CONSTITUTIVE MODEL FOR CYCLIC BEHAVIOR OF CLAYS. II: APPLICATIONS By C. S. Desai, 1 Fellow, ASCE, G. W. Wathugala, z Associate Member, ASCE, and H. Matlock,s Fellow, ASCE ABSTRACT: Development and validation of the hierarchical single surface g; model for cohesive soils are described in a companion paper, part I. The present paper, part II, first describest he details of the simulationa nd verificationo f various stages in the field behavior of piles, e.g. in situ stresses, driving, consolidation, tension tests, and the final cyclic loadings. Undisturbed samples were obtained for testing of cylindricala nd cubical specimens, the latter involved design and fabri- cation of a square, 13 x 13 x 13 cm (5 x 5 x 5 in.) sampler. Field measurements were obtained in terms of stresses, strains, and pore-water pressures for various stages. The constitutive model (part I) is introduced in a general finite-element (FE) procedure that allows dynamic analysis of porous soil media. The FE pro- cedure is used to back-predict the field behavior. It is found that the numerical procedure provides very good predictionso f the measured responses. It is felt that the proposed unified (parts I and II) procedure can provide an excellent tool for a wide range of dynamic soil-structurei nteraction problems. INTRODUCTION The traditional approach to solving most geotechnical engineering prob- lems tends toward empirical design techniques. These methods are based on years of experience with particular materials and types of loadings, and work well within those limited conditions. However, these empirical meth- ods may not perform well under new materials and loading conditions en- countered in problems such as offshore structures. In contrast, if there is a general approach based on the proper characterization of material properties and the governing equations, it would be applicable to a wide range of situations. The present study is aimed at improving our understanding of the behavior of geological materials and to develop a general approach for solving geotechnical engineering problems through dynamic finite-element analysis of nonlinear porous media. Here, saturated soil is considered to be a mixture of soil particles and water. Material behavior of the soil skeleton is modeled using a plasticity- based constitutive model. It is also assumed that water seeps through pores according to generalized Darcy's law. The theory of dynamics of porous media, pioneered by Biot (1941), is used to characterize the soil-water mixture. The finite-element method is used to develop the numerical so- lution procedure based on the governing differential equations. The pro- posed procedure is verified by back-predicting laboratory and field tests. ~Regents' Prof., Dept. of Civ. Engrg. and Engrg. Mech., Univ. of Arizona, Tuc- son, AZ 85721. 2Asst. Prof., Dept. of Civ. Engrg., Louisiana State Univ., Baton Rouge, LA 70803-05. 3Consultant, HCR 5, Box 574-655, KerrviUe, TX 78028. Note. Discussion open until September 1, 1993. Separate discussions should be submitted for the individual papers in this symposium. To extend the closing date one month, a written request must be filed with the ASCE Manager of Journals. The manuscript for this paper was submitted for review and possible publication on August 8, 1991. This paper is part of the Journal of Geotechnical Engineering, Vol. 119, No. 4, April, 1993. 9 ISSN 0733-9410/93/0004-0730/$1.00 + $.15 per page. Paper No. 2411. 