层状地基三维Biot固结问题的一个解耦解法

通过引入位移函数和中间变量,并对时间t进行Laplace变换,对坐标x,Y进行双重Fourier变换,将直角坐标系下通常包含8个相互耦合状态量的三维Biot固结方程解耦成一组包含6个状态量和一组包含2个状态量的2组方程;进而获得了单层地基三维Biot固结问题的传递矩阵;结合边界条件和连续条件,应用传递矩阵法得到层状地基三维Biot固结问题在Laplace-Fourier变换域内的解,通过进行Laplace-Fourier逆变换得到了该问题物理域的真实解.编制了计算程序,并进行了计算与分析,验证了解的正确性.

Uncoupled method for three-dimensional Biot's consolidation of multilayered soils

By introducing displacement functions and intermediate variables,combined with taking Laplace transform with respect to time t and double Fourier transform with respect to coordinates x,y,the three dimensional Biot's consolidation equations usually comprised of 8 coupled state vectors in the cartesian co-ordinate system are uncoupled into two sets of equations with 6 and 2 state vectors respectively;then the transfer matrix for the three dimensional Biot's consolidation of a single soil layer is acquired.The solution of multilayered soils in the Laplace-Fourier transform domain is obtained by using the transfer matrix method combined with the continuity conditions of adjacent layers and boundary conditions.The solution in physical domain can be obtained by inverting the Laplace-Fourier transforms.Calculations and analysis are carried out,and the solution in this study is validated.