多层横观各向同性地基沉降理论解的推导

Elementary solution of ground settlement for the layered transversely isotropic medium

从应力平衡方程出发,引入位移调和函数,采用亨克尔积分变换法,推导了多层横观各向同性地基内任一点集中荷载作用下的弹性理论解.通过与文献结果比较,计算结果表明:采用Euler变换能够加快Hankel逆变换数值积分的收敛速度,该方法不仅可以考虑土体在竖直方向上由于地质沉积过程而形成的成层性,还可分析同一水平面上土的固有各向异性性质,使得理论计算的基本假定更接近于工程实际情形.

Based on the stress equation of equilibrium and the induction of the displacement regulating functions ,the elementary solutions of ground settlement for the layered transversely isotropie medium subjected to concentrated load are derived with the method of Hankel integral transform. Numerical results show that Euler transform can improve both the convergent speed and the quality of the solution of the Hankel inverse transform. The proposed method can consider the character of the layer soil in the vertical direction of the geological deposition and the inherent anisotropy nature of layer soil in the horizontal plane, which makes the calculation of basic assumptions closer to the actual project situation.