基于扁拱突变理论的路基下伏溶洞顶板稳定性分析

Analysis on Stability of Underlying Cave Roof of Subgrade Based on Flat Arch Catastrophe Theory

根据路基下伏溶洞受荷体系的力学特性,将结构体系简化为两端固定铰支的扁拱模型;基于突变理论推导得到扁拱的能量势函数和分叉集方程,从而建立了路基下伏溶洞顶板突变模型平衡曲面;根据溶洞顶板突变失稳的条件,提出了确定路基下伏溶洞顶板的极限承载力及最小安全厚度的方法;并对溶洞顶板厚度h、溶洞顶板跨径l、溶洞顶板失高f、岩层的弹性模量E、溶洞顶板上覆荷载q五个影响因素进行参数分析,可得如下结论:溶洞顶板的极限承载力随着溶洞顶板厚度的增加,溶洞顶板失高的增加、岩层弹性模量的增加而增加,随着溶洞顶板跨径、溶洞顶板上覆荷载的增加而减小。

According to the mechanical characteristics of the loading system of the underlying cave of subgrade,the structure system is simplified as a flat arch model with fixed hinged supports at both ends.Based on the catastrophe theory,the energy potential function and bifurcation set equation of flat arch are derived,and the equilibrium surface of catastrophe model of underlying cave roof of subgrade is established.According to the conditions of sudden instability of karst cave roof,the method to determine the ultimate bearing capacity and the minimum safe thickness of underlying cave roof of subgrade is proposed.The five influencing factors of the cave roof thickness h,the cave roof span I,the cave roof loss height f,the elastic modulus E of rock stratum and the cave roof overlying load q are analyzed.The following conclusions show that the ultimate bearing capacity of karst cave roof increases with the increase of cave roof thickness,the increase of cave roof height loss and the increase of rock elastic modulus of rock stratum,and decreases with the increase of cave roof span and cave roof overlying load.