnished with contract documents is illustrated in Figure 3.3. 3.1.3 ground Water Conditions At the time of soil exploration, the ground water table was at a depth of approximately 9.0 feet as shown in Figure 3.1. Assuming a static ground water table elevation, the existing ground water conditions appeared favorable to ground freezing for support of excavation walls. The boring S. 66 logs (Figure 3.2) showed an extremely permeable soil stratum at 60 to 70 foot depths. Any ground water gradients across the site could result in excessive ground water velocities through that particular stratum and which would be detrimental to the freezing process. Piezometer measurements continued to show the existing ground water level at approximately 9.0 feet below the surface, ensuring saturation of subsurface soils for design purposes. 3.2 Required Excavation Limits The CT-B dropshaft and approach structure is one of six similar structures designed primarily to transfer storm runoff from surface collector systems into the large diameter deep tunnel. The CT-8 dropshaft was designed with an inside diameter of 18.5 feet, extending to a depth of 280 feet. Of this 280 feet, 165 feet would be through water bearing soils, while the remaining 115 feet would be through rock. Each of these structures has a vortex type entrance, an approach box structure, and a trash rack structure. The trash rack structure is located near the ground surface. It is composed of a de-aeration chamber and air vent, and a connecting tunnel at the interceptor level. These structures are illustrated in Figure 3.2. The excavation required for construction of these structures required two separate phases, each with two 67 different methods of earth support. The dropshaft was to be constructed in a circular excavation with a diameter of approximately 20 feet and extending to bedrock at a depth of approximately 165 feet. Preliminary construction requirements and schedules required that the dropshaft be constructed first, and treated as an individual structure during the first phase of field activity. The trash rack structure has maximum rectangular dimensions of 20 feet by 20 feet with a required depth of 65 feet. From this structure, an approach structure would be constructed for the purpose of permitting effluent to flow into the dropshaft. While the rectangular shape of this structure was constant in plan view, the depth increased during transition to the dropshaft. The approach structure had a width of 12 feet, with varying depth, as illustrated in Figure 3.3. Note that these dimensional requirements are the minimum required to build the structure. The frozen earth wall geometry required to provide these minimum dimensions are described in Section 3.3. 3.3 Frozen Earth Wall geometry The trash rack, transition structure, and drop shaft form a single structure to be built in what would appear to be best suited for a rectangular excavation. Lateral earth support for such a structure using ground freezing would 68 require essentially straight parallel frozen earth walls. Such walls, as discussed in Chapter II, would be subjected to very high tensile stresses and bending moments. ,Most conventional frozen earth structures are typically circular or elliptical in shape, creating a structure which is typically in a state of total compressive stress. To enclose this particular excavation in a single elliptical cofferdam would have not only required an excessively large number of refrigeration pipes and related freezing equipment, but additionally a large volume of soil to excavate. Such measures would have been economically unfeasible and cost prohibitive. In order to minimize the frozen wall length and keep compressive stresses at acceptable levels, a series of four separate, but interconnected frozen soil structures were selected. Each of these structures could be curved compressive structures if they were constructed independently. These four structures each enclosed a 20 foot diameter dropshaft to be frozen to bedrock, a depth of approximately 180 feet. Immediately adjacent to the dropshaft, a frozen earth structure was designed to provide support for the transition structure (designated cell 1) during construction. Cell 1 involved two elliptical structures with a major axis of 40 feet and a minor axis of 39 feet. The north end of this ellipse intersected the dropshaft. This particular 69 geometry permitted the east and west end walls of cell 1 to react against the dropshaft, breaking continuity of the ellipse. Cell 1 extended to a depth of 140 feet. Cell 2, a second elliptical structure with major and minor axis of 42 feet and 40 feet respectively, was tangent to the south end of cell 1. Cell 2 was designed to provide wall support for the excavation required to construct the entrance to the approach structure. The depth of this structure was approximately 100 feet. Cell 3 was a circular cofferdam with diameter of approximately 35 feet, extending to a depth of 100 feet. The trash rack structure would be constructed within this excavation. The north end of cell 3 was tangent to the south end of cell 2. .After freezing and excavation of these separate frozen earth wall structures, subsequent construction involved connection of the separate chambers/structure. This was accomplished by mining through adjacent walls of cells 1, 2 and 3, and through a section of the frozen wall at the drapshaft. .A composite, three dimensional illustration of these structures is shown in Figure 3.4. A.major concern throughout the design phase was development of tensile stresses along the perimeter of ”windows” formed by mining between the cells at points of tangency. These areas, referred to as buttress sections, would ultimately support the reactions created by the 70 imposition of loads on two separate elliptical structures. Methods for compensating for stress states during the design phase are discussed in Chapter V. The principal criterion used for selection of the geometric sections was economy, safety, and cost effectiveness during the initial phases of the project. Once the wall geometry had been selected and preliminary cost estimates made, a comprehensive engineering analysis was required to determine if the proposed wall concept was structurally feasible. \l ..- LOCATION 2 2nd and Sccboth St. E I: t WATER CONTENT. % UNDRAINED SHEAR STRENGTH : ..I 3 Milwaukee, Wisconsin 1: gm :3 . 0 ,1 W -c72 >0 Plum: uoula KIPS PER son I g a. m 3 “ LImII mum! len I; > 2 g <§ DE, 1 _ 1 0,5 1.0 1.5 20 2.5 g 0, 3 O :0 5:; v v I I I I I In WROPASULS SURFACE EL 5’ 2 3.. 20 40 so rs so A IN m —— Fill Soils _ Sands and clayey silt: too 24 I ' erratic to generalize —‘ 17 10‘ , — Post Glacial Estuarine Silts and —I silty Clays/clayey silt: with _ Organics (NH/CH) . 20- 5 I - - A O _ 3 76 9 ‘O- O 0 o D '_ 3 - 30" XI -— 7 — 7 0 ~ - .- —— 4- L 40. 6 I—I _. 21 A __ 13 S O 9 40l- 100+ _ ‘fl Polt Glacial Alluvial Sand and 80 12 Gravel with Silt (SP/SM, GP/GW) u -— III 52 . 7O 33 Glacial silty, sandy Clays 33 ‘°"' (ML/CL) _ J2 ' 80' _ ‘6 IV 50 >—I . 90 ‘ I" —- 62 ‘00 I9 124 __ ‘ ‘_¢ 33 —I 38 SAMPLER: 2 in. Split Barrel ’ "flagcmtmmo . o moon! mm COMPLETION DEPTH . 166.0 Ft. ‘ Lhcomolmvod-wntm Tun-w Com 'Oqun DEPTH TO WATER IN BORING : 9 .0 DRILLING METHOD : Wet Rotary Figure 3.1 Generalized soil profile Q N LOCATION 2 2nd and Sccboth St . WATER CONTENT. % UNDRAINED SHEAR STRENGTH '1 x . w ~ ‘n "1"“ m” ”“3"“ PIum: u a stpsnsos‘r DEPTH. FT 'b PASSING NO, 200 SIEVE 5.5 M51. Glacial lacustrine Sand lacustrine sand and silt Deposit: Top of Rock MPL R: . _ - STRENGTH LEGEND SA E 2 in Split Darrel . ”momma Comm-ulna COMPLETION DEPTH : 166 . 0 Pt A Unconwhauod-undnlm Inn-m Commune" DEPTH TO WATER IN BORING : 9.0 DRILLING METHOD: Wet Rotary Figure 3.1 (continued) Generalized soil profile O I 73 SURCHARGE ' PRESSURE / 50‘ HYDROSTATIC EARTH ‘I PRESSURE PRESSURE A m l Lu: 100— I TOTAL PRESSURE I 1' I TOP OF ROCK .. I CT-5/6 AND CT-8 CL 150 -1 3 I I775]? 77E” " TOP OF ROCK I cm 200 —W 250 l I I I I I I I I 0 1 2 3 4 5 6 9 10 PRESSURE, P (TSP) Figure 3.2 Lateral earth pressure diagram as presented in the project specifications. 74 \N . ISL—3 Trash Ruck \_J Transition Structure (60-90 ft deep) Drop Sinai—L ¢\ 135 f3; (nppro:<.) / 4‘] F I Figure 3.3 Proposed underground structure as shown in the contract documents. lM)fL 75 fi-— _.__ v C” J c .- flh~u_‘:_“_uu _.-« - -- _ A — ,-' Shaft Cell 1 Cell 2 Cell 3 Geometry was formed by installing 3 inch diameter steel pipes on approximately 3.0 foot centers. Figure 3.4 Three dimensional illustration of proposed frozen earth structure(s). IV. MATERIAL PROPERTIES Mechanical properties of frozen soil provide a basis for predicting its behavior and in turn the behavior of the frozen earth structure to be designed. Uniaxial compression and tensile behavior, including measurement and properties, are described in the following sections. 4.1 uniaxial compression Tests Structural analysis and design of a frozen earth structure, including its estimated design life, requires information on the strength characteristics of frozen soil in compression. These characteristics include the elastic modulus and the timeItemperature-dependent creep parameters. The elastic modulus permits computation of an initial deformation occurring immediately after excavation when the initial "at-rest" soil pressures would be acting against walls of the structure. The time-dependent properties permit computation of both structural deformation with time and life expectancy of the structure based on the internal stresses developed within the frozen earth mass. Two different types of compression tests were conducted on the undisturbed samples recovered from the boring. A 76 77 constant strain rate test was completed to determine an approximate value of the elastic modulus and constant load creep tests were conducted to determine the time-dependent creep behavior and parameters. 4.1.1 Qompression §ample Preparation The soft consistency of site materials (see boring report) made extrusion of reasonably undisturbed and intact 'samples from shelby tubes extremely difficult. Freezing of samples prior to removal from the tubes provided a solution to this problem. The tubes were covered with insulation, as shown in Figure 4.1, to permit freezing in one direction along the axis of the sample. This avoids.entrapment of an unfrozen section within the sample followed by nonuniform expansion during final freezing. The samples were then placed in a cold room at -25°C in an effort to "quick- freeze" the samples, thus reducing moisture movement and the possibility of ice lens formation. The samples remained in the cold room for approximately 24 hours. .After freezing, the tubes were cut into six inch lengths using a standard pipe cutter and then cutting the frozen soil with a sharpened hacksaw. The frozen samples were extruded from the tubes using a hydraulic jack and as {little pressure as possible to remove the soil. Occasionally, it was necessary to place a warm, wet towel around the exterior of the tube while applying this pressure 78 so as to thaw and reduce any bond between the steel tube and the frozen soil. This minimized damage to the soil sample. After extrusion, the frozen samples were trimmed to four inch lengths in the cold room environment. Trimming was accomplished by placing each sample into two inch diameter soil miter boxes and trimming with a utility knife and straight edge. The procedure was expedited by occasionally heating the tools with a propane torch. On completion of the trimming process, each sample was measured, weighed, wrapped in cellophane, and stored in an air-tight plastic container for no longer than 20 hours prior to testing. .All samples for compression testing were prepared in the same manner. 4.1.2 Equipment and Test Procedures The compression tests were conducted in modified triaxial cells as illustrated in Figure 4.2. These cells were designed so that refrigerated ethlyne glycol fluid could be circulated through the cell. This fluid was cooled to approximately -12°C, and then warmed to -10°C using an electronically controlled heating apparatus. This technique permitted a high degree of temperature control. During testing, the cell exterior was wrapped with insulating rubber to reduce any effects of ambient air temperature changes. The loading piston was connected to a lever arm (Figure 79 4.3) which permitted load multiplication by a factor of 10 or 20. A.bubble level, mounted on the lever arm, helped ensure more uniform adjustments prior to each load application. A screw jack supported the lever arm prior to loading. .After placement of the desired load onto the load hangers the jacks were slowly turned permitting a smooth application of the load to the sample. Sample deformation was measured using a displacement transducer (LVDT). The LVDT was connected to both an incremental data logger, and a strip chart recorder for continuous, but somewhat less precise measurement. Data from this test was presented in a Strain vs. Stress plot (Figure 4.4), with the slope representing the elastic modulus E. The equipment necessary for this type of test was not readily available, creating the need for altering somewhat the procedure defined in Chapter II. The available equipment did not have the capability of compressing the soil at a prescribed strain rate. In order to acquire the stress-strain relationship needed to determine the modulus, a series of increasing loads was applied to the sample. The load was sustained only long enough to permit the primary loreep to occur. The applied stress and corresponding stains are illustrated in Figure 4.4. As shown in Figure 4.4, the straight line portion of the curve is located between 10 and 38 ksf. Closer 80 examination of the strip chart recorder data indicated that the sample was deforming at a rate close to 4.01:10'5 inches/minute. The slope of this line yields an elastic modulus of 1147 ksf. This value was used in subsequent FEM analysis. This test method may not be the most desirable for determining the elastic modulus, but it did permit use of available equipment. The value was very comparable to values reported by Klein (1980), for similar frozen soil materials at comparable strain rates. 