The assessment of forces exerted on walls by the backfill is a recurrent problem in geotechnical engineering, owing to its relevance for both retaining systems and underground structures. In particular, the work by Arias and colleagues, and later also the one by Veletsos and Younan, among others, becomes pertinent when considering pressure increments on underground structures triggered by seismic events. As a first step, they studied the response of a rigid retaining wall resting on rigid bedrock subjected to SV waves, introducing some simplifying assumptions. This paper presents the exact solution to this reference problem. The solution is given in horizontal wavenumber domain; hence, it comes in terms of inverse Fourier transforms, which can be approximated numerically in Mathematica , which in turn are verified against finite‐element simulations. Specific features of this exact solution that were not captured by prior engineering approximations are highlighted and discussed.

中文翻译：

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刚性土上光滑刚性挡土墙的精确地震反应

由于回填土对墙体施加的力的评估与挡土系统和地下结构相关，因此它是岩土工程中经常出现的问题。特别是 Arias 及其同事的工作，以及后来 Veletsos 和 Younan 等人的工作，在考虑由地震事件引发的地下结构的压力增量时变得中肯。作为第一步，他们研究了位于刚性基岩上的刚性挡土墙在 SV 波作用下的响应，并引入了一些简化假设。本文给出了这个参考问题的精确解。该解在水平波数域中给出；因此，它来自傅立叶逆变换，可以在 Mathematica 中进行数值近似，这反过来又通过有限元模拟进行验证。强调并讨论了先前工程近似未捕获的这种精确解决方案的特定特征。