730 NUMERICAL PROCEDURE The constitutive model ~ for cohesive soils and the incremental form of the constitutive equations are given in part I (Wathugala and Desai 1993). These equations are introduced in the finite-element procedure, which is based on the generalized nonlinear form of Biot's equations (Biot 1941, 1962; Sandhu 1976; Zienkiewicz and Shiomi 1984; Prevost 1980; Ghaboussi and Wilson 1972; Desai and Galagoda 19) and details can be found in Wathugala (1990). Only brief details of the special drift correction scheme for the implementation of the proposed constitutive model are presented here. Drift Correction Scheme With advanced plasticity-based constitutive models for highly nonlinear problems, it is essential that the solution scheme be reliable and consistent. Since the constitutive model subroutine, which calculates stresses for given strain increments, is called thousands of times, it should be numerically efficient. A procedure that is robust, reliable, and efficient was developed and used in the present study. Some of the main features are given below and more details are available elsewhere (Wathugala 1990; Desai et al. 1990). For an incremental loading, the yield surface moves from F(cr ~ a~ = 0 to F(~7/, C~s) = 0, where c denotes the correct final position of F. Here, %s is the hardening parameter. At the correct yield surface, the following general relationships should be satisfied: crTj -- ~o + C~l degl ........................................ %s = .f~({7) ................................................ (la) (lb) (lc) (ld) {7 = {7 + f~(de~}) ........................................... de~j = deTj + de~ ........................................... and = 0 ............................................. (le) Here, f~ = %, as a function of {i, which are different trajectories of plastic strains such as {, {D, and {~; and the function f~ relates incremental plastic strains to incremental strain trajectories. The converged material state defined by ~7j and ~, is found in two stages using a predictor corrector algorithm. The intermediate state I is obtained by ~,5 = ~o + C,j~, d4, ......................................... (2) Various methods are possible to calculate the predictor stress a~5 in (2). For instance, in the elastic predictor plastic corrector method (Ortiz and Simo 1986), the elastic constitutive tensor CTjkl is used in (2), and in the plastic- predictor plastic-corrector method (Potts and Gens 1985), the elastoplastic matrix CTj~I is used in (2). It was found that both methods lead to similar results for the case of small increments. However, special procedures are necessary for large strain increments, so as to obtain convergent, accurate, and stable solutions (Wathugala 1990; Desai et al. 1990). After some al- gebraic manipulations, and neglecting higher-order terms, ~Tj can be ob- tained as 731 = + F(~r~,~ t[os)o , OC ~ij ktn kOOtps ................... (3a) OF zf(n~) -- C~O.m\"'~n OF l e Q C mnopH op oQ O~r~ ........................................ (3b) and Q = potential function. In the present study, the associative model, ~ is used and therefore the yield function Fis used as the potential function; i.e. Q --- F. Since higher-order terms have been neglected in (3), the result- ing F(cr~, @,) will not be equal to zero. Therefore, this material state (~r~; a~,) can be considered as another intermediate state. Then (3) is reap- plied until F(~r~, c~) = 0. Iterative procedure used here is schematically shown in Fig. 1. It is noted here that both ~ru and ecp~ are modified simul- taneously, so that the yield surface and the stress point move towards each other until they meet (converge). Details of the numerical analysis for the algorithm and for dealing with various situations such as J( < 0; J~ < 0; F(cr,~, @,) < 0; and F(o-~, @~)< 0 are given elsewhere (Wathugala 1990). FIELD TESTING One of the unique aspects of the present study is the integration of field testing and verification with theoretical constitutive modeling and labora- tory testing. Field testing was performed by the Earth Technology Corpo- ration at a site near Sabine Pass, Tex. (\"Pile\" 1986). The location of the test site is shown in Fig. 2. The field testing program included: (1) Collec- tion of undisturbed samples; (2) installation of instrumented pile segments with different diameters and cutting shoes; (3) monitoring consolidation; (4) performing axial tension tests at different levels of consolidation; and (5) performing cyclic axial load tests at the end of consolidation. The pile segments were instrumented so as to measure total lateral earth pressure Predict~ ~7 ~ rrector \"7\"o ci- o o o =; 0.0 2 .0 ; 5 .0 ; 75.0 10.0.0. 