4.1.3 Time Dependent Qompression Tests .A series of three creep compression tests were performed on individual samples taken from the same two foot shelby tube. The stress levels, 29.34, 32.5, and 41.7 kg/cmz, gave plots of time versus defamation as shown in Figure 4.5. These tests permitted evaluation of VYlov creep parameters (b and n) in compression as shown graphically in Figures 4.5b and 4.5c. These parameters are presented in Table 4.1. To determine the expected life of the frozen earth structure in terms of structural integrity, the compressive strength of the frozen soil was extrapolated from the plot of Time vs Reciprocal of Stress, illustrated in Figure 4.6. 4.2 uniaxial Tension Tests 81 4.2 uniaxial Tension Tests As with the compression tests, initial tension tests were conducted on undisturbed samples extracted from shelby tubes. Both constant strain rate and time-dependent frozen soil creep tests were conducted for determination of tensile properties needed for analyses of the frozen earth structure . 4.2.1 Tensile Sample Preparation Initial plans called for samples to be frozen in the tube and extracted in the same manner as those for compression tests. Upon extraction of samples visual observation showed many voids along the sample sides making them unsuitable for tensile testing. The possibility of redrilling and retrieving additional samples was cost prohibitive, making it necessary to remold the soil from the two tubes and forming new samples. Moisture content and samples density measurements were determined from various competent sections of the shelby tube samples. The samples were then shredded with a grating apparatus and oven dried at 110°C. After drying, the samples were broken down into a fine powder at which time a measured quantity of distilled water was added to return the material to the original moisture content. A two-inch section of shelby tube was then measured and volumes were determined. Portions of the moist soil material were 82 weighed to correspond to the tube volumes so as to prepare samples with densities corresponding to the original samples. The moist soil was compacted using a Harvard miniature compaction apparatus. A trial and error procedure was implemented as it typically was not possible to achieve the desired density on the first attempt. Individual samples were frozen and extruded in the same manner as with compression test samples. Sample ends were trimmed square while frozen. After initial trimming, a more extensive preparation process was necessary to prepare samples with a "dog bone“ shape. Bond to the end caps (Figure 4.7) was achieved by preparing a thick paste composed of water and bentonite tablets and partially filling the end caps. The sample was then inserted into the end caps, forcing some paste out of the end cap opening. Samples were next frozen so that the close fitting aluminum end caps were tightly attached as shown in Figure 4.7. The sample was then mounted in a conventional wood lathe, inside the cold room, and trimmed to the dimensions illustrated in Figure 4.8. A steel template was machined to the same dimensions and mounted parallel to the sample on the lathe. The sample was then trimmed using a variety of steel chisels which had been milled to match the specific curvature of different sample sections. The template was 83 mounted on an advancing bolt, so that as trimming progressed, it was possible to advance the template and keep it parallel to the sample axis. The trimming apparatus is illustrated in Figure 4.9. The trimming process was time consuming and required careful attention by the operator with as little pressure as possible on the sample and trimming tools. Greater success was achieved in sample trimming when the cold room temperature was kept below -25°C. After trimming, samples were weighed and measured to ensure that all dimensions were consistent with predetermined sizes. In the event that samples deviated from the desired dimensions, measurements were recorded and retained to be used in the data reduction phase of the analysis. Prepared samples were wrapped in two layers of cellophane wrap and ends were sealed with rubber bands. No sample was stored for more than 24 hours prior to testing. 4.2.2 Egpipmenp Test Prgcedure The tension test apparatus used on this project is illustrated in Figure 4.10. This device was intended for operation in a cold room where ambient temperatures are at least 2°C below the desired test temperature. To maintain a controlled sample temperature, within ‘1 0.5 degrees of the desired temperature, the test frame was enclosed within an insulated test box. An electronic controller with sensing 84 device was mounted adjacent to the sample. This controller regulated three 200 watt lamps which would increase the temperature from that of the cold room to the desired test temperature, at which time the current to the lights would be interrupted. This on/off cycle would be repeated several times each minute, allowing accurate sample temperature to 5; o.5°c. The test frame was fabricated using 1/2 inch steel channels and 1 inch threaded steel rods as shown in Figure 4.10. The loading piston was a 3/4 inch diameter rod with a six inch vertical stroke. Compressed nitrogen was used to drive the piston and apply load to the sample. To insure a constant load, surges in pneumatic pressure were controlled using a filter, lubricator, and regulator. For this system two regulators were used and reserve pressure was maintained in a larger capacity reservoir. End caps used for the test were the same as used for sample trimming. The base of each endcap included stainless steel screw eyes turned into threaded openings. Steel cables were attached to each end cap and to the loading bar and base of the loading frame. The connector rod at the base of the loading frame was connected to an electronic load cell which measured the force applied to the sample. The concept of attaching the sample end caps to the loading apparatus with cables reduced the possibility of applying moments or eccentric loads to the sample. 85 Axial deformation was measured with the same displacement transducer (LVDT) as used for the compression test, however, it was necessary to increase sensitivity and decrease the range using the signal conditioning equipment. Prior to conducting any tension test with frozen soil samples, a lucite sample was attached with set screws into the end caps. A.load was applied, proportional to that which would be required to produce a 50 ksf load on a 2 inch frozen soil sample. This procedure was used to determine. the system stiffness and to test the long term consistency of the pneumatic load application devices. Initial deformation resulting from the machine stiffness was observed and recorded. This deformation was later subtracted from test readings to ensure that axial deformation recorded was that of the sample and not the apparatus. Long-term load application to the lucite sample was maintained for 24 hours. This time period served to verify that the filter lubricator regulator system did maintain a constant load. The load was essentially constant for the first 12 hours and then fluctuated within 1/2 percent. This fluctuation was more than desired, but once tensile tests were begun all tests were much shorter, and there was no need to alter or modify the equipment. Following the constant strain rate tests, a series of two creep tests were conducted as with the compression 86 tests. Deformations were measured with both the strip chart and data logger. The stresses applied were 1.23 and 2.79 MN/mz. 4.2.3 Elastic Modulus Determination As with the tests run in compression, determination of the elastic modulus is best accomplished using a constant strain rate deformation test and determining the corresponding load. Data from this test is presented in Figure 4.11. From this data, an elastic modulus of 16,833 kg/cm2 was extrapolated. Results were taken from a test being run at a strain rate of 3.086x10é/sec. The value of the elastic modulus would be used in the FEM analysis for the initial deformations, prior to any time-dependent behavior. 4.2.4 Time-Dependent Tension Tests A series of three creep tension tests were performed on individual samples removed from the undisturbed samples retrieved in the shelby tubes. Plots of time vs. deformation for each test are shown in Figure 4.12. From these tests it was possible to determine the vylov creep parameters in compression. Determination of these parameters were computed graphically, using the relationships illustrated in Figures 4.12b and 4.12C. The parameters determined from this analysis are given in Table 87 4.2. Figure 4.13 illustrates the log time vs. reciprocal of stress to determine structural life. For the purpose of analysis, this data was not used, as will be explained in Chapter V. 87a 2” diam. Shelby tube Styrofoam block 10" Figure 4.1 Cross section of sample freezing apparatus. 88 Figure 4.2 Load frame for compression testing 89 Figure 4.3 Lever arm scenario for compression tests. 90 llllJlllllJJlLJJluLlIJJIJJ[ill]llllllllleJLllll WWW) llllllllllJ[IJJJJJJJllllllllJlLllllellIll m IIIIIIIIIIIIIItIIII[IIIITIIITIIIIIIIIII m Figure 4 . 4 m 4.00 “MM Axial strain vs compressive stress for modified constant strain rate compression test. 91 25a: .. 32.8 KSF' ; 3 l 20.00 _: 41.7 KSF 3 ,\ 2 “ E 15.00 - 1 “J ‘- -1 o - _ 0: - _ hJ .- Q. .1 "I v _ 29.34 KSF : z - ~ $10.00 :- I l I a Z 5.00 -: 1 .- 'I q - -1 -1 1 d 1 o°m IIIIIIIIII1IIWIIIl|III[WIIIIIIIITIIIIIIIIIITTII[IIIIUIIII 0.00 50.00 100.00 150.00 200.00 250.00 300.00 TIME (MINUTES) Figure 4.5A Time vs. axial strain for compression creep tests at various applied stresses. 92 ‘0 1 1111111] 1 1111111] 1 111111.-4 : ., ‘ 2&540GW’ ' 4 -1 .1 .1 ' 1 § 3 1 fl - .1 .1 g - 3 .1 .. E ‘ 32.8KSF 41.7KSF _ 10": I I .. q - ~ I q - 10‘ 1 1111111] 1 1 111111] 1 1 111111. I 10 10' 10 “£(HMMS) Figure 4.5B Logarithmic plot of time vs. strain for compression creep tests where the tangent of the angle of plotted data is the creep parameter b. 10 Figure 4.5C 93 10' W 0mm m (KS) Logarithmic plot of compressive deviator stress vs. strain rate where the tangent of the resulting line is the cree parameter n. 1/STRESS (KSF) 94 0". I I IIIIIII I I I IIIII] I I I IIIIIIV I I I TITII - d “ -1 2 R _ -1 (M2- 1 q CI! I 1 fi q 4 d '1 .. nus: . q d 1 1 1 1 -1 -1 "4 -1 a q 9 4 1 - 001— _ ..I 1 1 / 1 q q -1 'l A w I I I ITIII] I I I IrIIII I l l IIIIII l l IlIIll 1 10 10' 10' 10‘ 1111501011115) Figure 4.6 Logarithmic plot of time vs. reciprocal of applied compressive stress. Extrapolation of the plotted line is used to determine the maximum allowable compressive stresses for a given length of time (for factor of safety equal to l). 95 Figure 4.7 Tension test sample showing endcap assembly. Figure 4.8 Dimensions of tension test samples. 97 1’1ch1 11111.] 111‘ l..1Li1c "“ "" ' ‘1 'l'l' 111.1111 11); 'l'unl If] . .4 1 Soil Sample | I ] Fixed find I ; b (:11 fl H.P. Electric SuLur Figure 4.9 Trimming lathe for tension test samples. High pressure nitrogen extends ra- resultlng in tension load on sample. 98 Llc Jack Line to Nitrogen Regulator Ea LVIH‘ LVDT Cable IIIIIIIIIIIIIIIIIIIIIIII llllt"z Load Cell Cable Load Cell Figure 4.10 Tension test load frame. TENSILE smess (KSF) 99 “Mn III VII 1r11 III III III III III III III IIW III II E 111411141J141111111I1111111111141141114111114111 B leillJllLlllJllllJLJlllllilJJIIIIIIIIIJIILJJJJJ 09" 1111111]111111111]111111111]1111111W1 0.00 0.50 1.00 I.” 2.00 AXIAL STRNN (PERCENT) Figure 4.11 Axial strain vs. tension stress for constant strain rate tension test. TENSILE 51mm (PERCENT) 100 m IIIIIIIIIIIIIIIIIIIIIIIIIIIIjIII—I1IIIIIIIIIIIIIIII ‘1 a: q . q -1 3 12.5K5F .4 1 ‘1 - -1 q a 1.501 3 q 2 A .1 -1 -I .1 "4 '1 "‘ -1 q - 1.00~ .1 'I 4 q q 3 "' -I 'I . 0.50- -' : 28.4KSF : .1 d ‘1 -1 q i 1 q .1 d .1 -1 0.00 ‘ 0.0000 0.0000 0.0100 0.01” 0.0000 0.0050 W 1111: (11111111125) Figure 4.12A Time vs. axial strain for tension creep tests at various applied stresses. AXIAL STRAIN (IN/IN) 101 ‘0 1 1 1 1 1 1 1] 1 1 1 1 1 1 1 q " 'I q q 1 - 1 1 q q q d "i 12.5 w "‘ 1 -l ': 7 7 .( 1 -1 ‘I a 28.416!“ q "l O 1 .1 O -1 -1 10" 1 1 1 1 1 In] 1 1 1 1 1 1 1 1 10" 10" 10" TIME (HOURS) Figure 4.12B Logarithmic plot of time vs. strain for tension creep tests where the tangent of the angle of plotted date is the creep parameter b. MMMIEW) 102 10‘ 10 10‘ Figure 4.12C 1 10 10' nmmsnmwmasmasosn Logarithmic plot of compressive deviator stress vs. strain rate where the tangent of the resulting line is the creep parameter n. 1/mmmrsmssosn 1.00 § 103 I I I T jjI] I I I I I I I I - 1 1 "I d - : q — d In] '1 . - 1 .. 1 - 1 .1 -4 - 1 d ‘ q 1 q d _ _ q q q -I q A q d 4 q -1 "I .1 "I q 1 ..I 1—1 -1 d d d ‘ q q q d d - q .1 q q q .11 _ c- u d .1 -1 d - d _ - d “/0 " .4 u-A . 