Necessary and sufficient conditions for reaching and maintaining critical state

According to classical critical state theory (CST) of granular mechanics, two analytical conditions on the ratio of stress invariants and the void ratio are postulated to be necessary and sufficient for reaching and maintaining critical state (CS). The present work investigates the sufficiency of these two conditions based on the results of a virtual three-dimensional discrete element method experiment, which imposes continuous rotation of the principal axes of stress with fixed stress principal values at CS. Even though the fixity of the stress principal values satisfies the two analytical CST conditions at the initiation of rotation, contraction and abandonment of CS occur, which proves that these conditions may be necessary but are not sufficient to maintain CS. But if fixity of stress and strain rate directions in regard to the sample is considered at CS, the two analytical conditions of CST remain both necessary and sufficient. The recently proposed anisotropic critical state theory (ACST) turned this qualitative requirement of fixity into an analytical condition related to the CS value of a fabric anisotropy variable A defined in terms of an evolving fabric tensor and the plastic strain rate direction, thus, enhancing the two CST conditions by a third. In this way, the three analytical conditions of ACST become both necessary and sufficient for reaching and maintaining CS. In addition, the use of A explains the observed results by relating the stress-strain response, in particular the dilatancy, to the evolution of fabric by means of the relevant equations of ACST.     

鄂尔多斯块体北缘Pn波层析成像研究

基于鄂尔多斯块体北缘2008～2018年台网数字化波形记录,利用Pn波层析成像技术获得研究区高精度的上地幔速度结构与各向异性。结果表明,研究区上地幔顶部Pn波速度存在明显的横向不均匀性,且与研究区构造活动及地震分布密切相关;河套断陷带各向异性快波方向呈近EW向。研究区多数历史强震发生在低速异常区或高低速异常过渡带上,该结果为理解研究区地震发生的相关性提供了新的地震学依据。     

Shear-wave polarizations in the Peter the First Range indicating crack-induced anisotropy in a thrust-fault regime

Summary. Three-component seismograms of small local earthquakes recorded in the Peter the First Range of mountains near Garm, Tadzhikistan SSR, display shear-wave splitting similar to that previously observed near the North Anatolian Fault in Turkey. The Peter the First Range is in a region of compressional tectonics, whereas the North Anatolian Fault is a comparatively simple strike-slip fault. Detailed analysis of the Turkish records suggests that the splitting is diagnostic of crack-induced anisotropy caused by vertical microcracks aligned parallel to the direction of maximum compression. Preliminary examination of paper records from Garm shows that most shear waves arriving within the shear-wave window display shear-wave splitting, and that the polarizations of leading shear-waves are consistently aligned in a NE/SW direction. The area is complicated and the tectonics are not well-understood, but the NE/SW direction is approximately perpendicular to the compressional axis in many of the fault-plane mechanisms of the earthquakes. These earthquakes are usually at depths between 5 and 12 km, although there are some deeper events nearby.
Parallel shear-wave polarizations, such as those observed, are expected to indicate the strike of nearly vertical parallel microcracks, which would be aligned parallel to the direction of maximum compression. Thus the shear-wave polarizations in the Peter the First Range indicate that the directions of principal stress are reversed in the rock above the earthquake foci where thrust faulting is taking place.     

ANISOTROPY OF MAGNETIC SUSCEPTIBILITY AND IDENTIFICATION OF TILTED SEDIMENT CORES FROM THE BOHAI SEA

Anisotropy of magnetic susceptibility (AMS) is a well-developed technique increaseingly used in petro-fabric determination. ItS application to two Mackereth cores JX91-2A and JX91-2B, taken from thesame site in the central Bohai Sea, revealed 3D magnetic fabrics of the sediments as expressed with susce-ptibility ellipsoids. The flat seafloor and the relatively quiet depositional environment in the semi-isolatedBohai Sea should asult in a primary fabric with horisontally obate susocptibility el1ipsoids. Mormwr,the inaxing downcore totaI anisotropy comprising mainly of magntic foliation nsulting fIrom sedimentcompaction should also lead to flat ellipsoids. Therefore, the off-pole meam dindions of minimurn axes ofaseptibility ellipsoids on stermnets must indicate that the two coas are ti]ted re1ative to the flat anfloor.Use of Fisher statisties showh the tilt angles to be 14° for JX91-2A and 23°for JX91 -2B from whichthe tna depths of the coas were dedded accordingly.     

