采用Green函数法求解二维固结微分方程

以Terzaghi一维固结理论为基础，采用Green函数法对二维固结微分方程进行求解，得到了不同边界条件及地基应力条件下的二维固结微分方程的解析解，给出了计算表，进一步推导了线性加载下的解答。以一均质地基为例，将计算结果与一维解答、前人所得数值结果进行对比，验证了该方法的准确性与可靠性。研究结果表明：进行工程实际研究时应重点关注荷载中心点下的平均固结度，荷载宽度与地基宽度越接近，荷载中心点下的平均固结度与一维结果越接近；而当地基宽度远大于荷载宽度和软土厚度时，使用一维固结理论计算误差较小，工程设计中是可靠的。该方法解答考虑更多工程情况，更快捷方便，便于工程人员使用，可应用于工程计算。

Solving Two-dimensional Consolidation Differential Equation by Green"s Function Method

Based on Terzaghi''s one-dimensional consolidation theory, the Green function method is used to solve the two-dimensional consolidation differential equations, and the analytical solutions of the two-dimensional consolidation differential equations under different boundary conditions and foundation stress conditions are obtained, and the calculation table is given to further derive the solutions under linear loading. Taking a homogeneous foundation as an example, the calculation results are compared with the one-dimensional solution and the numerical results obtained by previous authors to verify the accuracy and reliability of the method. The results show that the average consolidation under the load center point should be focused on when conducting practical engineering studies, and the closer the load width is to the foundation width, the closer the average consolidation under the load center point is to the one-dimensional results; and when the foundation width is much larger than the load width and soft soil thickness, the calculation error using the one-dimensional consolidation theory is smaller and reliable in engineering design. This method answer considers more engineering situations, is faster and more convenient, is easy to use by engineers, and can be applied to engineering calculations.