THE NEW FORMULA OF CALCULATING DEPTH OF A TENSION CRACK IN THE UPPER SURFACE OF A SLIDING SLOPE USING INFLECTION PRINCIPLE

When a tension crack appears in a slope, it usually indicates the slope is reaching limited equilibrium and a landslide is most likely to occur. With a rainfall, pressure by the filling water in the tension crack becomes a triggering factor for the slope failure. Therefore the crack depth is one of the important factors in slope stability analysis since it determines the water pressure in the tension crack. This paper presents a potential triangle block model created by a tension crack in the upper slope. The crack depth equation is derived by the force balance. The angle of the sliding surface associated to angle of international friction at the tension crack is obtained by the inflection principle. The crack depth coefficient is calculated afterward. The analytical solution curves are prepared for practical determination of crack depth coefficients. The conditions for generation of a tension crack are identified as follows:the angle of the sliding surface at the tension crack should be smaller than the angle corresponding to the angle of internal friction determined by the limited values of the first degree derivative. The crack location formula are also given for both circular failure and non-circular failure slopes. The results are compared with the Spencer Method, proving potential for its applications in slope engineering.