Calculation of the stability safety factor of a rock wedge in static and dynamic conditions. It is possible to introduce stabilization elements.
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In the limit equilibrium conditions of a slope affected by a joint, with a flat upper face (see Figures), i.e., when a discontinuity has an inclination lower than the face inclination and a dip direction close (± 20°) to that of the face, the stability conditions analysis is performed exactly as for all other planar failure kinematics. Generally, two possible failure geometries are assumed: absence or presence of an open tension crack in the upper part of the slope and drainage at the toe favored or prevented.
The equilibrium condition is expressed through the classic safety factor relationship:
FS = resisting forces / destabilizing forces.
In general, the forces affecting the equilibrium are:
Inertia force due to the earthquake [FH]
Hydraulic thrust on the sliding plane [U]
External forces [Q]
Weight of the detached wedge [W]
Hydraulic thrust in the tension crack [V]
Resisting component of cohesion along the sliding plane [Ac]