高应力卸荷条件下砂岩扩容特征及其剪胀角函数
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摘要
为研究高应力水平条件下岩石卸荷扩容特性及其剪胀角变化规律,开展了若干不同初始围压水平的三轴峰前卸围压试验,同时进行了相应围压水平的常规三轴压缩试验。基于试验成果分析了卸荷应力路径对砂岩扩容的影响效应,总结了卸荷应力路径下剪胀角变化规律,进而提出了基于卸荷应力路径的剪胀角函数,并给出了其数值实现方法,最后通过对三轴峰前卸围压试验的数值模拟,验证了所提出的剪涨角函数的可行性与合理性。研究表明:(1)加载路径时,不同围压水平下峰前扩容体积应变值相差不大,而卸荷应力路径时,随着围压水平的增加,峰前扩容体积应变从最小值3.15×10~(-3)增加到最大值9.65×10~(-3),卸荷路径下的峰前扩容体积应变约为加载路径的1.1～4.0倍;(2)卸荷应力路径下偏应力峰值对应的体积应变基本为0或接近于0,而加载应力路径下偏应力峰值对应的体积应变均为负值;(3)卸荷应力路径条件下峰前扩容体积应变在总扩容体积应变中所占比例显著大于加载路径;(4)两种应力路径下,剪胀角随塑性剪切应变增加均经历了先增加后减小的过程,并且低围压工况下偏应力峰值对应的剪胀角和最大剪胀角均大于高围压工况;(5)与加载路径相比,卸荷路径下的剪胀角更快达到剪胀角最大值,并且其偏应力峰值对应的剪胀角和最大剪胀角更大;(6)基于砂岩三轴卸荷试验成果,采用线性拟合方法得出了以围压和峰后塑性剪切应变增量为自变量的剪胀角函数,基于该函数与应变软化本构模型的砂岩三轴峰前卸围压试验的数值模拟结果与试验结果吻合较好,表明该函数能较好地描述三轴峰前卸围压条件下砂岩的扩容特性。以上结论可为深部地下工程变形预测、稳定性分析与支护设计提供理论基础。
This study is aimed to investigate the unloading and dilatancy characteristics of rock under high-stress level and the variation law of the dilatancy angle. A series of triaxial pre-peak unloading confining pressure tests was carried out at different initial confining pressure levels, and the conventional triaxial compression tests were also conducted at corresponding confining pressure levels. Based on the experimental results, the effect of the unloading stress path on the dilatancy characteristics of sandstone was analysed, the variation law of dilatancy angle under the unloading stress path was summarized as well. Moreover, the dilatancy angle function under the unloading stress path was proposed, and its numerical realisation method was established. Finally, the feasibility and rationality of the proposed dilatancy angle function was verified by the numerical simulation of the triaxial pre-peak unloading confining pressure tests. Under different confining pressure levels, the volumetric strain values of pre-peak dilatation were similar under the loading paths. While under the unloading stress paths, the volumetric strain of pre-peak dilatation increased from the minimum value of 3.15×10~(-3) to the maximum value of 9.65×10~(-3) with increasing the confining pressure level. The volumetric strain of pre-peak dilatation under the unloading path was about 1.1-4.0 times than that under the loading path. The volumetric strain corresponding to the peak of the deviatoric stress was substantially zero or close to zero under the unloading condition, while the volumetric strain was negative under the loading condition. Under the unloading stress path condition, the proportion of the volume expansion strain before the peak of deviatoric stress in the total volume expansion strain was significantly larger than that under the loading path. The dilatancy angle firstly increased and then decreased with increasing the plastic shear strain under the two stress paths. Under lower confining pressure conditions, both the maximum dilatancy angle and the dilatancy angle corresponding to the peak were greater than those under the higher confining pressure conditions. Compared with the loading path, the dilatancy angle reached the maximum value faster, and the maximum dilatancy angle and the dilatancy angle corresponding to the peak were larger under the unloading path. According to the unloading test results, the linear fitting method was used to establish the dilatancy angle function with the confining pressure and post-peak plastic shear strain as independent variables. The experimental results showed good agreements with the simulation results from the established function and the strain softening constitutive model under the unloading path. The results indicate that the function can better describe the expansion characteristics of sandstone under the conditions of the triaxial pre-peak unloading path. This study can provide a theoretical basis for deformation prediction, stability analysis and support design of deep underground engineering.
