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.     

The elastic properties of single-crystal fayalite as determined by dynamical measurement techniques

We present new elasticity measurements on single-crystal fayalite and combine our results with other data from resonance, pulse superposition interferometry, and Brillouin scattering to provide a set of recommended values for the adiabatic elastic moduliC _ij and their temperature variations. We use a resonance method (RPR) with specimens that were previously investigated by pulse superposition experiments. The nineC _ij of fayalite are determined from three new sets of measurements. One set of our newC _ij data is over the range 300–500 K. We believe that the relatively large discrep ncies found in someC _ij are due in large part to specimen inhomogeneities (chemical and microstructural) coupled with differences in the way various techniques sample, rather than only systematic errors associated with experimental procedures or in the preparations of the specimens.Our recommendeaC _ij's (GPa) and (C _ij/T) _p (GPa/K) are: The resulting values for the isotropic bulk and shear moduli,K _s and , and their temperature derivatives are:K _s=134(4) GPa; =50.7(0.3) GPa; (K _s/T) _p =–0.024(0.005) GPa/K; and (/T) _p =–0.013(0.001) GPa/K. An important conclusion is thatK _s increases as the Fe/(Fe+Mg) ratio in olivine is increased.     

注水煤体应力能 V-f 转化与释放机理研究

文章分析了在煤层注水湿润后煤体弹性能的转化与消耗过程，给出在湿润状态下能量由体变弹性能向形变弹性能转化进而自耗释放的理论模型。指出在坚硬干燥煤体中，注水后在水压力和毛细力的切割作用下，裂隙大量扩展，丰富了自由裂隙，产生更多的裂隙启发(裂隙切口)，使原来近似的刚性煤体变成由裂隙分割的块体组成的组合体或半组合体。裂隙中水的粘滞作用及水分子吸附力使块体问粘性结合、刚度降低、形变增大。煤体形变弹性能自身消耗释放的形式有3种：产生剪应力导致自由裂隙问错动摩擦；强度降低，使裂隙启发被劈裂成自由裂隙；湿润煤体蠕变性增强，产生整体性移动作功。初步给出能量消耗的量化表达式。通过这一理论，能建立煤层注水湿润度与冲击地压灾害发生的更直接的关系，使进一步量化该关系成为可能。从更深层次解释煤层注水防治冲击地压的机理。     

Structure Functions In A Wall-Turbulent Shear Flow

Wavelet and quadrant analyses were applied to turbulent velocity data in order to investigate the transition from the anisotropy of energy-containing eddies to the isotropy of the inertial subrange scales. The quadrant analysis of the wavelet coefficients of longitudinal and vertical velocity components allows the evaluation of the velocity structure functions and the momentum cospectrum as a function of the separation distance and of the quadrants. In an isotropic condition the contribution both of ejections and sweeps (even quadrants), and both of reflections and deflections (odd quadrants), has to be equal. The analysis has shown that in neutrally stratified conditions the transition to isotropy occurs in a frequency range (0.2 < r/z < 3) usually referred to as internal to the inertial subrange (r is separation distance, z is height). In the transition region, as in the isotropic region, the velocity structure functions still agree with the 1941 and 1962 Kolmogorov theories; but on the other hand the structure functions of the even and odd quadrants are fitted by power laws of different slopes in the transition region. The proposed analysis allows the investigation within the transition region of the different dynamical structure in the energy transfer from the energy-containing scales to the isotropic scales.     

滑坡治理中格构锚固结构的解析解分析

在分析格构锚固结构受力的基础上 ,将格构梁简化为受集中力作用的弹性地基上的梁 ,提出了格构锚固结构的力学模型 ,利用 Winkler弹性地基上梁的解析解对格构梁进行了内力和变形的分析 ,发现格构梁的受力状况受弹性特征λ、梁格间距 ls以及悬臂长度影响 ;建议梁长 l与λ宜满足 lλ≥ 2π;采用较小间距的格构梁以及小吨位锚索 ,间距宜满足 lsλ<π/ 2 ,悬臂长度取 (0 .3～ 0 .5 ) ls,并将分析结论应用于三峡库区巴东太矶头东滑坡治理工程的设计中     

