应力解除法地应力测量中偏心岩芯弹性模量率定解析

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Abstract For the stress relief method to measure in-situ stress，the eccentricity of core samples is a common issue that leads to significant errors in the calibration of elastic modulus，severely impacting the accuracy of stress testing. This study employs a bipolar coordinate system and a generalized Hooke?s Law to derive an analytical solution for calibrating the elastic modulus of eccentric rock cores under plane stress conditions，utilizing stress and strain solutions associated with eccentric circular models. The correction coefficients for elastic modulus calibration based on the pressure application on the inner and outer sides of the eccentric core are introduced，along with the approximate correction coefficient for hollow eccentric cores. Numerical simulations have been conducted to analyze and validate the proposed methodology，yielding the following key findings：(1) The proposed elastic modulus calibration solution significantly enhances the accuracy of elastic modulus determination for eccentric rock cores. For the core with an eccentricity ratio of 0.6，the maximum calibration errors for single-strain gauges and tri-strain gauge measurements are reduced to 2.7% and 1.1%，respectively，compared to the solution for concentric cores，showing reductions of 16.5% and 11.7%. (2) The elastic modulus calibration on the thin-walled side of the eccentric core is significantly influenced by eccentricity. When the eccentricity ratio varies from 0.2 to 0.6，the calibration coefficient for the thick-walled side remains relatively stable at 2.14 to 2.15(a variation of only 0.5%)，while the thin-walled side exhibits a wide range between 2.20 to 2.47，reflecting a 12.3% variation. (3) The elastic modulus calibration coefficient tends to decrease on the thick-walled side as the radius ratio increases，while it increases on the thin-walled side. For an eccentricity ratio of 0.6，as the radius ratio increases from 0.3 to 0.7，the calibration coefficient for the thick-walled side decreases from 1.2% to 19.8%，whereas for the shin-walled side，it increases from 16.5% to 83.8%. (4) The introduced approximate correction coefficient effectively reduces calibration errors for hollow eccentric rock cores，particular when the eccentricity ratio is below 0.5，maintaining calibration errors below 2.0%. The proposed method can provide theoretical guidance to the determination of elastic modulus for the eccentric rock cores and precise stress calculation in stress relief method of geostress measurement.

Key words： mining engineering in-situ stress stress relief eccentric circle elastic modulus calibration analytical solution

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	Articles by authors
	WU Peinan1
	2
	ZHANG Qiang1
	2
	LI Yapeng1
	2
	LI Tao1
	2
	GU Qiuxin1
	2
	ZHAO Jun3

Cite this article:

WU Peinan1,2,ZHANG Qiang1, et al. An analytical elastic modulus solution for an eccentric hollow rock core in in-situ stress measurement with stress relief method[J]. , 2024, 43(12): 2956-2967.

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https://rockmech.whrsm.ac.cn/EN/Y2024/V43/I12/2956

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