在重庆地区古生界页岩裂缝发育南中国第二部分构造应力场数值模拟与裂缝分布预测

Fracture development in Paleozoic shale of Chongqing area (South China).Part two:Numerical simulation of tectonic stress field and prediction of fracturesdistributionWeite Zeng a ,b ,c ,Wenlong Ding a ,b ,c ,⇑,Jinchuan Zhang a ,b ,c ,Yeqian Zhang a ,b ,c ,Ling Guo d ,Kai Jiu a ,b ,c ,Yifan Li a ,b ,caSchool of Energy Resources,China University of Geosciences,Beijing 100083,ChinabKey Laboratory for Marine Reservoir Evolution and Hydrocarbon Abundance Mechanism,Ministry of Education,China University of Geosciences,Beijing 100083,China cKey Laboratory for Shale Gas Exploration and Assessment,Ministry of Land and Resources,China University of Geosciences,Beijing 100083,China dDepartment of Geology,Northwest University,Xi’an 710069,Chinaa r t i c l e i n f o Article history:Available online 19July 2013Keywords:Longmaxi ShaleMechanical rock properties Tectonic stress field Fractures distribution Southeast Chongqinga b s t r a c tA tectonics sedimentation evolution has been researched in Southeast Chongqing,and the reasonable Longmaxi shale highstand system tract (HST)and transgressive system tract (TST)geological model were built respectively based on the rock mechanical test and acoustic emission experiment which the sam-ples are from field outcrop and the Yuye-1well.The Longmaxi shale two-dimension tectonic stress field during the Cenozoic was simulated by the finite element method,and the distribution of fractures was predicted.The research results show that the tectonic stress field and the distribution of fractures were controlled by lithology and structure.As a result of Cretaceous movement,there are trough-like folds (wide spaced synclines),battlement-like folds (similar spaces between synclines and anticlines)and ejec-tive folds (wide spaced anticlines),which are regularly distributed from southeast to northwest in the study area.Since the strain rate and other physical factors such as the viscosity are not taken into account,and the stress intensity is the main factor that determines the tectonic strength.Therefore,the stronger tectonic strength leads the higher stress intensity in the eastern and southeastern study area than in the northwest.The fracture zones are mainly concentrated in the fold axis,transition locations of faults and folds,the regions where are adjacent to faults.The fragile mineral contents (such as siliceous rock,carbonate rock and feldspar)in the shelf facies shale from south of the study area are higher than in the bathyal facies and abyssal facies shale from center of the study area.The shales characterized by low Poisson’s ratio and high elastic modulus from south of the study area are easily broken during Cenozoic orogenic movement.Ó2013Elsevier Ltd.All rights reserved.0.IntroductionThe southeastern portion of Chongqing is the pilot experimen-tal area in China for the key strategic investigations of shale gas.In 2009,the Yuye-1well,which was the first Chinese well for the strategic investigation of shale gas,was drilled in this experimen-tal area.By 2011,the Yuke-1,Youke-1,Pengye-1,and Qianye-1wells had been successively drilled in this area.These five wells revealed the existence of two formations of high-quality shale in the region in question,namely,the Lower Silurian Longmaxi Shale and the Lower Cambrian Niutitang Shale.In particular,amaximum total hydrocarbon concentration of 22.50%has been reached by the Pengye-1well,which targets a shale layer in the Lower Silurian Longmaxi-Upper Ordovician Wufeng Shale,and the greatest desorption gas content of this field was 2.30m 3/t.Moreover,for the Qianye-1well,which also targets a shale layer of this formation,after hydraulic fracturing treatment and drain-age tests,a wellhead pressure of 3MPa was achieved,and the instantaneous flow rate for the initial shale gas test was 308m 3/h;this rate is sufficient for industrial gas operations.In recent years,various studies have been conducted to address shale gas exploration in the marine shale of North America.Most of these studies on shale gas exploitation have focused on identifying the most effective approaches for fracturing shale;in fact,fractures are a critical determinant of the success of shale gas wells (Hill and Nelson,2000;Curtis,2002;Warlick,2006;Gale et al.,2007;Li