Development of dynamic slip model for a shear crack

<正>The objective of this paper is to develop a dynamic slip model for a shear crack under constant stress drop.This crack problem is formulated by a traction boundary integral equation(BIE) in the frequency domain and then solved by the hyper-singular boundary element method as well as the regularization technique proposed in this paper.Based on the spectral integral form of the kernel function,the unbounded term can be isolated and extracted from the hyper-singular kernel function by using the method of subtracted and added back in wave number domain.Finally,based on the inverse transformation from the frequency domain to the time domain,the time histories of crack opening displacement under constant stress drop can be determined.Three rupture models(simultaneous rupture model,symmetric bilaterally-propagating model and unilaterally propagating model) with specified time histories of stress drop are considered in this paper.Even though these three models will cause the same final slip shapes because of the same constant stress drop,the associated slip time functions differ significantly from each other during the rupture process.     

The three-dimensional dynamic displacement discontinuity method: Theory and applications

A boundary element technique has been developed for solving three-dimensional elastodynamic problems in rock mechanics, such as joint slip and the sudden advance of excavations. Both implicit and explicit versions of the technique have been implemented. Comparisons of accuracy and computational efficiency are made for a simple verification problem. Examples in which the technique has been used to investigate the dynamic response of supported and unsupported excavations in tabular orebodies are presented.     

Numerical modelling of wave propagation in anisotropic soil using a displacement unit-impulse-response-based formulation of the scaled boundary finite element method

An efficient method for modelling the propagation of elastic waves in unbounded domains is developed. It is applicable to soil–structure interaction problems involving scalar and vector waves, unbounded domains of arbitrary geometry and anisotropic soil. The scaled boundary finite element method is employed to derive a novel equation for the displacement unit-impulse response matrix on the soil–structure interface. The proposed method is based on a piecewise linear approximation of the first derivative of the displacement unit-impulse response matrix and on the introduction of an extrapolation parameter in order to improve the numerical stability. In combination, these two ideas allow for the choice of significantly larger time steps compared to conventional methods, and thus lead to increased efficiency. As the displacement unit-impulse response approaches zero, the convolution integral representing the force–displacement relationship can be truncated. After the truncation the computational effort only increases linearly with time. Thus, a considerable reduction of computational effort is achieved in a time domain analysis. Numerical examples demonstrate the accuracy and high efficiency of the new method for two-dimensional soil–structure interaction problems.     

A viscous-spring transmitting boundary for cylindrical wave propagation in saturated poroelastic media

Based on the u–U formulation of Biot equation and the assumption of zero permeability coefficient, a viscous-spring transmitting boundary which is frequency independent is derived to simulate the cylindrical elastic wave propagation in unbounded saturated porous media. By this viscous-spring boundary the effective stress and pore fluid pressure on the truncated boundary of the numerical model are replaced by a set of spring, dashpot and mass elements, and its simplified form is also given. A u–U formulation FEA program is compiled and the proposed transmitting boundaries are incorporated therein. Numerical examples show that the proposed viscous-spring boundary and its simplified form can provide accurate results for cylindrical elastic wave propagation problems with low or intermediate values of permeability or frequency content. For general two dimensional wave propagation problems, spuriously reflected waves can be greatly suppressed and acceptable accuracy can still be achieved by placing the simplified boundary at relatively large distance from the wave source.     

桅杆结构纤绳连接拉耳孔边裂纹扩展形状变化特性研究

本文采用两自由度的裂纹扩展模型,以桅杆结构纤绳拉耳孔边裂纹前缘最深点和表面点的裂纹扩展增长量来追踪裂纹扩展。基于最小二乘法原理对通过有限元法所获得的各种裂纹形状所对应的裂纹前缘最深点和表面点的无因次形状因子进行多项式曲线拟合,用拟合曲线上的值代替离散的无因次形状因子扩充插值数据库,采用拉格朗日插值法计算任意形状裂纹前缘最深点和表面点无因次形状因子,并计算得到确定裂纹扩展速率所需要的应力强度因子幅度。最后根据裂纹前缘最深点和表面点的裂纹扩展速率确定桅杆结构纤绳连接拉耳孔边裂纹的扩展特性。     

