基于分段解除的深部空心包体应变计中非线性优化算法
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摘要
随着浅部资源的日益枯竭,地下开采的深度不断增大,千米级乃至更深的矿产资源开采已成为常态。因此弄清深部岩体原岩应力的赋存环境是至关重要的,目前CSIRO地应力测量作为国际岩石力学学会建议直接测量方法,在世界各地广泛使用。在浅部岩体空心包体应变计地应力测量解析式中,弹性模量和泊松比都是通过室内双轴加载数据拟合获得的常数。进入深部岩体表现出高度的非线性,在对解除岩芯进行高压双轴加卸载试验中发现围压与应变的关系非线性,并且随着围压不断增大非线性关系尤为突出。传统的双轴加载试验设备最大围压加载值试验室内测得20 MPa,不能满足深部岩体解除岩芯的高压双轴试验模拟解除岩石在深部所受的应力环境。因此对传统的设备进行改造,研发了一套高压双轴加载试验装置,所承受的理论最大径向压力为200 MPa以上,目前试验测试的最大围压为100 MPa。对三山岛金矿埋深800 m的解除岩芯进行了高压双轴加卸载试验,分析应力与应变的关系提出一种平均应力与体积模量和剪切模量之间的非线性双曲线模型,明确了模型中3个拟合参数的物理意义,推导出平均应力与应变之间的非线性关系特征公式。基于弹性力学理论原岩应力分量计算在不考虑解除路径时,应用最小二乘法进行计算后获得最大主应力大小为53. 11 MPa,西北312°,倾角为8°。本文提出的考虑解除路径的优化算法,将整个解除过程分成多个阶段,每个阶段的变形模量计算参数与解除岩芯所受应力状态有关,且符合推导的应力与应变的非线性关系公式,各个阶段叠加计算的最大主应力大小为47. 78 MPa,西北311°,倾角为5°。
Deep mining is gradually becoming more prevalent owing to the lack of shallow mineral resources. In the deep underground,the geological environment becomes complex,particularly has high in-situ stress. The CSIRO in-situ stress measurement method,as the international society for rock mechanics suggested as direct measurement method,is widely used all over the world. In shallow parsing type hollow inclusion strain gauge in-situ stress measurement of rock mass,the elastic modulus and Poisson's ratio are obtained from the indoor biaxial loading data fitting of constant. In the deep rock mass showing the highly nonlinear,it is found that the relation between confining pressure and strain is nonlinear in the high pressure biaxial loading and unloading test,and the nonlinear relation is especially prominent as the confining pressure increases. The maximum confining pressure of the traditional biaxial loading test equipment is20 MPa. It can not satisfy the high pressure biaxial test simulation of deep rock core release. Thus the traditional equipment is transformed to develop a set of high pressure biaxial loading test device. The theoretical maximum radial pressure is over 200 MPa,and the maximum confining pressure tested in the current test is 100 MPa. Based on the research and development of a set of high pressure biaxial loading test device,a high pressure biaxial loading-unloading test is carried out on the core of Sanshandao Gold Mine with a depth of 800 m. By analyzing the relationship between stress and strain,a non-linear hyperbola model between the mean stress vs volume modulus and shear modulus is proposed,the physical significance of the three fitting parameters in the model is defined,and the characteristic formula of the non-linear relationship between average stress and strain is derived. Based on the elastic mechanics theory,the maximum main in-situ stress without considering relieved strain path is 53.11 MPa,its direction is 312°,and dip angle is 8° after the application of least square method to calculate. The optimization algorithm proposed in this paper takes the relieved strain path into consideration and divides the entire decommissioning process into multiple stages. The calculated parameters of elastic modulus and Poisson's ratio at each stage are related to the stress state of the core,and conform to the deduced non-linear relation formula of stress and strain. The maximum principal stress of each stage superposition calculation of is 47.78 MPa,its direction is 311°,and dip angle is 5°.
