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I. t It: tyv 3:13.; .Ixh. i ..vt\ 0. t .- h.§!PV...«QV1 an“ ”I“? ”gamma: I u. #533 its THESIS ’7 iiiiiiiiiiiiiiiiiiiWit a 3 1293 01420 3412 This is to certify that the thesis entitled Characterizing Soil Strength for Probabilistic Analysis Working From Test Results: A Practical Approach Date presented by Ikhlaq Ur Rasul has been accepted towards fulfillment of the requirements for Masters Civil Engineering degree in Major professor 12/13/95 0-7 639 MS U is an Affirmative Action/Equal Opportunity Institution LIBRARY ‘ Michigan State. University i PLACE ll RETURN BOXto mnavothb chockoutfrom your record. TO AVOID FINES Mum on or More data duo. DATE DUE DATE DUE DATE DUE |[::l___|: r_—_|L_—:__:_l——l -i—1-"—j :J[ 1- MSU In An Affirmatm Action/Equal Opportunity Indium W DIG-9.1 CHARACTERIZING SOIL STRENGTH FOR PROBABILISTIC ANALYSIS WORKING FROM TEST RESULTS: A PRACTICAL APPROACH By Ikhlaq Ur Rasul A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Civil and Environmental Engineering 1995 ABSTRACT CHARACTERIZING SOIL STRENGTH FOR PROBABILISTIC ANALYSIS WORKING FROM TEST RESULTS, A PRACTICAL APPROACH By Ikhlaq Ur Rasul The purpose of this study was to investigate and critically compare a number of methods for probabilistic characterization of soil strength. In deterministic methods, personal judgment is involved in drawing of failure envelopes. The statistical approach is algorithmic and thus eliminates the effects of personal opinion. Several methods for statistical characterization can be found in literature which make use of regression analysis to achieve the best-fit line. Holtz and Noell(1950) suggested regression of 0, on 03, Balmer(l946) regressed r on on, Lumb(1970) combined all 61 , 63 values to execute pooled regression. Regression of q on p overestimates d), so Handy(1970) proposed rotation of p,q axes to prevent it. Some other methods have also been reviewed and some new methods proposed to widen the sc0pe of this comparative study. Eleven methods have been tested by applying them to seven different sets of data, based on total stress failure criterion only, obtained from a dam and a levee. The Holtz and Noel] method, which regresses c, on 03, appeared to be the simplest and the one yielding the most conservative mean value of 4). Regression of c, on 03 exactly matches the linear regression model in terms of variables and all the assumptions therein. Other methods contradict the model and overestimate 4) to varying degrees. ACKNOWLEDGMENTS All praises to Allah Ahnighty, due to Whose blessings I was able to complete this project. My profound thanks to the Pakistan Army and NUST for their generous support for this course work at MSU. Dr. Thomas F. Wolff, my major professor, really taught me the art of carrying out research. He was a continuous source of encouragement for me. During periods of utter frustration, he would always guide me and help me come out of that situation. I generally used to visit his office without formal appointments but he would always welcome me with a smiling face. I am thankful to him for permitting me to use some of his material in the literature review. My gratefulness to the St. Louis District of the US Corps of Engineers for the use of data during the analyses. I am also grateful to Dr. William C. Taylor, Dr. Gilbert Y. Baladi and Dr. Karim Chatti for their concern and continuous encouragement. My special thanks to Lieutenant Colonel Rahat Khan, who really helped me to settle down in relatively unfamiliar environments and then provided continuous support in my studies and other administrative affairs. I would like to thank my long-time companion, Major Anwar-ul-Haq Chaudhry who never missed any opportunity of feeding me with our traditional foods and making me feel less homesick. I will take this opportunity to thank the Pakistan Student Association and Pakistani Community for their care and concern. I also acknowledge and appreciate the assistance of Mr. Michael Miller iii in figure drawing. I am thankful to Mr. Evan Schumann and Mr. Hyung Bae Kim for their general computer assistance. My parents always pray to Allah Almighty for my success in every field. Without their moral support, this work could not have been completed in time. My very special thanks to my wife and children for letting this big chunk of time out of their share for my coming to MSU. Although they were back in Pakistan and I greatly missed their company, still they were very close to me through their letters, cards and photographs. iv TABLE OF CONTENTS List of figures List of tables CHAPTER 1. Introduction -Purpose -Objectives -Study approach 2. Soil strength description 2.1 General 2.2 Shear strength and its importance 2.3 Mohr-Coulomb failure criterion 2.4 Modeling undrained conditions 2.5 Stress path 2.6 Laboratory testing for shear strength 3. Probabilistic moments and regression analysis 3.1 General 3.2 Moments Page ix xiii 10 l3 16 18 19 3.3 Linear regression analysis 3.3.1 General 3.3.2 Linear regression model 3.3.3 The method of least squares 3.3.4 Uses of regression 3.3.5 Use of computer for regression analysis 4. Statistical characterization of strength data 4.1 General 4.2 Format of available strength data 4.3 Alternative approaches to characterizing strength data -Method 1 -Method 2 -Method 3 -Method 4 -Method 5 -Method 6 -Method 7 -Method 8 -Method 9 -Method 10 -Method 1 1 vi 21 21 22 23 25 25 27 28 29 29 31 34 36 37 39 4O 42 44 45 47 5. Application of methods to actual data sets 5.1 General 5.2 Clarance Cannon Dam results 5.2.1 Clarance Cannon Dam 5.2.2 Q(UU) tests on record samples - phase I fill 5.2.3 Q(UU) tests (borings) - phase I fill 5.2.4 R(CU) tests - phase I fill 5.2.5 Q(UU) tests - phase II fill 5.2.6 R(CU) tests - phase II fill 5.3 Perry County Bois Brule Levee results 5.3.1 Bois Brule Levee 5.3.2 Q(UU) tests 5.3.3 R(CU) tests 5.4 Method 6 - Lumb’s weighted regression 5.5 Negative «1) values 5.6 The problem of outliers 6. Conclusions and Recommendations 6.1 Conclusions 6.2 Recommendations 6.2.1 Recommendations for practitioners 6.2.2 Recommendations for further research vii 48 49 49 49 57 62 62 71 76 76 76 79 79 87 87 9O 94 94 95 Appendices -Appendix A- Individual samples regression 97 -Appendix B - Pooled regression 111 List of references 155 viii 2.1: 2.2 2.3 2.4 2.5 2.6 : 2.7 : 3.1 3.2 : 4.1: 4.2 : 4.3 : 4.4 : 4.5 : 4.6 : 4.7 : LIST OF FIGURES Mohr’s failure criterion : The Mohr-Coulomb strength criterion : Undrained strength from Q and R tests : Undrained Strength Envelope for Partially Saturated, Cohesive Soil : A Mohr’s circle and stress point (a) Stress state by Mohr’s circles (b) Stress path for constant 63 and increasing 0', Relationship between the Kf - line and Mohr-Coulomb failure envelope : The linear regression model Method of least squares minimizes the resulting errors Method 1 Method 2 Method 3 Method 4 Method 5 Method 7 Method 8 ix Page 11 12 13 14 14 15 22 24 30 32 33 35 37 4o 43 4.8 : 5.1 5.2 5.3 5.4 : 5.5 5.6 : 5.7 5.8 5.9: 5.10 5.11 5.12: 5.13 5.14: 5.15 5.16: 5.17: 5.18 5.19: 5.20 : 5.21 Method 10 : Method 2 - Sample No.1 - Q tests - Phase I : Method 3 - Sample No.1 - Q tests - Phase I : Method 4 - Sample No.1 - Q tests - Phase 1 Method 5 - Q tests - Phase I : Method 10 - Q tests - Phase I Method 8 - Q tests - Phase I : Method 9 - Q tests - Phase I : Sample 47U P-2, Method 2 - Q tests (Borings) Sample 47U P-2, Method 3 - Q tests (Borings) : Sample 47U P-2, Method 4 - Q tests (Borings) : Method 5 - Q test ( Borings)- Phase I Method 10 - Q test ( Borings)- Phase I : Method 8 - Q test ( Borings)- Phase I Method 9 - Q test ( Borings)- Phase I : Sample No.3 - Method 2 - R tests — Phase I Sample No.3 - Method 3 - R tests - Phase I Sample No.3 - Method 4 - R tests - Phase I : Method 5 - R tests - Phase I Method 10 - R tests - Phase I Method 8 - R tests - Phase I : Method 9 - R tests - Phase I 45 52 52 52 54 54 55 55 59 59 59 6O 6O 61 61 64 65 65 66 66 5.22 : 5.23 5.24 5.25 5.26 : 5.27 : 5.28 : 5.29 : 5.30: 5.31 5.32 : 5.33 5.34 : 5.35 5.36: 5.37: 5.38 : 5.39 : 5.40 : 5.41 5.42 5.43 Sample No.297 - Method 2 - Q tests : Sample No.297 - Method 3 - Q tests : Sample No.297 - Method 4 - Q tests : Method 5 - Q tests - Phase 11 Method 10 - Q tests - Phase II Method 8 - Q tests - Phase II Method 9 - Q tests — Phase 11 Sample No. 297 - Method 2 - R tests Sample No. 297 - Method 3 - R tests : Sample No. 297 - Method 4 - R tests Method 5 - R tests - Phase II : Method 10 - R tests - Phase II Method 8 - R tests - Phase II : Method 9 - R tests - Phase 11 Sample P-ZB, Method 2 - Levee Q tests Sample P-2B, Method 3 - Levee Q tests Sample P-2B, Method 4 - Levee Q tests Method 5 - Levee Q tests Method 10 - Levee Q tests : Method 8 - Levee Q tests : Method 9 - Levee Q tests : Sample P-ZB, Method 2 - Levee R tests xi 68 68 68 69 69 70 70 73 73 73 74 74 75 75 78 78 78 80 80 81 81 83 5.44 5.45 5.46 5.47 : 5.48 5.49 : 5.50 : 6.1 6.2 : Sample P-ZB, Method 3 - Levee R tests : Sample P-2B, Method 4 - Levee R tests : Method 5 - Levee R tests Method 10 - Levee R tests : Method 8 - Levee R tests Method 9 - Levee R tests Lumb’s weighted regression for Q test - Phase I : Methods for statistical characterization of soil strength considering individual samples : Methods for soil strength characterization for pooled regression xii 83 83 84 84 85 85 86 92 93 5.1 5.2 5.3 5.4: 5.5 5.6: 5.7 5.8 : 5.9: LIST OF TABLES : Cannon Dam Shear Testing - Q (UU) Tests Individual Samples(Phase I) : Cannon Dam Shear Testing - Q (UU) Tests Pooled Regression(Phase I) : Cannon Darn Shear Testing - Q (UU) Tests - Borings Individual Samples(Phase I) Cannon Dam Shear Testing - Q (UU) Tests - Borings Pooled Regression(Phase I) : Cannon Dam Shear Testing - R (CU) Tests Individual Samples(Phase I) Cannon Darn Shear Testing - R (CU) Tests Pooled Regression(Phase I) : Cannon Dam Shear Testing - Q (UU) Tests Individual Samples(Phase II) Cannon Dam Shear Testing - Q (UU) Tests Pooled Regression(Phase II) Cannon Dam Shear Testing — R (CU) Tests Individual Samples(Phase II) xiii Page 51 51 58 58 63 63 67 67 72 5.10 5.11 5.12 5.13 5.14 5.15 A.l A2 A3 A4 : A5 8.1 B2 B3 8.4 : B.5 : Cannon Dam Shear Testing - R (CU) Tests Pooled Regression(Phase lI) : Perry County Shear Testing - Q (UU) Tests Individual Samples : Perry County Shear Testing - Q (UU) Tests Pooled Regression : Perry County Shear Testing - R (CU) Tests Individual Samples : Perry County Shear Testing - R (CU) Tests Pooled Regression : Cannon Dam Shear Testing - Q (ULD Tests Lumb’s Weighted Regression : Method 2 - Individual samples : Method 3 - Individual samples : Method 4 - Rotation of axes Method 4 - Individual samples : Comparison and statistics of Methods 1 through 4 : Method 5 - Pooled regression : Method 8 - Pooled regression : Method 9 - Rotation of axes Method 9 - Pooled regression : Method 10 - First regression xiv 72 77 77 82 82 86 101 103 105 106 109 114 119 124 129 137 B.6 : Method 10 - Second regression 141 B.7 : Method 11 - First regression 146 B8 : Method 11 - Second regression 150 XV CHAPTER 1 INTRODUCTION This study deals with the characterization of soil strength for probabilistic analysis. Adequate description of soil strength is pre-requisite to almost all kinds of geotechnical analyses such as slope stability analysis, foundation design, earth retaining structure design, etc. Soil strength generally refers to shear strength of soil, because most failures in foundations and earthworks are shear failures. The shear strength of soils is an uncertain quantity. The testing of soils from an area under study gives scattered test results. Traditionally, engineers select a “design” value of soil strength from these scattered test results based on their best judgment. This is subjective, and in doing so, information regarding the uncertainty is discarded. The probabilistic approach shows promise of developing into a more rational approach than the traditional one. In the probabilistic approach, a statistical description of soil strength is used. Strength is treated as a random variable which in turn is a function of two random variables c and d). For soils whose strength requires a single component only, such as the undrained cohesion of saturated clays or drained angle of shearing resistance of clean sands, the interpretation is relatively simple. The strength of C41) soils involves two components, both cohesion and angle of shearing resistance, so a probabilistic interpretation is not quite straight-forward. 2 The statistical approach employs regression analysis to achieve the best-fit line. The earliest application of regression analysis to triaxial data was by Balmer (1946) who used regression of If on on. The other methods involving regression were suggested by Holtz and Noell (1950), Lumb (1970), Handy (1981), Schoenemann and Pyles (1990) and Wolff (1995). Some new methods have also been proposed to expand the horizon of this comparative study in order to reach at best possible conclusions. Purpose There are number of methods and alternative approaches available for characterizing soil strength working from triaxial test data. The purpose of this study is to critically review eleven different methods by considering their relative merits and demerits and recommend the better one out of all these methods. Objectives In pursuance to the above mentioned consideration, the following have been defined as the objectives of this study: 1. Critically review different methods for probabilistic characterization of soil strength which have been suggested from time to time. 2. Assess and compare the relative advantages and disadvantages of all these methods after applying them to actual data at two different sites and also highlight some of problems associated with their use. 3 3. Recommend a “best” method for use by practitioners on the basis of this study applicable to total stress parameters only. (The application of these methods to effective stress parameters and pore pressure changes is beyond the scope of this study). 4. Illustrate the construction of some simple spread sheets for characterizing soil strength parameters while applying each method to actual test results. Study Approach To realize these objectives, following study approach was pursued during the course of this study. Chapter 2 describes the deterministic ways of characterizing the soil strength. It involves the study of Mohr-Coulomb failure envelope to establish values of c and d) and how to use stress path theory to reach the same goal of defining c and 4). Also there is a brief description of laboratory tests which are conducted for determining the shear strength of soils. In Chapter 3, some basic concepts and definitions of statistics have been discussed as they are required for use in subsequent study. It also goes on to describe regression analysis, its use, and problems associated with its use. Chapter 4 gives a detailed account of each considered method (including some developed by author) along with its relative advantages and disadvantages. Each method has been applied to actual test data for materials from the Clarance Cannon Dam and Bois Brule Levee. The results of this comparative study are included in 4 Chapter 5. The detailed discussion on these results has been done to reach at plausible conclusions. Problems with outliers, which are frequently encountered during regression analysis, have also been addressed in this chapter. The diagnostic use of softwares like MINITAB and Microsoft Excel is briefly described. Chapter 6 includes the conclusions drawn as a result of this study. It recommends the better methods for use by practitioners both for individual samples case and for pooled regression. Some problems which have been identified during this study but were beyond its sc0pe, have been recommended for future research. The use of spreadsheets has been illustrated in the appendices by solving a complete example for each of the methods. Appendix A explains the use of Methods 1 through 4 which use regression analysis on individual samples while Appendix B deals with Method 5 and Methods 8 through 11 for pooled regression on whole set of data. CHAPTER 2 SOIL STRENGTH DESCRIPTION 2.1 General As discussed in the introduction, the strength of a soil is a significant factor in the design of retaining walls, embankments, bracing for excavations, and foundations. If the soil strength is exceeded, a failure in the soil mass will occur that may endanger life and property. Because of their complicated structure, soils do not have same reaction to stress changes and strains as do other familiar materials such as metals. Their variation of strength with time which is caused by pore pressure change during consolidation and condition of loading are major sources of uncertainty. Also soil is not homogeneous, but is a mixture of two or three materials (solids, water, and perhaps air) which vary substantially in their compressibility and ability to sustain shear stress. Solid particles are not very compressible, but are rearrangeable under stress changes such that the soil mass itself is compressible. Solid particles can sustain shear forces between the particles. Water is not very compressible, nor can it sustain shear stresses, but it can change pressure and move in and out of a soil element in response to normal stress changes. Pore pressure changes occur at a rate governed by soil permeability and described by consolidation theory. Air is both compressible and soluble; as it is a fluid, it cannot sustain shear stress. So factors like consolidation stress, 6 degree of saturation, over consolidation ratio, etc. are the significant contributors to the soil strength uncertainty. 2.2 Shear Strength and Its Importance In geotechnical engineering, when one speaks of soil strength, the reference actually is to its shear strength. Jumikis (1962) has given a very comprehensive definition of shear strength: “ The shear strength of soil is resistance to deformation by continuous shear displacement of soil particles upon the action of a tangential (shear) stress. The shear strength of soil is basically made up of : o The structural resistance to displacement of the soil because of the interlocking of the soil particles, 0 The fi'ictional resistance to translocation between the individual soil particles at their contact points, and o Cohesion (adhesion) between the surfaces of the soil particles.” Bowles (1988) has defined shear strength as: “Soil strength is resistance developed from a combination of particle rolling, sliding, and crushing and is reduced by any excess pore pressure which develops during particle movement. This resistance to deformation is the shear strength of soils as opposed to the compressive or tensile strength of other engineering materials.” The shearing strength enables the soil to maintain equilibrium on a sloping surface such as a natural hillside, the backslope of a highway or railway cut, or the sloping side of an embankment, levee or earth dam. Shear strength influences the bearing capacity of a foundation soil and the lateral pressure which a soil backfill exerts against a 7 retaining wall, bulkhead, or other type of restraining structures. Shearing stresses in the backfill over an underground conduit, such as a sewer or a culvert, exert a great influence upon the load to which this kind of structure is subjected in practice (Spangler, 1951). So one can hardly find a problem in the field of geotechnical engineering which does not involve shear properties of soil in some manner. 2.3 Mohr—Coulomb Failure Criterion The Mohr’s envelope in functional form is written as rg= f (65) (2.1) where rff = shear stress on failure plane at failure and off = normal stress on failure plane at failure The Mohr’s envelope shown in Figure (2.1) is a curved line. The physical meaning of Mohr’s envelope can be understood as follows: 0 If a Mohr’s circle lies entirely below the Mohr’s failure envelope (as circle A in Figure 2.1), then soil is stable for this state of stress. 0 If Mohr’s circles are tangent to Mohr’s failure envelope, it means that full strength of soil has been reached for that state of stress on some plane . This plane is called the failure plane with of; and rff as normal stress and shear stress on failure plane at failure. 0 It is not possible to have a stress state in soil such that the Mohr’s circle intersects the Mohr’s envelope (as circle B in Figure 2.1). The material would fail before reaching that stress state. Mohr failure envelope Fig 2.1 : Mohr’s failure criterion (after Holtz & Kovacs, 1981) Coulomb observed that shear strength has two components, one stress- independent and other stress-dependent. The stress-dependent component is called angle of internal friction and is denoted by d). The other component is cohesion which is denoted by c. So Coulomb’s equation is If = 0 tan cl) +c 3 (2-2) where o = applied normal stress and If = shear strength of soil Now the Mohr-Coulomb strength criterion gives a failure relationship which is a straight line (Fig 2.2). The Mohr-Coulomb criterion can be written as Tn": Untan t +c (2.3) Equation (2.3) provides a simple straight line relationship which is easy to use. It estimates the shear stress on a potential sliding surface where the normal stress can be determined. This is very useful in analyses of slope stability and foundations. (Una Ta“) T C l 2 Fig 2.2 : The Mohr-Coulomb strength criterion (after Holtz & Kovacs, 1981) As a method of describing real soil behavior, the Mohr-Coulomb model has three obvious defects (Scott, 1980). l. The Mohr-Coulomb model makes no statement about strains, and therefore provides no information about displacement resulting from the application of load. 2. This model implies that volume changes do not affect the shear strength, which is certainly untrue. 3. The model implies that intermediate principal stress does not affect shear strength. This may not always be absolutely true for real materials. 