Topographic stress and rock fracture: a two‐dimensional numerical model for arbitrary topography and preliminary comparison with borehole observations

Theoretical calculations indicate that elastic stresses induced by surface topography may be large enough in some landscapes to fracture rocks, which in turn could influence slope stability, erosion rates, and bedrock hydrologic properties. These calculations typically have involved idealized topographic profiles, with few direct comparisons of predicted topographic stresses and observed fractures at specific field sites. We use a numerical model to calculate the stresses induced by measured topographic profiles and compare the calculated stress field with fractures observed in shallow boreholes. The model uses a boundary element method to calculate the stress distribution beneath an arbitrary topographic profile in the presence of ambient tectonic stress. When applied to a topographic profile across the Susquehanna Shale Hills Critical Zone Observatory in central Pennsylvania, the model predicts where shear fractures would occur based on a Mohr–Coulomb criterion, with considerable differences in profiles of stresses with depth beneath ridgetops and valley floors. We calculate the minimum cohesion required to prevent shear failure, C_min, as a proxy for the potential for fracturing or reactivation of existing fractures. We compare depth profiles of C_min with structural analyses of image logs from four boreholes located on the valley floor, and find that fracture abundance declines sharply with depth in the uppermost 15 m of the bedrock, consistent with the modeled profile of C_min. In contrast, C_min increases with depth at comparable depths below ridgetops, suggesting that ridgetop fracture abundance patterns may differ if topographic stresses are indeed important. Thus, the present results are consistent with the hypothesis that topography can influence subsurface rock fracture patterns and provide a basis for further observational tests. Copyright © 2014 John Wiley & Sons, Ltd.     

不同摩擦本构关系对断层自发破裂动力学过程的影响

地震是断层的摩擦失稳过程.摩擦本构关系对断层的破裂成核、破裂传播、破裂速度、能量释放、破裂终止等起着至关重要的控制作用.为了比较不同摩擦关系在断层自发破裂动力学过程中的影响,文中引入目前应用最为广泛的4种典型摩擦本构关系,它们分别是：滑移弱化摩擦关系,速率弱化摩擦关系,以及速率-状态相依摩擦关系中的老化定律和滑动定律.研究中利用有限单元方法对上述4种摩擦关系控制的断层自发破裂过程分别进行模拟计算,模拟结果显示：当模型参数相同时,不同摩擦关系模拟的破裂行为总体上具有一致性,都可以产生亚剪切破裂或超剪切破裂,并且破裂传播速度的大小与摩擦本构关系的类型无关.此外,它们之间还存在着较大的差异：（1）速率弱化摩擦关系可以模拟脉冲型破裂;而其他3个摩擦关系只能模拟裂纹性破裂.（2）不同摩擦关系模拟的超剪切破裂转换长度不同,速率-状态相关摩擦关系的老化定律相比其他摩擦关系需要更大的转换长度才能实现亚剪切破裂转变为超剪切破裂;而速率弱化的摩擦关系的超剪切转换长度可以为0,即不需要转换距离就直接产生超剪切破裂.（3）速率弱化摩擦关系模拟的破裂速度自成核后很快就达到稳定值;而其他类型摩擦关系模拟的破裂传播则要经历由缓慢破裂到逐渐加速直至达到稳定破裂的过程.值得特别指出的是,本文所使用的4种摩擦关系都不能完整地反映实际大地震破裂过程的摩擦属性,需要进一步深入研究.

