Critical stress difference and orientation of faults in rocks with strength anisotropies: the two-dimensional case

Equations are derived for the critical stress difference on thrust, normal and strike-slip faults with finite cohesive strength, both in homogeneous, isotropic rock, and along pre-existing strength anisotropies with different cohesion and coefficient of friction, subject to the limitation that the plane of anisotropy contains the intermediate axis of stress. The range of orientations for which sliding occurs along pre-existing planes of weakness rather than along a new fault is given as a function of material parameters and critical stress difference for the intact rock. Given the principal stress directions, the equations allow the direct calculation of the stress and orientation conditions for the three faulting regimes.     

徐家围子断陷深层火石岭组致密火山岩储层地应力分布规律研究

徐家围子断陷位于松辽盆地北部,其深层中生代火石岭组为致密火山岩气藏,天然裂缝发育,地应力分布非均质性强。结合诱导裂缝法与井径崩落法进行单井现今地应力方向分析,利用声波测井法计算现今地应力大小的纵向分布。依据火石岭组构造顶底面图、火山岩相组及断层分布特征建立非均质三维地质模型;在动、静态岩石物理参数拟合校正的基础上,结合实验测试及已有研究成果,确定不同岩相组和断层岩石物理参数,建立三维力学模型;利用Ansys有限元数值模拟软件建立火石岭组三维数学模型并进行相关运算获得三维现今地应力分布模型。计算结果表明在火石岭组地层中,水平最大主应力方向主要为东西向,应力值范围在86~110 MPa;水平最小主应力方向主要为南北向,应力值范围在67~84 MPa。分析模拟结果可知火山岩相、断层和构造起伏三者对火石岭组现今地应力分布影响较大。其中水平主应力的方向主要受断层和近火山口相分布的影响,而水平主应力的大小则是受三者综合作用。在构造低部位,近火山口相组发育处,断层上盘及断层端部皆为主应力的集中区域。依据现今地应力研究成果可为徐家围子断陷下一步开发井网部署、压裂改造方案和水平井的设计以及注水管理提供重要指导。      

Using fault displacement and slip tendency to estimate stress states

We suggest that faults in high slip tendency orientations tend to develop larger displacements than other faults. Consequently, faults that accumulate larger displacements are more likely to be reliable indicators of the longer term stress field and should be weighted accordingly in paleostress estimation. Application of a stress inversion technique that uses slip tendency analyses and fault displacements to interpret populations of coherent normal faults within the Balcones Fault System of south-central Texas provides stress estimates that are consistent with established regional stress analyses. Although the method does not require measurement of slip directions, these data, where available, and sensitivity analyses of the angular mismatch between measured slip directions and those predicted by inverted stress states provide high confidence in the stress estimates generated using slip tendency analyses. Close inspection of the fault orientation and displacement data further indicates that subpopulations of faults with orientations different from the regional pattern have formed in response to stress perturbations generated by displacement gradients on an adjacent seismic scale fault.     

A dislocation model of aseismic fault slip under nonuniform friction

A model is proposed for studying the mechanical behaviour of faults during their interseismic periods. The model considers a plane fault surface in an elastic medium, subject to a uniform shear stress which increases slowly with time. A1-D friction distribution is assumed on the fault, characterized by asperities and a weaker zone. The traction vector on the fault plane has an arbitrary orientation: in particular, it can be nonperpendicular to the asperity borders. Aseismic fault slip takes place when the applied stress exceeds the frictional resistance: slip starts in weak zones and is confined by asperities, where it propagates at increasing velocity. Propagation into asperities is characterized by a dislocation front, advancing perpendicularly to the asperity border. Fault slip does not take prate in the direction of traction, except when traction is perpendicular or parallel to the asperity border. The propagation of such aseismic dislocations produces a stress redistribution along the fault and can play a key role in determining the conditions which give rise to earthquakes.     

