Modeling Embankment Induced Lateral Loads on Deep Foundations

Modeling Embankment Induced Lateral Loads on Deep Foundations

By Dr. Siva Kesavan URS CorporationAndProfessor Rajah AnandarajahJohns Hopkins University

Fig. A.IntroductionThe problem analyzed in this presentation is inspired by a real-world problem where the construction of a landfill at a rate too fast caused damage to an adjacent bridge. Without presenting actual names, the problem is described and analyzed using an elasto-plastic finite element computer code (HOPDYNE) to illustrate how an advanced numerical procedure can help develop an understanding of the failure mechanism, and reveal the true cause of the failure in a complex problem like this, where loading and consolidation take place simultaneously. The problem involves soil-structure interaction. The geometry is too complex, raising questions concerning the validity of one-dimensional assumptions used in Terzaghis one-dimensional consolidation theory. The clayey soil in the foundation is too soft and is certain to behave highly plastically, raising questions about the validity of using elastic theories to calculate the stresses in the foundation caused by the weight of the landfill. In other words, the problem is too complex, pointing to the need for a method like the finite element method for not only verifying the validity of the conventional methods normally used in analyses, but also to explain the true cause of failure.Problem DefinitionA landfill construction took place near a pile-supported bridge as shown in the figure. The foundation soil consisted of a very soft clay sandwiched between a dense sand and stiff clay layers. When the height of the landfill reached 80 feet, some of the piles had cracked at the pile head level and separated from the pile head laterally by about a foot (i.e., in the direction of X-axis shown in the figure). Objectives of the PresentationWe first discuss conventional methods of analyses that would normally be used (Part I). The problem is then idealized into a two-dimensional problem and analyzed by FEM using two different further assumptions as follows:Place a rigid vertical wall on section B-B, and calculate the changes in horizontal normally stresses on that wall during the construction of the landfill (Part II), andInclude the some of the piles in the model as shown in red in the figure above and repeat the analysis (Part III).The validity of the use of 2D model is then discussed.xzxyBB

Elevation(ft)Change in Horizontal Stress (psf)Elastic Change in Horizontal Normal Stress Near the First Pile Due to Embankment Loading:Using elastic equations, the change in horizontal stress near the first pile was calculated at different depths. As seen in the figure, the variation of the stress with depth is approximately linear, with about 1350psf at a depth of 70 feet. Assuming that the pile is fixed at both ends (anchored into the stiff clay at the bottom, and held by the bridge at the top), the end bending moments and shear forces are computed as

Assuming a compressive strength of about 3000 psi and a shear strength of about 1500 psi, the piles must have cracked in compression, supporting the observation. However, the validity of this analysis is highly questionable.Part I: Classical Approach:Elastic Analysis

Chart1

60

50

40

30

20

10

0

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57.51.14E+031.68E+032.26E+032.01E+031.32E+031.76E+031.84E+031.51E+031.53E+031.15E+033.09E+03602.15E+031.90E+015.09E+043.53E+031.12E+03

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67.53.97E+021.57E+041.36E+032.67E+031.63E+048.82E+025.48E+035.39E+032.99E+036.43E+034.38E+04zF_stauMsigy=9.59E+02

MY/I

m007-1m007-1

with pileswith piles

no slipno slip

cccc

sig-h.she

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Part I: Classical Approach: Plastic Flow AnalysisAssumption: The soft clay flows like a liquid around the pile, and as it does, it applies a drag force on the pile in the form of shear stress equaling to the undrained cohesion of the soil, which is estimated to be about 434 psf. Introducing this drag force as a uniformly distributed force on the pile, fixed at both ends, one calculates the bending and shear stresses as follows:

The maximum calculated bending stress and the shear stress exceeds the limits (3000 psi for bending stress and 1500 psi for shear stress), suggesting that the pile must have experienced cracking. Again, the validity of the assumption on which the calculations are based on needs verification.

See TableWT SandSoft ClayStiff Clay7080100Industrial WasteSand seams (p=0)Part II: Finite Element Analysis Using HOPDYNE with a Rigid Wall Placed at the Location of the First PileLoading: As the failure of the landfill embankment is not of concern here, instead of using staged construction, the loading is applied as followed: A single finite element mesh, including the 80 tall landfill is used in the analysis. The weight of the landfill is applied as gravity loading with the full loading applied over a period of one year. The analysis is carried out as a fully-coupled analysis. Followed by the load application, the analysis is continued for another year, during which time, excess pore water pressure further dissipates and the soil consolidates.Fig. B

What Constitutive Models to Choose?Fig. C

DPSee TableDP: Drucker-Prager (1955)ABS: Anisotropic Bounding Surface Clay Model(Anandarajah and Dafalias, 1986)CC: Modified Cam-Clay (Roscoe & Burland, Schofield and Wroth, 1968)EE: Linear ElasticCC or ABS with OCR=10DPWTSilty SandSoft ClayStiff Clay7080100Industrial WasteSand seams (p=0) Analysis Types1 2 3 4All elastic CC with M=0.6 ABS with M=0.6 CC with M=1.2 OCR=1 OCR=1, A=1.3 OCR=10Constitutive Models Used for Various LayersFully-Coupled Analysis with k = 1.0E-12 ft/s for clays and k=1.0E+02 ft/s for sands

Analysis Types:For reference, one analysis is performed with a linear elastic material model (EE) for the materials in the entire embankment.

In all of the remaining analyses, the landfill material and the top 10-foot thick foundation sandy layer were modeled by the Drucker-Prager model (DP) with a friction angle of 45 degrees, zero cohesion and a dilation parameter of 0.8

The middle and bottom layers of the foundation soil were either modeled with the modified cam-clay model (CC) or the anisotropic bounding surface model (ABS) (Anandarajah and Dafalias, 1986).

To make the middle layer very weak and soft as in the real-world problem, very low value was used for the slope of critical state line (M=0.6) with an OCR of 1

To make the bottom layer very stiff, the following parameters wereUsed: M=1.2, and OCR=10.The stress distributions presented in the following pages are those at the end of five years (i.e., almost at the end of consolidation)

InitialElasticHorizontal Effective Stress (psf)Elevation(ft)Horizontal Stresses in the Soil Near the PileFig. 1. Comparison of initial stresses before embankment construction and elastic stresses after embankment construction

Chart2

2.52.5

7.57.5

12.512.5

17.517.5

22.522.5

27.527.5

32.532.5

37.537.5

42.542.5

47.547.5

52.552.5

57.557.5

62.562.5

67.567.5

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67.53.97E+021.57E+041.36E+032.67E+031.63E+048.82E+025.48E+035.39E+032.99E+036.43E+03

Sheet1

Sheet2

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InitialElastic CC Horizontal Effective Stress (psf)Elevation(ft)Horizontal Stresses in Soil Near the PileFig. 2. Comparison of initial stresses before embankment construction, and elastic and elasto-plastic stresses after embankment construction

Chart3

2.52.52.5

7.57.57.5

12.512.512.5

17.517.517.5

22.522.522.5

27.527.527.5

32.532.532.5

37.537.537.5

42.542.542.5

47.547.547.5

52.552.552.5

57.557.557.5

62.562.562.5

67.567.567.5

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InitialElasticAll StiffABSCCHorizontal Effective StressDepthHorizontal Stresses in Soil Near the PileFig. 3. Comparison of initial stresses before embankment construction, and elastic and elasto-plastic stresses after embankment construction

Chart1

2.52.52.52.52.5

7.57.57.57.57.5

12.512.512.512.512.5

17.517.517.517.517.5

22.522.522.522.522.5

27.527.527.527.527.5

32.532.532.532.532.5

37.537.537.537.537.5

42.542.542.542.542.5

47.547.547.547.547.5

52.552.552.552.552.5

57.557.557.557.557.5

62.562.562.562.562.5

67.567.567.567.567.5

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37.52.10E+033.19E+033.28E+033.33E+032.56E+032.83E+033.17E+032.56E+032.78E+031.33E+03

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47.51.62E+032.53E+032.82E+032.79E+032.00E+032.42E+032.60E+032.10E+032.19E+031.01E+03

