The development of marine energy requires reliable foundations, which may be located near submarine slopes. This paper utilizes the lower bound limit analysis (LBLA) to analyze the undrained bearing capacity of foundations on slopes with anisotropy and linearly increasing strength with depth. The anisotropic undrained strength (AUS) model is employed to simulate the anisotropy of the slope soil. This study considers five variables that affect the bearing capacity: the normalized foundation setback (L/B), load angle (theta), strength ratio (suc/gamma B), heterogeneous index (rho B/suc), and anisotropy ratio (re). Here, suc represents the soil strength obtained from triaxial compression tests, while rho denotes the strength gradient. The results indicate that the bearing capacity increases with the increase in L/B, suc/gamma B, rho B/suc, and re, while the maximum bearing capacity corresponds to a load angle ranging from 75 degrees to 90 degrees. The failure modes of foundations under different boundary conditions were presented and discussed. To establish the relationship between the foundation bearing capacity and each variable, the multivariate adaptive regression splines (MARS) is introduced. The MARS results indicate that theta is the most significant variable, while the relative importance of L/B is the lowest; neither can be neglected in practical engineering. The empirical equation based on the MARS algorithm can accurately predict the bearing capacity of foundations in non-homogeneous and anisotropic clay. These results offer critical guidance for engineering practice, enabling efficient design of marine foundations near slopes while accounting for soil anisotropy and heterogeneous strength gradients, thereby reducing risks of instability in offshore energy infrastructure.

This study aims to explore the significant impact of soil fabric anisotropy on the ultimate bearing capacity of eccentrically and obliquely loaded shallow foundations overlying a geosynthetic-reinforced granular deposit. For this purpose, the well-established lower bound theorems of limit analysis (LA) in conjunction with the finite elements (FE) formulations and second-order cone programming (SOCP) are exploited to perform the bearing capacity estimations. The consideration of the soil mass's inherently anisotropic response in the granular layer involves the utilization of distinct internal friction angles in various directions. The lower bound FELA framework adopted in this study incorporates both the pull-out and tensile mechanisms of failure in the reinforcement layer. The marked contribution of soil inherent anisotropy to the impacts of ultimate tensile strength (Tu) T u ) and embedment depth (u) u ) of the geosynthetic reinforcement on the failure mechanism, bearing capacity ratio (BCR), BCR ), and failure envelope of the overlying obliquely/eccentrically strip footing is rigorously examined and discussed. It is generally concluded that for a given embedment depth, failure envelopes of the surface footing in both V-H H and V-M M planes shrink appreciably with the increase in the soil anisotropy ratio as well as the decrease in the geosynthetic ultimate tensile strength. Moreover, the influence of soil inherent anisotropy on the overall bearing capacity of shallow foundations is more evident in the case of using strong reinforcement compared to the weak geosynthetic. The findings of this investigation demonstrate that overlooking the soil inherently anisotropic behaviour in the numerical analysis of shallow foundations would give rise to undesirable non-conservative and precarious designs.