Study of hydro-mechanical behaviours of rough rock fracture with shear dilatancy and asperities using shear-flow model

The geometric properties of fracture surfaces significantly influence shear-seepage in rock fractures,introducing complexities to fracture modelling.The present study focuses on the hydro-mechanical behaviours of rough rock fractures during shear-seepage processes to reveal how dilatancy and fracture asperities affect these phenomena.To achieve this,an improved shear-flow model(SFM)is proposed with the incorporation of dilatancy effect and asperities.In particular,shear dilatancy is accounted for in both the elastic and plastic stages,in contrast to some existing models that only consider it in the elastic stage.Depending on the computation approaches for the peak dilatancy angle,three different versions of the SFM are derived based on Mohr-Coulomb,joint roughness coefficient-joint compressive strength(JRC-JCS),and Grasselli’s theories.Notably,this is a new attempt that utilizes Grasselli’s model in shearseepage analysis.An advanced parameter optimization method is introduced to accurately determine model parameters,addressing the issue of local optima inherent in some conventional methods.Then,model performance is evaluated against existing experimental results.The findings demonstrate that the SFM effectively reproduces the shear-seepage characteristics of rock fracture across a wide range of stress levels.Further sensitivity analysis reveals how dilatancy and asperity affect hydraulic properties.The relation between hydro-mechanical properties(dilatancy displacement and hydraulic conductivity)and asperity parameters is analysed.Several profound understandings of the shear-seepage process are obtained by exploring the phenomenon under various conditions.

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.

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.

Scratching by pad asperities in copper electrochemical-mechanical polishing

Low dielectric constant materials/Cu interconnects integration technology provides the direction as well as the challenges in the fabrication of integrated circuits(IC) wafers during copper electrochemical-mechanical polishing(ECMP). These challenges arise primarily from the mechanical fragility of such dielectrics, in which the undesirable scratches are prone to produce. To mitigate this problem, a new model is proposed to predict the initiation of scratching based on the mechanical properties of passive layer and copper substrate. In order to deduce the ratio of the passive layer yield strength to the substrate yield strength and the layer thickness, the limit analysis solution of surface scratch under Berkovich indenter is used to analyze the nano-scratch experimental measurements. The modulus of the passive layer can be calculated by the nano-indentation test combined with the FEM simulation. It is found that the film modulus is about 30% of the substrate modulus. Various regimes of scratching are delineated by FEM modeling and the results are verified by experimental data.

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.

Numerical parametric study on the influence of location and inclination of large-scale asperities on the shear strength of concreterock interfaces of small buttress dams

When assessing the sliding stability of a concrete dam,the influence of large-scale asperities in the sliding plane is often ignored due to limitations of the analytical rigid body assessment methods provided by current dam assessment guidelines.However,these asperities can potentially improve the load capacity of a concrete dam in terms of sliding stability.Although their influence in a sliding plane has been thoroughly studied for direct shear,their influence under eccentric loading,as in the case of dams,is unknown.This paper presents the results of a parametric study that used finite element analysis(FEA)to investigate the influence of large-scale asperities on the load capacity of small buttress dams.By varying the inclination and location of an asperity located in the concrete-rock interface along with the strength of the rock foundation material,transitions between different failure modes and correlations between the load capacity and the varied parameters were observed.The results indicated that the inclination of the asperity had a significant impact on the failure mode.When the inclinationwas 30
and greater,interlocking occurred between the dam and foundation and the governing failure modes were either rupture of the dam body or asperity.When the asperity inclination was significant enough to provide interlocking,the load capacity of the dam was impacted by the strength of the rock in the foundation through influencing the load capacity of the asperity.The location of the asperity along the concrete-rock interface did not affect the failure mode,except for when the asperity was located at the toe of the dam,but had an influence on the load capacity when the failure occurred by rupture of the buttress or by sliding.By accounting for a single large-scale asperity in the concrete-rock interface of the analysed dam,a horizontal load capacity increase of 30%e160%was obtained,depending on the inclination and location of the asperity and the strength of the foundation material.

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.

Forecasting the Epicenter Area of a Future Strong Earthquake

It is clear from the literature data that the geometric characteristics of the seismogenic source are directly related to the nucleation of their strong earthquakes. Our study starts from the observation of the proximity relationship between the epicenter of a strong earthquake and the surface trace of the seismogenic source. The proposed model is based on the mathematical analysis of seismicity falling within an area, through a polynomial function to determine a curve. The experimental results of our model confirm that 97% of the epicenters of strong earthquakes are located near the concavities or at the inflection points of the polynomial curve. Only 3% of strong earthquakes are located at the edges of the analyzed areas, where the number of data is not significant. The proposed model makes it possible to locate, with good approximation, the areas most likely to be the site of future strong earthquakes.

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.

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.

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.

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.

Study on Potential Strong Earthquake Risks Around the Mabian Area,Southern Sichuan

Based on seismic data from the regional network for the last 34 years, we analyzed the present fault behavior of major fault zones around the Mabian area, southern Sichuan, and identified the risky fault-segments for potential future. The method of analysis is a combination of activity background of historical strong earthquakes mainly show ~ （ 1 ） The spatial distribution of b-values strong and large earthquakes in the spatial distribution of b-values with and current seismicity. Our results indicates significant heterogeneity in the studied area, which reflects the spatial difference of cumulative stress levels along various fault zones and segments. （2） Three anomalously low b-value areas with different dimensions were identified along the Mabian-Yanjin fault zone. These anomalies can be asperities under relatively high cumulated stress levels. Two asperities are located in the north of Mabian county, in Lidian town in western Muchuan county, and near Yanjin at the south end of the fault zone. These two areas represent potential large earthquake seismogenic sites around the Mabian area in the near future. Besides them, the third relatively smaller asperity is identified at southern Suijiang, as another potential strong- earthquake source. （3） An asperity along the southwestern segment of the Longquanshan fault zone indicates the site of potential moderate-to-strong earthquakes. （4） The asperity along the segment between Huangmu town in Hanyuan county and Longchi town in Emeishan city on Jinkouhe-Meigu fault has potential for a moderate-strong earthquake.