Analysis on velocity distribution and displacement along the profile of a slope using both empirical and analytical methods

Abstract

Assessing the slope deformation is significant for landslide prediction. Many researchers have studied the slope displacement based on field data from the inclinometer in combination with complicated numerical analysis. They found that there was a shear zone above the slip surface, and they usually focused on the distribution of velocity and displacement within the shear zone. In this paper, two simple methods are proposed to analyze the distribution of displacement and velocity along the whole profile of a slope from the slip surface to the slope surface during slow movement. In the empirical method, the slope soil above the shear zone is assumed as a rigid body. Dual or triple piecewise fitting functions are empirically proposed for the distribution of velocity along the profile of a slope. In the analytical method, the slope soil is not assumed as a rigid body but as a deformable material. Continuous functions of the velocity and displacement along the profile of a slope are directly obtained by solving the Newton's equation of motion associated with the Bingham model. Using the two proposed methods respectively, the displacement and velocity along the slope profiles of three slopes are determined. A reasonable agreement between the measured data and the calculated results of the two proposed methods has been reached. In comparison with the empirical method, the analytical method would be more beneficial for slope deformation analysis in slope engineering, because the parameters are material constants in the analytical solution independent of time t, and the nonlinear viscosity of the soil can be considered.