承压水作用下基坑底板突涌的突变理论分析

Catastrophe theory analysis on surge of foundation pit floor under action of confined water

鉴于基坑底板突涌是一个非线性过程,引入了一种新的基坑底板突涌稳定性理论分析方法。通过把承压水作用下基坑底板隔水土层简化为一有预压力的受均布荷载的固支梁力学模型,构建其力学结构系统的总势能函数。基于突变理论,求出基坑底板隔水土层突涌失稳尖点突变模型的标准函数型式和分叉集方程,分析底板突涌失稳的破坏机理,并推导出隔水土层突涌的必要条件和充分条件。研究结果表明:基坑底板隔水土层突涌的必要条件和充分条件具有一致性,可作为基坑底板是否突涌的判据。工程实例的分析证明,该评价模型科学合理、准确可信,可为预防基坑工程突涌、采取合理的支护措施等提供理论依据。

In view of the non-linear process of foundation pit floor gushing,a new theoretical analysis method for gushing stability of foundation pit floor was introduced.By simplifying the water-proof layer of foundation pit into a mechanical model of a preloaded fixed-supported beam under uniform load,the total potential energy function of the mechanical structure system was constructed.Based on catastrophe theory,the standard function type and bifurcation set equation of cusp catastrophe model for gushing instability of foundation pit floor were derived,and the failure mechanism of gushing instability of water-proof layer was analyzed.The necessary and sufficient conditions for gushing of water-proof layer were deduced.The results showed that the necessary and sufficient conditions for the gushing of the water-proof layer of foundation pit floor were consistent,which could be used as a judging criterion for the gushing.Through the analysis of an engineering example,it is proved that the evaluation model is scientific,reasonable,accurate and credible.It could provide theoretical basis for preventing the gushing of foundation pit engineering and adopting reasonable supporting measures.