Physical model of ground collapse of hourglass type in karst region

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.