论地震序列的一种可能的重要成因

本文在Asperity模式和Barrier模式的基础上,提出了另外一种不均匀体模式——障碍体模式,并对该模式进行了数值模拟的研究。结果除证实了我们以前做过的单轴压力下模拟障碍体的实验结果以外,还表明在含有障碍体的断层面上,破裂的扩展与破裂的传播速度、始破裂区域的大小、裂纹的类型以及障碍体所在断层的介质有关。在有围压的情况下,破裂可以先越过或绕过强度较高或尺度较大的障碍体,经一段时间的应力积累过程后,再使障碍体发生破坏。本文通过对震源区中障碍体的性质和影响的研究,解释了海城和邢台两个地震序列形成和发展的可能原因,得到一些较为合理的结果。     

General energetic analysis of fracture instabilities in elastic media and the elastic field rupture

The singular integral equations method makes it possible to determine a general analytical solution to the problem of a crack subjected to any stresses, including singular ones. The singularity of stresses means that they tend to infinity in the concentration point. In exponential functions describing this relationship, the exponent characterizes the stress curvature growth. Also the energy released by crack opening can be described by a simple analytical formula. The problem is solvable for an exponent greater than −1. The class of all the cracks subject to stresses that exponentially grow to one of the crack ends is divided into three sub-classes. One of these embraces most of crack types, also Griffith’s. The remaining two are a source of microcracks in an elastic medium. The onset of such a stress concentration gives rise to a microcrack which cancels the stress singularity up to that with the exponent of −1/2, ensuring a strong stability of the medium. An analysis of the nucleation of such cracks brought about a concept of elastic field rupture without destruction of interatomic bonds, which has implications relating to the conductivity of metals. A general formula for the crack energy singles out a special crack of unit length, whose energy is constant and independent of stress concentration.     

非穿透裂纹平板试件三维破裂的实验研究

在研究地震孕育及震源破裂的问题时,用三维破裂来模拟地震破裂过程,比二维破裂与实际更加接近。我们设计了一组实验,采用几种不同的材料（玻璃、有机玻璃和大理石等）做成平板试件,在其中心预制非穿透裂纹,并在单轴压下进行了实验研究。 实验结果表明,非穿透裂纹与穿透裂纹的扩展情况有质的差别。非穿透裂纹的扩展并不沿原裂纹面延伸,而是沿裂纹前缘扩展出许多裂纹面,每一个破裂面都是复杂的扭曲、拐折的曲面。这可能意味着实际地震断层的扩展情况也是极为复杂的。     

板内逆断层地震破裂的基本特征及分段标志研究

通过对１６ 个板内逆断层地震的基本类型、构造环境、地震地表破裂尺度、几何形态、运动学特征及余震分布图像的研究分析,较系统地归纳了板内逆断层地震破裂的基本特征及分段标志．研究表明：（１） 逆断层破裂往往沿走向延伸较短,常表现为二维面状分布形态;（２） 地震断层未出露地表或仅有部分出露地表;（３） 逆断层地震破裂较走滑断层和正断层产生的地震破裂更为复杂,不仅表现在构成整体破裂带的各个单条破裂的力学性质差异方面,而且表现在几何结构方面．     

Compaction of a Rock Fracture Moderated by Competing Roles of Stress Corrosion and Pressure Solution

Unusually rapid closure of stressed fractures, observed in the initial stages of loading and at low temperatures, is examined using models for subcritical crack growth and pressure solution. The model for stress corrosion examines tensile stress concentrations induced at the Hertzian contact of propping fracture asperities, and mediates fracture growth according to a kinetic rate law. Conversely, pressure solution is described by the rate-limiting process of dissolution, resulting from the elevated stresses realized at the propping asperity contact. Both models are capable of following the observed compaction of fractures in novaculite. However, closure rates predicted for stress corrosion cracking are orders of magnitudes faster than those predicted for pressure dissolution. For consistent kinetic parameters, predictions from stress corrosion better replicate experimental observations, especially in the short-term and at low temperature when mechanical effects are anticipated to dominate. Rates and magnitudes of both stress corrosion and pressure solution are dependent on stresses exerted over propping asperities. Rates of closure due to stress corrosion cracking are shown to be always higher than for pressure solution, except where stress corrosion ceases as contact areas grow, and local stresses drop below an activation threshold. A simple rate law is apparent for the progress of fracture closure, defined in terms of a constant and an exponent applied to the test duration. For current experimental observations, this rate law is shown to replicate early progress data, and shows promise to define the evolution of transport properties of fractures over extended durations.     

