Decadal Seismicity before Great Earthquakes—Strike-Slip Faults and Plate Interiors: Major Asperities and Low-Coupling Zones

Decadal forerunning seismic activity is examined for very large, shallow earthquakes along strike-slip and intraplate faults of the world. It includes forerunning shocks of magnitude Mw ≥ 5.0 for 21 mainshocks of Mw 7.5 to 8.6 from 1989 to 2020. Much forerunning activity occurred at what are interpreted to be smaller asperities along the peripheries of the rupture zones of great mainshocks at transform faults and subduction zones. Several great asperities as ascertained from forerunning activity agree with the areas of high seismic slip as determined by others using geodetic, mapping of surface faulting, and finite-source seismic modeling. The zones of high slip in many great earthquakes were nearly quiescent beforehand and are identified as the sites of great asperities. Asperities are strong, well-coupled portions of plate interfaces. Different patterns of forerunning activity on time scales of up to 45 years are attributed to the sizes and spacing of asperities (or lack of). This permits at least some great asperities along transform faults to be mapped decades before they rupture in great shocks. Rupture zones of many great mainshocks along transform faults are bordered either along strike, at depth or regionally by zones of lower plate coupling including either fault creep forerunning activity, aftershocks and/or slow-slip events. Forerunning activity to transforms in continental areas is more widespread spatially than that adjacent to oceanic transforms. The parts of the San Andreas fault themselves that ruptured in great California earthquakes during 1812, 1857 and 1906 have been very quiet since 1920;moderate to large shocks have been concentrated on their peripheries. The intraplate shocks studied, however, exhibited few if any forerunning events, which is attributed to the short period of time studied compared to their repeat times. The detection of forerunning and precursory activities for various time scales should be sought on the peripheries of great asperities and not just along the major faults themselves. This paper compliments that on decadal forerunning activity to great and giant earthquakes along subduction zones.

Decadal Seismicity Prior to Great Earthquakes at Subduction Zones: Roles of Major Asperities and Low-Coupling Zones

Decadal forerunning seismic activity of magnitude Mw ≥ 5.0 is mapped for all 45 mainshocks of Mw 7.7 to 9.1 at subduction zones of the world from 1993 to mid 2020. The zones of high slip in nearly all great earthquakes were nearly quiescent beforehand and are identified as the sites of great asperities and zones of strong seismic coupling. Much forerunning activity occurred at smaller asperities along the peripheries of the rupture zones of many great and giant mainshocks. Those sizes of great asperities as ascertained from forerunning activity generally agree with the areas of high seismic slip as determined by others from geodetic and tide-gauge data and finite-source seismic modeling. Asperities are strong, well-coupled portions of plate interfaces. Different patterns of forerunning activity on time scales of about 5 to 45 years are attributed to either the sizes and spacing of asperities (or lack of). This permits many great asperities to be mapped decades before they rupture in great and giant shocks. Several poorly coupled subduction zones such as Java, Lesser Sunda, Marianas, Tonga and Kermadec are characterized by few great thrust earthquakes and little, in any forerunning activity. Rupture zones of many great and giant earthquakes are bordered either along strike, updip, or downdip by zones of lower plate coupling. Several bordering regions were sites of forerunning activity, aftershocks, and slow-slip events. The detection of forerunning and precursory activities of various kinds should be sought on the peripheries of great asperities as well as within zones of high co-seismic slip.

Instantaneous stress release in fault surface asperities during mining-induced fault-slip

Fault-slip taking place in underground mines occasionally causes severe damage to mine openings as a result of strong ground motion induced by seismic waves arising from fault-slip. It is indicated from previous studies that intense seismic waves could be generated with the shock unloading of fault surface asperities during fault-slip. This study investigates the shock unloading with numerical simulation. A three-dimensional （3D） numerical model with idealized asperities is constructed with the help of discrete element code 3DEC. The idealization is conducted to particularly focus on simulating the shock unloading that previous numerical models, which replicate asperity degradation and crack development during the shear behavior of a joint surface in previous studies, fail to capture and simulate. With the numerical model, static and dynamic analyses are carried out to simulate unloading of asperities in the course of fault-slip. The results obtained from the dynamic analysis show that gradual stress release takes place around the center of the asperity tip at a rate of 45 MPa/ms for the base case, while an instantaneous stress release greater than 80 MPa occurs near the periphery of the asperity tip when the contact between the upper and lower asperities is lost. The instantaneous stress release becomes more intense in the vicinity of the asperity tip, causing tensile stress more than 20 MPa. It is deduced that the tensile stress could further increase if the numerical model is discretized more densely and analysis is carried out under stress conditions at a great depth. A model parametric study shows that in-situ stress state has a significant influence on the magnitude of the generated tensile stress. The results imply that the rapid stress release generating extremely high tensile stress on the asperity tip can cause intense seismic waves when it occurs at a great depth.

