Numerical Methods in Soil Mechanics 29.PDF Numerical Methods in Geotechnical Engineering contains the proceedings of the 8th European Conference on Numerical Methods in Geotechnical Engineering (NUMGE 2014, Delft, The Netherlands, 18-20 June 2014). It is the eighth in a series of conferences organised by the European Regional Technical Committee ERTC7 under the auspices of the International Society for Soil Mechanics and Geotechnical Engineering (ISSMGE). The first conference was held in 1986 in Stuttgart, Germany and the series has continued every four years (Santander, Spain 1990; Manchester, United Kingdom 1994; Udine, Italy 1998; Paris, France 2002; Graz, Austria 2006; Trondheim, Norway 2010). Numerical Methods in Geotechnical Engineering presents the latest developments relating to the use of numerical methods in geotechnical engineering, including scientific achievements, innovations and engineering applications related to, or employing, numerical methods. Topics include: constitutive modelling, parameter determination in field and laboratory tests, finite element related numerical methods, other numerical methods, probabilistic methods and neural networks, ground improvement and reinforcement, dams, embankments and slopes, shallow and deep foundations, excavations and retaining walls, tunnels, infrastructure, groundwater flow, thermal and coupled analysis, dynamic applications, offshore applications and cyclic loading models. The book is aimed at academics, researchers and practitioners in geotechnical engineering and geomechanics.
Anderson, Loren Runar et al "APPLICATION OF FINITE ELEMENT ANALYSIS TO A BURIED PIPE" Structural Mechanics of Buried Pipes Boca Raton: CRC Press LLC,2000 CHAPTER 29 APPLICATION OF FINITE ELEMENT ANALYSIS TO A BURIED PIPE Introduction As discussed in Chapter 28, the finite-element analysis of buried flexible pipes requires capabilities generally not included in most finite-element analysis applications Many types of buried pipes (such as fiberglas-reinforced plastic pipe) are very flexible, thus, requiring a finite-element analysis of the system to accommodate large deflections The sensitivity of the pipe and the soil properties to compaction loading may be an important consideration The stress history of each soil element should be monitored at each loading increment to determine whether the element is in a state of primary loading, unloading or reloading, and then appropriate parameters need to be used for each increment of the analysis Properly accounting for all elements of the soil structure system makes the finite-element method a useful tool for the analysis of buried flexible pipes when subjected to various installation conditions, backfill material types, surcharge loadings, and internal pressurization This chapter illustrates the application of the finiteelement method to the solution of a soil structure interaction problem The response as computed by a finite-element analysis (FEA) of a buried flexible fiberglas-reinforced plastic (FRP) pipe, when subjected to various installation and static loading conditions, was compared with measured strains and deflections taken from physical tests in a soil box at the Buried Structures Laboratory at Utah State University, Sharp et al (1985) The FEA modeled the actual soil box installation conditions The approach that was taken in the study was to simulate the backfill and loading conditions that had been used in the soil-box tests in order to compare the predicted response of the pipe from FEA results with the measured response This required that the ©2000 CRC Press LLC four soils that were used in the soil box be tested for engineering properties, including triaxial testing at several densities for evaluation of the hyperbolic parameters for the Duncan soil model Results from the tests are described by Sharp et al (1984) In the following discussion, only the results of the applications of the finite-element program to the installation conditions for silty sand are presented The results of the remaining applications are included in the report by Sharp et al (1984) Determination of Duncan Soil Parameters The silty sand that was used in the soil-box tests is characterized as a nonplastic material with about 40% passing the 0.075-mm sieve and about 10% clay-size particles Maximum dry density is 124.7 lb/ft3 and the optimum water content is 9.5 % based on AASHTO T-99 compaction Triaxial shear tests on the silty sand were performed by using samples compacted at water contents similar to those used in soil-box tests Figure 29-1 is the sketch of a "soil box." Elastic modulus and bulk modulus parameters are required in the FEA for each density Testing of the