1 -1 1 I 1 1 1 1i] 1 r —t 1 l I 1 1 10“ 10“ 1 Figure 4.13 Logarithmic plot of time vs. reciprocal of applied tensile stress. Extrapolation of the plotted line is used to determine the maximum allowable tensile stresses for a given length of time (for factor of safety equal to l). V. THE RETI ANALY I The proposed structure discussed in Section 3.1 has presented a significantly complex structural system which requires more detailed analysis than previously used on the majority of frozen earth cofferdams. Specifically, the major thrust of the analysis would be to predict the behavior of the frozen soil adjacent to openings cut through . the two adjoining cofferdams. Should the stresses (particularly tensile) in these areas he too large, it would be necessary to redesign the entire cellular cofferdam system, or to reinforce to the frozen earth. Analysis of this reinforced system requires new techniques since this form of reinforcement has not been previously used in a construction application. Prior to a detailed analysis, several approximate analyses were performed to select a practical geometric configuration. Such approximations, based on experience from previous projects, were used even though they have an inherently large margin of error. Due to the complexity and risk of this particular project, it was important that a much more precise numerical analysis on the frozen earth structures be performed. 105 106 5.1 conventional Design Approximation Less precise conventional design methods were used to approximate internal stresses and the potential design life of individual structures (cells). An approximate solution for determining the required frozen wall thickness for a circular dropshaft (Figure 5.1) is: ".-1 UN¢‘1 o ’ E 5.1 an 1 Q ( ) where: a is the internal radius of the cylinder, b is b/a = p. the external radius of the cylinder, (b-a) is the wall thickness, c is the limiting value of the frozen soil cohesion, N is the flow value = ( 1+ sim) (1 - sin¢) = tan? (45 + ¢/2), and q is the limiting uniaxial compressive strength of the frozen soil. The dropshaft design was based on a lateral earth pressure value of 7.13 ksf extrapolated from Figure 3.2. The uniaxial compressive soil strength was 57.1 ksf, as determined from laboratory tests. Conventional design methods use a factor of safety of 1.5 applied to the soil strength. Using this method the adjusted uniaxial strength 38.1 ksf. For the appropriate of the soil was 57.1/1.5 soil parameters, the design wall thickness based on Eq (5.1) is calculated: N¢= tan: (45 + 12.5/2) = 1.55 1/0.55 b/a = 7.13(1.55-1) + 1 38.1 b/a = [0.187 + 1] = 1.366 Wit frd Thi 110‘ ea Cy 6C ri t1 In 107 With the internal dropshaft radius (a) equal to 16 feet, the frozen wall thickness is computed: b = (16)(1.366) = 21.856 ft. (b-a) = 21.856 - 16 = 5.856 or 6.0 ft. This six foot thick wall is based on elastic theory and does not account for the time dependent creep behavior of frozen earth. Eq (5.1) is based on a thick, hollow circular cylinder. This model provides an approximation for the actual structure, and as previously mentioned, the inherent risk on this project warranted a more refined analysis. This phase of the analysis did yield an approximate wall thickness to be used in design, even though it appeared to be conservative. Continuing with the approximate solution analysis, the wall thickness is determined for cell 3. The circular shape of cell 3 permits use of Eq (5.1). Using the following values: a = 45 ft., q“ = 38.1 ksf, p = 5.0 ksf, N¢ = 1.55. Substitution into Equation (5.1) gives 9 = 5.9 (1.55 - 1) + 1 "“5 45 38.1 and b 51.05 ft. The wall thickness was determined: (b-a) = 51.05 - 45 = 6.05 or 6.0 ft. Experience on similar projects indicated that this wall thickness was conservative, and once again did not model the ‘- 108 actual structure, showing the need for more complete analysis methods. Both the dropshaft and cell 3 were circular, permitting the approximation on which Eq (5.1) is based. Cells 1 and 2, however, are more parabolic in shape, requiring an approach different from Eq (5.1). The approximate solution used to analyze the structural adequacy of these cells involves an oversimplification of structural arch theory. While this method has been applied to frozen earth structures, it has many inherent inaccuracies. For lack of any better analysis techniques, it has been used on many other projects. The arch theory assumes that a section of the frozen wall (Figure 5.2) can be treated as a horizontal arch. The arch is subjected to lateral earth pressure and internal stresses are computed. The equations used include: Fx 8 2.1-L'- EQ (5'2) 2 and FY = Eli EQ (5.3) 8f where F; is the reaction in the x direction, Fy is the reaction in the y direction, w is the lateral earth pressure at a particular depth, L is the length of the structure in the X direction, and f is the width of the structure in the y direction. After determining the forces F; and Fy, the internal force (FR) of the arch is computed: 2 1/2 FR = (Ff + FY) EQ (5.4) 109 This internal force can be converted to an internal stress by dividing FR by the wall thickness. This form of analysis was considered too simplistic and inaccurate for this project, due to the complex geometry and interaction of four separate, yet integrated structures (dropshaft, cell 1, cell 2, cell 3). The nonuniform geometry of this frozen earth structure placed limitations on the analytic approximations used on other projects in the Milwaukee area. Specifically: 1. Lateral pressures increase with depth making load approximations for any given depth incomplete since the entire structure must be analyzed. 2. The frozen earth structure(s) are embedded into the ground to depths greater than the internal excavation, thus producing a cantilevered effect on the side walls at the bottom of excavation. 3. The temperature distribution varies, being coldest at the refrigeration pipe, to zero degrees Celsius at the wall surface, making frozen soil strength parameters difficult to approximate. 4. The frozen soil exhibits time-dependent rheological behavior. 5. Each individual soil strata has different mechanical properties. .After reviewing these limitations, and considering the risk associated with potential failure, it was necessary to 110 utilize methods available from engineering mechanics. A review of existing techniques indicated that the FEM would provide the best solution for this, and possibly future design problems. 5.2 Elastic Finite Element Analysis The five limiting factors listed for simple analysis methods showed the need for a more in-depth analysis of the frozen wall behavior. The FEM appeared to be the only available option that could address all concerns for frozen soil that does not behave elastically under long term loading conditions. However, for initial loading (t = 0) the assumption of elastic behavior would provide initial deformations and stress distributions. Use of the FEM.with a three-dimensional model does permit evaluation of four of the five limitations associated with simple analysis methods. For example: 1. Increase in lateral pressures with depth can be modeled by increasing normal pressures on individual elements representing the frozen earth structure. 2. Embedment of the frozen wall into unexcavated earth can be modeled by employing springs at nodes with stiffness representing the passive earth pressure mobilized when the structure deforms under lateral loading. 3. The elastic moduli for individual elements can be varied, if necessary, to conform with predicted changes 111 caused by a change in temperature. 4. Different moduli can be used for each soil strata and can be represented by specific rows of elements. The initial phase of the elastic FEM analysis incorporated the use of three-dimensional models which were used to: (1) Determine the internal stresses within each individual cell; (2) Determine initial elastic deformations at nodal points; and (3) Compute cell force reactions on the tangential ”buttress" sections. 5.2.1 Elastic Finite Element Models of Individual Cells The initial FEM grids, used to model the individual cells, provide information on internal stresses and forces transferred to the buttress sections. The grids for these models are shown in Figure 5.3. An individual grid, generated for each cell and dropshaft, was scaled to actual field dimensions. A four node shell element was selected for this phase of the analysis, primarily because it could model the three- dimensional geometry of the actual structure, while limiting the total nodes to reduce computer time. The nodal coordinates in the z direction (Figure 5.3) were selected to 112 best correspond with major soil strata changes. Nodal coordinates in the x and y directions were selected to best define the plan shape of the structures, but were set at spacings so that a 2 to 1 aspect ratio for each element would not be exceeded. Some of the thicker soil strata were defined with several rows of elements. This selection of nodal points allowed for variation of material properties in different strata as desired. The element thickness was originally selected as 4.5 feet for the dropshaft, and 3.0 feet for the individual cells. These were practical thicknesses which could be attained in the field using cost effective refrigeration pipe spacing, with a single row of refrigeration pipes. It should be noted that these thicknesses are significantly less than those indicated in the approximate conventional solutions. Boundary conditions were essentially the same for all four models. Each node at the bottom of the grid was restrained against x, y and z translations, and permitted to rotate about the x and y axes. Nodal points along the vertical edge of the grids were restrained as illustrated in Figure 5.4. A significant advantage of the elastic FEM analysis was the ability to determine reactive forces which would be imposed on the buttress sections. In order to solve these forces, it was necessary to replace the restrained nodal 113 joints with boundary elements which would compute the reactive forces and moments at the boundaries. Each node was fixed with two boundary elements, one parallel to the x and y axes, respectively. The resultant forces and moments are computed manually later in the analysis. The nodal points which represented those portions of the frozen earth wall embedded in unexcavated earth were restrained with springs directed radially from each node toward the center of the shaft. Since it was uncertain whether or not passive earth pressure would develop, some analyses were run without spring restraints for comparison purposes. These results will be discussed in subsequent sections. Normal pressures were applied to the external surface of all elements. These pressures were extrapolated from the loading diagram illustrated in Figure 3.3. This loading diagram was prepared by the original geotechnical consultant on the project. The internal stresses computed in this first phase of the analysis were evaluated for the purpose of identifying the location and magnitude of maximum stresses. These results are summarized in Table 5.1. The constant strain rate test results (Figure 4.4) show a maximum compressive stress of 65 ksf for the frozen organic soil material. Comparing the FEM stress results with this soil strength, as shown in Eq 5.5, permits computation of a Factor of Safety. 114 F.S. = gm; EQ (5.5) max where F.S. equals the Factor of Safety, Cuf is the unconfined compressive strength of the frozen soil, and max is the maximum compressive stress for each cell as determined by the FEM analysis. Applying Eq (5.5) to the analyses gives F.S. Cell l/Dropshaft 65.0 ksf = 3.2 20.1 ksf F.S. Cell 2 65.0 ksf = 5.4 12.1 ksf F.S. Cell 3 65.0 ksf = 4.1 15.7 ksf While these Factors of Safety imply an adequate design, they neglect the time-dependent deformation and decrease in strength with time. The method used to approximate time- dependent behavior using an elastic analysis was based on the results of the creep compression tests discussed in Chapter IV. Using results from compression creep tests conducted on the organic silt material (Figure 4.5), a relation for time vs. reciprocal of stress was established (Figure 4.6). Based on these relationships, the expected duration of the structure was determined using the maximum compression stresses (Table 5.1) and the compression strengths for the organic silt (Table 5.2). Results of these comparisons are presented in Table 5.3. Based on results from this portion of the analysis, it was determined that integrity of the walls for cells 2 and 3 115 would be adequate during the excavation process for each individual cell. The cell 1/dropshaft analyses indicated high compressive stresses, particularly at the intersection of cell walls and the dropshaft. To compensate for these higher stresses, an additional row of refrigeration pipes was installed so as to double the wall thickness at these critical areas, thereby reducing stresses to an acceptable level. As noted earlier in this chapter, the greatest concern regarding the frozen earth cofferdams centered around the buttress sections and the ability of the frozen earth to withstand the potentially high tensile stresses when openings were excavated between two adjacent cells. To proceed with this phase of the analysis, reaction forces and moments determined by the boundary elements were computed and are summarized in Tables 5.3, 5.4, and 5.5. 5.2.2 Elastic Finite Element Models for the Buttress Sections The major thrust of the structural analysis was to determine the magnitude of stresses in buttress sections at tangential areas between two adjacent cofferdams. The first phase involved use of a three-dimensional elastic model. A representation of this model is illustrated in Figure 5.5. The purpose of this model included the following: 1. Determine nodal deflections in the y direction (Figure 5.5 axes). 116 2. Determine magnitude and location of maximum compressive stresses. 3. Determine location and magnitude of any tensile stresses. 