This study is aimed to investigate the unloading and dilatancy characteristics of rock under high-stress level and the variation law of the dilatancy angle. A series of triaxial pre-peak unloading confining pressure tests was carried out at different initial confining pressure levels, and the conventional triaxial compression tests were also conducted at corresponding confining pressure levels. Based on the experimental results, the effect of the unloading stress path on the dilatancy characteristics of sandstone was analysed, the variation law of dilatancy angle under the unloading stress path was summarized as well. Moreover, the dilatancy angle function under the unloading stress path was proposed, and its numerical realisation method was established. Finally, the feasibility and rationality of the proposed dilatancy angle function was verified by the numerical simulation of the triaxial pre-peak unloading confining pressure tests. Under different confining pressure levels, the volumetric strain values of pre-peak dilatation were similar under the loading paths. While under the unloading stress paths, the volumetric strain of pre-peak dilatation increased from the minimum value of 3.15×10~(-3) to the maximum value of 9.65×10~(-3) with increasing the confining pressure level. The volumetric strain of pre-peak dilatation under the unloading path was about 1.1-4.0 times than that under the loading path. The volumetric strain corresponding to the peak of the deviatoric stress was substantially zero or close to zero under the unloading condition, while the volumetric strain was negative under the loading condition. Under the unloading stress path condition, the proportion of the volume expansion strain before the peak of deviatoric stress in the total volume expansion strain was significantly larger than that under the loading path. The dilatancy angle firstly increased and then decreased with increasing the plastic shear strain under the two stress paths. Under lower confining pressure conditions, both the maximum dilatancy angle and the dilatancy angle corresponding to the peak were greater than those under the higher confining pressure conditions. Compared with the loading path, the dilatancy angle reached the maximum value faster, and the maximum dilatancy angle and the dilatancy angle corresponding to the peak were larger under the unloading path. According to the unloading test results, the linear fitting method was used to establish the dilatancy angle function with the confining pressure and post-peak plastic shear strain as independent variables. The experimental results showed good agreements with the simulation results from the established function and the strain softening constitutive model under the unloading path. The results indicate that the function can better describe the expansion characteristics of sandstone under the conditions of the triaxial pre-peak unloading path. This study can provide a theoretical basis for deformation prediction, stability analysis and support design of deep underground engineering.
引文
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[7]刘建,李建朋.砂岩高应力峰前卸围压试验研究[J].岩石力学与工程学报,2011,30(3):473-479.LIU Jian,LI Jian-peng.Experimental research on sandstone pre-peak unloading process under high confining pressure[J].Chinese Journal of Rock Mechanics and Engineering,2011,30(4):473-479.
[8]CRISTESCU N.Rock dilatancy in uniaxial tests[J].Rock Mechanics Felsmechanik Mecanique des Roches,1982,15:133-144.
[9]VERMEER P A,DE BORST R.Non-asscioated plasticity for soils,concrete and rock[J].Heron,1984,29(3):3-64.
[10]DETOURNAY E.Elastoplastic model of a deep tunnel for a rock with variable dilatancy[J].Rock Mechanics and Rock Engineering,1986,19:99-108.
[11]HOEK E,BROWN E T.Practical estimates of rock mass strength[J].International Journal of Rock Mechanics and Mining Sciences,1997,34(8):1165-1186.
[12]KUDOH K,KOYAMA T,NAMBO S.Support design of a large underground cavern considering strain-softening of the rock[C]//9th ISRM Congress.Rotterdam:A.A.Balkema,1999:407-411.
