A New Method for Inverse Calculation of c and φ on a Slip Surface (Part III)

Inverse Calculation Based on the Bishop Method

Abstract

In the previous two papers, Parts I and II, the authors have described the fundamental concept of the newly proposed inverse calculation method of c and φ along a given slip surface and a calculation procedure based on the ordinary method of slices (Fellenius Method). This paper is concerned with an extension of the method to the situation in which the Bishop Method is used to calculate the factors of safety. The factors of safety equation in the Bishop Method is rather complicated in comparison with that of the Fellenius Method. A way to determine the c-tanφ relationship, therefore, is first described for the Bishop Method. The strength parameters c and φ to be obtained must lie on the c-tanφ curve. In addition to this requirement, a complete inverse calculation method must satisfy the condition that the factor of safety along the given slip surface is a minimum of all the possible adjacent slip surfaces. An approach to satisfy these two conditions is then developed, thereby giving an extremely limited range within which the unknown parameters, c and φ, should exist. Finally, a graphical solution is shown to determine c and φ uniquely and efficiently with the aid of a digital computer. Applications of this method to three fictitious problems indicate that it is of much practical use due to its accuracy and reasonable computer time.