4. Solve for reactions in the y direction (Figure 5.5 axes) to be used in subsequent analyses. The buttress section between cells 1 and 2 was selected for analysis since it had the higher stresses of the two buttress sections. Elements illustrated in the FEM grid (Figure 5.5) are the eight-node brick (type 5) available in the SAP IV program. Loads in this model, which were imposed at the various nodes, included the forces and moments determined in the previous elastic analysis for cells 1 and 2. Nodes along the base of the model were restrained to represent hinges with three degrees of freedom. Boundary nodes along the internal side of the buttress section were restrained with boundary elements representing rollers with five degrees of freedom. Boundary elements were used to determine the y component of the loads imposed on the buttress section from the cells. These components will be used in a later two-dimensional analyses. Due to different shapes of adjoining cells, there was concern that there could be excessive deflection in the y direction. Results of the analysis indicated the following: 1. Excessive tensile stresses near the face of the 117 opening through the buttress sections would most likely result in structural failure. 2. Compressive stresses within the buttress section were well within the acceptable range as compared with laboratory strength results. 3. Deflections along the x axis due to stress imbalance from adjacent cells were negligible. After reviewing stresses within the buttress section, it was observed that there were several zones of tensile stresses with magnitude of 0.19 to 1.3 ksf. Location of these zones are illustrated in Figure 5.6. These stresses were well above accepted values shown in Figure 4.13. Since these stresses were greater than those that could be safely permitted, several options were possible including altering the cofferdam cross-section. This would not be practical since any significant changes in cofferdam geometry would most likely be cost prohibitive. A second, more practical option was to install structural bracing across the opening during construction. While feasible, there were two major drawbacks. First, the bracing would interfere with construction of the proposed structure, and second, there was no practical method to attach the bracing to the frozen earth. A third option to be considered included the use of reinforcing materials to augment the low tensile strength of the frozen earth. This concept, while tested in the 118 laboratory, had never been used on a frozen earth construction project.’ Should the reinforcing option be selected, it would be necessary to conduct detailed analyses. Preliminary construction considerations revolved around providing reinforcement for the frozen soil by drilling a large diameter hole (approximately 3 ft. diameter) prior to the start of ground freezing. The steel reinforcement could then be lowered into the hole which would be backfilled with Portland Cement Concrete. While this method of augmenting the structural capacity of the frozen cofferdam appeared practical, there were several considerations related to this untested, original construction method: 1. What would be a sufficient section size for a composite steel/concrete beam needed to reduce the tensile stresses and wall flexure? 2. Would sufficient adfreeze bond develop to permit load transfer from the frozen soil to the reinforcing members? 5.3 Apalysis of the Reinforced Section To answer questions related to selection and analysis of the reinforced sections, it was necessary to perform a detailed analysis based on material properties from the laboratory tests, and the introduction of reinforcing 119 elements. 5.3.1, Elastic FEM Analysis of the Reinforced Sectign Analysis of the reinforced section began with the use of a two-dimensional plane strain linear elastic model as illustrated in Figure 5.7. The purpose of the elastic model was to evaluate nodal displacements along the proposed opening between two adjacent cells and to determine the magnitude of shear stresses developed between the composite steel/concrete beam and the frozen soil. The FEM grid illustrated in Figure 5.7 is a section taken vertically through the buttress area between cell 1 and cell 2. Boundary conditions consisted of simulated hinges along the horizontal base of the grid, and simulated rollers along the vertical symmetric slice. The loads were applied at nodal points as shown in Figure 5.7. These loads were those taken from the boundary element forces used in the model shown in Figure 5.5. Extraction of these nodal forces from the previous model provided the most accurate method for determining the y component of loads originating from the cells. It would be this component of load that would contribute to bending of the reinforcing element. Material properties for the soil elements were determined from the laboratory tests described in Chapter IV. The reinforcing elements are described by Merritt (1983). A.summary of these properties is illustrated in 120 Table 5.6. Results of this analysis indicated that tensile stresses along the opening between cells 1 and 2 would be transferred to the composite beam/reinforcing element, reducing the computed nodal displacements along the face of the opening to less than 0.0053 ft. Examination of shear stresses at the interface between the frozen soil and the reinforcing elements revealed stresses no larger than 6.0 ksf. These stresses appeared to be below the range which would cause adfreeze bond failure. As noted previously, one of the major design/analysis criteria was the load transfer ability of this particular interface. While this analysis indicated satisfactory results, they were based on linear elastic properties at time t = 0. In order to further analyze this critical section of the proposed frozen earth structure, it was necessary to use an FEM program better suited to model the time-dependent properties of frozen soil. 5.4 Time Dependent Nonlinear Finite Element Analysis Due to the complex wall geometry and inherent risk associated with possible failure of the frozen earth buttress sections, it was necessary to refine the previous elastic analysis. The SAP IV linear analysis included several limitations. There was a definite need to perform an analysis which would account for time-dependent behavior of the frozen soil. A computer program described by 800 121 (1983) appeared to offer the features needed for this analysis. (A summary of Soo's (1983) program follows: 1. At the beginning of the analysis, a small time increment is assumed, and elastic stresses are computed. 2. A creep law, based on the creep parameters from the laboratory tests, is used to determine creep strains. Among the several features within this program were the ability to use several different element types. Among these elements are three types needed for analysis of the frozen earth buttress sections. The first and most common of these elements was the nonlinear plane stress element representing the unreinforced frozen soil. Properties representing both linear and nonlinear material parameters in both tension and compression could be assigned to the individual elements. The reinforcing element (steel/concrete) was modeled with linear elastic elements using the same parameters in tension and compression. The third element type, a bond link element, was capable of modeling the adfreeze bond between the composite beam and the frozen soil. These elements permit simulation of the time dependent creep deformation of an adfreeze bond up to some limiting deformation, at which time slip failure would occur. The particular model used in this analysis is illustrated in Figure 5.8. This model uses the same 122 boundary conditions and nodal point loads used in the elastic analysis model shown in Figure 5.7. The shaded area, representing the reinforcing section, was modeled with two-dimensional linearly elastic elements. The material properties required are those used previously and identified in Table 5.6. The frozen soil section, comprising the majority of elements, was modeled with the two-dimensional nonlinear elements. Properties selected for these elements were determined from the laboratory tests and are summarized in Table 5.7. The bond-link elements, represented by narrow elements between the linear and nonlinear elements in Figure 5.7, were used to model interface between the frozen soil and reinforcing material. Properties used in the analysis for bond-link elements are from $00 (1983) and are presented in Table 5.8. Time steps used to evaluate creep deformation were arbitrarily selected as one, seven, and thirty days. In order to ensure proper execution of the program using these time steps, it was necessary to select compatible creep proof stresses and proof strain rates. The method for selecting these values is discussed by $00 (1983). In this analysis, the proof parameters were selected to be compatible with the described time steps. Note that selection of these parameters directly affected the programfs ability to execute the nonlinear time-dependent 123 phase of the analysis. Parameters used are identified in Table 5.9. Results of this time-dependent analysis indicated that the most significant deformation occurred during the initial elastic time step (t = 0). The corresponding time-dependent deformations, illustrated with an exaggerated scale in Figures 5.9 to 5.11, represent the initial, seven day, and thirty day deformations, respectively. There are significant differences when interpreting the results produced by Soo's (1983) program and those generated by the SAP IV linearly elastic program when designing frozen earth structures. The SAP IV analysis relied on evaluation of the internal stresses within the frozen earth wall. These stresses were then compared with the plot in Figure 4.6 to determine the approximate time to failure. This method does not permit the design engineer to predict deformations at any given time, only a predicted time to failure. When using the time-dependent program, it is possible to determine nodal deformations at any specific time. These deformations can be verified by measurement of actual deformations in the field, thus verifying the validity of the design method and soil parameters used. 5.5 Structural Analysis Summapy The structural analysis completed in this study used several different analyses techniques to determine the 124 integrity of the proposed frozen earth structure. The main focus of the analyses was to determine if reinforced frozen earth could be used in an actual construction application. The structural analysis was begun only after the wall geometry had been selected (Chapter III) and material properties established (Chapter IV). Initial conventional analyses indicated that the frozen earth structures required would be much larger than previous experience in the area indicated. In addition to conservative results, geometry of the buttress sections required extremely complex solutions. To compensate for these problems, it was necessary to perform numerical analyses with the FEM. Initially the linearly elastic SAP IV program, using a three-dimensional model with shell/plate elements, was used to determine both internal stresses for each cell and the forces transferred by these cells to the buttress sections. Loads for this model were based on predetermined lateral earth pressures. A second three-dimensional elastic model was used to model the buttress section with the proposed opening between cells. Loads for this model were determined from the reactions computed in the cell models. Results from this particular model clearly indicated a need for reinforcement, due to excessive tensile stresses. Computations showing the need for reinforcement was a significant accomplishment in the design/analysis phase of this project. FEM models, using frozen soil properties 125 determined by laboratory testing, permitted evaluation of highly stressed zones within the frozen earth structure. This advanced design capability would not be possible using the older conventional analyses methods. .After determining the need for reinforcement, practical field methods for providing the required reinforcement were evaluated. Selection of appropriate reinforcement was significantly influenced by the availability of equipment which could facilitate installation. A caissor drill rig, capable of installing a three foot diameter hole, was used. After drilling the hole to approximately 3 ft., a W24 x 145 steel beam was lowered into the hole. The hole was then backfilled with Portland Cement Concrete.. While there was very little latitude in selecting the reinforcement, it was necessary to perform a detailed analysis as to predicted performance of the reinforced section. This analysis was performed using the nonlinear FEM program developed by 800 (1983). The program permitted evaluation of the buttress section with respect to the following features: 1) modeling of the time-dependent behavior; 2) use of different frozen soil parameters in compression and tension; and 3) use of a bond-slip element to model the interface between frozen soil and the reinforcing elements. This analysis indicated that the reinforcement would provide the additional strength needed to augment the 126 overstressed frozen soil. Results of the analysis showed that most of the deformation occurred in the initial elastic phase, with very small deformations occurring at one, seven, and thirty day intervals. Total deformations were extremely small and would be difficult to measure in the field. 127 TABLE 5.1 INTERNAL STRESSES FROM ELASTIC ANALYSIS MAXIMUM INTERNAL MAXIMUM INTERNAL STRQQTQRE STRE MPRE I N STRESS (TENSIQN) Cell 1/Dropshaft 20.1 N/A Cell 2 12.1 N/A Cell 3 15.7 N/A TABLE 5.2 PREDICTED STRUCTURAL LIFE BASED ON ELASTIC ANALYSIS AND COMPRESSION CREEP TEST STRATUM RECIPROCAL STRUCTURAL STRUCTURE DESCRIPTION QF STRESS (lzksf) DQRATIQN Cell 1 Organic Silt 0.049 190 Hrs. Cell 2 Organic Silt 0.083 990 Hrs. Cell 3 Organic Silt 0.067 700 Hrs. TABLE 5.3 SUMMARY OF FORCE AND MOMENT REACTIONS CELL 1 ACTING ON BUTTRESS BETWEEN CELL 1 AND CELL 2 DEPTH FORCE MOMENT DEPTH FORCE MOMENT (Ft.) (Kips) (Ft.