Математическая модель развития подрезаемого склона и ее приложение к вопросу его устойчивости

Аннотация

A diffusive model of undercut slope is developed, where the undercutting effect is taken into account by the zero condition at the moving boundary. A partial auto-modeling solution has been got, which corresponds to the stationary dynamic regime stage (parallel retreat of the slope); the result is that the more active undercutting is (when compared to erosional downwearing), the steeper the slope becomes. A character of general solution of the problem is studied for the initial exponential slope profile similar to the profile of stationary dynamic regime. Analyzing both theoretical and numerical solutions together, the following conclusions have been drawn: 1) if the rate of undercutting is below the critical one, the slope down-wearing occurs; 2) is the rate is equal to critical (b=CK), the parallel retreat occurs; 3) if the rate is above critical, the steepness at the base of the slope increases and it loses its stability. In conclusion some prerequisites of experimental modeling are discussed as well as some further trends of the mathematic modeling.