et al.,2007,2009;Nie et al.,2009a;1367-9120/$-see front matter Ó2013Elsevier Ltd.All rights reserved./10.1016/j.jseaes.2013.07.015⇑Corresponding author at:School of Energy Resources,China University ofGeosciences,Beijing 100083,China.Tel.:+861082320629;fax:+861082326850.E-mail address:dingwenlong2006@ (W.Ding).Tan,2009).Organic-rich shale with low porosity and permeability can form effective natural gas reservoirs if this shale has devel-oped sufficient natural fractures,microfractures,and nanometer-scale pores and fractures within rocks(Sun et al.,2008)or if frac-turing treatments can generate a fracture system that features a large number of fractures.The development of natural fracture systems not only directly affects the mining efficiency of shale gas reservoirs but also determines the quality and production lev-els of these reservoirs(Montgomery et al.,2005;Bowker,2007; Zhang et al.,2003).Higher levels of fracture development increase the total gas content of a shale formation by both enlarging the volume of unbound natural gas that is contained in this formation and promoting the desorption of adsorbed natural gas from the shale(Curtis,2002;Nie et al.,2009b;Zhang et al.,2003,2004; Chen et al.,2009).Based on a detailed analysis of the tectonic and sedimentary evolution in southeastern Chongqing area that combines investigations of rock mechanics and acoustic emis-sions experiments,this study applies thefinite element method to simulate the two-dimensional tectonic stressfield that existed during the development of the fracture in Cenozoic for the Lower Silurian Longmaxi Shale of the study region.This approach al-lowed fracture distributions in this shale to be predicted.These fracture distribution predictions can provide an important theo-include many types of faults,which are mainly inclined to the northwest and southwest(Zhang et al.,2010).As a result of the subduction of the Pacific plate under the Asian plate in the Creta-ceous,the compressive strain transfers and the energy decays in the SE–NW direction sequentially produced Jura-type te in the Cretaceous movement,the direction of regional stress twisted in a counterclockwise direction,altering the morphology of the existing fold structure by causing S-shaped or arc-like folds to form in the axial plane.The tectonic stresses of folds formed in the Cretaceous underwent relaxation or release in the Cenozoic, leading to the creation of a series of large-scale NNE-trending nor-mal faults along anticlinal axes and wings that consisted of horst and graben fault systems;these processes ultimately created the modern tectonic landscape of the study area(see Figs.1and2).The graptolite Longmaxi Shale in southeastern Chongqing(i.e., the lower strata of the Longmaxi Formation)was created during a brief large-scale transgression that occurred early in the Silurian and provided important hydrocarbon source rocks of the Yangtze plate,particularly in the Sichuan Basin and its surrounding regions (Wo et al.,2007;Zhang et al.,1987).There is a lack of applicable logging data and seismic data in the research area;therefore, cross-sectional analyses of local outcrops and core facies of the Yuye-1well were parative assessments of theFig.1.Tectonic map of Southeast Chongqing area.268W.Zeng et al./Journal of Asian Earth Sciences75(2013)267–279Fig.2.Tectonic cross-section of southeastern Chongqing area.Fig.3.Paleo-geographic reconstruction of the transgressive system tract(TST)for the Longmaxi Shale. Fig.4.Paleo-geographic reconstruction of the highstand system tract(HST)for the Longmaxi Shale.were deposited in this region were black carbonaceous shale,dark gray shale,dark gray silty shale,and siliceous shale.The northeast region of the study area was likely affected by the‘Hunan-Hubei Underwater Plateau’(Fan et al.,2012;Chen et al.,2004),and there-fore largely featured a shallow-water shelf sedimentary environ-ment.The major rock types that were deposited in this region were gray shale,black shale,and calcareous shale.The south region of the study area was mostly a shallow-water shelf during the TST, although portions of this region consisted of sandy shelf.The rock types that were deposited in this region were primarily gray silty mudstone,calcareous shale,and gray siltstone.The HST featured lower