The long-term stability of an underground deep cavity involves a lot of complex time-dependent mechanical processes. This paper presents an analytical approach for the post-closure behaviour of a deep spherical cavity inside a dilatant viscoplastic rock mass considering three stages: (1) excavation, (2) free convergence and (3) backfill contact and post-closure. The viscoplasticity is modelled by means of a linear Norton-Hoff’s law, and the dilation is incorporated by assuming that the volumetric plastic strain rate is a simple function of the equivalent deviatoric plastic strain. The analytical model proposed in this paper completes a previous work of the authors by adding the consideration of the dilatant behaviour of the rock mass. After presenting the analytical developments, a few numerical examples are presented to illustrate the applicability of the model. In particular, a parametric study shows the influence of key parameters such as dilation parameter, backfill stiffness, viscosity and delay of contact between the rock mass and the internal backfill. This analytical model provides a useful benchmark for complex numerical simulations as well as a useful tool for quick preliminary studies.

地下深腔的长期稳定性涉及许多复杂的与时间相关的机械过程。本文提出了一种考虑三个阶段的膨胀粘塑性岩体内深球形空腔的闭合后行为的分析方法：（1）开挖，（2）自由收敛和（3）回填接触和闭合后。粘塑性通过线性诺顿霍夫定律建模，并通过假设体积塑性应变率是等效偏塑性应变的简单函数来合并膨胀。本文提出的分析模型通过加入对岩体剪胀行为的考虑，完成了作者之前的工作。在介绍了分析进展之后，给出了一些数值例子来说明该模型的适用性。特别是，一项参数研究显示了关键参数的影响，例如膨胀参数、回填刚度、粘度以及岩体与内部回填之间的接触延迟。该分析模型为复杂的数值模拟提供了一个有用的基准，也为快速初步研究提供了一个有用的工具。