Critical Sensitivity in Driven Nonlinear Threshold Systems

— Rupture in heterogeneous brittle media, including earthquakes, can be regarded as complicated phenomena in driven nonlinear threshold systems. It displays catastrophe transition and sample-specificity, which results in difficulty of rupture prediction. Our numerical simulations indicate that critical sensitivity might be a common precursor of catastrophe transition and thus give a clue to catastrophe prediction. In this paper we present an analytical examination of critical sensitivity in driven nonlinear threshold systems, based on mean field approximation and damage relaxation time model. The result suggests that critical sensitivity is in reality a common feature prior to catastrophe transition in driven nonlinear threshold systems, with disordered mesoscopic heterogeneity. This result seems to be supported by rock experiments.     

Damage Localization,Sensitivity of Energy Release and the Catastrophe Transition

-- Large earthquakes can be viewed as catastrophic ruptures in the earth's crust. There are two common features prior to the catastrophe transition in heterogeneous media. One is damage localization and the other is critical sensitivity; both of which are related to a cascade of damage coalescence. In this paper, in an attempt to reveal the physics underlying the catastrophe transition, analytic analysis based on mean-field approximation of a heterogeneous medium as well as numerical simulations using a network model are presented. Both the emergence of damage localization and the sensitivity of energy release are examined to explore the inherent statistical precursors prior to the eventual catastrophic rupture. Emergence of damage localization, as predicted by the mean-field analysis, is consistent with observations of the evolution of damage patterns. It is confirmed that precursors can be extracted from the time-series of energy release according to its sensitivity to increasing crustal stress. As a major result, present research indicates that the catastrophe transition and the critical point hypothesis (CPH) of earthquakes are interrelated. The results suggest there may be two cross-checking precursors of large earthquakes: damage localization and critical sensitivity.     

Critical Sensitivity and Trans-scale Fluctuations in Catastrophic Rupture

-- Rupture in the heterogeneous crust appears to be a catastrophe transition. Catastrophic rupture sensitively depends on the details of heterogeneity and stress transfer on multiple scales. These are difficult to identify and deal with. As a result, the threshold of earthquake-like rupture presents uncertainty. This may be the root of the difficulty of earthquake prediction. Based on a coupled pattern mapping model, we represent critical sensitivity and trans-scale fluctuations associated with catastrophic rupture. Critical sensitivity means that a system may become significantly sensitive near catastrophe transition. Trans-scale fluctuations mean that the level of stress fluctuations increases strongly and the spatial scale of stress and damage fluctuations evolves from the mesoscopic heterogeneity scale to the macroscopic scale as the catastrophe regime is approached. The underlying mechanism behind critical sensitivity and trans-scale fluctuations is the coupling effect between heterogeneity and dynamical nonlinearity. Such features may provide clues for prediction of catastrophic rupture, like material failure and great earthquakes. Critical sensitivity may be the physical mechanism underlying a promising earthquake forecasting method, the load-unload response ratio (LURR).     

岩石损伤模量分析

从能量的角度出发定义损伤变量,通过应力-应变曲线卸载段有效应力与总应力之间的假定关系,确定损伤模量的计算方法。在单轴和三轴条件下,对岩石损伤相关参数进行统计研究,重点对损伤模量进行计算和对比分析。结果表明,单轴及低围压下损伤模量基本呈逐渐减小的趋势,而随着围压的增大,损伤模量呈先减小后保持动态稳定的趋势。损伤变量的计算充分考虑到围压的影响,可进一步增进对岩石损伤的认识。     

Coupling multiscale finite element method for consolidation analysis of heterogeneous saturated porous media

The multiscale finite element method is developed for solving the coupling problems of consolidation of heterogeneous saturated porous media under external loading conditions. Two sets of multiscale base functions are constructed, respectively, for the pressure field of fluid flow and the displacement field of solid skeleton. The coupling problems are then solved with a multiscale numerical procedure in space and time domain. The heterogeneities induced by permeabilities and mechanical parameters of the saturated porous media are both taken into account. Numerical experiments are carried out for different cases in comparison with the standard finite element method. The numerical results show that the coupling multiscale finite element method can be successfully used for solving the complicated coupling problems. It reduces greatly the computing effort in both memory and time for transient problems.     

