Phenomenology of seismic macrofracture formation

A phenomenological scheme is proposed for the formation of a seismic macrofracture in the crust through multiscale avalanche-like crack coalescence of the inverse cascade type. Relations connecting fractal dimensions of crack sets and the concentration criterion of coalescence of cracks that are required for the onset of multiscale fracture are obtained. It is shown that the enlargement of cracks from micro-to macroscales includes a relatively small number of hierarchical coalescence stages.     

Earthquake rupture complexity due to dynamic nucleation and interaction of subsidiary faults

We numerically study the dynamic interaction of propagating cracks. It is assumed that propagating cracks can nucleate and drive subsidiary cracks because of shear strain enhancement near the propagating crack tips. The critical strain fracture criterion is assumed in the analysis. Intense interaction is expected to occur among the cracks. All the cracks are assumed to be parallel and antiplane strain deformation is assumed in the computation.In the interaction of two non-coplanar cracks, a strain shadow is formed in the neighborhood of each crack because of the strain release by the introduction of the crack. The growth of each crack is accelerated when the propagating tips of each crack are outside of the strain shadow of the other crack. In general, the crack tips enter the strain shadow, and the crack tips decelerate. The calculation shows that only one of the two cracks can continue to grow, and the other's growth is decelerated and arrested. If we can assume that the suite of cracks interact in a pairwise manner only, then this may suggest that only a limited number of cracks can continue to grow during the final stage of the rupture process. Hence the crack interaction causes complexity in dynamic earthquake faulting. The concepts of barrier and asperity have been employed by many researchers for the interpretation of complex seismic wave data. However, the physical realities of such concepts are obscure. Our calculations show that dynamic crack interactions can produce barriers and asperities in some cases; the crack tip deceleration or arrest due to the interactions among non-coplanar cracks can be interpreted as being due to a barrier. The dynamic coalescence among the coplanar cracks can be regarded as an asperity.Umeda found a localized area that strongly radiates high-frequency seismic waves in the epicentral areas of some large shallow earthquakes. He defined this as an earthquake bright spot. Our analysis implies that only a limited number of cracks continue to grow when many interactive cracks nucleate, and that all other cracks stop extending soon after nucleation. Hence, if the nucleation and termination of several cracks occur in a localized area, it will be observed seismologically as an earthquake bright spot. This is because it is theoretically known that the sudden termination of crack growth and dynamic crack coalescence efficiently emits high-frequency elastic waves.     

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.     

A Network Approach to Fracture: The Effect of Heterogeneity and Loading Conditions

—Fracture in a heterogeneous solid is simulated on a triangular network of bonds which figure the potential cracks of the medium. Heterogeneity is introduced by assuming a statistical strength distribution for the bonds. External stresses are applied to the network and the evolution of the bond population is analyzed when the stresses are increased. Bond-breaking is controlled by the crack-exten sion force which takes into account crack interactions by using an iterative procedure. Crack propaga tion leads to the coalescence of broken bonds crack clusters are formed. By using this kind of approach which combines fracture mechanics and network modelling, we are able to simulate the rupture of a rock specimen under various loading conditions without heavy computation. We discuss physical properties of the rupture process by examining the rupture stress and the geometric properties of the macroscopic fracture and their dependence on loading conditions and heterogeneity. Analysis of the geometric characteristics shows that the number of broken bonds can be fitted by a power law of the lattice size, the exponent depending on the loading conditions. Furthermore, an approximate computation of the mechanical response of the network demonstrates that the threshold secant modulus may be a more legitimate choice for a damage parameter in terms of system size independence.     

裂纹间动态相互作用的实验观测与理论分析──以共线剪切裂纹归并为例

本文以共线剪切裂纹的归并为例,研究裂纹系的动态相互作用．实验结果表明：在张破裂的意义上,小间距共线剪切裂纹的内端部实际上是阻碍结构,通过迂回弯曲的张破裂归并．本文提出一种估计张破裂扩展途径的近似方法,利用张应力破裂判据找出了潜在的破裂扩展途径的第一近似,较好地模拟了共线裂纹的破裂途径,和现有的数值模拟方法比较,可以大大缩短机时,简化计算程序,保证精确度．本研究结出了岩石剪切破裂“隧道效应”（即破裂跳过障碍体,而障碍体本身不破坏）的机理,还给出了脆性介质在摩擦、磨损过程中碎屑产生的机理．     

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。     

孔、裂隙并存地层中的声波测井理论及多极子声场特征

在油、气储层的勘探和开发中观察到的一个现象是储层岩石中普遍存在孔隙和裂隙.随着近年来孔、裂隙介质弹性波动理论的进展,我们可以将此理论应用于测井技术,以此来指导从声波测井中测量孔、裂隙地层的声学参数.本文计算了孔、裂隙地层里充流体井眼中的多极子声场,分析了声场随裂隙介质的两个主要参数(即裂隙密度和裂隙纵横比)的变化特征.井孔声场的数值计算表明裂隙密度可以大幅度地降低井中声波纵、横波的波速和振幅.随着裂隙密度的增加,在测井频段内也可以看到纵、横波速的频散现象(这种频散在孔隙地层中一般是观察不到的).本文还研究了多极子模式波 (即单极的Stoneley波、伪瑞利波以及偶极的弯曲波)随裂隙参数的变化特征.结果表明,这些模式波的振幅激发和速度频散都受裂隙密度的影响.裂隙密度越高影响越大.此外,裂隙还对模式波的传播造成较大的衰减.相对裂隙密度而言,裂隙纵横比是一个频率控制参数,它控制裂隙对声场影响的频率区间.本文的分析结果对裂缝、孔隙型地层的声波测井具有指导意义.     

