A rigorous solution aimed at accounting for the superposition and flow rule assumptions in the assessment of the bearing capacity of shallow strip footings under plane strain conditions has been developed using the method of characteristics and the finite element method. With reference to the Hill and Prandtl failure mechanisms, a bearing capacity factor N_γq and a superposition corrective coefficient μ that allow to directly obtain the actual bearing capacity of shallow strip foundations have been proposed. The geometry of the plastic volume involved in the failure mechanism has been also investigated, highlighting the influence of the superposition and flow rule assumptions. Starting from the numerical results obtained using the method of characteristics, several empirical relationships have been proposed for an accurate estimate of N_γq and μ as well as for the lateral extension and depth of the plastic volume. The accuracy of the numerical results has been checked through finite element analyses under the assumption of associated and non-associated flow rule showing that the proposed superposition corrective coefficient μ is not influenced by the flow rule assumption. Thus, a general bearing capacity equation for shallow strip footings has been provided which accounts for superposition approximation and non-associated flow rule.

使用特征法和有限元法开发了一种严格的解决方案，旨在考虑平面应变条件下浅条形基础承载力评估中的叠加和流动规则假设。参考Hill和Prandtl破坏机制，提出了能够直接获得浅层条形基础实际承载力的承载力系数N _γq和叠加修正系数μ 。还研究了失效机制中涉及的塑料体积的几何形状，突出了叠加和流动规则假设的影响。从使用特征方法获得的数值结果出发，提出了几种经验关系式，用于准确估计N _γq和μ以及塑性体积的横向延伸和深度。在关联和非关联流动法则假设下通过有限元分析检查了数值结果的准确性，表明所提出的叠加校正系数μ不受流动法则假设的影响。因此，提供了浅条形基础的通用承载力方程，该方程考虑了叠加近似和非关联流动规则。