考虑孔隙压密的岩石非线性变形行为计算分析
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摘要
含孔隙裂隙岩石的非线性变形对分析岩体工程中的力学响应和安全评价具有重要意义.需要考虑岩石的孔隙性建立能够反映岩石变形非线性特性的本构模型.本文首先分析了岩石非线性变形的力学机理,将岩石的全应力应变曲线分成两段.然后对两段分别建立本构关系:在压密闭合阶段,提出压密因子的概念,以表征孔隙率变化对岩石变形特性的影响;除压密闭合阶段外的另一阶段,基于损伤理论,采用岩石细观单元本构模型来描述,以最大拉应变准则和摩尔-库仑准则作为损伤判断准则.借助有限元分析软件COMSOL Multiphysics,通过MATLAB编程实现对该模型的数值求解.为验证模型的正确性,将数值模拟得到的结果与试验数据进行对比.最后,对6种孔隙率不同但岩石基质相同的岩石进行了单轴压缩破坏过程数值模拟.研究结果表明:运用提出的压密因子所建立的本构模型可以很好地模拟岩石的压密闭合阶段的非线性,对同种岩石孔隙率越大单轴抗压强度越小,随孔隙被压密弹性模量越来越大.
The nonlinear behavior of porous or fractured rocks plays an important role for analyzing the mechanical response and stability in many geological and geotechnical applications. A stress-strain relationship considering the porosity is established for modeling the nonlinear deformation. In the present paper, firstly, on the basis of nonlinear deformation mechanism of porous or fractured rocks, the typical stress-strain curve was divided into two parts factitiously. Then, two constitutive models were established for the two parts,respectively. In order to describe the effect of the change of porosity on deformation behavior of rock, a new microcracks closure factors D?was proposed in the microcracks closure phase. For the other part, elastic damage mechanics is used to describe the constitutive law of meso-level elements, the maximum tensile strain criterion as well as the Mohr-Coulomb criterion is utilized as the damage threshold. The proposed model is implemented using finite element method by MATLAB programming under the environment of COMSOL Multiphysics. Then the model was validated by comparing the numerical simulations with our experimental result and the previously published experimental data. At last, numerical simulation on failure process of 6 rock specimens with different porosities but same rock matrix under uniaxial compression is presented. It is found that the established model accurately reproduces the typical stress-strain curve, the microcracks closure phase, especially. With the increase of porosity,the uniaxial compressive strength(UCS) decreases. And the elasticity modulus increases with the porosity decrease.
The nonlinear behavior of porous or fractured rocks plays an important role for analyzing the mechanical response and stability in many geological and geotechnical applications. A stress-strain relationship considering the porosity is established for modeling the nonlinear deformation. In the present paper, firstly, on the basis of nonlinear deformation mechanism of porous or fractured rocks, the typical stress-strain curve was divided into two parts factitiously. Then, two constitutive models were established for the two parts,respectively. In order to describe the effect of the change of porosity on deformation behavior of rock, a new microcracks closure factors D?was proposed in the microcracks closure phase. For the other part, elastic damage mechanics is used to describe the constitutive law of meso-level elements, the maximum tensile strain criterion as well as the Mohr-Coulomb criterion is utilized as the damage threshold. The proposed model is implemented using finite element method by MATLAB programming under the environment of COMSOL Multiphysics. Then the model was validated by comparing the numerical simulations with our experimental result and the previously published experimental data. At last, numerical simulation on failure process of 6 rock specimens with different porosities but same rock matrix under uniaxial compression is presented. It is found that the established model accurately reproduces the typical stress-strain curve, the microcracks closure phase, especially. With the increase of porosity,the uniaxial compressive strength(UCS) decreases. And the elasticity modulus increases with the porosity decrease.