Deep mining is gradually becoming more prevalent owing to the lack of shallow mineral resources. In the deep underground,the geological environment becomes complex,particularly has high in-situ stress. The CSIRO in-situ stress measurement method,as the international society for rock mechanics suggested as direct measurement method,is widely used all over the world. In shallow parsing type hollow inclusion strain gauge in-situ stress measurement of rock mass,the elastic modulus and Poisson's ratio are obtained from the indoor biaxial loading data fitting of constant. In the deep rock mass showing the highly nonlinear,it is found that the relation between confining pressure and strain is nonlinear in the high pressure biaxial loading and unloading test,and the nonlinear relation is especially prominent as the confining pressure increases. The maximum confining pressure of the traditional biaxial loading test equipment is20 MPa. It can not satisfy the high pressure biaxial test simulation of deep rock core release. Thus the traditional equipment is transformed to develop a set of high pressure biaxial loading test device. The theoretical maximum radial pressure is over 200 MPa,and the maximum confining pressure tested in the current test is 100 MPa. Based on the research and development of a set of high pressure biaxial loading test device,a high pressure biaxial loading-unloading test is carried out on the core of Sanshandao Gold Mine with a depth of 800 m. By analyzing the relationship between stress and strain,a non-linear hyperbola model between the mean stress vs volume modulus and shear modulus is proposed,the physical significance of the three fitting parameters in the model is defined,and the characteristic formula of the non-linear relationship between average stress and strain is derived. Based on the elastic mechanics theory,the maximum main in-situ stress without considering relieved strain path is 53.11 MPa,its direction is 312°,and dip angle is 8° after the application of least square method to calculate. The optimization algorithm proposed in this paper takes the relieved strain path into consideration and divides the entire decommissioning process into multiple stages. The calculated parameters of elastic modulus and Poisson's ratio at each stage are related to the stress state of the core,and conform to the deduced non-linear relation formula of stress and strain. The maximum principal stress of each stage superposition calculation of is 47.78 MPa,its direction is 311°,and dip angle is 5°.
引文
[1]SJ?BERG J,CHRISTIANSSON R,HUDSON J A.ISRM suggested methods for rock stress estimation-part 2:Overcoring methods[J].International Journal of Rock Mechanics and Mining Sciences,2003,40(7-8):999-1010.
[2]ZANG A,STEPHANSSON O,HEIDBACH O,et al.World stress map database as a resource for rock mechanics and rock engineering[J].Geotechnical and Geological Engineering,2012,30(3):625-646.doi:10,1007/s10706-012-9505-6.
[3]蔡美峰.岩石力学与工程[M].北京:科学出版社,2013.
[4]李远,乔兰,孙歆硕.关于影响空心包体应变计地应力测量精度若干因素的讨论[J].岩石力学与工程学报,2006,25(10):2140-2144.LI Yuan,QIAO Lan,SUN Xinshuo.Analyses of some factors affecting precision in in-situ stress measurement with method of CSIRO cells[J].Chinese Journal of Rock Mechanics and Engineering,2006,25(10):2140-2144.
[5]李远,王卓.基于双温度补偿的瞬接续采型空心包体地应力测试技术研究[J].岩石力学与工程学报,2017,36(6):1479-1487.LI Yuan,WANG Zhuo.Development of CSIRO cell with the compromised application of instantaneous datalogging,no-power data-connection and twin temperature compensation techniques[J].Chinese Journal of Rock Mechanics and Engineering,2017,36(6):1479-1487.
[6]闫振雄,郭奇峰,王培涛.空心包体应变计地应力分量计算方法及应用[J].岩土力学,2018,39(2):725-721.YAN Zhenxiong,GUO Qifeng,WANG Peitao.Calculation and application of in-situ stress components in hollow inclusion measurement[J].Rock and Soil Mechanics,2018,39(2):725-721.
[7]董诚,王连婕,孙东生,等.空心包体三轴地应力测量系统的升级改造[J].实验技术与管理,2009,26(1):51-55.DONG Cheng,WANG Lianjie,SUN Dongsheng,et al.The upgrading and improvement of hollow inclusion triaxial strain gauge for geostress measurement[J].Experimental Technology and Management,2009,26(1):51-55.
[8]王衍森,吴振业.地应力测量应变值检验及应变计最佳布片方式[J].岩土工程学报,1999,21(1):53-55.WANG Yansen,WU Zhenye.Direct method to verify virgin stress measurement and the optimum rosette arrangement style of hollow inclusion cell[J].Chinese Journal of Geotechnical Engineering,1999,21(1):53-55.
[9]刘少伟,樊克松,尚鹏翔.空心包体应力计温度补偿元件的设计及应用[J].煤田地质与勘探,2014,42(6):105-109.LIU Shaowei,FAN Kesong,SHANG Pengxiang.Design and application of temperature compensating element of hollow inclusion stress gauge[J].Coal Geology&Exploration,2014,42(6):105-109.