clean granular materials (washed sand and gravel) was performed by using saturated samples, and the volume change was monitored by measuring the volume of water extruded or imbibed in the samples during drained shear Because the stress-strain and strength properties of the silty sand and clay are dependent on drainage, density, compaction water content, and water content at shear, it was necessary for the soil parameters to represent field conditions as much as possible Therefore, the silty sand and the clay were tested by using unsaturated undrained conditions The triaxial device was not equipped to Figure 29-1 Sketch of the large USU soil cell (soil box) for investigating pipe-soil interaction of buried pipes The cell is an elliptical steel cylinder with horizontal radius of curvature at the spring lines equal to three times the vertical radius at the invert The ellipse reduces boundary effects by simulating a one-third ratio of horizontal to vertical soil stresses as load is applied Boundary effects are negligible for pipes up to about 60 inches (1.5 m) in diameter The cell is 15 ft (4.6 m) wide, 18 ft (5.5 m) high to the hydraulic cylinders, and 22 ft (6.7 m) long Vertical pressure is applied by 50 hydraulic cylinders on ten beams The beams are pinned at one end such that they can be tilted up out of the way for installing pipes This is the larger of two soil cells used, primarily, for investigating performance of pipes under high soil pressures, and for comparison with finite element analyses ©2000 CRC Press LLC measure volumetric strain of undrained samples Therefore, bulk modulus parameters were not measured for the fine-grained soils (silty sand and clay) complete description of sensitivity is contained in the report by Sharp et al (1984) Triaxial testing was performed on the silty sand at three different densities (95%, 80%, and 77% relative compaction based on Standard Proctor) Stress-strain curves were obtained for three confining pressures within the range used in the soilbox tests for each density The triaxial testing procedure involved preparing the sample with compaction techniques similar to those in the field and by applying the deviator by initial loading, unloading, and reloading to failure This resulted in data that were interpreted with procedures outlined by Duncan et al (1980) for determination of shear strength and the hyperbolic parameters for the elastic moduli The modeling of the fiberglass pipe performance in silty sand consisted of several installation conditions and 10 and 100 psi pipe stiffnesses (ASTM D2412) Installation conditions included homogeneous compaction at 90 and 80% relative compaction, poor haunches, and soft crown In general the poorhaunch and soft-crown conditions were obtained by not compacting the soil in those areas Figure 29-2 shows the finite-element mesh and soil materials or types that were used in this study The poor-haunch condition used 90% relative compaction for all soil types except that in the haunches (soil type 6) The soft-crown condition used 90% relative compaction for all soil types except that in the area from the shoulders to the crown of the pipe, shown in Figure 29-2 as soil type Thes e installation conditions were used because of the way in which materials were placed around the pipe during installation When the pipe has low stiffness, it is difficult to compact the fill material over the crown until sufficient cover has been placed Also, extra effort is required to compact the soil in the haunches, so it was desired to model installation conditions in which there was loose material in the haunches The other soil types that are shown were included to investigate effects due to split installation, different foundation materials, and other types of installations The unloading and reloading data were also evaluated to obtain the rebound parameters for each density Because data were not obtained for the hyperbolic bulk modulus parameters, an FEA sensitivity study was performed using soil-box test results to calibrate the silty-sand data using 90 and 80% relative compaction The elastic modulii for the 90% relative c ompaction were obtained by interpolating the measured values from the 95%, 80%, and 77% percent relative compaction data Sensitivity studies were performed by using a 90% homogeneous relative compaction and an 80% homogeneous relative compaction in the finite-element mesh to determine the bulk modulus parameters These sensitivity studies show that the shape of the loaddeflection curve can be adjusted by modifying the bulk modulus exponent Pipe strain plots can also be adjusted because of complex interrelationships between hyperbolic elastic and bulk modulus