成层地基土中水平受荷桩桩身响应的矩阵传递解

Transfer matrix solutions for responses of laterally loaded piles in multilayered soil deposits

目前关于成层地基土体中水平受荷桩内力与变形的研究相对较少。将成层地基土体假设为均质弹性介质,将桩视为竖向放置的弹性地基梁,同时将桩-土之间的相互作用关系假设为一般形式的三参数地基反力模型,建立桩身响应的微分方程,并采用Laplace变换解得任意土层深度处桩身响应的矩阵传递系数进而得到成层地基土中水平荷载作用下桩身位移、转角、弯矩和剪力的矩阵传递解。相比传统的有限差分法与幂级数法,矩阵传递法求解成层地基土中的水平受荷桩时更加便捷。通过算例对比,验证了矩阵传递法解的正确性。最后进行了桩身响应的参数影响分析,结果表明:桩顶边界条件对桩身变形与内力沿桩身的分布规律影响显著;同时,地基反力模型中的参数0z和n对桩身最大水平位移、最大弯矩的影响较为明显。

Currently, there are few references available on the researches on the internal force and deflection of laterally loaded piles in multilayered soil deposits. Based on the assumptions of postulating that layered soils are homogeneous elastic media and the pile is a vertically embedded foundation beam, as well as the interaction between pile and soil is simulated by three-parametric subgrade reaction model, the governing differential equations for the pile responses in different soil layers are established, and the transfer matrix coefficients at arbitrary depth are obtained using the Laplace transform. Subsequently, the transfer matrix solutions for pile deflection, slope, bending moment and shear force under lateral loading are obtained. Compared with the conventional finite difference method and power series approach, the transfer matrix method is more convenient to solve pile responses in layered soils. Some comparisons are made between the results of references and the calculated ones by the proposed approach, and reasonable agreement is obtained. Finally, parametric studies on influence factors are also performed. The results indicate that the boundary conditions at pile head have a significant impact on the distribution of pile internal force and deflection along pile shaft. Besides that, z0 and n of reaction model have a remarkable influence on the maximum pile deflection and bending moment.