[10]白金朋,彭华,马秀敏,等.深孔空心包体法地应力测量仪及其应用实例[J].岩石力学与工程学报,2013,32(5):902-908.BAI Jnpeng,PENG Hua,MA Xiumin,et al.Hollow inclusion strain gauge geostress measuring instrument in deep borehole and its application example[J].Chinese Journal of Rock Mechanics and Engineering,2013,32(5):902-908.
[11]DUNCAN J M,CHANG C Y.Nonlinear analysis of stress and strain in soils[J].Journal of the Soil Mechanics and Foundations Division,1970,96(3):1629-1653.
[12]KULHAWY F H,DUNCAN J M.Stresses and movements in Oroville dam[J].Journal of the Soil Mechanics and Foundations Division,1972,98(1):653-655.
[13]席道瑛,王鑫,陈运平.描写岩石非线性弹性滞后和记忆的宏观模型[J].岩石力学与工程学报,2005,24(20):2212-2219.XI Daoying,WANG Xin,CHEN Yunping.Macroscopic model of hysteresis and memory for the description of rock nonlinear elastic[J].Chinese Journal of Rock Mechanics and Engineering,2005,24(20):2212-2219.
[14]席道瑛,陈运平,陶月赞.岩石的非线性弹性滞后特征[J].岩石力学与工程学报,2006,25(6):1083-1096.XI Daoying,CHEN Yunping,TAO Yuezan.Nonlinear elastic hysteric characteristics of rocks[J].Chinese Journal of Rock Mechanics and Engineering,2006,25(6):1083-1096.
[15]孔志鹏,孙海霞,陈四利.岩石材料的一种非线性三参数强度准则及应用[J].岩土力学学报,2017,38(12):3524-3531.KONG Zhipeng,SUN Haixia,CHEN Sili.A nonlinear tri-parameter strength criterion for rock materials and its application[J].Rock and Soil Mechanics,2017,38(12):3524-3531.
[16]蔡美峰.地应力测量中温度补偿方法的研究[J].岩石力学与工程学报,1991,10(3):227-235.CAI Meifeng.Studies of temperature compensation techniques in rock stress measurements[J].Chinese Journal of Rock Mechanics and Engineering,1991,10(3):227-235.
[17]葛修润,侯明勋.钻孔局部壁面应力解除法(BWSRM)的原理及其在锦屏二级水电站工程中的初步应用[J].中国科学,2012,42(4):359-368.GE Xiurun,HOU Mingxun.Principle of in-situ 3D rock stress measurement with borehole wall stress relief method and its preliminary applications to determination of in-situ rock stress orientation and magnitude in jinping hydropower station[J].Science China Technological Sciences,2012,42(4):359-368.
[18]蔡美峰,刘卫东,李远.玲珑金矿深部地应力测量及矿区地应力场分布规律[J].岩石力学与工程学报,2010,29(2):227-233.CAI Meifeng,LIU Weidong,LI Yuan.In-situ stress measurement at deep position of linglong gold mine and distribution law of in-situ stress field in mine area[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(2):227-233.
[19]FANG Shulin,ZHANG Jian.In-situ measure to internal stress of shotcrete layer in soft-rock roadway[J].International Journal of Coal Science&Technology,2014,1(3):321-328.
[2]ZANG A,STEPHANSSON O,HEIDBACH O,et al.World stress map database as a resource for rock mechanics and rock engineering[J].Geotechnical and Geological Engineering,2012,30(3):625-646.doi:10,1007/s10706-012-9505-6.
[3]蔡美峰.岩石力学与工程[M].北京:科学出版社,2013.
[4]李远,乔兰,孙歆硕.关于影响空心包体应变计地应力测量精度若干因素的讨论[J].岩石力学与工程学报,2006,25(10):2140-2144.LI Yuan,QIAO Lan,SUN Xinshuo.Analyses of some factors affecting precision in in-situ stress measurement with method of CSIRO cells[J].Chinese Journal of Rock Mechanics and Engineering,2006,25(10):2140-2144.
[5]李远,王卓.基于双温度补偿的瞬接续采型空心包体地应力测试技术研究[J].岩石力学与工程学报,2017,36(6):1479-1487.LI Yuan,WANG Zhuo.Development of CSIRO cell with the compromised application of instantaneous datalogging,no-power data-connection and twin temperature compensation techniques[J].Chinese Journal of Rock Mechanics and Engineering,2017,36(6):1479-1487.
[6]闫振雄,郭奇峰,王培涛.空心包体应变计地应力分量计算方法及应用[J].岩土力学,2018,39(2):725-721.YAN Zhenxiong,GUO Qifeng,WANG Peitao.Calculation and application of in-situ stress components in hollow inclusion measurement[J].Rock and Soil Mechanics,2018,39(2):725-721.
