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运用对偶积分方程来求解层状横观各向同性地基与墙下条形基础的共同作用问题。从直角坐标平面应变问题控制方程出发,通过傅里叶(Fourier)变换和层间连续性条件,可以得到层状横观各向同性地基的传递矩阵解。基于该传递矩阵解,并利用条形基础与地基接触的混合边值条件,推导出一组关于基础挠度和地基反力的对偶积分方程。考虑墙下条形基础受到竖向集中荷载的情况,利用弹性薄板理论先求解出条形基础挠度;随后应用雅可比(Jacobi)正交多项式和级数展开的方法,将对偶积分方程转化为线性代数方程组进行求解。编制了相应的计算程序,其计算结果与有限元软件ABAQUS的结果基本吻合,从而验证了所提理论的正确性。算例分析表明,板土相对刚度与地基成层性对地基反力、地表沉降和沿z轴竖向正应力有很大的影响。
Applying Dual Integral Equations to Solve the Problem of the Interaction between Layered and Transversely Isotropic Subgrade and Wall Strip Foundation. Based on the control equations of rectangular coordinate plane strain problem, the transfer matrix solution of layered transversely isotropic soils can be obtained by the Fourier transform and the continuity between layers. Based on the transfer matrix solution and using the mixed boundary conditions of the strip foundation and the foundation contact, a set of dual integral equations about the foundation deflection and the foundation reaction force are deduced. Considering the vertical concentrated load on the strip foundation under the wall, the deflection of the strip foundation is first solved by using the elastic thin plate theory. Then the dual integral equation is transformed into the linearity by using Jacobi orthogonal polynomials and series expansion method Algebraic equations for solving. The corresponding calculation program is compiled, and its calculation results are basically consistent with the results of the finite element software ABAQUS, which verifies the correctness of the proposed theory. The case study shows that the relative stiffness of soils and the stratification of foundation have a great influence on the foundation reaction force, the settlement of the ground surface and the vertical normal stress along z-axis.