Rupture and particle velocity during frictional sliding

Summary Laboratory measurements of rupture and particle velocity are in surprisingly good agreement with seismic values, providing further evidence that stick-slip friction is a suitable mechanism for shallow earthquakes. A simple theory is developed to explain the linear relationship observed between average particle velocity and stress drop for stick-slip events. Both stick-slip ruptures and cracks in brittle material commonly propagate at velocities roughly comparable to theS wave velocity of the material. Rupture normally begins relatively slowly and accelerates to a steady velocity in a few centimeters. Observations suggest that stick-slip ruptures can propagate atS wave speeds or occasionally greater and that cracks in pre-stressed glass can also propagate faster than theS waves. Fracture and thus rupture velocity of intact rock specimens is greatly influenced by the inhomogeneous structure of rock. Fracture may be modeled by coalescence of many cracks rather than growth of a single crack.Lamont-Doherty Geological Observatory Contribution No. 2627.     

“入”字式断层声发射b值及震级-频度关系的物理意义

本文从实验上研究了“人”字式断层声发射b值并从理论上对频度—震级关系及b值变化的物理机理进行了探讨。“人”字式断层的引入使b值呈现低值,b值随载荷呈现单调下降以及下降又上升或波状上升两类变化,反映了不同的破裂过程。根据微破裂的产生、发展和聚合过程的物理图象,建立了微破裂的分布方程。在裂纹无相互作用时,分布方程的解即是Gutenberg-Richter公式。在裂纹相互作用时,分布方程的解不是简单的幂函数,在对数坐标中频度—震级关系偏离线性     

岩石中裂纹对弹性波速度的影响

本文在常温常压下,对岩石中的层理,裂纹或裂缝引起的弹性波速变化特征进行了实验研究,并通过简化的人工裂缝模型,研究了裂缝密度和相对位置的变化对波速的影响取得了一些有意义的结果。     

考虑劣化屈服老化裂纹后混凝土水库堤坝排水边坡抗震性研究

针对在水库堤坝排水边坡混凝土裂纹的抗震性研究中,未考虑岩土体抗剪强度参数的劣化屈服效应以及混凝土裂纹的老化,存在抗震性判断结果准确率较差等问题,提出水库堤坝排水边坡混凝土考虑老化后产生裂纹的抗震性能研究方法。模拟强震下边坡混凝土的开裂破坏过程,根据D-P屈服准则,实现对闸墩混凝土材料的屈服判断。采用薄层整体单元模拟和分离式裂纹单元,实现混凝土裂纹的数值模拟,加载地震波后,获取混凝土裂纹的强震响应规律与破坏特征。实验结果可知,本文方法对坝体位移变化的研究精度高,得到的混凝土裂纹扩展范围更为准。运用本文方法对水库堤坝排水边坡混凝土的抗震性研究准确率以及可信度较高,说明本文方法具有一定的可取性。     

山西峨嵋台地的挤压型地裂

考察了山西峨嵋台地万荣城区一带的挤压型地裂,发现其呈北西-南东的条带状,1985年发生,至今仍在发展。地裂带上墙砖、水泥地砖拱曲翘起,水泥地面条带状拱曲,土体发育呈波浪条带状垅岗;墙体开裂,墙体裂缝中间宽上下两头细,地裂带上X型破裂发育。分析了万荣城区一带地裂的特征,讨论了万荣挤压型地裂的力学成因机制。     

Elastic anisotropy due to aligned cracks in porous rock1

All theoretical expressions which relate the characteristics of saturated aligned cracks to the associated elastic anisotropy are restricted in some important way, for example to the case of stiff pore fluids, or of the absence of equant porosity, or of a moderately high frequency band. Because of these restrictions, previous theory is not suitable for application to the upper crust, where the pore fluid is brine (K_f? K₈20), the equant porosity is often substantial (φ_p > 0.1), and the frequency band is sonic to seismic. This work removes these particular restrictions, recognizing in the process an important mechanism of dispersion. A notable feature of these more general expressions is their insensitivity, at low frequency, to the aspect ratio of the cracks; only the crack density is critical. An important conclusion of this more general model is that many insights previously achieved, concerning the shear-wave splitting due to vertical aligned saturated cracks, are sustained. However, conclusions on crack orientation or crack aspect ratio, which were derived from P-wave data or from shear-wave‘critical angles’, may need to be reconsidered. Further, the non-linear coupling between pores and cracks, due to pressure equalization effects, means that the (linear) Schoenberg-Muir calculus may not be applied to such systems. The theory receives strong support from recent data by Rathore et al. on artificial samples with controlled crack geometry.     