52.51.38E+032.06E+032.55E+032.29E+031.64E+031.98E+032.14E+031.76E+031.86E+038.77E+02

57.51.14E+031.68E+032.26E+032.01E+031.32E+031.76E+031.84E+031.51E+031.53E+031.15E+03

62.51.01E+033.40E+042.03E+037.05E+033.17E+042.21E+031.28E+041.23E+045.20E+031.52E+04

67.53.97E+021.57E+041.36E+032.67E+031.63E+048.82E+025.48E+035.39E+032.99E+036.43E+03

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M003-1: z = 10 to 60 ABS with M=0.6 and OCR=1: Deformation(click on the picture)

M003-1: z = 10 to 60 ABS with M=0.6 and OCR=1: Pore Pressure(click on the picture)

M003-1: z = 10 to 60 ABS with M=0.6 and OCR=1: Shear Strain(click on the picture)

DPSee TableDP: Drucker-PragerABS: Anisotropic Bounding Surface Clay Model(Anandarajah and Dafalias, 1986)CC: Modified Cam-ClayEE: Linear ElasticCC or ABS with OCR=10DPWTSilty SandSoft ClayStiff Clay7080100Industrial WasteSand seams (p=0) Analysis Types1 2 3 4All elastic CC with M=0.6 ABS with M=0.6 CC with M=1.2 OCR=1 OCR=1, A=1.3 OCR=10Soil Failure: Remove Sand Seams and Double the Construction Rate

M003-1: z = 10 to 60 ABS with M=0.6 and OCR=1: Deformation(click on the picture)

M003-1: z = 10 to 60 ABS with M=0.6 and OCR=1: Pore Pressure(click on the picture)

M003-1: z = 10 to 60 ABS with M=0.6 and OCR=1: Shear Strain(click on the picture)

No Sand SeamsFast Loading (ABS)Slow Loading with Sand Seams (ABS)InitialHorizontal Stresses in Soil Near the PileHorizontal Effective StressDepthFig. 4. Comparison of initial stresses before embankment construction, and elastic and elasto-plastic stresses after embankment construction

Chart2

2.52.52.5

7.57.57.5

12.512.512.5

17.517.517.5

22.522.522.5

27.527.527.5

32.532.532.5

37.537.537.5

42.542.542.5

47.547.547.5

52.552.552.5

57.557.557.5

62.562.562.5

67.567.567.5

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32.52.34E+033.54E+033.47E+033.65E+032.84E+033.07E+033.49E+032.81E+033.04E+031.61E+03

37.52.10E+033.19E+033.28E+033.33E+032.56E+032.83E+033.17E+032.56E+032.78E+031.33E+03

42.51.86E+032.91E+033.06E+033.14E+032.31E+032.70E+032.95E+032.37E+032.49E+031.15E+03

47.51.62E+032.53E+032.82E+032.79E+032.00E+032.42E+032.60E+032.10E+032.19E+031.01E+03

52.51.38E+032.06E+032.55E+032.29E+031.64E+031.98E+032.14E+031.76E+031.86E+038.77E+02

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Comparison of DeformationFast Loading with no Sand SeamsFast (10 times) Loading with No Sand Seams (ABS Model) 0.9 0.65 3.85 4.0Slow Loading with Two Sand Seams (ABS Model)Fig. D

What happens to forces on piles when DP is used for the middle soft layer as well?InitialABS with M=0.6DP with M=0.6Horizontal Stresses in Soil Near the PileHorizontal Effective Stress (psf)Depth(ft)Fig. 5. Comparison of initial stresses before embankment construction, and elastic and elasto-plastic stresses after embankment construction

Chart1

2.52.52.5

7.57.57.5

12.512.512.5

17.517.517.5

22.522.522.5

27.527.527.5

32.532.532.5

37.537.537.5

42.542.542.5

47.547.547.5

52.552.552.5

57.557.557.5

62.562.562.5

67.567.567.5

Sheet1

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27.52.58E+033.93E+033.64E+034.06E+033.12E+033.37E+033.88E+033.07E+033.29E+032.00E+0327.54.14E+033.08E+03

32.52.34E+033.54E+033.47E+033.65E+032.84E+033.07E+033.49E+032.81E+033.04E+031.61E+0332.53.88E+032.86E+03

37.52.10E+033.19E+033.28E+033.33E+032.56E+032.83E+033.17E+032.56E+032.78E+031.33E+0337.53.56E+032.63E+03

42.51.86E+032.91E+033.06E+033.14E+032.31E+032.70E+032.95E+032.37E+032.49E+031.15E+0342.53.21E+032.38E+03

47.51.62E+032.53E+032.82E+032.79E+032.00E+032.42E+032.60E+032.10E+032.19E+031.01E+0347.52.88E+032.12E+03

52.51.38E+032.06E+032.55E+032.29E+031.64E+031.98E+032.14E+031.76E+031.86E+038.77E+0252.52.62E+031.84E+03

57.51.14E+031.68E+032.26E+032.01E+031.32E+031.76E+031.84E+031.51E+031.53E+031.15E+0357.52.48E+031.55E+03

62.51.01E+033.40E+042.03E+037.05E+033.17E+042.21E+031.28E+041.23E+045.20E+031.52E+0462.52.29E+038.54E+03

67.53.97E+021.57E+041.36E+032.67E+031.63E+048.82E+025.48E+035.39E+032.99E+036.43E+0367.59.57E+023.47E+03

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Part III: 2D Finite Element Analysis Using HOPDYNE with Some of the PilesFig. E

Fig. F

Horizontal Stresses in Soil Near the First Pile at the End of ConsolidationDepth(ft)Horizontal Effective Stress (psf)InitialElastic (without piles) CC (without piles)CC (with piles)Fig. 6. Results from 2D FEA with Piles

Chart2

2.52.52.52.5

7.57.57.57.5

12.512.512.512.5

17.517.517.517.5

22.522.522.522.5

27.527.527.527.5

32.532.532.532.5

37.537.537.537.5

42.542.542.542.5

47.547.547.547.5

52.552.552.552.5

57.557.557.557.5

62.562.562.562.5

67.567.567.567.5

Sheet1

2.53.86E+034.17E+034.23E+034.19E+034.13E+034.20E+034.13E+034.10E+034.14E+033.80E+033.71E+03

7.53.54E+034.11E+034.10E+034.12E+034.03E+034.11E+034.07E+033.98E+033.96E+033.70E+032.90E+03

12.53.30E+034.07E+034.02E+034.09E+033.49E+033.48E+034.05E+033.47E+033.84E+033.24E+034.58E+03

17.53.06E+034.11E+033.92E+034.17E+033.38E+033.47E+034.07E+033.34E+033.69E+032.87E+035.38E+03

22.52.82E+034.13E+033.79E+034.25E+033.30E+033.50E+034.08E+033.23E+033.51E+032.45E+035.33E+03

27.52.58E+033.93E+033.64E+034.06E+033.12E+033.37E+033.88E+033.07E+033.29E+032.00E+035.01E+03

32.52.34E+033.54E+033.47E+033.65E+032.84E+033.07E+033.49E+032.81E+033.04E+031.61E+035.39E+03

37.52.10E+033.19E+033.28E+033.33E+032.56E+032.83E+033.17E+032.56E+032.78E+031.33E+034.56E+03

42.51.86E+032.91E+033.06E+033.14E+032.31E+032.70E+032.95E+032.37E+032.49E+031.15E+034.56E+03

47.51.62E+032.53E+032.82E+032.79E+032.00E+032.42E+032.60E+032.10E+032.19E+031.01E+033.83E+03

52.51.38E+032.06E+032.55E+032.29E+031.64E+031.98E+032.14E+031.76E+031.86E+038.77E+023.63E+03

57.51.14E+031.68E+032.26E+032.01E+031.32E+031.76E+031.84E+031.51E+031.53E+031.15E+033.09E+03

62.51.01E+033.40E+042.03E+037.05E+033.17E+042.21E+031.28E+041.23E+045.20E+031.52E+041.89E+04

67.53.97E+021.57E+041.36E+032.67E+031.63E+048.82E+025.48E+035.39E+032.99E+036.43E+034.38E+04

m007-1

with piles

no slip

cc

Sheet1

Sheet2

Sheet3

Shear Stress in the First Pile (psi)Bending (normal) stresses in the First Pile (psi)Elevation (ft)Elevation (ft)Stresses in the First Pile at the End of Consolidation (Analysis with piles using CC for the middle soft layer)Key Observations:Shear stress in the pile reaches about 900 psi near the pile head, which is adequate to cause shear failure (assuming a shear strength of about 1/3 of the compressive strength of about 3000 psi)The bending stress exceeds 3000 psi at many locations, including near the pile head, as well as at locations in the middle soft clay layer. The pile, thus, could have failed in compression as well.The values calculated for the stresses here are much smaller than those calculated by the plastic flow analysis (e.g., about 6000 psi here for the bending stresses versus 12500 psi calculated by the flow analysis). Further conclusions are differed until the correspondence between 2D and 3D analyses are established, because the real problem is 3D. This is done in the next few slides.

