沙漏型岩溶地面塌陷物理模型

摘要

为了进一步研究覆盖型岩溶地面塌陷的发生条件和机理,在作者关于土体塌陷理论的基础上,着重研究了渗漏型地面塌陷的地质现象、地质模型、物理模型及其数学表达式.根据地质现象和砂性土中砂颗粒在塌陷过程中的运动学响应特征,建立沙漏型岩溶地面塌陷的地质模型.在此基础上,概化出物理模型,并根据物质守恒定律推演沙漏型塌陷的数学表达式.由此探讨了沙漏型塌陷规模与岩溶和水文地质条件的关系,认为沙漏型塌陷历时与砂性土的摩擦系数的平方、水力坡降的平方根及可溶岩洞径的8/3次方根成反比,与塌陷坑深度的立方成正比.文章从地质现象→地质模型→物理模型→数学表达式来研究沙漏型岩溶地面塌陷,地质理论依据充分,物理过程可靠,数学逻辑严密,所推导出的数学表达式较好地反映了沙漏型地面塌陷的基本规律.经工程案例验证,该物理力学模型与实际情况较为吻合.%In order to further study the occurrence conditions and mechanism of covered karst ground collapse (CKGC),on the basis of Luo Xiaojie's theory about CKGC,We studies the geological phenomena,geological model,physical model and mathematical expression of the Hourglass Type Ground Collapse (HTGC).According to geological phenomena and the characteristics of the kinematic response of sand particles in sandy soil during collapse,the geological model of HTGC is established.On this basis,a generalized physical model is summarized,and the mathematical expression is established according to the law of conservation of matter.The relationship between the scale of HTGC and the hydrological condition are discussed.It is pointed out that the duration of HTGC is proportional to cubic of collapse pit depth,and inversely proportional to square of the sandy soil friction coefficient,the square root of hydraulic gradient and the root of 8/ 3 of the soil-cave diameter.This paper studies HTGC from the geological phenomena,the geological model,the physical model and the mathematical expression.The geological theory is based on sufficient evidence,the physical process is reliable,and the mathematical logic is rigorous.The mathematical expression well reflects the basic law of HTGC.Engineering examples show that the physical and mechanical model is in good agreement with the actual situation.