-Kips) (Ft.) (Kips) (Ft.-Kips) 0.00 131.01 30.23 74.25 2892.20 92.50 8.25 264.00 60.90 82.50 2278.90 165.30 16.50 396.90 91.60 90.75 1779.40 184.50 24.75 783.30 140.50 99.00 1279.90 203.70 33.00 1169.60 189.40 107.25 850.50 119.20 41.25 1497.60 172.30 115.50 421.00 34.60 49.50 1825.50 155.20 123.75 189.40 15.50 57.75 2665.60 87.50 140.25 - - 66.00 3505.60 19.70 128 TABLE 5.4 SUMMARY OF FORCE AND MOMENT REACTION CELL 2 ACTING ON BUTTRESS BETWEEN CELL 1 AND CELL 2* DEPTH FORCE MOMENT DEPTH FORCE _MQM§NT (Ft.) (Kips) (Ft.-Kips) (Ft.) (Kips) (Ft.-Kips) 0.00 771.00 -8.40 58.33 1134.10 -209.10 8.33 920.70 -9.30 66.66 555.80 -333.20 16.66 1070.40 -11.40 75.00 515.40 -311.10 25.00 1278.10 -10.10 83.33 475.10 -290.00 33.33 1485.80 -9.10 91.67 237.60 -237.60 41.66 1599.10 -47.60 100.00 - - 50.00 1712.40 -86.10 *Due to symmetry of Cell 2, these forces were the same as those acting on the buttress between Cell 2 and Cell 3. TABLE 5.5 SUMMARY OF FORCE AND MOMENT REACTION CELL 3 ACTING ON BUTTRESS BETWEEN CELL 2 AND CELL 3 DEPTH FORCE MOMENT DEPTH FQRQE MQMENT (Ft.) (Kips) (Ft.-Kips) (Ft.) (Kips) (Ft.-Kips) 0.00 149.50 - 58.33 386.50 -14.10 8.33 240.90 - 66.66 162.60 -27.30 16.66 332.30 -0.10 75.00 174.70 -73.10 25.00 408.90 -1.10 83.33 93.40 -59.50 33.33 485.40 -2.00 91.67 89.10 -53.60 41.66 547.90 -1.50 100.00 - - 50.00 610.20 -0.90 TABLE 5.6 MATERIAL PROPERTIES USED IN ELASTIC ANALYSIS (Merrit, 1983) MATERIAL ELASTIC MODQLQS BQLSSQNLS BATIQ (KSF) Frozen Soil 1147 6 0.33 Composite Steel/Concrete 9.1 x 10 0.45 129 TABLE 5.7 MATERIAL PROPERTIES REQUIRED FOR FROZEN SOIL IN NONLINEAR ANALYSIS (Alawhabb, $00, 1983) PR PERTY QOMPRESSIQN TENSIQN Parameter n 1.61 5.00 Parameter b 0.26 0.55 TABLE 5.8 MATERIAL PROPERTIES FOR BOND LINK ELEMENTS (800, 1983) KY 9500 Kz 3000 PMX 100 PMY 100 Parameter n 1.6 Parameter b 0.2 TABLE 5.9 TIME-DEPENDENT PARAMETERS OF FROZEN SOIL (Soc, 1983) PR PERTY 0MPRE I N TENSION Proof Stress (st) 1993.6 195.8 Time Step (Days) 7 7 130 I.» l _J r’ I Figure 5.1 Conventional approximation for a circular shaft. 131 an nypiied load // // 2: a. Figure 5.2 Conventional method for elliptical cofferdam. 1...... .._. ....i ”a Figure 5.3 132 Ki” “vs-N I \\\\ CELL SIZE: 35-40ft length r.” ‘\.\\ I \\\ 1 o 0 ft deep (".../"'— \\\\\ \ \ /¢/r-'1F"‘ N\\\\\ \ ///’ N\\N\\ \ M’Id ~7~\‘\\ \ \ M/(‘p’ ~N\\ m, \ N ,z" N\‘\( r N\ \ V ///FJ N\N\\N \ #V’flfl H\\\ \. \ ///"‘ NW\N\ [\\ LL.» ~~~J\N\ Typical three dimensional grid used in elastic analysis. \ \ \ \ \ \ --(TIII\.I ll\|| l I\Iu I I \ \ \ 1 \ x \ --_.::i x \ Boundary conditions imposed on grids used in Figure 5.3. Figure 5.4 OD \’\O\ OOOO \\\ _ ....y...) L’. x Figure 5.5 Three dimensional Finite Element Method grid of buttress between adjacent cells. Figure 5.6 Regions of excessive tensile stresses as computed by elastic Finite Element Method. 136 Figure 5.7 Two dimensional grid used in elastic model of buttress section. 137 Figure 5.8 Two dimensional nonlinear Finite Element Method Grid of Buttress Section. 138 VERTICAL (FT) HORIZONTAL (FT) \l 1 -1.0 x 10" 4.4 x 10-3 l _ _ I 2 -1.1 x 10 3 4.5 x 10 3 I _ _ I 3 -1.0 x 10 3 4.5 x 10 3 l -3 -3 I 4 -0.9 x 10 4.7 x 10 I _ _ / 5 -0.8 x 10 3 4.8 x 10 3 / Figure 5.9 Exaggerated Nodal Deformation at Time = 0. 139 Figure 5.10 Exaggerated Seven Days. VERTICAL —1.3 x -l.2 x -1.1 x -l.0 x -0.9 x Nodal Deformation (FT) HORIZONTAL (FT) 4.0 x 10-3 4.7 x 10 4.9 x 10 5.0 x 10 5.1 x 10 at k) Figure 5.11 Exaggerated days. 140 VERTICAL (FT) -1.1 x 10'3 4.7 x -1.1 x 10‘3 4.9 x -1.0 x 10'3 5.0 x -1.0 x 10"3 5.2 x —3 -0.9 x 10 5.3 x Nodal Deformation at 30 HORIZONTAL (FT) 10'} 10’3 10"3 10’3 10’3 M‘. VI. FIELD PERF RMANCE The use of reinforcing elements in the frozen earth structure to provide additional support in highly stressed wall sections is a new and previously untested construction technique. The method of analysis, while described by many in the literature, had never been evaluated under field conditions. The analysis presented in Chapter V indicated that the frozen earth structure should not exhibit any measurable deformation during and following excavation. A definite need for evaluation of the field performance was needed to 1) verify that wall deformations were acceptable, and 2) to indicate what (if any) modifications should be made for successful design on future projects. To ensure adequate and safe performance of the structure, electronic, mechanical, and optical measurement techniques were used. The deformation predicted by the structural analysis was extremely small and would.most likely have been undetected by the instrumentation used on this project. Due to the uniqueness of the construction technique, the instrumentation used was required by the owner's engineer to serve as a warning system in the event that reinforcement and/or adfreeze bond was about to fail and would result in 141 142 potentially dangerous situations. Any measured deformation would be useful in evaluating the field performance of the frozen wall system. 6.1 Field Instrumentation Instrumentation installation was implemented to act as a ”warning" system in the event the excavation might become unstable. The small deformations indicated by the structural analysis would have been extremely difficult to measure under field conditions. Electronic displacement transducers, similar to those used in the laboratory phase of this analysis, were considered to be an excellent method to produce accurate measurements. This type of instrumentation was considered too delicate to perform adequately inside the excavation on an active heavy construction site. Reinforced sections on the sides of the wall opening excavated through the buttresses were the critical stress areas. Failure of these sections would be a result of excessive bending of the beams. Deflection measurement of the beams was planned using four different methods. The first method, initially presumed to be the most accurate, consisted of installing electronic vibrating wire strain gauges on the steel sections, prior to installation in the drilled boreholes. The strain gauge installation and details are illustrated in Figure 6.1. While strain gauges would measure small deformations at 143 specific points, they would not define gross beam movement should excessive bending occur. For this reason, an orientable inclinometer was to be used for measurement of the relative orientation of refrigeration pipes welded along the neutral axis of the reinforcing element. The inclinometer has limitations on measurement of deformations, and its reliability was questionable due to cold operating temperatures encountered with the frozen earth structure. A third method for measuring deformations again centered around the possibility of unexpected excessive beam deformation. This method involved the positioning of a 20- second theodolite on the ground surface for measurement of 'any changes in the angle between the beams and a fixed benchmark on the surface. This concept is illustrated in Figure 6.2. The fourth, and perhaps most straight-forward method of measuring possible beam deflections, consisted of using a standard surveyor tape with a tension scale to measure the distance between the opposing beams as shown in Figure 6.3. 6.2 Wall Mpvement Qbservations During the construction phase of the project, a major setback occurred when wires and conduits leading from the strain gauges were damaged during drilling on adjacent refrigeration pipes. Attempts were made to salvage the gauges, but the damage had occurred in inaccessible areas 144 well below the ground surface. The other three methods, the inclinometer, theodolite, and surveyor's tape, were used on a daily basis during the excavation process. No measurable deformations were observed indicating that the reinforced wall section was performing as planned. 6.3 Qomparison with Predicted Deformations Due to the extremely small (trivial) deformations predicted in the analysis, it would be very difficult, if not impossible, to accurately measure the predicted movements under field conditions. From a practical standpoint, the predicted observations were essentially zero. From a researcher's perspective, it may appear that the structure was overdesigned and extremely conservative, ‘warranting some type of measurable deformations in order to make reasonable comparisons between the numerical solutions and actual field deformations. The owner of the project, the Milwaukee Metropolitan Sewer District, had retained a consulting engineer to review all FEM computer output. Had that computer output shown any measurable deformation, it ‘would have been necessary to redesign and resubmit the results, since any significant deformation of the earth support system could have the potential for failure resulting in the loss of life. In summarizing, the field instrumentation confirmed the 145 design requirement that no measurable deformation of the reinforced frozen earth walls would be tolerated. While the resolutiOn was not capable of measuring the extremely small movements as indicated in the computer analyses, it did serve to notify the engineer and contractor that no significant movement was observed. The field instrumentation, as used in this project, did serve to clearly demonstrate that the concept of using reinforcing elements in frozen earth structures was a safe and reliable method for lateral earth support. Refrigeration Pipes Welded to Beam Strain Gauge-—~\\\\‘ Strain Gauge _\\\\\\ ~ 1‘ . ‘., .1. Steel Beam in Concrete Vs..." ...—.1..." “...-... / Strain Cause \\.3 Tee Standing j? 4 efrigeration Pipes 5‘: 1 \ Figure 6-1A Location of strain gages on reinforcing elements. 147 0.94 in. Diameter Cross Section through weldable block. Vibrating Wire weldable End Block Set Screw J J Figure 6.1B Detail of strain gages used on reinforcing elements. 148 Fixed Reference Point ,- I... - - - 0 f3::;;::::§;;;;;;;;;l 7 ~ - ._.in. ' . E) Shaft Cell 1 VV Section A-A illustrated in Figure 6.3. ‘\~T____.—wrj Relative angle was measured from fixed reference point to steel rods welded to reinforcing elements. Figure 6.2 Angles measured to monitor reinforcement deformation. r— t CL CL 5 I 8 ,_ ,_ 8. e e e .‘ 1 e a a a 5 v _, ...V/V/V/VWV////////////////////////////// ONaJAu — mflfl/ /a/fl/////////////////////////////w 11.0 ft. 5 11.5 ft. ement scheme on Detail of tape measur .3 ng elements. VII. DI U I N AND RE MMENDED DE I N Many of the factors incorporated into this totally integrated design/construction concept were used for the first time to the author's knowledge. Due to many unknown factors regarding the reliability of certain analysis aspects, particularly selection of reinforcement sections, the design was conservative. It is emphasized that the design, analysis, and construction procedures did indeed ‘work, resulting in a safe and cost-effective earth retaining system. Since the project was considered very successful, the procedures used can and should be applied to future (projects. The following sections summarize topics for use in future design and construction procedures. 7.1 clarification of Site conditions Prior to design of any frozen earth structure, both surface and subsurface site conditions must be investigated. Surface conditions should be reviewed for drilling and construction equipment accessibility, as well as site drainage. Subsurface conditions include determination of the groundwater level, soil stratification and identification of soil types, as well as engineering 3properties of these soils. 150 151 When plans include the use of ground freezing for temporary ground support, consideration must be given to the physical installation of the refrigeration system. Sites must be well drained and reasonably level. Overhead obstructions should be considered, as they can interfere with drilling equipment and the lowering of refrigeration pipes into predrilled holes. Availability of power for the refrigeration plant must be accounted for. On this particular project, an electric plant was used, requiring 480 volt, three phase, 600 ampere service. While most plants rely on electric power, diesel operated plants have been used where the required electrical power supply is not available. Subsurface conditions can be more complex than surface conditions. Boring logs and geotechnical reports must be closely reviewed and should contain as a minimum the following information: 1. Identification of all soil strata, 2. index tests on all strata, 3. soil strength characteristics, and 4. ground water levels. Based on the boring logs and associated laboratory tests presented in the geotechnical report, several analyses are required. Soil stratigraphy should be examined to determine: 1. The presence of an impermeable bottom strata to "key” the frozen wall into, 2. the presence of any highly permeable strata that could result in high ground water flow velocities which could retard the freezing process and possibly prevent x ‘ 152 frozen wall closure when using conventional refrigeration methods. Soil index tests should be carefully reviewed with particular attention to grain size characteristics and water contents. Typically, the finer grained, higher water content materials require a longer time to freeze than coarser grained materials, due to higher latent heat properties. On this particular project, the soil in stratum II (Figure 3.1) involved a particularly high water content (68%). In addition to its very fine grained and organic characteristics, it exhibited low strength characteristics. For these reasons, Stratum II governed design criteria for both strength and thermal properties. Chapter IV discussed the structural design methods used based on the strength of this material when frozen. Due to its high water content and long time required to freeze, the refrigeration pipe spacing