Fig. 7

Chart3

15

20

25

30

35

40

45

50

55

60

65

Sheet1

2.53.86E+034.17E+034.23E+034.19E+034.13E+034.20E+034.13E+034.10E+034.14E+033.80E+033.71E+03

7.53.54E+034.11E+034.10E+034.12E+034.03E+034.11E+034.07E+033.98E+033.96E+033.70E+032.90E+03

12.53.30E+034.07E+034.02E+034.09E+033.49E+033.48E+034.05E+033.47E+033.84E+033.24E+034.58E+03151.62E+041.43E+022.41E+041.67E+03

17.53.06E+034.11E+033.92E+034.17E+033.38E+033.47E+034.07E+033.34E+033.69E+032.87E+035.38E+03209.11E+038.06E+01-5.69E+04-3.95E+03


27.52.58E+033.93E+033.64E+034.06E+033.12E+033.37E+033.88E+033.07E+033.29E+032.00E+035.01E+0330-7.54E+02-6.67E+00-1.21E+05-8.40E+03







62.51.01E+033.40E+042.03E+037.05E+033.17E+042.21E+031.28E+041.23E+045.20E+031.52E+041.89E+0465-9.83E+04-8.70E+024.01E+042.78E+03

67.53.97E+021.57E+041.36E+032.67E+031.63E+048.82E+025.48E+035.39E+032.99E+036.43E+034.38E+04zF_stauMsigy=

MY/I

m007-1m007-1


no slipno slip

cccc

sig-h.she

Sheet1

Sheet2

Sheet3

Chart4

15

20

25

30

35

40

45

50

55

60

65

Sheet1

2.53.86E+034.17E+034.23E+034.19E+034.13E+034.20E+034.13E+034.10E+034.14E+033.80E+033.71E+03

7.53.54E+034.11E+034.10E+034.12E+034.03E+034.11E+034.07E+033.98E+033.96E+033.70E+032.90E+03











62.51.01E+033.40E+042.03E+037.05E+033.17E+042.21E+031.28E+041.23E+045.20E+031.52E+041.89E+0465-9.83E+04-8.70E+024.01E+042.78E+03

67.53.97E+021.57E+041.36E+032.67E+031.63E+048.82E+025.48E+035.39E+032.99E+036.43E+034.38E+04zF_stauMsigy=

MY/I

m007-1m007-1


no slipno slip

cccc

sig-h.she

Sheet1

Sheet2

Sheet3

Correspondence Between the Results of 2- and 3-Dimensional Analyses.From the literature on buried structures, it can be deduced that when horizontal stresses are increased near a pile, the pile experiences passive arching. That is, the stress in front of the pile increases to a value larger than the value of the increase in stress in the soil (i.e., free-field stresses) and that in the back of the soil decreases to a value smaller than the value of the increase in stress in the soil. The net result is that the pile carries a load larger than that implied by the stress increase in the soil. To illustrate this, we placed a square pile in a plane strain container and increased the stress in the soil by 800 psf. The stress increase in the front and back of the soil are shown in the figure on the following page.

Distance X (ft)Horizontal Stress (psf)Pile (1x1)800 psfx41Initial Horizontal Stress = 2000 psfNote that the stress in the soil far from the pile increases from 2000 to 2800 psf, whereas it increases to over 4500psf in front on the pile and decreases to almost zero in the back of the pileFig. 8

Chart1

26972678

26982678

27002679

27032680

27082681

27152683

27252682

27432668

27922556

31751585

4519159.4

31751585

27922556

27432668

27252682

27152683

27082681

27032680

27002679

26982678

26972680

Sheet1

12.70E+032.68E+03

32.70E+032.68E+03

52.70E+032.68E+03

72.70E+032.68E+03

92.71E+032.68E+03

112.72E+032.68E+03

132.73E+032.68E+03

152.74E+032.67E+03

172.79E+032.56E+03

193.18E+031.59E+03

20.54.52E+031.59E+02

223.18E+031.59E+03

242.79E+032.56E+03

262.74E+032.67E+03

282.73E+032.68E+03

302.72E+032.68E+03

322.71E+032.68E+03

342.70E+032.68E+03

362.70E+032.68E+03

382.70E+032.68E+03

402.70E+032.68E+03

Sheet1

Sheet2

Sheet3

Horizontal Distance X (ft)Vertical Stress (psf)Pile (1x1)800 psfxInitial Vertical Stress = 2000 psfThe results here shows the influence of the boundary conditions on the stresses on the pile

Chart2

2697267826752645

2698267826762645

2700267926772645

2703268026802645

2708268126822644

2715268326862638

2725268226892619

2743266826932558

2792255627232296

3175158532961409

4519159.45482342.8

3175158532961409

2792255627232296

2743266826932558

2725268226892619

2715268326862638

2708268126822644

2703268026802645

2700267926772645

2698267826762645

2697268026752650

Sheet1

12.70E+032.68E+032.68E+032.65E+03

32.70E+032.68E+032.68E+032.65E+03

52.70E+032.68E+032.68E+032.65E+03

72.70E+032.68E+032.68E+032.65E+03

92.71E+032.68E+032.68E+032.64E+03

112.72E+032.68E+032.69E+032.64E+03

132.73E+032.68E+032.69E+032.62E+03

152.74E+032.67E+032.69E+032.56E+03

172.79E+032.56E+032.72E+032.30E+03

193.18E+031.59E+033.30E+031.41E+03

20.54.52E+031.59E+025.48E+033.43E+02

223.18E+031.59E+033.30E+031.41E+03

242.79E+032.56E+032.72E+032.30E+03

262.74E+032.67E+032.69E+032.56E+03

282.73E+032.68E+032.69E+032.62E+03

302.72E+032.68E+032.69E+032.64E+03

322.71E+032.68E+032.68E+032.64E+03

342.70E+032.68E+032.68E+032.65E+03

362.70E+032.68E+032.68E+032.65E+03

382.70E+032.68E+032.68E+032.65E+03

402.70E+032.68E+032.68E+032.65E+03

Sheet1

Sheet2

Sheet3

Determination of Modified Pile Parameters by Elastic MethodFrom , it follows that if you match the deflection line, the bending stresses must be equal to each other. Referring to the figure above, .But we want: Hence: Let be the load vector corresponding to and be the modified stiffness matrix which will render where is a modifier to be determined.

Fig. 9

By least square minimizationSteps:Carry out an elastic 3D analysis and determine Carry out an elastic 2D analysis and determineCarry out an elastic 2D analysis with imposed along pile locations and determine 4. Determine by conducting a pile analysis

Determination of Modified Pile Parameters by an Approximate MethodFig. 10

2D Mesh

3D MeshFig. 11

3D Mesh: Plan View of a Portion of the Mesh Around the PilesFig. 12Pile

Deformation of a Sectional Elevation of the 3D MeshFig. 13

Elevation(ft)Elevation(ft)Horizontal Deflection (ft)Bending Stress (psi)Green: Optimization Method (F=.0327)Red: 45 deg Approx. Method (F=0.0196)2DF=13DF=1Elevation(ft)Shear Stress (psi)Elevation(ft)Axial Stress (psi)Comparison of Pile Stresses from Various Types of Elastic AnalysesFig. 14Observation: With modified pile properties, stresses from 2D analyses are closer to those from 3D Analyses

