Improved method of rigid body spring for 2D hydraulic fracturing simulation
YAO Chi1，ZHAO Ming1，YANG Jianhua1，JIANG Shuihua1，JIANG Qinghui1，2，ZHOU Chuangbing1
(1. School of Civil Engineering and Architecture，Nanchang University，Nanchang，Jiangxi 330033，China；2. School of Civil Engineering，Wuhan University，Wuhan，Hubei 430072，China)
Abstract：A two-dimensional numerical method based on the method of improved rigid body spring and equivalent discrete fracture network model was proposed for modeling of hydraulic fracturing. The interaction between the water pressure and mechanical response was described by Biot?s theory，and the analytic formula of hydro-mechanical coupling for thick-walled cylinder under elastic condition was deduced. The accuracy of the numerical model was verified by comparison with the analytical solution. The numerical model was used to analyze the hydraulic fracturing process of thick-walled cylinders under plane stress conditions. The influence of Biot?s coefficient on hydraulic fracturing process was highlighted. Results show that the Biot?s coefficient，as an important parameter to reflect the hydraulic coupling effect，has the significant effect on the displacement and failure pressure in the hydraulic fracturing process.
[1] OLIAEI M N，PAK A，SOGA K. A coupled hydro-mechanical analysis for prediction of hydraulic fracture propagation in saturated porous media using EFG mesh-less method[J]. Computers and Geotechnics，2014，55(1)：254–266.
[2] MOHAMMADNEJAD T，KHOEI A R. An extended finite element method for hydraulic fracture propagation in deformable porous media with the cohesive crack model[J]. Finite Elements in Analysis and Design，2013，73(1)：77–95.
[3] DAMJANAC B，CUNDALL P. Application of distinct element methods to simulation of hydraulic fracturing in naturally fractured reservoirs[J]. Computers and Geotechnics，2016，71(1)：283–294.
[4] 李 根，唐春安，梁正召，等. 水压致裂过程的三维数值模拟研究[J]. 岩土工程学报，2011，32(12)：1 875–1 881.(LI Gen，TANG Chun?an，LIANG Zhengzhao，et al. Numerical simulation of 3D hydraulic fracturing process[J]. Chinese Journal of Geotechnical Engineering，2011，32(12)：1 875–1 881.(in Chinses))
[5] 马 收，陈佳亮，杨 勇. 低渗透储层岩石水压致裂裂纹扩展的数值模拟研究[J]. 煤炭工程，2013，45(9)：94–97.(MA Shou，CHEN Jialiang，YANG Yong. Study on numerical simulation of crack expansion by hydraulic fracturing in low permeability reservoir rock strata[J]. Coal Engineering，2013，45(9)：94–97.(in Chinese))
[6] 郭天魁，张士诚，葛洪魁. 评价页岩压裂形成缝网能力的新方法[J]. 岩土力学，2013，34(4)：947–954.(GUO Tiankui，ZHANG Shicheng，GE Hongkui. A new method for evaluating ability of forming fracture network in shale reservoir[J]. Rock and Soil Mechanics，2013，34(4)：947–954.(in Chinese))
[7] 赵金洲，任 岚，胡永全，等. 裂缝性地层水力裂缝张性起裂压力分析[J]. 岩石力学与工程学报，2013，32(增1)：2 855–2 862.(ZHAO Jinzhou，REN Lan，HU Yongquan，et al. Hydraulic fracture tensile initiation pressure analysis for fractured formations[J]. Chinese Journal of Rock Mechanics and Engineering，2013，32(Supp.1)：2 855–2 862. (in Chinese))
[8] 潘鹏志，冯夏庭，吴红晓，等. 水压致裂过程的弹塑性细胞自动机模拟[J]. 上海交通大学学报，2011，45(5)：722–727.(PAN Pengzhi，FENG Xiating，WU Hongxiao，et al. Modeling hydraulic failure process using elasto-plastic cellular automaton[J]. Journal of Shanghai Jiaotong University，2011，45(5)：722–727.(in Chinese))
[9] HARPER T R，LAST N C. Response of fractured rock subject to fluid injection Part III. Practical application[J]. Tectonophysics，1990，172(1/2)：53–65.
[10] ZHANG X，SANDERSON D J. Effects of stress on the two-dimensional permeability tensor of natural fracture networks[J]. Geophysical Journal International，1996，125(3)：912–924.
[11] GRASSL P，FAHY C，GALLIPOLI D，et al. On a 2D hydro-mechanical lattice approach for modelling hydraulic fracture[J]. Journal of the Mechanics and Physics of Solids，2015，75(1)：104–118.
[12] AL-BUSAIDI A，HAZZARD J F，YOUNG R P. Distinct element modeling of hydraulically fractured Lac du Bonnet granite[J]. Journal of Geophysical Research：Solid Earth，2005，110(B6)：B06302.
[13] JIAO Y Y，ZHANG H Q，ZHANG X L，et al. A two‐dimensional coupled hydromechanical discontinuum model for simulating rock hydraulic fracturing[J]. International Journal for Numerical and Analytical Methods in Geomechanics，2015，39(5)：457–481.