10 2.4 Modeling Undrained Conditions Mohr- Coulomb failure envelope can be non-linear both during drained and undrained conditions which necessitates the use of some fitting procedure to define strength parameters. This study however, uses results of undrained conditions only. In deterministic analysis, it is important to be aware of the “true” and “approximated” shapes of the strength envelope and to ensure that the approximation is a good one in the actual stress range of interest. In probabilistic analysis, it is important to be aware that the linear approximation of the strength envelope in terms of c and (I) itself adds an additional source of uncertainty. Undrained conditions occur when strain occurs sufficiently quickly that consolidation (volume change) cannot occur, and pore pressure changes occur instead. This is the typical case immediately after loading fine-grained, low permeability soils. Undrained conditions may be modeled in terms of total stresses or effective stresses. However, total stress modeling is favored in practice as pore pressure changes due to shear, need not be explicitly predicted. Rather, the total stress parameters c and :1) reflect the apparent behavior of the combined solid-fluid system, including both shear strength of the solids and pore pressure changes in the fluid which may change effective stresses. Saturated, cohesive soils. For saturated, cohesive soils, the undrained strength SD is a function of the effective consolidation stress. As the stress under which a soil has been consolidated increases, its undrained strength is increased. Undrained strength may be measured in either Q (UU) tests or R (CU) tests. If properly interpreted, the two tests 11 should yield consistent evaluations of undrained strength. For R tests, a tangent strength envelope provides an approximation of the function relating undrained strength to effective consolidation stress (Lowe, 1966; Johnson, 1975). For Q tests, all specimens have the same consolidation stress (the field value), regardless of confining stress, and hence should have the same strength. The relationship between Q and R tests is illustrated in Figure 2.3. Figure 2.3 : Undrained strength from Q and R tests.(afier Wolff, 1995) For the R (CU) test on the left side of the figure, the first specimen was consolidated under stress (IC = 1 and its undrained strength is sul. The second specimen, consolidated under cc = 2, has the greater undrained strength Su2~ Hence, the parameters ccu and (1),,“ define a relationship between su and 00. If su were directly plotted against (so, as shown by Lowe (1966), the strength function would be greater. The use of the tangent envelope, although theoretically incorrect, works in practice with some conservatism. Had the samples been consolidated in-situ to these stresses and tested with the Q (UU) 12 test, the results in the right side of the figure would be obtained. The first sample would have the strength s“! shown by the solid circles, and the second sample would have the strength suz. Partially saturated, cohesive soils. Partially saturated conditions may prevail in ’ compacted embankments and near-surface natural soils. As optimum water content typically occurs at about 75 to 80% saturation, compacted soils should be only partially saturated at the end of construction. Near-surface soils are commonly partially saturated due to evaporation. 1 straight line approxnmatlon \ approaching \‘\ saturation ——> \5, :1. ¢ . / 1 H c t \ ‘ i l o Figure 2.4 : Undrained Strength Envelope for Partially Saturated, Cohesive Soil. (after Wolff, 1995) A typical strength envelope for a partially saturated cohesive soil tested in undrained shear is shown in Figure 2.4. In the lower stress range the envelope is curved; 13 increasing normal stresses compress and dissolve the air, reducing the void ratio and increasing strength. Above some normal stress where saturation is achieved, the undrained strength becomes constant. Although the curved envelope can be modeled by some slope-stability programs such as UTEXASB, it is commonly modeled by a straight line approximation as shown, so that it can be defined by a single c,(p pair. For probabilistic analysis, the straight line approximation is required by the present state-of- the practice. Stress point 0'3 0' l + 63 01 2 Fig 2.5 : A Mohr’s circle and stress point (after Holtz & Kovacs , 1981) 2.5 Stress Path A change in the stress state of a soil can be described using stress paths. A stress path is a curve drawn through the stress points for successive stress state (Lambe, 1967). In Section 2.3, Mohr’s circles in a 0-1: coordinate system were used to represent the states 14 of stress at a point in equilibrium. Sometimes it is convenient to use stress point concept which has coordinates p and q (see Fig 2.5) such that p= ———(°‘ 3‘“) (2.4) and q = £33) (2.5) Sometimes it is desired to depict the successive stress states of a specimen when it is subjected to loading and unloading in the field. Figure 2.6(a) shows the stress states while using Mohr’s circles. This stress state is simpler to show in p-q space as in Figure 2.6(b). This locus of stress points is what is called stress path. 61 increasing (a) (b) Fig 2.6 : (a) Stress state by Mohr’s circles; (b) Stress path for constant 63 and increasing 0, (after Lambe and Whitman, 1969) The use of stress points provides an alternative way to plot the results of series of triaxial strength tests. The points give the values of p and q corresponding to peak points 15 of stress-strain curves. The curve drawn through these points is called the Krline. The Krline may be fitted by a straight line over the stress range of interest. A useful relationship between Krlme and Mohr-Coulomb failure envelope can now be established. Figure 2.7(a) represents failure in terms of p-q diagram. Figure 2.7(b) shows identical circle on Mohr’s o-r diagram. Kf - line \. it (a) (b) Fig 2.7 : Relationship between the Krline and Mohr-Coulomb failure envelope (alter Holtz & Kovacs, 1981) The equation of the Krline is: Clr=PrtanW+a (2-6) where a = intercept on q - axis, and w = the angle of Kf - line with respect to horizontal. From equations (2.3) and (2.6), this can be shown that: sin (I) = tan \u (2-7) 16 a and C: cow (2.8) Hence values of c and d) can be computed from the Krline. The choice between these two methods is largely of personal preference. However when there are many tests in the series, it is less confusing to plot results on p-q diagram and also it is easier to fit a line through a series of data points than to attempt to pass a line tangent to many circles (Lambe & Whitman, 1979). 2.6 Laboratory Testing For Shear Strength The actual test results which will be used in the subsequent study, are mainly from undrained triaxial testing. The results pertain to two embankments, one a dam and the other a levee. Bertram, et al. 1967, summarize soil testing usually performed for embankment design: “ The shear strength values to be used in stability analyses are determined by triaxial tests made under three carefully controlled conditions of load application and sample drainage. For convenience, these tests are designated by the letter Q, R, and S. In the Q test (unconsolidated - undrained) the initial water content is maintained constant during the shearing process. In the R test ( consolidated - undrained) the sample is first consolidated under one set of stress conditions and then subjected to the shearing process during which the water content is kept constant. In the S test, (consolidated- drained) the sample is consolidated and sheared at a sufficiently slow rate to prevent buildup of excess pore pressures. This latter test can be conducted with either triaxial or direct shear apparatus.” Detailed testing methods used by the Corps are described in Engineering Manual 1110-2-1906 (Corps of Engineers, 1970). 17 In this chapter, the deterministic methods like Mohr-Coulomb failure envelope and stress path method were described in some detail. Holtz and Kovacs (1981) has given an excellent description of these methods. Chapter 3 will now cover the background theory for the statistical methods to be described latter in Chapter 4. CHAPTER 3 PROBABILISTIC MOMENTS AND REGRESSION ANALYSIS 3.1 General In this chapter, some basic concepts and definitions will be described which are pre-requisite for statistical description of soil strength. These are the measures adopted to determine the centrality and the variability of two random variables and the extent to which they depend on each other. It is an established fact that soil strength is a random variable which in itself is function of two other random variables c and ‘1’- In the preceding chapter, two deterministic methods were discussed which involve drawing of Mohr-Coulomb failure envelope or drawing of the Krline. Those methods can be alternatively employed to characterize the soil strength. In both cases, a straight line is required to be drawn through three to four points but often this line must be passed “near” them mainly due to reasons mentioned in Section 2.1. So it will involve some sort of judgment on part of engineers to achieve the best-fit line. This process can be subjective and thus further magnifies the already existing uncertainty of soil strength. Regression analysis, however, provides a better alternative being algorithmic. In this chapter, the regression analysis is briefly discussed in order to facilitate the assimilation of the subsequent description of alternative methods for characterizing soil strength. 18 19 3.2 Moments A random variable can be characterized completely by a function or approximately by moments. Because the c and 6 soil strength parameters may assume a continuous range of values, representation of these parameters as a continuous function is most appropriate. However, soil testing provides only a discrete series of strength values. To fit a continuous function or “probability distribution” to the values, requires that moments be estimated and that some assumptions be made regarding the shape of the function. Wolff (1985) has summarized the definitions of probabilistic moments and coefficients, however, discussion about probability functions is beyond the scope of this study. Following convention, capital letters are used herein to denote random variables and lower case letters are used to represent values which the random variables may assume. The kth moment about the origin for a discrete sequence of test results is defined m.(X)=EIX"1 =...2.. x.“f(x.) (3.1) where E[Xk] is the expected value of Xk and f(xi) is the frequency of occurrence of value xi. That is , f(x.)=1‘i (3.2) n where n is the total number of test values and 11, is the number of values having the value xi. The mean is the first moment about the origin, 20 m(X) = EIX] = X = allzxi Xi f(Xi) (3-3) The mean is based on information contained in all of the observations in the data set. The mean is a simple point that can be viewed as the point where all the mass or weight of the observations is concentrated. This gives the mean some advantage over other measures of centrality such as mode or median ( the median is an observation in the center of data set and mode is the value that occurs most frequently). The median however, is resistant to extreme observations whereas mean is sensitive to outliers. Central moments are calculated with respect to the mean value. The kth central moment is, u.(X)=...>:.. (x.- flax.) (3.4) The second central moment is called the variance, 92 (X)=Var(X)=..2.. (x.- 702 RX.) (35) A convenient measure of dispersion is the standard deviation which is described in same units as mean, 0x = [VaI(X)]”2 (3.6) Another measure of variability or dispersion is range which is the difference between largest and the smallest observation. The variance and stande deviation are more useful than range because, like the mean, they use the information contained in all the observations in the data set but they too are sensitive to outliers. A non-dimensional measure of dispersion is the coefficient of variation, vx = (3.7) > for each sample by hand- drawing a linear strength envelope tangent to Mohr’s circles, or as close to tangent as possible (For direct shear tests, the line is drawn through the off, 1” pairs). 30 Perform conventional statistical analysis on set of (c,¢) pairs to obtain E[c], E[¢]: cc, O'¢, pc,¢ 0 straight line approximation \ Fig 4.1: Method 1 The following may be perceived as advantages of Method 1: It preserves the judgment of the engineer looking at the test data expressed as Mohr’s circles. Very inconsistent tests or obviously “bad results” are easily spotted and may be deleted. Testing laboratories may often make the interpretations of c and (I) and report the values; where this is the case, the data are already in the required form. Statistical analyses are easily performed using routine statistical software or modern spreadsheet programs where the required functions are built-in. 31 The following may be perceived as disadvantages of Method 1: o The engineer’s judgment in selecting c and (11 itself introduces variability and possibly bias. Two engineers may make different selections of c and 4) from the same set of Mohr’s circles. The method is not as consistent as using some algorithm that would assign a unique value to a given set of specimen failure data. 0 Results of tests on individual specimens are uniquely tied to the results of other specimens tested from the same sample; they are not each taken as “independent” pieces of information which can be treated as a “pooled” sample. The latter approach may be preferred statistically in the case of relatively homogeneous soils. 0 Tests with three and four specimens are weighted equally. The regression of 0', on 03 provides the simplest approach to finding (c, 4)) for individual samples. This method was suggested by Holtz (1947) and later explained by Holtz and Noell (1950). In this method, regression equation takes the form (Figure 4.2): ol=a+bo3 (4.1) where a is intercept and b is slope of regression line. Method 2 : Determine c and 4) for individual samples by regression of 01 on 63 and then perform a statistical analysis on (c, 11)) pairs. The Method 2 is illustrated in Figure 4.2 and summarized below. 32 Fig 4.2 : Method 2 (after Handy, 1981) 0 Test three to four specimens for each sample. 0 Perform linear regression analysis on (0'3, 01) pairs for each sample to obtain the regression parameters a and b as shown in Figure 4.2. o The parameters a and b are used to calculate c, 11> pair for each sample as follows: b—l tan =——— 4.2 ¢ 2J3 ( ) and c — l— (4 3) 24/6 ' 0 Perform a statistical analysis on (c, (1)) pairs as in Method 1. The advantages of Method 2 include the following : o The method provides a straightforward approach for calculating c and 11) parameters. 33 o The method assumes the variability in the y(ol) direction for a given x(o3) which is consistent with total stress paths in the conventional triaxial test procedure. The disadvantages of Method 2 include the following: 0 Bad results and outliers can affect the regression line and may not be easily spotted. o The method does not allow any judgment on part of engineer. 0 Negative 4) values may be obtained which are physically impossible. o This method assumes a “transformed” stress path at 01,63 coordinates as a vertical line. This is true for total stresses, but in an undrained test, the paths in ol',o3' space are neither vertical nor straight.(Schoenemann and Pyles, 1990) q -/, /..:.,.;.__—1 _, ,zL—N’. ., '1" r ression on /»« ._ (9.9) pairs Figure 4.3 Method 3 (after Wolff, 1995) 34 The third method, proposed by Wolff (1995), utilizes the stress path concept (Lambe, 1967) to circumvent the problem of finding of a tangent line, but does so by performing regression analysis from within a set. The method which can be applied to total stress analysis, is described below and illustrated in Figure 4.3. Method 3 : Determine c and 4) for individual samples using stress points (p, q) from sample specimens and develop the five required moments from these (c,¢) pairs. 0 For each set of specimens in a sample, determine the stress points p and q using Equations (2.4) and (2.5) respectively. 0 For each sample, perform a linear regression analysis on the set of stress points (p, q) to get a best-fit total stress Kf-line with parameters a, and ‘11,. 0 Convert a, and ‘1’, for each sample to (ci, (1),) values for each sample by using Equations (2.7) & (2.8). 0 Obtain statistics on the (01,411) pairs following Method 1. The advantages of Method 3 include the following: o The method is algorithmic: unique results are obtained for a given data set. 0 The method is easily programmed using spreadsheet software. The disadvantages of Method 3 include the following: o For some combinations of specimen data, notably from Q (UU) tests where d) is near zero, negative friction angles may result. As this is unreasonable, some additional algorithm or rule must be invoked to deal with this situation. 35 In this method, the data variability is not along the y-axis, but is typically inclined 45° from the vertical, this violates a fundamental assumption of regression analysis and results in an overestimation of (l) which is on the unsafe side.(Handy, 1981) /qr / /- 4‘ / / / \ / / / \ p \ x \ Figure 4.4 : Method 4 (after Handy, 1981) A fourth method, which was suggested by Handy (1981), corrects the direction of data variability by rotation of p, q axes. As 63 is an independent variable and 01 is a dependent variable, these two variables get amalgamated in the process of conversion to p, q points. This causes the data variability to sway from y(q)-axis as much as 45°. Handy proposed to perform regression analysis of transformed p,q data obtained by rotating the 36 p and q axes through an angle A0 such that qr is in the direction of variability as shown in Figure 4.4. For constant 03, A0 = 45°, but angle can be different for other stress paths. Method 4 : Perform regression on (p,, q,) pairs for each sample after rotating p—q axes through an angle, A0. 0 For each pair of (o, , 03) values, find the corresponding stress points p,q. 0 Change each pair of rectangular coordinates p, q to polar coordinates r, 0 . 0 Add A9 to each 0 coordinate to obtain 9+A0. (A9 = 45° for total stress path). 0 Convert back to obtain rectangular coordinates pr and q,. 0 Perform linear regression analysis on the p,, q, points to obtain the best-fit line on rotated axes. Parameters w, and ar are obtained which are converted to w and a as follows : w = w, - A0 (4.4) :1: sin(90 — A9 - w) cos w a = a, (4.5) 0 Follow Method 3 to obtain rest of the statistics. The following is an advantage of Method 4: o This method puts the variability in the correct direction and prevents a possible overestimation of (I) value. The following may be perceived as disadvantages of Method 4: o This method is only workable when all stress paths in a group of tests are aligned in the same direction. This is the case for total stress parameters. 37 However, the direction of effective stress paths during undrained tests generally vary during the test.(Schoenemann and Pyles, 1990) o The method does not allow users to generate confidence or prediction limits about an estimated Mohr-Coulomb failure envelope as shown in Figure 4.8. In the fifth method, the 0,,63 values are used, but all specimens data are pooled for one regression analysis (Fig 4.5). This method however, will efficiently work if the soil is grossly uniform. This method was suggested by Lumb(1970). 01 I Ab . 2/ 1 a Fig 4.5 : Method 5 Method 5 : Perform regression analysis on pooled 0'1, 63 values. 0 Obtain 0,, 03 values from each individual specimen. 0 Perform regression analysis on pooled set of data to obtain regression parameters a and b. 0 Obtain E[c] and E[¢] using Equations (4.2) and (4.3). 38 The following are advantages of Method 5 : For a large set of data, less effort is required to perform pooled regression as compared to performing a regression analysis on each individual sample. Suppose that each of the 11 test results was obtained at m different 03 values (m 2 2). The degrees of freedom for the variance estimate of pooled regression is v = nm - 2 which is about twice the degrees of freedom for individual sample analysis, v = n - 1. Thus for an equal number of test results, the variance is more efficiently estimated in pooled regression. (Lumb, 1970) The following are disadvantages of Method 5 : This method cannot yield reasonable results for soils with larger degree of variability. The variance of the regression line is taken as constant in this method but it actually increases with 03 as can be seen in Table 5.15. So the estimated variance is higher than the actual variance of regression line. (Lumb, 1970) This method does not provide the values for variance of c and 4) or their correlation coefficient. In a redefinement of Method 5, Lumb (1970) suggested a method involving weighted regression. For a large set of test results, when 0, is plotted against 63, the scatter of data points about their mean trend increases with increase in 63. Therefore the variance s2 of the regression line is not constant but is a function of 63. If each a, value is 39 multiplied by a function w proportional to 1/32, an estimate of least variance can be obtained. Method 6 : Multiply each 0, value by a weighting function before performing pooled regression on 6,, 63 values of individual specimens. 0 Obtain 6,,63 values for each individual specimen. 0 Calculate the variance 52 of o, for each value of 03 pooled together. 0 Estimate a weighting function w ocl/s2 and multiply each 0', value by its corresponding weight factor. 0 Follow steps in Method 5 for subsequent regression and statistical analysis. The following may be perceived as an additional advantage of Method 6 over Method 5. o The introduction of weighting function leads to finding an estimate of minimum variance and this can be regarded a best estimate obtainable from a given amount of data. However, Lumb concluded, after applying Method 5 and Method 6 to various soil test results, that the increase of variance 52 with 03 was not significantly different from zero. As the gain in precision is not significant , Lumb did not recommend the use of Method 6 due to involvement of additional arithmetic. The earliest application of regression analysis to characterizing soil test data was carried out by Balmer(l946). The regression in effect was of 1, versus 0,, which is more applicable to direct shear tests. Balmer took on as the independent variable. Test results 40 variability was therefore, assumed parallel to the t-axis (Fig 4.6). Method 7 was used by Wolff and Wang (1992) to evaluate direct shear test results of large cores on shale materials from the foundations of Monongahela River locks and dams. 14>] E[c] Figure 4.6 : Method 7. Method 7 : Develop moments of c and d) from individual (6, 1:) points at failure for each specimen. 0 Obtain of, and If, for each specimen. 0 Perform a linear regression analysis on the pooled (6,1) points and take E[c] and E[¢] as the intercept and slope, respectively, of the best-fit line. 0 Use the statistics of the best fit line to estimate O'c, 0,3,, ,, and pc,tan ,, The third item above can be done as follows (Wolff and Wang, 1992): The standard error of 1.’ given on is: 41 -Jer-Eicizr.