<p>The elastic strain energy at peak strength of rock material is a critical parameter for evaluating rockburst proneness from an energy-based perspective. To accurately determine peak-strength strain energy, a series of single cyclic uniaxial and triaxial loading–unloading compression tests were conducted to characterize the energy evolution behavior of rocks under pre-peak unloading conditions. The relationships among elastic strain energy (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">$U_{{\text{e}}}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>U</mi> <mtext>e</mtext> </msub> </math></EquationSource> </InlineEquation>), dissipated strain energy (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">$U_{{\text{d}}}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>U</mi> <mtext>d</mtext> </msub> </math></EquationSource> </InlineEquation>), and input strain energy (<InlineEquation ID="IEq3"> <EquationSource Format="TEX">$U_{{\text{t}}}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>U</mi> <mtext>t</mtext> </msub> </math></EquationSource> </InlineEquation>) were systematically analyzed under both uniaxial and triaxial unloading conditions. By fitting functional relationships between each energy component and the unloading stress ratio (<InlineEquation ID="IEq4"> <EquationSource Format="TEX">$k$</EquationSource> <EquationSource Format="MATHML"><math> <mi>k</mi> </math></EquationSource> </InlineEquation>), the variation in <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$U_{\text{e}}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>U</mi> <mtext>e</mtext> </msub> </math></EquationSource> </InlineEquation> with <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$k$</EquationSource> <EquationSource Format="MATHML"><math> <mi>k</mi> </math></EquationSource> </InlineEquation> was found to exhibit a high consistency. A novel energy-based method for estimating the peak-strength strain energy associated with rockburst proneness was proposed by extrapolating the fitted function to <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$k = 1.0$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>k</mi> <mo>=</mo> <mn>1.0</mn> </mrow> </math></EquationSource> </InlineEquation>. The evolution of the energy dissipation ratio (<InlineEquation ID="IEq8"> <EquationSource Format="TEX">$\eta$</EquationSource> <EquationSource Format="MATHML"><math> <mi>η</mi> </math></EquationSource> </InlineEquation>), along with variations in <InlineEquation ID="IEq9"> <EquationSource Format="TEX">$k$</EquationSource> <EquationSource Format="MATHML"><math> <mi>k</mi> </math></EquationSource> </InlineEquation>, was examined to track progressive damage during unloading. Additionally, the peak-strength energy storage index (<InlineEquation ID="IEq10"> <EquationSource Format="TEX">$W_{{{\text{et}}}}^{{\text{p}}}$</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi>W</mi> <mrow> <mtext>et</mtext> </mrow> <mtext>p</mtext> </msubsup> </math></EquationSource> </InlineEquation>), which reflects the brittle failure potential of rock materials, was determined under various confining pressures. Compared with existing calculation methods, the proposed calculation method for estimating <InlineEquation ID="IEq11"> <EquationSource Format="TEX">$U_{{\text{e}}}^{{\text{p}}}$</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi>U</mi> <mrow> <mtext>e</mtext> </mrow> <mtext>p</mtext> </msubsup> </math></EquationSource> </InlineEquation> demonstrated higher consistency with experimental data and greater practical convenience when <InlineEquation ID="IEq12"> <EquationSource Format="TEX">$k \le 0.9$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>k</mi> <mo>≤</mo> <mn>0.9</mn> </mrow> </math></EquationSource> </InlineEquation>. These findings offer a reliable and precise approach for evaluating peak-strength strain energy and provide a new theoretical foundation for assessing rockburst proneness of deep rocks during unloading.</p>

A Novel Approach for Estimating Peak-Strength Storage Strain Energy in Rockburst Proneness

期刊论文
发表日期：

2026年4月8日

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Fengyun Wang,
Rui Pan,
Guojun Cai,
Yi Cai,
Kun Huang,
Jian Lin

摘要

The elastic strain energy at peak strength of rock material is a critical parameter for evaluating rockburst proneness from an energy-based perspective. To accurately determine peak-strength strain energy, a series of single cyclic uniaxial and triaxial loading–unloading compression tests were conducted to characterize the energy evolution behavior of rocks under pre-peak unloading conditions. The relationships among elastic strain energy ( $U_{{\text{e}}}$ $U_{e}$ ), dissipated strain energy ( $U_{{\text{d}}}$ $U_{d}$ ), and input strain energy ( $U_{{\text{t}}}$ $U_{t}$ ) were systematically analyzed under both uniaxial and triaxial unloading conditions. By fitting functional relationships between each energy component and the unloading stress ratio ( $k$ $k$ ), the variation in $U_{\text{e}}$ $U_{e}$ with $k$ $k$ was found to exhibit a high consistency. A novel energy-based method for estimating the peak-strength strain energy associated with rockburst proneness was proposed by extrapolating the fitted function to $k = 1.0$ $k = 1.0$ . The evolution of the energy dissipation ratio ( $\eta$ $η$ ), along with variations in $k$ $k$ , was examined to track progressive damage during unloading. Additionally, the peak-strength energy storage index ( $W_{{{\text{et}}}}^{{\text{p}}}$ $W_{et}^{p}$ ), which reflects the brittle failure potential of rock materials, was determined under various confining pressures. Compared with existing calculation methods, the proposed calculation method for estimating $U_{{\text{e}}}^{{\text{p}}}$ $U_{e}^{p}$ demonstrated higher consistency with experimental data and greater practical convenience when $k \le 0.9$ $k \leq 0.9$ . These findings offer a reliable and precise approach for evaluating peak-strength strain energy and provide a new theoretical foundation for assessing rockburst proneness of deep rocks during unloading.