Effects of cohesive zones on small faults and implications for secondary fracturing and fault trace geometry

Fracture mechanics theory and field observations together indicate that the shear stress on many faults is non-uniform when they slip. If the shear stress were uniform, then: (a) a physically implausible singular stress concentration theoretically would develop at a fault end; and (b) a single curved ‘tail fracture’ should open up at the end of every fault trace, intersecting the fault at approximately 70 °. Tail fractures along many small faults instead range in number, commonly form behind fault trace ends, have nearly straight traces and intersect a fault at angles less than 50 °. A ‘cohesive zone’, in which the shear stress is elevated near the fault end, can eliminate the stress singularity and can account for the observed orientation, shape, and distribution of tail fractures. Cohesive zones also should cause a fault to bend. If the cohesive zone shear stress were uniform, then the distance from the fault end to the bend gives the cohesive zone length. The nearly straight traces of the tail fractures and the small bends observed near some fault ends implies that the faults slipped with low stress drops, less than 10% of the ambient fault-parallel shear stress.     

A simulation of upper crustal stresses for great and moderate thrust earthquakes of the Himalaya

We assume that great and moderate Himalayan earthquakes occur through reactivation of subhorizontal thrust faults by frictional failure under the action of stresses induced by Himalayan topography, isostasy related buoyancy forces, crustal overburden and plate tectonic causes. Estimates of stresses are based on two dimensional plane strain calculations using analytical formulae of elasticity theory and rock mechanics under suitable simplifying assumptions. Considerable attention is focussed on a point on the detachment at a depth of 17 km below mean sea level under the surface trace of the Main Central Thrust (MCT). According to recent views, great Himalayan earthquakes should nucleate in the detachment in the vicinity of such a point. Also many moderate earthquakes occur on the detachment similarly under the MCT. Vertical and horizontal normal stresses of 622 and 262 MPa and a corresponding shear stress of 26 MPa are estimated for this point due to topography, buoyancy and overburden. For fault friction coefficient varying between 0.3 to 1.0, estimates of plate tectonic stress required are in the range of 386 to 434 MPa, when the cumulative principal stresses are oriented favourably for reactivation of the detachment. Estimates of shear stress mobilized at the same point would be from 27 to 32 MPa for the identical range of fault friction coefficient. Our calculations suggest that presence of pore water in the fault zones is essential for reactivation. Pore pressure required is between 535 to 595 MPa for friction coefficient in the range of 0.3 to 1.0 and it is less than lithostatic stress of 603 MPa at the above point. For the specific nominal value of 0.65 for fault friction coefficient, the estimated values of plate tectonic stress, shear stress and pore pressure at the above point on the detachment are 410 MPa, 30 MPa and 580 MPa respectively. Similar estimates are obtained also for shallower points on the detachment up to the southern limit of the Outer Himalaya. Our estimates of the plate tectonic stress, shear stress and pore pressure for reactivation of upper crustal thrust faults compare favourably with those quoted in the literature.     

渤海湾地区不同方向断裂带的封闭性

构造应力场的最大主压应力方向与同时期活动断裂走向的相互关系决定着断裂的封闭程度 ,两者的锐夹角越大 ,断裂的封闭性越好 ;两者的锐夹角越小 ,断裂的封闭性越差 ,渗透性越好 ,有利于流体的运移。据此用线性代数法换算出的断裂闭合系数可半定量地评价断裂的封闭条件 ;再结合不同油气主运移期的封闭性变化的历史 ,可对断裂带的有利的油气聚集部位进行预测。通过对渤海湾地区的油气聚集进行综合评价 ,认识到东西向和南北向展布的断陷带对油气的聚集最为有利 ,北西向展布的和现今断裂活动性较弱的北东向展布的断陷带中的部分地段也很有前景。预测庙西 1号、垦利 3号、庙西 3号等断裂带为下一步有利的油气勘探构造带。     

Stress triggering of normal aftershocks due to strike slip earthquakes in compressive regime

