Impact of Underground Waters on the Stability of the Mountain Rock Slope. Depression Surface Equation

The underground waters move in the slope massif of a homogeneous mountain rocks. It is demonstrated that the filtration forces are the main cause for the decreased soil strength and slope deformation that further causes landslides. It was found that calculating the variability of groundwater levels and the location of the depressive curve plays an important role in the slope sustainability analysis. To solve this problem, the movement of the filtration water flow is considered within the slope of a homogeneous soil, which relies on the water-permeable cliffy bed sloping at an angle to the horizon. A common differential equation for the motion of the filtration water flow is deduced and reduced to the first-order linear equation, which is satisfied by the equation of the depression line. The method to draft a theoretical depression curve by using the solution of the differential equation is discussed. Based on this method, several typical points on the depression curve were selected. By using different values of geometrical parameters and ground characteristics of the slope, the coordinates of the typical points were determined. Auxiliary graphs were construed based on the results obtained by the numerical method to determine the coordinates of the outcrop of the depression curve on the slope surface and midpoint. The solution of a test example is given for illustration purposes. As the filtration water moves through the ground of the mountain rock slope, the impact of filtration forces or hydrodynamic pressure on the reduction of the slope ground stability is substantiated. Additional shear forces are taken into account in the calculation of the slope stability: hydrostatic and hydrodynamic pressures. The impact of the sums of these two forces results in the decreased ground mass strength, landslides and avalanches. For the slope stability analysis, the condition of the stability of the unit volume of the ground particle on the slope surface is considered. The formula to calculate the shear strength coefficient is deduced.