井点抽水时饱和分层地基的传递矩阵解

从直角坐标系下三维Biot固结问题控制方程出发,引入位移函数,并对各个变量进行关于时间t的Laplace变换和关于x、y的双重Fourier变换,得到了z=z处和z=0处的8×8传递矩阵;根据各土层间以及井点抽水作用处的连续条件、边界条件,并结合传递矩阵的性质和Laplace-Fourier逆变换技术,求得井点抽水时饱和分层地基的真实解答。数值计算结果表明,随着井点抽水时间的增加,饱和多层地基的地表位移逐渐增大。

TRANSFER MATRIX SOLUTIONS FOR SATURATED MULTI-LAYERED SOIL DUE TO PUMPING FROM WELL POINT

Starting from the governing equations of Biot three dimensional consolidation problem and introducing the displacement functions,the 8 order transfer matrix between z=z and z=0 is obtained by taking the Laplace transform with respect to time(t) and the double Fourier transform with respect to coordinate x and y.According to the continuity conditions between adjacent layers and the horizon plane of well point pump and boundary conditions,the actual solutions of multi-layered soil due to pumping from well point are obtained by using the transfer matrix properties and the techniques of the Laplace-Fourier inverse transforms.Numerical results show that the surface settlement of saturated multi-layered soil increases with the increase of time.