基于能量耗散原理的非均质岩石损伤破坏元胞自动机模型研究

基于能量耗散理论建立非均质岩石的动态损伤破坏元胞自动机,分析单轴压缩试验中岩石破坏截面的损伤状态,得到该情况下的岩石裂隙微观动态发展过程、损伤演化关系以及全程应力应变曲线。研究发现：①加载过程中,均质度较低的岩样裂纹的萌生和扩展较为分散,损伤速率低;均质度较高的岩样裂纹的萌生和扩展非常集中,表现为脆性破坏。②损伤演化曲线呈3阶段S形发展。③随着岩石均质度参数的增加,岩石的峰值强度和峰值应变都有所提高,峰后曲线越来越陡。④给出的衡量岩石脆性破坏强弱程度的指标参数,能够较好地描述岩石破坏形式随着均值度参数m变化的规律。     

Load-Unload Response Ratio (LURR), Accelerating Moment/Energy Release (AM/ER) and State Vector Saltation as Precursors to Failure of Rock Specimens

— In order to verify some precursors such as LURR (Load/Unload Response Ratio) and AER (Accelerating Energy Release) before large earthquakes or macro-fracture in heterogeneous brittle media, four acoustic emission experiments involving large rock specimens under tri-axial stress, have been conducted. The specimens were loaded in two ways: monotonous or cycling. The experimental results confirm that LURR and AER are precursors of macro-fracture in brittle media. A new measure called the state vector has been proposed to describe the damage evolution of loaded rock specimens.     

Damage evolution and fluid flow in poroelastic rock

We present a formulation for mechanical modeling of the interaction between fracture and fluid flow. Our model combines the classic Biot poroelastic theory and a damage rheology model. The model provides an internally consistent framework for simulating coupled evolution of fractures and fluid flow together with gradual transition from brittle fracture to cataclastic flow in high-porosity rocks. The theoretical analysis, based on thermodynamic principles, leads to a system of coupled kinetic equations for the evolution of damage and porosity. A significant advantage of the model is the ability to reproduce the entire yield curve, including positive and negative slopes, in high-porosity rocks by a unified formulation. A transition from positive to negative values in the yield curve, referred to as a yield cap, is determined by the competition between the two thermodynamic forces associated with damage and porosity evolution. Numerical simulations of triaxial compression tests reproduce the gradual transition from localized brittle failure to distributed cataclastic flow with increasing pressure in high-porosity rocks and fit well experimentally measured yield stress for Berea sandstone samples. We modified a widely used permeability porosity relation by accounting for the effect of damage intensity on the connectivity. The new damage-permeability relation, together with the coupled kinetics of damage and porosity evolution, reproduces a wide range of realistic features of rock behavior. We constrain the model variables by comparisons of the theoretical predictions with laboratory results reporting porosity and permeability variation in rock samples during isotropic and anisotropic loading. The new damage-porosity-permeability relation enables simulation of coupled evolution of fractures and fluid flow and provides a possible explanation for permeability measurements in high-porosity rocks, referred to as the “apparent permeability paradox.” The text was submitted by the authors in English.     

