弥散裂缝模型水力压裂数值方法的网格敏感性分析
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摘要
在非线性岩土/石力学问题中,网格质量是影响计算结果的一个重要因素.本文分析了弥散裂缝模型水力压裂数值求解方法中单元高宽比(AR)对计算结果的影响.材料的弹性部分采用线弹性和多孔弹性两种本构关系,屈服和破坏准则采用Drucker-Prager(DP)和Mohr-Coulomb(MC)两种模型.通过综合分析,无论采用何种本构关系,均存在网格敏感性问题.当裂缝的传播方向已知时,可以将单元的AR值控制在2.8~8.0之间,以避免弥散裂缝模型的网格敏感性问题,并得到稳定的结果.如果裂缝传播方向未知,建议使用线弹性本构关系和DP或者MC塑性模型,同时建议AR的取值为1.0.
Mesh quality is an important factor that affects the simulation results in nonlinear soil /rock mechanic problems. The effect of aspect ratio of element( AR) on calculation was analyzed in numerical solution of hydraulic fracture for the smeared crack model. Elasticity was measured by adopting the porous elastic( PE) and linear elastic( LE) constitutive models. Regarding to material yielding and failure,both the Drucker-Prager( DP) and Mohr-Coulomb( MC) models were considered. Based on a comprehensive analysis,it is concluded that no matter which constitutive model is adopted,there always exists mesh sensitivity. If the direction of fracture propagation is known,the AR should be between 2. 8 and 8. 0 to obtain stable results. If the direction is unknown,it is recommended that the LE constitutive model as well as the MC / DP plasticity model should be used together with the AR equal to 1. 0.
Mesh quality is an important factor that affects the simulation results in nonlinear soil /rock mechanic problems. The effect of aspect ratio of element( AR) on calculation was analyzed in numerical solution of hydraulic fracture for the smeared crack model. Elasticity was measured by adopting the porous elastic( PE) and linear elastic( LE) constitutive models. Regarding to material yielding and failure,both the Drucker-Prager( DP) and Mohr-Coulomb( MC) models were considered. Based on a comprehensive analysis,it is concluded that no matter which constitutive model is adopted,there always exists mesh sensitivity. If the direction of fracture propagation is known,the AR should be between 2. 8 and 8. 0 to obtain stable results. If the direction is unknown,it is recommended that the LE constitutive model as well as the MC / DP plasticity model should be used together with the AR equal to 1. 0.
引文
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[2]Hu Y J,Chen G l,Cheng W P,et al.Simulation of hydraulic fracturing in rock mass using a smeared crack model[J].Computers and Structures,2013,137(1):72-77.
[3]Pak A.Numerical modeling of hydraulic fracturing[D].Edmonton:University of Alberta,1997.
[4]Dugdale D S.Yielding of steel sheets containing slits[J].Journal of the Mechanics and Physics of Solids,1960,8(2):100-104.
[5]Barenblatt G L.The mathematical theory of equilibrium cracks in brittle fracture[J].Advances in Applied Mechanics,1962,7(1):55-129.
[6]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.
[7]Lecampion B.An extended finite element method for hydraulic fracture problems[J].Communications in Numerical Methods in Engineering,2009,25(1):121-133.
[8]Adachi J,Siebrits E,Peirce A,et al.Computer simulation of hydraulic fractures[J].International Journal of Rock Mechanics&Mining Sciences,2007,44(5):739-754.
[9]Bazant Z P,Lin F B.Nonlocal smeared cracking model for concrete fracture[J].Journal of Structural Engineering,1988,114(11):2493-2510.
[10]Bazant Z P,Oh B H.Crack band theory for fracture of concrete[J].Matériaux et Constructions,1983,16(3):155-177.
[11]Wang S Y,Sun L,Au A S,et al.2D-numerical analysis of hydraulic fracturing in heterogeneous geo-materials[J].Construction and Building Materials,2009,23(1):2196–2206.
[12]Zhu W,Montesi L G,Wong T F.A probabilistic damage model of stress-induced permeability anisotropy during cataclastic flow[J].Journal of Geophysical Research,2007,112(1):1-20.
[13]Brace W F,Paulding B,Scholz C.Dilatancy in the fracture of crystalline rocks[J].Journal of Geophysical Research,1966,71(16):3939–3953.
[14]冷雪峰,唐春安,杨天鸿.岩石水压致裂过程的数值模拟分析[J].东北大学学报:自然科学版,2002,23(11):1104-1107.(Leng Xue-feng,Tang Chun-an,Yang Tian-hong.Numerical simulation and analysis on heterogeneous and permeable rocks under hydraulic fracturing[J].Journal of Northeastern University:Natural Science,2002,23(11):1104-1107.)
[15]Lasry D,Belytschko T.Localization limiters in transient problems[J].International Journal of Solids and Structures,1988,24(6):581-597.
[16]Fernandes R,Chavant C.Evaluating the reliability of hydromechanical:a benchmark of numerical techniques carried out by research group of Mo Mas[J].Laboratoire de Mécanique des Structures Industrielles Durables,Clamart Cedex,2005,37(1):211-212.
[17]Oliver J.A consistent characteristic length for smeared cracking models[J].International Journal for Numerical Methods in Engineering,1989,28(2):461-474.
[18]Mosalam K M,Paulino G H.Evolutionary characteristic length method for smeared cracking finite element models[J].Finite Elements in Analysis and Design,1997,27(1):99-108.