This paper presents a numerical study of 3$\times$3 pile groups embedded in clay under vertical and inclined eccentric loads. Simplified modelling, based on elastic beams embedded in a soil continuum, is used to explore the soil-pile-cap response. This simple model allows rigorous treatment of the 3D foundation geometry and local soil plasticity, demonstrated through validation with 3D finite element analysis. The numerical results reveal that complex roto-translational displacements of the pile group are induced by eccentric or inclined loads, with highly nonlinear relationships when soil plasticity is considered. Interestingly, vertical eccentric loads mobilise the lateral soil resistance at large cap displacements. Thus, while existing t-z type models are shown to be adequate for serviceability predictions, they could provide overly-conservative estimates of the ultimate load capacity. Also, foundation internal forces can exceed allowable bending moments of reinforced concrete piles under multi-directional loads. For performance based design of pile groups under inclined eccentric actions, engineers should estimate the impact of soil yielding on both displacements and rotations of the cap, to satisfy limit state requirements. Dimensionless charts are presented, which describe the reduction in vertical capacity, for a prescribed cap displacement, as a function of load eccentricity and inclination.

本文提出了3的数值研究$\times$在垂直和倾斜的偏心荷载作用下，将3个桩组埋入粘土中。基于嵌入在土壤连续体中的弹性梁的简化建模被用来研究土-桩-盖的响应。这个简单的模型可以对3D基础几何形状和局部土壤可塑性进行严格处理，并通过3D有限元分析进行验证。数值结果表明，桩组的复杂旋转平移位移是由偏心荷载或倾斜荷载引起的，当考虑土壤可塑性时，它们具有高度非线性关系。有趣的是，在偏大的顶盖位移下，垂直偏心荷载动员了土壤侧向阻力。因此，尽管现有的tz型模型显示出足以用于可维护性预测，但它们可能会提供过于保守的最终负荷能力估算值。还，在多向荷载下，地基内力可能会超过钢筋混凝土桩的允许弯矩。对于倾斜偏心作用下的群桩基于性能的设计，工程师应估计土壤屈服对顶盖位移和旋转的影响，以满足极限状态的要求。给出了无因次图，该图描述了规定的顶盖位移时垂直承载力的减少情况，它是载荷偏心率和倾斜度的函数。