-tan¢zo. n—2 (4.6) This is a measure of the scatter of individual points around the regression line. It could be taken as 0,, but doing so lumps all uncertainty in c and none in 4). The variance of the slope of the best-fit line, tanij), is then: Var(tan 4)) = Z (fizifi), (4.7) where 6' is the average of the confining stress (6,) values. The variance of the intercept of the best-fit line, c, is: Var tan of Var(c)= ( ”El ') (4.8) n The covariance of the best-fit parameters c and tand) is Cov (c,tan 4)) = Var (tan ¢)(—6) (4.9) Finally, the correlation coefficient of the parameters describing the best fit line is C , tan “(C (l) (4.10) pm” = W Var(tan ¢)] As the number of data points is always finite and generally small, the calculated intercept and slope are estimates of the “true” intercept and $10pe. This explains why the slope and intercept each have a variance. Testing additional data sets from the same material deposits and repeating the regression analysis would yield different values. The standard error of the regression line intercept and slope can be taken as cc and own ¢ respectively. The correlation coefficient, pm" 4, can, in turn, be calculated. 42 The advantages of Method 7 include: 0 Data from every specimen are equally weighted. o The method works directly with shear stresses at failure. The disadvantages of Method 7 include: o It requires knowledge of stresses on failure surface, which are not usually known and may require that an assumption be made regarding d). o Variances of c and tend) relate to the best-fit line, which may be smaller than variances derived from c,¢ pairs associated with samples. 0 It may yield large negative correlation coefficients; as the best-fit line must pass through the mean values of o and 1:, the slope and intercept are always strongly negatively correlated.(Wolff, 1995) 0 Data variability is assumed to occur parallel to the y (1) axis. For triaxial tests where 03 is held constant, the variability is not in the direction of 1: axis, but along a line substantially inclined from it (Handy, 1981). Staying with the concept of stress points, an 8th method would be to pool all specimen data. An illustration of Method 8 can be seen in Figure 4.7. Method 8: Treat the p-q data from all specimens equally and perform a regression analysis on this “pooled” data set. 0 Obtain ( 6,03) values for each individual specimen and convert them to respective (p, q) values for each specimen. 43 EN) E[a] Figure 4.7 : Method 8 0 Perform regression analysis on the pooled data to obtain values of a and w corresponding to the K, -line. 0 Find values of E[c] and E[¢] using equations (2.7) and (2.8). The following can be perceived as an advantage of Method 8: o This method provides an alternative way of calculating E[c] and E[o]. The following can be perceived as disadvantages of Method 8: o This method overestimates the value of d) considerably. o The variance of c and <1) and the correlation coefficient pm cannot be determined. 0 The variability in q is not orthogonal (and independent) to the variability in p. 44 In method 9, the rotation of p,q axes is undertaken as suggested by Handy(1981), and explained in Figure 4.4, but data is combined together to perform pooled regression. Method 9 : Treat p,q data from all specimens as individual samples, plot them on rotated p,q axes and perform pooled regression analysis. 0 Convert 6,,0'3 values for each specimen to respective p,q values. 0 Change p,q points from rectangular to polar coordinates r, 0. 0 Add A9 to all 9 values. (A0 = 450 for total stress paths) 0 Change back to rectangular coordinates pr and q, for each specimen. 0 Perform regression analysis on all p 45 Figure 4.8 : Method 10 (after Schoenemann and Pyles, 1981) Another method, published by Schoenemann and Pyles (1990) and illustrated in Figure 4.8, circumvents the problem of needing to know the failure plane stresses by using the stress path concept and performing the regression on p,q data. Method 10 : Develop E[c], cc, and E[4)] working from stress points (p,q) of specimen data. 0 Consider every specimen an independent test and calculate the effective stress points (p,q) at the top of Mohr’s circle at failure. 0 Perform a regression analysis on the (p,q) pairs and determine the best-fit Krline. This line has a slope angle corresponding to the expected slope of the Kf-line, l1’, and an intercept a. 0 Take the obtained L1’ as E[‘I’]. o Detemtine the expected value of the friction angle from the identity sin 4) = tan‘I’. 46‘ 0 Use the resulting E[4)] to calculate the (off, In) coordinate from each (p,q) coordinate by following equations : ofi=p-(q sin4)) (4.11) 1,, = q cos4) (4.12) 0 Perform a second regression analysis, now on the (off, 1:3) values and take the best-fit line to have the parameters E[c] and E[4)]. 0 Calculate the standard error of the regression line and take it as (rc . The following may be perceived as advantages of Method 10: o The method is “nearly” algorithmic: for any set of data, a unique procedure is defined; however, the authors suggest that iteration between the two methods may be required to achieve consistency between 4) and w. o The method allows the user to generate prediction or confidence limits about an estimated Mohr-Coulomb failure envelope as shown in Figure 4.8. The following may be perceived as disadvantages of this method: 0 At least two separate regression analyses are required. 0 The method doesn’t account for uncertainty in the slope of the strength envelope (tan 4)); all uncertainty is lumped into the c parameter. 0 As uncertainty in 4) is not characterized, pm cannot be determined. Finally an alternate approach to method 10 can be considered. Method 10 first performs regression analysis on (p, q) values which leads to excessively large values of 4). It is more realistic to work from (6,, 63) values to obtain a lower value of 4) during first 47 analysis and then calculate corresponding values for (0, 1) pairs to complete the second regression analysis. Method 11 : Develop E[c], 0c, and E[4)] working from (0,, 03) values of specimen data. 0 Consider (0,, 03) values for each specimen of the data individually. 0 Perform regression analysis on (0,, 03) pairs and obtain parameters of the best-fit line following Method 5. 0 Determine expected values of intercept and fiiction angle by using Equations (4.2) and (4.3) respectively. 0 Use the resulting E[4)] to calculate the (0g, 13) values by using following equations: o,=“':“3—G';°3*sin¢ (4.13) and r, =G—'%g3Jcos4) (4.14) 0 Now follow Method 10 to perform second regression analysis on (Orr, 1,7) values. This method possesses all the advantages and disadvantages of Method 10, except that it uses (0, , 03) values instead of stress points (p, q) thereby assigning more conservative values to friction angle during first regression analysis. This method however, reports a somewhat higher value of 4) as compared to Method 10 hence cannot be preferred over Method 10. CHAPTER 5 APPLICATION OF METHODS TO ACTUAL DATA SETS 5.1 General In chapter 4, eleven possible methods for probabilistic characterization of soil strength were discussed in detail. These methods will now be put through further scrutiny by using them to analyze seven sets of data; five fiom the Clarance Cannon Dam and two from the Bois Brule Levee, both located in Missouri and constructed by the St. Louis District of the Corps of Engineers. The available test results were obtained by triaxial compression testing under undrained condition, on both unconsolidated and consolidated samples. Results of soil shear tests used here are all in terms of total stresses. These tests were performed by the US. Army Engineers, Waterways Experiment Station (WES) Geotechnical Laboratory in Vicksburg, Mississippi. The c and 4) values for Method 1 were in fact, reported by WES and are being compared with other results in this report. Method 7, which takes into account the Direct Shear Test results, will not be discussed further due to non-availability of appropriate data. This chapter will only show the summary of the results in the form of tables and graphs. However, the detailed working of each method will be illustrated in the appendices by using only one set of data. 48 49 5.2 Clarance Cannon Dam Results 5.2.1 Clarance Cannon Dam Clarance Cannon Dam is located in the Salt River in northeastern Missouri and forms Mark Twain Lake. The dam is part of a multi-purpose project which provides flood control, recreation, water supply, fish and wildlife conservation, and hydropower. Completed in 1983, the dam has a 1000 foot long earth embankment, a gated concrete spillway section, and a concrete powerhouse adjacent to the spillway. The earth embankment volume is approximately 3 million cubic yards. The dam crest at elevation 654 feet above mean sea level is about 115 feet above the floodplain and 138 feet above the stream bed. The embankment at Cannon Dam was constructed fi'om clays classified as CL and CH by the Unified Soil Classification System. Two major embankment zones were defined during construction and are considered separately in this study, the Phase I and Phase II fill materials. The Phase I fill consists of the foundation cutoff trench and a zone about 30 feet thick at the base of the embankment. The remainder of the embankment was constructed from the Phase II fill material. Phase I was compacted wetter than Phase II. (Wolff, 1985) 5.2.2 Q(UU) Tests on Record Samples- Phase I Fill To maintain consistency with the reported data, the notations Q, R and S tests, developed by Casagrande, are used rather than the more common UU, CU and CD respectively. The record samples were trimmed from completed dam embankment. The Q 50 test expressed in terms of total stresses are generally used to analyze the “end of construction” conditions. The dataset being used here was obtained as a result of Q(UU) testing on record samples of Phase I Pill. The data consists of 70 samples with each sample having 3 test specimens. As samples are partially saturated compacted clays, they exhibit both c and 4 values as explained in Section 2.4. Table 5.1 shows the results of application of Methods 2 through 4 on individual samples. Each sample has a value of c and 4 resulting from regression analyses on three specimen. Complete analysis gives 70 pairs of c and 4 values which are compared with WES reported values (Method 1) and rest of statistics are performed on this set of data. Figures 5.1 through 5.3 show the best-fit line drawn through 3 points of Sample No. l for Methods 2 through 4 respectively. It is evident from Table 5.1, that mean values of c and 4 are generally comparable to each other. Yet Method 3, which involves the regression of q on p, reports the highest mean value of 4 and lower value of c. But when p,q axes are rotated through 450 (true for total stresses only), as in Method 4, the values of c and 4 exactly match with those of values in Method 2. During regression analysis of individual samples, some negative 4 values were also obtained. Negative 4 values are generally observed during Q tests, when value of 4 is relatively close to zero. For the laboratory values reported by WES, the slightly negative best-fit line is taken as zero but regression analysis will report the actual slope of line, may it be negative. This obviously results in more scatter of 4 values and a higher standard deviation and coefficient of variation are observed for Methods 2 through 4. 5 1 Table 5.1 Cannon Dam Shear Testing - Q (UU) Tests Individual Samples Method 1 Method 2 Method 3 Method 4 Phase I fill Q tests on record samples number of tests 70 70 70 70 c parameter mean 1.238tsf 1.25 tsf 1.214tsf 1.25 tsf standard deviation 0.565tsf 0.62 tsf 0.587tsf 0.62 tsf coefficient of variation 45.6% 49.6% 48.4% 49.6% skewness coefiicient +0.436 +0.76 +0.667 +0.76 ¢ parameter mean 8.07“ 8.235 8.584° 8.235 standard deviation 8.92“ 9.23 921° 9.23 coefficient of variation 110% 112% 107% 112% skewness coefficient +0.921 +0.663 +0666 +0.663 covariance 0.55 0.018 0.194 0.018 correlation coefficient p9,, +0.11] +0.003 +0.036 +0.003 Table 5.2 Cannon Dam Shear Testing - Q (UU) Tests Pooled Regression Methods No. 5 No. 8 No.9 No. 10 No. 11 Phase I fill Q tests on record samples numberoftests 210 210 210 210 210 c parameter mean 1.232 tsf -0.207 tsf 1.232 tsf 0.24 tsf -0.037 tsf variance - - - 0.032 0.031 standard deviation - - - 0.179 tsf 0.179 tsf t parameter mean 10.030 24.8150 10.o3° 20.240 2255" tan 4 parameter variance - - - 0.001 0.001 standard deviation - - - o.o32° o.o32° covariancec‘m. - - - -0.005 -0.005 correlation coefficient pw—nt - - - -0.904 -O.904 52 y = 1.2095x + 6.82 ‘11 l l 3.8 4 y = 0.0982x + 3.062 Fig 5.2 : Method 3 - Sample No.1 - Q tests - Phase I O .fil 444 y = 1.2095x + 4.8225 F 4.- ‘Ir (3 '-‘ N 1» ¥ M 0‘ \l on \O . ,,., —‘9 4 '44 2.5 3 3.5 4 Pr o e: . \lt tit N Fig 5.3 : Method 4 - Sample No.1 - Q tests - Phase I l l 1 l i l l t I l 1 10 53 In the present case, the coefficient of variation is more than 100%. This means that the value of standard deviation is greater than mean itself. For the case of a parameter which cannot assume values below zero (e.g., strength), coefficients of variation greater than about 30% indicate the distribution must be skewed, and a coefficient on the order of 100% indicates it is highly skewed. In such case one must avoid selecting values at some number of standard deviations below the mean, but rather select them to correspond to some confidence level. The 67% confidence level is used by US Corps of Engineers. Table 5.2 presents the results of pooled regression by Method 5 and Methods 8 through 11. Just by looking at the results of pooled regression, it can be concluded that Methods 5 and 9 report the closest expected values of c and 4 compared to those of individual samples. Method 8, which regresses q on p, results into considerably higher value of E[c] and E[4]. But when p,q axes are rotated through 450 (Method 9), the values of c and 4 become exactly equal to those of Method 5. This process can be explained by looking at Figures 5.4 through 5.7. These figures represent Methods 5 and Methods 8 through 10 respectively. Talking purely in terms of data variability, Method 5 is the only method which matches all the assumptions of linear regression model as described in Chapter 3. In linear regression model, the x-value is independent and so is 03 here. The dependent variable is along y-axis and so is 0,. In case of triaxial testing, the confining pressure 03, is selected and the corresponding value of 0, is noted. So all of the variability is assumed to occur in 0, direction which is actually the case. Figure 5.4 shows the plot of 0, versus 03 values and the variation in 0, values is exactly along vertical axis for fixed values of 03. This analogy however is true only for total stresses and variability may 01 54 o 20 l ° 0 l y = 1.4218x + 2.9379 3 15 4 0 l t 10 4 . l 54 l 0 .4 4— - _ ,. _ 4-4—.4. 0 1 2 3 4 5 6 03 Fig 5.4 : Method 5 - Q tests - Phase I 3 T . O 7 4. ' O l y = 0.3688x + 0.2402 6 t if I 5 + 4 + 3 4 l 2 t 1 -.L o i . _ o 2 4 6 8 10 12 Fig 5.5 : Method 10 - Q tests - Phase I (Ii qr 55 U! 0‘ \I co 0 «+ —+— -—+——~ +——-+ ——1 .b N w +-— +-——r——+——— # Fig 5.6 : Method 8 - Q tests - Phase I 164— 14 4. . y = 1.4218x + 2.0774 12 7 O .000. O O 10 i. Pr Fig 5.7 : Method 9 - Q tests - Phase I 56 follow a totally different trend for effective stresses obtained by subtracting developed pore pressures. Now in case of regression of q on p, the direction of data variability is not accounted for. This method so amalgamates the dependent and independent variables that data variability is as much as 45° from vertical while dealing with total stresses. As 0, increases, it affects both p and q simultaneously, hence non out of two variables p and q is independent. This phenomenon so rotates the failure envelope that E[4] value becomes much higher and E[c] value becomes negative in this particular case. As suggested by Handy (1981), and already explained in Chapter 4, if p, q axes are rotated through 450 so that q-axis is in the direction of the data variability, the overestimation of 4 value can be averted. This phenomenon can be observed in Figure 5.7, that the plot of data in p,-qr space show a variability similar to that in 03-0, space as in Figure 5.4. Also as obvious from Table 5.2 that results obtained from Method 9 are exactly similar to those of Method 5. Method 10 involves two regression analyses to reach the final values of E[c] and E[4] but these are still quite different from values reported by individual samples methods. Again, considering the variability of data, Figure 5.5 shows that data variability is not quite parallel to r-axis. The severity of this difference is milder than that of p,q plot but still it will result in an inflated value of 4. Considering the pooled regression, 0—t is the only space which can allow the direct estimation of 0,, 0m, and their correlation coefficient. This is to be noted that in pooled regression, the 0,, or pg, are not found straight-away. It might also be noted that some authors consider the cohesion and the 57 tangent of friction angle as the shear strength parameters and not the c and 4 values themselves (e.g. Lumb, 1970). Method 11 is different from Method 10 in the sense that first regression is between 03 and 0, and not between p and q. This method reports higher values of 4 as compared to Method 10 but still these values are lower than those of Method 8. Although regression of ‘t on 0 gives an intermediate value and it facilitates further statistical description of soil test data, the value of E[4] is unreliably high and should not be trusted blindly. 5.2.3 Q(UU) Tests (Borings) - Phase 1 Fill The borings samples were also taken from Phase I, but from pushed tubes rather than cut blocks. This set of data contains 15 samples with 3 specimens tested for each sample. This data set is quite smaller compared to first set of data but it does not contradict from results obtained therein. This data set is however not small in terms of common geotechnical practice. Table 5.3 shows the results of Methods 1 through 4. The mean values of c and 4 from all four methods are much the same but still Method 3 gives slightly higher value. Figures 5.8 through 5.10 show a plot of the regression analysis on Sample No. 47U P-2 by Methods 2,3 and 4 respectively. In pooled regression, the regression was performed on 45 data points considering each individual specimen as one data point. These results totally agree with those obtained from statistics on first set of data. Figures 5.1] through 5.14 show the plots and resulting regression lines for Method 5 and Method 8 through 10 respectively. 58 Table 5.3 Cannon Dam Shear Testing - Q (UU) Tests - Borings Individual Samples Method 1 Method 2 Method 3 Method 4 :hase I fill Q tests on record samples - Borings numberoftests 15 15 15 15 : parameter mean 1.657tsf 1.65 tsf 1.633tsf 1.65 tsf standard deviation 0.53tsf 0.637 tsf 0.631tsf 0.637 tsf coefficient of variation 32.0% 38.6% 38.6% 38.6% skewness coefficient -0.397 -0.787 -0.767 -0.787 ¢ parameter mean 18.33° 18.77l° 18.903° 18.771° standard deviation 11.55° 10.997° 11.006° 10.997° coefficient of variation 63.0% 58.6% 58.2% 58.6% skewness coefficient -0.512 -0.184 -0.213 -0. l 84 covariance -l .591 -1.636 -1 .621 -1.636 correlation coefficient pm -0.278 -0.25 -0.25 —0.25 Table 5.4 Cannon Dam Shear Testing - Q (UU) Tests - Borings _ Pooled Regression fiethods No. 5 No. 8 No. 9 No. 10 No. 11 Phase I fill Q tests on record samples - Borings mlxmber of tests 45 45 45 45 45 9 Parameter mean 1.582 tsf -0.005 tsf 1.582 tsf 0.60 tsf 0.345 tsf variance - - - 0.188 0.188 standard deviation - - - 0.433 tsf 0.433 tsf ¢ parameter mean 21.15° 33.36° 21.150 28.75° 30.330 tan (b parameter variance - - - 0.005 0.004 standard deviation - — - 0.071o 0.063° covariancecm, - - - -0.028 -0.025 - - -0.909 -0.911 finelation coefficient pen—n! - 124 01 on _+ 6 i y=l.4867x+5.18 Fig 5.8 : Sample 47U P-2, Method 2 - Q tests (Borings) 4.5 4 + 3.5 4 3 4 _ 2.5 a 2 4— =0197lx+2.0734 . y . 1.5 4 l + 0.5 l o .. - . , _, _ .._--_--_.__--- ,-- 0 2 4 6 8 10 12 Fig 5.9 : Sample 47U P-2, Method 3 - Q tests (Borings) 10+ y = 1.4867x + 3.6628 Pr Fig 5.10 : Sample 47U P-2, Method 4 - Q tests (Borings) 60 251- y=2.129x+4.6157 ”0.0.. l 204 Fig 5.11 : Method 5 - Q test ( Borings)- Phase I y = 0.549x + 0.5979 Fig 5.12 : Method 10 - Q test ( Borings)- Phase I (Ii 61 s l y = 0.549711 + 0.0048 0 - t 4 "—4-- 0 2 4 6 8 10 12 14 16 P1 Fig 5.13 : Method 8 - Q test ( Borings)- Phase I 20~ y = 2.129x + 3.2638 0.00000 00 .0 “0.0 Pr Fig 5.14 : Method 9 - Q test ( Borings)- Phase 1 62 5.2.4 R(CU) Tests - Phase I Fill This data set contains 18 samples of 3 specimens each. Table 5.5 shows the results of regression analysis on individual samples. The results show same trend as previous data sets did. Figure 5.15 through 5.17 show the plot of regression analysis on Sample No. 3 by Methods 2,3 and 4 respectively. Table 5.6 shows that value of E[4] reported by Method 8 is as much as 160 higher than value reported by WES. This type of error would be extremely serious for any kind of bearing capacity analysis as bearing capacity factors are very sensitive to value of friction angle. This much change in 4 will change the bearing capacity factor N, by many times. So not catering for the direction of variability in regression analysis of soil specimens introduces bias on the unsafe side. Figures 5.18 through 5.21 show the plots for Method 5 and Methods 8 through 10 respectively. Again the plots here are in total agreement with preceding sets of data. 5.2.5 Q(UU) Tests - Phase II Fill This set of data is the largest one set of data under consideration. The total number of samples tested were 68 to include 216 specimens in total for these samples. Table 5.7 confirms the previous deductions. Figures 5.22 through 5.24, plot the regression analysis on Sample No. 297 which consists of four test specimens. Table 5.8 shows that value of E[4] obtained from Method 5 is very close to the mean 4 value obtained by Method 1. It means that as the size of data set gets larger, the difference between the 4 value obtained by pooled regression of 0, on 03 and that obtained from individual samples is minimized. Figures 5.25 through 5.28 show the similar kind of plots as have been observed earlier. 