Modeling Foundations in RS

Transcription

1 Modeling Foundations in RS 3

2 Piled Raft Modeling in RS 3 Deep foundation piles are commonly used to increase foundation stability and to increase the bearing capacity of structural systems. The design and analysis of these piles may be done using a finite element program, and as numerical modeling becomes more common in geotechnical engineering and design, it becomes increasingly important to understand the accuracy, and limitations, of numerical modeling tools. This article looks at a number of piled raft models in RS 3 and consists of the following three sections, Vertically Loaded Pile in Clay, Piled Raft Foundation in Sand and Piled Raft Foundation in Multiple Material Strata. Model geometry and mesh for vertically loaded pile in clay Piled raft foundation in sand Piled raft foundation in multiple material strata

3 Vertically Loaded Pile in Clay The model in this first section is based on a paper recently presented at the DFI Conference 2013, which discusses a verification study for RS 3 of a pile in clayey soil. The verification was based on a field study by Han and Ye (2006). In addition, a parametric analysis was carried out to examine the influence of different input parameters on the numerical results. The effects of interface stiffness, skin resistance, and soil modulus parameters on load-displacement and axial force response are investigated. A plastic Mohr-Coulomb failure criterion was used, and residual values were equal to initial values. The pile properties are summarized in Table 2. The base normal stiffness and unit weight are assumed values. Model Details The in-situ soil profile consisted of three horizontal layers; properties for each layer are summarized in Table 1. Table 1: Soil Material Properties Table 2: Pile strength and Stiffness parameters

4 Multilinear Skin Friction was defined by a function of maximum skin traction with depth. The skin traction plot, shown in Figure 1, was derived from the undrained shear strength plot by assuming that skin resistance is proportional to undrained shear strength. In order to avoid boundary condition effects, as well as minimize computation time, a number of initial analyses were carried out to determine the appropriate model size. A square 10x10m model, 14.6m deep, was chosen after the preliminary analyses. The model geometry and mesh are shown in Figure 2. A total of 3,417 nodes and 20,198 four-noded tetrahedral elements were used. The mesh was customized to be denser near the pile. For the pile itself, a nonconforming, embedded element was used. This element introduces nodes at points of intersection between the pile element and tetrahedral elements. Figure 1: Multilinear skin traction function Figure 2: Base model geometry and finite element mesh

5 The vertical pile load was applied at a rate of 10kN/h. In terms of groundwater conditions, initially the water table was set at the pile head. The ground surface was treated as a free drainage surface in the analysis, and a fully coupled stress and pore pressure analysis was carried out. Figure 3: Comparison of load-displacement response for base model Model Verification The base model accuracy was established by comparing both the load-displacement and axial force responses. Figure 3 compares the pile load-displacement response from the field study and finite element model. In both the field study and numerical analysis, plunging occurs at 135kN (in the analysis, nonconvergence indicated failure), verifying the loaddisplacement results obtained by RS 3. The axial force response was also used to verify the base model. Strains measured in the field were converted to axial force and compared to RS 3 results. Figure 4 provides the verification of the base model for axial force response. Figure 4: Comparison of axial force response for base model

6 Parametric Analysis Interface stiffness, skin resistance, and material property parameters are examined. All parametric analysis results were compared to the base model analysis results only. A selection of results from the parametric analyses are summarized in Figures 5 and 6. The main conclusions of these analyses were the following: s Both linear and C-Phi skin resistance methods significantly decrease pile capacity in the cases analyzed s An increase in the soil modulus decreases downward displacement prior to failure and increases axial force resistance along the pile s A decrease in modulus increases displacement and decreases axial resistance For the full set of conclusions, see the paper published in the DFI (2013). Figure 5: Effect of linear skin resistance on load-displacement response Figure 6: Effect of c-phi skin resistance method on load-displacement response