大别造山带地壳泊松比结构与超高压变质带—来自宽角反射与近垂直反射剖面的启示

综合宽角反射、近垂直反射的探测结果和有关地质资料，对大别造山带地壳结构和超高压变质带研究显示：大别造山带地壳具有层块结构特征。沿安义－庄墓剖面，上地壳有7个弹性块体，中地壳有5个，下地壳有4个。扬子与华北地块的主缝合带是超高压变质带，扬子地块与大别造山带的现今分界线是与郯庐断裂相交的太湖－马庙断裂，磨子潭－晓天断裂是大别造山带的北界，北淮阳构造带呈楔状向下插入，它与华北地块的分界是肥中断裂。郯庐断裂在中、上地壳近于直立，下地壳向西倾斜。超高压变质带的厚度为5－7km，产状向北插入到北大别块体之下，折返过程是构造就位，不是大别山的均匀抬升，折返的主运动面是水吼－五河高温剪切带。     

Numerical evaluation of the damping‐solvent extraction method in the frequency domain

The damping‐solvent extraction method for the analysis of unbounded visco‐elastic media is evaluated numerically in the frequency domain in order to investigate the influence of the computational parameters—domain size, amount of artificial damping, and mesh density—on the accuracy of results. An analytical estimate of this influence is presented, and specific questions regarding the influence of the parameters on the results are answered using the analytical estimate and numerical results for two classical problems: the rigid strip and rigid disc footings on a visco‐elastic half‐space with constant hysteretic material damping. As the domain size is increased, the results become more accurate only at lower frequencies, but are essentially unaffected at higher frequencies. Choosing the domain size to ensure that the static stiffness is computed accurately leads to an unnecessarily large domain for analysis at higher frequencies. The results improve by increasing artificial damping but at a slower rate as the total (material plus artificial) damping ratio ζ_t gets closer to 0.866. However, the results do not deteriorate significantly for the larger amounts of artificial damping, suggesting that ζ_t≈0.6 is appropriate; a larger value is not likely to influence the accuracy of results. Presented results do not support the earlier suggestion that similar accuracy can be achieved by a large bounded domain with small damping or by a small domain with larger damping. Copyright © 2002 John Wiley & Sons, Ltd.     

裂隙型单斜介质中弹性系数的计算及波的传播特性研究

根据Hudson等关于裂隙介质弹性系数计算的扰动理论及Bond变换矩阵原理，给出了各向同性介质中含多组垂直裂隙时等效弹性系数的计算方法。计算了含两组斜交的垂直裂隙形成的单斜各向异性介质中的等效弹性系数，并根据Christoffel方程推导、得出水平面内平面波传播的相速度和群速度随方位变化的特性。     

A non-linear stress-stiffness model for geomaterials at small to intermediate strains

A double exponential fitting model (DEFM) capable of expressing the non-linear stress-stiffness relationship of geomaterials has been proposed by Shibuya et al. (1997). The model comprises two material constants; the elastic stiffness at very small strains and the strength, together with other free parameters to determine the complete stress-stiffness relationship. In this paper, the capability of the original function used for DEFM in simulating the tangent stiffness-stress relationship of geomaterials is first discussed. Second, the methods for determining the free model parameters, as well as its conversion to obtain a stress-strain relationship are proposed. The applicability of DEFM to predicting non-linear stress-stiffness relationship is examined in detail in a total of forty-nine fitting cases of compression test data on sedimentary rock, artificial soft rock and soft clay. It is found that the DEFM is effective in expressing the non-linear stress-stiffness relationship of various kinds of geomaterials at small to intermediate strains, say less than 0.5%. The superiority of this model compared to other fitting models currently in use is also demonstrated in some of the fitting cases.     

Static deformation of two welded monoclinic elastic half-spaces due to a long inclined strike-slip fault

Static deformation of two monoclinic elastic half-spaces in welded contact due to a long inclined strike-slip fault situated in one of the half-spaces is studied analytically and numerically. Closed-form algebraic expressions for the displacement at any point of the medium are obtained. The variation of the displacement at the interface with the horizontal distance from the fault is studied. The effect of anisotropy on the displacement field is examined. It is found that while the anisotropy of the source half-space has a significant effect on the displacement at the interface, the anisotropy of the other half-space has only a marginal effect.