Chart2

0000

5555

10101010

15151515

20202020

25252525

30303030

35353535

40404040

45454545

50505050

55555555

60606060

65656565

70707070

Sheet1

F=.0327F=.0196Bending Stresses0.03270.0196

zdel-3Ddel-2Ddel-2Ddel-2Dsig-3Dsig-2Dsig-2dsig-2d

00.00E+000.00E+000.00E+000.00E+00-2.19E+03-1.23E+03-2.65E+03-2.76E+03

51.05E-026.91E-031.22E-021.25E-023.12E+02-2.04E+026.40E+027.26E+02

102.31E-021.88E-022.45E-022.47E-021.53E+021.14E+024.66E+018.18E-01

153.32E-022.97E-023.44E-023.47E-026.85E+011.39E+029.92E+011.12E+02

204.19E-023.86E-024.29E-024.32E-028.26E+011.26E+021.04E+029.98E+01

254.93E-024.55E-024.98E-025.01E-028.47E+011.20E+021.01E+021.02E+02

305.55E-025.05E-025.50E-025.54E-028.68E+011.22E+021.07E+021.07E+02

356.03E-025.35E-025.86E-025.90E-028.96E+011.28E+021.11E+021.11E+02

406.37E-025.46E-026.05E-026.09E-029.31E+011.39E+021.19E+021.16E+02

456.56E-025.35E-026.04E-026.10E-021.04E+021.57E+021.30E+021.41E+02

506.59E-024.99E-025.84E-025.90E-021.33E+021.97E+021.20E+027.75E+01

556.44E-024.31E-025.38E-025.46E-026.25E+013.04E+023.79E+025.03E+02

606.08E-023.14E-024.68E-024.73E-024.14E+024.70E+02-6.91E+02-1.01E+03

654.11E-021.37E-023.43E-023.61E-024.51E+031.63E+024.45E+034.99E+03

700.00E+000.00E+000.00E+000.00E+000.00E+000.00E+000.00E+000.00E+00

Forces in bending elements: 3D

3.54E+04-7.15E+03-3.97E-120.00E+002.32E-11-3.13E+04-3.54E+047.15E+033.97E-120.00E+00-3.36E-12-4.45E+03

2.92E+044.52E+02-1.32E-110.00E+003.36E-124.45E+03-2.92E+04-4.52E+021.32E-110.00E+006.25E-11-2.19E+03

2.12E+042.41E+022.70E-110.00E+00-6.36E-112.19E+03-2.12E+04-2.41E+02-2.70E-110.00E+00-7.15E-11-9.78E+02

1.22E+04-4.02E+01-1.75E-110.00E+006.91E-119.78E+02-1.22E+044.02E+011.75E-110.00E+001.83E-11-1.18E+03

3.26E+03-6.61E+00-6.88E-120.00E+00-9.43E-121.18E+03-3.26E+036.61E+006.88E-120.00E+004.38E-11-1.21E+03

-4.81E+03-5.80E+001.59E-110.00E+00-4.66E-111.21E+034.81E+035.80E+00-1.59E-110.00E+00-3.28E-11-1.24E+03

-1.14E+04-7.64E+006.21E-120.00E+002.63E-111.24E+031.14E+047.64E+00-6.21E-120.00E+00-5.74E-11-1.28E+03

-1.61E+04-1.02E+01-1.84E-110.00E+003.31E-111.28E+031.61E+041.02E+011.84E-110.00E+005.88E-11-1.33E+03

-1.85E+04-3.02E+015.38E-120.00E+00-4.59E-111.33E+031.85E+043.02E+01-5.38E-120.00E+001.90E-11-1.48E+03

-1.84E+04-8.27E+01-1.75E-120.00E+003.40E-111.48E+031.84E+048.27E+011.75E-120.00E+00-2.52E-11-1.90E+03

-1.58E+042.00E+02-2.96E-110.00E+005.60E-111.90E+031.58E+04-2.00E+022.96E-110.00E+009.20E-11-8.93E+02

-1.16E+04-1.00E+032.50E-110.00E+00-6.44E-118.93E+021.16E+041.00E+03-2.50E-110.00E+00-6.05E-11-5.91E+03

-6.83E+03-1.17E+04-6.17E-120.00E+006.06E-115.91E+036.83E+031.17E+046.17E-120.00E+00-2.98E-11-6.44E+04

2.16E+034.20E+04-2.79E-110.00E+003.88E-116.44E+04-2.16E+03-4.20E+042.79E-110.00E+001.01E-101.46E+05


5.78E+03-2.94E+030.00E+000.00E+000.00E+00-1.76E+04-5.78E+032.94E+030.00E+000.00E+000.00E+002.91E+03

4.87E+03-9.07E+020.00E+000.00E+000.00E+00-2.91E+03-4.87E+039.07E+020.00E+000.00E+000.00E+00-1.63E+03

3.87E+03-7.00E+010.00E+000.00E+000.00E+001.63E+03-3.87E+037.00E+010.00E+000.00E+000.00E+00-1.98E+03

2.84E+033.62E+010.00E+000.00E+000.00E+001.98E+03-2.84E+03-3.62E+010.00E+000.00E+000.00E+00-1.80E+03

1.79E+031.51E+010.00E+000.00E+000.00E+001.80E+03-1.79E+03-1.51E+010.00E+000.00E+000.00E+00-1.72E+03

7.63E+02-4.53E+000.00E+000.00E+000.00E+001.72E+03-7.63E+024.53E+000.00E+000.00E+000.00E+00-1.74E+03

-1.98E+02-1.75E+010.00E+000.00E+000.00E+001.74E+031.98E+021.75E+010.00E+000.00E+000.00E+00-1.83E+03

-1.06E+03-3.07E+010.00E+000.00E+000.00E+001.83E+031.06E+033.07E+010.00E+000.00E+000.00E+00-1.98E+03

-1.82E+03-5.13E+010.00E+000.00E+000.00E+001.98E+031.82E+035.13E+010.00E+000.00E+000.00E+00-2.24E+03

-2.51E+03-1.16E+020.00E+000.00E+000.00E+002.24E+032.51E+031.16E+020.00E+000.00E+000.00E+00-2.82E+03

-3.16E+03-3.03E+020.00E+000.00E+000.00E+002.82E+033.16E+033.03E+020.00E+000.00E+000.00E+00-4.34E+03

-3.78E+03-4.75E+020.00E+000.00E+000.00E+004.34E+033.78E+034.75E+020.00E+000.00E+000.00E+00-6.71E+03

-4.10E+038.76E+020.00E+000.00E+000.00E+006.71E+034.10E+03-8.76E+020.00E+000.00E+000.00E+00-2.33E+03

-3.28E+038.23E+030.00E+000.00E+000.00E+002.33E+033.28E+03-8.23E+030.00E+000.00E+000.00E+003.88E+04

Forces in bending elements: 2D Using reduced b determined by single-width optimizationFac=0.0327

3.13E+03-3.11E+020.00E+000.00E+000.00E+00-1.25E+03-3.13E+033.11E+020.00E+000.00E+000.00E+00-3.02E+02

2.59E+035.60E+010.00E+000.00E+000.00E+003.02E+02-2.59E+03-5.60E+010.00E+000.00E+000.00E+00-2.20E+01

1.95E+03-4.95E+000.00E+000.00E+000.00E+002.20E+01-1.95E+034.95E+000.00E+000.00E+000.00E+00-4.68E+01

1.29E+03-4.44E-010.00E+000.00E+000.00E+004.68E+01-1.29E+034.44E-010.00E+000.00E+000.00E+00-4.90E+01

6.88E+022.31E-010.00E+000.00E+000.00E+004.90E+01-6.88E+02-2.31E-010.00E+000.00E+000.00E+00-4.78E+01

1.59E+02-5.29E-010.00E+000.00E+000.00E+004.78E+01-1.59E+025.29E-010.00E+000.00E+000.00E+00-5.05E+01

-2.86E+02-3.43E-010.00E+000.00E+000.00E+005.05E+012.86E+023.43E-010.00E+000.00E+000.00E+00-5.22E+01

-6.45E+02-7.70E-010.00E+000.00E+000.00E+005.22E+016.45E+027.70E-010.00E+000.00E+000.00E+00-5.60E+01

-9.24E+02-1.04E+000.00E+000.00E+000.00E+005.60E+019.24E+021.04E+000.00E+000.00E+000.00E+00-6.12E+01

-1.14E+039.73E-010.00E+000.00E+000.00E+006.12E+011.14E+03-9.73E-010.00E+000.00E+000.00E+00-5.64E+01

-1.32E+03-2.45E+010.00E+000.00E+000.00E+005.64E+011.32E+032.45E+010.00E+000.00E+000.00E+00-1.79E+02

-1.56E+031.01E+020.00E+000.00E+000.00E+001.79E+021.56E+03-1.01E+020.00E+000.00E+000.00E+003.26E+02

-1.94E+03-4.85E+020.00E+000.00E+000.00E+00-3.26E+021.94E+034.85E+020.00E+000.00E+000.00E+00-2.10E+03

-2.01E+031.25E+030.00E+000.00E+000.00E+002.10E+032.01E+03-1.25E+030.00E+000.00E+000.00E+004.14E+03

Forces in bending elements: 2D Using reduced b determined by the 45 degree approximate methodFac=0.0196

