Internal erosion induced by suffusion is a progressive process that can have negative consequences for dams, foundations and tunnel projects. The erosion ratio (denoting the ratio of the weight of cumulative eroded soils to the total weight of soils) is an important parameter in characterising this process, reflecting variations in porosity and hydraulic conductivity during suffusion. In this study, an erosion equation expressing the variation in the erosion ratio with respect to the hydraulic gradient and time is derived under arbitrary hydraulic loading conditions. This equation is based on investigations into the influence of both the hydraulic gradient and of time on the process of soil erosion. The derived erosion equation is applied in a case study and the results are compared with existing test data. It is shown that the expression proposed in this paper is in good agreement with observations. Finally, the influences of the hydraulic loading history and an erosion rate coefficient on the soil erosion process are discussed.

中文翻译：

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土壤中累积侵蚀比的数学模型

由溢流引起的内部侵蚀是一个渐进的过程，可能对大坝、地基和隧道项目产生负面影响。侵蚀比（表示累积侵蚀土壤的重量与土壤总重量的比值）是表征该过程的重要参数，反映了渗透过程中孔隙度和水力传导率的变化。在本研究中，在任意水力载荷条件下，推导出了表示侵蚀率随水力梯度和时间变化的侵蚀方程。该方程基于对水力梯度和时间对土壤侵蚀过程影响的研究。导出的侵蚀方程应用于案例研究，并将结果与​​现有的测试数据进行比较。结果表明，本文提出的表达式与观察结果非常吻合。最后，讨论了水力加载历史和侵蚀率系数对土壤侵蚀过程的影响。