Study on the characteristics of rock failure strain and acoustic emission field for two parallelling faults with the same slip direction including asperities

By dealing with strain and acoustic emission (AE) data for two parallelling faultss instability and failure with the same slip direction including asperities, the temporal-spatial evolution of strain and AE field distribution on the asperity of parallelling faults is analyzed. Furthermore the failure process of asperities and interaction among the asperities, i.e., positive and negative seismicity are discussed. Results show that instability and failure for the parallelling faults is a kind of negative seismicity.

New analytical model of elastic-plastic contact for three-dimensional rough surfaces considering interaction of asperities

The contact calculation of three-dimensional real rough surfaces is the frontier field of tribology and surface science.In this study,we consider the interaction and elastic-plastic deformation characteristics of asperities and further,propose an analytical contact calculation method for rough surfaces considering the interaction of asperities.Based on the watershed algorithm,the rough surface is segmented and the asperities are reconstructed into ellipsoids.According to the height relationship between the asperities,the definition of the deformation reference height of the matrix between each couple of asperities is provided.Subsequently,the calculation formula of the substrate deformation is provided according to the local contact pressure considering the elastic-plastic deformation of the asperity,and the contact state under a specific load is determined using the iterative correction method.The results correspond with those of finite element numerical calculation and the study reveals the following:(1)compared with the results obtained without considering the asperity interaction,contact area,distance,and stiffness will be reduced by 6.6%,19.6%,and 49.5%,respectively,when the influence of asperity interaction is considered;(2)the interaction of the asperities has the greatest influence on the surface contact distance and stiffness.Under the same load,the existence of asperity interaction will reduce the contact distance,area,and stiffness;(3)considering the interaction of the asperities,the higher asperity will bear more load,but it will simultaneously reduce the contact of the surrounding area and increase that of the distant area.The calculation method proposed in this study has the advantages of high calculation efficiency and accuracy,thus,providing the calculation basis and method for subsequent studies on service performance of rough surfaces,such as the calculation of contact stiffness and fatigue performance analysis of rough surfaces.

NORMAL CONTACT STIFFNESS OF THE ELLIPTIC AREA BETWEEN TWO ASPERITIES

A new expression for contact deformation is given, and the normal contact stiff- ness between single asperities is derived according to Hooke＇s law. A contact model between two ellipsoidal asperities is simulated by the FE method, the result compared with the theoretical solution. It is found that the curves of the normal contact stiffness versus the included angle in the principal curvature direction show similar trends and evolve as a cosine feature. The effects of the parameters on normal contact stiffness are found to show that normal contact stiffness increases and reaches the upper limit gradually with an increase in these parameters.

Shear behaviours and roughness degeneration based on a quantified rock joint surface description

The asperity wear of rock joints significantly affects their shear behaviour.This study discusses the wear damage of the asperities on the joint surface,highlighting the roughness degradation characteristics during the shear process.The direct shear experiment of artificial specimens containing rock joints was conducted under different normal stresses based on three-dimensional scanning technology.These experimental results showed the contribution of joint wear to roughness degeneration,such as the height,zone,and volume of asperity degeneration.The wear coefficient of the rock joint was obtained based on the volume wear of asperities in the laboratory experiment.The functional relationship between the friction coefficient and wear coefficient is subsequently determined.To quantitatively analyse the wear damage of a joint surface,a calculation method for determining the wear depth of the rock joint after shearing was proposed based on wear theory.The relationship between the ultimate dilation and wear depth was analysed.A coefficient m,which can describe the damage degree of the joint surface,and a prediction method of joint surface roughness after shearing are established.Good agreement between analytical predictions and measured values demonstrates the capability of the developed model.Lastly,the sensitivity factors on the wear depth are explored.

