Buried depth calculation of the slope of the unstable rock based on natural vibration frequency

The instability of the slope of the unstable rock poses a great threat to the safety of engineering and people's lives and properties. The buried depth of an unstable rock is a key factor affecting its stability. It is difficult to directly measure the buried depth of the unstable rock. Therefore, it is of vital importance to indirectly and quickly identify the buried depth of the unstable rock. Assuming that the foundation soil is homogeneous and isotropic, the damping ratio is less than 1; it can be found that the deformation is linear elastic deformation within the amplitude range, and the unstable rock vibration model is simplified to a multi-degree-of-freedom vibration model. Through theoretical derivation, the quantitative relationship between the rock mass, foundation reaction force coefficient, rock burial depth, and the natural vibration frequency in the horizontal direction is established. The quantitative relationship was verified to be correct by laboratory tests. From the tests, the relationship is verified and shows that with the increasing buried depth of the unstable rock, its natural vibration frequency increases nonlinearly in the horizontal direction and also acts in a weakening growing trend; the mass of the unstable rock is a monotonically decreasing function of the natural vibration frequency, and it decreases by a one-half square with the increasing mass of the unstable rock. The research results can calculate the buried depth by measuring the vibration frequency of the unstable rock, which provides a new idea and theoretical basis for the stability evaluation of the slope of the unstable rock and the rapid identification and monitoring of the unstable rock.