parameters in conjunction with the shear strength of the soil Table 29-1 shows the final values for the soil parameters that were used for the silty sand at 90% and 80% relative compaction A more ©2000 CRC Press LLC Finite-Element Modeling The finite-element modeling scheme consisted of two phases The first modeled construction increments without compaction simulation Four installation conditions were modeled for pipes with stiffnesses of 10 and 100 psi The second incorporated a compaction simulation on each construction increment before the next construction increment was added Three installation conditions were modeled by using the compaction simulation Table 29-2 shows the installation conditions that were used for the silty sand and indicates those that included compaction simulation Table 29-1 Soil Parameters for Silty Sand RC Stand density lb/in3 ϕ ∆ n Rf Kb m Ko Kur nur deg c psi K deg 90% 0.065 30 8.3 480 44 75 80 38 48 720 44 80% 0.058 3.5 350 28 89 15 40 37 525 28 30 Note: New report in Duncan et al., 1998) for definition of parameter Figure 29-2 Finite-element mesh for buried pipe installation, including pipe coordinate system ©2000 CRC Press LLC TABLE 29-2 Installation Conditions for Silty Sand Condition Pipe Stiffness (psi) Compaction Simulation 90% homogeneous 10 100 yes 90% backfill with soft top @ 80% RC 10 100 yes 90% backfill with soft top @ 99% RC 10 no 90% backfill with haunches @ 80% RC 10 100 yes 90% backfill with haunches @ 79% RC 10 no 90% backfill with haunches @ 77% RC 10 no 90% backfill with top and haunches @ 85% RC 10 no 10 100 no 80% homogeneous Soil elements in the foundation and up to the spring line (soil materials through 3) were treated as preexisting elements having stresses and strains predefined at the time of program execution In the construction sequence used in the first phase, placement of the remainder of soil and all of soils and was simulated as the first construction increment The second construction increment completed the mesh by placing soil material S appears to be in accordance with the actual installation conditions, in which it was found that effective soil compaction could not be performed over the pipe until sufficient cover had been placed Also, it was not possible to add compaction loads on the soil before placement of the first increment When loads were added adjacent to the spring line on soil material 3, pressures caused excessive deformation of the pipe The second phase or the modeling incorporated compaction simulation after each construction sequence The compaction simulation involved addition and removal of compaction loads at the end of the first and second construction increments The first compaction load was added to the first layer of soil material The second compaction loading was placed on the completed mesh over soil material It was found that the first loading sequence was critical in inducing initial ovalization of the pipe It was not possible to load directly over the pipe (soil material 7) without causing structural failure and large unrealistic deformation of the pipe and soil because of an unstable condition This result For compaction simulation, a uniform static load of 10 psi was used corresponding to the type of compaction equipment used in the soil-box test A more rigorous compaction sequence would have been to load each soil element individually with a larger pressure, which would result in a better simulation of the compaction process The load of 10 psi was an equivalent surface pressure over a large area The compaction load was added in two increments of psi each After the compaction load had been placed, a sequence of unloading was followed A series of unloading steps in small pressure increments was followed until the elements ©2000 CRC Press LLC in the top row of the mesh approached a tension condition with negative confining pressure Small increments were used in the loading and unloading sequence in order to assure that the soil elements were being evaluated correctly for either the primary loading or rebound parameters Magnitudes that were too large for compaction loading might have caused poor convergence and incorrect evaluation of the appropriate soil response model It was not possible with the silty sand to remove the same load magnitude that was placed without causing tension failures in all elements in the mesh This was not the case with the clay analysis, however, because it was numerically possible to remove the same quantity of compaction load that was placed Although it may seem invalid to model compaction loading without removing the same load that was placed, it must be pointed out that the solution is an incremental loading procedure