态矢量方法的实验研究

在地震等灾变的发生之前，会出现一定的前兆现象。中通过实验方法对这些前兆现象之一的态矢量的异常变化进行了研究。实验使用声发射技术(Acoustic Emission)，对三轴应力条件下岩石试件内部微裂纹的产生和扩展进行了记录。实验结果表明在岩石试件最终破坏之前，表征态矢量的相关参量都发生了异常明显的变化，这表明态矢量的异常变化可以被用作为岩石等脆性材料灾变的前兆，使用态矢量方法可以对脆性材料的破坏乃至地震作出预测。     

Long-range Stress Redistribution Resulting from Damage in Heterogeneous Media

— It has been shown in CA simulations and data analysis of earthquakes that declustered or characteristic large earthquakes may occur with long-range stress redistribution. In order to understand long-range stress redistribution, we propose a linear-elastic but heterogeneous-brittle model. The stress redistribution in the heterogeneous-brittle medium implies a longer-range interaction than that in an elastic medium. Therefore, it is surmised that the longer-range stress redistribution resulting from damage in heterogeneous media may be a plausible mechanism governing main shocks.     

Coupling upscaling finite element method for consolidation analysis of heterogeneous saturated porous media

The coupling upscaling finite element method is developed for solving the coupling problems of deformation and consolidation of heterogeneous saturated porous media under external loading conditions. The method couples two kinds of fully developed methodologies together, i.e., the numerical techniques developed for calculating the apparent and effective physical properties of the heterogeneous media and the upscaling techniques developed for simulating the fluid flow and mass transport properties in heterogeneous porous media. Equivalent permeability tensors and equivalent elastic modulus tensors are calculated for every coarse grid block in the coarse-scale model of the heterogeneous saturated porous media. Moreover, an oversampling technique is introduced to improve the calculation accuracy of the equivalent elastic modulus tensors. A numerical integration process is performed over the fine mesh within every coarse grid element to capture the small scale information induced by non-uniform scalar field properties such as density, compressibility, etc. Numerical experiments are carried out to examine the accuracy of the developed method. It shows that the numerical results obtained by the coupling upscaling finite element method on the coarse-scale models fit fairly well with the reference solutions obtained by traditional finite element method on the fine-scale models. Moreover, this method gets more accurate coarse-scale results than the previously developed coupling multiscale finite element method for solving this kind of coupling problems though it cannot recover the fine-scale solutions. At the same time, the method developed reduces dramatically the computing effort in both CPU time and memory for solving the transient problems, and therefore more large and computational-demanding coupling problems can be solved by computers.     

Flow and fracture maps for basaltic rock deformation at high temperatures

Understanding how the strength of basaltic rock varies with the extrinsic conditions of stress state, pressure and temperature, and the intrinsic rock physical properties is fundamental to understanding the dynamics of volcanic systems. In particular it is essential to understand how rock strength at high temperatures is limited by fracture. We have collated and analysed laboratory data for basaltic rocks from over 500 rock deformation experiments and plotted these on principal stress failure maps. We have fitted an empirical flow law (Norton’s law) and a theoretical fracture criterion to these data. The principal stress failure map is a graphical representation of ductile and brittle experimental data together with flow and fracture envelopes under varying strain rate, temperature and pressure. We have used these maps to re-interpret the ductile–brittle transition in basaltic rocks at high temperatures and show, conceptually, how these failure maps can be applied to volcanic systems, using lava flows as an example.     

The damage mechanics of brittle solids in compression

The development of microcrack damage in brittle solids in compression is analyzed, using a simple model. The model is developed from recent detailed analysis of the initiation, propagation and linkage of microfractures from pre-existing cracks, voids, or other inhomogeneities. It describes the evolution of damage with strain and from it a criteria for failure can be established. The results are used to construct failure surfaces in stress space which combine information about brittle failure with data describing the onset of plastic yielding. Such failure surfaces are constructed for a number of rocks and are compared with previously published experimental data.     

