National Academies Press: OpenBook

Design Guidelines for Increasing the Lateral Resistance of Highway-Bridge Pile Foundations by Improving Weak Soils (2011)

Chapter: Chapter 5 - Finite Element Modeling of Pile Group Load Tests

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Suggested Citation:"Chapter 5 - Finite Element Modeling of Pile Group Load Tests." National Academies of Sciences, Engineering, and Medicine. 2011. Design Guidelines for Increasing the Lateral Resistance of Highway-Bridge Pile Foundations by Improving Weak Soils. Washington, DC: The National Academies Press. doi: 10.17226/14574.
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Page 54
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Suggested Citation:"Chapter 5 - Finite Element Modeling of Pile Group Load Tests." National Academies of Sciences, Engineering, and Medicine. 2011. Design Guidelines for Increasing the Lateral Resistance of Highway-Bridge Pile Foundations by Improving Weak Soils. Washington, DC: The National Academies Press. doi: 10.17226/14574.
×
Page 55
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Suggested Citation:"Chapter 5 - Finite Element Modeling of Pile Group Load Tests." National Academies of Sciences, Engineering, and Medicine. 2011. Design Guidelines for Increasing the Lateral Resistance of Highway-Bridge Pile Foundations by Improving Weak Soils. Washington, DC: The National Academies Press. doi: 10.17226/14574.
×
Page 56
Page 57
Suggested Citation:"Chapter 5 - Finite Element Modeling of Pile Group Load Tests." National Academies of Sciences, Engineering, and Medicine. 2011. Design Guidelines for Increasing the Lateral Resistance of Highway-Bridge Pile Foundations by Improving Weak Soils. Washington, DC: The National Academies Press. doi: 10.17226/14574.
×
Page 57
Page 58
Suggested Citation:"Chapter 5 - Finite Element Modeling of Pile Group Load Tests." National Academies of Sciences, Engineering, and Medicine. 2011. Design Guidelines for Increasing the Lateral Resistance of Highway-Bridge Pile Foundations by Improving Weak Soils. Washington, DC: The National Academies Press. doi: 10.17226/14574.
×
Page 58
Page 59
Suggested Citation:"Chapter 5 - Finite Element Modeling of Pile Group Load Tests." National Academies of Sciences, Engineering, and Medicine. 2011. Design Guidelines for Increasing the Lateral Resistance of Highway-Bridge Pile Foundations by Improving Weak Soils. Washington, DC: The National Academies Press. doi: 10.17226/14574.
×
Page 59
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Suggested Citation:"Chapter 5 - Finite Element Modeling of Pile Group Load Tests." National Academies of Sciences, Engineering, and Medicine. 2011. Design Guidelines for Increasing the Lateral Resistance of Highway-Bridge Pile Foundations by Improving Weak Soils. Washington, DC: The National Academies Press. doi: 10.17226/14574.
×
Page 60