引文
[1]杨永明,鞠杨,王会杰.孔隙岩石的物理模型与破坏力学行为分析.岩土工程学报,2010,32:736–744
2 席道瑛,杜赟,易良坤,等.液体对岩石非线性弹性行为的影响.岩石力学与工程学报,2009,28:687–696
3 Lion?o A,Assis A.Behaviour of deep shafts in rock considering nonlinear elastic models.Tunn Undergr Sp Tech,2000,15:445–451
4 朱万成,唐春安,杨天鸿,等.岩石破裂过程分析(RFPA2D)系统的细观单元本构关系及验证.岩石力学与工程学报,2003,22:24–29
5 Wong T,Baud P.The brittle-ductile transition in porous rock:A review.J Struct Geol,2012,44:25–53
6 Perrin G,Leblond J B.Accelerated void growth in porous ductile solids containing two populations of cavities.Int J Plasticity,2000,16:91–120
7 Li L,Aubertin M.A general relationship between porosity and uniaxial strength of engineering materials.Can J Civ Eng,2003,30:644–658
8 Aubertin M,Li L.A porosity-dependent inelastic criterion for engineering materials.Int J Plasticity,2004,20:2179–2208
9 Vajdova V,Zhu W,Natalie Chen T M,et al.Micromechanics of brittle faulting and cataclastic flow in Tavel limestone.J Struct Geol,2010,32:1158–1169
10 Zhu W,Baud P,Vinciguerra S,et al.Micromechanics of brittle faulting and cataclastic flow in Alban Hills tuff.J Geophys Res,2011,116:B06209
11 Sammis C G,Ashby M F.The failure of brittle porous solids under compressive stress states.Acta Metall,1986,34:511–526
12 Baud P,Wong T,Zhu W.Effects of porosity and crack density on the compressive strength of rocks.Int J Rock Mech Min Sci,2014,67:202–211
13 陈咏梅.孔隙率对砂岩强度影响的损伤力学研究.四川水利发电,1997,16:39–43
14 Al-Harthi A A,Al-Amri R M,Shehata W M.The porosity and engineering properties of vesicular basalt in Saudi Arabia.Eng Geol,1999,54:313 –320
15 杜修力,金浏.含孔隙混凝土复合材料有效力学性能研究.工程力学,2012,29:70–77
16 金浏,杜修力.孔隙率变化规律及其对混凝土变形过程的影响.工程力学,2013,30:183–190
17 李春光,王水林,郑宏,等.多孔介质孔隙率与体积模量的关系.岩土力学,2007,28:293–296
18 唐春安,王述红,傅宇方.岩石破裂过程数值模拟.北京:科学出版社,2003
19 曹文贵,李翔,刘峰.裂隙化岩体应变软化损伤本构模型探讨.岩石力学与工程学报,2007,26:2488–2494
20 Liu H H,Rutqvist J,Berryman J G.On the relationship between stress and elastic strain for porous and fractured rock.Int J Rock Mech Min Sci,2009,46:289–296
21 Zhao Y,Liu H H.An elastic stress-strain relationship for porous rock under anisotropic stress conditions.Rock Mech Rock Eng,2012,45:389–39922李连崇,Liu H H,赵瑜.基于双应变胡克模型的岩石非线性弹性行为分析.岩石力学与工程学报,2012,32:2119–2126
23 Corkum A G,Martin C D.The mechanical behaviour of weak mudstone(Opalinus Clay)at low stresses.Int J Rock Mech Min Sci,2007,44:
196 –209
24 蔡美峰,何满潮,刘东燕.岩石力学与工程.北京:科学出版社,2005
25 Tang C.Numerical simulation of progressive rock failure and associated seismicity.Int J Rock Mech Min Sci,1997,34:249–261
26 Zhu W C,Tang C A.Micromechanical model for simulating the fracture process of rock.Rock Mech Rock Eng,2004,37:25–56
27 Rutqvist J,Tsang C F.A study of caprock hydromechanical changes associated with CO2-injection into a brine formation.Environ Geol,2002,42 :296–305
28 秦跃平.压缩实验煤岩孔隙率变化规律研究.矿业工程研究,2010,25:1–3
29 王青元,朱万成,刘洪磊,等.单轴压缩下绿砂岩长期强度的尺寸效应研究.岩土力学,2016,37:981–990
30 Wang Q Y,Zhu W C,Xu T,et al.Numerical simulation of rock creep behavior with a damage-based constitutive law.Int J Geomech,2017,17:04016044
31 Xu T,Tang C,Zhao J,et al.Modelling the time-dependent rheological behaviour of heterogeneous brittle rocks.Geophys J Int,2012,189:1781–1796
32 Heap M J,Xu T,Chen C.The influence of porosity and vesicle size on the brittle strength of volcanic rocks and magma.Bull Volcanol,2014,76:85633 Zhu W,Baud P,Wong T F.Micromechanics of cataclastic pore collapse in limestone.J Geophys Res,2010,115:B04405