     

不同摩擦本构关系对断层自发破裂动力学过程的影响

地震是断层的摩擦失稳过程.摩擦本构关系对断层的破裂成核、破裂传播、破裂速度、能量释放、破裂终止等起着至关重要的控制作用.为了比较不同摩擦关系在断层自发破裂动力学过程中的影响,文中引入目前应用最为广泛的4种典型摩擦本构关系,它们分别是：滑移弱化摩擦关系,速率弱化摩擦关系,以及速率-状态相依摩擦关系中的老化定律和滑动定律.研究中利用有限单元方法对上述4种摩擦关系控制的断层自发破裂过程分别进行模拟计算,模拟结果显示：当模型参数相同时,不同摩擦关系模拟的破裂行为总体上具有一致性,都可以产生亚剪切破裂或超剪切破裂,并且破裂传播速度的大小与摩擦本构关系的类型无关.此外,它们之间还存在着较大的差异：（1）速率弱化摩擦关系可以模拟脉冲型破裂;而其他3个摩擦关系只能模拟裂纹性破裂.（2）不同摩擦关系模拟的超剪切破裂转换长度不同,速率-状态相关摩擦关系的老化定律相比其他摩擦关系需要更大的转换长度才能实现亚剪切破裂转变为超剪切破裂;而速率弱化的摩擦关系的超剪切转换长度可以为0,即不需要转换距离就直接产生超剪切破裂.（3）速率弱化摩擦关系模拟的破裂速度自成核后很快就达到稳定值;而其他类型摩擦关系模拟的破裂传播则要经历由缓慢破裂到逐渐加速直至达到稳定破裂的过程.值得特别指出的是,本文所使用的4种摩擦关系都不能完整地反映实际大地震破裂过程的摩擦属性,需要进一步深入研究.     

Combined paraxial-consistent boundary conditions finite element model for simulating wave propagation in elastic half-space media

In this paper, a finite element model of a soil island is coupled to both a consistent transmitting boundary and a paraxial boundary, which are then used to model the propagation of waves in semi-infinite elastic layered media. The formulation is carried out in the frequency domain while assuming plane strain conditions. It is known that a discrete model of this type, while providing excellent results for a wide range of physical parameters in the context of a half-space problem, may deteriorate rapidly at low frequencies of excitation. This is so because at low frequencies the various waves in the model eventually attain characteristic wavelengths which exceed the distance of the bottom boundary, which then causes that boundary to fail. Also, the paraxial boundaries themselves break down at very low frequencies. In this paper, this difficulty is overcome and the model׳s performance is improved upon dramatically by incorporating an artificial buffer layer sandwiched between the bottom of the soil medium and the underlying elastic half-space. Applications dealing with rigid foundations resting on homogenous or layered half-space media are shown to exhibit significant improvement. Following extensive simulations, clear guidelines are provided on the performance of the coupled model and an interpretation is given on the engineering significance of the findings. Finally, clear recommendations are provided for the practical use of the proposed modelling strategy.     

Experimental observations of elastic wave radiation characteristics from tensile cracks and pre-existing shear faults

Elastic waves were recorded from tensile cracks and prepared shear faults in the laboratory. The velocity of tensile crack propagation was measured. The duration of crack propagation was correlated with the signal pulse duration. Experiments with prepared shear faults showed that obstacles on the fault change the pulse form and the relation between wave amplitude (magnitude) and seismic moment.     

无破碎带断层场地对SH波的散射

在层状半空间精确动力刚度矩阵和斜线荷载动力格林函数的基础上建立间接边界元方法,在频域内求解无破碎带断层场地对入射平面SH波的散射。为方便求解,将总波场分解为自由波场和散射波场,自由波场由直接刚度法求得,断层两侧的散射波场通过在断层面上分别对两侧施加均布斜线荷载产生的动力响应来模拟,虚拟荷载的密度可通过引入断层表面的边界条件确定,最后叠加自由波场和散射波场求得总波场。以有落差断层和无落差断层模型为例进行数值计算,分析断层落差、断层倾角以及断层两侧介质的刚度比对散射效应的影响。研究表明,断层落差与波长相当时,断层对SH波的放大作用最大;地表位移幅值随着断层倾角的增大逐渐增大;若断层无落差且其两侧刚度不同时,一般刚度较小一侧地表位移幅值较大且振荡更为剧烈,波从刚度较小一侧入射时位移幅值放大尤为显著。     