63 Table 5.5 Cannon Dam Shear Testing - R (CU) Tests Individual Samples Method 1 Method 2 Method 3 Method 4 Phase I fill R tests on record samples numberoftests 18 18 18 18 c parameter mean 1.069tsf 1.168tsf 1.113tsf 1.168tsf standard deviation 1.042tsf 0.922tsf 0.883tsf 0.922tsf coefficient of variation 97.5% 78.9% 79.3% 78.9% skewness coefficient +2.336 +1.033 +1.063 +1 .033 4 parameter mean 25.55 25.644 26.003 25.644 standard deviation 6.50 7.162 7.282 7.162 coefficient of variation 25.4% 27.9% 28.0% 27.9% skewness coefficient +0.36 +0.77 +0.72 +0.77 covariance +1.687 +1.626 +1.597 +1 .626 correlation coefficient pg. +0.264 +0.26] +0.263 +0.26] Table 5.6 Cannon Dam Shear Testing - R (CU) Tests Pooled Regression M°m°ds No. 5 No. 8 No.9 No. 10 No. 11 Phase I fill R tests on record samples number of tests 54 54 S4 54 54 c parameter mean 1.185 tsf -0.947 tsf 1.185 tsf -.004 tsf -0.402 tsf variance - - - 0.215 0.203 standard deviation - - - 0.464 tsf 0.451 tsf t parameter mean 26.950 41.670 26.950 35.22° 37.48° tan 4 parameter variance - - - 0.006 0.004 standard deviation - - - 008° 0.063° covariance,“ - - - -0.033 -0.026 _correlation coefficient pen—n, - - - -0.892 -0.893 y = 1.697lx + 3.33 ° 6 4 2. 0. . e f —-+_-'—++7———-l 0 1 2 3 4 5 6 03 Fig 5.15 : Sample No.3 - Method 2 - R tests - Phase I (11 N t 1.5 y=0.2612x+ 1.217 Pi Pr Fig 5.17 : Sample No.3 - Method 4 - R tests - Phase I 40 4 35 4 30 i 25 4 204 01 15 s. 10 -+- 12 r; 10: 65 y = 2.6575x + 3.8642 : ’ t . O i 1 2 3 4 0'3 Fig 5.18 : Method 5 - R tests - Phase I y = 0.6791x + 0.1184 Fig 5.19 : Method 10 - R tests - Phase I O. 30 - 25 ~- 20; 66 Pi Fig 5.20 : Method 8 - R tests - Phase I z 1 O .0. O.“ y = 2.6575x + 2.7324 . O... N w . A Fig 5.21 : Method 9 - R tests - Phase I 67 Table 5.7 Cannon Dam Shear Testing - Q (UU) Tests Individual Samples Method 1 Method 2 Method 3 Method 4 Phase II fill Q tests on record samples number of tests 68 68 68 68 c parameter mean 1.527tsf 1.56 tsf 1.487tsf 1.56 tsf standard deviation 0.861tsf 0.834 tsf 0.8351tsf 0.834 tsf coefficient of variation 56.4% 53.6% 56.2% 53.6% skewness coefficient +3.863 +3.522 +3.62 +3522 4 parameter mean 14.57° 14.70° 15.326" 14.7o° standard deviation 9.6o7° 9.1 18° 9.056° 9.118° coefficient of variation 65.9% 62.0% 59.1% 62.0% skewness coefficient -0.027 +0.181 +0.082 +0.181 covariance -3 .708 -3.244 -3.23 1 -3.244 correlation coefficient pc‘. -0.455 -0.433 -0.433 -0.433 Table 5.8 Cannon Dam Shear Testing - Q (UU) Tests Pooled Regression Methods No. 5 No. 8 No.9 No. 10 No. 11 Phase 11 fill Q tests on record samples numberoftests 216 216 216 216 216 c parameter mean 1.60 tsf 0.659 tsf 1.60 tsf 0.935 tsf 0.819 tsf variance - - - 0.022 0.023 standard deviation - - - 0.15tsf 0.152tsf a parameter mean 14.910 23.620 1491" 21 .06° 21.92° tan 4 parameter variance - - - 0.001 0.001 standard deviation - - - 0.032 0.032 covariance,“ - - - -0.003 -0.003 correlation coefficient M - - - -0.898 -0.902 68 y = 1.3575x + 4.2408 0 1 2 3 4 5 6 03 Fig 5.22 : Sample No.297 - Method 2 - Q tests 3. 2. 5, 3» O 5,- 2.. 5' 1.5 r qr O—‘wamaflmo 0. l .- y=0.l661x+ 1.7126 5 4 0,. ,l-- ,, _ . -_-.__ .___,-_. 0 2 4 6 8 10 P1 Fig 5.23 : Sample No.297 - Method 3 - Q tests y = 1.3575x + 2.9987 0 Pr Fig 5.24 : Sample No.297 - Method 4 - Q tests oo o ~—+ —4 \1 $——— ON 1—4w 69 y = 1.6929x + 4.1628 _4 l ‘r_ 4; Fig 5.25 : Method 5 - Q tests - Phase 11 y = 0.3851x + 0.9351 Fig 5.26 : Method 10 - Q tests - Phase II T 1 8 i l y = 0.400711 + 0.604 0 70 0 2 4 6 8 10 12 14 16 Fig 5.27 : Method 8 - Q tests - Phase II 18T l6 4 1 y = 1.6929x + 2.9436 Pr Fig 5.28 : Method 9 - Q tests - Phase II 71 5.2.6 R(CU) Tests - Phase 11 Fill This set of data consists of 55 samples, most of which consist of 4 specimens. Table 5.9 shows that mean of WES-reported 4 values in this case is considerably higher than the values obtained from regression analyses on individual samples. The one reason for this happening can be that many samples in this set consist of four specimens. Normally, a fourth specimen is tested when some unexpected value of 0, is encountered against a specific value of 03. So for that particular value of 03, the triaxial test is repeated. While drawing Mohr’s circles, engineers tend to discard the apparent bad result. But in regression analysis, the value is given equal weighting and this affects the outcome of the regression. The correlation coefficient in this case is somewhat different from rest of tables for individual samples. Method 1 gives a slightly positive correlation between c and 4 whereas regression methods give a negative correlation between c and 4. Figures 5.29 through 5.31 show the regression lines obtained for Sample No. 297 consisting of four specimens. Table 5.10 also depicts that 4 value based on 0,,03 is lower than WES values from Method 1 but still higher than its counterparts in individual samples (Methods 2 through 4). The 4 values from regression of q on p and t on 0 are significantly higher than WES value here also. Figures 5.32 through 5.35 show the pooled regression for Methods 5 and 8 through 10 respectively. 72 Table 5.9 Cannon Dam Shear Testing - R (CU) Tests Individual Samples Method 1 Method 2 Method 3 Method 4 Phase [I fill R tests on record samples number of tests 55 55 55 55 c parameter mean 1.067tsf 1.282tsf 1.125tsf 1.282tsf standard deviation 0.704tsf 0.892tsf 0.804tsf 0.892tsf coefficient of variation 66% 69.6% 71.5% 69.6% skewness coefficient +0.6 +0.996 +0.569 +0.996 4) parameter mean 21.12° 17.46° 18.842° 17.46° standard deviation 7.144° 7.612° 6.76° 7.612° coefficient of variation 33.8% 43.6% 35.9% 43.6% skewness coefficient +0613 -1 .102 0253 -l . 102 covariance +0984 -1 .667 -0.63 -1 .667 correlation coefficient pm +0.199 -0.25 -0.118 -0.25 Table 5.10 Cannon Dam Shear Testing - R (CU) Tests Pooled Regression flethods No.5 No. 8 No.9 No. 10 No. 11 Phase 11 fill R t¢Sts on record samples mt oftests 192 192 192 192 192 0 Parameter mean 1.156 tsf -0.02 tsf 1.156 tsf 0.392 tsf O..23 tsf variance - - - 0.031 0.031 standard deviation - - - 0.176 tsf 0.176 tsf 4‘ Parameter mean 19.6470 3o.04° 19.6470 26.4l7° 27.58 ta" 4) parameter variance - - - 0.001 0.001 standard deviation - - - 0.031 0.031 °°Varianee,,_,, - - - -0.005 -0004 wfion coefficient 9&1 - - - -0.886 -0.886 0'1 qr 73 164 14 4 ,2 +. y = 2.1204x + 2.7437 Fig 5.29 : Sample No. 297 - Method 2 - R tests :3} ML]. #1 5” Ut i +—t N 4 y = 0.3627x + 0.8559 Fig 5.30 : Sample No. 297 - Method 3 - R tests 12 .7. 10 . y=2.1204x+ 1.9401 8 6 4 . 2 o W Li... _ o l 2 3 4 5 Pr Fig 5.31 : Sample No. 297 - Method 4 - R tests 74 DJ Lit -4 30 4 ° 4 y = 2.013x + 3.2804 . 25 + a. l 6' ! 15 l. 1 10 4 | 4 5 «1 1 0 4* + e 1 a 0 1 2 3 4 5 6 0'3 Fig 5.32 : Method 5 — R tests — Phase II 12 4 4 o y = 0.4968x + 0.3921 10 4 . 1 8 4 ° . Fig 5.33 : Method 10 - R tests - Phase II 75 y = 0.5007x - 0.0171 y = 2.013x + 2.3196 Pr Fig 5.35 : Method 9 - R tests - Phase II 20 76 5.3 Perry County Bois Brule Levee Results 5.3.1 Bois Brule Levee Bois Brule Levee and Pumping Station are part of Perry County Drainage and Levee District Nos. 1, 2 & 3 project which is located in Perry County, Missouri, and Randolph County, Illinois, on the right bank of the Mississippi River. The districts are bounded on the northwest by the old Mississippi River channel, on the northeast and southeast by the Mississippi River and on the southwest by a diversion channel at the base of the bluffs. The Bois Brule Pumping Station has a pumping capacity of 215 c.f.s. The data sets are mix of embankment and foundation samples (Corps, 1978). 5.3.2 Q(UU) Tests The data sets for Bois Brule levee are considerably smaller than those of Clarance Cannon Dam. As this project consisted of minor alterations to an existing levee, only a few samples were taken to provide a basis for stability analysis. However, this is typical of the sparse data that might often be available. This data set consists of 11 samples of 3 to 4 specimens each. This is the smallest set of data under consideration. Even the results of this size of sample are quite similar to previous ones as shown in Tables 5.11 and 5.12. Figures 5.36 through 5.38 show the plots of regression analysis on Sample No. P-2B which has WES reported value of 4:0. But as in Figure 5.37, the regression analysis on this sample results in a best-fit line with a negative slope. A negative value of friction angle does not make any sense in practice. This problem will be addressed later in this chapter in more detail. Perry County Shear Testing - Q (UU) Tests 77 Table 5.1 1 Individual Samples Method 1 Method 2 Method 3 Method 4 number oftests ll 11 11 11 c parameter mean 0.299tsf 0.305 tsf 0.299tsf 0.305 tsf standard deviation 0.141tsf 0.138 tsf 0.1391tsf 0.138 tsf coefficient of variation 47.1% 45.4% 46.6% 45.4% skewness coefficient -0.257 -0.027 +0.072 -0.027 4 parameter mean 209° l.676° 1.871° 1.6760 standard deviation 2.879° 2.984° 3.308° 2.984° coefficient of variation 137.7% 178.0% 176.8% 178.0% skewness coefficient +1.487 +1.446 +1.824 +1 .446 covariance +0.099 +0.05] +0.016 +0.051 correlation coefficient p“ +0.244 +0.124 +0.035 +0.124 Table 5.12 Perry County Shear Testing - Q (UU) Tests Pooled Regression Methods No. 5 No. 8 No.9 No. 10 No. 11 number of tests 35 35 35 35 35 c parameter mean 0.285 tsf 0.223 tsf 0.285 tsf 0.227 tsf 0.224 tsf variance - - - 0.004 0.004 standard deviation - - - 0.063tsf 0.063tsf 1) parameter mean 248° 4.430 248° 429° 435° tan 4 parameter variance - - - 0.0010 0.001 standard deviation - - - 0.032° 0.032° covariancecm. - - - -0.002 -0.002 - - -0.871 -0.872 correlation coefficient pen-21 - 78 y = 0.9764x + 0.8949 0 +——————#— ‘1 4 m- ‘1 '———‘—* 0 0.5 l 1.5 2 2.5 3 03 Fig 5.36 : Sample P-2B, Method 2 - Levee Q tests 0.6 4 0.5 4 ° 0.4 4 fl 5- 0.3 4- 0.2 + y = -0.0079x + 0.4454 0.1 o 4-- ——~4 , 4 ‘ . .— 4 - 0 0.5 l 1.5 2 2.5 3 3.5 Pi Fig 5.37 : Sample P-2B, Method 3 - Levee Q tests y = 0.9764x + 0.6328 Pr Fig 5.38 : Sample P-2B, Method 4 - Levee Q tests 79 Figures 5.39 through 5.42 show a lot of scatter in data, because of different values of 03 for this smaller set of observations. In any case, trends of data still follow the same order as discussed earlier. 5.3.3 R(CU) Tests This set of data contains 12 samples of 3 specimens each. In Table 5.13, WES value of 4’ is slightly higher than Method 2, but regression of q on p still takes the lead. Figures 5.43 through 5.45 show a plot of Sample P-ZB by different methods. From Table 5.14, 4) value from Method 5 in significantly higher than those in Table 5.13. Rest of methods just follow suit. Figures 5.46 through 5.49 plot the whole set of data with obviously no surprises. 5.4 Method 6 - Lumb’s Weighted Regression This type of regression was described in Chapter 4 as Method 6. However this method could not work at least with these sets of data. Perhaps these sets of data were too small for this method to work. However, Lumb’s claim that the variance of the regression line is generally not constant but some function of 63, was verified during the course of this study. When test results were plotted in the form of 0', against 03, it was noticed that the scatter about the mean trend line increases with 03. The weighting function w cc 1/ s2 is calculated for each 03 value and then multiplied each 0, value by its corresponding weighting factor. The values of o, are so increased for lower values of 03 that slope of regression line becomes negative. Table 4.15 shows the process of 80 A I 5" UI __ §_..._.+ ____+._____4 U I y = 1.0903x + 0.5945 1.5 l 0.5 . .__. “Lg—2‘--- -. V a. _-. 0.5 1 1.5 2 2.5 3 3.5 4 03 Fig 5.39 : Method 5 - Levee Q tests 0 8 L y = 0.0749x + 0.2273 i Fig 5.40 : Method 10 - Levee Q tests 81 y = 0.0773x + 0.2219 0.6 T l 0.4 i l 0.2 + I l .' . g . ' O “— i. T ” T. L w T 0 0 5 l l 5 2 2 5 3 3 5 4 Pi Fig 5.41 : Method 8 - Levee Q tests 3 ,- * I 2-5 '* y = 1.0903x + 0.4204 I 2 a 5. 1 5 1 l. 0.5 ~- ' o , L -, L 0 O 5 l 1.5 2 2 5 Pr Fig 5.42 : Method 9 - Levee Q tests 82 Table 5.13 Perry County Shear Testing - R (CU) Tests Individual Samples Method 1 Method 2 Method 3 Method 4 number of tests 12 12 12 12 c parameter mean 0.472tsf 0.45 tsf 0.432tsf 0.45 tsf standard deviation 0.371tsf 0.308 tsf 0.2761tsf 0.308 tsf coefficient of variation 78.6% 68.3% 63.8% 68.3% skewness coefficient +1.347 +1.065 +1.057 +1 .065 0 parameter mean 13.170 17.970 18.23° 1797" standard deviation 5.7180 6.4750 7.0460 6.475° coefficient of variation 31.5% 36.0% 38.6% 36.0% skewness coefficient +0.98] +0.909 +1 .065 +0.909 covariance +1 .571 +1.456 +1.288 +1 .456 correlation coefficient pen, +0.742 +0.73] +0.662 +0.73] Table 5.14 Perry County Shear Testing - R (CU) Tests Pooled Regression Methods No.5 No. 8 No. 9 No. 10 No. 11 number of tests 36 36 36 36 36 c parameter mean 0.377 tsf -0.234 tsf 0.377 tsf -0.003 tsf -0.096 tsf variance - - - 0.042 0.041 standard deviation - - - 0.042tsf 0.042tsf ¢ parameter mean 21.107° 33.040 21 .107° 28.590 30.09° tan 6 parameter variance - - - 0.006 0.005 standard deviation - - - 0.080 0.070 covariancemm - - - -0.014 -0.01 2 correlation coefficient pug! - - - -0.861 -0.860 0'1 5' 83 y = 1.9032x + 0.6247 0'3 Fig 5.43 : Sample P-2B, Method 2 - Levee R tests 1.8 f 1.6 L 1.4 ' 1.2 . ' 1 0.8 + 0.6 L 0.4 4‘- 0.2 J.- 0 1T --— »— 4H — _- we ------ W—i 0 1 2 3 4 5 Pi y = 031le + 0.2148 y = 1.9032x + 0.4418 0 0.5 1 LS 2 2.5 Pr Fig 5.45 : Sample P-2B, Method 4 - Levee R tests 01 84 + y = 2.1256x + 1.0995 ° 0 0.5 l 1.5 2 2.5 3 3.5 0'3 Fig 5.46 : Method 5 - Levee R tests y = 0.5449x - 0.0032 b) - - 41- —-——- r Fig 5.47 : Method 10 - Levee R tests 9i Qr IO- 85 y = 0.5453x - 0.196] Pi Fig 5.48 : Method 8 - Levee R tests y = 2.1256x + 0.7774 0.5 l 1.5 2 2.5 Pr Fig 5.49 : Method 9 - Levee R tests 86 Table 5.15 Cannon Dam Shear Testing - Q(UU) Tests Lumb's Weighted Regression Phase I Fill - Q Testing on Record Samples Serial 03 32 Us2 w 1 1.5 3.694 0.2707 4.2574 2 3 7.007 0.1427 2.2442 3 6 15.726 0.0636 1 40 4 . 1 O 35 T ‘ y = -2.1297x + 23.843 1 : . 30 —. . f . i 3 25 a. g 8 - » 3 o - 3 20 § 15 f 10 _. I 5 .. 0 . LL __ + _L, 0 1 2 3 4 5 6 0’3 Fig 5.50 : Lumb's weighted regression for Q test - Phase I 87 calculation of weighting factor for one representative set of data (which is Q tests for Cannon Dam Phase I in this case) and Figure 5.50 plots the weighted 0', values against 03 values. 5.5 Negative (0 Values This problem was frequently encountered during regression analysis of Q(UU) tests. When actual value of d) is closer to zero and there is some scatter in the sizes of Mohr’s circles, the drawing of failure envelope, approximates anything near zero as equal to zero. But during regression, the negative slope, if it exists, will be depicted as such. There can be two possible ways to handle this problem. First, as followed during this study, the negative 11) values are incorporated into the statistical process “as is”. This makes more sense, because the values for which the Mohr-Coulomb failure envelope is taken equal to zero, the slope of regression line can be slightly negative or positive. If one takes into account both negative and positive values, the net value will be very close to zero. Secondly, the negative 6 values can be disregarded wherever these occur and taken equal to zero. The analogy for this suggestion can be that there is no physical interpretation of a negative value of friction angle. However a more deliberate study is needed to deal with this problem which is suggested in recommendations for further research. 4.6 The Problem of Outliers An outlier is an extreme observation. Residuals that are considerably larger in absolute value than the others, say three or four standard deviations from the mean, are potential outliers. Outliers are the data points that are not typical of the rest of the data. 88 Depending on their location, outliers can have moderate to severe effects on the regression model. An excellent general treatment of the outlier problem is in Barnett and Lewis (1994) and Rousseeuw and Leroy (1987). Outliers should be carefully investigated to see if a reason for their unusual behavior can be found. Sometimes outliers are “bad” values, occurring as a result of unusual but explainable events. In this case the outliers should be corrected or deleted from the data set. However, there should be strong nonstatistical evidence that the outlier is a bad value before it is discarded. Sometimes the outlier is an unusual but perfectly legitimate observation. Deleting these points to improve the fit of the equation can be dangerous because it can give a false sense of precision in estimation or prediction. There are two separate questions which come up while dealing with outliers. One problem is to have some statistical technique which may indicate outlying observations and to study them carefully. The second problem is what to do with these outliers, once they are located. Considering the first problem, Barnett and Lewis (1994) writes about outlier methods in some of the major statistical software packages, “The overall situation is not encouraging and suggests that none of the packages offers a comprehensive procedure-based or integrated approach to outlier handling.” In the Reference Manual for MINITAB (1989), there is no mention of outlier in the index. Residual—based diagnostics are however offered. Standardized residuals with absolute value in excess of 2 are marked (R). A label X is also placed against observations with much higher standardized residual value. The main feature is that the 89 program itself indicates the unusual observations and leaves the decision with the user to delete the unusual observation or not. The Spreadsheet Microsoft Excel can also be indirectly used for detection of potential outliers. During regression analysis, program can be asked to calculate the standardized residuals. The program does not indicate the unusual observations itself but standardized residuals with absolute values greater than 2 can be investigated. The following guidelines are suggested on what to do with outliers: 1. Use some statistical technique to determine the degree of discrepancy in terms of standardized residuals. 2. Check back to the developer of the data set if any reason can be found for the outliers, such as misrecording or unexpected experimental conditions. If some such reason can be found, the observation may be modified or dropped. 3. Carry out the analysis with and without the suspect observation, in order to see what effect that has. In the present study, the problem of outliers was not practically dealt with since the comparison was required to be made to WES values to establish the authenticity of different methods of soil strength description. But this should not undermine the importance of dealing with outlier problem. A more detailed and thorough study is required to go in to establish some standardized guidelines to counter this problem effectively. CHAPTER 6 CONCLUSIONS AND RECOMMENDATIONS 6.1 Conclusions The main objective of this study was to investigate and devise some ways and means to probabilistically characterize the soil strength working from test results. This included the review of some of the existing methods and their relative performance for total stress analysis. Manipulation of some of the methods was done to widen the scope of this study. Not contradicting with the basic principles, some alternatives approaches were considered to reach at best possible conclusions. The statistical approach has some advantages over the deterministic approach. The deterministic method enhances the intrinsic uncertainty of soil strength because of introduction of personal opinion. Statistical methods eliminate one source of variability i.e. the effect of personal opinion. This factor is of extreme importance in all types of research studies. Talking in broader terms, this study could be divided into two branches. The first included considering different methods which could possibly be used to carry out regression analysis on individual specimens to obtain values for each sample and then perform statistics on results obtained thereupon. The other set of methods combines all individual specimens together into one single pooled set and then performs regression analysis on whole set of data all at once. For a large set of data, the pooled regression 90 91 may be less time consuming but still regression on three to four specimens to obtain sample values performs better than pooled regression. The individual samples regression facilitates firrther statistical descriptions like finding of moments and distributions, etc. The individual samples regression methods (Methods 1 through 4) have been diagramatically described in Figure 6.1. It was observed in Chapter 5 that results obtained from all four methods are quite comparable to each other for almost all sets of data. Method 1, being a deterministic method, cannot get preference over other statistical methods. Methods 2, which regresses 01 versus 03, provides the simplest approach to finding soil strength parameters. Method 3, which uses the stress path approach, overestimates the value of 4) although it is not very significant for individual samples regression. When p—q axes are rotated through 45°, as in Method 4, values of c and 6 exactly match with those of Method 2. This process however, involves additional arithmetic and more space in spreadsheets. So Method 2 emerges as the most preferred method whether individual samples regression or pooled regression is used. Figure 6.2 summarizes all the methods for pooled regression analysis being considered in this study. Contrary to the previous case, the results from pooled regression are very significantly different from each other. Method 8, which involves regression of q on p, greatly inflates the value of angle of internal friction. The p and q values are neither independent nor dependent variables, as required by regression model but rather a combination of independent variable 63 and dependent variable 6,. This amalgamation of variables does not cater for data variability which results into overestimation of expected value of 11> by far. So values obtained from pooled regression of q on p should never be 92 mUHHwflkhm .8388 3:222: @5228 £985 :8 mo 2033:8835 Bowman; .8 26562 " fie charm fl @0532. 88:0 302 wag/SQ N @0502 n . a — mb . _b commonwom v 8502 “‘7 n a.“ a g kg :o_mm2wom a . a a . a coimonmom — 93 .568an “go—eon 8m 83356830 €9.25. :8 89 30502 " N6 0.5»?