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51 CHAPTER 4 Finite Element Modeling of Single Pile Load Test The soils in the field are all clays typically classified as CL The simplified distributions of shear wave velocity and or CH according to the borehole log shown in Figure 3-3(a). undrained shear strength based on the test data are plotted in The soil is modeled up to a depth of 45 ft. The soil was divided Figures 4-1 and 4-2, respectively. into 13 layers. The top 9 layers are all 2.5 ft thick, the next 3 lay- The total length of the pile is 46.5 ft and the pile toe depth ers are 5 ft thick, and the last layer is 7.5 ft thick, as shown in is 45 ft in the soil. The pile is modeled as a 1-D linear elastic Table 4-1. beam-column element. For the steel pipe pile with concrete Since all of these 13 soil layers are primarily clays, the soils fill, the composite EI is required. The pile EI is calculated as are modeled with a von Mises model without hardening. A 1.41 107 kip-in2, using a compressive strength of 5150 psi total of 13 sets of material parameters for von Mises type elasto- based on compression tests on concrete cylinders at the time plasticity were estimated from the lab or in-situ tests. In the of testing. The steel cross-sectional area is computed based on finite element model, the elastic Young's moduli and compres- an outside diameter of 12.75 in. and a 0.375-in. wall thickness. sion strengths are needed. The elastic Young's moduli can be Young's modulus for the pile is 29,000 ksi and the Poisson's estimated from the following relationships: ratio is 0.20. Since the 1-D beam-column element has no physical dimen- 2 sion in the cross-sectional plain, special measures were taken to G = rd vs (6) g include the diameter effects of the pile by connecting the soil nodes with pile nodes using radially rigid "spokes," which also E = 2 (1 + v )G (7) are modeled by a very stiff elastic beam-column element. Non-extension spring elements link the outer ends of the spokes and the soil nodes to model the gapping between the where pile and the soil. The compression stiffness of these spring G is the shear modulus; elements is very large but the extension stiffness is zero. To vs is the shear wave velocity measured from the downhole avoid possible numerical instability, a very small extension seismic cone testing; stiffness value is used in the finite element model. is the total soil unit weight that can be estimated by aver- The soil was modeled as 3456 3-D solid element accounting aging from the lab data along the depth; for large deformation and large strain effects. The pile was g is the gravity constant; modeled using 36 1-D elastic beam elements. The pile and the rd is a reduction factor that accounts for the large deforma- surrounding soil were linked by 468 non-extension spring ele- tion effect and remolding effect, here a value of 0.25; ments. A total of 4,717 nodes were in the FEM mesh, which is E is the Young's modulus in the elastic part of the von shown in Figure 4-3. The nodes on the outside surface of the Mises model; and cylinder are restrained against horizontal movements. The The Poisson's ratio, v, is assumed as 0.45 due to the nearly nodes on the bottom surface are restrained against move- undrained condition of the clay during the tests. ment in any directions. The movements of the nodes in the The yield strength in the von Mises yield function is twice middle plane are restricted to embody the load and geometry the measured undrained strength, as follows: symmetry. A displacement control method is used for this problem. k = 2su (8) The node on the pile top is selected for the displacement

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52 Table 4-1. Model parameters used for FEM model. Top Bottom Layer Depth Depth Thickness Su Vs # (Ft) (Ft) (Ft) (psf) (Fps) 1 0.0 2.5 2.5 950 416 2 2.5 5.0 2.5 325 389 3 5.0 7.5 2.5 350 357 4 7.5 10.0 2.5 400 338 5 10.0 12.5 2.5 450 355 6 12.5 15.0 2.5 500 425 7 15.0 17.5 2.5 525 495 8 17.5 20.0 2.5 550 565 9 20.0 22.5 2.5 600 550 10 22.5 27.5 5.0 655 500 11 27.5 32.5 5.0 750 500 12 32.5 37.5 5.0 845 500 13 37.5 45.0 7.5 940 500 Notes: Su is undrained shear strength; Vs is shear wave velocity; and Fps is feet per second. Shear Wave Velocity (fps) Undrained Shear Strength, Su (psf) 0 200 400 600 800 0 250 500 750 1000 1250 0 0 5 5 10 10 15 Depth Below Excavation (ft) 15 Depth Below Excavation (ft) Test 20 20 Simplified Model 25 25 30 30 35 35 Unconfined Torvane 40 40 Simplified Model 45 45 Figure 4-1. Tested, simplified, and Figure 4-2. Tested, simplified, and model shear wave velocity distribution. model undrained shear strength distribution.

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53 35 30 Pile Head Load (kips) 25 20 15 10 Test Model 5 0 0 0.5 1 1.5 2 2.5 3 Pile Head Deflection (in) Figure 4-4. Simulated and tested data on pile head load vs pile head displacement. 35 30 Pile Head Load (kips) 25 20 15 10 Test Figure 4-3. FEM mesh used for Model analysis of single pile lateral load 5 test. 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Pile Head Rotation (Degree) control, which is laterally pushed up to 2.5 in. The pile head Figure 4-5. Simulated and tested data on pile head is considered to be a free-head boundary with no rotational load vs pile head rotation. constraint. The static loading step number is 50 with pile head lateral displacement of 0.05 in. per loading step. The simulated pile head load versus pile head displacement with the test data. This suggests that the single pile in clay under and pile rotation are shown in Figures 4-4 and 4-5, respec- lateral loading can be satisfactorily simulated using the simple tively. The loads have been doubled to account for symmetry. von Mises soil model with the above-mentioned parameters. The curves exhibit the conventional hyperbolic shape that The calibrated parameters for the soil and pile will be used for would be expected for soft clay and are in good agreement the later pile group analysis.