selected was 3.0 ft. (A discussion of the computed time to freeze is beyond the scope of this study but is discussed in detail by Sanger (1968). When designing frozen earth structures, it is necessary to determine lateral earth pressures acting on the structure. Typically the "at rest" soil pressures are used. Parameters needed to compute these pressures are determined from tests performed on the unfrozen soil. Such tests include the Standard Penetration Test (STP), unconfined 153 compression, and triaxial compression tests. On this project the earth pressure parameters were derived from information presented in Figure 3.2, as well as from the geotechnical report prepared for the site. It was these lateral earth pressures which were used in the frozen wall structural analysis. Ground water levels should be reviewed in the initial geotechnical report, but more importantly, piezometers or monitoring wells should be installed on the site prior to design or construction. To provide meaningful data, these piezometers must be located in the more permeable soil strata. Piezometers should be located at the center of each individual frozen earth cell, and at some point at least 20 feet from the exterior limits of the frozen earth structure(s). Piezometers located within each cell will provide critical information relating to complete formation (closure) of the frozen earth cofferdam. If the sensing zone is located in a confined aquifer, the water level will begin to rise significantly once closure has occurred. Stratum III (Figure 3.1) on this project was considered to be a confined aquifer. Upon closure, the ground water in the piezometers of cells 1 and 2 rose to the top of standpipe and drained at approximately one gallon per minute until excavation began. Cell 3 did not exhibit this .behavior for reasons which are discussed later in this section. ‘L 154 Piezometers installed external to the frozen earth structure measured ground water levels across the entire site. Ideal freezing conditions exist when all piezometers indicate static ground water conditions. Any differential between these external water levels indicates a potential ground water gradient across the site. This gradient can result in high ground water velocities in strata with high permeability. High ground water velocities can retard or even prevent formation of a frozen earth wall. On this project, monitoring wells were located in the center of cells 1, 2 and 3. The wells, installed to a depth of approximately 70 feet, measured the piezometric head in soil Stratum III. Two piezometers were located on opposite sides of the structures, approximately 50 feet from the outer influence of the freezing system. These piezometers were also installed at depth of approximately 70 feet in Stratum III. During freezing of cell 3, a differential ground water level was observed between the two external piezometers. A tunneling contractor had started dewatering a 30 ft. diameter tunnel approximately 300 ft. below this project. These dewatering operations had created a significant draw- down in the immediate area. This gradient created high lateral ground water velocities which prevented freezing of Stratum III in cell 3. The failure to freeze was detected by the absence of a rise in the internal piezometer, as well 155 as warm temperatures in the monitoring pipes. In order to adequately freeze the cell, it was necessary to drill several holes on the exterior of the frozen wall and inject a cement-bentonite grout mixture. This grout decreased permeability of Stratum III, thereby reducing the ground water velocity. This decrease, coupled with the addition of more refrigeration pipes, resulted in the successful freezing of cell 3. Shortly after excavation of cell 3, pumping stopped, returning the ground water to an equilibrium, making the freezing of cells 1 and 2 a relatively quick (3 weeks) operation. After approximately two weeks of freezing, ground temperatures were below 0 degree Celsius, with closure confirmed during the third week of freezing when water began flowing out of the internal piezometers. 7.2 Stability and Deformation Analysis As mentioned in the previous section, the weaker fine grained soils governed the structural analysis. After identifying a potentially weak soil strata, deformation analysis required that laboratory tests be conducted on these soils in the frozen state. During the design phase of this project, examination of the boring logs identified the weak soil of Stratum II. An additional boring was conducted to retrieve undisturbed samples prior to conducting frozen strength tests. During the initial design phase, it was 156 observed that the limits of Stratum 11 coincided with the location of openings to be mined through tangential cofferdams. This condition required an extensive structural analysis based on the mechanical properties of these frozen soils. 7.2.1 Recommended Laboratopy Testing Procedures All laboratory tests on frozen soil should be conducted at temperatures close to the expected ground field temperatures. Experience with each individual refrigeration plant's capacity is the most reliable method for prediction of ground temperatures. Most refrigeration plants used for ground freezing refrigerate the coolant to temperatures between -20°C and -35°C. With these coolant temperatures, ground temperatures of -10°C are attainable. Many sources in the literature also report test results at -10W3. For these reasons, -10°C was selected as the upper limiting test temperature for this project. Note that the wall will be much colder near the refrigeration pipes. The -10%: temperature is recommended for use on future projects using similar refrigeration equipment. Unconfined constant strain rate compression tests should be conducted on samples from either the weakest strata or those subjected to the greatest loads. In this study a deformation rate of 4.0 x 10-5 inches/minute was used. This rate was selected primarily because of testing 157 equipment limitations. Strain rates must be carefully controlled as higher strain rates can yield strengths greater than those attained in the field under long term loading conditions. The constant strain rate compression test determined the unconfined compressive strength used in the conservative conventional analysis of circular frozen earth structures. Chapter V reviews the disadvantages of a conventional analysis. The stress-strain data produced in the unconfined compression test can be used to determine the elastic modulus used in the numerical analysis for computation of initial deformations. Test procedures, described in Section 4.1, were sufficient for use on this project. A significant improvement to the unconfined compression test would be to modify the equipment so as to better control the sample deformation rate. ' Time-dependent rheological properties of frozen soil require an unconfined compression creep test. While the ISGF working group recommends that these tests be conducted at 0.5, 0.3, and 0.1 of qc, data interpretation is more accurate if the time to failure for each load occurs in a different logarithmic cycle of time. It may take several tests to achieve these failure times using a trial and error load selection system. In the conventional analysis, results from creep tests were presented as a plot of failure time vs. the reciprocal 158 of applied stress. In the more refined and accurate time- dependent FEM analysis used on this project, results of these tests were used to determine the creep parameters b and m. When conducting these tests, care should be taken to ensure that stress levels remain constant as the sample deforms and the cross-sectional area increases. A simple way to accomplish this involved the addition of very small weights to the loading arm during the test. The time to failure can most accurately be determined using precise data acquisition equipment. Both data loggers and strip chart recorders were used in this testing program. The data logger permitted easy total strain interpretation data during the longer term tests, while the strip chart provided an accurate graphical representation of the exact time of failure or shorter term tests. While most frozen earth structures are designed with a circular cross-section so as to create a totally compressive stress state, some geometric shapes will result in tensile stresses. For these structures, it is necessary to determine the mechanical properties of the weakest or most highly stressed frozen soil samples in tension. One of the most difficult and possibly most critical procedures in the tension test was sample preparation. Minimal disturbance to a sample can be achieved by trimming the frozen undisturbed sample to a dog bone shape on a 159 lathe. Quite often stresses imposed by the lathe and trimming tools will result in rupture of the frozen sample during preparation. For this reason, it was necessary to have duplicate samples, which can be expensive and sometimes impractical. For this reason it was often necessary to perform the tension tests on remolded samples. Remolding can be accomplished in two different ways. On this project, the fine grained organic silts were remolded into cylindrically shaped samples which were frozen, and then trimmed on the lathe in the cold room. An alternative method would be to compact the soil into a split half dog bone mold. This method was well suited for saturated sands. It was very difficult to ensure uniform density with cohesive soils. Aluminum end caps were secured to the sample by placement of the sample ends in bentonite slurry and freezing. This method is recommended over other systems such as the insertion of screws directly into the frozen samples. The screws can result in stress concentrations which may have adverse effects on the test results in sample cracking during the test. The trimming procedure used in this study was the result of many trials and failures. While a temperature of -10°C was used for the actual test, it was found that this was too warm for sample trimming. .A temperature of - 15°C gave the sample more rigidity and helped prevent sample 160 rupture during the trimming process. Extreme care must be taken when trimming so as to remove the soil in very small increments. Too much pressure on the trimming tool would damage the sample. Final shaping was best accomplished using concave files and sandpaper. After trimming, sample dimensions were obtained with a caliper before weighing. Tension tests were conducted immediately after trimming so as to minimize loss of moisture. It is imperative that the sample be uniformly warmed to the test temperature. As with the compression tests, the unconfined tensile strength and elastic modulus in tension were obtained by conducting a uniform strain rate test. For this project the constant strain rate test, described in Chapter IV, was conducted using a pneumatic regulator with pressurized nitrogen. This system gave a deformation rate close to 3.086 x 10-5/sec. In future testing programs it is recommended that a mechanical system be used so that a selection of strain rates would be possible. To determine the creep parameters b and n in tension, creep tests must be conducted on prepared frozen samples. Samples for these tests can be trimmed in the same manner as the constant strain rate test. The tension creep tests required a displacement transducer with accuracy of 1.002 inches. Time to failure was difficult to measure since it occurred within 30 seconds after load application for stresses greater than 25 ksf. For stresses lower than 15 161 ksf, no measurable deformation occurred. This behavior made it difficult to select stresses which would result in failure during three separate logarithmic cycles. Selection of tensile stresses for a meaningful test may involve a trial and error procedure. Starting with lower stress levels and then gradually increasing stresses will reduce the number of required samples. While load application for strength and creep tests in this study used compressed nitrogen and a regulator valve, a dead weight or mechanical system for load application would reduce the need for adjustments when conducting tests in a cold room. Lead weights would further simplify the process by eliminating the need for a force transducer. 7.3 Structgrgl Design After evaluation of site conditions and material properties, the frozen earth structure design must ensure a safe, watertight excavation, while limiting the quantity of refrigeration equipment needed and required soil excavation. Shape of the frozen earth structure is generally governed by geometry of the proposed structure. It was desirable to keep the frozen earth structure as circular and small as possible. The depth of refrigeration pipes was dictated by bottom stability considerations. Based on comparisons between the analytical and numerical analyses presented in Chapter V, it was clear that 162 analytical methods based on elastic soil behavior gave conservative results and did not effectively consider the time-dependent creep behavior of frozen soil. For these reasons, the numerical FEM analysis is highly recommended. The linear elastic FEM programs can be used to determine internal stresses within the frozen earth structure. In this study the elastic analysis combined with the SAP IV program.permitted use of a three-dimensional wall model. This three-dimensional model provided both internal stresses and loads being transferred to the buttress section. When using the linear analysis to determine internal stresses, it was necessary to compare internal stresses to a plot of reciprocal of stress vs. time to failure. This procedure was used to determine the potential design life of the frozen earth structure. (A recommended alternative to this technique is to use a time-dependent FEM program, such as the one developed by $00 (1983). Use of this program incorporated time-dependent frozen soil properties eliminating the need to perform comparisons of stresses to the laboratory tests. .As with the elastic analysis, parameters needed for the program must be determined by a laboratory testing program. As noted in Chapter V, interpretation of computational results varies with both the linear and nonlinear analysis. With the linear analysis, stress computations are needed to determine structural integrity. The nonlinear analysis is 163 deformation oriented, making interpretation of the results much easier, since the total resultant deformation is usually a more positive measure of performance. For this reason, the nonlinear, time-dependent analysis is recommended. 