[14] YAN C，ZHENG H，SUN G，et al. Combined finite-discrete element method for simulation of hydraulic fracturing[J]. Rock Mechanics and Rock Engineering，2016，49(4)：1 389–1 410.
[15] BERRYMAN J G. Effective stress for transport properties of inhomogeneous porous rock[J]. Journal of Geophysical Research： Solid Earth，1992，97(B12)：17 409–17 424.
[16] SARRIS E，PAPANASTASIOU P. Modeling of hydraulic fracturing in a poroelastic cohesive formation[J]. International Journal of Geomechanics，2012，12(1)：160–167.
[17] CARRIER B，GRANET S. Numerical modeling of hydraulic fracture problem in permeable medium using cohesive zone model[J]. Engineering Fracture Mechanics，2012，79(1)：312–328.
[18] KAWAI T. New element models in discrete structural analysis[J]. Journal of the Society of Naval Architects of Japan，1977，1977(141)：174–180.
[19] BOLANDER J E，BERTON S. Simulation of shrinkage induced cracking in cement composite overlays[J]. Cement and Concrete Composites，2004，26(7)：861–871.
[20] NAGAI K，SATO Y，UEDA T. Mesoscopic simulation of failure of mortar and concrete by 2D RBSM[J]. Journal of Advanced Concrete Technology，2004，2(3)：359–374.
[21] UEDA T，HASAN M，NAGAI K，et al. Mesoscale simulation of influence of frost damage on mechanical properties of concrete[J]. Journal of Materials in Civil Engineering，2009，21(6)：244–252.
[22] QIAN L，XHANG X. Rigid finite element and its applications in engineering[J]. Acta Mechanica Sinica，1995，11(1)：44–50.
[23] ZHANG X. Slope stability analysis based on the rigid finite element method[J]. Geotechnique，1999，49(5)：585–593.
[24] 陈胜宏. 岩体的广义弹粘塑性块体理论[J]. 水利学报，1996，(1)：78–84.(CHEN Shenghong. A general formulation of elastic-viscoplastic block theory of rock masses[J]. Journal of Hydraulic Engineering，1996，(1)：78–84.(in Chinese))
[25] 卓家寿，赵 宁. 不连续介质静，动力分析的刚体—弹簧元法[J]. 河海大学学报：自然科学版，1993，21(5)：34–43.(ZHUO Jiashou，ZHAO Ning. Piecewise rigid body-interface spring method for problems of medium[J]. Journal of Hohai University：Natural Sciences，1993，21(5)：34–43.(in Chinese))
[26] 姚 池，姜清辉，邵建富，等. 一种模拟岩石破裂的细观数值计算模型[J]. 岩石力学与工程学报，2013，32(增2)：3 146–3 153.(YAO Chi， JIANG Qinghui， SHAO Jianfu， et al. A mesoscopic numerical model for simulation of rock fracturing[J]. Chinese Journal of Rock Mechanics and Engineering，2013，32(Supp.2)：3 146–3 153.(in Chinese))
[27] 姚 池，李 瑶，姜清辉，等. 应力作用下软硬互层岩石破裂过程的细观模拟[J]. 岩石力学与工程学报，2015，34(8)：1 542–1 551. (YAO Chi，LI Yao，JIANG Qinghui，et al. Mesoscopic model of failure process of interlayered rock under compression[J]. Chinese Journal of Rock Mechanics and Engineering，2015，34(8)：1 542– 1 551.(in Chinese))
[28] 姚 池，李 瑶，姜清辉，等. 基于改进刚体弹簧方法的开挖损伤演化分析[J]. 岩石力学与工程学报，2015，34(10)：1 959–1 966. (YAO Chi，LI Yao，JIANG Qinghui，et al. Numerical simulation of excavation damaged zone using the modified rigid body spring method[J]. Chinese Journal of Rock Mechanics and Engineering，2015，34(10)：1 959–1 966.(in Chinese))
[29] YAO C，JIANG Q H，SHAO J F. Numerical simulation of damage and failure in brittle rocks using a modified rigid block spring method[J]. Computers and Geotechnics，2015，64(1)：48–60.
[30] YAO C，JIANG Q H，SHAO J F，et al. A discrete approach for modeling damage and failure in anisotropic cohesive brittle materials[J]. Engineering Fracture Mechanics，2016，155(1)：102–118.
[31] YAO C，JIANG Q H，SHAO J F. A numerical analysis of permeability evolution in rocks with multiple fractures[J]. Transport in Porous Media，2015，108(2)：289–311.
[32] YAO C，SHAO J F，JIANG Q H，et al. Numerical study of excavation induced fractures using an extended rigid block spring method[J]. Computers and Geotechnics，2017，85(1)：368–393.
[33] JIANG Q，YAO C，YE Z，et al. Seepage flow with free surface in fracture networks[J]. Water Resources Research，2013，49(1)：176–186.
[34] 詹美礼，岑 建. 岩体水力劈裂机制圆筒模型试验及解析理论研究[J]. 岩石力学与工程学报，2007，26(6)：1 173–1 181.(ZHAN Meili，CEN Jian. Experimental and analytical study on hydraulic fracturing of cylinder sample[J]. Chinese Journal of Rock Mechanics and Engineering，2007，26(6)：1 173–1 181.(in Chinese))
2017, Vol. 36 
