In order to accurately evaluate the rock strength under different confining pressures, a new nonlinear strength criterion with three parameters is proposed based on the peak value of deviatoric stress. A comparison among the proposed criterion, modified Hoek-Brown (MH-B) criterion, modified Mohr-Coulomb (MH-C) criterion and exponential criterion regarded as an outstanding strength criterion in rock engineering is made by using triaxial data of 10 different kinds of rock. It is found that the average coefficient of variation (CV) of the parameters of the proposed criterion is smaller than the other three criteria. It shows that the parameters of the proposed criterion are less sensitive to the range of confining pressure, and the parameters of the proposed criterion, obtained from the first three triaxial tests, are directly used to predict the triaxial strength at higher confining pressure within a small error range. Comparing the predicted values of each strength criterion with rock triaxial testing values, it is found that the mean absolute deviation(MAD) and mean absolute error(MAE) of rock triaxial strength evaluated by the proposed criterion are smaller than the other three criteria. The results show that the proposed criterion has a higher accuracy than the other three criteria and can well predict the triaxial test strength for different types of rock with an universal applicability. In addition, the proposed criterion avoids the defect that MH-B criterion and MM-C criterion holding a constant after the confining pressure reaching uniaxial compressive strength. Finally, the physical meaning of the proposed criterion parameters is discussed. The fitting parameter <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_21961_Article_IEq1.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\({\sigma _{\text{c}}}\)</EquationSource> </InlineEquation> is completely consistent with the experimental value, and can be replaced by the actual uniaxial compressive strength. Therefore, it can be considered that the proposed criterion only contains two criterion parameters <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_21961_Article_IEq2.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="25" /> </InlineMediaObject> <EquationSource Format="TEX">\({\sigma _\infty }\)</EquationSource> </InlineEquation> and m. The extreme value of rock deviatoric stress depends on the parameter <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_21961_Article_IEq2.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="25" /> </InlineMediaObject> <EquationSource Format="TEX">\({\sigma _\infty }\)</EquationSource> </InlineEquation>. The larger the parameter <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_21961_Article_IEq2.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="25" /> </InlineMediaObject> <EquationSource Format="TEX">\({\sigma _\infty }\)</EquationSource> </InlineEquation>, the greater the extreme value of deviator stress. The increase magnitude of rock triaxial strength with confining pressure at initial stage depends on the parameters value of m. The larger the value of m, the smaller the increase magnitude of triaxial strength with increasing confining pressure at initial stage.

A nonlinear strength criterion for rock based on the peak value of deviatoric stress under conventional triaxial compression

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2025年10月31日

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Zhixiong Peng,
Yani Lu,
Yawu Zeng,
Ke Zhuo

摘要

In order to accurately evaluate the rock strength under different confining pressures, a new nonlinear strength criterion with three parameters is proposed based on the peak value of deviatoric stress. A comparison among the proposed criterion, modified Hoek-Brown (MH-B) criterion, modified Mohr-Coulomb (MH-C) criterion and exponential criterion regarded as an outstanding strength criterion in rock engineering is made by using triaxial data of 10 different kinds of rock. It is found that the average coefficient of variation (CV) of the parameters of the proposed criterion is smaller than the other three criteria. It shows that the parameters of the proposed criterion are less sensitive to the range of confining pressure, and the parameters of the proposed criterion, obtained from the first three triaxial tests, are directly used to predict the triaxial strength at higher confining pressure within a small error range. Comparing the predicted values of each strength criterion with rock triaxial testing values, it is found that the mean absolute deviation(MAD) and mean absolute error(MAE) of rock triaxial strength evaluated by the proposed criterion are smaller than the other three criteria. The results show that the proposed criterion has a higher accuracy than the other three criteria and can well predict the triaxial test strength for different types of rock with an universal applicability. In addition, the proposed criterion avoids the defect that MH-B criterion and MM-C criterion holding a constant after the confining pressure reaching uniaxial compressive strength. Finally, the physical meaning of the proposed criterion parameters is discussed. The fitting parameter \({\sigma _{\text{c}}}\) is completely consistent with the experimental value, and can be replaced by the actual uniaxial compressive strength. Therefore, it can be considered that the proposed criterion only contains two criterion parameters \({\sigma _\infty }\) and m. The extreme value of rock deviatoric stress depends on the parameter \({\sigma _\infty }\) . The larger the parameter \({\sigma _\infty }\) , the greater the extreme value of deviator stress. The increase magnitude of rock triaxial strength with confining pressure at initial stage depends on the parameters value of m. The larger the value of m, the smaller the increase magnitude of triaxial strength with increasing confining pressure at initial stage.