1.25..0 150.0 175.0 2 o' 0.0 22.5.0 .250.0. 27.5.0 3 00.0 325.0 ,350.0 d~ FIG. 1. Schematic for Iteration Procedure 732 Port Neches / Groves 9., ,----- F a nnett f Port / 0 TEXAS LOUISIANA ] 0 L 5 I ;abine River Sabine Pass h >ig hthouse Km 0 2 Miles Test \" Jetty Gulf of Mexico FiG. 2. Location of Sabine Pass Test Site Road and pore pressures at the pile wall and shear transfer versus pile displace- ment. Undisturbed Sampling and Laboratory Testing Over the years, a considerable number of laboratory and field pile load tests, both axial and lateral have been performed on the Sabine clay (Matlock and Tucker 1961; Matlock and Bogard 1973, 1975; Matlock and Holmquist 1976; Bogard and Matlock 1979; Grosch and Reese 1980; and \"Pile\" 1986). However, no cylindrical triaxial or multiaxia' (cubical) tests with pore-pressure measurements for the Sabine clay are reported in the literature. Therefore, a comprehensive laboratory testing program for the Sabine clay was planned (Katti 1991) so as to define the required constitutive parameters as discussed in part I (Wathugala and Desai 1993). To establish the soil profile, a borehole was drilled with continuous sam- pling using 7.6 cm (3 in.) diameter shelby tubes, up to a depth of 18 m (60 ft). It was found that the uniform layer of clay in which the instrumented pile segments were to be installed lies below 15 m (50 ft). Several boreholes 733 were drilled into the clay layer and undisturbed samples of 7.6 cm (3 in.) diameter cylindrical and 12.7 cm2 x 12.7 cm 2 (5 in. 2 x 5 in.:) square were obtained. The latter involved design and use of a special sampler to obtain square samples for laboratory testing with cubical 10x 10 x 10 cm (4 x 4 x 4 in.) samples. All the samples were waxed on the site to avoid moisture loss and were carefully transported to the constitutive modeling laboratory, University of Arizona, Tucson, Ariz., in specially designed casings to min- imize sample disturbance. Sample tubes were stored in a moisture room until they were extracted for laboratory testing. Tests for basic index prop- erties for the soil were conducted by the Earth Technology Corporation (\"Pile\" 1986) and advanced triaxial tests were performed at the University of Arizona (Katti 1991), Installation of Pile Segments The instrumented pile segments involved 7.6 cm (3 in.) probe and a 4.4 cm (1.72 in.) X-probe. Boreholes of 15.2 cm (6.0 in.) diameter were driven to the top of the uniform clay layer, which is of about 3.0-3.7 m (10-12 ft) thickness and occurs at a depth of about 15.3 m (50 ft). The boreholes were cased using PVC pipes. The probe and the N-rod string were lowered into the borehole until they are supported by the soil. Then the probe was driven into the clay until the whole probe was inside the clay. The 7.6 cm (3 in.) probe was driven using a 300-1b (1.338 kN) casing hammer, with a drop of 0.914 m (3 ft) on each blow. The X-probe [44 mm (1.72 in.) pile] was installed by pushing. There is a slip joint located between the body of the pile segment and the cutting shoe. The body of a direct current linear voltage displacement transducer (DC-LVDT) is mounted in the body of the pile segment and the core of the LVDT is attached to the cutting shoe. When the pile segment is driven, both the cutting shoe and the pile segment move together, but during subsequent load tests, only the pile segment moves due to the pres- ence of the slip joint. The DC-LVDT is used to measure the relative move- ment between the pile segment and the cutting shoe. In this case, the cutting shoe acts as the reference anchor [Fig. 3(a and b)], which does not move relative to the surrounding soil. Thus, accurate displacement measurements of the pile segment could be obtained. Under the present National Science Foundation (NSF) project, the Earth Technology Corp. performed three field tests with the X-probe and 7.6 cm (3 in.) probe: full displacement (blunt cutting shoe) 7.6 cm (3 in.) and X- probe, and partial displacement 7.6 cm (3 in.) pile with 3.175 mm (0.125 in.) thick cutting shoe. The test with the 3.175 mm (0.125 in.) cutting shoe developed some water leaks during the test and therefore is not used here. Tension tests at different consolidation levels were also carried out to investigate the increase in the pile capacity during consolidation. For both probes, two-way cyclic load tests were carried out near the end of consol- idation. SIMULATION OF FIELD TESTS General Both full-displacement tests with 7.6 cm (3 in.) and 4.4 cm (1.72 in.) pile probes were simulated numerically using the finite-element procedure, Here, the Sabine clay is modeled using the g~ model (Wathugala and Desai 1993). Material parameters for the soil skeleton are as follows: (1) The elasticity 734 3.s Pite (a) Segr~ent .,~..~~ I \\ DlaMeCer 0.044~ (1.72 In 15,; Anchor / L 7m5, Pile Segment~ T.~. (b) 8., 225 Nodes 192 Eter~ents Anchor~/ 225 Nodes 192 Elements FIG. 3. Finite-Element Mesh for Analysis: (a) 4.4 cm (1.72 in.) Pile Segment; (b) 7.6 cm (3 in.) Pile Segment (1 in. = 2,54 cm) parameters are Young's modulus = 11,777 kPa, and Poisson's ratio = 0.42; (2) the basic plasticity parameters are ~/ = 0.0476, 13 = 0, m = -0.5, and n = 2.4; (3) the hardening parameters are hi = 0.0034, h2 = 0.78, h3 = 0, and h 4 = not applicable (NA); (4) the interpolation parameters are rl = 500, and 1\"2 = 2.4; (5) permeability = 2.39 x 10 -1~ m/s; and (6) 735 porosity = 0.66. The material parameters for soil grains are as follows: (1) Density p, = 2.65 Mg/m3; and (2) bulk modulus Ks = 10 ~5 kPa. The material parameters for water are as follows: (1) Density Ps = 1 Mg/m3; and (2) bulk modulus Ks = 1011 kPa. Since shear deformations in saturated clays are almost volume conserved, shear locking was observed when eight node elements with four Gauss integration points are used. Therefore, as sug- gested by Nagtegaal et al. (1974), four node elements with one Gauss in- tegration point were used for both solid and fluid in all the finite-element analyses herein. The test series was simulated in stages starting from in situ conditions to cyclic loadings, as shown in Fig. 4. Here, each stage uses the results in terms of stresses, strains, pore-water pressures, and hardening parameters of the previous stage as the initial conditions. Initial Conditions before Pile Driving Before starting to simulate the process of pile driving, it is necessary to define the in situ conditions in the soil before pile driving. As is done in most geotechnical engineering problems where the water table is at the surface, it is assumed that in situ stresses and pore pressures are given by o'~ = %h = ................................................... ................................................. (4) (5) p = ,,/~ ................................................... (6) where (r~ and cr~ = effective vertical and horizontal stresses at the depth h below the surface, respectively; % = submerged unit weight of soil; ~/w = unit weight of water; p = pore-water pressure; and K0 = coefficient of earth pressure at rest. The value of Ko may be estimated using the empirical Jaky's formula for normally consolidated clays (Jaky 1944). A self-boring InitialC onditionsB eforeP ileD riving t Consolidation t I LoadT ests ] Consolidation LoadT ests ] FinalC yclicL oading FIG. 4. Schematic of Different Stages in Simulation 736 ~r pressuremeter test (PAM) was performed by the Institut Fran~ais du P6trole, France, in September 1985 at the Sabine Pass test site. However, due to the presence of a clay layer with many shell fragments, the test had to be stopped at a depth of 10 m (32.8 ft). The K0 value deduced from these tests agreed with the value calculated from the Jaky's formula. All the in situ stresses and pore-water