Hao Li, Ruizhi Zhong, Leo Pel, David Smeulders, Zhenjiang You
{"title":"一种基于体积应变的岩石压缩起裂阈值确定方法","authors":"Hao Li, Ruizhi Zhong, Leo Pel, David Smeulders, Zhenjiang You","doi":"10.1007/s00603-023-03619-2","DOIUrl":null,"url":null,"abstract":"Abstract The crack initiation stress threshold ( $${\\sigma }_{\\mathrm{ci}}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mi>σ</mml:mi> <mml:mi>ci</mml:mi> </mml:msub> </mml:math> ) is an essential parameter in the brittle failure process of rocks. In this paper, a volumetric strain response method (VSRM) is proposed to determine the $${\\sigma }_{\\mathrm{ci}}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mi>σ</mml:mi> <mml:mi>ci</mml:mi> </mml:msub> </mml:math> based on two new concepts, i.e., the dilatancy resistance state index ( $${\\delta }_{\\mathrm{ci}}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mi>δ</mml:mi> <mml:mi>ci</mml:mi> </mml:msub> </mml:math> ) and the maximum value of the dilatancy resistance state index difference ( $$\\left|{\\Delta \\delta }_{\\mathrm{ci}}\\right|$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mfenced> <mml:msub> <mml:mrow> <mml:mi>Δ</mml:mi> <mml:mi>δ</mml:mi> </mml:mrow> <mml:mi>ci</mml:mi> </mml:msub> </mml:mfenced> </mml:math> ), which represent the state of dilatancy resistance of the rock and the shear sliding resistance capacity of the crack-like pores during the compressive period, respectively. The deviatoric stress corresponding to the maximum $$\\left|{\\Delta \\delta }_{\\mathrm{ci}}\\right|$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mfenced> <mml:msub> <mml:mrow> <mml:mi>Δ</mml:mi> <mml:mi>δ</mml:mi> </mml:mrow> <mml:mi>ci</mml:mi> </mml:msub> </mml:mfenced> </mml:math> is taken as the $${\\sigma }_{\\mathrm{ci}}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mi>σ</mml:mi> <mml:mi>ci</mml:mi> </mml:msub> </mml:math> . We then examine the feasibility and validity of the VSRM using the experimental results. The results from the VSRM are also compared with those calculated by other strain-based methods, including the volumetric strain method (VSM), crack volumetric strain method (CVSM), lateral strain method (LSM) and lateral strain response method (LSRM). Compared with the other methods, the VSRM is effective and reduces subjectivity when determining the $${\\sigma }_{\\mathrm{ci}}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mi>σ</mml:mi> <mml:mi>ci</mml:mi> </mml:msub> </mml:math> . Finally, with the help of the proposed VSRM, influences from chemical corrosion and confining stress on the $${\\sigma }_{\\mathrm{ci}}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mi>σ</mml:mi> <mml:mi>ci</mml:mi> </mml:msub> </mml:math> and $${\\Delta \\delta }_{\\mathrm{ci}}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mrow> <mml:mi>Δ</mml:mi> <mml:mi>δ</mml:mi> </mml:mrow> <mml:mi>ci</mml:mi> </mml:msub> </mml:math> of the carbonate rock are analyzed. This study provides a subjective and practical method for determining $${\\sigma }_{\\mathrm{ci}}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mi>σ</mml:mi> <mml:mi>ci</mml:mi> </mml:msub> </mml:math> . Moreover, it sheds light on the effects of confinement and chemical corrosion on $${\\sigma }_{\\mathrm{ci}}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mi>σ</mml:mi> <mml:mi>ci</mml:mi> </mml:msub> </mml:math> .","PeriodicalId":21280,"journal":{"name":"Rock Mechanics and Rock Engineering","volume":"226 4","pages":"0"},"PeriodicalIF":5.5000,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A New Volumetric Strain-Based Method for Determining the Crack Initiation Threshold of Rocks Under Compression\",\"authors\":\"Hao Li, Ruizhi Zhong, Leo Pel, David Smeulders, Zhenjiang You\",\"doi\":\"10.1007/s00603-023-03619-2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract The crack initiation stress threshold ( $${\\\\sigma }_{\\\\mathrm{ci}}$$ <mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\"> <mml:msub> <mml:mi>σ</mml:mi> <mml:mi>ci</mml:mi> </mml:msub> </mml:math> ) is an essential parameter in the brittle failure process of rocks. In this paper, a volumetric strain response method (VSRM) is proposed to determine the $${\\\\sigma }_{\\\\mathrm{ci}}$$ <mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\"> <mml:msub> <mml:mi>σ</mml:mi> <mml:mi>ci</mml:mi> </mml:msub> </mml:math> based on two new concepts, i.e., the dilatancy resistance state index ( $${\\\\delta }_{\\\\mathrm{ci}}$$ <mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\"> <mml:msub> <mml:mi>δ</mml:mi> <mml:mi>ci</mml:mi> </mml:msub> </mml:math> ) and the maximum value of the dilatancy resistance state index difference ( $$\\\\left|{\\\\Delta \\\\delta }_{\\\\mathrm{ci}}\\\\right|$$ <mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\"> <mml:mfenced> <mml:msub> <mml:mrow> <mml:mi>Δ</mml:mi> <mml:mi>δ</mml:mi> </mml:mrow> <mml:mi>ci</mml:mi> </mml:msub> </mml:mfenced> </mml:math> ), which