Closed-Form Solution of Critical Inclination for Rock Slope with Weak Plane

Plane failure of rock slope is highly related to the inclination of the weak plane. The inclination of the weak plane is a general function of factors including: height of slope, factor of safety, horizontal coefficient of earthquake influence, inclination of slope, unit weight of rockmass, cohesion and friction angle on the plane. The closed-form solution of the critical inclination of the weak plane corresponding respectively is derived under two conditions (i.e., without earthquake and with earthquake), because the critical height of slope and the critical factor of safety are considered to and are easy to be adjusted in engineering practice. In the end, the relations between derived critical closed-form solution and each parameter are illustrated with an example.