pressures at any point in the soil can be cal- culated using (4)-(6). To determine the initial hardening parameters, it was assumed that this stress state is reached through a proportional stress path from zero stress state. Simulation of Pile Driving When a pile is driven into soil, the soil around and below is pushed away to accommodate the pile. Here, the pile segments were driven at the bottom of the borehole, and it is assumed that only the soil below the bottom level of the borehole is affected. The strain-path method (SPM) is used to simulate the effects of pile driving for both pile segments. Details of the SPM are given elsewhere (Baligh 1985; Teh and Houlsby 19; Wathugala and Desai 1990) and are not repeated here. For the finite-element analysis of the subsequent consolidation phase, stresses, pore pressures, and hardening parameters at all the Gauss points are required as input parameters. The finite-element meshes used for con- solidation and load tests for the X-probe and the 7.6 cm (3 in.) pile segment are shown in Fig. 3(a and b), respectively. Strain paths followed by all the Gauss points below the bottom of the borehole during the pile-driving process are computed using the strain-path method. The strain path followed by a Gauss point near the middle of the pile segment is illustrated in Fig. 5. Here, Z is the distance between the tip of the pile segment and the soil element. It may also be defined as the Z coordinate of the soil element if the coordinate system is fixed to the tip of the pile segment. R is the radius of the pile segment. According to Fig. 5, severe straining occurs when the pile segment passes the soil element. Even though some strain components increase and decrease during the pile-driving process, the second invariant of the deviatoric strain tensor ~ monotonically increases throughout the whole process. Stress history corresponding to this strain path can be ob- tained by integrating the constitutive equations developed in part I (Wa- ................. ~rr rz E \"~12D :6.0 -~o -,i.o '~-'-~~i'~o I'\"-~ I z/R .... 2.0 j ...... 3.0 P--- 4.0 i i ...... i-\" 5.0 6.0 \\ / FIG. 5. Variation of Strain (Strain Path) for Point near Pile during Pile Driving 737 thugala and Desai (1993). Variation of the effective stress components and invariants (tr~, (r/00, (r~, \"r=, X/~2D, and J~) in the soil element due to pile penetration as computed by using the constitutive model are illustrated in Fig. 6. It is observed here that J( and X/)-~2o remain essentially constant while the individual stress components are changing for z/R > -6. The effective stress path followed by the same soil element is shown in Fig. 7, which shows that soil reaches the critical state and remains there during the later part of the penetration process. This observation is compatible with that of Kirby (1977); Carter et al9 (1978) and others9 The distribution of effective stresses at a depth of 16 m (52.5 ft) with the distance from the pile r is shown in Fig. 8. As expected, most changes to the effective stresses from the initial stress distribution (K0 condition) have occurred near the pile. The SPM assumes inviscid flow to obtain an analytical solution for strain paths. This has the implicit assumption of a smooth pile. This can be the reason for the drop in ,r~ near the pile in Fig. 8. r o o o J'l ~_o_ d . O'rr' 0\" / %,, .............. ~ J O==' ...................... -3~.o-~o.o-2~.o-2b.o-~.o-;o.o-s.o~ %Z.J o 5.0 ;o.o ;5.0 2;.o 2~.o ~.o 3~,.o Z/R FIG. 6. Variation for Stresses at Point near Pile during Pile Driving Colculotated Effective Stress Path During Pile Driving Yield Surface at the End of Pile Driving Cdticol State Line .-\"\" o ..-\"\" .-'\" 4 ~ o ............i. ...... 2~..0 .......... J1, kPo o O.0 5~.o 75.0 ;o'o.o ;='s.o 4.0 ,;s.o =~o.o =35.0 =50.0 =~5.o FIG. 7. Stress Path for Soil Element near Pile during Pile Driving 738 G~t' q ...\" do C,\") ~ U ,.~o .-. o .* r \"t'rI ' ~.. ..... .