2.45E+03-1.97E+020.00E+000.00E+000.00E+00-7.81E+02-2.45E+031.97E+020.00E+000.00E+000.00E+00-2.05E+02

2.00E+034.11E+010.00E+000.00E+000.00E+002.05E+02-2.00E+03-4.11E+010.00E+000.00E+000.00E+00-2.31E-01

1.48E+03-6.30E+000.00E+000.00E+000.00E+002.31E-01-1.48E+036.30E+000.00E+000.00E+000.00E+00-3.17E+01

9.52E+027.06E-010.00E+000.00E+000.00E+003.17E+01-9.52E+02-7.06E-010.00E+000.00E+000.00E+00-2.82E+01

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7.41E+01-2.76E-010.00E+000.00E+000.00E+002.88E+01-7.41E+012.76E-010.00E+000.00E+000.00E+00-3.02E+01

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-5.17E+02-2.76E-010.00E+000.00E+000.00E+003.14E+015.17E+022.76E-010.00E+000.00E+000.00E+00-3.28E+01

-7.09E+02-1.42E+000.00E+000.00E+000.00E+003.28E+017.09E+021.42E+000.00E+000.00E+000.00E+00-3.98E+01

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Sheet1

Sheet2

Sheet3

Chart5

0000

5555

10101010

15151515

20202020

25252525

30303030

35353535

40404040

45454545

50505050

55555555

60606060

65656565

70707070

Sheet1

F=.0327F=.0196Bending Stresses0.03270.0196

zdel-3Ddel-2Ddel-2Ddel-2Dsig-3Dsig-2Dsig-2dsig-2d

00.00E+000.00E+000.00E+000.00E+00-2.19E+03-1.23E+03-2.65E+03-2.76E+03

51.05E-026.91E-031.22E-021.25E-023.12E+02-2.04E+026.40E+027.26E+02

102.31E-021.88E-022.45E-022.47E-021.53E+021.14E+024.66E+018.18E-01

153.32E-022.97E-023.44E-023.47E-026.85E+011.39E+029.92E+011.12E+02

204.19E-023.86E-024.29E-024.32E-028.26E+011.26E+021.04E+029.98E+01

254.93E-024.55E-024.98E-025.01E-028.47E+011.20E+021.01E+021.02E+02

305.55E-025.05E-025.50E-025.54E-028.68E+011.22E+021.07E+021.07E+02

356.03E-025.35E-025.86E-025.90E-028.96E+011.28E+021.11E+021.11E+02

406.37E-025.46E-026.05E-026.09E-029.31E+011.39E+021.19E+021.16E+02

456.56E-025.35E-026.04E-026.10E-021.04E+021.57E+021.30E+021.41E+02

506.59E-024.99E-025.84E-025.90E-021.33E+021.97E+021.20E+027.75E+01

556.44E-024.31E-025.38E-025.46E-026.25E+013.04E+023.79E+025.03E+02

606.08E-023.14E-024.68E-024.73E-024.14E+024.70E+02-6.91E+02-1.01E+03

654.11E-021.37E-023.43E-023.61E-024.51E+031.63E+024.45E+034.99E+03

700.00E+000.00E+000.00E+000.00E+000.00E+000.00E+000.00E+000.00E+00


3.54E+04-7.15E+03-3.97E-120.00E+002.32E-11-3.13E+04-3.54E+047.15E+033.97E-120.00E+00-3.36E-12-4.45E+03

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3.13E+03-3.11E+020.00E+000.00E+000.00E+00-1.25E+03-3.13E+033.11E+020.00E+000.00E+000.00E+00-3.02E+02

2.59E+035.60E+010.00E+000.00E+000.00E+003.02E+02-2.59E+03-5.60E+010.00E+000.00E+000.00E+00-2.20E+01

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1.29E+03-4.44E-010.00E+000.00E+000.00E+004.68E+01-1.29E+034.44E-010.00E+000.00E+000.00E+00-4.90E+01

6.88E+022.31E-010.00E+000.00E+000.00E+004.90E+01-6.88E+02-2.31E-010.00E+000.00E+000.00E+00-4.78E+01

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2.45E+03-1.97E+020.00E+000.00E+000.00E+00-7.81E+02-2.45E+031.97E+020.00E+000.00E+000.00E+00-2.05E+02

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-7.09E+02-1.42E+000.00E+000.00E+000.00E+003.28E+017.09E+021.42E+000.00E+000.00E+000.00E+00-3.98E+01

-8.47E+023.59E+000.00E+000.00E+000.00E+003.98E+018.47E+02-3.59E+000.00E+000.00E+000.00E+00-2.19E+01

-9.59E+02-2.40E+010.00E+000.00E+000.00E+002.19E+019.59E+022.40E+010.00E+000.00E+000.00E+00-1.42E+02

-1.13E+038.52E+010.00E+000.00E+000.00E+001.42E+021.13E+03-8.52E+010.00E+000.00E+000.00E+002.84E+02

-1.44E+03-3.39E+020.00E+000.00E+000.00E+00-2.84E+021.44E+033.39E+020.00E+000.00E+000.00E+00-1.41E+03

-1.56E+038.15E+020.00E+000.00E+000.00E+001.41E+031.56E+03-8.15E+020.00E+000.00E+000.00E+002.66E+03

Sheet1

Sheet2

Sheet3

Chart6

0000

5555

10101010

15151515

20202020

25252525

30303030

35353535

40404040

45454545

50505050

55555555

60606060

65656565

70707070

Sheet1

F=.0327F=.0196Bending Stresses0.03270.0196Shear Stresses

zdel-3Ddel-2Ddel-2Ddel-2Dsig-3Dsig-2Dsig-2dsig-2dtau-3Dtau-2Dtau-2Dtau-2D

00.00E+000.00E+000.00E+000.00E+00-2.19E+03-1.23E+03-2.65E+03-2.76E+033.13E+025.12E+018.47E+021.11E+03

51.05E-026.91E-031.22E-021.25E-023.12E+02-2.04E+026.40E+027.26E+022.58E+024.31E+017.01E+029.03E+02

102.31E-021.88E-022.45E-022.47E-021.53E+021.14E+024.66E+018.18E-011.88E+023.42E+015.27E+026.68E+02

153.32E-022.97E-023.44E-023.47E-026.85E+011.39E+029.92E+011.12E+021.08E+022.51E+013.49E+024.30E+02

204.19E-023.86E-024.29E-024.32E-028.26E+011.26E+021.04E+029.98E+012.89E+011.58E+011.86E+022.16E+02

254.93E-024.55E-024.98E-025.01E-028.47E+011.20E+021.01E+021.02E+02-4.26E+016.75E+004.30E+013.35E+01

305.55E-025.05E-025.50E-025.54E-028.68E+011.22E+021.07E+021.07E+02-1.01E+02-1.75E+00-7.74E+01-1.16E+02

356.03E-025.35E-025.86E-025.90E-028.96E+011.28E+021.11E+021.11E+02-1.42E+02-9.38E+00-1.74E+02-2.33E+02

406.37E-025.46E-026.05E-026.09E-029.31E+011.39E+021.19E+021.16E+02-1.64E+02-1.61E+01-2.50E+02-3.20E+02

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1.29E+03-4.44E-010.00E+000.00E+000.00E+004.68E+01-1.29E+034.44E-010.00E+000.00E+000.00E+00-4.90E+01

