The Janbu’s Generalised Procedure of Slice （GPS）

i. e.

the rigorous Janbu method

is the first method which takes into account all the equilibrium conditions for calculating factors of safety of slopes with arbitrary-shaped failure surfaces. But the problem of frequently encountered non-convergence associated with this method has frustrated slope researchers and practitioners for nearly half a century. In this paper

on the basis of the fundamental principle and assumptions inherent in the Janbu’s generalized procedure of slices

a more mathematically concise formula of factor of safety has been derived. By assuming the location of the line of thrust across the sliding body and considering the moment equilibrium condition for an infinitesimal slice

the shear thrust force can be expressed in terms of the normal thrust force and its first-order derivative. By considering the vertical force equilibrium condition as well as the above relation between the normal and shear thrust forces

the normal stress on the failure surface is expressed in terms of the normal thrust force and its first-and second-derivatives as well as other known parameters. By considering the horizontal force equilibrium condition

the factor of safety for the sliding mass is derived in terms of the normal stresses over the failure surface. A simple iterative procedure is developed for calculating the factor of safety: first

calculating the normal stresses on the failure surface （initially assuming zero thrust force）; second

calculating the improved factor of safety; third

calculating the thrust forces which is then used for calculating the improved normal stresses on the failure surface. The process is repeated until the difference in value of factor of safety between two adjacent steps is within tolerance. Either present or conventional computation procedure associated the Janbu’s generalized procedure involves the second-order derivative of thrust force

which cannot be reasonably determined by conventional finite difference method

particularly with large number of slices

say over 100 slices. It is the unreasonable errors in the second-order derivative of thrust forces that leads to the non-convergence associated with the conventional procedure. By employing numerical smoothing technique such errors can be eliminated

thus rendering the computation process being converged. It is demonstrated that the modified Janbu’s Generalised Procedure of Slices is still a theoretically rigorous and practicable method for analysing slope stability.