砾岩储层地震波传播方程:三重孔隙结构模型

针对砾岩储层的砂、砾、泥三重孔隙结构特征,本文分析砾岩孔隙区域、砂岩孔隙区域以及泥岩孔隙区域相互之间的孔隙流体流动机制,将静态的砾岩骨架本构方程与动态的孔隙流体运动方程联立,提出了复杂砾岩储层的弹性波传播理论方程.采用实测砾岩储层参数,在算例中与双重孔隙介质理论进行对比分析,验证了本文理论方程的合理性;基于三重孔隙介质模型,分析不同储层环境下纵波的传播特征,结果显示：随流体黏滞系数增大,在衰减-频率轴坐标系中,砾与砂、砂与泥孔隙区域间局域流导致的两个衰减峰向低频端移动,而Biot全局流导致的衰减峰向高频端移动;嵌入体尺寸及背景相介质渗透率的变化,主要影响纵波速度频散曲线沿频率轴左、右平移,不影响波速低频、高频极限幅值;嵌入体含量及孔隙度的变化改变了岩石干骨架的弹性、密度参数,不仅影响速度频散曲线沿频率轴平移,而且影响其上、下限幅值;砾包砂包泥三重孔隙介质模型所预测的衰减曲线中,低频段“第一个衰减峰”主要由砾岩孔隙区域与砂岩孔隙区域之间的局域流导致,中间频段“第二个衰减峰”主要由砂岩孔隙区域与泥岩孔隙区域之间的局域流导致,超声频段“第三个衰减峰”由Biot全局流导致.对慢纵波传播特征的分析显示,砂岩骨架（局部孔隙度较大）内部的宏观孔隙流体流动造成的耗散明显强于砾岩与泥岩骨架.

     

矿产预测评价中不确定性传播模型

矿产预测与评价是是由多个阶段组成的系统工程,包括数据收集,资料整理,信息提取,信息综合,预测评价、成果表达等.由于地质的复杂性和变化多样性及人类认识的不完备性致使矿产预测与评价的每一个阶段都包含了一定的不确定性,且前一阶段的不确定性会传播给后一阶段,从而导致相当数量的不确定性积累与传播.本文简要分析了矿产预测与评价不确定性的主要来源,给出矿产预测与评价的不确定性表达模型,研究了矿产预测与评价不确定性的合成算法和传播算法.     

挡土墙地震反应非线性波动模拟

本文运用解耦近场非线性波动数值模拟方法研究挡土墙地震反应，为反映墙土体系在地震作用下的位移机制，引入了Desai薄层单元模拟墙土间接触面，并采用双线型本构关系作为接触面单元和土体的非线性模型，在此基础上给出了解决P—SV问题的非线性显式有限元时域递推公式，为进一步发展非线性波动数值模拟技术提供了有益经验。为验证本文方法及适用性，将数值模拟结果与Zeng，X．和Madabhushi，X．P．G．等的离心机试验和弹塑性数值模拟结果进行对比。结果表明：墙土体系加速度、挡土墙顶底相对滑移、沉降和墙体倾角等同离心机试验模拟结果基本吻合，与弹塑性数值模拟结果相似。     

基于高阶双渐近透射边界的大坝-库水动力相互作用直接耦合分析模型

高阶双渐近时域透射边界能够同时模拟行波和快衰波的传播,并且能够在全频范围内迅速逼近准确解,具有优良的收敛性能和计算效率.本文将动水压力波高阶双渐近透射边界直接嵌入到近场有限元方程中,建立了大坝-库水动力相互作用的直接耦合分析模型.该模型的整体控制方程保留了近场有限元方程系数矩阵对称稀疏的优势,可以方便地利用现有的通用有限元求解器求解.基于有限元开源软件框架体系OpenSees（Open System for Earthquake Engineering Simulation）,编程实现了直接耦合分析模型,并将其应用于二维重力坝、三维拱坝与库水动力相互作用分析.数值算例表明,该直接耦合分析模型具有很高的精度和计算效率.     

