Relevance of the research. Stable parameters of dumps are critical in mining operations ensuring their safety and economic efficiency. This problem is particularly acute for mining enterprises engaged in surface mining and for coal open pit mines, in particular. One of the main problems of this issue is related to the substantiation of rigorous methods for assessing stability and determining the limiting parameters of external and internal dumps filling an embankment on weak gently dipping

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... face. In the technical and regulatory literature, this issue has been considered for a long time. However, there are no specific recommendations for finding the most dangerous sliding surfaces on slopes, as well as methods for calculating shearing and restraining forces along these surfaces. All the signs are that the reason for the stability loss of operated dumps is the absence of theoretically substantiated design schemes, respectively, there are errors in the design of dumping. Purpose of the work is to develop reliable methods for calculating the limiting parameters of dumps on weak gently dipping interface. The main idea of the work is to apply a new, not previously used scheme for calculating the stability of dumps on weak gently dipping interface. Research methods. The work deals with the apparatus of flow mechanics and more specifically, the rigid-plastic model (the method of limit equilibrium), and the variational, integral and differential branches of calculus act as a mathematical apparatus. Results and conclusions. Based on the results of previous studies, a new scheme for calculating the stability of the dump during its destruction along weak interface was proposed, which implies the absence of a curved section of the sliding surface under the slope and the convex shape of the sliding surface under the berm. In contrast to the existing calculation schemes, such a calculation scheme predicts significantly lower values of the critical parameters of dumps. It means that the use of the proposed scheme will prevent the destruction of dumps by landslides along the dumpbasement interface and increase the economic efficiency of enterprises. Because a sufficiently large overestimation of the critical parameters of dumps at weak interface limited by current regulatory documents has been determined, it is recommended to revise these parameters for the designed and operated dumps using the proposed schemes for calculating their stability.