Fractures: Finite-size scaling and multifractals

The distributions of contact area and void space in single fractures in granite rock have been determined experimentally by making metal casts of the void spaces between the fracture surfaces under normal loads. The resulting metal casts on 52 cm diameter core samples show a complex geometry for the flow paths through the fracture. This geometry is analyzed using finite-size scaling. The spanning probabilities and percolation probabilities of the metal casts are calculted as functions of observation scale. Under the highest stresses of 33 MPa and 85 MPa there is a significant size-dependence of the geometric flow properties for observation scales smaller than 2 mm. Based on this data, the macroscopic percolation properties of the extended fracture can be well represented by relatively small core samples, even under normal stresses larger than 33 MPa. The metal casts also have rich multifractal structure that changes with changing stress.     

Apparent stress scaling for tectonic and induced seismicity: Model and observations

A macroscopic model of seismic sources provides a scaling relationship for the apparent stress, treated as a function of three independent parameters: seismic moment, rupture area size, and average slip acceleration. These parameters represent three different factors: kinematic, geometric and material. This relationship allows us to distinguish and explain the following statistical characteristics of the log apparent stress versus log seismic moment plot. The regional trends, represented by a series of 1/2 slope lines, are related to the averaged shape of slip velocity pulses, so they reflect kinematic characteristics of the rupture process. The global trend, represented by the 1/6 slope line, is expected to characterize sets of events of wide range of rupture area sizes and assumes dependence of rupture area size on total slip, so it is related to the rupture initiation, propagation and arrest conditions; therefore, it reflects earthquake rupture dynamics. Additional shiftings among the trend lines obtained for the smallest induced tremors, larger tectonic earthquakes, and slow tsunami earthquakes, reflect differences between the intact rock failure and the frictional slip failure, that is, between fracture energies of these different earthquake classes.     

Interaction among fractures and stress field computation of fracture systems

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分析地震波估算地壳内的应力值

本文讨论了利用破裂力学理论说明地震破裂的过程, 认为地震本质上是岩石在应力作用下的低应力破裂现象.它是岩石中的裂纹不断稳态扩展、最后进入失稳扩展的结果.分析了在扩展过程中应力和位移的变化, 发现任何将要破裂的那一点的应力都要由初始应力0升高到屈服应力y 以后才破裂, 破裂后裂纹面上的点的应力降到0.在破裂前和破裂后的位移, 都可由弹性力学方程给出.在破裂的一瞬间破裂的端点产生的非弹性位移, 则不能由弹性力学方程给出.它可以由断裂力学中的裂纹滑开位移公式近似给出.根据位错模式由于计算弹性波辐射场的位错量 D(, t), 正是破裂瞬间产生的非弹性位移, 所以用弹性位移公式来计算地震位错量是错误的.我们采用了裂纹滑开位移公式来计算地震位错量, 从而导出了较合理的计算地震释放总能量的公式 ET=yDS(y 为屈服强度;D为平均位错;S 为断层面积)以及估算初始应力值0的公式:0 =[Dmax/L4y/(1-) ]1/2(L 为断层长度).用它们计算了一些地震的 Er 和0, 分别列于表1和表2.这些结果比以往的结果要更合理一些。 结果表明:(1)地震多数是在低应力作用下(即低初始应力)发生的(约100——200巴);(2)地震释放的总能量约比地震波能量大一个数量级.      