7 Piled Raft Foundation in Sand The previous section presented the results of a finite element parametric analysis of a single vertically loaded pile. In this section, 3D modeling of a piled raft foundation is discussed, highlighting the foundation analysis capabilities of RS 3. The model and material properties are adapted from Ryltenius (2011). Shown is a brief parametric investigation on the effect of pile spacing. Three different pile layouts were investigated, and a raft foundation with no piles was Figure 7: Raft foundation geometry and sample pile layout also examined. The model geometry is illustrated in Figures 7 and 8. The piled raft is seated on a layer of soft clay, with the water table located three meters below the ground surface. A uniform load of 30kN/m 2 is applied to the raft. Figure 9 (see next page) illustrates the displacement profile along the centre of the model for each pile layout. Figure 10 shows the effect of pile spacing on the axial force in the piles (the corner pile in each model was chosen for comparison purposes). Figure 8: Model geometry (in z-direction)

8 Displacement and axial force contours can also be examined to quickly see the effect that the pile layout has on the results. Deformed displacement contours, on an XZ plane in the centre of each model are compared in Figure 11. In creating the models, changing the pile layout was straightforward, since the pile pattern vertical and horizontal spacing can be quickly changed in the Edit Pile Pattern On Ends dialog. The ease with which pile layouts can be modified makes running a number of parametric analyses quite simple. In the same way, the pile length, orientation, and direction can be easily modified for additional analyses. Figure 9: Effect of pile layout on z-displacement Figure 11: Comparison of displacement contours for different pile layouts Figure 10: Effect of pile layout on pile axial force

9 Piled Raft Foundation in Multiple Material Strata In the previous set of parametric analyses, we examined the effect of pile layout on the behaviour of a piled raft foundation on a single material. This problem looks at 8x8m un-piled and piled raft foundations on sandy soil. Figure 12 illustrates the entire model, while Figure 13 shows the pile layout. Figure 13: Typical raft configuration Figure 12: 8x8m piled raft foundation

10 The subsurface consists of five different types of soil and a static water level of 3.5m below ground surface. Rock is assumed to be 30m below ground surface, which is considered as a rigid boundary in this analysis. The soil profile is summarized in Table 3. Table 3: Material layer elevations The following four cases were examined: Case 1-8m 8m un-piled raft with varying thickness: 0.25m, 0.4m, 0.8m, 1.5m, and 3m. The vertical load intensity is 215kN/m 2 Case 2-15m 15m un-piled raft with varying thickness: 0.25m, 0.4m, 0.8m, 1.5m, and 3m. The vertical load intensity is 215kN/m 2 Case 3-8m 8m piled raft with varying thickness: 0.25m, 0.4m, 0.8m, 1.5m, and 3m. The vertical load intensity is 215kN/m 2 and pile spacing is 3d. Figure 14: Bending moment of piled raft with different raft thicknesses Case 4 - Piled raft with varying pile spacing: 3d, 4d, 5d, 6d, and 7d. For each pile spacing the raft size changes proportionally and the vertical loading intensity of 215kN/m 2, 430kN/m 2, and 645kN/m 2 is applied. Figure 14 highlights some of the results obtained for Case 3. Bending moments obtained with different raft thicknesses are compared.

11 Figure 15 examines the bending moments obtained with different pile layouts. Notice that the pile layout has a much larger effect on the bending moment than raft thickness. References: Han, J., Ye, S. (2006). A field study on the behavior of micropiles in clay under compression and tension. Canadian Geotechnical Journal, 43(1), Ryltenius, A. (2011) FEM Modelling of Piled Raft Foundations in Two and Three Dimensions. Master s Dissertation. Geotechnical Engineering, Lund University. Figure 12: Bending moment of piled raft with uniform load of 215kN/m2 Sethna, E., Yacoub, T., Dang, K., and Curran, J. (2013). Finite Element Parametric Analysis of Vertically Loaded Pile in Clay. Presented in DFI. RS 3 Verification: Piled Raft Foundation in Sand