A few cases of occurrence of normal aftershocks after strike slip earthquakes in compressive regime have been reported in the literature. Occurrence of such aftershocks is intriguing as they occurred despite the apparent stabilizing influence of compressive plate tectonic stresses on the normal faults. To investigate the occurrence processes of such earthquakes, we calculate change in static stress on optimally oriented normal and reverse faults in the dilational and compressional step over zones, respectively, due to slip on a vertical strike slip fault under compressive regime. We find that change in static stress is much more pronounced on normal faults as compared to that on reverse faults, for all values of fault friction. Change in static stress on reverse fault is marginally positive only when the fault friction is low, whereas for normal faults it is positive for all values of fault friction, and is maximum for high fault friction. We suggest that strike slip faulting in compressive regime creates a localized tensile environment in the dilational step over zone, which causes normal faulting in that region. The aftershocks on such normal faults are considered to have occurred as an almost instantaneous response of stress transfer due to strike slip motion.     

Stress triggering of normal aftershocks due to strike slip earthquakes in compressive regime

A few cases of occurrence of normal aftershocks after strike slip earthquakes in compressive regime have been reported in the literature. Occurrence of such aftershocks is intriguing as they occurred despite the apparent stabilizing influence of compressive plate tectonic stresses on the normal faults. To investigate the occurrence processes of such earthquakes, we calculate change in static stress on optimally oriented normal and reverse faults in the dilational and compressional step over zones, respectively, due to slip on a vertical strike slip fault under compressive regime. We find that change in static stress is much more pronounced on normal faults as compared to that on reverse faults, for all values of fault friction. Change in static stress on reverse fault is marginally positive only when the fault friction is low, whereas for normal faults it is positive for all values of fault friction, and is maximum for high fault friction. We suggest that strike slip faulting in compressive regime creates a localized tensile environment in the dilational step over zone, which causes normal faulting in that region. The aftershocks on such normal faults are considered to have occurred as an almost instantaneous response of stress transfer due to strike slip motion.     

小尺度断层定量预测及对注水开发的影响——以渤中34油田为例

大尺度断层往往控制了沉积盆地的形成和油气成藏,而小尺度断层则影响着注水开发效果和剩余油分布.大尺度断层可以通过二维或三维地震资料识别,而小尺度断层的识别则特别困难.本文提出了一种基于断层分形生长模式和三维地质力学模拟相结合来确定小尺度断层的数量、发育位置和方位的方法,并根据油田开发动态资料来确定小尺度断层对注水开发和剩余油分布的影响.将地震上识别的大尺度断层引入到三维数值力学模型中,模拟大尺度断层形成时期断裂带附近的应力扰动作用,然后结合破裂准则来建立最易发生破裂的方位和最大库伦剪切应力网格,以这两套网格和断层尺度的幂律分布确定的小尺度断层数量为约束条件来确定随机模型,对小尺度断层的密度、产状和发育位置进行定量预测.研究表明:利用分形理论和三维地质力学模拟可以对大尺度断层伴生小尺度断层进行有效预测;小尺度断层对注水开发效果和剩余油分布的影响取决于小尺度断层的规模(断距)以及小尺度断层方位和注采方向的关系.     

Inversion of fault data with low diversity for stress: Principles and applications

Although a minimum of four independent, single-phase fault data are required to solve for a unique reduced stress tensor, we prove in this paper that a smaller number of fault data are sufficient in some instances to solve for part of the reduced stress tensor. One of the principal stress directions is determinable from either two faults with a common null shear direction on the fault planes or three faults with a common intersection in a principal stress plane of the fault planes. This direction is combined with the fault data to determine the possible ranges of other principal stress directions. Determining whether the direction is for the maximum, intermediate or minimum principal stress depends upon constraints provided by slip tendency or more fault data. This approach can also be applied to a set of four or more fault data with low orientation diversity. This new method is finally applied to two different sets of fault data from along the active Chelungpu fault, western Taiwan. The stress orientations determined from the method lie in acceptable ranges for the maximum/minimum principal stresses using other existing and comparable methods, such as the right dihedra/trihedra methods. They differ moderately in the maximum/minimum principal stress directions when compared to the moment tensor method for fault kinematic analysis. The new method has advantages over the right dihedra/trihedra methods in the accuracy of stress estimate and the independence of stress estimate upon the small number of faults that are not parallel to the dominant fault set(s).     

