Theoretical analysis of controlling parameters of direction independence of Kaiser effect

Based on the acknowledgement that the Kaiser effect is induced by the released elastic wave of crack propagation when the far-field stress is a compressive one, the variation of the Kaiser effect with loading direction is analyzed from the perspective of fracture mechanics. The theoretical relationship among the critical stress ${{\sigma }_{\text{c}}}$, the direction of the crack surface $\beta$ and the friction coefficient $f$ of the crack surface is established. The mechanism of the direction independence of the Kaiser effect and its control parameters are revealed. The results show that the direction independence of the Kaiser effect is affected by the relative value of the critical stress, and the control parameters include the angle between the initial loading direction and micro-crack surface ${{\beta }_{1}}$ and the crack surface friction coefficient $f$. When the angle ${{\beta }_{1}}$ is larger, the relative angle of loading deflection $\gamma$ is smaller to keep FR value greater than 1.1. There is greater difference between the stress obtained after the deflection of the loading direction and the initial loading stress, and the direction independence of Kaiser effect is more obvious. The accuracy of the initial stress measured by the Kaiser effect is related to the distribution of the initial microcrack of the rock mass. The smaller the friction coefficient $f$, the larger the relative angle $\gamma$ required for the FR value to be greater than 1.1, and the smaller the difference between the meseared stress and the initial loading stress after the deflection, the less obvious the independence of the Kaiser effect. The watter the rock sample, the greater the dispersion when measuring the initial stress with Kaiser effect. The above conclusions are consistent with the rules of the previous test results. By comparing the characteristic curves, the control parameters are established: friction coefficient on the microcrack surface is less than 0.5, the angle between the initial loading direction and the microcrack surface is about 30°~40°, which agrees well with the test conditions. They can provide references for further studies on the mechanism of the Kaiser effect.