镉胁迫对续断菊Sonchus asper L.Hill.根系分泌物的影响

通过盆栽试验,研究了不同Cd质量分数(0、50、100、200 mg.kg-1)对续断菊Sonchus asper L.Hill.根系分泌总有机酸、游离氨基酸、可溶性糖的影响,旨在探明根系分泌物对续断菊超积累Cd的影响。结果表明:Cd胁迫下续断菊根系分泌总有机酸、游离氨基酸和可溶性糖的质量浓度显著增加,同时,总有机酸、可溶性糖和游离氨基酸又促进了植株对Cd的吸收。随着Cd处理质量分数的增加,续断菊地上部和根部镉质量分数显著增加,90 d时续断菊地上部镉质量分数与可溶性糖、游离氨基酸的质量浓度呈极显著正相关,相关系数分别为0.999(P<0.01)和0.995(P<0.01),根部镉质量分数与可溶性糖、游离氨基酸的质量浓度也呈显著正相关,相关系数分别为0.998(P<0.01)和0.987(P<0.05);Cd对续断菊根系可溶性糖的分泌、游离氨基酸的合成有刺激作用,根系分泌的可溶性糖和游离氨基酸可能在续断菊累积镉的过程中有重要作用。

经验格林函数方法模拟强地面运动的研究进展

经验格林函数方法(简称EGFM)是当前模拟强地面运动的一种主流方法。主要介绍EGFM方法的发展历程和特点,重点解释了EGFM核心理论的沿革;详细介绍了加入凹凸体模型的改进的经验格林函数方法,并指出一种划分凹凸体区域新方法的可能性。

Elastoplastic Contact Mechanics Model of Rough Surface Based on Fractal Theory

Because the result of the MB fractal model contradicts with the classical contact mechanics, a revised elastoplastic contact model of a single asperity is developed based on fractal theory. The critical areas of a single asperity are scale dependent, with an increase in the contact load and contact area, a transition from elastic, elastoplastic to full plastic deformation takes place in this order. In considering the size distribution function, analytic expression between the total contact load and the real contact area on the contact surface is obtained. The elastic, elastoplastic and full plastic contact load are obtained by the critical elastic contact area of the biggest asperity and maximun contact area of a single asperity. The results show that a rough surface is firstly in elastic deformation. As the load increases, elastoplastic or full plastic deformation takes place. For constant characteristic length scale G, the slope of load-area relation is proportional to fractal dimension D. For constant fractal dimension D, the slope of load-area relation is inversely proportional to G. For constant D and G, the slope of load-area relation is inversely proportional to property of the material ~b, namely with the same load, the material of rough surface is softer, and the total contact area is larger. The contact mechanics model provides a foundation for study of the friction, wear and seal performance of rough surfaces.

A roughness parameter considering joint material properties and peak shear strength model for rock joints

This study aims at proposing a reasonable roughness parameter that can reflect the peak shear strength(PSS)of rock joints.Firstly,the contribution of the asperities with different apparent dip angles to shear strength is studied.Then the shear strength of the entire joint asperities is derived.The results showed that the PSS of the entire joint asperities is proportional to a key parameter hs,which is related to the geometric character of the joint surface and the joint material properties.The parameter hsis taken as the new roughness parameter,and it is reasonable to associate the PSS with the geometric characteristics of the joint surface.Based on the new roughness parameter and shear test results of 20 sets of joint specimens,a new PSS model for rock joints is proposed.The new model is validated with the artificial joints in this paper and real rock joints in published studies.Results showed that it is suitable for different types of rock joints except for gneiss joints.The new model has the form of the Mohr-Coulomb model,which can directly reflect the relationship between the 3 D roughness parameters and the peak dilation angle.

Dual threshold search method for asperity boundary determination based on geodetic and seismic catalog data

As an important model for explaining the seismic rupture mode,the asperity model plays an important role in studying the stress accumulation of faults and the location of earthquake initiation.Taking Qilian-Haiyuan fault as an example,this paper combines geodetic method and b-value method to propose a multi-source observation data fusion detection method that accurately determines the asperity boundary named dual threshold search method.The method is based on the criterion that the b-value asperity boundary should be most consistent with the slip deficit rate asperity boundary.Then the optimal threshold combination of slip deficit rate and b-value is obtained through threshold search,which can be used to determine the boundary of the asperity.Based on this method,the study finds that there are four potential asperities on the Qilian-Haiyuan fault:two asperities(A1 and A2)are on the Tuolaishan segment and the other two asperities(B and C)are on Lenglongling segment and Jinqianghe segment,respectively.Among them,the lengths of asperities A1 and A2 on Tuolaishan segment are 17.0 km and 64.8 km,respectively.And the lower boundaries are 5.5 km and 15.5 km,respectively;The length of asperity B on Lenglongling segment is 70.7 km,and the lower boundary is 10.2 km.The length of asperity C on Jinqianghe segment is 42.3 km,and the lower boundary is 8.3 km.

