Research Article Open Access

Establishment of Readily Mathematical Formulation for the Evaluation of Slope Stability in Earth-Fill Dams

Salah Saleh1 and Majda Ibobakr Almhdi Amer2
  • 1 Department of Civil Engineering, University of Tripoli, Tripoli, Libya
  • 2 Department of Mathematics, University of Zintan, Zintan, Libya


The assessment of slope stability has been considered to be one of the most common issues to deal with by geotechnical engineers. This is due to the amount of destruction that can be brought up by the slope failure of soil masses to roads, railways, and earth dams, for example. Therefore, the stability of soil mass slopes must be carefully analysed prior to, during, and after the construction of such a structure. Depending on the importance of the slope stability problem, a number of alternative methods have been proposed for the evaluation of slope safety. These can generally be divided into two main types: Limit equilibrium methods and finite element methods. In limit equilibrium methods, the soil mass is subdivided into a set of slices with a straight base where each slice must fulfil the equilibrium conditions of forces and/or moments. For the sake of accuracy, a large number of slices are needed to accurately represent the curved slip surface, which is computationally time-consuming. Moreover, the current approaches lack continuity as the inter-slice forces have different slope angles and so they are not equal. The purpose of the study is to develop a mathematical approach that precisely represents the curved slip surface and eliminates the process of slicing. A fast and accurate mathematical formulation that computes the resultant slope forces by just using the geometrics of slip surface and without the need for slicing has been presented in this study. The proposed approach uses the principle of integration with infinitesimal strips that address the issue of inter-slice continuity. Compared with different sets of slices, the new formulation outperformed the ordinary method of slices in terms of accuracy and efficiency.

Journal of Mathematics and Statistics
Volume 19 No. 1, 2023, 37-43


Submitted On: 11 July 2023 Published On: 13 November 2023

How to Cite: Saleh, S. & Amer, M. I. A. (2023). Establishment of Readily Mathematical Formulation for the Evaluation of Slope Stability in Earth-Fill Dams. Journal of Mathematics and Statistics, 19(1), 37-43.

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  • Infinitesimal Slices
  • Mathematical Formulation
  • Slope Stability
  • Limit Equilibrium
  • Earth-Fill Dam