We formulate a path-independent $J$-integral for the elastodynamic problem expressed in the frequency domain. We show that the path-independence of the integral can be exploited in order to derive ansatz-free identities and rigorous inequalities in certain problems arising in geotechnical engineering. By way of illustration, we specifically consider the problem of assessing seismic pressures on retaining walls. We show that the bounds for the earth thrust derived from the frequency-domain dynamic $J$-integral improve upon previous heuristic and conjectured bounds.

中文翻译：

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J积分在岩土工程中的动力学问题中的应用

我们制定与路径无关的 $Ĵ$-积分表示在频域中表达的弹性动力学问题。我们表明，可以利用积分的路径独立性来导出在岩土工程中出现的某些问题中无antz的恒等式和严格的不等式。通过说明，我们专门考虑评估挡土墙上地震压力的问题。我们表明，地推力的边界是从频域动态中得出的$Ĵ$-积分改进了先前的启发式和猜想的界限。