广州市主要断裂带特征震源模型研究

在广州市目标区内的主要活动断层危险性评价的基础上,综合活断层探测的研究成果和资料,对于具有潜在发震可能的主要断层,基于凹凸体震源模型建模理论进行了特征计算模型的建模。根据断层地震危险性分析确定的断层发震震级和几何参数,进行了断层的宏观参数和微观参数的设定。为通过复核预测方法计算与合成近断层强地震动场和城市危害性评价提供了科学的依据。

沈阳市F6断层的强地面运动分布模拟

目的研究沈阳市F6断层在设定地震6.0级时的强地面运动分布,为避免城市活动断层的地震破坏和为重要建筑合理的抗震设防提供依据.方法通过断裂所处应力环境、形变特征及活动性、结构、规模、地震活动、深部构造等综合分析,确定F6断层的地震危险性.以深、浅层人工地震、钻探、多道直流电法、探地雷达和地脉动数据为基础,建立了沈阳市接近真实的三维地下速度结构模型,强地面运动计算采用了三维有限差分法和统计学格林函数法的合成方法.结果 F6断层为中更新世活动断裂,最大潜在地震震级为6.0级;F6断层的震源模型为具有两个Asperity(凹凸体)的矩形断层:一个最大18km2的Asperity和一个7km2的Asperity.在设定地震作用下,F6断层强地震动PGA的影响范围集中于F6断层两侧,最大值达到285gal;PGV、PGD的分布形态与PGA相似.结论 F6断层发生6.0级时在沈阳市能够形成带状的强地面运动分布,其幅值甚至超出大震设防水准.

Mesh generation and optimization from digital rock fractures based on neural style transfer

The complex geometric features of subsurface fractures at different scales makes mesh generation challenging and/or expensive.In this paper,we make use of neural style transfer(NST),a machine learning technique,to generate mesh from rock fracture images.In this new approach,we use digital rock fractures at multiple scales that represent’content’and define uniformly shaped and sized triangles to represent’style’.The 19-layer convolutional neural network(CNN)learns the content from the rock image,including lower-level features(such as edges and corners)and higher-level features(such as rock,fractures,or other mineral fillings),and learns the style from the triangular grids.By optimizing the cost function to achieve approximation to represent both the content and the style,numerical meshes can be generated and optimized.We utilize the NST to generate meshes for rough fractures with asperities formed in rock,a network of fractures embedded in rock,and a sand aggregate with multiple grains.Based on the examples,we show that this new NST technique can make mesh generation and optimization much more efficient by achieving a good balance between the density of the mesh and the presentation of the geometric features.Finally,we discuss future applications of this approach and perspectives of applying machine learning to bridge the gaps between numerical modeling and experiments.

Anovelprofile error model to calculate contact error

A new profile model based on multi-scale asperities is developed and contact error is cal- culated. After stratified sampling, the model can get the distribution law of entity points on each cross section. Asperity radius of curvature is estimated by the relationship between circle radius and the section interval. Contact error is related to surface form error. A model equation of contact error plane is calculated through a method based on static equilibrium theory. Three contact asperities which determine the contact error plane on the rough surface are studied. The simulation results show that contact error can be accurately calculated according to the profile error model.