[13]ALEJANO L R,ALONSO E.Considerations of the dilatancy angle in rocks and rock masses[J].International Journal of Rock Mechanics and Mining Sciences,2005,42(4):481-507.
[14]赵星光,蔡明,蔡美峰.岩石剪胀角模型与验证[J].岩石力学与工程学报,2010,29(5):970-981.ZHAO Xing-guang,CAI Ming,CAI Mei-feng.A rock dilation angle model and its verification[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(5):970-981.
[2]BRIDGMAN P W.Volume changes in the plastic stages of simple compression[J].Journal of Applied Physics,1949,20:1241-1251.
[3]李宏哲,夏才初,闫子舰,等.锦屏水电站大理岩在高应力条件下的卸荷力学特性研究[J].岩石力学与工程学报,2007,26(10):2104-2109.LI Hong-zhe,XIA Cai-chu,YAN Zi-jian,et al.Study on marble unloading mechanical properties of Jinping hydropower station under high geostress conditions[J].Chinese Journal of Rock Mechanics and Engineering,2007,26(10):2104-2109.
[4]黄伟,沈明荣,张清照.高围压下岩石卸荷的扩容性质及其本构模型研究[J].岩石力学与工程学报,2010,29(增刊2):3475-3481.HUANG Wei,SHEN Ming-rong,ZHANG Qing-zhao.Study on unloading dilatancy property of rock and its constitutive model under high confining pressure[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(Suppl.2):3475-3481.
[5]邱士利,冯夏庭,张传庆,等.不同卸围压速率下深埋大理岩卸荷力学特性试验研究[J].岩石力学与工程学报,2010,29(9):1807-1817.QIU Shi-li,FENG Xia-ting,ZHANG Chuan-qing,et al.Experimental research on mechanical properties of deep-buried marble under different unloading rates of confining pressures[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(9):1807-1817.
[6]李天斌,王兰生.卸荷应力状态下玄武岩变形破坏特征的试验研究[J].岩石力学与工程学报,1993,12(4):321-327.LI Tian-bin,WANG Lan-sheng.An experimental study on the deformation and failure features of a basalt under unloading condition[J].Chinese Journal of Rock Mechanics and Engineering,1993,12(4):321-327.
[7]刘建,李建朋.砂岩高应力峰前卸围压试验研究[J].岩石力学与工程学报,2011,30(3):473-479.LIU Jian,LI Jian-peng.Experimental research on sandstone pre-peak unloading process under high confining pressure[J].Chinese Journal of Rock Mechanics and Engineering,2011,30(4):473-479.
[8]CRISTESCU N.Rock dilatancy in uniaxial tests[J].Rock Mechanics Felsmechanik Mecanique des Roches,1982,15:133-144.
[9]VERMEER P A,DE BORST R.Non-asscioated plasticity for soils,concrete and rock[J].Heron,1984,29(3):3-64.
[10]DETOURNAY E.Elastoplastic model of a deep tunnel for a rock with variable dilatancy[J].Rock Mechanics and Rock Engineering,1986,19:99-108.
[11]HOEK E,BROWN E T.Practical estimates of rock mass strength[J].International Journal of Rock Mechanics and Mining Sciences,1997,34(8):1165-1186.
[12]KUDOH K,KOYAMA T,NAMBO S.Support design of a large underground cavern considering strain-softening of the rock[C]//9th ISRM Congress.Rotterdam:A.A.Balkema,1999:407-411.
[13]ALEJANO L R,ALONSO E.Considerations of the dilatancy angle in rocks and rock masses[J].International Journal of Rock Mechanics and Mining Sciences,2005,42(4):481-507.
[14]赵星光,蔡明,蔡美峰.岩石剪胀角模型与验证[J].岩石力学与工程学报,2010,29(5):970-981.ZHAO Xing-guang,CAI Ming,CAI Mei-feng.A rock dilation angle model and its verification[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(5):970-981.