Calculation of Slope Safety Coefficient Based on Newton’s Iteration

Abstract

Sarma method is used to calculate the slope and dam stability of widely used methods, wherein a spreadsheet is typically utilized to solve the safety coefficient. Spreadsheet calculation of safety factor in programming efficiency is significantly low, although some correction methods of Sarma use Newton iterative solution. However, the algorithm is extremely complicated for programming and engineering applications, thus making the work difficult to complete. Based on traditional Sarma method, this work uses defined derivatives in Newton iterative to determine the safety factor and obtain the corresponding derivation formula. Through programming and inputting a random initial value, the iterative solution can provide the slop safety factor. Examples also show that the convergence of iteration is rapid and the iteration can reach its required precise value in 2 to 4 steps. The results obtained using the classic examples of Sarma method are exactly the same. The method for calculating the safety factor of Newton method usage is suitable for people who are familiar with traditional Sarma method. The process is simple, direct, effective, and precise.