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54 CHAPTER 5 Finite Element Modeling of Pile Group Load Tests 5.1 Pile Group FEM Mesh Design mass. This mesh design is advocated here for its generality and its convenience for parametric studies. The FEM mesh design for the pile group simulation is The basic mesh for pile group simulation is shown in Fig- tedious and time consuming. Since a considerable amount of ure 5-2. For boundary settings, all nodes at x = -22.5 (left side parametric study will be conducted, making a specific FEM surface of the model) and 31.5 ft (right side surface of the soil mesh for each case is not reasonable. Our strategy was to make model) have a zero displacement constraint in the x direction; a general mesh that reserves the same element groups for soil all nodes at y = 0 (symmetric plain of the soil block and toward improvements. A MATLAB program was coded for this pur- side surface of the model) and 22.5 ft (the forward side sur- pose. The mesh schematic is shown in Figure 5-1. According to face of the model) have a zero displacement constraint in the geometrical symmetry, only one-half of the domain was con- y direction; all nodes z = -45 ft (the bottom surface) have a sidered. The soil block is of 54 ft in. length (31.5 ft in the lateral zero displacement constraint in the z direction. load direction and 22.5 ft in the direction opposite to the lat- Since the cap concrete is much stiffer in comparison with the eral load direction), 22.5 ft width (half of the whole soil block) clays, it will introduce little error to the load-displacement rela- and 45 ft depth. The pile cap side is 9 ft square with a depth of tionship to model the cap as linear elastic material with a rela- 2.5 ft. The pile caps were constructed by excavating 2.5 ft into tively high Young's modulus. In our model, a typical concrete the virgin clay. In the tests, a corbel was constructed on each Young's modulus of 7.2 108 psf and a typical Poisson's ratio cap to allow the actuator to apply load above the ground sur- of 0.2 were used for the cap. The cap concrete was poured face without affecting the soil around the pile cap. The corbel against vertical soil faces on the front and back sides of each pile extended the full length of the pile cap for Cap 2 but was only cap. This construction procedure made it possible to evaluate about half of the pile length in Cap 1. The load was 0.92 ft above passive force against the front and back faces of the pile caps. the cap surface. In the FEM model, the 0.92 ft corbel was added In contrast, plywood forms were used along the sides of each to the cap thickness and the load was considered to be applied cap and were braced laterally against the adjacent soil face. This on the surface middle of the cap with 3.42 (2.5 + 0.92) ft thick- construction procedure created a gap between the cap sidewall ness. Considering symmetry, the cap length, width and depth and the soil so that side friction would be eliminated. In the dimension are 9 4.5 3.42 ft in the half FEM mesh shown in FEM model, the front face of the cap is linked with the soil by Figure 5-1. non-extension springs while the nodes at the other face of the The soil improvement zones in the FEM model are cap are modeled with different node numbers but with the located below the cap and on one side of the cap and can same coordinates as the adjacent soil nodes. extend to a depth of 12.5 ft. The model can accommodate a Similar to the single pile model, the piles are modeled as 1-D combination of soil improvement below and beside the cap. elastic beam elements. The pile is connected with the soil nodes The soil improvement zone is fixed at a width of 4.5 ft, which by radial rigid "spokes," which also are modeled by very stiff is the same as the width of the cap. However, the length of the elastic beam elements. Non-extension spring elements link the soil improvement zone is variable. The soil is also layered for outer ends of the spokes and the soil nodes to model the gap- different soil properties at different depths, as was the case for ping between the pile and the soil. The compression stiffness of the FEM model for the single pile simulation. For tests of soil these spring elements is very large but the extension stiffness is improvement, the material model of some zones can be zero. To avoid possible numerical instability, very small exten- changed from that of the virgin soil to that of the improved sion stiffness is alternatively input in the finite element model.

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55 Figure 5-1. FEM profile for the pile group.