sea levels than the TST;therefore,shale deposition occurred in shallower water during the HST than during the TST.During the HST,the subsidence center was located in the northern and north-western portions of the research area,and sediments primarily came from the south.In the southern portion of the study region, the area of sandy sediments increased during the HST,and sandy shelf depositions primarily occurred at this time;the major rock types that were deposited in this region were calcareous shale, gray argillaceous siltstone,and light gray siltstone.During the HST,the north-central region of the study area is represented by deep-water shelf and bathyal deposits,but the extend of these types of deposits decreased significantly during the HST relative to the TST.The main rock types deposited in this region were black carbonaceous shale,dark gray shale,and gray argillaceous silt-stone.The scope of the shallow-water shelf depositional area in the examined region increased in the HST compared with the TST,and the primary rock types deposited in this area were calcar-eous shale and silty shale.2.Methods for tectonic stressfield simulation and fracture distribution prediction2.1.Tectonic stressfield simulationThe tectonic stressfield typically refers to the crustal stressfield that causes tectonic movements.The purpose of tectonic stress field simulation is to model the distribution of stress inside a rock block through the application of boundary forces,usingfirst inver-sion and forward modeling approaches(Ye,2011;Li,2010;Liu, 2009).In this study,thefinite element method and ANSYS com-puter software were employed to produce a two-dimensional sim-ulation of the stressfield of the Longmaxi ShaleChongqing area.The simulation of a tectonic stressfieldsteps:(1)the establishment of a geological model;lishment of a mechanical model;(3)theematical model;and(4)computer calculations andsimulation results.2.1.1.Establishment of a geological modelThe geological model considers petrographyThefinite geometry of active structure will becessive tectonic stressfields during multipletory constitutes a comprehensive picture of thetectonic stressfields over time.However,thefected by the most recent tectonic stressfield(inthe Cenozoic movement).In the absence of seismicin the study region,the targeted layers to berated from their surrounding rock block based notture and the historical sedimentary evolution ofbut also on the outcrop data and drilling core dataThis approach allowed for the establishment ofgeological models of the TST and HST for thethe Cenozoic(Figs.3and4).2.1.2.Establishment of a mechanical modelThe establishment of a mechanical model includes the follow-ing tasks:(1)to determine the loading regime for geological bodies and constraints on types and methods of geological loading(i.e., determine the boundary conditions);(2)to determine the mechan-ical parameters for different rock units of the studied layers;and (3)to determine the mechanical parameters for faults and folds, which will directly affect the simulation results.(1)Determination of the loading regime for geological bodiesand constraints on the types and methods of geological load-ing(i.e.,the determination of the boundary conditions).To begin with examinations of macroscopic effects,geological bodies were assumed to be homogeneous blocks or slices of rock bodies and were simulated as pieces of uniformly elastic material. The boundary conditions included displacement boundary condi-tions and stress boundary conditions.It was assumed that the force on a boundary is a set of determined values and that this force is uniformly distributed across the boundary of interest.The acoustic emission experiments on rock samples were performed at the Geo-stress Measurement Laboratory of the Chinese Institute of Geome-chanics.In particular,the experimental setup utilized a4010 Acoustic Emission instrument,a300kN universal press,strain sen-sors,and a computer(Figs.5and6).This device can assess stresses from paleostress periods and reveal the maximum effective paleo-stress that have been experienced by the examined strata(Ding and Shao,2001).This study focused on measuring the maximum principal stress r1of Longmaxi Shale from the Yuye-1well during tectonic movements of different periods(Table1).The