— : e058: 9 no AS a : 858% e do 02m> 8335.85 commmocwo 288m 03—m> 30301— 2 8582 e co 8:; v.23: m @0502 “~232qu w @0562 commmocwom 38,—. BEE 94 entrusted. Again when p—q axes are forced to conform to direction of data variability as in Method 9, the results obtained are exactly similar to those of Method 5. The pooled regression of a, on 03 reports the closest values of c and 0) compared to those from individual samples. The regression of c, on 03 exactly meets the requirements of model for linear regression analysis as described in Chapter 3. This method clearly differentiates between dependent and independent variables while others just mix them up. Also this method caters for data variability completely. Methods 5, 8 and 9 offer a quick estimate of c and 4) values but no further statistics of strength parameters can be found. Methods 10 and 11 provide an answer to this problem but a second regression is required as explained in Figure 6.2. Out of these two methods, Method 11 reports higher value of 0 but still remains lower than value of 4) from Method 8. The expected value of friction angle is still questionable since it is much higher than the one estimated from individual samples regression. However, while working in o-r space, further statistics of cohesion and tangent of friction angle could be worked out. Hence from pooled regression case also, regression of c, on 63 (Method 5) proves out to be the preferred and most conservative approach for estimation of strength parameters. But when firrther statistics of a data set are desired, Method 10 could be preferred. 6.2 Recommendations 6.2.1 Recommendations for Practitioners For design practitioners, it is desirable that a probabilistic method be conceptually simple provided a simple method can yield reasonable results. Simplicity is helpful in 95 understanding and the communication of procedures to professionals who are good at soil mechanics but lack a background in statistics. A simple model also permits hand checking of simple problems or of critical parts of complex problems. Regression of 01 on 03 provides the simplest approach as it takes straight triaxial test results and regresses them to yield the values of soil strength parameters. Also it reports the most conservative value of 4), so if there can be any bias, it is on safer side. So Method 2 gives the most comprehensive results and should be preferred over all other methods considered in this study. But if the soil is grossly uniform, Method 5 can be the most efficient way to estimate soil strength parameters. These recommendations however, strictly apply to total stresses alone as effective stresses were not considered in this study. 6.2.2 Recommendations for Further Research The present study was restricted to total stress analysis only. It is recommended that a further research be pursued in this area by expanding the scope and taking into account the pore pressures and effective stresses also. May be for effective stresses, the stress path approach proves to be the only means to trace the data variability since trend may be different from 45°. Also data variability may not be along vertical axis for regression of c, on 63. During regression analyses, some negative values of friction angle are also possible. A negative friction angle has no physical interpretation. A deliberate study is required to find ways to prevent occurrence of negative 0 values or to deal with them effectively once they do occur. 96 The problem of outliers was briefly addressed during this study. The existence of outliers affects the outcome of regression but their deletion can give a false sense of precision. A simple but comprehensive solution to this problem is sought in any firture research. Lumb’s weighted regression (Method 6) could not work with present sets of data. A further research can be pursued since it can provide the best obtainable estimate of data variance. Multiplication of a, values by the weighting factor could possibly offer a solution to outliers problem also. APPENDIX A APPENDIX A INDIVIDUAL SAMPLES REGRESSION A.l General In this appendix, the use of spreadsheets for different statistical methods of soil strength description will be explained. These methods have been applied to only one set of data which is Q(UU) testing on record samples of Cannon Dam phase II fill. This set was largest of all data sets and includes samples of 2 to 4 specimens each. Since the objective is to explain the working, some representative samples will be considered to avoid unnecessary details. In the end, a comparison of c and 4) values will be made with the WES reported values of c and it) and statistics will also be tabulated. A.2 Method 2 - Regression of a, on 63 The values of c and d) for each individual sample are obtained by using the following procedure:- 0 Follow the format of Table A-1 for all columns headings. 0 List the values of 03 and corresponding values of 01. Note that two consecutive values of 63 should not be same otherwise column for 6’, will not calculate for division by zero. 0 Find (0'3)2 , (0'1)2 and 03 * o, for each specimen. 0 Find sums and means of all five columns. 97 98 0 Calculate regression parameters a, b by following formulae :- b=P_(__Z_63*Gl)-(ZO3XZOI) (A.l) :42 of Hz 002 a = 6, — b* 63 (A2) 0 Calculate 6, by following formulae :- 6,= a+b*63 (A3) 0 Now calculate b from 6, values, this value should be same as previously calculated b value. b: 511—512 (A.4) o 3, — 0' 32 where 6,, and 6, 2 are two consecutive predicted values of 6, and 63. and 0'32 are two consecutive original values of 0’3. 0 Then calculate (I) by following formula :- 4 = tan" [12:51 1 (4.5) 0 Compute a, this value should be same as previously calculated value of a. a = 6, - b* 0'3 (A6) 0 Find out c parameter by following equation:- a II I... 3 (A7) 99 A.3 Method 3 - Regression of q on p Following procedure is followed to obtain values of c and 4) for each sample as in Table A2:- 0 Calculate values of p and q for each 6, , 0'3 value using equations (2.4) and (2.5) respectively. 0 Use same procedure as given in previous section, till equation (AA), by substituting p for each 03 and q for each 6, value. 0 The slope of regression line b = tan 4!. 0 Use following relationship to calculate 4): sin 4) = tan 4! (A8) 0 Calculate c by using the relationship as under: a c = (A9) cos¢ A.4 Method 4 - Regression of qr on pr Table A3 is used to calculate the values of p, and q,:- 0 Convert the rectangular coordinates p,q into polar coordinates r,0. r= ,/p2+q2 (A.10) _ -1 q and 0—tan [—] (A.11) P 0 To rotate the axes through 450, 9,=0 +45O (A.12) 100 0 Again change polar coordinates r, 0, to rectangular coordinates, p,=r * cos 0r (A.13) and qr = r * sin0, (A.14) 0 Now carry out regression on pr and qr values by following same formulae as in section (A.2) by using pr and q, instead of 0'3 and 6, respectively as given in Table A4. 0 Here regression parameter b = tan 4),. o The actual slope of Krline w = w, - 45°. 0 The actual intercept of K, line is computed as under = a} sin(45o — 11;) cos \p (A.15) 0 Calculate values of c and 4) by using equations (A8) and (A9). A.5 Summary of c and 4) values and Statistics All the values of c and 4) for individual samples are listed against WES values (Method 1) and then other statistics are performed on each set of these values as explained in Table A.5. 101 TABLE A.l METHOD 2 - INDIVIDUAL SAMPLES Sample 63 6, 0‘32 6,2 63*6, & b 6 a c 297 3 7.65 9 58.523 22.950 8.313 1.357 8.721 4.241 1.820 1 5.47 1 29.921 5.470 5.598 1.357 8.721 4.241 1.820 3 9.19 9 84.456 27.570 8.313 1.357 8.721 4.241 1.820 6 12.3 36 151.290 73.800 12.385 1.357 8.721 4.241 1.820 sum 13 34.61 55 324.190 129.790 DOF 4 4 4 4 4 mean 3.25 8.6525 13.75 81.047 32.448 b 1.357 a 4.241 224 1 8.45 1 71.403 8.450 9.010 2.039 19.988 6.971 2.441 3 14.02 9 196.560 42.060 13.087 2.039 19.988 6.971 2.441 6 18.83 36 354.569 112.980 19.203 2.039 19.988 6.971 2.441 sum 10 41.3 46 622.532 163.490 dof 3 3 3 3 Mean 3.333 13.767 15.333 207.511 b 2.039 a 6.971 225 1 5.13 1 26.317 5.130 5.130 3.190 31.512 1.940 0.543 3 11.51 9 132.480 34.530 11.510 3.190 31.512 1.940 0.543 sum 4 16.64 10 158.797 39.660 dof 2 2 2 2 Mean 2 8.32 5 79.399 b 3.19 a 1.94 227 1 14.76 1 217.858 14.760 14.869 1.065 1.797 13.804 6.689 3 17.18 9 295.152 51.540 16.998 1.065 1.797 13.804 6.689 6 20.12 36 404.814 120.720 20.193 1.065 1.797 13.804 6.689 sum 10 52.06 46 917.824 187.020 dof 3 3 3 3 Mean 3.333 17.353 15.333 305.941 b 1.065 a 13.804 165 1.5 8.24 2.25 67.898 12.360 9.084 1.766 16.080 6.435 2.421 3 13 9 169.000 39.000 11.734 1.766 16.080 6.435 2.421 6 16.61 36 275.892 99.660 17.032 1.766 16.080 6.435 2.421 sum 10.5 37.85 47.25 512.790 151.020 dof 3 3 3 3 Mean 3.500 12.617 15.750 170.930 b 1.766 a 6.435 195 1 6.26 1 39.188 6.260 6.298 1.349 8.554 4.948 2.130 3 9.06 9 82.084 27.180 8.997 1.349 8.554 4.948 2.130 6 13.02 36 169.520 78.120 13.045 1.349 8.554 4.948 2.130 sum 10 28.34 46 290.792 1 1 1.560 dof 3 3 3 3 Mean 3.333 9.447 15.333 96.931 b 1.349 4.948 199 115 144 200 205 sum mean 2.750 1.095 3.989 5.1 10.16 8.5 16.95 40.71 4 10.178 3.75 10.05 8.64 13.67 36.11 9.0275 5.690 13.260 10.410 1 1.520 40.880 10.220 4.360 9.030 8.710 13.450 35.550 3.350 7.270 6.820 10.560 28.000 7.000 1 36 9 36 82 4 20.500 20.5 1.000 36.000 9.000 36.000 82.000 20.500 1.000 36.000 9.000 36.000 82.000 20.500 1.000 9.000 1.000 36.000 47.000 4 1 1.750 102 TABLE A.l (cont'd) 26.010 5.100 5.108 103.226 60.960 13.558 72.250 25.500 8.488 287.303 101.700 13.558 488.788 193.260 4 4 122.197 48.315 14.063 3.750 4.436 101.003 60.300 12.089 74.650 25.920 7.497 186.869 82.020 12.089 376.584 171.990 4 4 94.146 42.998 32.376 5.690 6.540 175.828 79.560 12.673 108.368 31.230 8.993 132.710 69.120 12.673 449.282 185.600 4 4 112.321 46.400 19.010 4.360 5.026 81.541 54.180 11.462 75.864 26.130 7.600 180.903 80.700 1 1.462 357.317 165.370 4 4 89.329 41.343 11.223 3.350 5.084 52.853 21.810 7.274 46.512 6.820 5.084 111.514 63.360 10.559 222.101 95.340 4 4 55.525 23.835 1.690 1.690 1.690 1.690 1.531 1.531 1.531 1.531 1.227 1.227 1.227 1.227 1.287 1.287 1.287 1.287 1.095 1.095 1.095 1.095 14.863 14.863 14.863 14.863 12.102 12.102 12.102 12.102 5.843 5.843 5.843 5.843 7.214 7.214 7.214 7.214 2.597 2.597 2.597 2.597 3.418 3.418 3.418 3.418 2.905 2.905 2.905 2.905 5.313 5.313 5.313 5.313 3.739 3.739 3.739 3.739 3.989 3.989 3.989 3.989 1.314 1.314 1.314 1.314 1.174 1.174 1.174 1.174 2.399 2.399 2.399 2.399 1.648 1.648 1.648 1.648 1.906 1.906 1.906 1.906 1 03 TABLE A.2 METHOD 3 - INDIVIDUAL SAMPLES 2 Sample p, (h J), 31 {13$ h, b=tanw 6 a c 297 3.235 2.235 10.465 4.995 7.230 2.250 0.166 9.563 1.713 1.737 5.325 2.325 28.356 5.406 12.381 2.597 0.166 9.563 1.713 1.737 6.095 3.095 37.149 9.579 18.864 2.725 0.166 9.563 1.713 1.737 9.150 3.150 83.723 9.923 28.823 3.233 0.166 9.563 1.713 1.737 sum 23.805 10.805 159.692 29.902 67.297 DOF 4.000 4.000 4.000 4.000 4.000 mean 5.951 2.701 39.923 7.476 16.824 b 0.166 a 1.713 224 4.725 3.725 22.326 13.876 17.601 3.881 0.349 20.437 2.231 2.381 8.510 5.510 72.420 30.360 46.890 5.203 0.349 20.437 2.231 2.381 12.415 6.415 154.132 41.152 79.642 6.566 0.349 20.437 2.231 2.381 sum 25.650 15.650 248.878 85.388 144.133 DOF 3.000 3.000 3.000 3.000 3.000 mean 8.550 5.217 82.959 28.463 48.044 1) 0.349 a 2.231 225 3.065 2.065 9.394 4.264 6.329 2.065 0.523 31.512 0.463 0.543 7.255 4.255 52.635 18.105 30.870 4.255 0.523 31.512 0.463 0.543 sum 10.320 6.320 62.029 22.369 37.199 DOF 2.000 2.000 2.000 2.000 2.000 mean 5.160 3.160 31.015 11.185 18.600 b 0.523 a 0.463 227 7.880 6.880 62.094 47.334 54.214 6.931 0.032 1.848 6.676 6.680 10.090 7.090 101.808 50.268 71.538 7.002 0.032 1.848 6.676 6.680 13.060 7.060 170.564 49.844 92.204 7.098 0.032 1.848 6.676 6.680 sum 31.030 21.030 334.466 147.446 217.956 DOF 3.000 3.000 3.000 3.000 3.000 mean 10.343 7.010 11 1.489 49.149 72.652 b 0.032 a 6.676 165 4.870 3.370 23.717 11.357 16.412 3.606 0.299 17.383 2.151 2.254 8.000 5.000 64.000 25.000 40.000 4.541 0.299 17.383 2.151 2.254 11.305 5.305 127.803 28.143 59.973 5.528 0.299 17.383 2.151 2.254 sum 24.175 13.675 215.520 64.500 116.385 DOF 3.000 3.000 3.000 3.000 3.000 mean 8.058 4.558 71.840 21.500 38.795 b 0.299 2.151 192 sum 223 sum mean 226 294 sum mean 295 sum mean 5.485 8.975 14.460 2.000 7.230 0.570 0.857 5.595 7.630 13.810 27.035 3.000 9.012 0.467 1.305 4.310 6.500 10.765 21.575 3.000 7.192 0.302 1.520 4.095 6.075 10.450 20.620 3.000 6.873 0.296 1.342 2.630 5.495 10.285 18.410 3.000 6.137 0.408 0.132 3 .985 5.975 9.960 2.000 4.980 4.095 4.630 7.810 16.535 3.000 5.512 2.810 3.500 4.765 1 1.075 3.000 3.692 2.595 3.075 4.450 10.120 3.000 3.373 1.130 2.495 4.285 7.910 3.000 2.637 30.085 80.551 110.636 2.000 55.318 31.304 58.217 190.716 280.237 3.000 93.412 18.576 42.250 1 15.885 176.71 1 3.000 58.904 16.769 36.906 109.203 162.877 3.000 54.292 6.917 30.195 105.781 142.893 3.000 47.631 104 TABLE A.2 (cont'd) 15.880 21.858 3.985 35.701 53.626 5.975 51.581 75.483 2.000 2.000 25.790 37.742 16.769 22.912 3.917 21.437 35.327 4.867 60.996 107.856 7.751 99.202 166.095 3.000 3.000 33.067 55.365 7.896 12.11 1 2.821 12.250 22.750 3.483 22.705 51.295 4.771 42.851 86.156 3.000 3.000 14.284 28.719 6.734 10.627 2.552 9.456 18.681 3.137 19.803 46.503 4.431 35.992 75.810 3.000 3.000 1 1.997 25.270 1.277 2.972 1.205 6.225 13.710 2.375 18.361 44.071 4.330 25.863 60.753 3.000 3.000 8.621 20.251 0.570 0.570 0.467 0.467 0.467 0.302 0.302 0.302 0.296 0.296 0.296 0.408 0.408 0.408 34.764 34.764 27.824 27.824 27.824 17.578 17.578 17.578 17.193 17.193 17.193 24.092 24.092 24.092 0.857 0.857 1.305 1.305 1.305 1.520 1.520 1.520 1.342 1.342 1.342 0.132 0.132 0.132 1 .044 1 .044 1 .476 1 .476 1 .476 1.594 1.594 1.594 1 .404 1 .404 l .404 0.144 0.144 0.144 1 05 TABLE A.3 METHOD 4 - 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All the methods use pooled regression for estimation of expected values of c and 6. For Method 10 and 11, both of which involve two regression analyses, the statistics for c and tan 6 will also be explained. This appendix also uses the same data set i.e. Q tests on record samples of Cannon Dam phase II fill. The results of this data set for pooled regression have already been tabulated in Table 5.8. 8.2 Method 5 - Regression of 0, on 03 Table B.1 explains the whole procedure for this method. The format of this table is similar to Table A.1 and this method essentially uses same procedure as Method 2 except that sample size now covers the whole data set. 8.3 Method 8 - Regression of q on p The pooled regression of q on p is given in Table B2 and follows the entire procedure of Method 3 as covered by Table A.2. 111 112 3.4 Method 9 - Regression of q, on pr Table B.3 has been used to convert all the p, q values to their respective pr and q, values using the procedures of Table A3 and using equations A.10 through A.14. Regression for Method 9 is explained in Table BA and is exactly on lines of Table A4 B.5 Method 10 - Regression of r on o This method involves two regression analyses. First regression is of q on p as for Method 8. The 6 value from this regression is used to calculate a, 1: values which is shown in Table B5 and uses following equations :- o=p—q*sin¢ (B.1) t = q*cos (1) (3.2) The second regression is then performed on o, 1: values to find values of c and 6 (Table B.6). Rest of statistics are found using following formulae:- Standard Error = SW: $2 I )— (21* z 1:- [bit 2 (6* 1)] (B3) n— 2 S r/o Varaan ¢) = Var = (20, ) __ (m 52) (13.4) Var(c) = Var = Vmbifl “2) (13.5) Cove. tan d») = [Var (b)1*[—61 (8.6) p°"““° = (Wig; Ergo» (8'7) Where pc, m ¢ is the correlation between cohesion and tangent of friction angle. 113 8.6 Method 11 - Regression of r on 0' Method 11 uses Method 5 for first regression and calculation of 4) value (Table B.7). The 0', 1: values are then calculated using following equations:- = (53$) cos¢ (R9) Regression of 1: on 0’ (Table B.8) then exactly follows the procedure of Method 10 (Table 3.6). 114 TABLE B.l METHOD 5 - POOLED REGRESSION Sample a, a, of 6,2 63‘61 01;; h o a c 297 3 7.65 9 58.523 22.950 9.241 1.693 14.910 4.163 1.600 1 5.47 1 29.921 5.470 5.856 1.693 14.910 4.163 1.600 3 9.19 9 84.456 27.570 9.241 1.693 14.910 4.163 1.600 6 12.3 36 151.290 73.800 14.320 1.693 14.910 4.163 1.600 224 1 8.45 1 71.403 8.450 5.856 1.693 14.910 4.163 1.600 3 14.02 9 196.560 42.060 9.241 1.693 14.910 4.163 1.600 6 18.83 36 354.569 112.980 14.320 1.693 14.910 4.163 1.600 225 1 5.13 1 26.317 5.130 5.856 1.693 14.910 4.163 1.600 3 11.51 9 132.480 34.530 9.241 1.693 14.910 4.163 1.600 227 1 14.76 1 217.858 14.760 5.856 1.693 14.910 4.163 1.600 3 17.18 9 295.152 51.540 9.241 1.693 14.910 4.163 1.600 6 20.12 36 404.814 120.720 14.320 1.693 14.910 4.163 1.600 165 1.5 8.24 2.25 67.898 12.360 6.702 1.693 14.910 4.163 1.600 3 13 9 169.000 39.000 9.241 1.693 14.910 4.163 1.600 6 16.61 36 275.892 99.660 14.320 1.693 14.910 4.163 1.600 165 1.5 8.24 2.25 67.898 12.360 6.702 1.693 14.910 4.163 1.600 3 13 9 169.000 39.000 9.241 1.693 14.910 4.163 1.600 6 16.61 36 275.892 99.660 14.320 1.693 14.910 4.163 1.600 192 1.5 9.47 2.25 89.681 14.205 6.702 1.693 14.910 4.163 1.600 3 14.95 9 223.503 44.850 9.241 1.693 14.910 4.163 1.600 223 1.5 9.69 2.25 93.896 14.535 6.702 1.693 14.910 4.163 1.600 3 12.26 9 150.308 36.780 9.241 1.693 14.910 4.163 1.600 6 21.62 36 467.424 129.720 14.320 1.693 14.910 4.163 1.600 226 1.5 7.12 2.25 50.694 10.680 6.702 1.693 14.910 4.163 1.600 3 10 9 100.000 30.000 9.241 1.693 14.910 4.163 1.600 6 15.53 36 241.181 93.180 14.320 1.693 14.910 4.163 1.600 294 1.5 6.69 2.25 44.756 10.035 6.702 1.693 14.910 4.163 1.600 3 9.15 9 83.723 27.450 9.241 1.693 14.910 4.163 1.600 6 14.9 36 222.010 89.400 14.320 1.693 14.910 4.163 1.600 295 1.5 3.76 2.25 14.138 5.640 6.702 1.693 14.910 4.163 1.600 3 7.99 9 63.840 23.970 9.241 1.693 14.910 4.163 1.600 6 14.57 36 212.285 87.420 14.320 1.693 14.910 4.163 1.600 296 1.5 7.19 2.25 51.696 10.785 6.702 1.693 14.910 4.163 1.600 3 12.72 9 161.798 38.160 9.241 1.693 14.910 4.163 1.600 6 19.69 36 387.696 118.140 14.320 1.693 14.910 4.163 1.600 193 1 5.32 1 28.302 5.320 5.856 1.693 14.910 4.163 1.600 3 7.61 9 57.912 22.830 9.241 1.693 14.910 4.163 1.600 6 14.33 36 205.349 85.980 14.320 1.693 14.910 4.163 1.600 194 1 5.1 1 26.010 5.100 5.856 1.693 14.910 4.163 1.600 3 10.03 9 100.601 30.090 9.241 1.693 14.910 4.163 1.600 6 14.6 36 213.160 87.600 14.320 1.693 14.910 4.163 1.600 228 1 3.64 1 13.250 3.640 5.856 1.693 14.910 4.163 1.600 3 6.03 9 36.361 18.090 9.241 1.693 14.910 4.163 1.600 6 9.18 36 84.272 55.080 14.320 1.693 14.910 4.163 1.600 229 1 4.08 1 16.646 4.080 5.856 1.693 14.910 4.163 1.600 3 7.59 9 57.608 22.770 9.241 1.693 14.910 4.163 1.600 6 10.75 36 115.563 64.500 14.320 1.693 14.910 4.163 1.600 230 1 4.66 1 21.716 4.660 5.856 1.693 14.910 4.163 1.600 3 9.69 9 93.896 29.070 9.241 1.693 14.910 4.163 1.600 6 15.14 36 229.220 90.840 14.320 1.693 14.910 4.163 1.600 231 195 232 196 197 198 199 88 89 115 116 86 87 111 141 142 aw—O‘w—O\—wuna‘w—QW—Qw—Qwas—O‘w—ow—O‘wQ—Qw—O‘w—a—w—@w—O‘w—Qw— 6.38 10.65 12.96 6.26 9.06 13.02 4.86 8.48 11.36 4.16 12.91 5.56 18.71 8.48 14.67 23.2 4.21 9.89 13.28 5.1 10.16 8.5 16.95 5.18 7.11 9.6 6.59 10.38 17.47 3.75 10.05 8.64 13.67 5.33 7.36 1 1.03 4.87 7.08 10.08 6.79 10.22 16.8 5.15 12.79 7.33 16.7 7.15 10.57 14.3 5.6 12.44 16.42 1 9 36 1 9 36 1 9 36 1 9 l 36 l 9 36 1 9 36 1 36 9 36 1 9 36 1 9 36 l 36 9 36 l 9 36 1 9 36 l 9 36 1 9 1 36 1 9 36 1 9 36 115 TABLE B.l (cont'd) 40.704 6.380 5.856 1 13.423 31.950 9.241 167.962 77.760 14.320 39.188 6.260 5.856 82.084 27.180 9.241 169.520 78.120 14.320 23.620 4.860 5.856 71.910 25.440 9.241 129.050 68.160 14.320 17.306 4.160 5.856 166.668 38.730 9.241 30.914 5.560 5.856 350.064 112.260 14.320 71.910 8.480 5.856 215.209 44.010 9.241 538.240 139.200 14.320 17.724 4.210 5.856 97.812 29.670 9.241 176.358 79.680 14.320 26.010 5.100 5.856 103.226 60.960 14.320 72.250 25.500 9.241 287.303 101.700 14.320 26.832 5.180 5.856 50.552 21.330 9.241 92.160 57.600 14.320 43.428 6.590 5.856 107.744 31.140 9.241 305.201 104.820 14.320 14.063 3.750 5.856 101.003 60.300 14.320 74.650 25.920 9.241 186.869 82.020 14.320 28.409 5.330 5.856 54.170 22.080 9.241 121.661 66.180 14.320 23.717 4.870 5.856 50.126 21.240 9.241 101.606 60.480 14.320 46.104 6.790 5.856 104.448 30.660 9.241 282.240 100.800 14.320 26.523 5.150 5.856 163.584 38.370 9.241 53.729 7.330 5.856 278.890 100.200 14.320 51.123 7.150 5.856 111.725 31.710 9.241 204.490 85.800 14.320 31.360 5.600 5.856 154.754 37.320 9.241 269.616 98.520 14.320 1.693 1 .693 1.693 1.693 1.693 1.693 1.693 1.693 1.693 1 .693 1.693 1 .693 l .693 1.693 1.693 1.693 1.693 1 .693 1.693 1.693 1.693 1.693 1 .693 1.693 1.693 1 .693 1 .693 1.693 1.693 1 .693 1 .693 1 .693 1.693 1.693 1.693 1 .693 1 .693 1 .693 1 .693 1 .693 1.693 1 .693 1 .693 1.693 1 .693 1 .693 1 .693 1 .693 1 .693 1 .693 1 .693 1 .693 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 143 144 145 166 167 168 169 170 171 200 201 234 235 236 237 238 258 6.5 8.49 12.83 5.69 13.26 10.41 11.52 3.93 7.74 12.81 6.75 11.59 17.28 4.97 9.92 14.74 4.47 8.49 11.92 4.44 9.01 14.59 5.12 7.69 11.07 4.31 8.43 12.99 4.36 9.03 8.71 13.45 5.71 10.47 15.04 4.88 8.14 11.99 3.63 5.97 8.22 3.24 6.03 9.22 5.51 8.63 1 1.8 4.91 10.99 18.84 4.54 8.85 13.36 1 2.25 116 TABLE B.1(cont'd) 42.250 6.500 5.856 72.080 12.735 6.702 164.609 38.490 9.241 32.376 5.690 5.856 175.828 79.560 14.320 108.368 31.230 9.241 132.710 69.120 14.320 15.445 3.930 5.856 59.908 23.220 9.241 164.096 76.860 14.320 45.563 6.750 5.856 134.328 34.770 9.241 298.598 103.680 14.320 24.701 4.970 5.856 98.406 29.760 9.241 217.268 88.440 14.320 19.981 4.470 5.856 72.080 25.470 9.241 142.086 71.520 14.320 19.714 4.440 5.856 81.180 27.030 9.241 212.868 87.540 14.320 26.214 5.120 5.856 59.136 23.070 9.241 122.545 66.420 14.320 18.576 4.310 5.856 71.065 25.290 9.241 168.740 77.940 14.320 19.010 4.360 5.856 81.541 54.180 14.320 75.864 26.130 9.241 180.903 80.700 14.320 32.604 5.710 5.856 109.621 31.410 9.241 226.202 90.240 14.320 23.814 4.880 5.856 66.260 24.420 9.241 143.760 71.940 14.320 13.177 3.630 5.856 35.641 17.910 9.241 67.568 49.320 14.320 10.498 3.240 5.856 36.361 18.090 9.241 85.008 55.320 14.320 30.360 5.510 5.856 74.477 25.890 9.241 139.240 70.800 14.320 24.108 4.910 5.856 120.780 32.970 9.241 354.946 113.040 14.320 20.612 4.540 5.856 78.323 26.550 9.241 178.490 80.160 14.320 1.693 1 .693 1.693 1.693 1 .693 1 .693 l .693 1.693 1.693 1 .693 1.693 1.693 1.693 1.693 1 .693 1.693 1.693 1 .693 1.693 1.693 1.693 1.693 1.693 1 .693 1 .693 l .693 1.693 1.693 1.693 1 .693 1.693 1 .693 1 .693 1 .693 1 .693 1 .693 1 .693 1 .693 1 .693 1.693 1 .693 l .693 1 .693 1 .693 1 .693 1 .693 1 .693 1.693 1 .693 1 .693 1 .693 1 .693 1 .693 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 259 260 117 118 172 204 205 206 119 173 202 203 207 239 233 Ow--05w—Oxw—oxw—o‘w—aw—oxw—chw—O-w—o~w—-Qw—osw—wow—oxw—oswox—osw—csw— 4.65 8.04 15.2 5.19 8.09 13.26 8.211 15.71 13.39 18.36 5.8 7.56 12.06 4.02 7.26 10.53 5.57 3.95 5.86 10.94 2.95 5.64 9.64 6.34 8.73 13.02 3.35 7.27 6.82 10.56 6.52 12.84 24 3.81 7.17 11.8 6.04 10.39 15.67 5.39 7.94 1 1.12 3.39 5.36 8.44 6.32 11.44 16.48 6.93 1 1.41 15.28 5.74 10.34 18.61 1 9 36 1 9 36 1 36 9 36 1 36 l 9 36 1 9 36 l 36 1 9 36 1 9 1 36 1 9 36 1 9 36 l 9 36 1 9 36 1 9 36 1 9 36 1 9 36 1 9 36 117 TABLE B.l(cont'd) 21.623 4.650 5.856 64.642 24.120 9.241 231.040 91.200 14.320 26.936 5.190 5.856 65.448 24.270 9.241 175.828 79.560 14.320 67.421 8.211 5.856 246.804 94.260 14.320 179.292 40.170 9.241 337.090 110.160 14.320 33.640 5.800 5.856 57.154 22.680 9.241 145.444 72.360 14.320 16.160 4.020 5.856 52.708 21.780 9.241 110.881 63.180 14.320 31.025 16.710 9.241 15.603 3.950 5.856 34.340 17.580 9.241 119.684 65.640 14.320 8.703 2.950 5.856 31.810 16.920 9.241 92.930 57.840 14.320 40.196 6.340 5.856 76.213 26.190 9.241 169.520 78. 