埋深基础地基极限承载力的数值求解方法

为确定作用在已知埋深、给定基础形状地基土上的极限承载力，对基底下的土体进行网格划分，先假定一均布荷载作用在此地基土上，运用明德林解的积分公式，结合角点法，编制MATLAB语言程序，求出每个网格节点上附加应力，进而求得每个网格节点上主应力，根据破坏准则，结合程序找出破坏点的坐标，利用MATLAB的图形处理功能，把破坏点的坐标在坐标图中显示出来。继续加大矩形荷载，直至这些破坏点在坐标图中刚好能够形成一个连续的破坏面，此时的矩形荷载即为此地基的极限承载力。此方法不仅可以有效地避免了地基承载力经验公式中一些不合理的假设带来的误差，更符合实际情况，而且可以直观地了解到地基土的三维破坏面。

Numerical analysis of ultimate bearing capacity of ground with deep buried foundation

The foundation soil is divided for finding the ultimate bearing capacity of a foundation with given buried depth and size. Supposing a uniform load acts on the foundation, Mindlin’s integral formula and corner points method are used to get extra stress of every mesh knot by MATLAB program, then the principal stress is found. Combining with failure criterion, MATLAB program is used to find coordinates of points which are destroyed. Using graphic processing function of MATLAB, the failure points are showed in the coordinate. Increasing the rectangular uniform load, the failure points are found until these points can form a continuous failure surface. This rectangular load is the ultimate bearing capacity of the foundation. The method can avoid errors brought by unreasonable hypotheses of the empirical formulas; and the three-dimensional failure surface of the foundation soil is obtained.