=, 000 0:2s 0:50 0'.75 ,.'00 r. meters ,:25 ,:50 ,:75 2:00 2:25 2:50 FIG. 8. Distribution of Effective Stresses at 16 m below Ground Surface after Pile Driving as Computed from Strain-Path Method q oo i~.Grr nO ~ field observotion ........ Cr,r ................ O'zl o.. P= o ~~ J, 0.00 0.25 1 ~'p ........ *\"\"\" 0.50 i 0.75 i 1.00 i 1.25 1.50 r, meters i J 1.75 i 2.00 ~ 2.25 i 2.50 i FIG. 9. Total Stress Distribution at 16 m below Ground Level Just after Pile Driving as Computed from Finite-Element Procedure That total stress distribution is in equilibrium is used to calculate the total stress and pore-pressure distribution from the computed effective stress distribution as follows. The stresses obtained from SPM are input to the finite-element program as initial stresses. Then the unbalanced load created by these stresses is balanced iteratively using the Newton-Raphson iterations under undrained conditions. This process modifies the assumed displace- ment field until constitutive equations and equilibrium equations are sat- isfied. Computed total and effective stresses and pore-water pressures at 16 m (52.5 ft) below ground are plotted in Figs. 9, 10, and 11, respectively. It can be seen that the drop in \"rrz near the pile computed from the SPM method (Fig. 8) has been corrected during the present Newton-Raphson iterations (Fig. 10). In these results, very small changes in effective stress are observed at locations other than those near the pile. The field measurements of total stress (r,r and pore pressure at the end 739 q m ....\" 9> -~_,O . A = On 9~ ------- ,1----.- o. + ~ + o.oo o:25 &o o:Ts i 1.00 i 1.25 i 1.50 1.'75 r, meters 2.'oo s 2150 FIG. 10. Effective Stress Distributions at 16 m below Ground Level Just after Pile Driving as Computed from Finite-Element Procedure q #_,~l t Computed distribution g_; ~g. q o. oo. o.oo oi2s o15o o'.Ts 1.bo r, meters 1:25 I.'5o 1:7~ s s 2:so FIG. 11. Pore Pressure Distribution at 16 m below Ground Level Just after Pile Driving as Computed from Finite-Element Procedure of the pile driving for the X-probe are also plotted in Figs. 9 and 11, respectively. It is observed here that the strain path method (SPM) under- predicted the excess pore pressures by a factor of 0.3 for the X-probe. Similar results were obtained for the 7.6 cm (3 in.) pile segment. Levadoux and Baligh (1980) also reported that SPM underpredicts the excess pore pressure by a factor of 0.5 for cone penetration in soft clays. Consolidation after Pile Driving Equilibrated pore pressures and stresses calculated from the preceding are input as the initial condition for the consolidation phase. The consoli- dation process is simulated until all the excess pore pressures are dissipated. Typical predicted pore-pressure dissipation curves are compared with field measurements by plotting the normalized excess pore pressures with the logarithmic time in Fig. 12 for the 4.4 cm (1.72 in.) pile. Predicted and field 740 8, n w a. d . x~~ o='\"~ \"o .......... Prediction ., .,%....,....~ 0 Z o.o ;.o ~.o ~.o Lo ~.o d.o 7.0 d.o ~.o ,;.o I;.o ,~.o ,~.o Ln (Time,s ee) FIG. 12. Comparison Between Field and Computed Consolidation Behavior at Point near Middle of 44 mm (1.72 in.) Pile Segment qN o i ~ ~-'e~o - \\~:: __ 1see 110s ee .......... 3110 see .... 30593 see .................... _ 124309 see O0 ~- ~ \" \"--~--~. ~._~ _ ~\" ~ .................. o.oo 0:=5 o'.~o 055 1:oo r, meters ,:2s ,~o ,35 2:00 ='.2s s FIG. 13. Pore-Pressure Distribution at Different Times during Consolidation at 16 m below Ground Level Using 44 mm (1.72 in.) Pile Segment consolidation curves have a similar shape, but the predicted curve shows faster initial dissipation. The predicted results for pore-pressure distribution with the distance from the pile during consolidation are plotted in Fig. 13. There are no field measurements to compare these results with. However, the shape of these distributions are similar to that predicted by other meth- ods (Carter et al. 1977). The effective stress path followed by a soil element near the middle of the pile and the initial yield surface are plotted in Fig. 14, which shows virgin loading during consolidation. Simulation of Load Tests just before Final Cyclic Load Test Earth Technology Corporation (\"Pile\" 1986) reported that the load tests performed at the initial stages of consolidation did not significantly affect the consolidation curve, and therefore, those tests are not simulated here. 741 ~. Effective Stress Path During Consolidotion .......... Yield Surfoce at the End of Pile Drivin9 ,-\" .