120 14.320 11.223 3.350 5.856 52.853 21.810 9.241 46.512 6.820 5.856 111.514 63.360 14.320 42.510 6.520 5.856 164.866 38.520 9.241 576.000 144.000 14.320 14.516 3.810 5.856 51.409 21.510 9.241 139.240 70.800 14.320 36.482 6.040 5.856 107.952 31.170 9.241 245.549 94.020 14.320 29.052 5.390 5.856 63.044 23.820 9.241 123.654 66.720 14.320 11.492 3.390 5.856 28.730 16.080 9.241 71.234 50.640 14.320 39.942 6.320 5.856 130.874 34.320 9.241 271.590 98.880 14.320 48.025 6.930 5.856 130.188 34.230 9.241 233.478 91.680 14.320 32.948 5.740 5.856 106.916 31.020 9.241 346.332 111.660 14.320 1.693 1.693 1.693 1 .693 1.693 1.693 1.693 1.693 1.693 1.693 1.693 1 .693 1 .693 1 .693 1.693 1.693 1.693 1.693 1 .693 1 .693 1.693 1.693 1.693 1.693 1 .693 1 .693 1 .693 1.693 1 .693 1 .693 1 .693 1 .693 1 .693 1 .693 1 .693 1 .693 1.693 1 .693 1 .693 1 .693 1 .693 1 .693 1 .693 1 .693 1 .693 1 .693 1 .693 1 .693 1 .693 1 .693 1 .693 1 .693 1 .693 1 .693 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1 .600 118 TABLE B.l (cont'd) 84 3 8.35 9 69.723 25.050 9.241 1 5.63 1 31.697 5.630 5.856 3 12.28 9 150.798 36.840 9.241 6 16.69 36 278.556 100.140 14.320 85 1 6.28 1 39.438 6.280 5.856 3 11.23 9 126.113 33.690 9.241 6 15.23 36 231.953 91.380 14.320 sum 719.5 2117.19 3288.25 24855.1 8561.75 dof 216 216 216 216 Mean 3.331 9.802 15.223 115.070 b 1.693 a 4.163 1.693 1 .693 1 .693 1 .693 1.693 1.693 1.693 14.910 14.910 14.910 14.910 14.910 14.910 14.910 4.163 4.163 4.163 4.163 4.163 4.163 4.163 1.600 1.600 1.600 1.600 1.600 1.600 1.600 TABLE B.2 119 METHOD 8 - POOLED REGRESSION 2 Sample p. ‘h p. q; p.*q1 915—“ tanw 6 a c 297 5.325 2.325 28.356 5.406 12.381 2.738 0.401 23.624 0.604 0.659 3.235 2.235 10.465 4.995 7.230 1.900 0.401 23.624 0.604 0.659 6.095 3.095 37.149 9.579 18.864 3.047 0.401 23.624 0.604 0.659 9.150 3.150 83.723 9.923 28.823 4.271 0.401 23.624 0.604 0.659 224 4.725 3.725 22.326 13.876 17.601 2.498 0.401 23.624 0.604 0.659 8.510 5.510 72.420 30.360 46.890 4.014 0.401 23.624 0.604 0.659 12.415 6.415 154.13 41.152 79.642 5.579 0.401 23.624 0.604 0.659 225 3.065 2.065 9.394 4.264 6.329 1.832 0.401 23.624 0.604 0.659 7.255 4.255 52.635 18.105 30.870 3.511 0.401 23.624 0.604 0.659 227 7.880 6.880 62.094 47.334 54.214 3.762 0.401 23.624 0.604 0.659 10.090 7.090 101.81 50.268 71.538 4.647 0.401 23 .624 0.604 0.659 13.060 7.060 170.56 49.844 92.204 5.838 0.401 23.624 0.604 0.659 165 4.870 3.370 23.717 11.357 16.412 2.556 0.401 23.624 0.604 0.659 8.000 5.000 64.000 25.000 40.000 3.810 0.401 23.624 0.604 0.659 1 1.305 5.305 127.80 28.143 59.973 5.134 0.401 23.624 0.604 0.659 165 4.870 3.370 23.717 11.357 16.412 2.556 0.401 23.624 0.604 0.659 8.000 5.000 64.000 25.000 40.000 3.810 0.401 23.624 0.604 0.659 1 1.305 5.305 127 .80 28.143 59.973 5.134 0.401 23.624 0.604 0.659 192 5.485 3.985 30.085 15.880 21.858 2.802 0.401 23.624 0.604 0.659 8.975 5.975 80.551 35.701 53.626 4.201 0.401 23.624 0.604 0.659 223 5.595 4.095 31.304 16.769 22.912 2.846 0.401 23.624 0.604 0.659 7.630 4.630 58.217 21.437 35.327 3.662 0.401 23.624 0.604 0.659 13.810 7.810 190.72 60.996 107.86 6.138 0.401 23.624 0.604 0.659 226 4.310 2.810 18.576 7.896 12.111 2.331 0.401 23.624 0.604 0.659 6.500 3.500 42.250 12.250 22.750 3.209 0.401 23.624 0.604 0.659 10.765 4.765 115.89 22.705 51.295 4.918 0.401 23.624 0.604 0.659 294 4.095 2.595 16.769 6.734 10.627 2.245 0.401 23.624 0.604 0.659 6.075 3.075 36.906 9.456 18.681 3.039 0.401 23.624 0.604 0.659 10.450 4.450 109.20 19.803 46.503 4.792 0.401 23.624 0.604 0.659 295 2.630 1.130 6.917 1.277 2.972 1.658 0.401 23.624 0.604 0.659 5.495 2.495 30.195 6.225 13.710 2.806 0.401 23.624 0.604 0.659 10.285 4.285 105.78 18.361 44.071 4.726 0.401 23 .624 0.604 0.659 296 4.345 2.845 18.879 8.094 12.362 2.345 0.401 23.624 0.604 0.659 7.860 4.860 61.780 23.620 38.200 3.754 0.401 23.624 0.604 0.659 12.845 6.845 164.99 46.854 87.924 5.752 0.401 23.624 0.604 0.659 193 3.160 2.160 9.986 4.666 6.826 1.870 0.401 23.624 0.604 0.659 5.305 2.305 28.143 5.313 12.228 2.730 0.401 23.624 0.604 0.659 10.165 4.165 103.33 17.347 42.337 4.678 0.401 23.624 0.604 0.659 194 3.050 2.050 9.303 4.203 6.253 1.826 0.401 23.624 0.604 0.659 6.515 3.515 42.445 12.355 22.900 3.215 0.401 23.624 0.604 0.659 10.300 4.300 106.09 18.490 44.290 4.732 0.401 23.624 0.604 0.659 228 2.320 1.320 5.382 1.742 3.062 1.534 0.401 23.624 0.604 0.659 4.515 1.515 20.385 2.295 6.840 2.413 0.401 23.624 0.604 0.659 7.590 1.590 57.608 2.528 12.068 3.646 0.401 23.624 0.604 0.659 229 230 231 195 232 196 197 198 199 88 89 115 116 86 87 2.540 5.295 8.375 2.830 6.345 10.570 3.690 6.825 9.480 3.630 6.030 9.510 2.930 5.740 8.680 2.580 7.955 3.280 12.355 4.740 8.835 14.600 2.605 6.445 9.640 3.050 8.080 5.750 1 1.475 3.090 5.055 7.800 3.795 6.690 1 1.735 2.375 8.025 5.820 9.835 3.165 5.180 8.515 2.935 5.040 8.040 3.895 6.610 1 1.400 1.540 2.295 2.375 1.830 3.345 4.570 2.690 3.825 3.480 2.630 3.030 3.510 1.930 2.740 2.680 1.580 4.955 2.280 6.355 3.740 5.835 8.600 1.605 3.445 3.640 2.050 2.080 2.750 5.475 2.090 2.055 1.800 2.795 3.690 5.735 1.375 2.025 2.820 3.835 2.165 2.180 2.515 1.935 2.040 2.040 2.895 3.610 5.400 6.452 28.037 70.141 8.009 40.259 1 1 1.72 13.616 46.581 89.870 13.177 36.361 90.440 8.585 32.948 75.342 6.656 63.282 10.758 152.65 22.468 78.057 213.16 6.786 41.538 92.930 9.303 65.286 33.063 131.68 9.548 25.553 60.840 14.402 44.756 137.71 5.641 64.401 33.872 96.727 10.017 26.832 72.505 8.614 25.402 64.642 15.171 43.692 129.96 120 TABLE B.2 (cont'd) 2.372 3.912 1.622 5.267 12.152 2.726 5.641 19.891 3.960 3.349 5.179 1.738 11.189 21.224 3.147 20.885 48.305 4.840 7.236 9.926 2.083 14.631 26.106 3.339 12.110 32.990 4.403 6.917 9.547 2.059 9.181 18.271 3.020 12.320 33.380 4.415 3.725 5.655 1.778 7.508 15.728 2.904 7.182 23.262 4.082 2.496 4.076 1.638 24.552 39.417 3.792 5.198 7.478 1.918 40.386 78.516 5.555 13.988 17.728 2.504 34.047 51.552 4.145 73.960 125.56 6.455 2.576 4.181 1.648 1 1.868 22.203 3.187 13.250 35.090 4.467 4.203 6.253 1.826 4.326 16.806 3.842 7.563 15.813 2.908 29.976 62.826 5.203 4.368 6.458 1.842 4.223 10.388 2.630 3.240 14.040 3.730 7.812 10.607 2.125 13.616 24.686 3.285 32.890 67.300 5.307 1.891 3.266 1.556 4.101 16.251 3.820 7.952 16.412 2.936 14.707 37.717 4.545 4.687 6.852 1.872 4.752 1 1.292 2.680 6.325 21.415 4.016 3.744 5.679 1.780 4.162 10.282 2.624 4.162 16.402 3.826 8.381 11.276 2.165 13.032 23.862 3.253 29.160 61.560 5.172 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 23.624 23.624 23.624 23.624 23.624 23 .624 23 .624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23 .624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23 .624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23 .624 23 .624 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 111 141 142 143 144 145 166 167 168 169 170 171 200 201 234 3.075 7.895 4.165 1 1.350 4.075 6.785 10.150 3.300 7.720 1 1.210 3.750 4.995 7.915 3.345 9.630 6.705 8.760 2.465 5.370 9.405 3.875 7.295 1 1.640 2.985 6.460 10.370 2.735 5.745 8.960 2.720 6.005 10.295 3.060 5.335 8.535 2.655 5.715 9.495 2.680 7.515 5.855 9.725 3.355 6.735 10.520 2.940 5.570 8.995 2.075 4.895 3.165 5.350 3.075 3.785 4.150 2.300 4.720 5.210 2.750 3.495 4.915 2.345 3.630 3.705 2.760 1.465 2.370 3.405 2.875 4.295 5.640 1.985 3.460 4.370 1.735 2.745 2.960 1.720 3.005 4.295 2.060 2.355 2.535 1.655 2.715 3.495 1.680 1.515 2.855 3.725 2.355 3.735 4.520 1.940 2.570 2.995 9.456 62.331 17.347 128.82 16.606 46.036 103.02 10.890 59.598 125.66 14.063 24.950 62.647 1 1.189 92.737 44.957 76.738 6.076 28.837 88.454 15.016 53.217 135.49 8.910 41 .732 107.54 7.480 33.005 80.282 7.398 36.060 105.99 9.364 28.462 72.846 7.049 32.661 90.155 7.182 56.475 34.281 94.576 1 1 .256 45.360 1 10.67 8.644 3 1 .025 80.910 4.306 23.961 10.017 28.623 9.456 14.326 17.223 5.290 22.278 27.144 7.563 12.215 24.157 5.499 13.177 13.727 7.618 2.146 5.617 1 1.594 8.266 18.447 31.810 3.940 1 1.972 19.097 3.010 7.535 8.762 2.958 9.030 18.447 4.244 5.546 6.426 2.739 7.371 12.215 2.822 2.295 8.151 13.876 5.546 13.950 20.430 3.764 6.605 8.970 121 6.381 38.646 13.182 60.723 12.531 25.681 42.123 7.590 36.438 58.404 10.313 17.458 38.902 7.844 34.957 24.842 24.178 3.61 1 12.727 32.024 1 1.141 31.332 65.650 5.925 22.352 45.317 4.745 15.770 26.522 4.678 18.045 44.217 6.304 12.564 21.636 4.394 15.516 33.185 4.502 1 1 .385 16.716 36.226 7.901 25.155 47.550 5.704 14.315 26.940 TABLE B.2 (cont'd) 1.836 3.768 2.273 5.152 2.237 3.323 4.672 1.926 3.698 5.096 2.107 2.606 3.776 1.945 4.463 3.291 4.1 15 1.592 2.756 4.373 2.157 3.527 5.269 1.800 3.193 4.760 1.700 2.906 4.195 1.694 3.010 4.730 1.830 2.742 4.024 1.668 2.894 4.409 1.678 3.616 2.950 4.501 1.949 3.303 4.820 1.782 2.836 4.209 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 23.624 23.624 23.624 23.624 23 .624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23 .624 23.624 23.624 23 .624 23 .624 23 .624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 235 236 237 238 258 259 260 66 117 118 172 204 205 206 2.315 4.485 7.1 10 2.120 4.515 7.610 3.255 5.815 8.900 2.955 6.995 12.420 2.770 5.925 9.680 2.825 5.520 10.600 3.095 5.545 9.630 4.606 10.855 8.195 12.180 3.400 5.280 9.030 2.510 5.130 8.265 4.285 2.475 4.430 8.470 1.975 4.320 7.820 3.670 5.865 9.510 2.175 5.135 3.910 8.280 3.760 7.920 15.000 1.315 1.485 1.110 1.120 1.515 1.610 2.255 2.815 2.900 1.955 3.995 6.420 1.770 2.925 3.680 1.825 2.520 4.600 2.095 2.545 3.630 3.605 4.855 5.195 6.180 2.400 2.280 3.030 1.510 2.130 2.265 1.285 1.475 1.430 2.470 0.975 1.320 1.820 2.670 2.865 3.510 1.175 2.135 2.910 2.280 2.760 4.920 9.000 5.359 20.115 50.552 4.494 20.385 57.912 10.595 33.814 79.210 8.732 48.930 154.26 7.673 35.106 93.702 7.981 30.470 1 12.36 9.579 30.747 92.737 21.215 1 17.83 67.158 148.35 1 1.560 27.878 81.541 6.300 26.317 68.310 18.361 6.126 19.625 71.741 3.901 18.662 61.152 13.469 34.398 90.440 4.731 26.368 15.288 68.558 14.138 62.726 225.00 122 TABLE B.2 (cont'd) 1.729 3.044 1.532 2.205 6.660 2.401 1.232 7.892 3.453 1 .254 2.374 1.454 2.295 6.840 2.413 2.592 12.252 3.654 5.085 7.340 1.908 7.924 16.369 2.934 8.410 25.810 4.171 3.822 5.777 1.788 15 .960 27.945 3 .407 41.216 79.736 5.581 3.133 4.903 1.714 8.556 17.331 2.978 13.542 35.622 4.483 3.331 5.156 1.736 6.350 13.910 2.816 21.160 48.760 4.852 4.389 6.484 1.844 6.477 14.1 12 2.826 13.177 34.957 4.463 12.996 16.605 2.450 23.571 52.701 4.954 26.988 42.573 3.888 38.192 75.272 5.485 5.760 8.160 1.967 5.198 12.038 2.720 9.181 27.361 4.223 2.280 3.790 1.610 4.537 10.927 2.660 5.130 18.720 3.916 1.651 5.506 2.321 2.176 3.651 1.596 2.045 6.335 2.379 6.101 20.921 3.998 0.951 1.926 1.396 1.742 5.702 2.335 3.312 14.232 3.738 7.129 9.799 2.075 8.208 16.803 2.954 12.320 33.380 4.415 1.381 2.556 1.476 4.558 10.963 2.662 8.468 11.378 2.171 5.198 18.878 3.922 7.618 10.378 2.111 24.206 38.966 3.778 81.000 135.00 6.615 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23 .624 23.624 23.624 23 .624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23 .624 23.624 23.624 23.624 23.624 23.624 23.624 23 .624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 sum dof Mean b a 119 173 202 203 207 239 233 84 85 2.405 5.085 8.900 3.520 6.695 10.835 3.195 5.470 8.560 2.195 4.180 7.220 3.660 7.220 1 1.240 3.965 7.205 10.640 3.370 6.670 12.305 5.675 3.315 7.640 1 1.345 3.640 7.1 15 10.615 1418.3 216 6.566 0.401 0.604 1 .405 2.085 2.900 2.520 3.695 4.835 2.195 2.470 2.560 1 .195 1.180 1 .220 2.660 4.220 5.240 2.965 4.205 4.640 2.370 3.670 6.305 2.675 2.3 l 5 4.640 5.345 2.640 4.1 15 4.615 698.9 216 3.235 5.784 25.857 79.210 12.390 44.823 1 17.40 10.208 29.921 73.274 4.818 17.472 52.128 13.396 52.128 126.34 15.721 51.912 1 13.21 1 1.357 44.489 151.41 32.206 10.989 58.370 128.71 13.250 50.623 1 12.68 1 1317 216 52.392 123 TABLE B.2 (cont'd) 1.974 3.379 1.568 4.347 10.602 2.642 8.410 25.810 4.171 6.350 8.870 2.015 13.653 24.738 3.287 23.377 52.387 4.946 4.818 7.013 1.884 6.101 13.511 2.796 6.554 21.914 4.034 1 .428 2.623 1 .484 1 .392 4.932 2.279 1.488 8.808 3.497 7.076 9.736 2.071 17.808 30.468 3.497 27.458 58.898 5.108 8.791 11.756 2.193 17.682 30.297 3 .491 21.530 49.370 4.868 5.617 7.987 1.955 1 3 .469 24.479 3 .277 39.753 77.583 5.535 7.156 15.181 2.878 5.359 7.674 1.932 21.530 35.450 3.666 28.569 60.639 5.150 6.970 9.610 2.063 16.933 29.278 3.455 21.298 48.988 4.858 2755.0 5391.7 216 12.755 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 23.624 23.624 23.624 23 .624 23.624 23 .624 23.624 23.624 23 .624 23 .624 23 .624 23.624 23 .624 23.624 23 .624 23 .624 23.624 23.624 23 .624 23.624 23.624 23 .624 23.624 23.624 23 .624 23.624 23 .624 23.624 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 124 TABLE B.3 METHOD 8 - ROTATION OF AXES Sample 1): <1; r (1 «1.; 11r q; 297 5.325 2.325 5.810 23.587 68.587 2.121 5.409 3.235 2.235 3.932 34.640 79.640 0.707 3.868 6.095 3.095 6.836 26.921 71.921 2.121 6.498 9.15 3.15 9.677 18.997 63.997 4.243 8.697 224 4.725 3.725 6.017 38.251 83.251 0.707 5.975 8.51 5.51 10.138 32.922 77.922 2.121 9.914 12.415 6.415 13.974 27.326 72.326 4.243 13.315 225 3.065 2.065 3.696 33.970 78.970 0.707 3.627 7.255 4.255 8.411 30.391 75.391 2.121 8.139 227 7.88 6.88 10.461 41.124 86.124 0.707 10.437 10.09 7.09 12.332 35.095 80.095 2.121 12.148 13.06 7.06 14.846 28.395 73.395 4.243 14.227 165 4.87 3.37 5.922 34.683 79.683 1.061 5.827 8 5 9.434 32.005 77.005 2.121 9.192 1 1.305 5.305 12.488 25.139 70.139 4.243 1 1.745 165 4.87 3.37 5.922 34.683 79.683 1.061 5.827 8 5 9.434 32.005 77.005 2.121 9.192 11.305 5.305 12.488 25.139 70.139 4.243 11.745 192 5.485 3.985 6.780 35.999 80.999 1.061 6.696 8.975 5.975 10.782 33.653 78.653 2.121 10.571 223 5.595 4.095 6.933 36.201 81.201 1.061 6.852 7.63 4.63 8.925 31.250 76.250 2.121 8.669 13.81 7.81 15.865 29.490 74.490 4.243 15.288 226 4.31 2.81 5.145 33.103 78.103 1.061 5.035 6.5 3.5 7.382 28.301 73.301 2.121 7.071 10.765 4.765 11.772 23.876 68.876 4.243 10.981 294 4.095 2.595 4.848 32.362 77.362 1.061 4.731 6.075 3.075 6.809 26.847 71.847 2.121 6.470 10.45 4.45 1 1.358 23.066 68.066 4.243 10.536 295 2.63 1.13 2.862 23.251 68.251 1.061 2.659 5.495 2.495 6.035 24.420 69.420 2.121 5.650 10.285 4.285 11.142 22.618 67.618 4.243 10.303 296 4.345 2.845 5.194 33.216 78.216 1.061 5.084 7.86 4.86 9.241 31.729 76.729 2.121 8.994 12.845 6.845 14.555 28.053 73.053 4.243 13.923 193 3.16 2.16 3.828 34.354 79.354 0.707 3.762 5.305 2.305 5.784 23.485 68.485 2.121 5.381 10.165 4.165 10.985 22.281 67.281 4.243 10.133 194 3.05 2.05 3.675 33.906 78.906 0.707 3.606 6.515 3.515 7.403 28.348 73.348 2.121 7.092 10.3 4.3 11.162 22.659 67.659 4.243 10.324 228 2.32 1.32 2.669 29.638 74.638 0.707 2.574 4.515 1.515 4.762 18.549 63.549 2.121 4.264 7.59 1.59 7.755 11.832 56.832 4.243 6.491 229 230 231 195 232 196 197 198 199 88 89 115 116 86 87 2.54 5.295 8.375 2.83 6.345 10.57 3.69 6.825 9.48 3.63 6.03 9.51 2.93 5.74 8.68 2.58 7.955 3.28 12.355 4.74 8.835 14.6 2.605 6.445 9.64 3.05 8.08 5.75 1 1.475 3.09 5 .055 7.8 3.795 6.69 1 1.735 2.375 8.025 5.82 9.835 3.165 5.18 8.515 2.935 5.04 8.04 3.895 6.61 1 1 .4 TABLE 83 (cont'd) 1.54 2.970 31.228 2.295 5.771 23.433 2.375 8.705 15.832 1.83 3.370 32.888 3.345 7.173 27.798 4.57 11.516 23.382 2.69 4.566 36.092 3.825 7.824 29.268 3.48 10.099 20.158 2.63 4.483 35.924 3.03 6.748 26.679 3.51 10.137 20.258 1.93 3.509 33.373 2.74 6.360 25.518 2.68 9.084 17.158 1.58 3.025 31.483 4.955 9.372 31.918 2.28 3.995 34.804 6.355 13.894 27.220 3.74 6.038 38.274 5.835 10.588 33.442 8.6 16.945 30.500 1.605 3.060 31 .638 3.445 7.308 28.126 3.64 10.304 20.686 2.05 3.675 33.906 2.08 8.343 14.436 2.75 6.374 25.560 5.475 12.714 25.507 2.09 3.730 34.073 2.055 5.457 22.123 1.8 8.005 12.995 2.795 4.713 36.371 3.69 7.640 28.880 5.735 13.061 26.045 1.375 2.744 30.069 2.025 8.277 14.162 2.82 6.467 25.852 3.835 10.556 21.302 2.165 3.835 34.374 2.18 5.620 22.824 2.515 8.879 16.455 1.935 3.515 33.396 2.04 5.437 22.036 2.04 8.295 14.237 2.895 4.853 36.622 3.61 7.532 28.641 5.4 12.614 25.346 125 76.228 68.433 60.832 77.888 72.798 68.382 81.092 74.268 65.158 80.924 71.679 65.258 78.373 70.518 62.158 76.483 76.918 79.804 72.220 83.274 78.442 75.500 76.638 73.126 65.686 78.906 59.436 70.560 70.507 79.073 67.123 57.995 81.371 73.880 71 .045 75.069 59.162 70.852 66.302 79.374 67.824 61.455 78.396 67.036 59.237 81.622 73.641 70.346 0.707 2.121 4.243 0.707 2.121 4.243 0.707 2.121 4.243 0.707 2.121 4.243 0.707 2.121 4.243 0.707 2.121 0.707 4.243 0.707 2.121 4.243 0.707 2.121 4.243 0.707 4.243 2.121 4.243 0.707 2.121 4.243 0.707 2.121 4.243 0.707 4.243 2.121 4.243 0.707 2.121 4.243 0.707 2.121 4.243 0.707 2.121 4.243 2.885 5.367 7.601 3.295 6.852 10.706 4.51 1 7.531 9.164 4.426 6.406 9.207 3.437 5.996 8.033 2.942 9.129 3.932 13.230 5.996 10.373 16.405 2.977 6.993 9.390 3.606 7.184 6.010 1 1.985 3.663 5.028 6.788 4.660 7.340 12.353 2.652 7.106 6.109 9.666 3.769 5.204 7.799 3.444 5.006 7.128 4.801 7.227 1 1.879 111 141 142 143 144 145 166 167 168 169 170 171 200 201 234 3.075 7.895 4.165 11.35 4.075 6.785 10.15 3.3 7.72 1 1.21 3.75 4.995 7.915 3.345 9.63 6.705 8.76 2.465 5.37 9.405 3.875 7.295 11.64 2.985 6.46 10.37 2.735 5.745 8.96 2.72 6.005 10.295 3.06 5.335 8.535 2.655 5.715 9.495 2.68 7.515 5.855 9.725 3.355 6.735 10.52 2.94 5.57 8.995 2.075 4.895 3.165 5.35 3.075 3.785 4.15 2.3 4.72 5.21 2.75 3.495 4.915 2.345 3.63 3.705 2.76 1.465 2.37 3.405 2.875 4.295 5.64 1.985 3.46 4.37 1.735 2.745 2.96 1.72 3.005 4.295 2.06 2.355 2.535 1.655 2.715 3.495 1.68 1.515 2.855 3.725 2.355 3.735 4.52 1.94 2.57 2.995 126 TABLE B.3 (cont'd) 3.710 34.01 1 9.289 31.799 5.231 37.231 12.548 25.238 5.105 37.038 7.769 29.155 10.966 22.238 4.022 34.875 9.049 31.442 12.362 24.927 4.650 36.254 6.096 34.980 9.317 31.839 4.085 35.032 10.291 20.654 7.661 28.924 9.185 17.488 2.867 30.724 5.870 23.814 10.002 19.902 4.825 36.573 8.465 30.488 12.934 25.852 3.585 33.624 7.328 28.174 1 1.253 22.851 3.239 32.390 6.367 25.539 9.436 18.281 3.218 32.307 6.715 26.584 1 1.155 22.646 3.689 33.949 5.832 23.818 8.904 16.542 3.129 31.937 6.327 25.411 10.118 20.208 3.163 32.082 7.666 1 1.398 6.514 25.995 10.414 20.959 4.099 35.066 7.701 29.011 1 1.450 23 .251 3.522 33.419 6.134 24.769 9.481 18.416 79.01 1 76.799 82.231 70.238 82.038 74.155 67.238 79.875 76.442 69.927 81.254 79.980 76.839 80.032 65.654 73.924 62.488 75.724 68.814 64.902 81.573 75.488 70.852 78.624 73.174 67.851 77.390 70.539 63.281 77.307 71.584 67.646 78.949 68.818 61.542 76.937 70.41 1 65.208 77.082 56.398 70.995 65.959 80.066 74.01 1 68.251 78.419 69.769 63.416 0.707 2.121 0.707 4.243 0.707 2.121 4.243 0.707 2.121 4.243 0.707 1.061 2.121 0.707 4.243 2.121 4.243 0.707 2.121 4.243 0.707 2.121 4.243 0.707 2.121 4.243 0.707 2.121 4.243 0.707 2.121 4.243 0.707 2.107 4.243 0.707 2.121 4.243 0.707 4.243 2.121 4.243 0.707 2.121 4.243 0.707 2.121 4.243 3.642 9.044 5.183 1 1.809 5.056 7.474 10.1 12 3.960 8.796 1 1.61 1 4.596 6.003 9.072 4.023 9.376 7.361 8.146 2.779 5.473 9.058 4.773 8.195 12.219 3.514 7.014 10.423 3.161 6.003 8.429 3.140 6.371 10.317 3.620 5.438 7.828 3.048 5.961 9.185 3.083 6.385 6.159 9.51 1 4.038 7.403 10.635 3.451 5.756 8.478 235 236 237 238 258 259 260 66 90 117 118 172 204 205 206 2.315 4.485 7.1 1 2.12 4.515 7.61 3.255 5.815 8.9 2.955 6.995 12.42 2.77 5.925 9.68 2.825 5.52 10.6 3.095 5.545 9.63 4.606 10.855 8.195 12.18 3.4 5.28 9.03 2.51 5.13 8.265 4.285 2.475 4.43 8.47 1.975 4.32 7.82 3.67 5.865 9.51 2.175 5.135 3.91 8.28 3.76 7.92 15 1.315 1.485 1.1 1 1.12 1.515 1.61 2.255 2.815 2.9 1.955 3.995 6.42 1.77 2.925 3.68 1.825 2.52 4.6 2.095 2.545 3.63 3.605 4.855 5.195 6.18 2.4 2.28 3.03 1.51 2.13 2.265 1.285 1.475 1.43 2.47 0.975 1.32 1.82 2.67 2.865 3.51 1.175 2.135 2.91 2.28 2.76 4.92 9 TABLE B.3 (cont'd) 2.662 29.598 4.724 18.320 7.196 8.873 2.398 27.848 4.762 18.549 7.778 1 1.946 3.960 34.713 6.461 25.831 9.361 18.048 3.543 33.488 8.055 29.732 13.981 27.335 3.287 32.578 6.608 26.274 10.356 20.815 3.363 32.863 6.068 24.538 1 1.555 23.459 3.737 34.094 6.101 24.654 10.291 20.654 5.849 38.049 1 1.891 24.097 9.703 32.372 13.658 26.903 4.162 35.218 5.751 23.356 9.525 18.549 2.929 31.031 5.555 22.548 8.570 15.325 4.474 16.693 2.881 30.793 4.655 17.890 8.823 16.258 2.203 26.274 4.517 16.991 8.029 13.102 4.538 36.037 6.527 26.035 10.137 20.258 2.472 28.379 5.561 22.576 4.874 36.658 8.588 15.396 4.664 36.280 9.324 31.849 17.493 30.964 127 74.598 63.320 53.873 72.848 63.549 56.946 79.713 70.831 63.048 78.488 74.732 72.335 77.578 71.274 65.815 77.863 69.538 68.459 79.094 69.654 65.654 83.049 69.097 77.372 71.903 80.218 68.356 63.549 76.031 67.548 60.325 61.693 75.793 62.890 61.258 71.274 61.991 58.102 81.037 71.035 65.258 73.379 67.576 81.658 60.396 81.280 76.849 75.964 0.707 2.121 4.243 0.707 2.121 4.243 0.707 2.121 4.243 0.707 2.121 4.243 0.707 2.121 4.243 0.707 2.121 4.243 0.707 2.121 4.243 0.708 4.243 2.121 4.243 0.707 2.121 4.243 0.707 2.121 4.243 2.121 0.707 2.121 4.243 0.707 2.121 4.243 0.707 2.121 4.243 0.707 2.121 0.707 4.243 0.707 2.121 4.243 2.567 4.221 5.812 2.291 4.264 6.520 3.896 6.102 8.344 3.472 7.771 13.322 3.210 6.258 9.447 3.288 5.685 10.748 3.670 5.720 9.376 5.806 1 1.109 9.468 12.982 4.101 5.346 8.528 2.843 5.134 7.446 3.939 2.793 4.144 7.736 2.086 3.988 6.817 4.483 6.173 9.207 2.369 5.141 4.822 7.467 4.610 9.079 16.971 119 173 202 203 207 239 233 84 85 2.405 5.085 8.9 3.52 6.695 10.835 3.195 5.47 8.56 2.195 4.18 7.22 3.66 7.22 11.24 3.965 7.205 10.64 3.37 6.67 12.305 5.675 3.315 7.64 1 1.345 3.64 7.1 15 10.615 1.405 2.085 2.9 2.52 3.695 4.835 2.195 2.47 2.56 1.195 1.18 1.22 2.66 4.22 5.24 2.965 4.205 4.64 2.37 3.67 6.305 2.675 2.315 4.64 5.345 2.64 4.1 15 4.615 128 TABLE B.3 (cont'd) 2.785 30.293 5.496 22.295 9.361 18.048 4.329 35 .599 7.647 28.894 1 1.865 24.048 3.876 34.489 6.002 24.302 8.935 16.650 2.499 28.565 4.343 15.764 7.322 9.591 4.525 36.009 8.363 30.306 12.401 24.995 4.95 1 36.789 8.342 30.269 1 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000.0 .0..0 A.5—.30 0... 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.0 . .0 505.0 000.0 .0 . .0 505.0 000.0 . 0. .0 505.0 000.0 505.0 .0..0 505.0 00 000 000 500 000 000 05. 0.. 000 000 136 000. . 000. . 000. . 000.. 000.. 000.. 000.0 000.0 000.0 0.0.0. 0.0.0. 0.0.0. 500.0 500.0 500.0 000.0. 000.0. 000.0. 000.00 000. . 00. .0. 000.00 000. . 0 0 0 .0 000.00 000. . .0..0 8.2.80 ...: 0.55. 0.0000 000.00 000.0. 00.0 000.50 0.0 0.5000. 0500.. 000.00 0.5.0. ..0.5 0.0 50.000. 000.0. 000.0 000.0 .000 0.0 00.500. 005.0. .00.5 .000 000.0 000.. 