Abstract: Physical similarity simulation is an important method for studying the deformation and failure of underground engineering. However, the classical similarity theory, which considers the mutual constraints of geometric similarity ratio and material mechanical parameter similarity ratio between similar models and engineering prototypes, often leads to a dilemma. This dilemma arises when the size of indoor physical similarity models and the material mechanical parameters cannot fully meet the similarity criteria, resulting in mechanical distortion and difficulties in interpreting simulation test results. In this article, a principle of mechanical similarity distortion mapping processing is developed to address this issue. This principle introduces a distortion coefficient and a mapping coefficient to compensate for the influence of distortion. By coupling analytical or numerical methods, the quantitative analysis of analog physical results for underground caverns can be achieved. To demonstrate the effectiveness of this approach, circular diversion tunnels are taken as the engineering prototype, and tunnels models are created using cement-based 3D printing. Overload tests are conducted, and the analog physical results are quantitatively analyzed and compared using the proposed coupling mechanics similar distortion principle and analytical method. Furthermore, a case study is conducted on a cavern group of a hydropower station. The failure deformation of the cavern group is obtained through physical overload tests on a 3D printed sandstone cavern group physical model. The analog physical results are then quantitatively analyzed using the coupling mechanical similitude distortion method and numerical method. The results of the case analysis demonstrate that this method enables quantitative engineering mapping analysis for analog physical results of circular tunnels or complex cavern groups, even when the geometric similarity ratio and mechanical similarity ratio do not satisfy the classical similarity criterion. This method has universal applicability for physical simulation mapping analysis of underground caverns with non-constant similarity ratios.

Key words: similarity theory, physical models, underground caverns, mechanical similar distortion, deformation and failure