[7]董诚,王连婕,孙东生,等.空心包体三轴地应力测量系统的升级改造[J].实验技术与管理,2009,26(1):51-55.DONG Cheng,WANG Lianjie,SUN Dongsheng,et al.The upgrading and improvement of hollow inclusion triaxial strain gauge for geostress measurement[J].Experimental Technology and Management,2009,26(1):51-55.
[8]王衍森,吴振业.地应力测量应变值检验及应变计最佳布片方式[J].岩土工程学报,1999,21(1):53-55.WANG Yansen,WU Zhenye.Direct method to verify virgin stress measurement and the optimum rosette arrangement style of hollow inclusion cell[J].Chinese Journal of Geotechnical Engineering,1999,21(1):53-55.
[9]刘少伟,樊克松,尚鹏翔.空心包体应力计温度补偿元件的设计及应用[J].煤田地质与勘探,2014,42(6):105-109.LIU Shaowei,FAN Kesong,SHANG Pengxiang.Design and application of temperature compensating element of hollow inclusion stress gauge[J].Coal Geology&Exploration,2014,42(6):105-109.
[10]白金朋,彭华,马秀敏,等.深孔空心包体法地应力测量仪及其应用实例[J].岩石力学与工程学报,2013,32(5):902-908.BAI Jnpeng,PENG Hua,MA Xiumin,et al.Hollow inclusion strain gauge geostress measuring instrument in deep borehole and its application example[J].Chinese Journal of Rock Mechanics and Engineering,2013,32(5):902-908.
[11]DUNCAN J M,CHANG C Y.Nonlinear analysis of stress and strain in soils[J].Journal of the Soil Mechanics and Foundations Division,1970,96(3):1629-1653.
[12]KULHAWY F H,DUNCAN J M.Stresses and movements in Oroville dam[J].Journal of the Soil Mechanics and Foundations Division,1972,98(1):653-655.
[13]席道瑛,王鑫,陈运平.描写岩石非线性弹性滞后和记忆的宏观模型[J].岩石力学与工程学报,2005,24(20):2212-2219.XI Daoying,WANG Xin,CHEN Yunping.Macroscopic model of hysteresis and memory for the description of rock nonlinear elastic[J].Chinese Journal of Rock Mechanics and Engineering,2005,24(20):2212-2219.
[14]席道瑛,陈运平,陶月赞.岩石的非线性弹性滞后特征[J].岩石力学与工程学报,2006,25(6):1083-1096.XI Daoying,CHEN Yunping,TAO Yuezan.Nonlinear elastic hysteric characteristics of rocks[J].Chinese Journal of Rock Mechanics and Engineering,2006,25(6):1083-1096.
[15]孔志鹏,孙海霞,陈四利.岩石材料的一种非线性三参数强度准则及应用[J].岩土力学学报,2017,38(12):3524-3531.KONG Zhipeng,SUN Haixia,CHEN Sili.A nonlinear tri-parameter strength criterion for rock materials and its application[J].Rock and Soil Mechanics,2017,38(12):3524-3531.
[16]蔡美峰.地应力测量中温度补偿方法的研究[J].岩石力学与工程学报,1991,10(3):227-235.CAI Meifeng.Studies of temperature compensation techniques in rock stress measurements[J].Chinese Journal of Rock Mechanics and Engineering,1991,10(3):227-235.
[17]葛修润,侯明勋.钻孔局部壁面应力解除法(BWSRM)的原理及其在锦屏二级水电站工程中的初步应用[J].中国科学,2012,42(4):359-368.GE Xiurun,HOU Mingxun.Principle of in-situ 3D rock stress measurement with borehole wall stress relief method and its preliminary applications to determination of in-situ rock stress orientation and magnitude in jinping hydropower station[J].Science China Technological Sciences,2012,42(4):359-368.
[18]蔡美峰,刘卫东,李远.玲珑金矿深部地应力测量及矿区地应力场分布规律[J].岩石力学与工程学报,2010,29(2):227-233.CAI Meifeng,LIU Weidong,LI Yuan.In-situ stress measurement at deep position of linglong gold mine and distribution law of in-situ stress field in mine area[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(2):227-233.
[19]FANG Shulin,ZHANG Jian.In-situ measure to internal stress of shotcrete layer in soft-rock roadway[J].International Journal of Coal Science&Technology,2014,1(3):321-328.
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