- '~ ~ .5.\" ,. ......ii.i.i.ii. . 2~.o r~.o ~.o ,o'o.o ,~'5.o 1~'o.o fA.o zdo.o 2~.o zs'o.o 27's.o Jl, kPo o.o FIG. 14. Effective Stress Path during Consolidation Process for Point near Middle of 44 mm (1.72 in.) Pile Segment However, the load tests performed just before the final cyclic load test should affect those tests and therefore are simulated here. Three load tests were performed on the X-probe just before the final cyclic load test. Typical predicted responses for one of the tests is compared with field behavior in Fig. 15(a, b, and c) for the shear transfer versus pile displacements, shear transfer versus time, and pore pressure versus time, respectively. Approximate shear stresses at the pile soil interface were determined by multiplying the shear stress at the Gauss point closest to the stress transducers by (rJrp), where rg is the r coordinate at the Gauss point and rp is the pile radius (Wathugala and Desai 19). The predicted and observed responses (Fig. 15) compare well. Simulation of Final Two-Way Cyclic Load Tests Two-way cyclic load tests were performed with both pile segments. They are simulated using the finite-element procedure and are compared with field measurements in this section. X-Probe Five loading unloading cycles were performed in this test. The pile was failed before reversing the direction in all the cycles. Predicted results are compared with field measurements in Fig. 16. The predicted shear transfer versus pile displacements [Fig. 16(a)] show good agreement with field mea- surements. The predicted shear transfer versus time [Fig. 16(b)], shows very good agreement with field measurements. Fig. 16(c) compares predicted variation of pore pressures with time with field measurements. Though all peak magnitudes are not predicted well, their locations indicated by small- sized peaks are predicted satisfactorily. Also the accumulation of pore pres- sures, indicated by a small increase with time, is predicted well. In practical applications, the accumulation of pore pressures is often more important than the exact shape of the pore-pressure variation during a cycle. Total horizontal stresses did not change significantly during the cyclic load test, 742 0 0bservotions .......... Prediction .... F~,d ~~/.., ....-..~ . ..\". /5. ....... .,.\" e,,, U3 ,.o o. o. I o o 2.o 4.0 //y (=) Co) ~.o ~ ~j~~\" =.o ..o ~.o .10-' o no ~ ~~ I 1.0 100.0 200.~.0Ti40~;s~d~00.0 S00.0:900.0 q o .............. .. .........: ....:::....:..~ ,.. ................... i 600.0 i 700.0 i 800.0 Observotions .......... Prediction Field 0.0 i 100.0 i 200.0 i 300.0 Time, seconds i 4.00.0 i 500.0 = 900.0 (e) FIG. 15. Comparison of Predicted and Measured Response for Tension Test on 44 mm (1.72 in.) Pile Segment: (a) Shear Transfer versus Pile Displacement; (b) Shear Transfer versus Time; (c) Pore Pressure versus Time the predicted values also show similar trend in Fig. 16(d). Field variation of effective horizontal stresses was calculated by subtracting measured pore pressures from the measured total horizontal stresses. They are compared with predicted values in Fig. t6(e). Although the trends are predicted well, the magnitudes are not. 743 o ] .. ~ ..-;-~ -'=,-~../~N .-:.'~ :7-\" _= \" ,l/ .... ! __ Field 0bservotlons .......... Prediction ., i ......... ~:_!, ~\" -~;o0 '= -,'.-~'oloo (,q a ~: 0 Lf ,.~o c,Y ~.'oo ~'~j~#/ ,o'.oo ..:~ ..