# Research on the Four-Component Borehole Strain Response to Rock Fracture

## TL;DR

This study uses numerical simulations to analyze how four-component borehole strain responds to rock fractures, helping improve rock engineering stability.

## Contribution

The study introduces three strain response indices to quantitatively characterize rock fracture events using four-component borehole strain data.

## Key findings

- The areal strain index remains constant with FCBSG installation angles, while shear strain indices show complementary variation trends.
- Strain indices decrease with increasing distance between the borehole and fracture zone, following a power-law function.
- Combined use of strain indices improves the reflection of rock fracture events, with an average detection range of 60.7 meters.

## Abstract

Rock fracture monitoring is crucial for the stability of rock engineering. Based on the four-component borehole strain (FCBS) theory, this study analyzes the response characteristics of FCBS through numerical simulations of large-scale local rock fracture. Drawing on linear elastic mechanics theory and combined with the Gaussian white noise model, three strain response indices (areal strain index pja and shear strain indices pj13, pj24) are proposed to quantitatively characterize rock fracture events. A criterion is defined that if any of these indices is greater than 1, the rock fracture event can be reflected, and the larger the index, the better the effect of this index in reflecting rock fracture. The effects of the installation angle of the four-component borehole strain gauge (FCBSG), the distance between the borehole and the fracture zone, and the orientation of the borehole on these three indices are systematically investigated. The results show that for the same borehole, the areal strain index remains constant for different installation angles of the FCBSG, while the two shear strain indices exhibit a complementary variation trend—one shear strain index is always greater than or equal to the characteristic value of the borehole shear strain index, and the other is less than or equal to it; the larger values of the areal strain index and shear strain index decrease with the increase in the distance between the borehole and the fracture zone, following the variation law of the function y = axb with a negative exponent; there are significant differences in the larger values of the areal strain index and shear strain index among different orientation of the borehole, while those in the same orientation of the borehole relative to the fault fractured zone show a certain degree of complementarity, and the combined use of shear strain indices and areal strain index can better reflect rock fracture events; within the range of orientation of the borehole β = 0° to β = 90°, the minimum range of rock fracture that can be reflected by the three strain response indices is 55 m, the maximum range is 65 m, and the average range is 60.7 m.