The total load vector is not evaluated at each iteration Only the total stresses and strains in each element are evaluated Thus although success at unloading the elements with the same compaction load magnitude was not achieved, it was possible to induce stress history in the soil due to compaction loads, which resulted in allowable soil stresses, strains, and deformations The inability to unload the soil element completely without complete tension failure might be attributed to numerical approximations with the finite-element technique Problems arise in the soil model in evaluating Poisson's ratio when the soil is in the unloading and reloading range Poisson's ratio is computed by using the theory of elasticity relationships between bulk modulus and elastic modulus When the elastic modulus increases as in unloading and reloading, Poisson's ratio is computed at its minimum of 0.0 if the bulk modulus does not increase proportionately Behavior of the bulk modulus is difficult to determine on unloading and reloading relative to primary loading Sharp et al (1984) tested bulk modulus ©2000 CRC Press LLC behavior in triaxial shear of saturated drained granular material for primary loading as well as rebound loading It was not possible to conclude how volumetric deformation behaves as a function of stress history for the coarse-grained material In addition, the granular material exhibited dilation at a small strain (a response that cannot be accommodated within the theory of elasticity) RESULTS OF FEA MODELING The results of the applications of FEA were compared with the measured response from the soilbox tests The comparisons that follow are for a pipe with 10 psi pipe stiffness Soil box compaction conditions that were used for comparisons were 90% relative compaction with homogeneous conditions, 90% relative compaction with poor haunches, and 80% relative compaction with homogeneous conditions In the soilbox testing, every attempt was made to achieve homogeneous conditions However, as noted, the flexible nature of the pipe does not always allow for thorough compaction in the haunches and around the shoulders and crown of the pipe Therefore, for the homogeneous conditions that were attempted in the soil box there was actually some variation in density When the pipe was installed with poor haunches in the soil box, no attempt was made to compact the soil Finiteelement modeling of homogeneous and poor-haunch conditions is better defined because, numerically, all soil elements in a homogeneous condition have identical stress-strain properties Comparisons of the FEA results with those of the soil-box tests are made by using pipe-strain and load-deflection results The pipe-strain plots indicate the bending strain in the outside fibers (tension is positive) and thrust strain around the circumference of the pipe for a given surcharge pressure The load-deflection plots indicate the vertical and horizontal ring deflections (the ratios of change in vertical and horizontal diameters to initial diameter) versus surcharge pressure In the soil-box tests, the load-deflection plots are referenced to the deformed state of the pipe after Figure 29-3 Vertical soil pressure versus pipe deflection for (curve A) soil-box data 90 percent relative compaction, silty sand and (curve B) FEA, no compaction simulation Figure 29-4 Pipe strains as functions of circumferential position, conditions as in Figure 29-3 ©2000 CRC Press LLC compaction In the FEA plots, the reference of ring deflection is based on the initial undeformed condition Thus in the comparison of figures that follow, the zero point of deflection should be considered when direct comparisons of load deflections between the FEA and the soil-box tests are performed Pipe-strain plots for both soil-box and FEA results are referenced from the same unstrained condition The pipe-strain plots show bending and thrust strain versus position on the pipe Zero degrees on the pipe is at the invert, 90 degrees is at the spring line, and 180 degrees is at the crown as shown in Figures 29-2 and 29-3 The values for pipe strain from 180 to 360 degrees are symmetric with to 180 degrees for the FEA because the FEA mesh presented here used an axis of symmetry for the analysis of symmetric bedding Homogeneous Installation at 90% Relative Compaction Figures 29-3 and 29-4 show the soil-box test results for a 10-psi pipe installed with homogeneous compaction at 90% of Standard Proctor maximum dry density Physical pipe date are: Parameter Stiffness (psi) Thickness (in.) Surface pressure (psi) Vertical deflection (t) Horizontal deflection (1) Curve A 10 0.285 40.9 5.53 3.74 B 10 0.300 50.0 4.82 2.52 Figure 29-3 shows the load-deflection