基于推覆分析的钢框架结构地震倒塌判别准则研究

结构地震倒塌判别准则是工程结构强震分析的关键问题。在层损伤模型的基础上,建立了基于推覆分析的建筑结构整体损伤模型,并以国内某2层2跨平面钢框架结构拟静力试验为背景,应用有限元程序ABAQUS对平面钢框架进行了强震倒塌数值模拟。分析了钢框架结构的倒塌破坏过程,基于建议地震倒塌判别准则研究了钢框架结构的损伤演化规律。结果表明:钢框架结构在强震作用下的损伤发展顺序与塑性发展顺序一致;基于推覆分析的结构整体损伤模型能较好的体现强震作用下钢框架结构的损伤演化规律,且在上下界处收敛;强震作用下,钢框架结构的初始损伤主要由结构的残余侧移引起,而后期损伤主要由结构的承载力和刚度退化引起。     

Seismic Rheological Model and Reflection Coefficients of the Brittle–Ductile Transition

It is well established that the upper—cooler—part of the crust is brittle, while deeper zones present ductile behaviour. In some cases, this brittle–ductile transition is a single seismic reflector with an associated reflection coefficient. We first develop a stress–strain relation including the effects of crust anisotropy, seismic attenuation and ductility in which deformation takes place by shear plastic flow. Viscoelastic anisotropy is based on the eigenstrain model and the Zener and Burgers mechanical models are used to model the effects of seismic attenuation, velocity dispersion, and steady-state creep flow, respectively. The stiffness components of the brittle and ductile media depend on stress and temperature through the shear viscosity, which is obtained by the Arrhenius equation and the octahedral stress criterion. The P- and S-wave velocities decrease as depth and temperature increase due to the geothermal gradient, an effect which is more pronounced for shear waves. We then obtain the reflection and transmission coefficients of a single brittle–ductile interface and of a ductile thin layer. The PP scattering coefficient has a Brewster angle (a sign change) in both cases, and there is substantial PS conversion at intermediate angles. The PP coefficient is sensitive to the layer thickness, unlike the SS coefficient. Thick layers have a well-defined Brewster angle and show higher reflection amplitudes. Finally, we compute synthetic seismograms in a homogeneous medium as a function of temperature.     

Study on the Seismogeny and Occurrence of Earthquakes by Using Pattern Dynamics

The mesoscopic damage dynamics and damage evolution have been applied to probe theevolutional process induced catastrophe in the earthquake activity.It is a new method.In thispaper,a brief introduction of the basic principle about damage dynamics and evolution ismade.At the same time,using the theory of the pattern dynamics we studied all earthquakes(M_L≥5.0)which occurred along Zhangjiakou-Bohai Sea earthquake belt in the capitalregion.The result indicates that the preparation and happening of the real earthquakes andthe theory are consistent.There are two kinds of evolutional model according to the finalstate,namely,global stability model(GS)and evolution induced catastrophe model(EIC).The two models haven’t evident boundary.The transitional zone exhibits the indeterminacyof the seismic process and the effect of the random variation.This research proposed newapproaches for earthquake prediction.     

Study of Shaking Table Test on Dynamic Response Characteristics and Failure Mechanism of the Loess Slope

The natural loess that covers the ground surface has good stability due to its low water content. However, when violent earthquakes occur, the strong dynamic stress generated in the slope may induce landslide disasters with different sizes. In this paper, a large-scale shaking table model test is used to reveal the dynamic response and instability failure process of the loess slope. The test results show that different parts of the slope have different vibration characteristics and the first natural frequency in the model increases with the increase of the slope height. The response acceleration of different parts may change due to the coupling relationship between the spectral characteristics of input wave and the natural frequencies of different parts of slope, suggesting the characteristics of regional differential dynamic response. Under the condition of different dynamic response, stress state and boundary conditions of different parts of slope, a rapid microstructural damage, cumulative residual deformation evolution, and tension-shear coupling instability failure process may appear at the top of the slope with the strong dynamic response associated with the increase of dynamic loading intensity. The S_d values presented in this paper may reflect soil damage and slope instability and failure.     