大震近场地震动数值模拟的不确定性研究

地震动数值模拟是研究地震发生、发展特征和规律性的基础研究,涉及震源、传播路径、场地三方面的一系列基本问题。研究结果可以直接用于强地震动基本参数的标定和地震动的工程预测以及地震危险性分析,是防震减灾中一项很重要的基础工作。当前考虑断层模型中的几个重要震源参数模拟未来地震动成为热点。例如,不管是随机有限断层方法,还是经验格林函数方法,都特别重视震源参数的选取,但当前对于强地面运动的数值模拟大多是对已发生地震的反演,反演所需的震源参数多是根据地震发生后的观测资料、经验关系推断或者人为的假定得到的。地震动特征预测的好坏,关键也在于震源参数的选取是否可靠,针对工程应用,对未来近断层地面运动的预测应当考虑参数选取的不确定性。强震动数值模拟方法已经比较成熟,比如随机有限断层法、经验格林函数法、混合方法等。但这些模拟地震动的方法多是确定性方法,对模拟过程中各个环节的不确定性因素考虑较少,尤其是断层震源参数的选取都是精确的数值,模拟结果自然不能综合表征未来地震发生时的地震动特征。另外一种地震动特性表征形式是利用地震动预测方程来表现参数的衰减关系,但是预测方程也会受观测数据、模型选取、随机因素的影响,不确定性无法避免。在地震动预测中每个步骤都带有很大的不确定性,主要包括认知的不确定性和随机的不确定性。震源模型的建立依赖各种专家的观点和意见,这种观点和意见往往相互差别很大,有很大的人为不确定性。地震资料的完整性、可靠性,以及理论模型等的建立也会造成很大的不确定性。因此,本论文的研究内容重点在预测未来大震近场地震动时震源环节的不确定性因素,系统地研究影响大震近场地震动数值模拟不确定性的影响因素,以期建立描述影响大震近场地震动数值模拟不确定性影响因素的模型,并将考虑不确定性因素的震源模型应用在破坏性大地震的地震动特征预测中去。针对地震发生时震源参数具有的随机不确定性,通过统计学方法得到震源参数间的经验关系。同时由于地球内部的不可入性以及观测技术手段的限制,地震震源模型还存在很多的认知不确定性因素,我们采用逻辑树方法处理认知不确定性因素,引入强震生成区的概念,重点分析Asperity的认知不确定性因素并在此基础上建立Asperity震源模型,取多种方案结果的最优值作为地震动的预测结果。论文具体的研究内容有以下5点:(1)在Hiroe Miyake工作的基础上,用经验格林函数法模拟了1997年日本九州鹿儿岛县的MJMA6.5地震,验证了经验格林函数法模拟强地面运动的有效性。数据使用的是日本K-NET强震台站数据。选择此次地震以及用日本K-NET数据的原因是日本的地震记录比较丰富,台站收集到的地震记录质量相对较好。同时分析了地震动模拟值中在工程领域使用较多的参数,表明模拟结果较好地反映了真实的地震动记录。证明经验格林函数预测未来强地震动是切实可行的。(2)本论文在大量地震记录及文献调研的基础上,运用统计学方法,通过统计回归分析得到地震密集区域震源参数间的经验关系,重点统计了包含龙门山断裂带在内的中国西南地区震源参数间的经验关系。为了得到更加适应于中国大陆区域的局部震源参数的经验关系,我们将地震样本局限在一定的区域内,缩小统计区域的范围,同时得到多个Asperity等局部震源参数的经验关系。(3)研究和分析各不确定性因素对地震动结果的影响程度对提高地震动预测的可靠性和准确性意义重大。本论文以2016年发生的日本熊本7.3级地震为例,通过参数敏感性分析技术筛选了对拟合结果有决定性影响的关键模型参数。未来地震动预测时会考虑在这几个不确定性因素中加入更高的权重,以提高地震动预测的可信度和准确性。(4)基于汶川地震资料,研究分析Asperity的认知不确定性对地震动预测的影响,运用逻辑树方法建立了考虑不确定性因素的Asperity震源模型。采用Hiroe Miyake提出的强震生成区的概念,将Asperity区域等同于强震生成区域,主要从Asperity的面积、数量、应力降、上升时间等方面进行了认知不确定性的分析研究,得到了针对强震的可能性较大的Asperity的面积和数量的最佳搭配形式。本文的创新点将概率地震危险性分析中不确定性因素的处理方法应用到未来大震近场地震动数值模拟中去。随机不确定性因素用统计学方法处理,认知不确定性用逻辑树方法处理。模拟结果能更好地表征未来大震近场的地震动特征,地震动参数的模拟结果在未来抗震设防及灾害预防中会有更好、更高的参考价值。考虑不确定性因素预测未来破坏性大地震,从而定量地评价发生地震时近场地面运动的综合特征,为防震减灾提供科学的依据,为工程设计决策提供参考依据。

Assessing current faulting behaviors and seismic risk of the Anninghe-Zemuhe fault zone from seismicity parameters

