This study introduces the Energy Method Upper-bound (abbreviated as EMU), originally proposed by Donald and Chen (1997), for calculating bearing capacities with a focus on earthquake loadings affecting layered geological strata. The theoretical components of this study consist of (1) an extension of Prandtl's solution for bearing capacity analysis to inclined surface loads, (2) a mathematical demonstration of the theoretical congruence between EMU and the Prandtl-Reissner solution, and (3) a validation of the numerical outcomes through four illustrative bearing capacity examples with known closed-form solutions. This innovative approach eliminates the semi-empirical coefficients typically required in conventional bearing capacity evaluations, thus enhancing its relevance to seismic analysis for stratified geological formation that can hardly be evaluated with empirical coefficients accurately. The study also discusses various technical aspects such as seismic load determination, the use of undrained shear strength, and specifications for allowable safety factors under seismic conditions. With these methodologies, the paper assesses the seismic bearing capacities of two different buildings, with different scales and footing types. Additionally, a computer program, BEARING-IWHR, featuring an Excel interface and open-source coding, is available online. This method provides a theoretically sound and practically feasible framework for addressing seismic bearing capacity on stratified foundations.

中文翻译：

---

层状地质地层地震承载力上限数值法评价


本研究引入了最初由 Donald 和 Chen (1997) 提出的能量法上限（缩写为 EMU），用于计算承载力，重点关注影响层状地质地层的地震荷载。本研究的理论部分包括 (1) 将普朗特承载力分析解决方案扩展到倾斜表面荷载，(2) 对 EMU 和普朗特-赖斯纳解决方案之间的理论一致性进行数学论证，以及 (3) 验证通过四个具有已知封闭式解的说明性承载力示例来描述数值结果。这种创新方法消除了传统承载力评估中通常需要的半经验系数，从而增强了其与难以用经验系数准确评估的分层地质构造地震分析的相关性。该研究还讨论了各种技术方面，例如地震荷载的确定、不排水抗剪强度的使用以及地震条件下允许安全系数的规范。通过这些方法，本文评估了两种不同规模和基础类型的不同建筑物的抗震承载能力。此外，还可以在线获取计算机程序 BEARING-IWHR，该程序具有 Excel 界面和开源编码。该方法为解决分层地基的地震承载力问题提供了理论上合理且实际可行的框架。