条形粗糙基础极限承载力求解与误差分析

利用滑移线法计算了粗糙条形基础极限承载力,计算时考虑了土的黏聚力c、内摩擦角φ和土体重度g的共同作用,避免了对破裂面形状的人为假定,并满足所有边界条件。将数值计算结果与其他学者的解答进行了对比,证明了解答的准确性。分析了地基承载力系数N_γ的影响因素,证实了N_γ除了与地基摩擦角φ有关外,还与超载比l有关。绘制了不同j值下N_γ随l的关系曲线,给出了N_γ的拟合公式,计算结果表明拟合公式的误差在±4%以内。最后对传统叠加方法计算承载力与精确解之间的误差进行了计算,总结了不同j值时误差e随l的变化规律,发现叠加计算结果比精确解小,且最大误差出现在l介于0.1~1之间。

Solution and error evaluation for bearing capacity of rough strip footings

The slip-line method is used to calculate the bearing capacity of rough strip footing on ponderable soil. This method takes account of the influence of cohesion c, friction angle φ and unit weight γ of soil in one failure mechanism, and thus avoids assuming the shape of slip surfaces. Moreover, the solution of this method strictly satisfies all the given boundary conditions. The accuracy of the solution is proved by comparing with the published results. The investigations on the influence factors of N_γ show that the bearing capacity factor N_γ of the rough strip footing is related to the surcharge ratio λ besides the friction angle φ. A curve-fitting-based formula is proposed to get the exact N_γ on the basis of the curves between N_γ and λ under different φ. The results from the suggested formula have the maximum errors within ±4%. Finally, the errors between the bearing capacity obtained by the superposition method and the exact solutions are evaluated. The relationship of the error ε and λ under different φ reveals that the superposition results are less than the exact ones with the largest error occurring when λ varies between 0.1 and 1.