5.4 Total Stress Analysis (Swedish slip circle method)
In a slope consisting of cohesive soil like clay or silty clay, the slope is also stable if the slope angle greater then friction angle. The soil possesses some cohesion that can be used to design the slope angle even at a steeper value. Slip circle technique is used for this purpose. It is based on the assumption that the rotational angle of sliding during failure is circular. This method requires summing of the moments of all forces acting on the slope, including the gravitational force on the soil mass and the shear stress along the failure surface. If the moments are unbalanced in favour of movement, the slope fails else it will remain stable. The factor of safety can be calculated in this case as the ratio of the moments resisting failure to those causing failure.
Figure 1 shows a trial slip circle, with radius r and the centre of rotation O. The weight of the soil of the wedge w is of unit thickness acting through its centroid and the centre of gravity of slip zone is G.
Figure 1: Analysis of a trial slipe circle
Considering the moment equilibrium about centre O for length of slip arc L, the restoring moment is CuLr and driving moment is Wx. Therefore, the factor of safety:
This procedure is repeated for other circles in order to find the most critical one having the lowest factor of safety. When a tension crack develops, it reduces the arc length over which the cohesion resists movement and it also applies an additional overturning moment if the crack is filled with water (figure 2).
Figure 2: Analysis of a trial slipe circle with tension crack filled with water
Under this condition, the factor of safety is calculated by the formula:
La = length of slip circle = (L – crack length), m
Cu = Cohesion (undrainded unconsodate), MPa
Pw = water Pressure = 0.5Yw h02, MPa
Yw, = density of water, KN/m3
h0 = heigth of water colum in crack, m
The forces acting on the deep seated slope prone failure are shown in figure 3. The radius of the arc is r, and the length of the sliding surface is L. The depth of the plane of weakness along which failure occurs is h. The weight of the slope is having two components, and , each of which acts along respective lever arm and , creating moments . The two moments act in opposite directions around the point O, first being a sliding moment and second the resisting moment. In addition, there is another resisting moment due to shear strength of soil.
Figure 3: Failure analysis by slip circle method
The shear strength is acting along the length of the sliding arc at moment arm length r. the slope is stable when
The factor of safety is