2 席道瑛,杜赟,易良坤,等.液体对岩石非线性弹性行为的影响.岩石力学与工程学报,2009,28:687–696
3 Lion?o A,Assis A.Behaviour of deep shafts in rock considering nonlinear elastic models.Tunn Undergr Sp Tech,2000,15:445–451
4 朱万成,唐春安,杨天鸿,等.岩石破裂过程分析(RFPA2D)系统的细观单元本构关系及验证.岩石力学与工程学报,2003,22:24–29
5 Wong T,Baud P.The brittle-ductile transition in porous rock:A review.J Struct Geol,2012,44:25–53
6 Perrin G,Leblond J B.Accelerated void growth in porous ductile solids containing two populations of cavities.Int J Plasticity,2000,16:91–120
7 Li L,Aubertin M.A general relationship between porosity and uniaxial strength of engineering materials.Can J Civ Eng,2003,30:644–658
8 Aubertin M,Li L.A porosity-dependent inelastic criterion for engineering materials.Int J Plasticity,2004,20:2179–2208
9 Vajdova V,Zhu W,Natalie Chen T M,et al.Micromechanics of brittle faulting and cataclastic flow in Tavel limestone.J Struct Geol,2010,32:1158–1169
10 Zhu W,Baud P,Vinciguerra S,et al.Micromechanics of brittle faulting and cataclastic flow in Alban Hills tuff.J Geophys Res,2011,116:B06209
11 Sammis C G,Ashby M F.The failure of brittle porous solids under compressive stress states.Acta Metall,1986,34:511–526
12 Baud P,Wong T,Zhu W.Effects of porosity and crack density on the compressive strength of rocks.Int J Rock Mech Min Sci,2014,67:202–211
13 陈咏梅.孔隙率对砂岩强度影响的损伤力学研究.四川水利发电,1997,16:39–43
14 Al-Harthi A A,Al-Amri R M,Shehata W M.The porosity and engineering properties of vesicular basalt in Saudi Arabia.Eng Geol,1999,54:313 –320
15 杜修力,金浏.含孔隙混凝土复合材料有效力学性能研究.工程力学,2012,29:70–77
16 金浏,杜修力.孔隙率变化规律及其对混凝土变形过程的影响.工程力学,2013,30:183–190
17 李春光,王水林,郑宏,等.多孔介质孔隙率与体积模量的关系.岩土力学,2007,28:293–296
18 唐春安,王述红,傅宇方.岩石破裂过程数值模拟.北京:科学出版社,2003
19 曹文贵,李翔,刘峰.裂隙化岩体应变软化损伤本构模型探讨.岩石力学与工程学报,2007,26:2488–2494
20 Liu H H,Rutqvist J,Berryman J G.On the relationship between stress and elastic strain for porous and fractured rock.Int J Rock Mech Min Sci,2009,46:289–296
21 Zhao Y,Liu H H.An elastic stress-strain relationship for porous rock under anisotropic stress conditions.Rock Mech Rock Eng,2012,45:389–39922李连崇,Liu H H,赵瑜.基于双应变胡克模型的岩石非线性弹性行为分析.岩石力学与工程学报,2012,32:2119–2126
23 Corkum A G,Martin C D.The mechanical behaviour of weak mudstone(Opalinus Clay)at low stresses.Int J Rock Mech Min Sci,2007,44:
196 –209
24 蔡美峰,何满潮,刘东燕.岩石力学与工程.北京:科学出版社,2005
25 Tang C.Numerical simulation of progressive rock failure and associated seismicity.Int J Rock Mech Min Sci,1997,34:249–261
26 Zhu W C,Tang C A.Micromechanical model for simulating the fracture process of rock.Rock Mech Rock Eng,2004,37:25–56
27 Rutqvist J,Tsang C F.A study of caprock hydromechanical changes associated with CO2-injection into a brine formation.Environ Geol,2002,42 :296–305
28 秦跃平.压缩实验煤岩孔隙率变化规律研究.矿业工程研究,2010,25:1–3
29 王青元,朱万成,刘洪磊,等.单轴压缩下绿砂岩长期强度的尺寸效应研究.岩土力学,2016,37:981–990
30 Wang Q Y,Zhu W C,Xu T,et al.Numerical simulation of rock creep behavior with a damage-based constitutive law.Int J Geomech,2017,17:04016044
31 Xu T,Tang C,Zhao J,et al.Modelling the time-dependent rheological behaviour of heterogeneous brittle rocks.Geophys J Int,2012,189:1781–1796
32 Heap M J,Xu T,Chen C.The influence of porosity and vesicle size on the brittle strength of volcanic rocks and magma.Bull Volcanol,2014,76:85633 Zhu W,Baud P,Wong T F.Micromechanics of cataclastic pore collapse in limestone.J Geophys Res,2010,115:B04405