Cohesive Crack Analysis of Toughness Increase Due to Confining Pressure

Apparent fracture toughness in Mode I of microcracking materials such as rocks under confining pressure is analyzed based on a cohesive crack model. In rocks, the apparent fracture toughness for crack propagation varies with the confining pressure. This study provides analytical solutions for the apparent fracture toughness using a cohesive crack model, which is a model for the fracture process zone. The problem analyzed in this study is a fluid-driven fracture of a two-dimensional crack with a cohesive zone under confining pressure. The size of the cohesive zone is assumed to be negligibly small in comparison to the crack length. The analyses are performed for two types of cohesive stress distribution, namely the constant cohesive stress (Dugdale model) and the linearly decreasing cohesive stress. Furthermore, the problem for a more general cohesive stress distribution is analyzed based on the fracture energy concept. The analytical solutions are confirmed by comparing them with the results of numerical computations performed using the body force method. The analytical solution suggests a substantial increase in the apparent fracture toughness due to increased confining pressures, even if the size of the fracture process zone is small.     

基于非监督学习的水力压裂裂缝平面识别

在水力压裂施工中,如何有效获取压裂过程中产生的裂缝形态以及裂缝的动态扩展过程一直是困扰学术界和工业界的问题.目前,常规利用微地震事件定位结果进行分析的方法存在需要人工干预、散点信息表示能力不足等问题;采用数值模拟分析的方法往往因复杂的地下介质情况而引入计算偏差.本文基于非监督学习算法,通过提取微地震事件的空间和时间信息...     

APPLICATION OF BOUNDARY ELEMENT ANALYSIS FOR MULTIPLE SEISMIC CRACKING IN CONCRETE GRAVITY DAMS

The previously developed two-dimensional boundary element procedure for analysing the propagation of a single discrete crack is extended to simultaneous multiple cracking in concrete gravity dams. A brief discussion of the generalized methodology is presented and the validity of the extended procedure is verified by performing a fracture analysis of the Fongman dam and comparing the predicted rupture process with the available experimental results. The fracture response of the Koyna dam is then studied extensively under the Koyna earthquake. Both single and multiple cracking models are employed to investigate the fracture process as well as final rupture in the dam. Similar final damage involving complete separation of the crest block of the dam is predicted, irrespective of whether single or multiple crack propagation models are employed. In relation to the phenomenon of hydrodynamic uplift pressure within propagating cracks, openings of the crack on the upstream face of the dam are examined in particular. The results indicate that this phenomenon is not expected to be significant during the crack development phase, and hence unlikely to affect the final rupture characteristics of dams undergoing strong earthquake excitation.     

不同距离力源作用下脆性破裂的稳定性和止裂

根据断裂力学的原理, 提出了脆性破裂的止裂准则, 给出了最小止裂方程. 利用Erdogan的集中力的零频Green函数解, 分析了点力和简单分布力的位置对脆性破裂的稳定性和止裂的作用, 给出了若干典型条件下临界载荷、 失稳边界线、 止裂点的计算结果. 近距离力源引起的稳定性破裂, 对于解释一些蠕裂和构造的形成是有意义的; 不同距离力源引起的失稳破裂, 对于解释不同震级地震的发生和停止是有意义的. 强地震的发生有可能是远场力与近场力各种复合作用的结果. 本文的结果对于认识诱发地震的力学机制也有重要意义.      

Steadiness and stop of brittle fracture driven by the forces in different distances

Introduction The problem of crack stop of fault is of special importance in geosciences. This is because the risk of rupture of large scale fault is taken as the object of investigation in the geosciences. In some meaning, the stop of earthquake rupture is more important than initial because of its influ-ence on the prediction of energy releasing during the earthquake. There are quite a few of factors that cause stop of the fault. For example, the effect of barriers, the rapid healing of shea…     

