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

Vol14 No.12: 2589-2602

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

Author】CHEN Tie-lin1; ZHOU Cheng2*; LIU En-long2,3; DAI Feng2; LIU Jiao2

Addresses】1 Key Laboratory of Urban Underground Engineering of Ministry of Education, Beijing Jiaotong University, Beijing 100044, China; 2 State Key Laboratory of Hydraulics and Mountain River Engineering, College of Water Resource and Hydropower Engineering, Sichuan University, Chengdu 610065, China; 3 Cold and arid regions environmental and engineering research institute, Chinese academy of sciences, Lanzhou 730000, China

Corresponding author】czhou1970nj@hotmail.com

Citation】Chen TL, Zhou C, Liu EL, et al. (2017) Analysis on velocity distribution and displacement along the profile of a slope using both empirical and analytical methods. Journal of Mountain Science 14(12). https://doi.org/10.1007/s11629-016-4127-8

DOI】https://doi.org/10.1007/s11629-016-4127-8

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.

Keywords】Slope deformation;progressive deformation; fitting function; analytical solution; Bingham model; nonlinear viscosity