6.88E+022.31E-010.00E+000.00E+000.00E+004.90E+01-6.88E+02-2.31E-010.00E+000.00E+000.00E+00-4.78E+01

1.59E+02-5.29E-010.00E+000.00E+000.00E+004.78E+01-1.59E+025.29E-010.00E+000.00E+000.00E+00-5.05E+01

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-1.32E+03-2.45E+010.00E+000.00E+000.00E+005.64E+011.32E+032.45E+010.00E+000.00E+000.00E+00-1.79E+02

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2.45E+03-1.97E+020.00E+000.00E+000.00E+00-7.81E+02-2.45E+031.97E+020.00E+000.00E+000.00E+00-2.05E+02

2.00E+034.11E+010.00E+000.00E+000.00E+002.05E+02-2.00E+03-4.11E+010.00E+000.00E+000.00E+00-2.31E-01

1.48E+03-6.30E+000.00E+000.00E+000.00E+002.31E-01-1.48E+036.30E+000.00E+000.00E+000.00E+00-3.17E+01

9.52E+027.06E-010.00E+000.00E+000.00E+003.17E+01-9.52E+02-7.06E-010.00E+000.00E+000.00E+00-2.82E+01

4.78E+02-1.15E-010.00E+000.00E+000.00E+002.82E+01-4.78E+021.15E-010.00E+000.00E+000.00E+00-2.88E+01

7.41E+01-2.76E-010.00E+000.00E+000.00E+002.88E+01-7.41E+012.76E-010.00E+000.00E+000.00E+00-3.02E+01

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-5.17E+02-2.76E-010.00E+000.00E+000.00E+003.14E+015.17E+022.76E-010.00E+000.00E+000.00E+00-3.28E+01

-7.09E+02-1.42E+000.00E+000.00E+000.00E+003.28E+017.09E+021.42E+000.00E+000.00E+000.00E+00-3.98E+01

-8.47E+023.59E+000.00E+000.00E+000.00E+003.98E+018.47E+02-3.59E+000.00E+000.00E+000.00E+00-2.19E+01

-9.59E+02-2.40E+010.00E+000.00E+000.00E+002.19E+019.59E+022.40E+010.00E+000.00E+000.00E+00-1.42E+02

-1.13E+038.52E+010.00E+000.00E+000.00E+001.42E+021.13E+03-8.52E+010.00E+000.00E+000.00E+002.84E+02

-1.44E+03-3.39E+020.00E+000.00E+000.00E+00-2.84E+021.44E+033.39E+020.00E+000.00E+000.00E+00-1.41E+03

-1.56E+038.15E+020.00E+000.00E+000.00E+001.41E+031.56E+03-8.15E+020.00E+000.00E+000.00E+002.66E+03

Sheet1

Sheet2

Sheet3

Chart7

0000

5555

10101010

15151515

20202020

25252525

30303030

35353535

40404040

45454545

50505050

55555555

60606060

65656565

Sheet1

F=.0327F=.0196Bending Stresses0.03270.0196Shear StressesAxial Stresses

zdel-3Ddel-2Ddel-2Ddel-2Dsig-3Dsig-2Dsig-2dsig-2dtau-3Dtau-2Dtau-2Dtau-2Dsig-3Dsig-2Dsig-2Dsig-2D

00.00E+000.00E+000.00E+000.00E+00-2.19E+03-1.23E+03-2.65E+03-2.76E+033.13E+025.12E+018.47E+021.11E+03-6.33E+01-2.60E+01-8.41E+01-8.89E+01

51.05E-026.91E-031.22E-021.25E-023.12E+02-2.04E+026.40E+027.26E+022.58E+024.31E+017.01E+029.03E+024.00E+00-8.03E+001.51E+011.86E+01

102.31E-021.88E-022.45E-022.47E-021.53E+021.14E+024.66E+018.18E-011.88E+023.42E+015.27E+026.68E+022.13E+00-6.20E-01-1.34E+00-2.84E+00

153.32E-022.97E-023.44E-023.47E-026.85E+011.39E+029.92E+011.12E+021.08E+022.51E+013.49E+024.30E+02-3.56E-013.20E-01-1.20E-013.19E-01

204.19E-023.86E-024.29E-024.32E-028.26E+011.26E+021.04E+029.98E+012.89E+011.58E+011.86E+022.16E+02-5.85E-021.34E-016.25E-02-5.19E-02

254.93E-024.55E-024.98E-025.01E-028.47E+011.20E+021.01E+021.02E+02-4.26E+016.75E+004.30E+013.35E+01-5.13E-02-4.01E-02-1.43E-01-1.25E-01

305.55E-025.05E-025.50E-025.54E-028.68E+011.22E+021.07E+021.07E+02-1.01E+02-1.75E+00-7.74E+01-1.16E+02-6.76E-02-1.55E-01-9.28E-02-1.09E-01



456.56E-025.35E-026.04E-026.10E-021.04E+021.57E+021.30E+021.41E+02-1.63E+02-2.22E+01-3.08E+02-3.82E+02-7.32E-01-1.03E+002.63E-011.62E+00

506.59E-024.99E-025.84E-025.90E-021.33E+021.97E+021.20E+027.75E+01-1.40E+02-2.80E+01-3.57E+02-4.33E+021.77E+00-2.68E+00-6.63E+00-1.08E+01

556.44E-024.31E-025.38E-025.46E-026.25E+013.04E+023.79E+025.03E+02-1.03E+02-3.35E+01-4.22E+02-5.10E+02-8.85E+00-4.20E+002.73E+013.85E+01

606.08E-023.14E-024.68E-024.73E-024.14E+024.70E+02-6.91E+02-1.01E+03-6.04E+01-3.63E+01-5.25E+02-6.50E+02-1.04E+027.75E+00-1.31E+02-1.53E+02

654.11E-021.37E-023.43E-023.61E-024.51E+031.63E+024.45E+034.99E+031.91E+01-2.90E+01-5.44E+02-7.04E+023.72E+027.28E+013.38E+023.68E+02

700.00E+000.00E+000.00E+000.00E+00


3.54E+04-7.15E+03-3.97E-120.00E+002.32E-11-3.13E+04-3.54E+047.15E+033.97E-120.00E+00-3.36E-12-4.45E+03

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2.12E+042.41E+022.70E-110.00E+00-6.36E-112.19E+03-2.12E+04-2.41E+02-2.70E-110.00E+00-7.15E-11-9.78E+02

1.22E+04-4.02E+01-1.75E-110.00E+006.91E-119.78E+02-1.22E+044.02E+011.75E-110.00E+001.83E-11-1.18E+03

3.26E+03-6.61E+00-6.88E-120.00E+00-9.43E-121.18E+03-3.26E+036.61E+006.88E-120.00E+004.38E-11-1.21E+03

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-1.84E+04-8.27E+01-1.75E-120.00E+003.40E-111.48E+031.84E+048.27E+011.75E-120.00E+00-2.52E-11-1.90E+03

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2.16E+034.20E+04-2.79E-110.00E+003.88E-116.44E+04-2.16E+03-4.20E+042.79E-110.00E+001.01E-101.46E+05


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3.87E+03-7.00E+010.00E+000.00E+000.00E+001.63E+03-3.87E+037.00E+010.00E+000.00E+000.00E+00-1.98E+03

2.84E+033.62E+010.00E+000.00E+000.00E+001.98E+03-2.84E+03-3.62E+010.00E+000.00E+000.00E+00-1.80E+03

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1.29E+03-4.44E-010.00E+000.00E+000.00E+004.68E+01-1.29E+034.44E-010.00E+000.00E+000.00E+00-4.90E+01

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1.48E+03-6.30E+000.00E+000.00E+000.00E+002.31E-01-1.48E+036.30E+000.00E+000.00E+000.00E+00-3.17E+01

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4.78E+02-1.15E-010.00E+000.00E+000.00E+002.82E+01-4.78E+021.15E-010.00E+000.00E+000.00E+00-2.88E+01

7.41E+01-2.76E-010.00E+000.00E+000.00E+002.88E+01-7.41E+012.76E-010.00E+000.00E+000.00E+00-3.02E+01

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-8.47E+023.59E+000.00E+000.00E+000.00E+003.98E+018.47E+02-3.59E+000.00E+000.00E+000.00E+00-2.19E+01