Stress-induced crack path in Aji granite under tensile stress

The double-torsion test using Aji granite was carried out to investigate the interaction between stress-induced crack path and mineral grains. Crack velocities were controlled at range 10^–7 m/s to 10^–1 m/s. After the stressed specimens were dyed, we checked the crack path by thin section analysis, using an optical microscope. The stress-induced crack path was divided into two types, transgranular and intergranular cracks, and each path was subdivided with respect to mineral grains. In spite of the extensive range of crack velocities, the ratios between the transgranular and intergranular crack lengths did not change. The crack paths were all jagged, and often showed detour around the grain boundary when faced with obstacles like hard grains or preexisting cracks. That is to say, quartz grain played an important role as an obstacle. Feldspar grain could change the crack path because of its cleavage plane. Biolite grain had a serious effect on the path even if its constitution ratio is very small. Fractal dimensions of the crack paths were calculated by three methods, as indicators of surface roughness. The fractal dimensions were shown in a slight trend with the change of crack velocity. This trend can be explained from the point of limited cracking rate in stress corrosion.     

Monte Carlo Studies of Relations between Fractal Dimensions in Monofractal Data Sets

—Within the fractal approach to studying the distribution of seismic event locations, different fractal dimension definitions and estimation algorithms are in use. Although one expects that for the same data set, values of different dimensions will be different, it is usually anticipated that the direction of fractal dimension changes among different data sets will be the same for every fractal dimension.¶Mutual relations between the three most popular fractal dimensions, namely the capacity, cluster and correlation dimensions, have been investigated in the present work. The studies were performed on the Monte Carlo generated data sets. The analysis has shown that dependence of the fractal dimensions on epicenter distribution, and relations among the fractal dimensions, are complex and variable. Neither values nor even inequalities among dimension estimates are preserved when different fractal dimensions are used. The correlation and the capacity dimensions seem to be good tools to trace collinear tendencies of eipicenters while the cluster dimension is more appropriate to studying uniform clustering of points.     

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.     

原始电阻率各向异性岩石电阻率变化的方向性

在3种非含岩成分造成的岩石原始电阻率各向异性标本(在采集和加工过程中，标本完整性遭 到破坏的标本)，和一种由含岩成分形成的 岩石原始电阻率各向异性标本上，布设多个电极，并将标本用水饱和. 然后用多电极组合法 ，将己布电极组合成不同方向、不同极距的电阻率各向异性测线. 采用单轴压缩、低围压 三 轴压缩和剪切3种加载方式，对标本进行动态电阻率变化实验. 观测标本电阻率随承载力的 变化. 实验结果表明∶对于岩石原始电阻率各向异性标本，在电阻率变化各向异性方面，与 岩石 原始电阻率各向同性标本相似，即∶裂隙和破碎带通过区域的测点，视电阻率变化各向异性 结果好，４种组合求得的４个各向异性主轴方向趋向一致，且与破碎带方向基本吻合；裂隙 和破碎带不经过区域的测点，４个视电阻率变化各向异性主轴方向不一致，或者根本求不出 各向异性解. 这后一种情况，在裂隙面平行测量面时，表现最为明显.     

Effects of soil cracking on the seismic response of soil–structure systems

A numerical study on the influence that cracks and discontinuities (closed cracks) can have on the seismic response of a hypothetical soil–structure system is presented and discussed. A 2-D finite-difference model of the soil was developed, considering a bilinear failure surface using a Mohr–Coulomb model. The cracks are simulated with interface elements. The soil stiffness is used to characterize the contact force that is generated when the crack closes. For the cases studied herein, it was considered that the crack does not propagate during the dynamic event. Both cases, open and closed cracks, are considered. The nonlinear behavior was accounted for approximately using equivalent linear properties calibrated against several 1-D wave propagation analyses of selected soil columns with variable depth to account for changes in depth to bed rock. Free field boundaries were used at the edges of the 2-D finite-difference model to allow for energy dissipation of the reflected waves. The effect of cracking on the seismic response was evaluated by comparing the results of site response analysis with and without crack, for several lengths and orientations. The changes in the response obtained for a single crack and a family of cracks were also evaluated. Finally, the impact that a crack may have on the structural response of nearby structures was investigated by solving the seismic-soil–structure interaction of two structures, one flexible and one rigid to bracket the response. From the results of this investigation, insight was gained regarding the effect that discontinuities may have both on the seismic response of soil deposits and on nearby soil–structure systems.     

双轴压缩下组合裂纹的动态扩张实验研究

本文运用动态光弹性技术，实验研究了几种与地震孕育构造背景相近的组合裂纹在双轴压缩下的扩展规律，对裂纹扩展路径、稳定性作了分析，并与单轴压缩情况进行了对比，同时还研究了摩擦力对裂纹扩展的影响。通过上述研究，得出了压剪应力场中裂纹稳定扩展等结论。