~ 12'.50 o10-' o] lal ('0) ~ o. # .. . o.o ~ 6 o.o ,~ , : i~ .oo.o ~ boo.ol / [~2oo.o e \"secon 03 :,. F . ~ 0,0 200.0 400.0 600.0 800.0 Time, seconds 1000.0 , I200.0 n~ a .......... FieT{J Observotions Prediction (d) \"d o. C~ ~176 o 0,0 200.0 .................................... \"E o 400.0 600.0 800.0 1000.0 1200.0 ~o\" ~Time in seconds ~or ~ O o (~0.0 \"~ Time, seconds ....... ......... .......... FIG. 16. Comparison of Predicted and Measured Response for Cyclic Load Test on 44 mm (1.72 in.) Pile Segment: (a) Shear Transfer versus Pile Displacement; (b) Shear Transfer versus Time; (c) Pore Pressure versus Time; (d) Total Horizontal Stress versus Time; (e) Effective Horizontal Stress versus Time 744 q o ........... _ Field Observotlons Prediction 1J/,5 //~'/.:-j:>\" ::/ 9. \";\" ~ q Displocements,'m.,.\" /'// ,10-' ~'~ ~ c;. ...{.--V' . 9 . a)q ~ o ~/ (,o \"... \"'.. \"\".. \"\".. \"\"~ o ~'\" ~o to'of Time, se'~nds ~ ~ oo -~]~ ................................................... (c) -~176 0.0 ~o ~c5 500.0 1000.0 !500.0 2000.0 2500.0 ii3000.0 Time, seconds Field Observotions .........P. rediction (d) ~., ~ 0.0 So 0.0 sdo.o 1oGoo 156o.o 2o~oo 2sGoo sobo.o Time in seconds (e) o ~ Oo] '. ......... 1000.0 ~500.0 1500.0 F2000.0 2500.0 3000.0 Time, seconds m., FIG. 17. Comparison of Predicted and Measured Response for Cyclic Load Test on 7.6 r (3 in.) Pile Segment: (a) Shear Transfer versus Pile Displacement; (b) Shear Transfer versus Time; (c) Pore Pressure versus Time; (d) Total Horizontal Stress versus Time; (e) Effective Horizontal Stress versus Time 745 Z6 cm (3 in.) Probe Five cycles of loading and unloading in compression and extension were also performed on the 7.6 cm (3 in.) probe. Results from the finite-element simulation are compared with field measurements in Fig. 17(a, b, c, d, and e). Predicted values of shear transfer versus pile displacements are compared in Fig. 17(a). Here the cycles except the first cycle show good agreement with field behavior. For all the cycles, the predicted failure load was less than the measured value. Fig. 17(b) shows the predicted variation of shear transfer with time and compares well with field measurements. Fig. 17(c) compares the predicted variation of pore pressure with time, which also compares well with field measurements. Even though the initial predicted values were higher than the measured values, they became closer after few cycles of loading. Total horizontal stresses did not change much during the cyclic load tests, and predictions agreed very well with field measurements [Fig. 17(d)]. Effective horizontal stresses did not compare well at the be- ginning of the test, but became close at the end of the test. From these results it may be anticipated that the finite-element method used would provide good predictions for cyclic load tests with many cycles. COMMENTS All the stages of field tests on both 7.6 cm (3 in.) and 4.4 cm (1.72 in.) (X-probe) pile segments were simulated and results are compared herein. Even though the predicted pore pressures due to pile driving were less than the measured values, the final load tests on the pile are predicted well by the model. It should be noted here that an important parameter for the design of piles is its final load capacity, which can be easily calculated from the shear transfer values. Since shear transfer was predicted well, pile ca- pacity also can be predicted well with this method. CONCLUSIONS This study (parts I and II) is an example of a general approach to solving geotechnical engineering problems. For the dynamic soil-structure inter- action problems, the proposed method consist of: (1) Realistic constitutive modeling; (2) laboratory verification; (3) dynamics of nonlinear porous media; (4) finite-element method; (5) efficient algorithms for implemen- tation of constitutive models in nonlinear finite-element procedures; and (6) numerically simulating the complete field behavior starting from the in situ stresses. 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