地下洞室变形破坏物理模拟的力学相似畸变映射原理与实例分析

Mechanical similarity distortion mapping principle and case analysis for underground cavern physical simulation of deformation and failure

相似物理模拟是研究地下工程变形破坏问题的重要手段,然而经典相似理论关于相似模型与工程原型之间的几何相似比和材料力学参数相似比的相互约束,导致室内物理相似模型尺寸和材料力学参数一直面临难以完全满足相似准则的困局,从而产生力学畸变和模拟试验结果解译困难。为此,提出了地下洞室变形破坏物理模拟的力学相似畸变映射处理方法,引进畸变系数和映射系数,通过耦合解析法或数值法来映射畸变效应,实现地下洞室物理模拟结果对原型力学行为的定量解译;以圆形隧洞为工程原型,采用水泥基3D打印隧洞物理模型进行相似物理超载试验,基于提出的耦合力学相似畸变法与解析法对物理模拟结果进行了定量分析和对比验证;以某水电站地下洞室群为研究原型,通过砂岩3D打印洞室群物理模型的超载试验获得洞室破坏的变形值,采用耦合力学相似畸变法与数值方法对物理模拟结果进行定量分析。实例分析结果表明,在物理相似模拟中几何相似比和力学相似比不满足经典相似准则条件下,该方法可实现圆形隧洞或复杂洞室群原型的相似物理模拟结果的定量映射分析,对非恒定相似比的地下洞室物理模拟畸变分析具有普适性。

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.