Mesh Sensitivity Analysis of the Solution to Hydraulic Fracture Problems Based on a Smeared Crack Model
LI Ming1,2， LIANG Li1， GUO Pei-jun2， LI Xin1
1. School of Resources & Civil Engineering， Northeastern University， Shenyang 110819， China; 2. Department of Civil Engineering， McMaster University， Hamilton L8S4L8， Canada.
LI Ming， LIANG Li， GUO Pei-jun， LI Xin. Mesh Sensitivity Analysis of the Solution to Hydraulic Fracture Problems Based on a Smeared Crack Model[J]. Journal of Northeastern University:Natural Science, 2015, 36(9): 1337-1341.
[1]Rahman M M，Rahman M K.A review of hydraulic fracture models and development of an improved pseudo-3D model for stimulating tight oil gas sand［J］.Energy Sources，Part A:Recovery，Utilization，and Environmental Effects，2010，32(1):1416–1436. [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 hydro-mechanical :a benchmark of numerical techniques carried out by research group of MoMas［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.