000.0 0.0 05.000 000.0 .0..0 505.0 :82 .8 830 00 137 TABLE 3.5 METHOD 10 - FIRST REGRESSION Sample pi 4 pi: (h: £01 ‘32: now Q a c a t 297 5.325 2.325 28.356 540612.381 2.738 040123.624 0.604 0.659 4.393 2.130 3.235 2.235 10.465 4.995 7.230 1.900 0.401 23.624 0.604 0.659 2.339 2.048 6.095 3.095 37.149 9.579 18.864 3.047 0.401 23.624 0.604 0.659 4.855 2.836 9.150 3.150 83.723 9.923 28.823 4.271 0.401 23.624 0.604 0.659 7.888 2.886 224 4.725 3.725 22.326 13.876 17.601 2.498 0.401 23.624 0.604 0.659 3.232 3.413 8.510 5.510 72.420 30.360 46.890 4.014 0.401 23.624 0.604 0.659 6.302 5.048 12.415 6.415 154.13 41.152 79.642 5.579 0.401 23.624 0.604 0.659 9.844 5.877 225 3.065 2.065 9.394 4.264 6.329 1.832 0.401 23.624 0.604 0.659 2.237 1.892 7.255 4.255 52.635 18.105 30.870 3.511 0.401 23.624 0.604 0.659 5.550 3.898 227 7.880 6.880 62.094 47.334 54.214 3.762 0.401 23.624 0.604 0.659 5.123 6.303 10.090 7.090 101.81 50.268 71.538 4.647 0.401 23.624 0.604 0.659 7.249 6.496 13.060 7.060 170.56 49.844 92.204 5.838 0.401 23.624 0.604 0.659 10.231 6.468 165 4.870 3.370 23.717 11.357 16.412 2.556 0.401 23.624 0.604 0.659 3.520 3.088 8.000 5.000 64.000 25.000 40.000 3.810 0.401 23.624 0.604 0.659 5.996 4.581 11.305 5.305 127.80 28.143 59.973 5.134 0.401 23.624 0.604 0.659 9.179 4.860 165 4.870 3.370 23.717 11.357 16.412 2.556 0.401 23.624 0.604 0.659 3.520 3.088 8.000 5.000 64.000 25.000 40.000 3.810 0.401 23.624 0.604 0.659 5.996 4.581 11.305 5 .305 127.80 28.143 59.973 5.134 0.401 23.624 0.604 0.659 9.179 4.860 192 5.485 3.985 30.085 15.880 21.858 2.802 0.401 23.624 0.604 0.659 3.888 3.651 8.975 5.975 80.551 35.701 53.626 4.201 0.401 23.624 0.604 0.659 6.581 5.474 223 5.595 4.095 31.304 16.769 22.912 2.846 0.401 23.624 0.604 0.659 3.954 3.752 7.630 4.630 58.217 21.437 35.327 3.662 0.401 23.624 0.604 0.659 5.775 4.242 13.810 7.810 190.72 60.996 107.86 6.138 0.401 23.624 0.604 0.659 10.680 7.155 226 4.310 2.810 18.576 7.896 12.111 2.331 0.401 23.624 0.604 0.659 3.184 2.575 6.500 3.500 42.250 12.250 22.750 3.209 0.401 23.624 0.604 0.659 5.097 3.207 10.765 4.765 115.89 22.705 51 .295 4.918 0.401 23.624 0.604 0.659 8.855 4.366 294 4.095 2.595 16.769 6.734 10.627 2.245 0.401 23.624 0.604 0.659 3.055 2.378 6.075 3.075 36.906 9.456 18.681 3.039 0.401 23.624 0.604 0.659 4.843 2.817 10.450 4.450 109.20 19.803 46.503 4.792 0.401 23.624 0.604 0.659 8.667 4.077 295 2.630 1.130 6.917 1.277 2.972 1.658 0.401 23.624 0.604 0.659 2.177 1.035 5.495 2.495 30.195 6.225 13.710 2.806 0.401 23.624 0.604 0.659 4.495 2.286 10.285 4.285 105.78 18.361 44.071 4.726 0.401 23.624 0.604 0.659 8.568 3.926 296 4.345 2.845 18.879 8.094 12.362 2.345 0.401 23.624 0.604 0.659 3.205 2.607 7.860 4.860 61 .780 23.620 38.200 3.754 0.401 23.624 0.604 0.659 5.912 4.453 12.845 6.845 164.99 46.854 87.924 5.752 0.401 23.624 0.604 0.659 10.102 6.271 193 3.160 2.160 9.986 4.666 6.826 1.870 0.401 23.624 0.604 0.659 2.294 1.979 5.305 2.305 28.143 5.313 12.228 2.730 0.401 23.624 0.604 0.659 4.381 2.112 10.165 4.165 103.33 17.347 42.337 4.678 0.401 23.624 0.604 0.659 8.496 3.816 194 3.050 2.050 9.303 4.203 6.253 1.826 0.401 23.624 0.604 0.659 2.228 1.878 6.515 3.515 42.445 12.355 22.900 3.215 0.401 23.624 0.604 0.659 5.106 3.220 10.300 4.300 106.09 18.490 44.290 4.732 0.401 23.624 0.604 0.659 8.577 3.940 228 2.320 1.320 5.382 1.742 3.062 1.534 0.401 23.624 0.604 0.659 1.791 1.209 4.515 1.515 20.385 2.295 6.840 2.413 0.401 23.624 0.604 0.659 3.908 1.388 7.590 1.590 57.608 2.528 12.068 3.646 0.401 23.624 0.604 0.659 6.953 1.457 229 2.540 1.540 6.452 2.372 3.912 1.622 0.401 23.624 0.604 0.659 1.923 1.411 5.295 2.295 28.037 5.267 12.152 2.726 0.401 23.624 0.604 0.659 4.375 2.103 8.375 2.375 70.141 5.641 19.891 3.960 0.401 23.624 0.604 0.659 7.423 2.176 230 2.830 1.830 8.009 3.349 5.179 1.738 0.401 23.624 0.604 0.659 2.097 1.677 6.345 3.345 40.259 1 1.189 21.224 3.147 0.401 23.624 0.604 0.659 5.005 3.065 10.570 4.570 11 1.72 20.885 48.305 4.840 0.401 23.624 0.604 0.659 8.739 4.187 231 3.690 2.690 13.616 7.236 9.926 2.083 0.401 23.624 0.604 0.659 2.612 2.465 6.825 3.825 46.581 14.631 26.106 3.339 0.401 23.624 0.604 0.659 5.292 3.504 9.480 3.480 89.870 12.1 10 32.990 4.403 0.401 23.624 0.604 0.659 8.085 3.188 195 232 196 197 198 199 88 89 115 116 86 87 111 141 142 143 144 145 3.630 6.030 9.510 2.930 5.740 8.680 2.580 7.955 3.280 12.355 4.740 8.835 14.600 2.605 6.445 9.640 3.050 8.080 5.750 11.475 3.090 5.055 7.800 3.795 6.690 11.735 2.375 8.025 5.820 9.835 3.165 5.180 8.515 2.935 5.040 8.040 3.895 6.610 1 1.400 3.075 7.895 4.165 11.350 4.075 6.785 10.150 3.300 7.720 1 1.210 3.750 4.995 7.915 3.345 9.630 6.705 8.760 2.465 5.370 9.405 2.630 3.030 3.510 1.930 2.740 2.680 1.580 4.955 2.280 6.355 3.740 5.835 8.600 1.605 3.445 3.640 2.050 2.080 2.750 5.475 2.090 2.055 1.800 2.795 3.690 5.735 1.375 2.025 2.820 3.835 2.165 2.180 2.515 1.935 2.040 2.040 2.895 3.610 5.400 2.075 4.895 3.165 5.350 3.075 3.785 4.150 2.300 4.720 5.210 2.750 3.495 4.915 2.345 3.630 3.705 2.760 1.465 2.370 3.405 13.177 36.361 90.440 8.585 32.948 75.342 6.656 63.282 10.758 152.65 22.468 78.057 213.16 6.786 41.538 92.930 9.303 65.286 33.063 131.68 9.548 25.553 60.840 14.402 44.756 137.71 5.641 64.401 33.872 96.727 10.017 26.832 72.505 8.614 25.402 64.642 15.171 43.692 129.96 9.456 62.331 17.347 128.82 16.606 46.036 103.02 10.890 59.598 125.66 14.063 24.950 62.647 1 1 . 189 92.737 44.957 76.738 6.076 28.837 88.454 6.917 9.181 12.320 3.725 7.508 7.182 2.496 24.552 5.198 40.386 13.988 34.047 73.960 2.576 11.868 13.250 4.203 4.326 7.563 29.976 4.368 4.223 3.240 7.812 13.616 32.890 1.891 4.101 7.952 14.707 4.687 4.752 6.325 3.744 4.162 4.162 8.381 13.032 29. 160 4.306 23.961 10.017 28.623 9.456 14.326 17.223 5.290 22.278 27.144 7.563 12.215 24.157 5.499 13.177 13.727 7.618 2.146 5.617 1 1.594 138 TABLE 3.5 (cont'd) 9.547 18.271 33.380 5.655 15.728 23.262 4.076 39.417 7.478 78.516 17.728 51.552 125.56 4.181 22.203 35.090 6.253 16.806 15.813 62.826 6.458 10.388 14.040 10.607 24.686 67.300 3.266 16.251 16.412 37.717 6.852 1 1.292 21.415 5.679 10.282 16.402 1 1.276 23.862 61.560 6.381 38.646 13.182 60.723 12.531 25.681 42.123 7.590 36.438 58.404 10.313 17.458 38.902 7.844 34.957 24.842 24.178 3.61 1 12.727 32.024 2.059 3.020 4.415 1.778 2.904 4.082 1.638 3.792 1.918 5.555 2.504 4.145 6.455 1.648 3.187 4.467 1.826 3.842 2.908 5.203 1.842 2.630 3.730 2.125 3.285 5.307 1.556 3.820 2.936 4.545 1.872 2.680 4.016 1.780 2.624 3.826 2.165 3.253 5.172 1.836 3.768 2.273 5.152 2.237 3.323 4.672 1.926 3.698 5.096 2.107 2.606 3.776 1.945 4.463 3.291 4.1 15 1.592 2.756 4.373 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23 .624 23.624 23.624 23.624 23.624 23.624 23 .624 23 .624 23.624 23.624 23 .624 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 2.576 4.816 8.103 2.157 4.642 7.606 1.947 5.969 2.366 9.808 3.241 6.497 1 1.154 1.962 5.064 8.181 2.228 7.246 4.648 9.281 2.252 4.231 7.079 2.675 5.21 1 9.437 1.824 7.214 4.690 8.298 2.297 4.306 7.507 2.160 4.222 7.222 2.735 5.163 9.236 2.243 5.933 2.897 9.206 2.843 5.268 8.487 2.378 5.829 9.122 2.648 3.594 5.945 2.405 8.175 5.220 7.654 1.878 4.420 8.040 2.410 2.776 3.216 1.768 2.510 2.455 1.448 4.540 2.089 5.822 3.427 5.346 7.879 1.470 3.156 3.335 1.878 1.906 2.520 5.016 1.915 1.883 1.649 2.561 3.381 5.254 1.260 1.855 2.584 3.514 1.984 1.997 2.304 1.773 1.869 1.869 2.652 3.307 4.947 1.901 4.485 2.900 4.902 2.817 3.468 3.802 2.107 4.324 4.773 2.520 3.202 4.503 2.148 3.326 3.394 2.529 1.342 2. l 71 3. 120 166 167 168 169 170 171 200 201 234 235 236 237 238 258 259 260 66 90 117 3.875 7.295 11.640 2.985 6.460 10.370 2.735 5.745 8.960 2.720 6.005 10.295 3.060 5.335 8.535 2.655 5.715 9.495 2.680 7.515 5.855 9.725 3.355 6.735 10.520 2.940 5.570 8.995 2.315 4.485 7.1 10 2.120 4.515 7.610 3.255 5.815 8.900 2.955 6.995 12.420 2.770 5.925 9.680 2.825 5.520 10.600 3.095 5.545 9.630 4.606 10.855 8.195 12. 180 3.400 5.280 9.030 2.510 5.130 8.265 2.875 4.295 5.640 1.985 3.460 4.370 1.735 2.745 2.960 1.720 3.005 4.295 2.060 2.355 2.535 1.655 2.715 3.495 1.680 1.515 2.855 3.725 2.355 3.735 4.520 1.940 2.570 2.995 1.315 1.485 1.1 10 1.120 1.515 1.610 2.255 2.815 2.900 1.955 3.995 6.420 1.770 2.925 3.680 1.825 2.520 4.600 2.095 2.545 3.630 3.605 4.855 5.195 6.180 2.400 2.280 3.030 1.510 2.130 2.265 15.016 53.217 135.49 8.910 41.732 107.54 7.480 33.005 80.282 7.398 36.060 105.99 9.364 28.462 72.846 7.049 32.661 90.155 7.182 56.475 34.281 94.576 11.256 45.360 110.67 8.644 31 .025 80.910 5.359 20.1 15 50.552 4.494 20.385 57.912 10.595 33.814 79.210 8.732 48.930 154.26 7.673 35.106 93.702 7.981 30.470 1 12.36 9.579 30.747 92.737 21.215 1 17.83 67.158 148.35 1 1.560 27.878 81 .541 6.300 26.317 68.310 8.266 18.447 31 .810 3.940 11.972 19.097 3.010 7.535 8.762 2.958 9.030 18.447 4.244 5.546 6.426 2.739 7.371 12.215 2.822 2.295 8.151 13.876 5.546 13.950 20.430 3.764 6.605 8.970 1.729 2.205 1.232 1.254 2.295 2.592 5.085 7.924 8.410 3.822 15.960 41.216 3.133 8.556 13.542 3.331 6.350 21.160 4.389 6.477 13.177 12.996 23.571 26.988 38.192 5.760 5.198 9.181 2.280 4.537 5.130 139 TABLE 3.5 (cont'd) 11.141 31.332 65.650 5.925 22.352 45.317 4.745 15.770 26.522 4.678 18.045 44.217 6.304 12.564 21.636 4.394 15.516 33.185 4.502 11.385 16.716 36.226 7.901 25.155 47.550 5.704 14.315 26.940 3.044 6.660 7.892 2.374 6.840 12.252 7.340 16.369 25.810 5.777 27.945 79.736 4.903 17.331 35.622 5.156 13.910 48.760 6.484 14.1 12 34.957 16.605 52.701 42.573 75.272 8.160 12.038 27.361 3.790 10.927 18.720 2.157 3.527 5.269 1.800 3.193 4.760 1.700 2.906 4.195 1.694 3.010 4.730 1.830 2.742 4.024 1.668 2.894 4.409 1.678 3.616 2.950 4.501 1.949 3.303 4.820 1.782 2.836 4.209 1.532 2.401 3.453 1.454 2.413 3.654 1.908 2.934 4.171 1.788 3.407 5.581 1.714 2.978 4.483 1.736 2.816 4.852 1.844 2.826 4.463 2.450 4.954 3.888 5.485 1.967 2.720 4.223 1.610 2.660 3.916 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 23.624 23.624 23.624 23.624 23.624 23 .624 23.624 23.624 23.624 23.624 23.624 23.624 23 .624 23 .624 23.624 23.624 23 .624 23 .624 23.624 23 .624 23.624 23.624 23.624 23.624 23.624 23 .624 23 .624 23 .624 23 .624 23.624 23 .624 23 .624 23.624 23 .624 23.624 23 .624 23 .624 23 .624 23 .624 23 .624 23 .624 23 .624 23 .624 23.624 23.624 23.624 23 .624 23 .624 23 .624 23 .624 23 .624 23 .624 23 .624 23 .624 23 .624 23 .624 23 .624 23 .624 23 .624 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 2.723 5.574 9.380 2.190 5.073 8.619 2.040 4.645 7.774 2.031 4.801 8.574 2.234 4.391 7.519 1.992 4.627 8.094 2.007 6.908 4.711 8.232 2.411 5.238 8.709 2.163 4.540 7.795 1.788 3.890 6.665 1.671 3.908 6.965 2.351 4.687 7.738 2.172 5.394 9.847 2.061 4.753 8.205 2.094 4.510 8.757 2.255 4.525 8.175 3.161 8.909 6.1 13 9.703 2.438 4.366 7.816 1.905 4.276 7.357 2.634 3.935 5.167 1.819 3.170 4.004 1.590 2.515 2.712 1.576 2.753 3.935 1.887 2.158 2.323 1.516 2.487 3.202 1.539 1.388 2.616 3.413 2.158 3.422 4.141 1.777 2.355 2.744 1.205 1.361 1.017 1.026 1.388 1.475 2.066 2.579 2.657 1.791 3.660 5.882 1.622 2.680 3.372 1.672 2.309 4.214 1.919 2.332 3.326 3.303 4.448 4.760 5.662 2.199 2.089 2.776 1.383 1.951 2.075 sum dof Mean 1) a 118 172 204 205 206 119 173 202 203 207 239 233 85 4.285 2.475 4.430 8.470 1.975 4.320 7.820 3.670 5.865 9.510 2.175 5.135 3.910 8.280 3.760 7.920 15.000 2.405 5.085 8.900 3.520 6.695 10.835 3.195 5.470 8.560 2.195 4.180 7.220 3.660 7.220 11.240 3.965 7.205 10.640 3.370 6.670 12.305 5.675 3.315 7.640 1 1.345 3.640 7.1 15 10.615 1418.3 216 6.566 0.401 0.604 1.285 1.475 1.430 2.470 0.975 1.320 1.820 2.670 2.865 3.510 1.175 2.135 2.910 2.280 2.760 4.920 9.000 1.405 2.085 2.900 2.520 3.695 4.835 2.195 2.470 2.560 1.195 1.180 1.220 2.660 4.220 5.240 2.965 4.205 4.640 2.370 3.670 6.305 2.675 2.315 4.640 5.345 2.640 4.1 15 4.615 698.9 216 3.235 18.361 6.126 19.625 71.741 3.901 18.662 61.152 13.469 34.398 90.440 4.731 26.368 15.288 68.558 14.138 62.726 225.00 5.784 25.857 79.210 12.390 44.823 117.40 10.208 29.921 73.274 4.818 17.472 52.128 13.396 52.128 126.34 15.721 51.912 1 13.21 1 1.357 44.489 151.41 32.206 10.989 58.370 128.71 13.250 50.623 1 12.68 1 1317 216 52.392 1.651 2.176 2.045 6.101 0.951 1.742 3.312 7.129 8.208 12.320 1.381 4.558 8.468 5.198 7.618 24.206 81 .000 1.974 4.347 8.410 6.350 13.653 23.377 4.818 6.101 6.554 1.428 1.392 1.488 7.076 17.808 27.458 8.791 17.682 21.530 5.617 13.469 39.753 7.156 5.359 21.530 28.569 6.970 16.933 21.298 2755.0 216 12.755 140 TABLE 3.5 (cont'd) 5.506 3.651 6.335 20.921 1.926 5.702 14.232 9.799 16.803 33.380 2.556 10.963 11.378 18.878 10.378 38.966 135.00 3.379 10.602 25.810 8.870 24.738 52.387 7.013 13.51 1 21.914 2.623 4.932 8.808 9.736 30.468 58.898 1 1.756 30.297 49.370 7.987 24.479 77.583 15.181 7.674 35.450 60.639 9.610 29.278 48.988 5391.7 2.321 1.596 2.379 3.998 1.396 2.335 3.738 2.075 2.954 4.415 1.476 2.662 2.171 3.922 2.1 1 1 3.778 6.615 1.568 2.642 4.171 2.015 3.287 4.946 1.884 2.796 4.034 1.484 2.279 3.497 2.071 3.497 5.108 2.193 3.491 4.868 1.955 3.277 5.535 2.878 1.932 3.666 5.150 2.063 3.455 4.858 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 0.401 23 .624 23.624 23.624 23 .624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23 .624 23 .624 23.624 23.624 23.624 23.624 23.624 23.624 23 .624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23.624 23 .624 23.624 23.624 23.624 23.624 23.624 23 .624 23.624 23 .624 23 .624 23.624 23.624 23.624 23 .624 23 .624 23 .624 23.624 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.604 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 0.659 3.770 1.884 3.857 7.480 1.584 3.791 7.091 2.600 4.717 8.103 1.704 4.279 2.744 7.366 2.654 5.948 11.393 1.842 4.249 7.738 2.510 5.214 8.897 2.315 4.480 7.534 1.716 3.707 6.731 2.594 5.529 9.140 2.777 5.520 8.781 2.420 5.199 9.778 4.603 2.387 5.781 9.203 2.582 5.466 8.766 1.177 1.351 1.310 2.263 0.893 1.209 1.667 2.446 2.625 3.216 1.077 1.956 2.666 2.089 2.529 4.508 8.246 1.287 1.910 2.657 2.309 3.385 4.430 2.011 2.263 2.345 1.095 1.081 1.1 18 2.437 3.866 4.801 2.717 3.853 4.251 2.171 3.362 5.777 2.451 2.121 4.251 4.897 2.419 3.770 4.228 141 TABLE B.6 METHOD 10 -SECOND REGRESSION 2 Sample a 1: on I... b=tan¢ 6 a=c 297 4.393 2.130 19.301 4.538 9.358 2.627 0.385 21.060 0.935 2.339 2.048 5.473 4.193 4.790 1.836 0.385 21.060 0.935 4.855 2.836 23.568 8.041 13.766 2.804 0.385 21.060 0.935 7.888 2.886 62.215 8.329 22.764 3.972 0.385 21 .060 0.935 224 3.232 3.413 10.447 11.647 11.031 2.180 0.385 21.060 0.935 6.302 5 .048 39.714 25.485 31.814 3.362 0.385 21 .060 0.935 9.844 5.877 96.909 34.544 57.858 4.726 0.385 21 .060 0.935 225 2.237 1.892 5.006 3.579 4.233 1.797 0.3 85 21 .060 0.935 5.550 3.898 30.801 15.198 21.636 3.072 0.385 21 .060 0.935 227 5.123 6.303 26.244 39.733 32.292 2.908 0.385 21 .060 0.935 7.249 6.496 52.545 42.195 47.087 3.726 0.385 21.060 0.935 10.231 6.468 104.669 41.839 66.176 4.875 0.385 21.060 0.935 165 3.520 3.088 12.387 9.533 10.867 2.290 0.385 21.060 0.935 5.996 4.581 35.956 20.985 27.469 3.244 0.385 21.060 0.935 9.179 4.860 84.256 23.623 44.614 4.470 0.385 21 .060 0.935 165 3.520 3.088 12.387 9.533 10.867 2.290 0.385 21.060 0.935 5.996 4.581 35.956 20.985 27.469 3.244 0.385 21 .060 0.935 9.179 4.860 84.256 23.623 44.614 4.470 0.385 21 .060 0.935 192 3.888 3.651 15.117 13.330 14.195 2.432 0.385 21 .060 0.935 6.581 5.474 43 .304 29.967 36.024 3.469 0.385 21 .060 0.935 223 3.954 3.752 15.634 14.076 14.835 2.458 0.385 21.060 0.935 5.775 4.242 33.346 17.994 24.496 3.159 0.385 21 .060 0.935 10.680 7.155 1 14.067 51.201 76.422 5 .048 0.385 21 .060 0.935 226 3.184 2.575 10.137 6.628 8.197 2.161 0.385 21.060 0.935 5.097 3.207 25.984 10.283 16.346 2.898 0.385 21.060 0.935 8.855 4.366 78.420 19.059 38.660 4.345 0.3 85 21 .060 0.935 294 3.055 2.378 9.334 5.653 7.264 2.1 1 1 0.385 21 .060 0.935 4.843 2.817 23.452 7.937 13.643 2.800 0.385 21.060 0.935 8.667 4.077 75.1 12 16.622 35.335 4.272 0.385 21 .060 0.935 295 2.177 1.035 4.740 1.072 2.254 1.773 0.385 21 .060 0.935 4.495 2.286 20.206 5.225 10.275 2.666 0.385 21.060 0.935 8.568 3.926 73.408 15.413 33.636 4.234 0.385 21 .060 0.935 296 3 .205 2.607 10.271 6.794 8.354 2.169 0.385 21 .060 0.935 5.912 4.453 34.957 19.826 26.326 3.212 0.385 21.060 0.935 10.102 6.271 102.049 39.330 63.353 4.825 0.385 21.060 0.935 193 2.294 1.979 5.264 3.916 4.541 1.819 0.385 21.060 0.935 4.381 2.112 19.196 4.460 9.253 2.622 0.385 21.060 0.935 8.496 3.816 72.181 14.561 32.420 4.207 0.385 21.060 0.935 194 2.228 1.878 4.966 3.528 4.186 1.793 0.385 21 .060 0.935 5.106 3.220 26.075 10.371 16.445 2.901 0.385 21.060 0.935 8.577 3.940 73.562 15.521 33.789 4.238 0.385 21.060 0.935 228 1.791 1.209 3.208 1.463 2.166 1.625 0.385 21 .060 0.935 3.908 1.388 15.272 1.927 5.424 2.440 0.385 21 .060 0.935 6.953 1.457 48.342 2.122 10.128 3.612 0.385 21.060 0.935 229 230 231 195 232 196 197 198 199 88 89 115 116 86 87 1.923 4.375 7.423 2.097 5.005 8.739 2.612 5.292 8.085 2.576 4.816 8.103 2.157 4.642 7.606 1.947 5.969 2.366 9.808 3.241 6.497 1 1.154 1.962 5.064 8.181 2.228 7.246 4.648 9.281 2.252 4.231 7.079 2.675 5.21 1 9.437 1.824 7.214 4.690 8.298 2.297 4.306 7.507 2.160 4.222 7.222 2.735 5.163 9.236 1.411 2.103 2.176 1.677 3.065 4.187 2.465 3.504 3.188 2.410 2.776 3.216 1.768 2.510 2.455 1.448 4.540 2.089 5.822 3.427 5.346 7.879 1.470 3.156 3.335 1.878 1.906 2.520 5.016 1.915 1.883 1.649 2.561 3.381 5.254 1.260 1.855 2.584 3.514 1.984 1.997 2.304 1.773 1.869 1.869 2.652 3.307 4.947 TABLE B.6 (cont'd) 3.697 1.991 2.713 19.143 4.421 9.200 55.105 4.735 16.153 4.396 2.811 3.515 25.045 9.392 15.337 76.364 17.531 36.589 6.823 6.074 6.437 28.007 12.281 18.546 65.374 10.166 25.779 6.636 5.806 6.207 23.192 7.707 13.369 65.665 10.342 26.059 4.651 3.127 3.813 21.548 6.302 11.653 57.852 6.029 18.676 3.790 2.095 2.818 35.633 20.609 27.099 5.599 4.364 4.943 96.203 33.900 57.108 10.506 11.741 11.106 42.207 28.580 34.731 124.404 62.083 87.882 3.849 2.162 2.885 25.649 9.962 15.985 66.934 1 1.122 27.284 4.966 3.528 4.186 52.511 3.632 13.809 21.604 6.348 11.711 86.136 25.162 46.555 5.074 3.667 4.313 17.905 3.545 7.967 50.108 2.720 1 1.674 7.155 6.557 6.850 27.157 11.429 17.618 89.052 27.608 49.584 3.327 1.587 2.298 52.035 3.442 13.383 21.995 6.675 12.117 68.860 12.345 29.156 5.278 3.934 4.557 18.545 3.989 8.601 56.357 5.309 17.298 4.664 3.143 3.829 17.829 3.493 7.892 52.164 3.493 13.499 7.479 7.035 7.254 26.660 10.939 17.077 85.304 24.477 45.695 142 1.675 2.620 3.793 1.742 2.862 4.300 1.941 2.973 4.048 1.927 2.789 4.055 1.765 2.723 3.864 1.685 3.234 1.846 4.712 2.183 3.437 5.230 1.690 2.885 4.085 1.793 3.725 2.725 4.509 1.802 2.564 3.661 1.965 2.942 4.569 1.637 3.713 2.741 4.130 1.820 2.593 3.826 1.767 2.561 3.716 1.988 2.923 4.492 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.3 85 0.3 85 0.385 0.3 85 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 111 141 142 143 144 145 166 167 168 169 170 171 200 201 234 2.243 5.933 2.897 9.206 2.843 5.268 8.487 2.378 5.829 9.122 2.648 3.594 5.945 2.405 8.175 5.220 7.654 1.878 4.420 8.040 2.723 5.574 9.380 2.190 5.073 8.619 2.040 4.645 7.774 2.031 4.801 8.574 2.234 4.391 7.519 1.992 4.627 8.094 2.007 6.908 4.71 1 8.232 2.41 1 5.238 8.709 2.163 4.540 7.795 1.901 4.485 2.900 4.902 2.817 3.468 3.802 2.107 4.324 4.773 2.520 3.202 4.503 2.148 3.326 3.394 2.529 1.342 2.171 3.120 2.634 3.935 5.167 1.819 3.170 4.004 1.590 2.515 2.712 1.576 2.753 3.935 1.887 2.158 2.323 1.516 2.487 3.202 1.539 1.388 2.616 3.413 2.158 3.422 4.141 1.777 2.355 2.744 TABLE B.6 (cont'd) 5.033 3.614 4.265 35.205 20.113 26.610 8.391 8.409 8.400 84.751 24.026 45.125 8.081 7.937 8.009 27.754 12.026 18.269 72.028 14.457 32.269 5.656 4.440 5.012 33 .972 18.701 25.205 83.214 22.785 43.543 7.012 6.348 6.672 12.920 10.253 11.510 35.347 20.278 26.772 5.785 4.616 5.168 66.836 11.061 27.189 27.251 1 1.523 17.720 58.583 6.394 19.354 3.527 1.802 2.521 19.539 4.715 9.598 64.649 9.732 25.083 7.414 6.938 7.172 31.068 15.485 21.933 87.981 26.701 48.469 4.794 3.307 3.982 25.740 10.049 16.083 74.283 16.030 34.507 4.160 2.527 3.242 21.576 6.325 1 1.682 60.432 7.355 21.082 4.124 2.483 3.200 23.047 7.580 13.217 73.510 15.485 33.738 4.993 3.562 4.217 19.283 4.655 9.475 56.537 5.394 17.464 3.967 2.299 3.020 21.409 6.187 11.509 65.520 10.253 25.919 4.027 2.369 3.089 47.719 1.927 9.588 22.192 6.842 12.322 67.770 1 1.647 28.095 5.814 4.655 5.203 27.439 1 1.710 17.925 75.841 17.149 36.064 4.677 3.159 3.844 20.613 5.544 10.690 60.759 7.530 21.389 143 1.799 3.220 2.050 4.480 2.030 2.964 4.203 1.851 3.179 4.448 1.955 2.319 3.224 1.861 4.083 2.945 3.882 1.658 2.637 4.031 1.984 3.081 4.547 1.778 2.889 4.254 1.720 2.724 3.928 1.717 2.784 4.237 1.795 2.626 3.830 1.702 2.717 4.052 1.708 3.595 2.749 4.105 1.864 2.952 4.288 1.768 2.683 3.937 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 235 236 237 238 258 259 260 66 117 118 172 204 205 206 1.788 3.890 6.665 1.671 3.908 6.965 2.351 4.687 7.738 2.172 5.394 9.847 2.061 4.753 8.205 2.094 4.510 8.757 2.255 4.525 8.175 3.161 8.909 6.1 13 9.703 2.438 4.366 7.816 1.905 4.276 7.357 3.770 1.884 3.857 7.480 1.584 3.791 7.091 2.600 4.717 8.103 1 .704 4.279 2.744 7.366 2.654 5 .948 1 1 .393 1.205 1.361 1.017 1.026 1.388 1.475 2.066 2.579 2.657 1.791 3.660 5.882 1.622 2.680 3.372 1.672 2.309 4.214 1.919 2.332 3.326 3.303 4.448 4.760 5.662 2.199 2.089 2.776 1.383 1.951 2.075 1.177 1.351 1.310 2.263 0.893 1.209 1.667 2.446 2.625 3.216 1.077 1.956 2.666 2.089 2.529 4.508 8.246 TABLE B.6 (cont'd) 3.197 1.452 2.154 15.131 1.851 5.292 44.425 1.034 6.778 2.793 1.053 1.715 1 5.272 1 .927 5.424 48.509 2.176 10.274 5.529 4.268 4.858 21.967 6.652 12.088 59.874 7.059 20.559 4.716 3.208 3.890 29.096 13.397 19.743 96.968 34.597 57.921 4.246 2.630 3.342 22.589 7.182 12.737 67.327 11.368 27.665 4.383 2.796 3.501 20.341 5.331 10.413 76.678 17.762 36.905 5.087 3.684 4.329 20.477 5.437 10.551 66.836 1 1.061 27.189 9.994 10.909 10.441 79.378 19.786 39.630 37.371 22.654 29.096 94.157 32.059 54.941 5.945 4.835 5.361 19.065 4.364 9.121 61.086 7.707 21.697 3.629 1.914 2.635 18.288 3.808 8.345 54.130 4.306 15.268 14.213 1.386 4.439 3.549 1.826 2.546 14.876 1.717 5.053 55.953 5.121 16.928 2.510 0.798 1.415 14.372 1.463 4.585 50.277 2.780 1 1.823 6.760 5.984 6.360 22.249 6.890 12.381 65.665 10.342 26.059 2.904 1.159 1.835 18.313 3.826 8.371 7.529 7.108 7.315 54.263 4.364 15.388 7.044 6.394 6.711 35.383 20.319 26.813 129.808 67.992 93.946 144 1.624 2.433 3.502 1.579 2.440 3.617 1.840 2.740 3.915 1.771 3.012 4.727 1.729 2.765 4.095 1.741 2.672 4.307 1.804 2.678 4.083 2.152 4.366 3.289 4.672 1.874 2.616 3.945 1.669 2.582 3.768 2.387 1.660 2.420 3.815 1.545 2.395 3.665 1.936 2.751 4.055 1.591 2.583 1.992 3.772 1.957 3.226 5.322 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 sum dof Mean 119 173 202 203 207 239 233 84 85 1.842 4.249 7.738 2.510 5.214 8.897 2.315 4.480 7.534 1.716 3.707 6.731 2.594 5.529 9.140 2.777 5.520 8.781 2.420 5.199 9.778 4.603 2.387 5.781 9.203 2.582 5.466 8.766 1 138.28 216 5.270 0.385 0.935 1.287 1.910 2.657 2.309 3.385 4.430 2.011 2.263 2.345 1.095 1.081 1.1 18 2.437 3.866 4.801 2.717 3.853 4.251 2.171 3.362 5.777 2.451 2.121 4.251 4.897 2.419 3.770 4.228 640.286 216 2.964 TABLE B.6 (cont'd) 3.393 1.657 2.371 18.058 3.649 8.118 59.874 7.059 20.559 6.301 5.331 5.795 27. 