岩溶塌陷临界土洞的极限平衡高度公式

土洞的产生和发展是岩溶塌陷的基础，临界土洞是土洞发展的最终阶段，以临界土洞为界，岩溶塌陷在时间和空间上划分为内部塌陷阶段和地表塌陷阶段。内部塌陷阶段是土洞在覆盖层土体内部的发育扩展阶段，土洞顶板土体的破坏形式类似于地下洞室洞顶围岩的破坏。根据地下洞室普氏平衡拱理论，建立覆盖层土体的天然平衡拱高度，即临界土洞的极限平衡高度公式，并以唐山市体育场岩溶塌陷为例，对该公式进行验证评价，计算所得塌陷的临界土洞高度与实际情况相符合，误差仅为4.3 %。

Study on limit equilibrium height expression of critical soil cave of karst collapse

The occurring and developing of soil cave is the base of karst collapse; and critical soil cave is the final developing phase. In time and space, the critical soil cave can divide the whole developing process of karst collapse into two phases: inter-collapse phase and surface-collapse phase. The inter-collapse phase is the developing and enlarging process of soil cave in over-layer soil, and the failure of superstratum soil above soil cave is similar to the failure of apical plate surrounding rock of underground cavity. Therefore, based on the equilibrium arch theory of М•М•Протодьяконов , the maximum height of limit equilibrium arch of superstratum, which is the limit equilibrium height of critical soil cave, can be determined. In addition, an evaluation of a critical soil cave of karst collapse at Tangshan Palaestra in Hebei Provinces, was completed using limit equilibrium height expression. The results show that the height of critical soil cave by calculating accords with fact, and the error only is 4.3%.