Nonlinear solutions of lateral response for piles under axial and lateral load embedded in layered soils
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摘要: 对于承受轴向荷载的水平受荷桩，以往研究大多基于线弹性或弹塑性水平荷载传递模型。为提升轴横受荷桩的计算设计水平，采用轴向荷载传递法计算桩身轴力，考虑桩身轴力引起的P-Δ效应，基于双曲线型水平荷载传递模型考虑桩-土体系变形的非线性特征，对成层土中轴横受荷桩的水平响应进行分析求解，得到了轴横荷载作用下桩身变形和内力的非线性有限差分解，并采用MATLAB语言编制了计算程序。使用模型试验算例与基于现场试验的有限元算例对非线性解的准确性进行对比验证，结果表明：计算结果与算例数据吻合良好，可靠性较高；采用不同荷载传递模型的计算结果在不同荷载水平下有所差异，在较大荷载水平下桩-土变形的非线性特点不容忽视。Abstract: Most of the previous studies were based on the linearly elastic or linearly elastic-plastic horizontal load transfer model for the laterally loaded piles undergoing axial load.In order to improve the calculation and design accuracy of axially and laterally loaded piles, considering the P-Δ effect caused by axial force of piles using the axial load transfer method, this paper proposes a nonlinear analysis approach based on hyperbola load transfer model to calculate the lateral response of elevated piles embedded in layered soils.The nonlinear finite difference solutions of the deformation and internal force for the pile shaft are obtained, and the relevant computer program is developed by MATLAB software.The accuracy of the nonlinear solutions is verified by utilizing the model test and the finite element calculation based on the field test.The calculation results showed that the results obtained by the nonlinear approach are in good agreement with the model test and finite element data.Besides, the results calculated by the approaches with different load transfer models are compared under different load levels.The nonlinear characteristics of pile-soil deformation cannot be ignored in calculation of lateral pile responses under large load.
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图 1 计算模型
H0.桩顶承受水平荷载; V0.轴向荷载；M0.弯矩; L0.桩身自由段长度; Lb.地面埋深段长度; d.桩径; EI.桩体刚度
Figure 1. Calculation model
图 2 土层i内桩体微单元受力图
Q.微元体受到的剪力；M.微元体受到的弯矩; N.微元体受到的轴力；p.单位桩长受到的地基土反力
Figure 2. Force diagram of pile segment in the i th soil layer
图 6 桩身弯矩预测值与实测值对比
Figure 6. Comparison between predicted and measured bending moments of piles
图 7 水平荷载-位移曲线
Figure 7. Comparison of horizontal load and horizontal deflection from calculated, FEM analysis and field tests
图 9 桩身轴力计算值与有限元结果对比
Figure 9. Comparison between calculation results and FEM axial force of piles
图 10 桩身位移计算值与有限元结果对比
Figure 10. Comparison between calculation results and FEM of displacements of piles
图 11 桩身弯矩计算值与有限元结果对比
Figure 11. Comparison between calculation results and FEM bending moments of piles
图 12 不同分析方法计算结果对比
Figure 12. Comparison of calculation results of different calculation methods
表 1 现场试验地基土主要物理参数
Table 1. Main physical properties of soils
土层 层厚/m 内摩擦角/(°) 黏聚力/kPa 弹性模量/MPa 泊松比ν 桩 - - - 4.2×104 0.2 回填土 3 12 8 40 0.31 砂土 3 28 13 65 0.33 黏土1 4 14 30 18 0.4 黏土2 17 18 35 26 0.4 风化岩 1 35 28 675 0.25 
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表 2 各土层理论计算参数
Table 2. Computed parameters of each soil layer
土层 地基反力系数ηh/(MN·m-3) Ng n α0 回填土 35 1.4 1.7 0 砂土 45 1.9 1.7 0 黏土1 15 0.8 0.5 0.2 黏土2 18 1 0.8 0.3 风化岩 100 2.3 1.7 0
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