Using the data of regional seismic network, this paper analyzes the current faulting behaviors of different segments of the Anninghe-Zemuhe fault zone, western Sichuan, and identifies the likely risky segments for potential large earthquakes. The authors map the probable asperities from the abnormally low b-value distribution, develop and employ a method for identifying current faulting behaviors of individual fault segment from the combinations of multiple seismicity parameter values, and make an effort to estimate the average recurrence intervals of character-istic earthquakes by using the parameters of magnitude-frequency relationship of the asperity segment. The result suggests that the studied fault zone contains 5 segments of different current faulting behaviors. Among them, the Mianning-Xichang segment of the Anninghe fault has been locked under high stress, its central part is probably an asperity with a relatively large scale. The Xichang-Puge segment of the Zemuhe fault displays very low seismicity under low stress. Both the locked segment and the low-seismicity segment can be outlined on the across-profile of relocated hypocenter depths. The Mianning-Xichang segment is identified to be the one with potential large earth-quake risk, for which the average recurrence interval between the latest M = 6.7 earthquake in 1952 and the next characteristic event is estimated to be 55 to 67 years, and the magnitude of the potential earthquake between 7.0 and 7.5. Also, it has been preliminarily suggested that for a certain fault segment, its faulting behaviors may change and evolve with time gradually.

Effect of rock joint roughness on its cyclic shear behavior

Rock joints are often subjected to dynamic loads induced by earthquake and blasting during mining and rock cutting. Hence, cyclic shear load can be induced along the joints and it is important to evaluate the shear behavior of rock joint under this condition. In the present study, synthetic rock joints were prepared with plaster of Paris(Po P). Regular joints were simulated by keeping regular asperity with asperity angles of 15°-15° and 30°-30°, and irregular rock joints which are closer to natural joints were replicated by keeping the asperity angles of 15°-30° and 15°-45°. The sample size and amplitude of roughness were kept the same for both regular and irregular joints which were 298 mm×298 mm×125 mm and 5 mm, respectively. Shear test was performed on these joints using a large-scale direct shear testing machine by keeping the frequency and amplitude of shear load under constant cyclic condition with different normal stress values. As expected, the shear strength of rock joints increased with the increases in the asperity angle and normal load during the first cycle of shearing or static load. With the increase of the number of shear cycles, the shear strength decreased for all the asperity angles but the rate of reduction was more in case of high asperity angles. Test results indicated that shear strength of irregular joints was higher than that of regular joints at different cycles of shearing at low normal stress. Shearing and degradation of joint asperities on regular joints were the same between loading and unloading, but different for irregular joints. Shear strength and joint degradation were more significant on the slope of asperity with higher angles on the irregular joint until two angles of asperities became equal during the cycle of shearing and it started behaving like regular joints for subsequent cycles.

Numerical manifold method modeling of coupled processes in fractured geological media at multiple scales

The greatest challenges of rigorously modeling coupled hydro-mechanical(HM)processes in fractured geological media at different scales are associated with computational geometry.These challenges include dynamic shearing and opening of intersecting fractures at discrete fracture scales as a result of coupled processes,and contact alteration along rough fracture surfaces that triggers structural and physical changes of fractures at micro-asperity scale.In this paper,these challenges are tackled by developing a comprehensive modeling approach for coupled processes in fractured geological media based on numerical manifold method(NMM)at multiple scales.Based on their distinct geometric features,fractures are categorized into three different scales:dominant fracture,discrete fracture,and discontinuum asperity scales.Here the scale is relative,that of the fracture relative to that of the research interest or domain.Different geometric representations of fractures at different scales are used,and different governing equations and constitutive relationships are applied.For dominant fractures,a finite thickness zone model is developed to treat a fracture as a porous nonlinear domain.Nonlinear fracture mechanical behavior is accurately modeled with an implicit approach based on strain energy.For discrete fractures,a zero-dimensional model was developed for analyzing fluid flow and mechanics in fractures that are geometrically treated as boundaries of the rock matrix.With the zero-dimensional model,these fractures can be modeled with arbitrary orientations and intersections.They can be fluid conduits or seals,and can be open,bonded or sliding.For the discontinuum asperity scale,the geometry of rough fracture surfaces is explicitly represented and contacts involving dynamic alteration of contacts among asperities are rigorously calculated.Using this approach,fracture alteration caused by deformation,re-arrangement and sliding of rough surfaces can be captured.Our comprehensive model is able to handle the computational challenges with accurate representation of intersections and shearing of fractures at the discrete fracture scale and rigorously treats contacts along rough fracture surfaces at the discontinuum asperity scale.With future development of three-dimensional(3D)geometric representation of discrete fracture networks in porous rock and contacts among multi-body systems,this model is promising as a basis of 3D fully coupled analysis of fractures at multiple scales,for advancing understanding and optimizing energy recovery and storage in fractured geological media.