地热规模化开发断层滑动概率评估——以雄安新区深部岩溶热储为例

雄安新区地热资源丰富，具有广阔的规模化开发利用前景，对于实现"绿色雄安"具有重要意义。许多学者的研究集中在地质结构探测、地热资源量评价、地壳稳定性等方面，关于深部岩溶热储规模化开发可能引起的断层滑动研究薄弱。本文在地热地质综合调查的基础上，基于地质力学理论，采用蒙特卡罗随机模拟方法，评价雄安新区主要断层特征（走向、倾角、滑动摩擦系数等）、地应力分布（孔隙压力、最大/最小/垂直主应力大小及方向等），量化雄安新区天然断层在规模化开发利用情况下的激活可能性，结果显示已探明断层在天然、规模化回灌和水力压裂条件下的最大滑动趋势分别为0.26、0.27和0.40，地热开发不会引起断层激活。本研究树立了地热规模化开发的信心，可为雄安新区地热资源安全利用提供支撑。     

广东核电站地应力测量及其应用

基于广东省3个核电站厂址区的水压致裂地应力测量结果,获得了各核电站厂址区现今地应力场分布特征,结果表明,各核电站厂址区以水平应力为主导;大亚湾、阳江核电站水平应力值随深度增加而呈线性增大,台山核电站水平应力随深度线性增加不明显;大亚湾、阳江核电站厂址区最大水平主应力方向为NW-NWW,台山核电站为NNW。根据地应力测量结果、相关理论及判据分析认为,大亚湾核电站拟建隧洞长轴方向较不利于隧洞围岩的稳定,台山和阳江核电站拟建隧洞长轴方向利于围岩的稳定和维护;各核电站拟建隧洞横截面形状以水平长轴、垂向短轴且长、短轴比近似于各隧洞截面上侧压力系数的椭圆形为宜;各隧洞在埋深范围内开挖时均没有发生岩爆的可能性。最后,依据Byerlee滑动摩擦准则,探讨了核电站外围现今活动断层的稳定性。     

Tectonic Stress State Changes Before and After the Wenchuan Ms 8.0 Earthquake in the Eastern Margin of the Tibetan Plateau

Crustal tectonic activities are essentially the consequences of the accumulation and release of in situ stress. Therefore, studying the stress state near active faults is important for understanding crustal dynamics and earthquake occurrences. In this paper, using in situ stress measurement results obtained by hydraulic fracturing in the vicinity of the Longmenshan fault zone before and after the Wenchuan Ms 8.0 earthquake and finite element modeling, the variation of stress state before and after the Wenchuan Ms 8.0 earthquake is investigated. The results show that the shear stress, which is proportional to the difference between principal stresses, increases with depth and distance from the active fault in the calm period or after the earthquakes, and tends to approach to the regional stress level outside the zone influenced by the fault. This distribution appears to gradually reverse with time and the change of fault properties such as frictional strength. With an increase in friction coefficient, low stress areas are reduced and areas with increased stress accumulation are more obvious near the fault. In sections of the fault with high frictional strengths, in situ stress clearly increases in the fault. Stress accumulates more rapidly in the fault zone relative to the surrounding areas, eventually leading to a stress field that peaks at the fault zone. Such a reversal in the stress field between the fault zone and surrounding areas in the magnitude of the stress field is a potential indicator for the occurrence of strong earthquakes.     

