Hypothesis of the slip surface shape in retained soils makes most of the existing methods for active earth pressure on rigid walls be of no logical basis. The present work aims to rigorously calculate the earth pressure under general conditions. Based on the limit equilibrium conditions of a soil mass retained by rigid walls under a distanced backfill strip surcharge, a variational calculus method was developed to compute the active earth pressure on the walls. A functional relationship between the earth thrust and critical slip surface of the retained soil, and the normal stress acting on it without considering the hypothesis of the slip surface shape, were established. A unified closed-form solution for the earth thrust was derived and could be obtained using an implicit solution technique via MATLAB. The analysis model is of high generality, and the effects of 11 basic parameters on the earth thrust and the corresponding slip surface were analyzed. Some of the considered parameters were the soil properties, soil–wall interface friction angle, wall height, strip surcharge, dip angle between the wall back and soil top surface, horizontal net distance from the wall back to the surcharge, and distribution width of the surcharge. The examples showed that the earth thrusts calculated using the proposed method were approximately 4–16% higher than Coulomb’s solutions but 3–11% lower than traditional stress distribution solutions based on the elastic theory. The proposed method in which the critical slip surface shape need not be subjectively assumed has comparatively more extensive applicability.

中文翻译：

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保留土带状超载下刚性墙主动土压力的变分法通用解

保留土中滑动面形状的假设使得大多数现有的刚性墙主动土压力方法没有逻辑基础。目前的工作旨在严格计算一般条件下的土压力。基于刚性墙体在远距离回填带附加费下保持土体的极限平衡条件，提出了一种计算墙体主动土压力的变分法。在不考虑滑移面形状假设的情况下，建立了土推力与滞留土临界滑移面与作用在其上的法向应力之间的函数关系。推导出了地球推力的统一封闭形式解，并且可以通过 MATLAB 使用隐式求解技术获得。分析模型具有较高的通用性，并分析了11个基本参数对地球推力及相应滑移面的影响。一些考虑的参数是土壤性质、土-墙界面摩擦角、墙高度、带状超载、墙背和土壤顶面之间的倾角、从墙背到超载的水平净距离和分布宽度。附加费。实例表明，使用所提出的方法计算的地球推力比库仑解高约 4-16%，但比基于弹性理论的传统应力分布解低 3-11%。所提出的不需要主观假设临界滑移面形状的方法具有相对更广泛的适用性。