Abstract In geotechnical engineering, the stability of rigid footings under eccentrically inclined loads is an important issue. This is because the number of superstructures has increased and the situation of structures being subjected to eccentrically inclined loading is occurring more and more frequently. The objective of this paper was to evaluate the bearing capacity of a rigid footing on the free surface of uniform sandy and clayey soils under the action of eccentric and inclined loading using a finite element analysis by assuming that the soils follow the Drucker-Prager yield function. In the two-dimensional analysis of the footing-soil system, the rigid plastic finite element method (RPFEM) was applied to calculate the ultimate bearing capacity of the eccentric-inclined loaded footing. In the numerical analysis, an interface element was introduced to simulate the footing-soil system with the rigid plastic constitutive equation developed by the authors. The footing was considered to be rigid and rough, as it most often is in reality. This study thoroughly considered the effect of the soil properties on load inclination factors iγ and ic in order to investigate the validity of the current design methods. In particular, the effects of the horizontal load in two directions on the ultimate bearing capacity of the footing and the failure envelopes in the V-H-M space were clarified, namely, positive and negative horizontal loads. The results showed that the positive horizontal load had a negative effect on the bearing capacity, while the negative horizontal load had the opposite effect in the presence of eccentrically inclined loading. The failure mode of the footing-soil system was clearly seen in the difference between the two directions of horizontal load. Through a series of numerical analyses, new equations were proposed for load inclination factors iγ and ic, and for the failure envelopes in the V-H-M space, taking into account the direction of the horizontal load. The obtained limit load space was proved to be rational in comparison to those given in the literature. Furthermore, the applicability of the limit load space to different loading paths, and moreover, to the independently prescribed loads of V, H, and M, was examined. Consequently, the failure envelope for each type of soil in the V-H-M space was clearly seen to be unique.

中文翻译：

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偏斜荷载作用下刚性基础的极限荷载空间

摘要 在岩土工程中，偏斜荷载作用下刚性基础的稳定性是一个重要问题。这是因为上层建筑数量增加，结构承受偏斜荷载的情况越来越频繁。本文的目的是通过假设土壤遵循 Drucker-Prager 屈服函数，使用有限元分析来评估在偏心和倾斜荷载作用下均匀沙质和粘质土壤自由表面上刚性基础的承载能力. 在地基-土体系统的二维分析中，应用刚塑性有限元法（RPFEM）计算偏心倾斜加载地基的极限承载力。在数值分析中，引入了一个界面元素，用作者开发的刚性塑性本构方程来模拟基脚-土系统。基础被认为是僵硬和粗糙的，因为它在现实中最常见。本研究彻底考虑了土壤特性对荷载倾角因子 iγ 和 ic 的影响，以研究当前设计方法的有效性。特别是明确了两个方向的水平荷载对基脚极限承载力和VHM空间破坏包络的影响，即正负水平荷载。结果表明，正水平荷载对承载力有负面影响，而在偏斜荷载存在下，负水平荷载则相反。从两个方向的水平荷载的差异可以明显看出地基-土系统的破坏模式。通过一系列数值分析，考虑了水平载荷的方向，提出了载荷倾角因子 iγ 和 ic 以及 VHM 空间中的破坏包络的新方程。与文献中给出的那些相比，所获得的极限载荷空间被证明是合理的。此外，还检验了极限载荷空间对不同载荷路径的适用性，以及对 V、H 和 M 独立规定的载荷的适用性。因此，VHM 空间中每种类型土壤的破坏包络显然是独一无二的。为载荷倾角因子 iγ 和 ic 以及 VHM 空间中的破坏包络提出了新方程，同时考虑了水平载荷的方向。与文献中给出的那些相比，所获得的极限载荷空间被证明是合理的。此外，还检验了极限载荷空间对不同载荷路径的适用性，以及对 V、H 和 M 独立规定的载荷的适用性。因此，VHM 空间中每种类型土壤的破坏包络显然是独一无二的。为载荷倾角因子 iγ 和 ic 以及 VHM 空间中的破坏包络提出了新方程，同时考虑了水平载荷的方向。与文献中给出的那些相比，所获得的极限载荷空间被证明是合理的。此外，还检验了极限载荷空间对不同载荷路径的适用性，以及对 V、H 和 M 独立规定的载荷的适用性。因此，VHM 空间中每种类型土壤的破坏包络显然是独一无二的。检查了极限载荷空间对不同载荷路径的适用性，以及对 V、H 和 M 的独立规定载荷的适用性。因此，VHM 空间中每种类型土壤的破坏包络显然是独一无二的。检查了极限载荷空间对不同载荷路径的适用性，以及对 V、H 和 M 的独立规定载荷的适用性。因此，VHM 空间中每种类型土壤的破坏包络显然是独一无二的。