中国陆区S波分型与上地幔地震各向异性

本文利用中国大陆区共8个台站所观测到地震事件的S波数据，采用相关分析的手段以 观测数据重建的技术，进行了S波分裂参数－快慢波延迟时间与快波偏振方向的计算，并分析了S波分裂参数与中国陆区上地幔物质运动的相互关系，研究了结果表明，兰州台下的S波分裂时差最小，北京台下的最大，中国东部地区上地幔运动方向以西北向为主，西部地区以北偏西为优势。     

上地幔各向异性研究综述及在川滇地区的研究思路

简要介绍了地球介质各向异性研究的发展历程,重点介绍了国内外有关上地幔各向异性的研究工作及成果;阐述了上地幔各向异性的起源及其地球动力学意义;较详细地分析了上地幔各向异性研究的各种方法及其优缺点;论述了川滇地区各向异性研究的意义和目的,并提出了整个研究工作的内容和步骤.     

K_o固结粘土各向异性不排水剪强度研究

在三维各向异性弹塑性本构关系基础上，求解不排水条件和破坏条件，导出各种不同试验条件下K0团结粘土的各向异性不排水剪强度表达式。对常规超固结比定义下的不排水剪强度进行研究，将理论计算结果与试验结果进行比较，验证所提理论的合理性。     

Electrical anisotropy and conductivity distribution functions of fractal random networks and of the crust: the scale effect of connectivity

All explanations of the high-conductivity layers (HCL) found by magnetotellurics in the middle or lower crust incorporate a mixture of a low-conductivity rock matrix and a highly conductive phase, for example graphite or saline fluids. In most cases the bulk conductivity of the mixture does not depend on the conductivity of the rock matrix but rather (1) on the amount of high-conductivity material and, in particular, (2) on its geometry. The latter is quantitatively described by the parameter 'electrical connectivity'. Decomposition of the observed bulk conductivity of the mixture into these two parameters results in an ill-posed problem. Even if anisotropy occurs in the HCL, three output parameters (highly conductive phase fraction, connectivity with respect to the X direction, connectivity with respect to the Y direction) have to be estimated from the two bulk conductivities of the anisotropic HCL. The additional information required for solving this problem is provided if instead of single-site data the conductivities from many field sites are evaluated: a sample distribution of the conductivity can then be obtained. Ensembles of random networks are used to create theoretical distribution functions which match the empirical distribution functions to some extent. The use of random resistor networks is discussed in the context of other established techniques for the treatment of two-phase systems, such as percolation theory and the renormalization group approach. Models of embedded networks explain the discrepancy between 'small' anisotropy (2-3) on the laboratory scale and large anisotropy (10-100) found in electromagnetic field surveys encompassing volumes of several cubic kilometres. Strong anisotropy can indicate low electrical connectivity, and a possible explanation is that a network stays close to the percolation threshold.     

Experiments with Higdon's absorbing boundary conditions for a number of wave equations

Simulation of wave propagation for seismic purposes is usually restricted to a small portion of the earth. Artificial boundary conditions are required where the subsurface model is truncated. Absorbing boundaries should ensure that waves hitting the artificial boundaries are not reflected. The vast amount of literature on the subject suggests that “good” conditions have not been found, and only “reasonable” solutions exist. A cursory overview of existing and a few new ideas is presented that may guide the construction of suitable boundary conditions. Because the intended application of the boundary conditions was a high-order finite-difference code that runs on a parallel computer, we have restricted our attention to local boundary conditions. A fundamental problem in the design of accurate local boundary conditions is pointed out: accuracy is required to keep the amount of reflected energy small, but at the same time allows for growing low-frequency modes. We have settled for Higdon’s boundary conditions. Higdon proposes to include some damping to suppress the growing low-frequency modes. We show that third-order conditions provide acceptable results for the simple scalar wave equation and the acoustic equation. In the elastic case, an additional low-frequency growing mode may occur. This mode can be suppressed by using a dissipative boundary scheme and by increasing the amount of damping. The increase in damping results in an increase in the amount of reflected energy, which is larger than in the scalar case. Numerical experiments exhibit a reasonable performance, although some improvement would be useful, particularly in the anisotropic elastic case. This revised version was published online in July 2006 with corrections to the Cover Date.     

变形岩石磁性各向异性及其应变相关性的模拟

本文介绍处于弱磁场中的磁性砂岩人工样品,在三种应变作用下磁化率各向异性特征的研究结果.结果表明,磁化率椭球与应变椭球之间,显示了密切的相关性.文中并对上述情况下,磁化率各向异性特征及剩磁特征,从机理上进行了分析.