土石坝管涌溃坝过程数学模型及应用

通过国内外土石坝管涌溃坝模型试验发现,管涌通道断面在溃坝过程中呈现城门洞形,并不断发展扩大直至坝顶发生坍塌。而目前常用的管涌溃坝过程数学模型大多假设管涌通道为圆形或矩形,与实际情况不符。基于土石坝管涌破坏机理,提出一个土石坝管涌溃坝过程数学模型,模型假设初始管涌通道断面为底部正方形顶部半圆形的城门洞形,采用基于水流剪应力的冲蚀公式模拟冲蚀过程管涌通道两侧边向外的发展,采用普罗托季亚科诺夫压力拱理论模拟管涌通道顶拱的发展;通过比较管涌通道上部坝体的重力与管涌通道两侧土体的抗剪强度判断管涌通道的垮塌,分别选择孔流和堰流公式模拟管涌通道坍塌前后的溃口流量;当管涌通道坍塌后,假设坍塌的土体立刻被溃坝水流带走,随后发生漫顶破坏,使用极限平衡法模拟漫顶溃坝过程中的溃口边坡稳定性。模型采用按时间步长迭代的数值计算方法模拟溃口的水土耦合过程,选择国内外25个具有实测资料的土石坝管涌溃坝案例对模型进行验证,比对峰值流量、溃口最终宽度及溃坝历时等参数发现,模型计算结果与实测值的相对误差可满足工程需求,验证了模型的合理性。

Numerical Model for Piping Failure of Earth-rock Dam and Its Application

According to the model test results for piping failure of earth-rock dams at home and abroad, it is found that the pipe has an approximately rectangular channel with a crown at the top before the collapse of pipe roof. However, the pipe channel is often assumed to have a rectangular or circular cross-section in numerical modeling of piping failure. In this study, based on the piping failure mechanism of earth-rock dams, a numerical model is established. The model assumes that initially the pipe has a square cross-section with a top crown, and a shear stress-based erosion rate formula is utilized to simulate the erosion process, in which the arched pipe tunnel is enlarged along its length and width. Protodyakonov''s pressure arch theory is adopted to simulate the evolution process of the top crown of the pipe channel. The collapse of the pipe roof is evaluated by comparing the weight of the top soil and the shear strength of soil on the two sidewalls of the pipe channel. The equations of orifice flow and open channel flow are adopted to calculate the breach flow discharge for piping flow and overtopping flow, respectively. The model assumes that the failed soil is instantaneously removed towards downstream when the collapse occurs, and then overtopping dominates. The limited equilibrium method is adopted to check the stability of the breach slope after the collapse of pipe roof. The iterative method of time step is adopted to simulate the coupling process of water and soil. The piping failure cases of 25 earth-rock dams which have measured data are adopted to verify the proposed model. The comparison of measured and calculated results on peak breach flow, final breach width, and failure time shows that the relative errors of calculation can meet the engineering requirements, which verifies the reliability of the proposed model.