curve and Figure 29-4 shows pipe strain versus location on the pipe for a surcharge pres sure of 48.9 psi Noteworthy features of these results are the shape of the load-deflection curve, relative magnitudes of horizontal and vertical ring deflections, and the shapes and magnitudes of bending and thrust strain This condition was modeled with FEA in several ways Figures 29-3 and 29-4 also show the results from the FEA using homogeneous 90% relative compaction and no compaction simulations These ©2000 CRC Press LLC figures show a similarity in the general shape of the load-deflection curve The pipe-strain plots in Figure 29-4 indicates that the magnitudes of pipe strain for this case at a surface pressure of 50.0 psi are comparable, but several maxima and points of inflection are missing The magnitude of ring deflection at the 50 psi surface pressure is also comparable within one-half of 1% of the measured deflection Figures 29-5 and 29-6 show the results of the FEA for the homogeneous dense soil condition with compaction simulation during construction The physical pipe data are: Parameter Stiffness (psi) Thickness (in.) Surface pressure (psi) Vertical deflection (t) Horizon deflection (1) Curve A 10 0.285 48.9 5.53 3.74 B 10 0.300 50.0 5.42 3.14 The load-deflection plot in Figure 29-5 has lost some of the initial steepness, but the difference between vertical and horizontal deflection is maintained Compared to Figure 29-3, the magnitudes of deflection are similar Figure 29-6 shows the pipestrain plots from the compaction simulation at a surface pressure of 50.0 psi Comparison of Figure 29-6 with the measured values from the soil-box results in Figure 29-4 shows that compaction simulation improved correlation In fact, the general shape, maxima, and magnitudes all compare well This result is the best comparison between any soilbox test and FEA result Additional comparisons included soft elements in the shoulders of the pipe Because techniques did not allow compaction above the pipe, a theoretically homogeneous installation would still have soil of a lesser density at the crown FEA results for this condition included various degrees of compaction simulation From additional load-deflection and pipestrain plots it is evident that with the soft-crown analyses the pipe strain at the Figure 29-5 Vertical soil pressure versus pipe deflection for (curve A) soil-box data, 90% compaction, silty sand and (curve B) FEA with compaction simulation Figure 29-6 Pipe strains as functions of circumferential location, conditions as in Figure 29-5 ©2000 CRC Press LLC relative 135-degree location increases See Figure 29-3 This is due to decreased stiffness of the soil in the shoulders which allows for more bending deformation in the pipe Compaction simulation for the soft-crown condition decreases the bending strains and ring deformations because the soil responds initially in the rebound range and inhibits deformation at the low pressures Because compaction simulation does not include adding loads directly over the pipe at the first construction increment, a soft-crown condition is actually created in the homogeneous case The soil at the crown is uncompacted and does not respond to the stiffer rebound modulus at the lower pressure ranges as does the surrounding soil elements that receive compaction loads directly Poor-Haunch Installation at 90% Relative Compaction Figures 29-7 and 29-8 show the results for the poorhaunch installation with the silty sand in the soil-box tests The physical pipe data are: Parameter Stiffness (psi) Thickness (in.) Surface pressure (psi) Vertical deflection (%) Horizontal deflection (%) Curve A 10 0.285 35.5 3.14 1.30 B 10 0.300 30.0 2.21 1.09 Figure 29-7 shows the load-deflection response and Figure 29-8 shows the pipe strain around the pipe for a surface pressure of 35.5 psi Again the initial steepness of the load-deflection curve, the relative magnitudes between the vertical and horizontal deflections, and the shapes and magnitude of the strain plots are noteworthy The bending strains are higher at the 30 to 45 degree locations on the pipe because of the lack of support in the haunch area Also, a comparison of the homogeneous installation and the poor-haunch installation in Figures 29-6 and 29-8, respectively, shows noticeable differences in ©2000 CRC Press LLC the pipe-strain plots from soil-box tests Figures 297 and 29-8 also show the FEA results for the poorhaunch condition without compaction simulation The load-deflection plot shows similar behavior, yet the deformations are larger in the FEA results The pipe-strain plot shows a peak of large strain at 45 degrees and low strains from spring line to crown that are similar