by the unbalanced tangential force along the arc and by the external load. Therefore, con-
sider a tangential force as positive if its moment with respect to an axis through O is
clockwise and negative if this moment is counterclockwise. In the method of slices, it is
assumed that the lateral forces on each soil strip approximately balance each other.
- Evaluate the moment tending to cause rotation about O
In the absence of external loads,
DM = rST (24)where DM = disturbing moment; r - radius of arc; ST = algebraic sum of tangential
forces.
In the present instance, DM = 82.7(115) + 52.6(8) = 9930 ft-kips (13,465.1 kN-m).
- Sum the frictional and cohesive forces to find the maximum
potential resistance to rotation; determine the stabilizing moment
In general,
F= SN tan 0 C = cL (25)SM = r(F + O (26)where F = frictional force; C = cohesive force; SN= sum of normal forces; L = length of
arc along which cohesion exists; SM = stabilizing moment.
In the present instance, F = 425 tan 10° + 31.9 tan 28° = 91.9 kips (408.77 kN); C =
0.65(120) = 78.0; total of F + C = 169.9 kips (755.72 kN); SM = 82.7(169.9) = 14,050
ft-kips (19,051.8 kN-m).
- Compute the factor of safety against failure
The factor of safety is FS = SM/DM = 14,050/9930 =1.41. - Select another trial arc of failure; repeat the foregoing
procedure - Continue this process until the minimum value of FS
is obtained
The minimum allowable factor of safety is generally regarded as 1.5.
STABILITY OF SLOPE BY ^CIRCLE METHOD
Investigate the stability of the slope in Fig. 15 by the ^-circle method. The properties of
the soil are w 120 lb/ft^3 (18.85 kN/m^3 ); c = 550 lb/ft^2 (26.3 kPa); <f> = 4°.Calculation Procedure:- Locate the first trial position
The 0-circle method of analysis formulated by Krey is useful where standard conditions
are encountered. In contrast to the assumption concerning the stabilizing forces stated ear-
lier, the ^-circle method assumes that the soil has mobilized its maximum potential fric-
tional resistance plus whatever cohesive resistance is needed to prevent failure. A com-
parison of the maximum available cohesion with the required cohesion serves as an index
of the stability of the embankment.