Rupture progression along discontinuous oblique fault sets: implications for the Karadere rupture segment of the 1999 Izmit earthquake, and future rupture in the Sea of Marmara

Large earthquakes in strike-slip regimes commonly rupture fault segments that are oblique to each other in both strike and dip. This was the case during the 1999 Izmit earthquake, which mainly ruptured E–W-striking right-lateral faults but also ruptured the N60°E-striking Karadere fault at the eastern end of the main rupture. It will also likely be so for any future large fault rupture in the adjacent Sea of Marmara. Our aim here is to characterize the effects of regional stress direction, stress triggering due to rupture, and mechanical slip interaction on the composite rupture process. We examine the failure tendency and slip mechanism on secondary faults that are oblique in strike and dip to a vertical strike-slip fault or “master” fault. For a regional stress field well-oriented for slip on a vertical right-lateral strike-slip fault, we determine that oblique normal faulting is most favored on dipping faults with two different strikes, both of which are oriented clockwise from the strike-slip fault. The orientation closer in strike to the master fault is predicted to slip with right-lateral oblique normal slip, the other one with left-lateral oblique normal slip. The most favored secondary fault orientations depend on the effective coefficient of friction on the faults and the ratio of the vertical stress to the maximum horizontal stress. If the regional stress instead causes left-lateral slip on the vertical master fault, the most favored secondary faults would be oriented counterclockwise from the master fault. For secondary faults striking ±30° oblique to the master fault, right-lateral slip on the master fault brings both these secondary fault orientations closer to the Coulomb condition for shear failure with oblique right-lateral slip. For a secondary fault striking 30° counterclockwise, the predicted stress change and the component of reverse slip both increase for shallower-angle dips of the secondary fault. For a secondary fault striking 30° clockwise, the predicted stress change decreases but the predicted component of normal slip increases for shallower-angle dips of the secondary fault. When both the vertical master fault and the dipping secondary fault are allowed to slip, mechanical interaction produces sharp gradients or discontinuities in slip across their intersection lines. This can effectively constrain rupture to limited portions of larger faults, depending on the locations of fault intersections. Across the fault intersection line, predicted rakes can vary by >40° and the sense of lateral slip can reverse. Application of these results provides a potential explanation for why only a limited portion of the Karadere fault ruptured during the Izmit earthquake. Our results also suggest that the geometries of fault intersection within the Sea of Marmara favor composite rupture of multiple oblique fault segments.     

基于地应力实测数据分析郯庐断裂带中段滑动趋势

郯庐断裂带潜在滑动趋势对于区域地壳稳定性评价具有重要的意义。对郯庐断裂带中段(新沂至渤海段)附近12个钻孔共65条实测地应力数据分析,得出该区段最大和最小水平主应力与垂直应力之比Kmax和Kmin的范围,结果表明郯庐断裂带中段主要表现为逆断层的应力状态,局部地区呈现出有利于走滑断层的特征。研究区内应力比K值由西向东逐渐增大,并在东北部达到最大。通过计算得出断层面上的剪应力与有效正应力比值小于Byerlee准则所定义的摩擦系数,说明目前郯庐断裂带中段处于相对稳定状态;同时发现北西向断裂面上的剪应力与有效正应力比值比北东向断裂的大。区内应力积累指标μm的计算结果和地震的分布特征表明,郯庐断裂带中段北西向断裂上地震活动频繁,应力积累程度低;而北东向断层上应力积累程度高,特别是处于郯庐断裂带中段东北部的北东向断层,在应力集中的区域出现地震空白区,推测为断层的锁固段。最终认为在现今应力场下郯庐断裂带中段更易沿北西向的断裂滑动。     

高邮凹陷真武断裂带西部低级序断层发育规律预测

在应用蚂蚁追踪技术对真武断裂带西部低级序断层进行解释并根据主要断层走向确定阜宁期构造应力方向的基础上,应用构造应力场数值模拟法模拟阜宁期古构造应力的分布,从应力的角度对低级序断层的平面及剖面发育规律进行预测,最后将预测结果与构造解析结果进行对比。研究结果表明,应用蚂蚁追踪技术对低级序断层进行解释获得的蚂蚁属性体断裂痕迹清晰直观,应用效果要优于相干体技术、方差体技术等其他地震属性技术;真武断裂带西部阜宁期最小主应力方向为NW333°-SE153°;低级序断层的发育主要受阜宁期最小主应力及剪应力控制,最小主应力控制断层的优势发育区,平面剪应力控制断层的平面展布,左旋剪应力区主要发育近东西走向断层,右旋剪应力区主要发育北东走向断层,剖面剪应力控制断层的倾向,左旋剪应力区主要发育北倾、西倾断层,右旋剪应力区主要发育南倾、东倾断层。      