experimen-tal samples were obtained from the Yuye-1well;in particular,15 standard25mmÂ50mm cylindrical samples were acquired by drilling in the core column,perpendicularly to the bedding plane of core.The most intense tectonic movement in the research area was the Cretaceous movement,followed by the Cenozoic movement. Therefore,it is reasonable to believe that the maximum tectonic stress that was experienced by the Longmaxi Shale of the Yuye-1 well would have been148.8MPa in the Cretaceous and 122.5MPa in the Cenozoic.During the Cenozoic,the research area as a whole experienced a compressional stressfield in the north-west–southeast direction.Given that the Yuye-1well is located on the axis of the Guochangba anticline of the city of Lianhu,it5.Curve of paleostress measurements based on initial pressures of acoustic emissions for shale samples from the Yuye-1well.270W.Zeng et al./Journal of Asian Earth Sciences75(2013)267–279applied to the upper right and lower left boundary;constraints were placed on displacement in the X and Y directions for the nodes at the right corner and the left corner of the model,allowing all other units to move freely;and a set of25MPa pull tensions were applied in parallel in the direction of maximum principal stress at the nodes of the upper left and the lower right corner to simulate the sinistral shear stress that was experienced in the Cenozoic(Fig.7).(2)Determination of mechanical parameters for various rockunits of the studied layers.The geological model of this study divided the examined units into the following major unit types(Table2):fault zones,fold zones,and zones of ordinary sedimentary strata.Based on fault size,fault zones were subclassified intofirst-order,second-order, and third-order faults.The onlyfirst-order fault in the research area is the Qiyao Mountain basement fault,and other faults in the region were divided into second-order and third-order faults based on morphological scale and extension range.Fold zones, which have been produced by southeast-northwest energy trans-fers and energy decays,were divided into trough-like folds(wide spaced synclines),battlement-like folds(similar spaces between synclines and anticlines)and ejective folds(wide spaced anti-clines).Lithological differences were utilized to subdivide the examined sedimentary layers into various unit types,including carbonaceous shale,siliceous shale,black shale,calcareous shale, and argillaceous siltstone.Because this study primarily seeks to provide two-dimensional simulations of tectonic stressfields,the major mechanical param-eters of rocks that are required are the elastic modulus and Pois-son’s ratio.Experiments to examine rock mechanics were performed in the Rock Mechanics Testing Laboratory of the Univer-sity of Science and Technology Beijing.In particular,these experi-ments used not only a uniaxial rock mechanical testing platform that consisted of a WGE-600universal testing machine,100-ton pressure sensors,7V14program-controlled recorder,and an E4800computer but also used a triaxial rock mechanical testing platform that consisted of a TYS-500triaxial rock testing machine,100-ton pressure sensors,a7V14program-controlled recorder,and an E4800computer.The experiment was performed in accordance with the protocols specified by Chinese standard SL264-2001,‘‘Specifications for Rock Tests in Water Conservancy and Hydro-electric Engineering’’.In accordance with the burial depth of the Longmaxi Shale in the study area and the actual number of sam-ples that were examined,the confining pressures that were uti-lized in the triaxial rock mechanics experiments were0,5,10, and15MPa,and the influence of ground temperature was not con-sidered.The uniaxial rock mechanics experiment was primarily de-signed to measure the parameters of rock density,uniaxial compressive strength,elastic modulus,Poisson’s ratio,and tensile strength,although other parameters were also examined.In the triaxial rock mechanics experiment,measurements of axial rupture stress,elastic modulus,and Poisson’s ratio of samples at different confining pressures were used to calculate cohesion and internal friction angle,and other shear strength parameters(Table2).The Longmaxi Shale samples for rock mechanics measurements were collected from the Yuye-1well and outcrops in thefield.In partic-ular,for each examined lithology,the samples were obtained by drilling vertically to the bedding plane;these samples were then processed into19standard25mmÂ50mm cylindrical samples for each examined lithology.