层状地基中单桩负摩擦问题积分方程解法

利用Biot固结理论和积分方程方法研究了表面有堆载的层状地基中单桩负摩擦问题。根据层状饱和土的圆形载荷基本解得出了单桩在圆形均布载荷作用下在时间域内的第二类Fredholm积分方程组。运用Laplace变换对上述积分方程组进行简化。再结合传递和刚度矩阵传递到各个层中去，对变换域内的积分方程采用Schapery 逆变换方法得到时域内单桩的近似积分方程。求解积分方程组并进行相应的数值逆变换，就可得出层状地基中的单桩在表面圆形均布载荷作用下的位移、轴力、孔压和桩侧摩阻力随时间的变化情况。计算结果表明，桩侧剪力和孔压分层明显。

Integral equation method to analyze negative skin friction on single pile in layered deposits

The negative friction problem of single pile, which is in layered porous half-space under the surface load, is studied by using Biot’s consolidation theory and integral equation method. The poroelastic half-space considered rheology is governed by Biot’s consolidation theory and the Merchant model is used to describe the porous half-space’s rheology. The second kind of Fredholm integral equations of the pile subjected to circular load in layered porous half-space is obtained by using the fundamental solution. The integral equations can be simplified by means of Laplace transform methods .These equations can be transferred to each layer by the transfer matrix and stiffness-matrix approach. By the numerical solutions of the integral equations and the corresponding inverse integral transforms the displacement, axial force, pore pressure and shear stress of the pile and pore pressure along the pile axis are obtained. It is indicated that the shear stress of the pile and pore pressure along the pile axis are obviously layer built.