represent the state of dilatancy resistance of the rock and the shear sliding resistance capacity of the crack-like pores during the compressive period, respectively. The deviatoric stress corresponding to the maximum $$\\\\left|{\\\\Delta \\\\delta }_{\\\\mathrm{ci}}\\\\right|$$ <mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\"> <mml:mfenced> <mml:msub> <mml:mrow> <mml:mi>Δ</mml:mi> <mml:mi>δ</mml:mi> </mml:mrow> <mml:mi>ci</mml:mi> </mml:msub> </mml:mfenced> </mml:math> is taken as the $${\\\\sigma }_{\\\\mathrm{ci}}$$ <mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\"> <mml:msub> <mml:mi>σ</mml:mi> <mml:mi>ci</mml:mi> </mml:msub> </mml:math> . We then examine the feasibility and validity of the VSRM using the experimental results. The results from the VSRM are also compared with those calculated by other strain-based methods, including the volumetric strain method (VSM), crack volumetric strain method (CVSM), lateral strain method (LSM) and lateral strain response method (LSRM). Compared with the other methods, the VSRM is effective and reduces subjectivity when determining the $${\\\\sigma }_{\\\\mathrm{ci}}$$ <mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\"> <mml:msub> <mml:mi>σ</mml:mi> <mml:mi>ci</mml:mi> </mml:msub> </mml:math> . Finally, with the help of the proposed VSRM, influences from chemical corrosion and confining stress on the $${\\\\sigma }_{\\\\mathrm{ci}}$$ <mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\"> <mml:msub> <mml:mi>σ</mml:mi> <mml:mi>ci</mml:mi> </mml:msub> </mml:math> and $${\\\\Delta \\\\delta }_{\\\\mathrm{ci}}$$ <mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\"> <mml:msub> <mml:mrow> <mml:mi>Δ</mml:mi> <mml:mi>δ</mml:mi> </mml:mrow> <mml:mi>ci</mml:mi> </mml:msub> </mml:math> of the carbonate rock are analyzed. This study provides a subjective and practical method for determining $${\\\\sigma }_{\\\\mathrm{ci}}$$ <mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\"> <mml:msub> <mml:mi>σ</mml:mi> <mml:mi>ci</mml:mi> </mml:msub> </mml:math> . 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A New Volumetric Strain-Based Method for Determining the Crack Initiation Threshold of Rocks Under Compression
Abstract The crack initiation stress threshold ( $${\sigma }_{\mathrm{ci}}$$ σci ) is an essential parameter in the brittle failure process of rocks. In this paper, a volumetric strain response method (VSRM) is proposed to determine the $${\sigma }_{\mathrm{ci}}$$ σci based on two new concepts, i.e., the dilatancy resistance state index ( $${\delta }_{\mathrm{ci}}$$ δci ) and the maximum value of the dilatancy resistance state index difference ( $$\left|{\Delta \delta }_{\mathrm{ci}}\right|$$ Δδci ), which represent the state of dilatancy resistance of the rock and the shear sliding resistance capacity of the crack-like pores during the compressive period, respectively. The deviatoric stress corresponding to the maximum $$\left|{\Delta \delta }_{\mathrm{ci}}\right|$$ Δδci is taken as the $${\sigma }_{\mathrm{ci}}$$ σci . We then examine the feasibility and validity of the VSRM using the experimental results. The results from the VSRM are also compared with those calculated by other strain-based methods, including the volumetric strain method (VSM), crack volumetric strain method (CVSM), lateral strain method (LSM) and lateral strain response method (LSRM). Compared with the other methods, the VSRM is effective and reduces subjectivity when determining the $${\sigma }_{\mathrm{ci}}$$ σci . Finally, with the help of the proposed VSRM, influences from chemical corrosion and confining stress on the $${\sigma }_{\mathrm{ci}}$$ σci and $${\Delta \delta }_{\mathrm{ci}}$$ Δδci of the carbonate rock are analyzed. This study provides a subjective and practical method for determining $${\sigma }_{\mathrm{ci}}$$ σci . Moreover, it sheds light on the effects of confinement and chemical corrosion on $${\sigma }_{\mathrm{ci}}$$ σci .
期刊介绍:
Rock Mechanics and Rock Engineering covers the experimental and theoretical aspects of rock mechanics, including laboratory and field testing, methods of computation and field observation of structural behavior. The journal maintains the strong link between engineering geology and rock engineering, providing a bridge between fundamental developments and practical application. Coverage includes case histories on design and construction of structures in rock such as underground openings, large dam foundations and rock slopes.
Fields of interest include rock mechanics in all its varied aspects including laboratory testing, field investigations, computational methods and design principles. The journal also reports on applications in tunneling, rock slopes, large dam foundations, mining, engineering and engineering geology.