(3)Determination of mechanical parameters for faults andfolds.In this study,to address fault zones and fold zones(Table3), fault zones were defined as‘weak zones’.The elastic modulus of a fault zone is typically smaller than the elastic modulus of a nor-mal stratum;in particular,this modulus is generally50–70%of the modulus of a corresponding normal stratum.The Poisson’s ratio of a fault zone is larger than the Poisson’s ratio of a corresponding normal sedimentary rock stratum,and the difference between these two ratios is typically between0.02and0.1.Fold zones are defined as‘‘hard zones’’.The elastic modulus of a fold zone is typ-ically larger than the elastic modulus of a normal stratum;in par-ticular,this modulus is generally150–300%of the elastic modulus of a corresponding normal stratum.The Poisson’s ratio of a fold zone is smaller than the Poisson’s ratio of a corresponding normal sedimentary rock stratum,and the difference between these two ratios is typically between0.01and0.15.6.Curve of paleostress measurements based on repeated pressures of acoustic emissions for shale samples from the Yuye-1well.Table1results of tectonic stress measurements from acoustic emissions for shale samples from the Yuye-1well.Well#Depth(m)Formation Effective tectonicstress r1duringvarious periods(MPa)Major stages ofknown tectonicmovement(episode)Yuye-10–325.5Longmaxi23.1,40.8,57.4,91.0,122.5,148.86Mechanical model of the Longmaxi Shale in southeast Chongqing during Cenozoic.2.1.3.Establishment of the mathematical modelA geological model was constructed in the form of a triangular mesh that was subdivided into a series of node and element grids. The geological model of the HST strata included9965nodes and 19,670elements,whereas the geological model of the TST strata included8270nodes and16,330elements.After the model bound-ary conditions and the applied load had been determined,thefinite element method was applied to solve the model.The fundamental notion underlying thefinite element method involves dividing the domain of a continuousfield function that must be solved into a series of elements that are only connected at nodes,allowing for an unknown function value at an element to be obtained through interpolation of known values from the selected function.In gen-eral,finer elemental divisions produce more accurately computed results.We divided the geological model into a number of planar, triangular mesh elements.For an arbitrary triangular mesh ele-ment,the displacement u and v of an arbitrary point(x,y)in the element can be expressed in matrix form as follows:½f e¼uv¼N i u iþN j u jþN m u mN i v iþN j v jþN m v m¼N i0N j0N m00N i0N j0N mu i v i u j v j u m v m½ T¼½N ½d eð1Þwhere N i,N j,N m are the shape functions describing the element’s displacement;[N]is the shape function matrix;and[d]e is the ma-trix of node displacement components.To determine the displacement function and express the dis-placement of an element in terms of the nodal displacement,the strain of the element must be calculated;the following geometric equation was utilized to accomplish this task:½e ¼e xe ye xy264375¼@@x0@@y@@264375uvð2ÞBy substituting Eq.(1)into Eq.(2),the strain matrix of the ele-ment may be obtained:½e ¼½B ½d eð3Þwhere the conversion matrix[B]is a geometric matrix.From elasticity equations,stress and strain exhibit the following relationship:½r ¼½D ½e ð4ÞBy substituting Eq.(3)into Eq.(4),the stress matrix for the ele-ment may be derived as follows:½r ¼½D ½B ½d e¼½S ½d eð5Þwhere[S]is the stress matrix.As illustrated above,the nodal force for a triangular element in-volves a total of six components,as follows:½P e¼½U i V i U j V j U m V m Tð6ÞThe stress that is caused by this nodal force on the element may be expressed as follows:½r ¼½r x r y t xy Tð7ÞAccording to the principles of virtual displacement and virtual work,the following stiffness matrix for the element may be de-rived as follows:½P e¼½K e½d eð8Þwhere[K]e is the element stiffness matrix,which expresses the rela-tionship between nodal force and nodal displacement.A