<p>A novel methodology for predicting rock’s peak axial stress (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(q_{f}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>q</mi> <mi>f</mi> </msub> </math></EquationSource> </InlineEquation>) is proposed based on the stress–strain results of unconfined and confined monotonic compression tests on different rocks. The method is developed based on the observations of the behaviour of secant Young’s modulus (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(E_{sec}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>E</mi> <mrow> <mi mathvariant="italic">sec</mi> </mrow> </msub> </math></EquationSource> </InlineEquation>). During monotonic loading, it is observed that the <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(E_{sec}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>E</mi> <mrow> <mi mathvariant="italic">sec</mi> </mrow> </msub> </math></EquationSource> </InlineEquation> is maximized at a point before peak axial stress (<InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(q_{f}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>q</mi> <mi>f</mi> </msub> </math></EquationSource> </InlineEquation>). This point is defined as indicator stress (<InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(q_{id}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>q</mi> <mrow> <mi mathvariant="italic">id</mi> </mrow> </msub> </math></EquationSource> </InlineEquation>) and is used to predict <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(q_{f}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>q</mi> <mi>f</mi> </msub> </math></EquationSource> </InlineEquation> by defining an offset value at which a suitable <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\({{q_{id} } \mathord{\left/ {\vphantom {{q_{id} } {q_{f} }}} \right. \kern-0pt} {q_{f} }}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>q</mi> <mrow> <mi mathvariant="italic">id</mi> </mrow> </msub> <mrow> <mfenced open="/"> <mphantom> <mpadded width="0pt"> <msub> <mi>q</mi> <mrow> <mi mathvariant="italic">id</mi> </mrow> </msub> <msub> <mi>q</mi> <mi>f</mi> </msub> </mpadded> </mphantom> </mfenced> </mrow> <msub> <mi>q</mi> <mi>f</mi> </msub> </mrow> </math></EquationSource> </InlineEquation> ratio can be achieved. The proposed methodology is validated against the confined stress–strain results of Hawkesbury sandstone. The application of the proposed method to predict the peak strength of various rocks is further investigated using uniaxial compressive strength data from a wide range of rock strengths. It is found that for UCS ranging from 6 to 60&#xa0;MPa, a high offset value is required, whereas for UCS ranging from 70 to 220&#xa0;MPa, a low offset value is sufficient for a reasonable prediction. It is observed that, when testing the rock under confined loading conditions, the offset value should be increased, with higher values selected at higher confining pressures.</p>

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A Secant Modulus-Based Approach for Estimating Peak Strength of Rocks from Stress–Strain Curves

  • Abbas Taheri

摘要

A novel methodology for predicting rock’s peak axial stress ( \(q_{f}\) q f ) is proposed based on the stress–strain results of unconfined and confined monotonic compression tests on different rocks. The method is developed based on the observations of the behaviour of secant Young’s modulus ( \(E_{sec}\) E sec ). During monotonic loading, it is observed that the \(E_{sec}\) E sec is maximized at a point before peak axial stress ( \(q_{f}\) q f ). This point is defined as indicator stress ( \(q_{id}\) q id ) and is used to predict \(q_{f}\) q f by defining an offset value at which a suitable \({{q_{id} } \mathord{\left/ {\vphantom {{q_{id} } {q_{f} }}} \right. \kern-0pt} {q_{f} }}\) q id q id q f q f ratio can be achieved. The proposed methodology is validated against the confined stress–strain results of Hawkesbury sandstone. The application of the proposed method to predict the peak strength of various rocks is further investigated using uniaxial compressive strength data from a wide range of rock strengths. It is found that for UCS ranging from 6 to 60 MPa, a high offset value is required, whereas for UCS ranging from 70 to 220 MPa, a low offset value is sufficient for a reasonable prediction. It is observed that, when testing the rock under confined loading conditions, the offset value should be increased, with higher values selected at higher confining pressures.