Multiscale Brittle-Ductile Coupling and Genesis of Slow Earthquakes

We present the first attempt to explain slow earthquakes as cascading thermal-mechanical instabilities. To attain this goal we investigate brittle-ductile coupled thermal-mechanical simulation on vastly different time scales. The largest scale model consists of a cross section of a randomly perturbed elasto-visco-plastic continental lithosphere on the order of 100 × 100 km scale with no other initial structures. The smallest scale model investigates a km-scale subsection of the large model and has a local resolution of 40 × 40 m. The model is subject to a constant extension velocity applied on either side. We assume a free top surface and with a zero tangential stress along the other boundaries. Extension is driven by velocity boundary conditions of 1 cm/a applied on either side of the model. This is the simplest boundary condition, and makes it an ideal starting point for understanding the behavior of a natural system with multiscale brittle-ductile coupling. Localization feedback is observed as faulting in the brittle upper crust and ductile shearing in an elasto-viscoplastic lower crust. In this process brittle faulting may rupture at seismogenic rates, e.g., at 10²–10³ ms^?1, whereas viscous shear zones propagate at much slower rates, up to 3 × 10^?9 ms^?1. This sharp contrast in the strain rates leads to complex short-time-scale interactions at the brittle-ductile transition. We exploit the multiscale capabilities from our new simulations for understanding the underlying thermo-mechanics, spanning vastly different, time- and length-scales.     

A Continuum Damage–Breakage Faulting Model and Solid-Granular Transitions

We present a thermodynamically-based formulation for mechanical modeling of faulting processes in the seismogenic brittle crust using a continuum damage–breakage rheology. The model combines previous results of a continuum damage framework for brittle solids with continuum breakage mechanics for granular flow. The formulation accounts for the density of distributed cracking and other internal flaws in damaged rocks with a scalar damage parameter, and addresses the grain size distribution of a granular phase in a failure slip zone with a breakage parameter. The stress–strain relation and kinetics of the damage and breakage processes are governed by the total energy function of the system, which combines the energy of the damaged solid with the energy of the granular material. A dynamic brittle instability is associated with a critical level of damage in the solid, leading to loss of convexity of the solid energy function and transition to a granular phase associated with lower energy level. A non-local formulation provides an intrinsic length scale associated with the internal damage structure, which leads to a finite length scale for damage localization that eliminates the unrealistic singular localization of local models. Shear heating during deformation can lead to a secondary finite-width internal localization. The formulation provides a framework for studying multiple aspects of brittle deformation, including potential feedback between evolving elastic moduli and properties of the slip localization zone and subsequent rupture behavior. The model has a more general transition from slow deformation to dynamic rupture than that associated with frictional sliding on a single pre-existing failure zone, and gives time and length scales for the onset of the dynamic fracturing process. Several features including the existence of finite localization width and transition from slow to rapid dynamic slip are illustrated using numerical simulations. A configuration having an existing narrow slip zone with localized damage produces for appropriate loading conditions an overall cyclic stick–slip motion. The simulated frictional response includes transitions from friction coefficient of ~0.7 at low slip velocity to dynamic friction below 0.4 at slip rates above ~0.1 m/s, followed by rapidly increasing friction for slip rates above ~1 m/s, consistent with laboratory observations.     

热水条件下黑云母断层泥的摩擦强度与稳定性

黑云母是自然界常见的层状硅酸盐矿物,其摩擦系数不高且化学稳定性好,对其摩擦性质的关注可能会对弱断层的研究有所帮助.本次工作选取的实验温度条件对应于典型地壳强度模型中脆塑性转化带的范围,为300 ℃和400 ℃.有效正应力为200 MPa,孔隙水压包括10 MPa和30 MPa,在此条件下对黑云母模拟断层泥进行摩擦实验研究.实验得出黑云母的摩擦系数平均在0.36左右.速度依赖性随温度升高速度弱化的程度增强,表现为300 ℃为十分微弱的速度弱化,而在400 ℃出现了黏滑行为,代表了更强的速度弱化.显微结构中同时出现了脆性剪切变形和塑性扭折变形,但决定宏观力学性质的显然是脆性剪切变形.在黑云母存在的情况下,本研究的实验结果有助于理解大陆地壳脆塑性转化带中地震的可能性和弱断层深部的变形机制、宏观力学行为以及地震活动.