transformation of the element stiffness matrix can be imple-mented to derive the integral stiffness matrix.The boundary con-ditions may then be introduced into the equation,and the integral stiffness matrix may be transformed to derive the follow-ing overall stiffness equation:½P ¼½K ½d ð9Þwhere[K]is the integral stiffness matrix,[P]is the integral nodal load matrix,and[d]is the nodal displacement matrix for the inte-gral structure of the examined elemental array.By solving the linear equation(9),[d],the nodal displacement vector for the integral structure,may be obtained;therefore,the nodal displacement of each element may be derived.The substitu-tion of this displacement into the element equations(2)–(5),can then be performed to determine the displacement,strain,and stress of each individual element in the structure.For every element,the maximum principal stress was typically derived through a coordinate transformation that involved solving the following eigenvalue problem:r xÀr s yxs yx r yÀr¼0ð10ÞThe solving of the above equation allows the maximum princi-pal stress r1and the minimum principal stress r3to be determined (and no r2exists for a two-dimensional simulation of the tectonic stressfield).Table2A calculation table for the uniaxial compression test of various rock types.Lithology Natural density,q o(g cmÀ3)Tensile strength,r t(MPa)Compressive strength,r c(MPa)Elastic modulus,E(GPa)Poisson’sratio,lCohesion,C(MPa)Internal frictionangle,u(°)Carbonaceousshale2.71516.67100.9552.830.26622.3334.53Black shale 2.657 5.95149.6059.750.25527.7134.56 Argillaceoussiltstone2.68812.23102.7565.820.2863.8456.36Calcareousshale2.655 6.79132.8742.870.20516.4249.01Siliceous shale 2.7479.06101.8354.060.26112.4258.11Table3The mechanical properties of different types of rock units.Unit type Elastic modulus(MPa)Poisson’s ratioFault zoneFirst-order fault21,4350.332Second-order fault32,4360.317Third-order fault36,9810.305Fold zoneTrough-like fold102,180–137,4600.200–0.211Battlement-like fold85,660–102,1800.211–0.248Ejective fold65,740–85,6600.248–0.256272W.Zeng et al./Journal of Asian Earth Sciences75(2013)267–2792.1.4.Calculation of solutionsThe ANSYS software package was utilized to simulate the tec-tonic stressfield in the two-dimensional plane for the Longmaxi Shale in southeastern Chongqing area.The simulation results indi-cated the distributions of the maximum principal stress,shear stress,and stress intensity.These parameters were primarily se-lected for the following two reasons.First,the maximum principal stress is the main factor that determines tectonic deformation and the formation and distribution of faults,whereas the stress inten-sity determines the tectonic strength and the density of faults and folds in an area.The shear stress significantly affects the cracking and distortion that are produced by faults and folds.2.2.Methods for simulating and predicting fracturesThere are two major types of fractures in rocks that occur due to stress:shear fractures and tension fractures.Shear fractures were generally predicted using the combined Mohr–Coulomb shear rup-ture criterion,whereas tension fractures were predicted using the Griffith criterion.2.2.1.Griffith criterionGriffith proposed a strength theory that addressed the ruptur-ing of brittle materials(Griffith,1921).In particular,Griffith sug-gested that for brittle materials with a large number offine and elliptical cracks that are influenced by stressfield,tangential ten-sile stresses will be concentrated around the periphery of these oval cracks.Once the concentration of tangential tensile stress at a point near the peripheral edge of a crack reaches the intramolec-ular cohesive strength of the examined material,the material will begin to undergo brittle rupturing in this area;this fracture will ex-tend in a particular direction that may be determined.In the Grif-fith strength theory,the following expressions exist for the planar rupture criterion.If r1+3r3P0,the rupture criterion may be expressed as follows:ðr1Àr3Þ2À8ðr1þr3Þr T¼0ð11ÞIf r1+3r3<0,the rupture criterion may be expressed as follows,r3þr T¼0ð12Þwhere r1is the maximum principal stress of a rock,r2is the min-imum principal stress of this rock,and r T is the tensile stress of the rock in question.2.2.2.The Mohr–Coulomb shear fracture