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The ultimate bearing capacity of shallow strip footings using slip-line method

机译：滑移线法分析浅层地基的极限承载力

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Based on the limit equilibrium theory, an accurate approach is proposed to solve the ultimate bearing capacity of shallow strip footings under general conditions. The foundation soil is considered to be an ideal elastic-plastic material, which obeys the Mohr-Coulomb yield criterion, and is assumed to be an ideal continuous medium which is isotropic, homogeneous and incompressible or non-expansive. Through analyzing the relative motion and interaction between the footing and soil, the problem of the ultimate bearing capacity of shallow strip footings is divided into two categories. A minimum model with the total vertical ultimate bearing capacity as its objective function is established to solve the ultimate bearing capacity using the slip-line method with no need to make any assumptions on the plastic zone and non-plastic wedge in advance. A convenient and practical simplified method is also proposed for practical engineering purposes. Furthermore, the first category of the problem in the case of the same uniform surcharges on both sides of footings is the focus of the study: the applicable conditions of Terzaghi's ultimate bearing capacity equation as well as the theoretical exact solutions to its three bearing capacity factors are derived, and a new bearing capacity equation is put forward as a replacement for Terzaghi's equation. The geometric and mechanical similarity principle is proposed by a dimensionless analysis. The results show that for perfectly smooth footings, the total vertical ultimate bearing capacity obtained by the present method is in good agreement with those by existing methods, whereas the existing methods underestimate the ultimate bearing capacity in the case of perfectly rough footings. The classic Prandtl mechanism is not the plastic failure mechanism of the ultimate bearing capacity problem of perfectly smooth footings on weightless soil. (C) 2019 Production and hosting by Elsevier B.V. on behalf of The Japanese Geotechnical Society.
机译：基于极限平衡理论，提出了一种求解一般条件下浅层地基极限承载力的精确方法。基础土壤被认为是符合Mohr-Coulomb屈服准则的理想弹塑性材料，并且被认为是各向同性，均质，不可压缩或非膨胀的理想连续介质。通过分析地基与土壤之间的相对运动和相互作用，将浅层地基的极限承载力问题分为两类。建立了一个以总垂直极限承载力为目标函数的最小模型，可以使用滑线法求解极限承载力，而无需事先对塑性区和非塑性楔形进行任何假设。为了实用的工程目的，还提出了一种方便实用的简化方法。此外，在地基两侧均布相同附加费的情况下，该问题的第一类是研究的重点：特扎吉的极限承载力方程的适用条件以及其三个承载力因子的理论精确解推导得出一个新的承载力方程，以代替Terzaghi方程。通过无量纲分析提出了几何和机械相似性原理。结果表明，对于完全光滑的基础，本方法获得的总竖向极限承载力与现有方法完全吻合，而现有方法低估了完全粗糙基础的情况下的极限承载力。经典的Prandtl机制不是在失重土壤上完全光滑的基础的极限承载力问题的塑性破坏机制。 （C）2019年由Elsevier B.V.代表日本岩土工程学会制作和主持。

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