The circle sliced method of analysis of earth slope stability analysis under gravity erosion is widely employed in engineering practice. However

it involves a complex calculation process

and the identification of a potential slip surface is associated with uncertainty. First

on the two dimensional section of slope

the ground surface is regressed as linear equations

while the slip surface is defined by a circle equation; then the accumulation can be substituted by integration with the equation of the Fellenus method. From this the analytical formula was derived. An alternate method for identifying the most likely slip surface is to convert the factor of safety to a function of a parameter of length t

aided by a geometric relation. If it is supposed that the first derivative of the function equals zero

it is possible to solve the equation to get the value of t. Accordingly

the minimum factor of safety and the corresponding radius of the slip circle can be defined. As differential positions for the top point and the thrust point of the slip surface were supposed

the minimum factor of safety and the corresponding slip circle can be defined.