基于模糊和突变理论的岩溶区桩端溶洞顶板稳定性分析方法研究

首先根据岩溶区桩端溶洞顶板系统的工程特点,引入突变理论和模糊理论,对岩溶区桩端溶洞顶板系统进行多层次目标分解,建立出符合其工程特点的岩溶区桩端溶洞顶板稳定性评判层次结构模型;其次,依据突变理论基本原理,对各评判指标进行突变类型确定和突变类型归一化公式的推导,在此基础上,根据归一化公式进行量化递归运算得到岩溶区桩端溶洞顶板稳定性评判的总突变隶属函数值的计算方法;然后,引入模糊隶属函数构造方法,利用初始模糊隶属函数和突变级数将突变理论和模糊分析结合起来,建立出岩溶区桩端溶洞顶板稳定性分析的突变评判新方法;最后将本文方法应用于工程实例,分析结果验证了该方法的可行性与合理性。

Research on Stability Evaluation Method for Cave Roof under Pile Tip in Karst Region Based on Fuzzy Theory and Catastrophe Theory

According to the engineering characteristics of cave roof under pile tip in karsts region and inducing the catastrophe theory and fuzzy theory,the stability evaluation hierarchy structural model in keeping with the engineering features of cave roof under pile tip was proposed by making multilevel objective decomposition on the discussed structure.Based on the catastrophe theory,a recursive calculation was conducted according to the derived catastrophe type normalization formula to obtain the catastrophic affiliated functional values.Then with help of introducing the construction method of fuzzy membership function,a new stability evaluation method for cave roof under pile tip in karsts region was established by combining catastrophe theory and fuzzy analysis with fuzzy initial membership function and catastrophe progression.The method was applied to a practical engineering project and the result shows that the method is reasonable and feasible.