On the propagation of an in-plane shear fault with super-S-wave velocity

The speedv, especially the problem whether super S-wave velocity in the classical model (linear elasticity fracture mechanics) exists, of spontaneous propagation of a shear fault is investigated theoretically. An in-plane shear crack propagating in the crack plane is taken as the model of the shear fault. The results obtained firstly by Kostrov (1975) is extended from sub-Rayleigh wave velocity to super S-wave velocity, and the analytical expression for the stress intensity factorK ₂ in the case ofα>v>β is derived. It is proved that for Poisson mediumK ₂ is positive and real in the velocity range (β, 1.70β). This demonstrates that (β, 1.70β) is the velocity range which fulfils the conditions for spontaneous crack propagation. The existence, convergence and positiveness or negativeness ofK ₂ forv in individual sections are examined, and it is found that for an in-plane shear crack: 1. There are three sections forv, i.e., [0.v _R], (β, 1.70β), andα, respectively, and 2. There are two physically reasonable sections forv, the first is [v _R, β], and the second is [1.70β, α]. These two forbidden sections behave as barriers to fault propagation. The analytical expressions derived in this paper are not only suitable to classical model, but also to the other derivative models (e. g., the slip-weakening model and the renomalization model etc.). The model considered in this paper is more realistic than the static model employed by previous authors. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica, 15, 9–14, 1993.     

A simple displacement control technique for pushover analyses

This paper explains how to control in displacement any force proportional loading. Such a procedure makes it possible to derive the complete (i.e. including the possible softening branch) response curve of a structure along any radial loading path in the force space. This is exactly what is required in the so‐called pushover analysis used in the seismic assessment of structures. The proposed procedure is simple in the sense that it can be easily implemented in any classical (displacement‐based) finite element code through a standard displacement control loading process. Furthermore, it leads to an interesting definition of the controlled degree‐of‐freedom, which, in the case of the pushover analysis, could substitute the classical roof displacement. Copyright © 2006 John Wiley & Sons, Ltd.     

基于BEM的水力裂缝起裂与扩展数值模拟

水力压裂是对低渗透油气田进行储层改造的重要技术,现已在国内外得到广泛应用.但井壁上原有的裂缝会造成水力裂缝在近井筒区域发生转向,诱发提前脱砂、砂堵等现象,甚至导致压裂作业失败.本文以边界元方法、流体力学为理论依据,考虑了近井筒处裂缝的转向行为,建立了含裂缝的井壁起裂及水力裂缝扩展的流固耦合模型.研究发现:当压裂液黏度较小时,裂缝迅速转向至垂直于最小水平主应力的方向;随着黏度的逐渐增大,井底注入压力不断升高,裂缝转向半径亦逐渐增大;压裂液排量对井壁裂缝延伸的影响和黏度对其的影响相似;井壁上原有裂缝的长度对井壁破裂压力有着显著的影响,其长度越长,井壁破裂压力越小;随着水平主应力差值的增大,裂缝的延伸路径会发生明显的转变,所需的延伸压力不断增大;井壁原有裂缝与最大水平主应力方向间的夹角越小,所需的破裂压力及延伸压力也越小.     

基于弯曲弹簧模型的裂纹混凝土梁动力特性分析

利用结构振动波传播理论,将含裂纹混凝土梁以裂纹为界划分为两段连续的波导体,为了表征由裂纹引起的梁中波传播的不连续特性,引入了模拟裂纹的弯曲弹簧模型。通过理论计算得到了裂纹简支梁的特征方程,并以一裂纹混凝土简支梁为例进行数值分析,讨论了裂纹的深度和位置对裂纹梁各阶固有频率的影响。     

基于辛算法模拟探地雷达在复杂地电模型中的传播

近年来,探地雷达(GPR)凭借其快速、高效、无破损等特点,已经广泛应用于浅地层目标探测中.数值模拟是研究探地雷达电磁波在地下结构中传播规律的有效手段.辛算法是一种保持Hamilton系统总能量不变的时域数值计算方法.本文提出了基于一阶显式辛分块龙格库塔方法的探地雷达数值模拟方法.通过对比本文算法与时域有限差分方法计算结果可知,在同等计算精度下,本文算法可以节省25%的计算时间.并基于本文算法对两个复杂GPR模型进行正演模拟,得到模拟GPR探测wiggle图,这有助于更好的理解和分析实测雷达数据.