189 11.460 17.652 79.164 19.623 39.414 5.361 4.044 4.656 20.072 5.121 10.139 56.763 5.501 17.671 2.945 1.199 1.879 13.743 1.169 4.008 45.308 1.249 7.524 6.729 5.939 6.322 30.569 14.949 21.376 83.542 23.048 43.880 7.71 1 7.379 7.543 30.469 14.842 21.266 77.098 18.072 37.327 5.858 4.715 5.255 27.033 1 1.306 17.482 95.616 33.369 56.485 21.188 6.006 11.281 5.699 4.499 5.063 33.415 18.072 24.574 84.696 23.981 45.068 6.667 5.850 6.245 29.877 14.214 20.607 76.836 17.878 37.063 7437.67 2312.57 3928.35 216 216 34.434 10.706 145 1.644 2.571 3.915 1.902 2.943 4.361 1.827 2.660 3.836 1.596 2.363 3.527 1.934 3.064 4.455 2.004 3.061 4.316 1.867 2.937 4.700 2.708 1.854 3.161 4.479 1.929 3.040 4.310 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.385 21 .060 21 .060 21 .060 21 .060 21 .060 21 .060 2 1 .060 21 .060 2 1 .060 2 1 .060 21 .060 2 1 .060 2 1 .060 21 .060 2 1 .060 21 .060 21 .060 21 .060 2 1 .060 21 .060 2 1 .060 2 1 .060 21 .060 21 .060 2 1 .060 2 1 .060 21 .060 2 1 .060 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 146 TABLE 11.7 METHOD 11 - FIRST REGRESSION Sample a, 01 032 012 0390, 0M 11 Q a c a t 297 3 7.65 9 58.523 22.950 9.241 1.693 14.910 4.163 1.600 5.156 2.319 1 5.47 1 29.921 5.470 5.856 1.693 14.910 4.163 1.600 3.073 2.229 3 9.19 9 84.456 27.570 9.241 1.693 14.910 4.163 1.600 5.870 3.087 6 12.3 36 151.29 73.800 14.320 1.693 14.910 4.163 1.600 8.921 3.142 224 1 8.45 1 71.403 8.450 5.856 1.693 14.910 4.163 1.600 4.455 3.715 3 14.02 9 196.56 42.060 9.241 1.693 14.910 4.163 1.600 8.110 5.495 6 18.83 36 354.57 112.98 14.320 1.693 14.910 4.163 1.600 11.949 6.398 225 1 5.13 1 26.317 5.130 5.856 1.693 14.910 4.163 1.600 2.915 2.060 3 11.51 9 132.48 34.530 9.241 1.693 14.910 4.163 1.600 6.946 4.244 227 1 14.76 1 217.86 14.760 5.856 1.693 14.910 4.163 1.600 7.381 6.862 3 17.18 9 295.15 51.540 9.241 1.693 14.910 4.163 1.600 9.575 7.071 6 20.12 36 404.81 120.72 14.320 1.693 14.910 4.163 1.600 12.548 7.041 165 1.5 8.24 2.25 67.898 12.360 6.702 1.693 14.910 4.163 1.600 4.625 3.361 3 13 9 169.00 39.000 9.241 1.693 14.910 4.163 1.600 7.637 4.987 6 16.61 36 275.89 99.660 14.320 1.693 14.910 4.163 1.600 10.920 5.291 165 1.5 8.24 2.25 67.898 12.360 6.702 1.693 14.910 4.163 1.600 4.625 3.361 3 13 9 169.00 39.000 9.241 1.693 14.910 4.163 1.600 7.637 4.987 6 16.61 36 275.89 99.660 14.320 1.693 14.910 4.163 1.600 10.920 5.291 192 1.5 9.47 2.25 89.681 14.205 6.702 1.693 14.910 4.163 1.600 5.196 3.974 3 14.95 9 223.50 44.850 9.241 1.693 14.910 4.163 1.600 8.541 5.959 223 1.5 9.69 2.25 93.896 14.535 6.702 1.693 14.910 4.163 1.600 5.298 4.084 3 12.26 9 150.31 36.780 9.241 1.693 14.910 4.163 1.600 7.294 4.618 6 21.62 36 467.42 129.72 14.320 1.693 14.910 4.163 1.600 13.243 7.789 226 1.5 7.12 2.25 50.694 10.680 6.702 1.693 14.910 4.163 1.600 4.106 2.803 3 10 9 100.00 30.000 9.241 1.693 14.910 4.163 1.600 6.246 3.491 6 15.53 36 241.18 93.180 14.320 1.693 14.910 4.163 1.600 10.419 4.752 294 1.5 6.69 2.25 44.756 10.035 6.702 1.693 14.910 4.163 1.600 3.907 2.588 3 9.15 9 83.723 27.450 9.241 1.693 14.910 4.163 1.600 5.852 3.067 6 14.9 36 222.01 89.400 14.320 1.693 14.910 4.163 1.600 10.127 4.438 295 1.5 3.76 2.25 14.138 5.640 6.702 1.693 14.910 4.163 1.600 2.548 1.127 3 7.99 9 63.840 23.970 9.241 1.693 14.910 4.163 1.600 5.314 2.488 6 14.57 36 212.28 87.420 14.320 1.693 14.910 4.163 1.600 9.974 4.274 296 1.5 7.19 2.25 51.696 10.785 6.702 1.693 14.910 4.163 1.600 4.138 2.837 3 12.72 9 161.80 38.160 9.241 1.693 14.910 4.163 1.600 7.507 4.847 6 19.69 36 387.70 118.14 14.320 1.693 14.910 4.163 1.600 12.348 6.827 193 1 5.32 1 28.302 5.320 5.856 1.693 14.910 4.163 1.600 3.003 2.154 3 7.61 9 57.912 22.830 9.241 1.693 14.910 4.163 1.600 5.138 2.299 6 14.33 36 205.35 85.980 14.320 1.693 14.910 4.163 1.600 9.863 4.154 194 1 5.1 1 26.010 5.100 5.856 1.693 14.910 4.163 1.600 2.901 2.045 3 10.03 9 100.60 30.090 9.241 1.693 14.910 4.163 1.600 6.260 3.506 6 14.6 36 213.16 87.600 14.320 1.693 14.910 4.163 1.600 9.988 4.289 228 1 3.64 1 13.250 3.640 5.856 1.693 14.910 4.163 1.600 2.224 1.317 3 6.03 9 36.361 18.090 9.241 1.693 14.910 4.163 1.600 4.405 1.511 6 9.18 36 84.272 55.080 14.320 1.693 14.910 4.163 1.600 7.475 1.586 229 1 4.08 1 16.646 4.080 5.856 1.693 14.910 4.163 1.600 2.428 1.536 3 7.59 9 57.608 22.770 9.241 1.693 14.910 4.163 1.600 5.128 2.289 6 10.75 36 115.56 64.500 14.320 1.693 14.910 4.163 1.600 8.203 2.369 230 1 4.66 1 21.716 4.660 5.856 1.693 14.910 4.163 1.600 2.697 1.825 3 9.69 9 93.896 29.070 9.241 1.693 14.910 4.163 1.600 6.102 3.336 6 15.14 36 229.22 90.840 14.320 1.693 14.910 4.163 1.600 10.238 4.558 231 1 6.38 1 40.704 6.380 5.856 1.693 14.910 4.163 1.600 3.495 2.683 3 10.65 9 113.42 31.950 9.241 1.693 14.910 4.163 1.600 6.547 3.815 6 12.96 36 167.96 77.760 14.320 1.693 14.910 4.163 1.600 9.227 3.471 195 232 196 197 198 88 89 115 116 86 87 111 141 142 143 I44 145 as0.1—owe»—wia—oxu—asw—a~—w-—on»—asu—aw—axwax—oxw—ow—oua—aw—ow—ca—w—aw—asw— 6.26 9.06 13.02 4.86 8.48 11.36 4.16 12.91 5.56 18.71 8.48 14.67 23.2 4.21 9.89 13.28 5.1 10.16 8.5 16.95 5.18 7.1 1 9.6 6.59 10.38 17.47 3.75 10.05 8.64 13.67 5.33 7.36 11.03 4.87 7.08 10.08 6.79 10.22 16.8 5.15 12.79 7.33 16.7 7.15 10.57 14.3 5.6 12.44 16.42 6.5 8.49 12.83 5.69 13.26 10.41 1 1.52 3.93 7.74 12.81 39.188 82.084 169.52 23.620 71.910 129.05 17.306 166.67 30.914 350.06 71.910 215.21 538.24 17.724 97.812 176.36 26.010 103.23 72.250 287.30 26.832 50.552 92.160 43.428 107.74 305.20 14.063 101.00 74.650 186.87 28.409 54.170 121.66 23.717 50.126 101.61 46.104 104.45 282.24 26.523 163.58 53.729 278.89 51.123 1 1 1.72 204.49 31.360 154.75 269.62 42.250 72.080 164.61 32.376 175.83 108.37 132.71 15.445 59.908 164.10 147 TABLE B.7 (cont'd) 6.260 5.856 1.693 27.180 9.241 1.693 78.120 14.320 1.693 4.860 5.856 1.693 25.440 9.241 1.693 68.160 14.320 1.693 4.160 5.856 1.693 38.730 9.241 1.693 5.560 5.856 1.693 1 12.26 14.320 1.693 8.480 5.856 1.693 44.010 9.241 1.693 139.20 14.320 1.693 4.210 5.856 1.693 29.670 9.241 1.693 79.680 14.320 1.693 5.100 5.856 1.693 60.960 14.320 1.693 25.500 9.241 1.693 101.70 14.320 1.693 5.180 5.856 1.693 21.330 9.241 1.693 57.600 14.320 1.693 6.590 5.856 1.693 31.140 9.241 1.693 104.82 14.320 1.693 3.750 5.856 1.693 60.300 14.320 1.693 25.920 9.241 1.693 82.020 14.320 1.693 5.330 5.856 1.693 22.080 9.241 1.693 66.180 14.320 1.693 4.870 5.856 1.693 21.240 9.241 1.693 60.480 14.320 1.693 6.790 5.856 1.693 30.660 9.241 1.693 100.80 14.320 1.693 5.150 5.856 1.693 38.370 9.241 1.693 7.330 5.856 1.693 100.20 14.320 1.693 7.150 5.856 1.693 31.710 9.241 1.693 85.800 14.320 1.693 5.600 5.856 1.693 37.320 9.241 1.693 98.520 14.320 1.693 6.500 5.856 1.693 12.735 6.702 1.693 38.490 9.241 1.693 5.690 5.856 1.693 79.560 14.320 1.693 31.230 9.241 1.693 69.120 14.320 1.693 3.930 5.856 1.693 23 .220 9.241 1.693 76.860 14.320 1.693 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 3.439 5.810 9.255 2.790 5.541 8.485 2.465 7.595 3.1 14 11.894 4.469 8.41 1 13.976 2.488 6.195 9.376 2.901 7.929 5.550 1 1.078 2.938 4.906 7.669 3.592 6.422 1 1.319 2.275 7.878 5.615 9.557 3.008 5.022 8.332 2.795 4.892 7.892 3.685 6.348 1 1.008 2.924 7.540 3.935 10.962 3.852 6.510 9.849 3.133 7.377 10.832 3.550 4.741 7.558 3.175 9.366 6.436 8.560 2.359 5.198 9.158 2.623 3.022 3.501 1.925 2.733 2.673 1.576 4.942 2.274 6.338 3.730 5.820 8.577 1.601 3.436 3.630 2.045 2.075 2.743 5.461 2.084 2.050 1.795 2.788 3.680 5.720 1.371 2.020 2.813 3.825 2.159 2.174 2.508 1.930 2.035 2.035 2.887 3.600 5.386 2.070 4.882 3.157 5.336 3.067 3.775 4.139 2.294 4.708 5.196 2.743 3.486 4.902 2.339 3.620 3.695 2.753 1.461 2.364 3.396 167 168 169 170 171 200 201 234 235 236 237 238 258 259 260 66 90 117 O5w—05w—OxwO5—O~w—O~w~o~w—-O\w-—O~w—05w~Oxw—ow—osw—oxwa—ow—au—oxw—caw—ow—axw— 6.75 11.59 17.28 4.97 9.92 14.74 4.47 8.49 11.92 4.44 9.01 14.59 5.12 7.69 11.07 4.31 8.43 12.99 4.36 9.03 8.71 13.45 5.71 10.47 15.04 4.88 8.14 11.99 3.63 5.97 8.22 3.24 6.03 9.22 5.51 8.63 11.8 4.91 10.99 18.84 4.54 8.85 13.36 4.65 8.04 15.2 5.19 8.09 13.26 8.21 1 15.71 13.39 18.36 5.8 7.56 12.06 4.02 7.26 10.53 45.563 134.33 298.60 24.701 98.406 217.27 19.981 72.080 142.09 19.714 81.180 212.87 26.214 59.136 122.54 18.576 71 .065 168.74 19.010 81.541 75.864 180.90 32.604 109.62 226.20 23.814 66.260 143.76 13.177 35.641 67.568 10.498 36.361 85.008 30.360 74.477 139.24 24.108 120.78 354.95 20.612 78.323 178.49 21.623 64.642 231.04 26.936 65.448 175.83 67.421 246.80 179.29 337.09 33.640 57.154 145.44 16.160 52.708 1 10.88 148 TABLE B.7 (cont'd) 6.750 5.856 1.693 34.770 9.241 1.693 103.68 14.320 1.693 4.970 5.856 1.693 29.760 9.241 1.693 88.440 14.320 1.693 4.470 5.856 1.693 25.470 9.241 1.693 71.520 14.320 1.693 4.440 5.856 1.693 27.030 9.241 1.693 87.540 14.320 1.693 5.120 5.856 1.693 23 .070 9.241 1.693 66.420 14.320 1.693 4.310 5.856 1.693 25.290 9.241 1.693 77.940 14.320 1.693 4.360 5.856 1.693 54.180 14.320 1.693 26.130 9.241 1.693 80.700 14.320 1.693 5.710 5.856 1.693 31.410 9.241 1.693 90.240 14.320 1.693 4.880 5.856 1.693 24.420 9.241 1.693 71.940 14.320 1.693 3.630 5.856 1.693 17.910 9.241 1.693 49.320 14.320 1.693 3.240 5.856 1.693 18.090 9.241 1.693 55.320 14.320 1.693 5.510 5.856 1.693 25.890 9.241 1.693 70.800 14.320 1.693 4.910 5.856 1.693 32.970 9.241 1.693 113.04 14.320 1.693 4.540 5.856 1.693 26.550 9.241 1.693 80.160 14.320 1.693 4.650 5.856 1.693 24.120 9.241 1.693 91.200 14.320 1.693 5.190 5.856 1.693 24.270 9.241 1.693 79.560 14.320 1.693 8.211 5.856 1.693 94.260 14.320 1.693 40.170 9.241 1.693 110.16 14.320 1.693 5.800 5.856 1.693 22.680 9.241 1.693 72.360 14.320 1.693 4.020 5.856 1.693 21.780 9.241 1.693 63.180 14.320 1.693 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 3.666 6.983 11.231 2.841 6.209 10.053 2.609 5.546 8.745 2.595 5.787 9.983 2.910 5.175 8.351 2.535 5.518 9.241 2.558 7.405 5.648 9.455 3.184 6.464 10.192 2.799 5.383 8.778 2.220 4.377 7.029 2.039 4.405 7.493 3.091 5.611 8.689 2.813 6.705 11.954 2.642 5.713 9.413 2.693 5.337 10.266 2.943 5.360 9.366 4.344 10.503 7.818 1 1.731 3.226 5.1 14 8.810 2.400 4.975 8.101 2.867 4.284 5.625 1.980 3.451 4.358 1.730 2.738 2.952 1.715 2.997 4.284 2.055 2.339 2.528 1.651 2.708 3.486 1.676 1.51 1 2.847 3.715 2.349 3.725 4.508 1.935 2.563 2.987 1.312 1.481 1.107 1.1 17 1.511 1.606 2.249 2.808 2.892 1.950 3.984 6.403 1.765 2.917 3.670 1.820 2.513 4.588 2.089 2.538 3.620 3.596 4.842 5.181 6.164 2.394 2.274 3.022 1.506 2.124 2.259 sum dof Mean 118 172 204 205 206 119 173 202 203 207 239 233 85 w—osw~wa~w-—osm—axw—oxw—ow—asw—axw—oxw—‘as—w—o~w—o~w—o~w-—u 719.5 216 3.331 1.693 4.163 5.57 3.95 5.86 10.94 2.95 5.64 9.64 6.34 8.73 13.02 3.35 7.27 6.82 10.56 6.52 12.84 24 3.81 7.17 11.8 6.04 10.39 15.67 5.39 7.94 11.12 3.39 5.36 8.44 6.32 11.44 16.48 6.93 1 1.41 15.28 5.74 10.34 18.61 8.35 5.63 12.28 16.69 6.28 1 1.23 15.23 21 17.2 216 9.802 36 3288.3 216 15.223 31 .025 15.603 34.340 119.68 8.703 31 .810 92.930 40.196 76.213 169.52 1 1.223 52.853 46.512 111.51 42.510 164.87 576.00 14.516 51 .409 139.24 36.482 107.95 245.55 29.052 63.044 123.65 11.492 28.730 71.234 39.942 130.87 271.59 48.025 130.19 233.48 32.948 106.92 346.33 69.723 31.697 150.80 278.56 39.438 126.1 1 231.95 24855 216 1 15 .07 149 TABLE B.7 (cont'd) 16.710 9.241 1.693 3.950 5.856 1.693 17.580 9.241 1.693 65.640 14.320 1.693 2.950 5.856 1.693 16.920 9.241 1.693 57.840 14.320 1.693 6.340 5.856 1.693 26. 190 9.241 1.693 78. 120 14.320 1.693 3.350 5.856 1.693 21.810 9.241 1.693 6.820 5.856 1.693 63.360 14.320 1.693 6.520 5.856 1.693 38.520 9.241 1.693 144.00 14.320 1.693 3.810 5.856 1.693 21.510 9.241 1.693 70.800 14.320 1.693 6.040 5.856 1.693 31.170 9.241 1.693 94.020 14.320 1.693 5.390 5.856 1.693 23.820 9.241 1.693 66.720 14.320 1.693 3.390 5.856 1.693 16.080 9.241 1.693 50.640 14.320 1.693 6.320 5.856 1.693 34.320 9.241 1.693 98.880 14.320 1.693 6.930 5.856 1.693 34.230 9.241 1.693 91.680 14.320 1.693 5.740 5.856 1.693 31.020 9.241 1.693 11 1.66 14.320 1.693 25.050 9.241 1.693 5.630 5.856 1.693 36.840 9.241 1.693 100.14 14.320 1.693 6.280 5.856 1.693 33.690 9.241 1.693 91.380 14.320 1.693 8561 .7 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 14.910 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 4.163 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 1.600 4.192 2.368 4.326 8.291 1.904 4.224 7.688 3.476 5.657 9.255 2.090 4.980 3.699 8.1 14 3.560 7.563 14.347 2.303 4.934 8.689 3.337 6.427 10.484 3.036 5.291 8.374 2.108 4.094 7.131 3.467 6.914 10.860 3.750 6.900 10.303 3.198 6.404 1 1.847 5.481 3.147 7.303 10.957 3.448 6.816 10.280 1.282 1.471 1.426 2.463 0.972 1.317 1.815 2.663 2.857 3.501 1.172 2.129 2.902 2.274 2.753 4.907 8.976 1.401 2.079 2.892 2.513 3.685 4.822 2.189 2.463 2.553 1.192 1.177 1.217 2.653 4.209 5.226 2.957 4.194 4.628 2.364 3.660 6.288 2.668 2.309 4.628 5.331 2.633 4.104 4.603 150 TABLE B.8 METHOD 1] - POOLED REGRESSION Sllllpk a 1: a t 0*! 1: h, b=tan¢ 6 a=c 297 5.156 2.319 26.587 5.377 11.957 2.894 0.402 21 .918 0.819 3.073 2.229 9.442 4.969 6.850 2.056 0.402 21 .918 0.819 5.870 3.087 34.461 9.529 18.121 3.181 0.402 21 .918 0.819 8.921 3.142 79.590 9.870 28.028 4.409 0.402 21 .918 0.819 224 4.455 3.715 19.843 13.803 16.550 2.612 0.402 21 .918 0.819 8.110 5.495 65.773 30.200 44.568 4.082 0.402 21 .918 0.819 11.949 6.398 142.787 40.935 76.453 5.627 0.402 21 .91 8 0.819 2.915 2.060 8.498 4.242 6.004 1.992 0.402 21 .918 0.819 6.946 4.244 48.249 18.010 29.478 3.614 0.402 21 .91 8 0.819 7.381 6.862 54.473 47.085 50.644 3.789 0.402 21 .918 0.819 9.575 7.071 91.687 50.003 67.710 4.672 0.402 21 .91 8 0.819 12.548 7.041 157.440 49.581 88.352 5.868 0.402 21 .918 0.819 4.625 3.361 21.394 11.297 15.546 2.680 0.402 21 .918 0.819 7.637 4.987 58.324 24.868 38.084 3.892 0.402 21 .918 0.819 10.920 5.291 1 19.244 27.995 57.777 5.213 0.402 21.918 0.819 4.625 3.361 21.394 11.297 15.546 2.680 0.402 21 .918 0.819 7.637 4.987 58.324 24.868 38.084 3.892 0.402 21 .918 0.819 10.920 5.291 119.244 27.995 57.777 5.213 0.402 21.918 0.819 192 5.196 3.974 26.996 15.797 20.650 2.910 0.402 21 .91 8 0.819 8.541 5.959 72.953 35.513 50.899 4.256 0.402 21 .918 0.819 223 5.298 4.084 28.066 16.681 21.637 2.951 0.402 21 .918 0.819 7.294 4.618 53.201 21.324 33.682 3.754 0.402 21 .918 0.819 13.243 7.789 175.379 60.675 103.156 6.148 0.402 21.918 0.819 226 4.106 2.803 16.859 7.854 11.507 2.471 0.402 21 .918 0.819 6.246 3.491 39.012 12.185 21.803 3.332 0.402 21 .918 0.819 10.419 4.752 108.558 22.586 49.516 5.012 0.402 21 .918 0.819 294 3.907 2.588 15.262 6.699 10.111 2.391 0.402 21 .918 0.819 5.852 3.067 34.243 9.406 17.947 3.174 0.402 21 .918 0.819 10.127 4.438 102.556 19.698 44.946 4.894 0.402 21 .918 0.819 295 2.548 1.127 6.492 1.270 2.872 1.845 0.402 21 .918 0.819 5 .3 14 2.488 28.237 6.192 13.223 2.957 0.402 21 .918 0.819 9.974 4.274 99.480 18.264 42.626 4.832 0.402 21.918 0.819 296 4.138 2.837 17.127 8.051 11.743 2.485 0.402 21 .918 0.819 7.507 4.847 56.358 23.495 36.389 3.840 0.402 21.918 0.819 12.348 6.827 152.476 46.607 84.300 5.788 0.402 21 .918 0.819 1 93 3.003 2.154 9.019 4.641 6.470 2.028 0.402 21 .91 8 0.819 5.138 2.299 26.396 5.285 11.811 2.887 0.402 21 .918 0.819 9.863 4.154 97.272 17.256 40.970 4.788 0.402 21 .918 0.819 1 94 2.901 2.045 8.417 4.180 5.932 1.987 0.402 21 .918 0.819 6.260 3.506 39.186 12.290 21.945 3.338 0.402 21 .918 0.819 9.988 4.289 99.757 18.393 42.834 4.838 0.402 21 .918 0.819 228 2.224 1.317 4.947 1.733 2.928 1.714 0.402 21.918 0.819 4.405 1.511 19.404 2.283 6.656 2.592 0.402 21 .918 0.819 7.475 1.586 55.869 2.515 11.853 3.827 0.402 21 .918 0.819 229 230 231 195 232 196 197 198 199 88 89 115 116 86 87 2.428 5.128 8.203 2.697 6.102 10.238 3.495 6.547 9.227 3.439 5.810 9.255 2.790 5.541 8.485 2.465 7.595 3.1 14 1 1.894 4.469 8.41 1 13.976 2.488 6.195 9.376 2.901 7.929 5.550 1 1.078 2.938 4.906 7.669 3.592 6.422 1 1.319 2.275 7.878 5.615 9.557 3.008 5.022 8.332 2.795 4.892 7.892 3.685 6.348 1 1.008 1.536 2.289 2.369 1.825 3.336 4.558 2.683 3.815 3.471 2.623 3.022 3.501 1.925 2.733 2.673 1.576 4.942 2.274 6.338 3.730 5.820 8.577 1.601 3.436 3,630 2.045 2.075 2.743 5.461 2.084 2.050 1.795 2.788 3.680 5.720 1.371 2.020 2.813 3.825 2.159 2.174 2.508 1.930 2.035 2.035 2.887 3.600 5.386 151 TABLE B.8 (cont'd) 5.896 2.359 3.730 26.301 5.239 11.739 67.283 5.611 19.430 7.275 3.331 4.923 37.237 11.130 20.358 104.822 20.775 46.665 12.213 7.198 9.376 42.868 14.554 24.978 85.145 12.047 32.027 1 1.827 6.880 9.021 33.757 9.133 17.558 85.659 12.255 32.400 7.784 3.705 5.370 30.704 7.468 15.143 72.003 7.145 22.681 6.078 2.483 3.885 57.689 24.423 37.535 9.700 5.171 7.082 141.460 40.173 75.385 19.968 13.914 16.668 70.752 33.868 48.951 195.321 73.570 119.874 6.193 2.562 3 .983 38.377 11.805 21.285 87.905 13.180 34.038 8.417 4.180 5.932 62.869 4.304 16.449 30.807 7.523 15.223 122.712 29.818 60.490 8.634 4.345 6.125 24.067 4.201 10.055 58.819 3.223 13.768 12.903 7.771 10.013 41.244 13.544 23.635 128.113 32.717 64.741 5.176 1.881 3.120 62.063 4.079 15.91 1 31.532 7.910 15.793 91.329 14.630 36.553 9.047 4.663 6.495 25.218 4.727 10.919 69.429 6.292 20.901 7.809 3.724 5.393 23.931 4.140 9.953 62.282 4.140 16.057 13.578 8.337 10.639 40.296 12.963 22.856 121.176 29.006 59.286 1.796 2.883 4.120 1.905 3.275 4.939 2.226 3.454 4.532 2.203 3.157 4.543 1.942 3.049 4.234 1.81 1 3.875 2.073 5.605 2.617 4.204 6.443 1.821 3.312 4.592 1.987 4.010 3.053 5.277 2.002 2.793 3.905 2.265 3.403 5.374 1.735 3.989 3.079 4.665 2.030 2.840 4.172 1.944 2.788 3.995 2.302 3.374 5.249 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 111 141 142 143 144 145 166 167 168 169 170 171 200 201 234 2.924 7.540 3.935 10.962 3.852 6.510 9.849 3.133 7.377 10.832 3.550 4.741 7.558 3.175 9.366 6.436 8.560 2.359 5.198 9.158 3.666 6.983 1 1.231 2.841 6.209 10.053 2.609 5.546 8.745 2.595 5.787 9.983 2.910 5.175 8.351 2.535 5.518 9.241 2.558 7.405 5.648 9.455 3.184 6.464 10.192 2.799 5.383 8.778 2.070 4.882 3.157 5.336 3.067 3.775 4.139 2.294 4.708 5.196 2.743 3.486 4.902 2.339 3.620 3.695 2.753 1.461 2.364 3.396 2.867 4.284 5.625 1.980 3.451 4.358 1.730 2.738 2.952 1.715 2.997 4.284 2.055 2.339 2.528 1.651 2.708 3.486 1.676 1.51 1 2.847 3.715 2.349 3.725 4.508 1.935 2.563 2.987 152 TABLE B.8 (cont'd) 8.552 4.283 6.052 56.847 23.835 36.809 15.486 9.964 12.422 120.158 28.472 58.490 14.836 9.406 1 1.813 42.383 14.251 24.576 96.998 17.132 40.764 9.816 5.262 7.187 54.426 22.161 34.729 1 17.328 27.001 56.285 12.605 7.523 9.738 22.480 12.151 16.527 57.127 24.030 37.051 10.079 5.470 7.425 87.731 13.107 33.911 41.423 13.655 23.783 73.268 7.577 23.562 5.563 2.135 3.446 27.019 5.587 12.287 83.866 11.533 31.100 13.442 8.222 10.513 48.765 18.350 29.914 126.126 31.642 63.173 8.071 3.919 5.624 38.550 11.909 21.426 101.058 18.996 43.815 6.807 2.994 4.515 30.755 7.495 15.183 76.477 8.715 25.817 6.735 2.943 4.452 33.488 8.982 17.344 99.665 18.350 42.765 8.471 4.221 5.980 26.778 5.470 12.103 69.739 6.392 21.1 14 6.426 2.725 4.184 30.447 7.332 14.942 85.402 12.151 32.213 6.544 2.808 4.286 54.834 2.283 1 1.189 31.897 8.108 16.082 89.389 13.803 35.125 10.138 5.517 7.479 41.782 13.877 24.079 103.875 20.323 45.946 7.835 3.744 5.416 28.981 6.570 13.799 77.046 8.923 26.220 1.996 3.853 2.403 5.230 2.369 3.439 4.782 2.080 3.788 5.178 2.248 2.727 3.860 2.097 4.588 3.409 4.263 1 .768 2.91 1 4.504 2.295 3.629 5.338 1 .962 3.318 4.864 1 .869 3.051 4.338 1 .864 3.148 4.836 1 .990 2.901 4.179 1.839 3.040 4.538 1 .849 3.799 3.092 4.623 2. 100 3.420 4.920 1 .946 2.985 4.351 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 235 236 237 238 258 259 260 66 90 117 118 172 204 205 206 2.220 4.377 7.029 2.039 4.405 7.493 3.091 5.61 1 8.689 2.813 6.705 1 1.954 2.642 5.713 9.413 2.693 5.337 10.266 2.943 5.360 9.366 4.344 10.503 7.818 1 1.731 3.226 5.1 14 8.810 2.400 4.975 8.101 4.192 2.368 4.326 8.291 1.904 4.224 7.688 3.476 5.657 9.255 2.090 4.980 3.699 8.1 14 3.560 7.563 14.347 1.312 1.481 1.107 1.1 17 1.51 1 1.606 2.249 2.808 2.892 1.950 3.984 6.403 1.765 2.917 3.670 1.820 2.513 4.588 2.089 2.538 3.620 3.596 4.842 5.181 6.164 2.394 2.274 3.022 1.506 2.124 2.259 1 .282 1 .471 1.426 2.463 0.972 1.317 1.815 2.663 2.857 3.501 1 .172 2.129 2.902 2.274 2.753 4.907 8.976 153 TABLE B.8 (cont'd) 4.926 1.720 2.91 1 19.160 2.194 6.483 49.413 1.226 7.782 4.156 1.248 2.277 19.404 2.283 6.656 56.147 2.578 12.032 9.556 5.058 6.953 31.479 7.882 15.752 75.507 8.366 25.133 7.913 3.802 5.485 44.957 15.876 26.716 142.897 40.999 76.542 6.978 3.116 4.663 32.635 8.51 1 16.665 88.602 13.471 34.548 7.250 3.313 4.901 28.484 6.317 13.414 105.392 21.049 47.099 8.661 4.366 6.149 28.732 6.443 13.606 87.731 13.107 33.911 18.868 12.931 15.620 1 10.304 23.447 50.855 61.1 19 26.846 40.507 137.626 37.991 72.309 10.406 5.730 7.721 26.158 5.171 11.630 77.617 9.133 26.624 5.762 2.268 3.615 24.754 4.513 10.570 65.619 5.103 18.299 17.571 1.643 5.372 5.607 2.164 3.483 18.716 2.034 6.170 68.736 6.069 20.424 3.626 0.946 1.852 17.844 1.733 5.561 59.104 3.295 13.955 12.084 7.091 9.257 32.002 8.165 16.165 85.659 12.255 32.400 4.367 1.373 2.449 24.801 4.534 10.604 13.681 8.423 10.735 65.845 5.171 18.452 12.671 7.577 9.799 57.197 24.079 37.111 205.827 80.573 128.780 1.712 2.581 3.648 1.640 2.592 3.834 2.063 3.077 4.316 1.951 3.517 5.629 1.882 3.1 18 4.607 1.903 2.967 4.950 2.003 2.976 4.588 2.567 5.045 3.965 5.540 2.1 17 2.877 4.364 1.785 2.821 4.079 2.506 1.772 2.560 4.155 1.586 2.519 3.913 2.218 3.096 4.543 1.660 2.823 2.308 4.084 2.252 3.862 6.592 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 119 173 202 203 207 239 233 84 85 2.303 4.934 8.689 3.337 6.427 10.484 3.036 5.291 8.374 2.108 4.094 7.131 3.467 6.914 10.860 3.750 6.900 10.303 3.198 6.404 1 1.847 5.481 3.147 7.303 10.957 3.448 6.816 10.280 1367.62 216 6.332 0.405 0.663 1.401 2.079 2.892 2.513 3.685 4.822 2.189 2.463 2.553 1.192 1.177 1.217 2.653 4.209 5.226 2.957 4.194 4.628 2.364 3.660 6.288 2.668 2.309 4.628 5.331 2.633 4.104 4.603 697.00 216 3.227 154 TABLE B.8 (cont'd) 5.304 1.964 3.227 24.341 4.324 10.260 75.507 8.366 25.133 11.136 6.317 8.387 41.303 13.581 23.684 109.915 23.254 50.557 9.215 4.793 6.646 27.992 6.069 13.034 70.127 6.519 21.381 4.445 1.421 2.513 16.764 1.385 4.819 50.857 1.481 8.677 12.019 7.038 9.198 47.799 17.715 29.099 1 17.931 27.313 56.754 14.061 8.745 11.089 47.607 17.589 28.937 106.156 21.416 47.681 10.227 5.587 7.559 41.006 13.398 23.439 140.359 39.544 74.500 30.039 7.1 18 14.623 9.903 5.331 7.266 53.336 21.416 33.797 120.056 28.418 58.411 1 1.891 6.933 9.080 46.462 16.844 27.975 105.678 21.186 47.317 10548.4 2740.44 5178.02 216 216 48.835 12.687 1.746 2.804 4.316 2.162 3.405 5.038 2.041 2.948 4.189 1.668 2.467 3.689 2.214 3.601 5.189 2.328 3.596 4.965 2.106 3.396 5.586 3.025 2.086 3.758 5.228 2.207 3.562 4.956 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 21.918 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 0.819 LIST 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