7.4 Reinforcing Methods and Selection When the results of a structural analysis indicate stress levels or deformations greater than those considered acceptable for a particular soil type, modifications to the structure must be made. Two common modifications include altering the wall geometry and/or using thicker frozen earth walls. A third method involves placement of reinforcement in the walls. Mbdification of the structural geometry normally involves adding curvature to the straighter portion of elliptical shapes. Referring to the geometry of cell 2 (Figure 3.3), both the major and minor axes define the elliptical shape. Had the FEM analysis given high stresses indicating potential failure or a short structural life, the minor axis of the elliptically shaped structure could be increased, thus lowering internal stresses. This would result in two significant disadvantages. First, the increase in total perimeter would increase the number of refrigeration pipes required. Second, a large cofferdam requires more excavation and higher excavation costs. Both 164 of these disadvantages result in increased construction time and cost for the project. The alternate solution, increasing the wall thickness, can be accomplished by adding an additional row of refrigeration pipes, parallel to the original row. This increases installation costs significantly and would require almost twice as much refrigeration capacity. The introduction of reinforcing materials, the third method, is used to transfer loads to adjacent frozen soil sections. Allowable total deformation governs selection of the reinforcement. On this project, no measurable deformation of openings between cells was permitted. This stringent requirement is typical for frozen earth structures because once significant creep movement has begun, it will continue and eventually lead to failure. It is considered imprudent to permit men and equipment to operate in an excavation that is continually deforming at a measurable rate. Tensile test failure on frozen samples for this project occurred at approximately 1.5 percent strain after exhibiting minor creep strain. This behavior is similar to a brittle material. Time-dependent deformation was too small to associate with field behavior. Tensile strength contribution of the frozen soil was not considered in the analysis due to the low unconfined tensile strengths of the frozen soil and questions as to continuity over a period of 165 time. Stress magnitude within any overstressed zones shown by the FEM analyses should be compared with yield stresses after the reinforcing elements have been placed. After making this comparison, a cross-sectional area of the reinforcing material can be approximated. Unlike steel or concrete design, reinforcement selection is not based on selecting a moduli section to accommodate movement and shear. The installation of sufficient reinforcement must be practical and cost effective. Additionally, the reinforcing material must be installed in such a manner to ensure adequate adfreeze bond between the reinforcement material and the frozen earth. On this project, reinforcement installation was contingent on the availability of subsurface drilling equipment. A three foot diameter hole was the smallest large bore drilling equipment available. Since drilling and installation labor were much.more expensive and the strain and deformations were to be kept to an absolute minimum, a 24 x 146 steel beam section was selected. This size had sufficient cross-sectional area and was readily available. Following placement of the steel beams, the drilled .bore holes were backfilled by pumping and vibrating a six- inch slump Portland Cement Concrete into the hole. During excavation it was desirable to maximize adfreeze bond Jbetween the composite steel/concrete reinforcement and the 166 frozen soil. This was accomplished by keeping the interface area as cold as possible by using two three-inch diameter steel refrigeration pipes welded onto the beam prior to insertion into the bore hole. To ensure a stronger adfreeze bond, coolant was circulated through these pipes at a temperature of approximately -30%:. .After selecting the most cost effective method of reinforcement, an FEM analysis was conducted using a model of the reinforced section. The program used should have the capability to evaluate both deformation and stresses within the reinforced structure. Should this analysis yield deformations which are larger than those permitted, the cross sectional area of the reinforcement.must be increased. It is possible to have a sufficient reinforcement cross- sectional area and an inadequate adfreeze bond. If this condition exists, the contact surface area at the soil/reinforcement interface must be increased. Several trials may be required before an acceptable deformation is achieved. Section 5.2 summarizes steps used in the structural analysis. As noted previously, this is the first time such an analysis has been attempted and followed by construction in the field. The results were considered very successful. To improve on this design method, more precise instrumentation should be used on subsequent projects so that more accurate comparisons can be made between predicted 167 and actual field performance. 7.5 Qreep Effects and Factor of Safety .A comparison of the time-dependent FEM behavior with the elastic analysis for the reinforced section indicates that most of the total deformation was represented by the initial elastic (time = 0) deformation of the nonlinear analysis. This was most likely a result of the elastic reinforcing element bearing the majority of the load. While this was the case in the buttress section, reference is now made to the elastic analysis for the cell l/dropshaft model. In this model the computed elastic deformation appeared to be insignificant, but a comparison of stresses on the log-time vs. reciprocal of stress plot indicated an approximate structural life of less than 1000 hours. This phenomenon showed the need for a time-dependent analysis. Use of Soo's (1983) program permitted an evaluation of the computed nodal deformations for comparison with permitted values. On this project, 0 easura efo a ' s sta da fiel s e e ' ent a e ’ . One of the keys to successful design on this project was knowledge of the creep effects of the frozen soil/reinforcing element interface. The program developed by $00 (1983) used bond link elements permitting an evaluation of the critical adfreeze bond at successive time increments. Results of ‘this analysis indicated minimal deformations due to long 168 term creep behavior. Failure times of the adfreeze bond due to creep would not have been detected using the linear elastic analysis. In many engineering design procedures, an appropriate factor of safety against failure is assigned at some phase in the design computations. This factor of safety is based on the designer's confidence in the design procedures, knowledge of material properties and behavior, and potential loss of life and/or property in the event of failure. In the design of frozen earth structures, there is no design code, or even standard procedures to adhere to in the design process. In the conventional design procedures discussed in Chapter V, mention was made to reducing the unconfined compressive strength of the frozen soil by a preselected degree, thus applying a resulting factor of safety. This procedure has been used with success on typical circular shafts and cofferdams. In a numerical analysis, altering the material properties can have a significant impact on computed displacements and stresses. Specifically, altering the parameters may result in output which may not only be meaningless but may have an opposite effect on the final results. For example, reducing the elastic modulus may produce conservative deformation values, with lower values of internal stresses resulting in less time-dependent creep deformation in the nonlinear phase of the computer analysis. 169 In the interim, appropriate factors of safety must be applied to complex and traditional frozen earth structures. The recommended method for ensuring safe design is to apply a multiplier (factor of safety) to the design life of the frozen earth cofferdams. While many frozen earth cofferdams have been successfully constructed within required project schedules, it is not uncommon for the excavation to remain open for two to three times longer than planned. For this reason it is recommended that the design life be multiplied by factors no less than three, and corresponding time steps be added to the time-dependent phase of the analysis. This factor of three should be increased if any of the following conditions apply: 1. Material properties have not been satisfactorily determined or are open to question. 2. Project refrigeration capacity may be less than desirable. 3. The excavation will remain open for long periods of time during which frozen walls will be exposed to ambient air temperatures greater than 85°F. 4. Impurities or dissolved salts are contained with the ground water which can weaken the frozen soil. Numerical factors of safety should not be considered replacements for close attention to detail of all phases of the analysis, from field exploration to laboratory testing and design, and quality control during construction. VIII. N L I N The concepts and procedures used on this project have resulted in a more systematic method for site evaluation and selection of design parameters suitable for analysis and design of reinforced frozen earth walls with complex geometrical sections. Field construction of the deep shaft and connecting structures, along with observations on wall stability and movements, helped demonstrate the success of this project. Methods presented in this study should be suitable for future design applications. While the design itself was conservative relative to the amount of reinforcement, both analytical and numerical analyses indicated that the frozen earth structure would have failed without reinforcing elements. The reinforced wall was designed to reduce tensile stresses to a minimum in the frozen soil and at the same time to minimize wall :movement. This project has shown that the following procedures, 'when correctly accomplished, can be successfully used for 'the design of reinforced frozen earth retaining structures. 1. Available subsurface geological and geotechnical data, particularly soil stratification and ground water levels and flow gradients, should be assembled and ‘thoroughly evaluated relative to the proposed frozen retaining structure. 170 171 2. Required geometry of the frozen soil retaining structure should be planned so as to develop a wall that is both economical and space efficient for proposed construction at the site. 3. Frozen soil tests should be performed to determine mechanical properties of the weaker soils and/or soils in the more highly stressed wall sections. Required material properties include the elastic modulus, unconfined compressive strength, and creep parameters in both uniaxial compression and tension. 4. Laboratory test results should be analyzed to determine not only the parameters listed in Item 3, but also the effects on mechanical behavior when the structure is subjected to loads over an extended time period. 5. Simple closed form solutions (if possible) may be used to determine relative feasibility of selected wall geometry, however, without experience with similar structures, they could yield meaningless results. Specialized computational methods are then required. 6. A linearly elastic three-dimensional finite element analysis should be completed on models representing the desired wall geometry. This analysis can be used to verify that internal stresses do not exceed the maximum permitted soil strength for a specified duration of loading. 7. If the linear finite element models indicate stress zones higher than permissible for the frozen earth and the ‘wall geometry cannot be changed, reinforcement elements are required. 8. Numerical methods, both linear and nonlinear, can be used to model the reinforced sections within the frozen earth structure. If internal and bond stresses are within allowable ranges, the structure can be constructed without danger of collapse. 9. Field instrumentation suitable for displacement and strain (or stress) measurements should be installed on reinforcement members to monitor and verify field performance of the reinforced frozen earth structure. The procedures outlined above were shown to be appropriate for design of the frozen earth structures. They have also answered questions regarding the feasibility of ‘using reinforcement elements in frozen earth as a practical 172 construction technique. There is the possibility that future design refinements will permit a less conservative approach to be used in the design of similar structures. These improvements, although cost prohibitive for actual construction projects, may warrant further computational studies in combination with the laboratory phase. Three recommendations include the following: 1. On future projects it would be desirable to conduct strength tests at both colder and/or warmer temperatures. The resultant moduli and creep parameters could then be varied in the numerical analysis to better represent the proximity of individual soil elements to the refrigeration pipes. 