Source codes and data files from Application of low-order potential solutions to higher-order vertical traction boundary problems in an elastic half-space

New solutions of potential functions for the bilinear vertical traction boundary condition are derived and presented. The discretization and interpolation of higher-order tractions and the superposition of the bilinear solutions provide a method of forming approximate and continuous solutions for the equilibrium state of a homogeneous and isotropic elastic half-space subjected to arbitrary normal surface tractions. Past experimental measurements of contact pressure distributions in granular media are reviewed in conjunction with the application of the proposed solution method to analysis of elastic settlement in shallow foundations. A numerical example is presented for an empirical ‘saddle-shaped’ traction distribution at the contact interface between a rigid square footing and a supporting soil medium. Non-dimensional soil resistance is computed as the reciprocal of normalized surface displacements under this empirical traction boundary condition, and the resulting internal stresses are compared to classical solutions to uniform traction boundary conditions.

本文推导并给出了双线性竖向面力（traction）边界条件下势函数的新型解答。通过对高阶面力进行离散化与插值，并叠加双线性解答，可构建出受任意法向面力作用的各向同性均匀弹性半空间平衡状态的近似连续解。本文结合所提解答方法在浅基础弹性沉降分析中的应用，综述了过往颗粒介质接触压力分布的实验测量结果。针对刚性方形基础与承托土体介质间接触界面处的经验"鞍形"面力分布，本文给出了一个数值算例。在该经验面力边界条件下，本文将无量纲土体抗力计算为归一化表面位移的倒数，并将所得内部应力与均布面力边界条件下的经典解答进行了对比。