-9.59E+02-2.40E+010.00E+000.00E+000.00E+002.19E+019.59E+022.40E+010.00E+000.00E+000.00E+00-1.42E+02

-1.13E+038.52E+010.00E+000.00E+000.00E+001.42E+021.13E+03-8.52E+010.00E+000.00E+000.00E+002.84E+02

-1.44E+03-3.39E+020.00E+000.00E+000.00E+00-2.84E+021.44E+033.39E+020.00E+000.00E+000.00E+00-1.41E+03

-1.56E+038.15E+020.00E+000.00E+000.00E+001.41E+031.56E+03-8.15E+020.00E+000.00E+000.00E+002.66E+03

Sheet1

Sheet2

Sheet3

Use of Combined 1D/3D Meshes for Modeling the 3D ProblemFig. 15

Elevation(ft)Horizontal Displacement (ft)Full 3D & 1D/3DComparison Between Results from Full 3D and Combined 1D/3D MeshesFig. 16

Chart1

00

55

1010

1515

2020

2525

3030

3535

4040

4545

5050

5555

6060

6565

7070

Sheet1

Z3d3d-SLAVED

00.00E+000.00E+00

51.05E-021.05E-02

102.31E-022.31E-02

153.32E-023.32E-02

204.19E-024.19E-02

254.93E-024.94E-02

305.55E-025.55E-02

356.03E-026.03E-02

406.37E-026.38E-02

456.56E-026.57E-02

506.59E-026.60E-02

556.44E-026.45E-02

606.08E-026.09E-02

654.11E-024.12E-02

700.00E+000.00E+00

Sheet1

Sheet2

Sheet3

Validity of the Use of Modifier from Elastic Analysis in Elasto-Plastic AnalysisSimplified 3D Mesh

3D Mesh: Plan View of a Portion of the Mesh Around the PilesFig. 17

2D Mesh

Pile

Pile

Pile

PilePile

F

Time

Single Pile4 Piles

(a) Slab with Single Pile Element (b) Slab with 4 pile Elements

(c) Variation of F with TimeFig. 13. Comparison of Values of F Calculated with Single and 4 PilesAnalysis of a Horizontal Slab to Find FObservation: F varies with loading

3D2D2D (F=0.162)Observation: Stresses in the piles calculated by the 2D analysis with modified pile properties are close to those calculated by the 3D analysis

Chart3

000

555

101010

151515

202020

252525

303030

353535

404040

454545

505050

555555

606060

656565

707070

Horizontal Deflection (ft)

Z (ft)

Sheet1

StressesStressesStressesStresses

inc=1: t=.058inc=1 3D bending etcinc=1 2D bending etc, F=1inc=1 2D bending etc, F=.056inc=1 2D bending etc, F=.162inc=1 3D bending etcinc=1 2D bending etc, F=1inc=1 2D bending etc, F=.056inc=1 2D bending etc, F=.162

z3D2dF=.056F=.162axisheMaxisheMaxisheMaxisheMaxisheMaxisheMaxisheMaxisheM

00.00E+000.00E+000.00E+000.00E+00-6.01E+01-7.38E+01-2.93E+02-8.03E+003.86E+012.20E+022.36E+006.85E+002.68E+01-1.23E+001.49E+016.33E+01-1.06E+00-1.31E+00-4.07E+01-7.11E-02-0.34161-15.403.73E-01-1.0823-33.232-6.72E-02-0.81354-27.3456

51.85E-048.44E-051.49E-041.29E-048.34E+002.24E+017.56E+016.22E+003.17E+002.65E+011.13E+01-2.01E+00-7.45E+009.92E+00-2.86E+00-1.11E+011.48E-013.96E-011.05E+015.50E-02-0.0280545-1.85551.79E+000.317589.2385.42E-010.1561564.7952

103.81E-042.30E-042.97E-042.83E-04-1.25E+01-8.09E+00-3.65E+019.58E+004.72E+001.07E+011.29E+018.58E-012.62E+001.20E+011.28E+003.24E+00-2.21E-01-1.43E-01-5.07E+008.48E-02-0.041772-0.749102.04E+00-0.135564-3.24886.55E-01-0.069888-1.39968

156.00E-043.85E-044.49E-044.36E-045.97E-01-5.89E+004.02E+00-1.77E+019.74E-01-1.29E+01-1.18E+01-3.19E-01-1.67E+00-1.44E+01-3.29E-01-3.18E+001.06E-02-1.04E-015.59E-01-1.57E-01-0.00861990.90315-1.86E+000.0504022.0708-7.86E-010.01796341.37376

208.14E-045.30E-045.88E-045.76E-04-4.50E+018.55E+003.35E+01-2.16E+011.17E+00-1.78E+01-1.70E+012.87E-01-7.17E-02-1.92E+014.13E-01-1.53E+00-7.97E-011.51E-014.66E+00-1.91E-01-0.01035451.24620-2.69E+00-0.0453460.088908-1.05E+00-0.02254980.66096

259.82E-046.56E-047.16E-047.02E-04-3.30E+02-6.22E+00-9.28E+00-2.05E+011.59E-01-2.37E+01-1.84E+01-2.49E-01-1.51E+00-2.02E+01-3.30E-01-3.60E+00-5.84E+00-1.10E-01-1.29E+00-1.81E-01-0.001407151.65925-2.91E+000.0393421.8724-1.10E+000.0180181.5552

301.14E-037.56E-048.23E-048.08E-04-8.15E+017.88E+002.18E+01-2.10E+011.12E+00-2.44E+01-1.94E+012.70E-01-2.64E-01-2.09E+014.18E-01-1.95E+00-1.44E+001.39E-013.03E+00-1.86E-01-0.0099121.70830-3.07E+00-0.042660.32736-1.14E+00-0.02282280.8424

351.28E-038.29E-049.17E-048.97E-04-1.85E+02-1.90E+01-1.76E+01-1.49E+011.65E+00-3.01E+01-1.52E+01-1.60E-01-1.61E+00-1.54E+01-1.35E-01-4.04E+00-3.27E+00-3.36E-01-2.45E+00-1.32E-01-0.01460252.10735-2.40E+000.025281.9964-8.41E-010.0073711.74528

401.41E-038.69E-049.87E-049.61E-04-1.07E+013.09E+017.72E+01-1.22E+013.89E+00-3.83E+01-1.31E+011.03E-01-8.10E-01-1.28E+015.63E-01-3.37E+00-1.89E-015.47E-011.07E+01-1.08E-01-0.03442652.68140-2.07E+00-0.0162741.0044-6.99E-01-0.03073981.45584

451.46E-038.66E-041.04E-039.99E-04-1.34E+02-6.56E+01-7.71E+01-1.82E+015.37E+00-5.77E+01-1.54E+011.04E+00-1.32E+00-1.54E+012.20E+00-6.18E+00-2.37E+00-1.16E+00-1.07E+01-1.61E-01-0.04752454.03945-2.43E+00-0.164321.6368-8.41E-01-0.120122.66976

501.51E-037.98E-041.04E-039.87E-048.28E+017.21E+012.51E+02-1.08E+01-2.43E+00-8.46E+01-9.45E+00-4.06E-01-6.51E+00-8.91E+00-6.57E-01-1.72E+011.47E+001.28E+003.49E+01-9.56E-020.02150555.92250-1.49E+000.0641488.0724-4.86E-010.03587227.4304

551.26E-036.45E-049.50E-048.75E-041.49E+02-5.89E+01-1.10E+023.94E+01-8.58E+00-7.24E+013.28E+01-8.76E-01-4.48E+003.57E+01-4.40E-01-1.39E+012.64E+00-1.04E+00-1.53E+013.49E-010.0759335.068555.18E+000.1384085.55521.95E+000.0240246.0048

601.01E-034.19E-047.76E-046.69E-042.58E+021.36E+011.84E+024.56E+01-1.09E+01-2.95E+013.75E+017.09E+00-9.93E-024.06E+016.77E+00-1.17E+014.57E+002.41E-012.56E+014.04E-010.0964652.065605.93E+00-1.120220.1231322.22E+00-0.3696425.0544

654.89E-041.64E-044.71E-043.44E-043.61E+021.70E+021.16E+024.41E+01-8.28E+012.49E+012.30E+01-2.52E+01-3.55E+013.03E+01-4.44E+01-4.56E+016.39E+003.01E+001.61E+013.90E-010.73278-1.743653.63E+003.981644.021.65E+002.4242419.6992