to the soil-box results Figures 29-9 and 29-10 show the FEA results for poor haunches with compaction simulation The load-deflection plots show larger deflections and the pipe-strain plots show larger strains from spring line to cro w n than in Figure 28-8 However, strain at the invert of the pipe with compaction simulation was closer to the measured results than to the FEA results that did not include compaction simulation The physical pipe data for Figures 29-9 and 29-10 are: Parameter Stiffness (psi) Thickness (in.) Surface pressure (psi) Vertical deflection (%) Horizontal deflection (%) Curve A 10 0.285 35.5 3.14 1.30 B 10 0.300 30.0 5.14 2.92 Homogeneous Installation with 80% Relative Relative Compaction Figures 29-11 and 29-12 show the soil-box results for 80% relative compaction homogeneous installation The physical pipe data are: Parameter Stiffness (psi) Thickness (in.) Surface pressure (psi) Vertical deflection (%) Horizontal deflection (%) Curve A 10 0.285 14.6 8.78 7.87 B 10 0.300 15.0 3.85 2.06 The vertical and horizontal deflections are similar throughout the test, which includes elliptical deformation as shown in Figure 29-11 Figures 2911 and 29-12 also show the results from the FEA Figure 29-7 Vertical soil pressure versus pipe deflection for (curve A) soil-box data, 90% relative compaction, silty sand, and poor haunch support; and (curve B) FEA, no compaction simulation, and poor haunch support Figure 29-8 Pipe strains as functions of circumferential location, conditions as in Figure 29-7 ©2000 CRC Press LLC Figure 29-9 Vertical soil pressure versus pipe deflection for (curve A) soil-box data, 90% relative compaction, silty sand, and poor haunch support; and (curve B) FEA with compaction simulation and poor haunch support Figure 29-10 Pipe strains as functions of circumferential location, conditions as in Figure 29-9 ©2000 CRC Press LLC Figure 29-11 Vertical soil pressure versus pipe deflection for (curve A) soil-box data, 80% relative compaction and (curve B) FEA, no compaction simulation Figure 29-12 Pipe strains as functions of circumferential location, conditions as in Figure 29-11 ©2000 CRC Press LLC for the 80% relative compaction homogeneous condition Although the load-deflection curve shows more deformation with the loose material than with the dense material, the actual comparison of soil-box tests with FEA tests shows that the FEA does not compare as well for the looser soil condition The pipe-strain plots in Figure 29-12 also confirm the poorer comparison In terms of magnitude of the maximum strain, there is correlation, but the overall shape of the pipe-strain plots not match measured values as well as the analyses with 90% density DISCUSSION OF RESULTS Soil compaction simulation for the FEA response of the FRP pipe improves the comparison with soil-box tests for homogeneous soil For nonhomogeneous soil installation conditions, compaction simulation did not improve the comparison of FEA with soil-box tests enough to justify the additional computational effort required The FEA results were generally better for dense soil installation conditions than for loose soil conditions This is due to a combination of numerical difficulties with the finite-element method and lack of similitude in the soil-box model that arises with loose soil conditions Entries in the stiffness matrix become s ensitive to the magnitudes of the elastic and bulk moduli at low soil stiffness In order to achieve larger deflections, lower values of the bulk modulus are required This, however, can result in singular matrix warnings, which indicates that entries in the stiffness matrix will not produce reliable results The geometric nonlinear analysis (wherein the formulation of the stiffness matrix accounts for the nodal deflections at each loading increment) does not significantly change the results for installation condition modeling The inclusion of the geometric nonlinear analysis would generally predict higher deflections For example, an analysis that did not include geometric nonlinearities might predict a vertical ring deflection of 7% The same conditions including geometric nonlinearities would predict ring ©2000 CRC Press LLC deflections of around 8% However, for the other types of loading conditions (such as rerounding), the formulation of the stiffness matrix must reflect the shape of the pipe SUMMARY AND CONCLUSIONS Good correlation of finite-element modeling of flexible pipes with test data requires modeling c apabilities not readily available in most computer programs Such capabilities include analysis of the stress history of the soil elements to determine whether each element is in primary loading or in unloading and