A Model for the Mechanical Behaviour of Bentheim Sandstone in the Brittle Regime

— The mechanical behaviour of Bentheim sandstone, a homogeneous quartz-rich sandstone with porosity of 22.8%, was investigated by triaxial compression tests conducted on dry samples. At confining pressures up to 35 MPa, the failure mode was characterized by a typical brittle deformation regime, as the samples showed dilatancy and failed by strain softening and brittle faulting. Previous studies have shown that the mechanical behaviour and failure mode of brittle porous granular rocks are governed by the time-dependent growth of microcracks. We analyse this process using the “Pore Crack Model” based on fracture mechanics analysis. It is consistent with the microstructure of porous granular rocks since it considers the growth of axial cracks from cylindrical holes in two dimensions. These cracks grow when their stress intensity factors reach the subcritical crack growth limit. Interaction between neighbouring cracks is introduced by calculating the stress intensity factor as the sum of two terms: a component for an isolated crack and an interaction term computed using the method of successive approximations. It depends on crack length, pore radius, pore density, and applied stresses. The simulation of crack growth from cylindrical holes, associated with a failure criterion based on the coalescence of interacting cracks, is used to compare the theoretical stress at the onset of dilatancy and at macroscopic rupture to the experimental determined values. Our approach gives theoretical results in good agreement with experimental data when microstructural parameters consistent with observations are introduced.     

Static and dynamic analysis on slope stability using a DFN-DEM approach on the right abutment of the Karun 4 dam

Uncertainty in input fracture geometric parameters during analysis of the stability of jointed rock slopes is inevitable and therefore the stochastic discrete fracture network (DFN) — distinct element method (DEM) is an efficient modeling tool. In this research, potentially unstable conditions are detected in the right abutment of the Karun 4 dam and downstream of the dam body as a case study. Two extreme states with small and relatively large block sizes are selected and a series of numerical DEM models are generated using a number of validated DFN models. Stability of the rock slope is assessed in both static and dynamic loading states. Based on the design basis earthquake (DBE) and maximum credible earthquake (MCE) expected in the dam site, histories of seismic waves are applied to analyze the stability of the slope in dynamic earthquake conditions. The results indicate that a MCE is likely to trigger sliding of rock blocks on the rock slope major joint. Furthermore, the dynamic analysis also shows a local block failure by the DBE, which can consequently lead to slope instability over the long term. According to the seismic behavior of the two models, larger blocks are prone to greater instability and are less safe against earthquakes.

     

研究地震和岩石破裂现象的非线性科学方法

本文以地震孕育和岩石破裂过程的阶段(包括裂纹系形成、变形局部化和断层形成、断层活动和松弛)为线索,阐述了非线性科学方法(包括分形几何学,自组织临界现象和混沌动力学)的应用,提出了地震孕育过程和岩石破裂各阶段的普适性特征、机理和要着重研究的课题.     

Fracture Toughness Measurements and Acoustic Emission Activity in Brittle Rocks

Fracture toughness measurements under static loading conditions have been carried out in Barre and Lac du Bonnet granites. An advanced AE technique has been adopted to monitor real-time crack initiation and propagation around the principal crack in these tests to understand the processes of brittle failure under tension and related characteristics of the resulting fracture process zone. The anisotropy of Mode I fracture toughness has been investigated along specific directions. Microcrack density and orientation analysis from thin section studies have shown these characteristics to be the primary cause of the observed variation in fracture toughness, which is seen to vary between 1.14 MPa.(m)^1/2 and 1.89 MPa.(m)^1/2 in Barre granite. The latter value represents the case in which the crack is propagated at right angles to the main set of microcracks. The creation of a significant fracture process zone surrounding the propagating main crack has been confirmed. Real-time imaging of the fracture process and formation of fracture process zone by AE techniques yielded results in very good agreement with those obtained by direct optical analysis.     

基于方位地震数据的地应力反演方法

在页岩油气藏的开发和勘探阶段,需要对储层进行水力压裂改造,形成有利于油气聚集和运移的裂缝.地应力是进行水力压裂改造的重要参数,能够决定裂缝的大小、方向以及分布形态,影响着压裂的增产效果,且最大和最小水平应力差异比（ODHSR,Orthorhombic Differential Horizontal Stress Ratio）是评价储层是否可压裂成网的重要因子.本文探讨了基于地震数据估算地应力的方法,以指导页岩气的水力压裂开发.首先,利用叠前方位地震数据反演得到地层的弹性参数和各向异性参数;其次,基于正交各向异性水平应力差异比近似公式,利用反演得到的弹性参数和各向异性参数估算地层的ODHSR;最后,选取某工区的裂缝型页岩储层的叠前方位地震数据对该方法进行实际应用.实际工区地震数据应用表明,基于叠前方位地震数据反演得到的ODHSR能够有效的识别储层中易于压裂成网的区域.