The temporal relationship between joints and faults

Examples are presented of three temporal relationships between joints and faults: joints that pre-date faults; joints that are precursors to, or synchronous with, faults; and joints that post-date faults. Emphasis is placed on strike-slip faults in carbonate beds, but other examples are used. General rules are given for identifying the three temporal relationships between joints and faults. Joints that formed before faults can be dilated, sheared or affected by pressure solution during faulting, depending on their orientation in relation to the applied stress system. Faulted joints can preserve some original geometry of a joint pattern, with pinnate joints or veins commonly developing where faulted joints interact. Joints formed synchronously with faults reflect the same stress system that caused the faulting, and tend to increase in frequency toward faults. In contrast, joints that pre- or post-date faults tend not to increase in frequency towards the fault. Joints that post-date a fault may cut across or abut the fault and fault-related veins, without being displaced by the fault. They may also lack dilation near the fault, even if the fault has associated veins. Joints formed either syn- or post-faulting may curve into the fault, indicating stress perturbation around the fault. Different joint patterns may exist across the fault because of mechanical variations. Geometric features may therefore be used in the field to identify the temporal relationships between faults and joints, especially where early joints affect or control fault development, or where the distribution of late joints are influenced by faults.     

Modeling branched and intersecting faults in reservoir-geomechanics models with the extended finite element method

Faults are geological entities with thickness several orders of magnitude smaller than the grid blocks typically used to discretize geological formations. On using the extended finite element method (X-FEM), a structured mesh suffices and the faults can arbitrarily cut the elements in the mesh. Modeling branched and intersecting faults is a challenge, in particular when the faults work as internal fluid flow conduits that allow fluid flow in the faults as well as to enter/leave the faults. By appropriately selecting the enrichment function and the nodes to be enriched, we are able to capture the special characteristics of the solution in the vicinity of the fault. We compare different enrichment schemes for strong discontinuities and develop new continuous enrichment functions with discontinuous derivatives to model branched and intersecting weak discontinuities. Symmetric fluid flows within the regions embedded by branched, coplanar intersecting, and noncoplanar intersecting faults are considered to verify the effectiveness of the proposed enrichment scheme. For a complex fault consisting of branched and intersecting faults, the accuracy and efficiency of the X-FEM is compared with the FEM. We also demonstrate different slipping scenarios for branched and intersecting faults with the same friction coefficient. In addition, fault slipping triggered by an injection pressure and three-dimensional fluid flows are modeled to show the versatility of the proposed enrichment scheme for branched and intersecting weak discontinuities.     

A dynamic model for fault nucleation and propagation in a mechanically layered section

When a mechanically layered section of rock is subject to a horizontal strain, faults often nucleate preferentially in one or more layers before propagating through the rest of the section. The result is a high density of small, low-throw faults within these layers, and a much smaller number of large, through-cutting faults which nevertheless accommodate most of the strain due to their much larger displacement. A dynamic model of fault nucleation and propagation has been created by combining analytical and finite element techniques to calculate the energy balance of these propagating faults. This model shows that: 1) faults may nucleate in either mechanically weak layers, or in stiff layers with a high differential stress; 2) fault propagation may be halted either by strong layers (in which the sliding friction coefficient is high), or by layers which deform by flow and thus have low differential stress. This model can predict quantitatively the horizontal strain required for faults to nucleate, and to propagate across mechanical layer boundaries. The model is able to explain the complex pattern of fault nucleation and propagation observed in a mechanically layered outcrop in Sinai, Egypt.