2. Modification of testing equipment used on this project would permit refinement of some testing procedures, particularly in the constant strain rate tests used to determine the elastic moduli. These changes should include a mechanized apparatus with variable speeds to control deformation rates. 3. An improvement in the analysis phase of the project would be to develop a nonlinear program with bond-slip elements for use with three-dimensional shell elements. Such a program could significantly reduce the number of iterations required for the cross-sectional analysis. Perhaps the most significant setback of the entire project was the failure of strain gauges mounted on reinforcement elements. It should be noted that even if the strain gauges had functioned as planned, the deformation predicted by the analysis would most likely have been too small to measure. On future projects, the deformation instrumentation used on reinforcing members should be of high precision and protected against damage during placement so that data can be obtained for a more complete 173 verification of the design computations. Even though several areas of refinement and improvement were noted pertaining to the design methods used in this dissertation, several topics very critical to the design of frozen earth structures were not covered. These topics included bottom stability, refrigeration plant requirements, thermodynamic analysis of the secondary coolant, and project management. Research should be conducted using actual data taken from field projects. It is important that researchers work with the contractors to develop workable and practical design methods based on actual data. These are topics which, in themselves, deserve in-depth research. They were extremely critical to the success of this project. In summation, this dissertation has described a system of analysis for a virtually untested construction technique, the use of reinforcement in frozen earth structures. It has provided a useful engineering procedure for the design of such structures. These procedures have been described in detail, beginning with site reconnaissance and project requirements, standardized frozen soil laboratory tests, and a refined method of numerical structural analysis. The field performance of this particular frozen earth structure proved that previously untested methods may serve as a basic guide for future projects in which structural reinforcement may be required. REFERENCES Akagawa, S. 1980. Poisson's ratio of sandy frozen soil under long term stress, by creep tests. Second International Symposium on Ground Freezing, Trondheim, 253- 247. Alwahhab, M.R.M. 1983. Bond and slip of steel bars in frozen sand. Unpublished Ph.D. Dissertation, Michigan State University, E. Lansing, Michigan. Andersland, O.B., and Akili, W. 1967. Stress effect on creep rates of a frozen clay soil. Geotechnique, 17, 27- 39. Andersland, O.B., and Alwahhab, M.R.M. 1982. Bond and slip of steel bars in frozen sand. GROUND FREEZING, Proc. 3rd International Symposium, U. S. Army CRREL, Hanover, New Hampshire, 27-34. Andersland, O.B., and Alwahhab, M.R.M. 1984. Load capacity of model piles in frozen ground. Proc. 3rd International Conference on COLD REGIONS ENGINEERING, Canadian Society for Civil Engineering, Montreal, Quebec, Canada, ;, 29-39. Andersland, O.B.; Sayles, F. H.; and Ladanyi, B. 1978. Mechanical properties of frozen ground. Chapter 5 in GEOTECHNICAL ENGINEERING FOR COLD REGIONS, MCGraw-Hill Book Company, New York, New York. Bragg, R. A. 1980. Material properties for sand-ice structural systems. Unpublished Ph. D. Thesis, Michigan State University, E. Lansing, Michigan. Bragg, R. A. and Andersland, O. B. 1982a. Strain dependence of Poisson's ratio for frozen sand. THE ROGER J.E. BROWN MEMORIAL VOLUME, ed. by H.M. French, Proc. 4th Canadian Permafrost Conference, National Research Council, Canada, 365-373. Bragg, R. A. and Andersland, O.B. 1982b. Strain rate, temperature, and sample size effects on compression and tensile properties of frozen sand. GROUND FREEZING 1980, 174 Developments in Geotechnical Engineering V01. 28, ed. by P. E. Frivik, N. Janbu, R. Saetersdal, and L. I. Finborud, Elsevier Scientific Publishing Company, Amsterdam, 35-46. Burdick, J. L.; Rice, E. F.; and Phukan, A- 1978. Cold regions: descriptive and geotechnical aspects. Chapter 1 in GEOTECHNICAL ENGINEERING FOR COLD REGIONS, McGraw-Hill Book Company, New York, New York. Domke, O. 1915. Uber die beanspruchung der froustmaur beim schachtebteufen nach dem gefrierverfahren. Gluckauf, Si, 1129-1135. Eckardt, H. 1981. Creep tests with frozen soils under uniaxial tension and uniaxial compression. THE ROGER J. E. BROWN MEMORIAL VOLUME, ed. by H.M. French. Proc. 4th Canadian Permafrost Conference. National Research Council of Canada, 394-405. Eckardt, H. 1979. Creep behavior of frozen sands in uniaxial compression tests. Engineering Geology, ;1, 185- 195. Goodman, R. E.; Taylor, R. L.; and Brekke, T. L. 1968. A model for the mechanics of jointed rock. Journal of the Soil Mechanics and Foundations Division. ASCE, SS, 8M3, Goughnour, R. R. and Andersland, O. B. 1968. Mechanical properties of a sand-ice system. Journal of the Soil Mechanics and Foundations Division. ASCE, 21 SM4, 923- 950. Greenbaum, G. A. and Rubinstein, M. F. 1968. Creep analysis of axisymetric bodies using finite elements. Nuclear Engineering and Design, 1, 379-397. Hawkes, I. and Mellor, M. 1970. Uniaxial testing in rock mechanics laboratories. Engineering Geology, 4, 3, 177- 285. Haynes, F. D. 1978. Strength and deformation of frozen silt. PERMAFROST, 3rd International Conference, National Research Council of Canada, Ottawa, ;, 656-661. Haynes, F. D.; Karalius, J. A.; and Kalafut. 1975. Strain rate effect on the strength of frozen silt. U. S. A. Cold Regions, Research and Engineering Laboratory, Research Report 350. Heginbottom, J. A. 1985. Personal Communication. 175 Jessberger, H. L. 1980. State of the art report ground freezing: mechanical properties, processes and design. GROUND FREEZING, 1980, ed. by P. E. Frivik, N. Janbu, R. Saetersdal, and L. I. Finbound. Developments in Geotechnical Engineering, 2S, Elsevier Scientific Publishing Company, Amsterdam. Jessberger, H. L. and Nussbaumer, M. 1973. Anwendung des Gefrierverfahrens. Bautechnick, 12, 414-420. Klein, J. 1981. Finite element method for time dependent problems of frozen soils. International Journal for Numerical and Analytical Methods in Geomechanics, S, 263- 283. Klein, J. and Jessberger, H. L. 1979. Creep analysis of frozen soils under multiaxial states of stress. Engineering Geology, 11, 353-365. Krause, H. 1980. Creep Analysis. John Wiley and Sons, New York. Ladanyi, B. 1982. Ground pressure development on artificially frozen soil cylinder in shaft sinking. "Amie et Alumni." E. E. DeBeer Special VOlume, Brussels, 187- 195. Linell, K. A., and Kaplar, C. W. 1966. Description and classification of frozen soils. U. S. Army CRREL. Hanover, New Hampshire, Technical Report 150. Mellor, M.; Cox, G. F. N.; and Bosworth. 1984. Mechanical properties of multi-year sea ice testing techniques. U. S. A. Cold Regions Research and Engineering Laboratory, Report 84-8 0 Mendelson, A.; Hirschberg, M. H.; and Manson, S. S. 1959. A general approach to the practical solution of creep problems. Transactions ASME, S1, 585-589. Parameswaran, V. R. 1980. Deformation behavior and strength of frozen sand. Canadian Geotechnical Journal, 2, 74-88 a Parameswaran, V. R. and Jones, S. J. 1981. Triaxial testing of frozen sands. Journal of Glaciology, ;§, 147- 155. Sanger, F. J. 1968. Ground freezing in construction. Journal of the Soil Mechanics and Foundations Division. ASCE, 21' 5M1; 131-1580 176 I?) Sego, D. C., and Morgenstern, N. R. 1983. Deformation of ice under low stresses. Canadian Geotechnical Journal, 20, 587-600. Shuster, J. A. 1972. Controlled freezing for temporary ground support. Proc. lst North American Rapid Excavation and Tunneling Conference, Chicago, 2, 863-894. Shuster, J. A. 1982. Engineering quality assurance for construction ground frezing. GROUND FREEZING 1980, ed. by P. E. Frivik, N. Janbu, R. Saetersdal, and L. I. Finbourd. Developments in Geotechnical Engineering, 2S, Elsevier ' Scientific Publishing Company. Amsterdam, 333-347. Shuster, J. A.; Braun, E.; and Burnham, E. W. 1979. Ground freezing for support of open excavations. GROUND FREEZING, ed. by H. L. Jessberger. Developments in Geotechnical Engineering, SS, Elsevier Scientific Publishing Company, Amsterdam, 429-453. 500, S. 1983. Studies of plain and reinforced frozen soil structures. Unpublished Ph.D. dissertation. Michigan State University, E. Lansing, MI. 300, S.; Wen, R. K.; and Andersland, O. B. 1984. Analysis of plain and reinforced frozen soil structures. COLD REGIONS ENGINEERING, Proc. 3rd, International Conference. Canadian Society for Civil Engineering, Montreal, Quebec, 1, 507-521. 800, S.; Wen, R. K.; and Andersland, O.B. 1985. Finite element models for structural creep problems in frozen ground. GROUND FREEZING 1985. Proc. 4th International Symposium, ed. by S. Kinosita, M. Fukuda, and A. A. Balkema, Rotterdam, 2, 23-28. Thompson, E. G. and Sayles, F. H. 1972. In-situ creep analysis of room in frozen soil. Journal of Soil Mechanics and Foundations Division. ASCE, SS, 8M9, 899-915. vyalov, S. S. 1962. The strength and creep of frozen soils and calculations for ice-soil retaining structures. U. S. .Army, CRREL, Hanover, New Hampshire, Translation 76. 177 "1 I APPENDIX A LABORATORY TEST DATA _.._i _ I‘l- Point \OOQGU'IoFIANI-d Deformation Rate : Test Temperature : Load Rdg. 0.0000 0.6520 1.1411 1.7931 2.1191 2.9341 3.5862 4.2382 4.7272 5.3792 6.0313 6.5203 7.8243 8.9654 10.1064 11.4105 12.5516 14.0186 Disp. Rdg. 0.2477 178 CONSTANT STRAIN RATE COMPRESSION TEST Stress KSF 0.00 4.00 7.00 11.00 13.00 18.00 22.00 26.00 29.00 33.00 37.00 40.00 48.00 55.00 62.00 70.00 77.00 86.00 Strain Percent 0.00 0.10 0.30 0.40 0.60 1.10 1.50 1.70 2.10 2.40 2.70 3.00 3.40 3.80 4.20 4.60 5.60 6.30 Length: 6.0 inches Diamter: 1.89 inches VOlume: 16.83 inches **3 Weight: 521.31grams Water Content: 34% Wet Density: 119 pcf Dry Density: 88.4 pcf COMPRESSION CREEP TEST Stress Level: 41.7 ksf Test Temperature: Point 1 2 3 4 5 6 Elapsed Time(min) 0.0000 20.0000 40.0000 60.0000 80.0000 100.0000 -10 Deg. Disp. Rdg. 0.0000 0.1736 0.2243 0.2724 0.3445 0.5180 179 C Strain (%) 0.0000 6.5000 8.4000 10.2000 12.9000 19.4000 Length: 6.0 inches Diamter: 1.89 inches Volume: 16.83 in**3 Weight: 519.24 grams Water Content: 32% Wet Density: 118 pcf Dry Density: 89.4 pcf COMPRESSION CREEP TEST Stress Level: 29.34 ksf Test Temperature: Point ...: ommqmmbwnw Elapsed Time(min) 0.0000 20.0000 40.0000 60.0000 100.0000 140.0000 160.0000 200.0000 245.0000 260.0000 180 -10 Deg. C Disp. Rdg. Strain (%) 0.0000 0.0000 0.0320 1.2000 0.0534 2.0000 0.0641 2.4000 0.0908 3.4000 0.1282 4.8000 0.1469 5.5000 0.1736 6.5000 0.2510 9.4000 0.3097 11.6000 Length: 6.0 inches Diamter: 1.89 inches VOlume: 16.83 in**3 Weight: 527.6 grams Water Content: 36% Wet Density: 120 pcf Dry Density: 88.2 pcf COMPRESSION CREEP TEST Stress Level: 29.34 ksf Test Temperature: Point *DQNIONUIIFDJNH Elapsed Time(min) 0.0000 20.0000 40.0000 60.0000 80.0000 100.0000 120.0000 140.0000 160.0000 180.0000 200.0000 220.0000 Disp. Rdg. 0.0000 0.1469 0.1869 0.2270 0.2537 0.2804 0.3204 0.3605 0.4085 0.4593 0.5127 0.6008 181 Strain (%) 0.0000 5.5000 7.0000 8.5000 9.5000 10.5000 12.0000 13.5000 15.3000 17.2000 19.2000 22.5000 Length: 6.0 inches Diamter: 1.89 inches VOlume: 16.83in **3 Weight: 521.72 grams Water Content: 34% Wet Density: 119 pcf Dry Density: 88.5 pcf h Strain Rate: Point wdeSU'I-hUNH NMNNHHHPHHH unwommdmmawgtz .24 :25 126 27' :28 .29 Test Temperature: Load Rdg. 0.0000 0.0204 0.3423 0.5216 0.6357 0.7498 0.9128 1.0758 1.2552 1.4182 1.5160 1.7605 1.9561 2.1354 2.3310 2.5429 2.7385 2.8689 3.0156 3.1949 3.3742 3.5210 3.6188 (3.8307 ‘4.0263 g .2382 4 -4175 4 -6620 4 -8739 3.086EE-5/sec -10 Deg. C Disp. Rdg. 0.2477 182 CONSTANT STRAIN RATE TENSION TEST Stress KSF 0.00 0.13 2.10 3.20 3.90 4.60 5.60 6.60 7.70 8.70 9.30 10.80 12.00 13.10 14.30 15.60 16.80 17.60 18.50 19.60 20.70 21.60 22.20 23.50 24.70 26.00 27.10 28.60 29.90 0.00 0.01 0.19 0.25 0.28 0.35 0.42 0.44 0.46 0.48 0.50 0.52 0.54 0.56 0.58 0.60 0.63 0.64 0.65 0.65 0.66 0.68 0.69 0.73 0.74 0.74 0.76 0.77 0.80 Length: 6.0 in Diamter: 1.89 inces volume: 16.83 in**3 weigth: 531.2 grams Water Content: 37% Wet Density: 121pcf Dry Density: 88.1 pcf MEASURED PRIOR TO CUTTING Corr. Strain Percent TENSION CREEP TEST 183 Stress Level: 28.4 ksf Test Temperature : Point UubtthH Elapsed Time(min) 0.0000 0.0026 0.0055 0.0083 0.0110 -10 Deg. C Disp. Corr. Rdg. Strain (%) 0.0000 0.0000 0.5682 0.2600 0.6556 0.3000 0.7430 0.3400 0.8086 0.3700 Length: 6.0 inches Diamter: 1.89 inches VOlume: 16.83 in**3 Weight: 534.3 grams Water Content: 34% Wet Density: 121 Dry Density: 90.6 pcf MEASURED PRIOR TO CUTTING TENSION CREEP TEST Stress Level Test Temperature 3 Point P'H HOWQQO‘U‘DUJNH Elapsed Time(min) 0.0000 0.0025 0.0050 0.0075 0.0100 0.0125 0.0150 0.0174 0.0198 0.0224 0.0248 12.5 184 -10 Deg. C Disp. Corr. Rdg. Strain (%) 0.0000 0.0000 0.3278 0.1500 0.5463 0.2500 0.8086 0.3700 1.1364 0.5200 1.4642 0.6700 1.7701 0.8100 2.0760 0.9500 2.4913 1.1400 2.9502 1.3500 3.8243 1.7500 Length: 6.0 inches Diamter: 1.89 inches VOlume: 16.83 in**3 Weight: 530.22 grams Water Content: 35% Wet Density: 121 pcf Dry Density: 89.3 pcf MEASURED PRIOR TO CUTTING