A numerical implementation of the upper-bound theorem of limit analysis is applied to determine two-dimensional (2D) and three-dimensional (3D) active horizontal earth pressure coefficients considering seismic actions through a horizontal seismic coefficient. Results are obtained for vertical wall, horizontal soil, different friction angles of the soil, soil-to-wall friction ratios, horizontal seismic coefficients and wall width-to-height ratios. The few cases for which 3D active earth pressure coefficients are available in the literature using upper-bound methods were used for comparison with the corresponding earth pressure coefficients obtained in this study. This showed a general improvement of these results, which allows expecting a good accuracy for the set of cases studied. The ratios between the 3D and 2D horizontal active earth pressure coefficients are found to be practically independent of the soil-to-wall friction ratio. An equation is proposed for calculating these ratios. This equation can be easily used in the design of geotechnical structures requiring the determination of 3D active earth pressure coefficients.

中文翻译：

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三维地震主动土压力系数的上限

应用极限分析上限定理的数值实现，通过水平地震系数确定考虑地震作用的二维 (2D) 和三维 (3D) 主动水平土压力系数。得到了垂直墙、水平土、不同土体摩擦角、土墙摩擦比、水平地震系数和墙宽高比的结果。文献中使用上限方法获得 3D 主动土压力系数的少数情况被用于与本研究中获得的相应土压力系数进行比较。这显示了这些结果的普遍改进，这使得所研究的案例集具有良好的准确性。发现 3D 和 2D 水平主动土压力系数之间的比率实际上与土壁摩擦比无关。提出了一个公式来计算这些比率。该方程可轻松用于需要确定 3D 主动土压力系数的岩土结构设计。