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

Abstract

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.

Experimental research on damage identification of topping dangerous rock structural surface based on dynamic characteristic parameters

“…Deformation in the amplitude range is linear elastic, and the vibration model of the rock block can be simplified into a pendulum dynamic characteristic model, with the constitutive equation given by Eqs. 4, 5 (Jia et al, 2021):…”

“…The damage identification method of rock structures based on dynamic characteristic parameters can rapidly assess rock block stability. (Jia et al, 2021). However, the existing dynamic characteristic model is narrow in focus and does not accurately reflect the variation law of the dynamic characteristic parameters of rock masses in all failure modes.…”

Effect of rock porosity on the natural frequency of the sample: theoretical model and experiment

“…Among others, Song et al (2019a) investigated the effects of natural frequencies on the slope dynamic characteristics, and they concluded that the high-and low-frequency components mainly induce local and overall deformation of the surface slope of the rock, respectively. In order to achieve the stability evaluation of the perilous rock, Jia et al (2023aJia et al ( , 2022 found that the natural frequency increases nonlinearly in the horizontal direction with the increasing buried depth of the unstable rock, and they established the quantitative relationship model between the safety factor and natural frequency. Xie et al (2021) established a three-dimensional (3-D) analysis method for the rock vibration, and they proved the effectiveness for the rock stability analysis based on the natural frequency.…”

Stability Evaluation of Sliding-Type Perilous Rock in Huangzangsi Hydrojunction Project Based on Natural Vibration Frequency

“…Xie et al found that a ground-penetrating radar (GPR) survey can be used to evaluate the slope stability [29]. Du et al and Jia et al further conducted experimental research on dumping perilous rock and found that the natural vibration frequency is closely related to the stability [30][31][32][33]. However, the above research has just started and is in the experimental stage, and the theory has not yet been perfected [34,35].…”