Different types of the toppling failure are still a major instability for slopes in nature and slopes all over the world. Combined circular–toppling failure is a kind of instability not studied before in details. In this paper, a complete solution was presented for this type of failure. A new formulation was developed to investigate the stability of slope components (the soil and rock part).
The developed solution in this paper has taken all the effective parameters (external forces, water pressure and earthquake) into account. Every column can be in any mode of failure, including a stable mode. The presented solution unstable forms were widely analyzed from the point of limit equilibrium method in discontinuous rock and allowed for any combination of failure in the columns, i.e., failure mode of each column could be different with the mode of neighboring columns. Another advantage of the proposed solution is that the topmost column can have any inclination and the applied force by soil mass can be calculated by plasticity theory, which has good accuracy.
A computer code was developed to ease the use of the proposed solution. The code was simple and fast; it gave the final state of stability as well as safety factor of the slope. By using this code, the effect of different parameters (like block inclination, friction, etc.) on stability can be simply and quickly studied. Such a study can help the users decide on the necessary measures for making the slope more stable.