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

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

56 The pile heads are extended into the cap base for 0.5 ft to account for the cap pinning effects on the pile head rotation. 5.2 FEM Model for Pile Group Model in Virgin Clay The pile group in virgin clay provides the basic data for com- parison with the pile group with soil improvements. The mesh used for the FEM pile group model in virgin soil is shown in Figure 5-2. A total of 50,247 nodes and 44,796 elements were in the FEM mesh. A displacement control method is used in analyzing the pile group test. The node on the pile top is selected for the displacement control, which is laterally pushed up to a maximum displacement of 1.5 in. The static displace- ment is applied in 50 steps with a pile head lateral displacement of 0.03 in. per loading step. The load-displacement response curves computed by the FEM are plotted in Figure 5-3 in comparison with the measured curve. Generally, they exhibit good agreement with test data from both Cap 1 and 2 of Test 1. The load-rotation response curve computed by the FEM is plotted in Figure 5-4 and the results seem to plot between the test data Cap 1 and 2 of Test 1 at the beginning loading stage and thereafter tend to be close to test data of Cap 2 and has considerable discrepancy to the test data of Cap 1. However, the load rotation test data of Cap 1 was somewhat smaller than that of Cap 1; it was unclear whether this resulted from measurement errors or from the fact that the corbel on Cap 1 did not extend across the entire cap as did the corbel for Cap 2. It can be seen that the soil parameters calibrated from the single pile test in virgin clay appear to be appropriate to the pile group test. The FEM model of pile group in virgin clay can sim- ulate the essential load-displacement response of the test. 5.3 Pile Group Model in Virgin Clay with Excavation The pile group in virgin clay with excavation provides the estimation of the passive force by the unsaturated clay against the pile group. A similar mesh design strategy was followed for the FE model of pile group in virgin clay without excava- tion. Once again, a displacement control method was used for this problem. The node on the pile top was selected for the displacement control, which is laterally displaced to 1.5 in. The maximum displacement was produced using 50 loading Figure 5-2. Finite element mesh for model of pile group in virgin soil. Figure 5-3. Simulated and tested displacement-load results for pile group in virgin clay. Figure 5-4. Simulated and tested load-rotation response curve results for pile group in virgin clay. 0 50 100 150 200 250 300 350 400 0.0 0.5 1.0 1.5 2.0 Displacement (in) La te ra l F o rc e (ki ps ) Test1, Cap1 Test1, Cap2 Model 0 50 100 150 200 250 300 350 400 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Rotation (degree) La te ra l F or ce (k ip s- ft) Test1 Cap1 Test1 Cap2 Model

steps with pile head lateral displacement of 0.03 in. per load- ing step. The mesh of the FEM pile group model in virgin soil with excavation adjacent to the cap is shown in Figure 5-5. A total of 49,977 nodes and 44,666 elements were in the FEM mesh. The load-displacement curves computed using the FEM model with and without excavation adjacent to the cap were used to produce the passive force-displacement curve. The passive force on the pile cap was obtained by subtracting the load with excavation from that without excavation. The simulated pas- sive force-displacement curve is compared with the measured curve in Figure 5-6. The simulated force is greater than the measured force for displacements less than about 0.3 in., which is as expected for small displacement due to the residual dis- placement. However, the agreement is satisfactory for displace- ments more than 0.3 in. 5.4 FEM Model of Pile Group with Mass Mixing The mass mixing treatment zone in the FEM model is shown in Figure 5-7. The modeled zone is 10 ft deep, 4 ft long in the direction of the lateral loading direction, and 11 ft wide trans- verse to the loading direction. These dimensions are the same as in the field test. Six 3-in. diameter core samples were extracted and tested after 38 and 63 days of curing. The test results indicated an aver- age strength of 131 psi after 38 days and an average strength of about 140 psi after 63 days with a standard deviation of about 8 psi. Assuming that the soil-cement mixture cured at the same rate as concrete alone, the compressive strength of the mixture at the time of testing would be approximately 126 psi. Preliminary analyses suggested that the shear strength of the mass mixed wall was sufficient to allow the wall to behave essentially as a rigid block. Based on this conclusion and the fact that the mass mix has much higher strength than the clay, the mass mix is modeled as elastic material. This assump- tion will introduce little error to the pile load-displacement response against a more complicated material model for the mass mix. The Young’s modulus of the mass mix zone is estimated as 6.4 × 105 psi from the compressive strength of the mixture at the time of testing (126 psi) with the assump- tion that the Young’s modulus can be estimated with the same formula as that for concrete [E = 57000(f ′c)0.5]. The Poisson’s ratio of the mass mix is assumed to be 0.2. A comparison of load-displacement curves from the test data and the FEM model is provided in Figure 5-8. The FEM model provides very good agreement with the measured results. These results indicate that the linear elastic material model with the material properties described previously can reasonably represent the lateral resistance of the pile group after treatment with mass mixing. Furthermore, this result provides confidence that additional parametric studies can be used as “virtual load tests” for the purpose of developing a simplified model. 5.5 Pile Group Model with Jet Grouting Soil improvement using jet grouting was undertaken in Test 8. For Cap 1, improvement was limited to zones in the front and back sides of the pile cap, while for Cap 2 the improve- 57 Figure 5-5. Finite element mesh for model of pile group with excavation adjacent to cap. Figure 5-6. Simulated and tested pile cap passive pressure. 0 50 100 150 200 250 300 350 400 0.0 0.5 1.0 1.5 2.0 Displacement (in) La te ra l F or ce (ki ps ) Model, without Excavation Model, with Excavation Model, Passive Force Test, Passive Force