700.00E+000.00E+000.00E+000.00E+00


inc=50Deflection-elastic: t=.7902d2dinc=50 3D bending etcinc=50 2D bending etc, F=1inc=50 2D bending etc, F=.056inc=50 2D bending etc, F=.162inc=50 3D bending etc, F=1inc=50 2D bending etc, F=1inc=50 2D bending etc, F=.056inc=50 2D bending etc, F=.162

z3d2dF=.0388F=.127axisheMaxisheMaxisheMaxisheMaxisheMaxisheMaxisheMaxisheM

00.00E+000.00E+000.00E+000.00E+006.67E+03-3.05E+03-1.20E+041.67E+031.46E+039.66E+031.44E+033.04E+021.21E+031.61E+036.27E+022.79E+031.18E+02-5.40E+01-1.67E+031.48E+01-12.921-676.20002.28E+02-48.032-1500.48.79E+01-34.2342-1205.28

57.52E-033.93E-036.83E-035.85E-031.25E+041.25E+033.25E+031.02E+033.93E+012.34E+031.00E+03-1.20E+02-3.10E+021.08E+03-1.78E+02-3.47E+022.21E+022.21E+014.52E+029.03E+00-0.347805-163.850701.58E+0218.96384.45.90E+019.7188149.904

101.58E-021.17E-021.45E-021.39E-025.80E+03-5.20E+02-3.02E+031.39E+032.58E+022.15E+031.34E+035.75E+012.88E+021.41E+038.47E+015.42E+021.03E+02-9.20E+00-4.20E+021.23E+01-2.2833-150.5102.12E+02-9.085-357.127.70E+01-4.62462-234.144

152.74E-022.16E-022.49E-022.41E-021.52E+04-6.41E+01-4.18E+028.32E+021.71E+028.57E+028.25E+02-1.37E+011.16E-018.66E+026.03E+001.19E+022.69E+02-1.13E+00-5.81E+017.36E+00-1.51335-59.99151.30E+022.1646-0.143844.73E+01-0.329238-51.408

204.07E-023.25E-023.64E-023.55E-027.46E+035.58E+01-9.80E+015.58E+022.27E+023.13E+005.80E+023.95E+016.85E+016.01E+026.56E+018.87E+011.32E+029.88E-01-1.36E+014.94E+00-2.00895-0.2191209.16E+01-6.241-84.943.28E+01-3.58176-38.3184

255.45E-024.33E-024.84E-024.72E-026.63E+01-2.52E+02-3.77E+02-3.66E+011.32E+02-1.13E+035.36E+01-2.97E+01-1.29E+023.88E+01-3.11E+01-2.39E+021.17E+00-4.46E+00-5.24E+01-3.24E-01-1.168279.1258.47E+004.6926159.962.12E+001.69806103.248

306.85E-025.31E-025.91E-025.78E-022.99E+033.38E+028.84E+02-2.94E+022.53E+02-1.79E+03-1.47E+023.34E+011.98E+01-1.86E+025.56E+01-8.36E+015.29E+015.98E+001.23E+02-2.60E+00-2.23905125.330-2.32E+01-5.2772-24.552-1.02E+01-3.0357636.1152

358.17E-026.07E-026.91E-026.74E-02-4.39E+03-9.59E+02-8.05E+02-6.75E+022.72E+02-3.06E+03-4.31E+02-7.34E+00-1.47E+02-5.05E+023.05E+01-3.62E+02-7.77E+01-1.70E+01-1.12E+02-5.97E+00-2.4072214.235-6.81E+011.15972182.28-2.76E+01-1.6653156.384

409.42E-026.50E-027.69E-027.47E-02-1.41E+031.38E+033.99E+03-7.37E+022.78E+02-4.42E+03-5.29E+024.39E+01-1.11E+02-6.11E+021.03E+02-5.14E+02-2.50E+012.44E+015.55E+02-6.52E+00-2.4603309.440-8.36E+01-6.9362137.64-3.34E+01-5.6238222.048

451.02E-016.45E-028.17E-027.81E-02-6.22E+03-2.93E+03-2.90E+03-8.47E+021.31E+00-5.81E+03-6.14E+025.17E+01-3.30E+02-7.12E+028.30E+01-1.03E+03-1.10E+02-5.19E+01-4.03E+02-7.50E+00-0.0115935406.745-9.70E+01-8.1686409.2-3.89E+01-4.5318444.96

501.09E-015.80E-028.00E-027.48E-02-4.86E+033.45E+031.17E+04-8.83E+02-3.71E+02-5.81E+03-6.33E+02-3.41E+01-5.88E+02-7.42E+02-9.21E+01-1.45E+03-8.60E+016.11E+011.63E+03-7.81E+003.28335406.750-1.00E+025.3878729.12-4.05E+015.02866626.4

551.02E-014.55E-026.82E-026.27E-02-4.10E+03-5.54E+03-5.53E+03-1.20E+02-7.25E+02-3.96E+03-1.96E+01-2.01E+02-4.18E+02-9.54E+01-2.72E+02-9.86E+02-7.26E+01-9.81E+01-7.69E+02-1.06E+006.41625277.255-3.10E+0031.758518.32-5.21E+0014.8512425.952

609.01E-022.90E-025.11E-024.50E-02-6.80E+032.34E+032.22E+04-4.83E+02-1.26E+02-3.34E+02-4.24E+026.44E+025.85E+02-5.25E+028.21E+023.72E+02-1.20E+024.14E+013.09E+03-4.27E+001.115123.3860-6.70E+01-101.752-725.4-2.87E+01-44.8266-160.704

654.46E-021.15E-023.16E-022.37E-02-2.29E+041.54E+041.05E+04-1.39E+03-6.27E+032.96E+02-2.44E+03-1.77E+03-2.63E+03-2.23E+03-3.24E+03-3.73E+03-4.05E+022.73E+021.46E+03-1.23E+0155.4895-20.7265-3.86E+02279.663261.2-1.22E+02176.9041611.36

700.00E+000.00E+000.00E+000.00E+00

Sheet1

Sheet2


Z (ft)

Sheet3

Axial stress (psi)

Z (ft)

Shear stress (psi)

Z (ft)

bending stress, inc=1

Chart4

0000

55570

101010

151515

202020

252525

303030

353535

404040

454545

505050

555555

606060

656565

Axial Stress (psi)

Z (ft)

Sheet1


















700.00E+000.00E+000.00E+000.00E+00















551.02E-014.55E-026.82E-026.27E-02-4.10E+03-5.54E+03-5.53E+03-1.20E+02-7.25E+02-3.96E+03-1.96E+01-2.01E+02-4.18E+02-9.54E+01-2.72E+02-9.86E+02-7.26E+01-9.81E+01-7.69E+02-1.06E+006.41625277.255-3.10E+0031.758518.32-5.21E+0014.8512425.952

609.01E-022.90E-025.11E-024.50E-02-6.80E+032.34E+032.22E+04-4.83E+02-1.26E+02-3.34E+02-4.24E+026.44E+025.85E+02-5.25E+028.21E+023.72E+02-1.20E+024.14E+013.09E+03-4.27E+001.115123.3860-6.70E+01-101.752-725.4-2.87E+01-44.8266-160.704

654.46E-021.15E-023.16E-022.37E-02-2.29E+041.54E+041.05E+04-1.39E+03-6.27E+032.96E+02-2.44E+03-1.77E+03-2.63E+03-2.23E+03-3.24E+03-3.73E+03-4.05E+022.73E+021.46E+03-1.23E+0155.4895-20.7265-3.86E+02279.663261.2-1.22E+02176.9041611.36

700.00E+000.00E+000.00E+000.00E+00

Sheet1

Sheet2


Z (ft)

Sheet3

Axial stress (psi)

Z (ft)

Shear stress (psi)

Z (ft)

bending stress, inc=1

Axial Stress (psi)

Z (ft)

Shear Stress (psi)

Z (ft)

Bending Stress (psi)

Z (ft)

Chart5

0000

55570

101010

151515

202020

252525

303030

353535

404040

454545

505050

555555

606060

656565

Shear Stress (psi)

Z (ft)

Sheet1


















700.00E+000.00E+000.00E+000.00E+00















Documents

Modeling Embankment Induced Lateral Loads on Deep Foundations