reloading, modification of the iteration scheme to better model the soil response when there is a change from one stress condition to another, and large-deflection theory by modifying nodal coordinates after each load increment In addition, postprocessing plotting routines are needed to graphically analyze the pipe response to each loading condition The development of these features makes possible the analysis of flexible pipe under compaction simulation, surcharge pressures, rerounding caused by internal pressure, and various installation conditions The results of analyses for various installation conditions show the effects of shoulder and haunch support on the pipe and suggest that these conditions can be considered in FEA analysis of pipe and installation conditions The results of the USU study of four soil types and various loading conditions, show a good correlation between FEA results and the measured responses from physical model tests in a soil-box The finiteelement method can be used for analyzing performance of buried flexible pipes with various installation conditions, soil types and densities, loading conditions, and pipe sizes and stiffnesses T he cost of FEA is less than physical testing However, calibration of the FEA requires results from physical tests The two techniques used together are applicable and cost effective for analyzing buried flexible pipe performance REFERENCES Duncan, J.M (1979) Behavior and design of longspan metal culverts Journal of Geotechnical Engineering, ASCE, Vol 105, No GT3, March 1979 Duncan, J.M (1980), P Byrne, K.S.Wong, and P.Mabry Strength, stress-strain and bulk modulus parameters for finite element analyses of stresses and movements in soil masses Geotechnical Engineering Report UCB/GT/80-81 University of California, Berkeley, 1980 Katona, M.G (1976), J.B.Forrest, R.J.Odello, and J.R.Allgood CANDE—A modern approach for the structural design and analysis of buried culverts Report FHWA-RD-77-5, FHWA, U.S.Department of Transportation, 1976 Katona, M.G (1982) Effects of frictional slippage of soil-structure interfaces of buried culverts In Transportation Research Record 878, TRB, National Research Council, Washington, D.C., 1982, pp 8-10 Knight, G.K (1983), and A.P.Moser The structural response of fiberglass reinforced plastic pipe under earth loadings Buried Structures Laboratory, Utah State University, Logan, 1983 Kulhawy, F.N (1969), J.M.Duncan, and H.B.Seed Finite element analysis of stresses and movements in embankments during construction Geotechnical Engineering Report TE-69-4 University of California, Berkeley, 1969 Leonards, G.A (1982), T.H.Wu, and C.H.Juang Predic ting performance of buried conduits Report FHWA/IN/JHRP-81/3 FHWA, U.S Department of Transportation, 1982 ©2000 CRC Press LLC Medrano, (1984), A P.Moser, and O.K.Shupe Performance of fiberglass reinforced plastic pipe to various soil loads and conditions Buried Structures Laboratory, Utah State University, Logan, 1094 Nyby, D.W (1981) Finite element analysis of soilstructure interaction Ph.D dissertation, Utah State University, Logan, 1981 Ozawa, Y (1973),and J.M.Duncan ISBILD: A computer program for analysis of static stresses and movements in embankments Geotechnical Engineering Report, University of California, Berkeley, 1973 Sharp, K.D (1984), F.W.Kiefer, L.R.Anderson, and E.Jones Soils testing report for applications of finite element analysis of FRP pipe performance Soils Testing Report, Buried Structures Laboratory, Utah State University, Logan, 1984 Sharp, K.D (1984), L.R.Anderson, A.P.Moser, and M.J.Warner Applications of finite element analysis of FRP pipe performance Buried Structures Laboratory, Utah State University, Logan, 1984 Sharp, K.B (1985), L.R.Anderson, A.P.Moser, and R.R.Bishop Finite element analysis applied to the response of buried FRP pipe under various installation conditions In Transportation Research Record 1008, Transportation Research Board, National Research Council, pp 63-72, 1985 Wilson, E.L (1963) Finite element analysis of twodimensional structures Ph.D dissertation, University of California, Berkeley 1963 ... Proctor) Stress-strain curves were obtained for three confining pressures within the range used in the soilbox tests for each density The triaxial testing procedure involved preparing the sample with... the large USU soil cell (soil box) for investigating pipe -soil interaction of buried pipes The cell is an elliptical steel cylinder with horizontal radius of curvature at the spring lines equal... four soils that were used in the soil box be tested for engineering properties, including triaxial testing at several densities for evaluation of the hyperbolic parameters for the Duncan soil