ment extended underneath the entire pile cap as shown in Fig- ure 5-9. Figure 5-10 shows a schematic profile diagram of the FEM model with the jet grout treatment zone. The model shown in Figure 5-2 was used to model the pile with jet grout treatment after appropriate elements in the model were assigned the properties corresponding to the soilcrete. Analy- ses suggested that the shear strength of jet grouting soilcrete was sufficient to allow the soilcrete zone to behave as a rigid block. Based on this conclusion and the fact that the soilcrete has a much higher strength than the clay, the soilcrete was modeled as an elastic material. This assumption will introduce little error into the pile load-displacement response relative to a more complicated material model for jet grouting soilcrete. The Young’s modulus of the soilcrete is estimated as 1.4 × 106 psi based on the compressive strength of the mixture at the time of testing, which would be approximately 600 psi. This modulus value is based on the assumption that the Young’s 58 Figure 5-7. FEM model profile with mass mix treatment zone beside the cap—mass mix zone is 10 ft deep, 4 ft long, and 11 ft wide transverse to loading. Figure 5-8. Comparison of load-displacement curves from FEM model and field test with mass mix zone adjacent to the pile cap. 0 100 200 300 400 500 600 0.0 0.5 1.0 1.5 2.0 2.5 Displacement (in) Lo ad (k ip s ) Model Test

59 Figure 5-9. Layout of test using jet grouting under Cap 2. Figure 5-10. Schematic profile drawing of FEM model with jet grouting beside and/or underneath the cap.

modulus can be reasonably well estimated based on the same formula as that for concrete, E = 57000(f′c)0.5. The Poisson’s ratio of the mass mix is assumed to be 0.2. A comparison of the measured load-displacement curve with that computed with the FEM model is provided in Fig- ure 5-11. Once again, the agreement between measured and computed results is generally satisfactory especially for pile cap displacement more than 0.5 in. The researchers noted that for small displacements of the cap less than 0.5 in., the load- displacement curve from the test is somewhat stiffer than the curve obtained by the FEM model. This could be due to the linkage between the pile cap and jet grouting soilcrete. Once again, the relatively good agreement suggests that using the linear elastic material model with the above-mentioned prop- erties can produce reliable estimates of the measured load- deflection curve obtained from the field tests with jet grout treatment around the pile group. Therefore, the same model can be used for parametric studies using the variations on geometries to expand our understanding of the increased lat- eral resistance provided by jet grouting. 60 0 100 200 300 400 500 600 700 800 900 1000 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Displacement (in) La te ra l F or ce (ki ps ) Test Model Figure 5-11. Comparison of FEM computed and measured load-displacement curve with jet grouting below and beside the cap. The jet grouting soilcrete has a depth of 10 ft from the cap base, a length of 15 ft, and a width of 9 ft.

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TRB’s National Cooperative Highway Research Program (NCHRP) Report 697: Design Guidelines for Increasing the Lateral Resistance of Highway-Bridge Pile Foundations by Improving Weak Soils examines guidance for strengthening of soils to resist lateral forces on bridge pile foundations.

The report presents computational methods for assessing soil-strengthening options using finite-element analysis of single piles and pile groups and a simplified approach employing commercially available software.

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