criterionThe Mohr–Coulomb criterion suggests that the shear fracture of rocks along a fault plane depends not only on s,the magnitude of shear stress on the fault plane,but also on r,the normal stress on the plane of interest.In other words,the shear fracture on a plane is related to the combination of the normal stress r and the shear stress s that are acting on the plane.The Coulomb–Navier shear fracture criterion may be written as follows:j s j¼Cþr N tg uð13Þwhere|s|is the shear strength of the rock;r N is the normal stress;C is cohesion,which is the shear strength of the rock if the normal stress is zero;u is the internal friction angle;and tg u is the internal friction coefficient.2.2.3.Determination of tectonic fracturesTectonic stressfield simulations of fracture formation periods may be used to calculate the tensile stress and shear stress of rocks during these periods.The aforementioned fracture criterion may then be employed to compare these tensile and shear stresses with the tension and shear strengths,respectively,of the examined rocks,allowing for the determination of whether ruptures will oc-cur in these rocks.To facilitate computer processing and quantitative analyses,the tension rupture rate of fractures,I t,is introduced:I t¼r T=r tð14Þwhere r T is the effective tensile stress and r t is the tensile strength of the rock.If I t P1,a tension rupture will occur in an examined rock.Similarly,to facilitate computational processing and quantita-tive analyses,the shear rupture rate,I n is also introduced:I n¼s n=j s jð15Þwhere s n is the effective shear stress and|s|is the shear strength of the rock.If I n P1,a shear rupture will occur in an examined rock.In present situations,tension fracture systems and shear frac-ture systems do not exist alone in fractured reservoirs;instead, both types of fractures develop concurrently.The level of rock rup-ture is a comprehensive reflection of both fracture rates.Therefore, we introduce the comprehensive rupture rate,I n:I z¼ðaI tþbI nÞ=2ð16Þwhere a and b are the proportions of tension fractures(including tension shear fractures)and shear fractures observed in the core, respectively.Investigations and statistical analyses of fractures in the core of the Yuye-1well and relevant data from the research area produced the result that the ratio of the number of tension fractures to the number shear fractures in the research area during the Ceno-zoic was6:4.In the equation above,for I z P1,the rock ruptures, and higher values of the comprehensive rupture rate correspond to greater degrees of rupture.2.2.4.Determination of tectonic fracturesUsing the comprehensive rupture rate of fractures as an indica-tor,we evaluated the degree of fracture development for two sys-tem tracts,the HST and TST,of the Longmaxi Formation in the research area.The degrees of fracture development in the exam-ined tracts were divided into three grades:developed zones,sec-ondary developed zones,and undeveloped zones(Table4).3.Results and interpretations3.1.Stressfield simulation results for the Longmaxi Shale in southeastern Chongqing during the CenozoicAs illustrated in Fig.8,the maximum principal stress in the TST strata of the Longmaxi Shale in southeastern Chongqing was gen-erally distributed betweenÀ217.404MPa andÀ4.109MPa.In this situation,a positive sign indicates tensile stress,whereas a nega-tive sign indicates compressive stress.The interiors of fault zones were defined to be‘weak zones’;higher levels of rock fragmenta-tion and lower levels of maximum principal stress(ranging from À46.768MPa toÀ4.109MPa)were observed in these fault zones than in ordinary pared with the fault zones,zones with continuous strata exhibited stable lithologies,and the magnitudes of maximum principal stress for these zones of continuous strata ranged betweenÀ103.647MPa andÀ46.768MPa.This range of maximum principal stress magnitudes encompassed the widest distribution of rocks in the research area.The interiors of fold zones were defined as‘hard zones’.There,rocks experienced fold-ing deformations without rupturing or reaching critical states of fracture.Thus,these zones featured highly concentrated stress and were therefore found in regions with high levels of stress;inW.Zeng et al./Journal of Asian Earth Sciences75(2013)267–279273。