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。     

Experimental seismic investigation of Sefid‐rud concrete buttress dam model on shaking table

Owing to the devastating M7.6 earthquake of 20 June 1990 that occurred in the northern province of Iran, Sefid‐rud concrete buttress dam located near the epicenter was severely shaken. The crack penetrated throughout the dam thickness near slope discontinuity, causing severe leakage, but with no general failure. In this study, nonlinear seismic response of the highest monolith with empty reservoir is investigated experimentally through model testing. A geometric‐scaled model of 1:30 was tested on a shaking table with high‐frequency capability to study dynamic cracking of the model and serve as data for nonlinear computer model calibration. Three construction joints are set up in the model to simulate effects of construction aspects. The experimental results are then compared with smeared crack and damage mechanics finite‐element simulations using nonlinear concrete constitutive models based on fracture mechanics. The crack patterns obtained from numerical models are in good agreement with those obtained from shaking table tests for the case of including construction joint effects and rigid foundation. Copyright © 2008 John Wiley & Sons, Ltd.     

Can Damage Mechanics Explain Temporal Scaling Laws in Brittle Fracture and Seismicity?

Time delays associated with processes leading to a failure or stress relaxation in materials and earthquakes are studied in terms of continuum damage mechanics. Damage mechanics is a quasi-empirical approach that describes inelastic irreversible phenomena in the deformation of solids. When a rock sample is loaded, there is generally a time delay before the rock fails. This period is characterized by the occurrence and coalescence of microcracks which radiate acoustic signals of broad amplitudes. These acoustic emission events have been shown to exhibit power-law scaling as they increase in intensity prior to a rupture. In case of seismogenic processes in the Earth's brittle crust, all earthquakes are followed by an aftershock sequence. A universal feature of aftershocks is that their rate decays in time according to the modified Omori's law, a power-law decay. In this paper a model of continuum damage mechanics in which damage (microcracking) starts to develop when the applied stress exceeds a prescribed yield stress (a material parameter) is introduced to explain both laboratory experiments and systematic temporal variations in seismicity.     

Catastrophic Rupture Induced Damage Coalescence in Heterogeneous Brittle Media

In heterogeneous brittle media, the evolution of damage is strongly influenced by the multiscale coupling effect. To better understand this effect, we perform a detailed investigation of the damage evolution, with particular attention focused on the catastrophe transition. We use an adaptive multiscale finite-element model (MFEM) to simulate the damage evolution and the catastrophic failure of heterogeneous brittle media. Both plane stress and plane strain cases are investigated for a heterogeneous medium whose initial shear strength follows the Weibull distribution. Damage is induced through the application of the Coulomb failure criterion to each element, and the element mesh is refined where the failure criterion is met. We found that as damage accumulates, there is a stronger and stronger nonlinear increase in stress and the stress redistribution distance. The coupling of the dynamic stress redistribution and the heterogeneity at different scales result in an inverse cascade of damage cluster size, which represents rapid coalescence of damage at the catastrophe transition.     

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.     

A mechanical model for deformation and earthquakes on strike-slip faults

A two-dimensional model for stress accumulation and earthquake instability associated with strike-slip faults is considered. The model consists of an elastic lithosphere overlying a viscous asthenosphere, and a fault of finite width with an upper brittle zone having an elastoplastic response and a lower ductile zone having an elastoviscoplastic response. For the brittle, or seismic, zone the behavior of the fault material is assumed to be governed by a relation which involves strain hardening followed by a softening regime, with strength increasing with depth. For the fault material in the ductile, or aseismic, section, the viscous effect is included through use of a nonlinear creep law, and the strength is assumed to decrease with depth. Hence, because of the lesser strength and the viscous effect, continuous flow occurs at great depths, causing stress accumulation at the upper portion of the fault and leading to failure at the bottom of the brittle zone. The failure is initially due to localized strain softening but, with further flow, the material above the softened zone reaches its maximum strength and begins to soften. This process accelerates and may result in an unstable upward rupture propagation.Relations are developed for the history of deformation within the lithosphere, specifically for the velocity of particles within the fault and at the ground surface. The boundary-element method is used for a quantitative study, and numerical results are obtained and compared with the recorded surface deformation of the San Andreas fault. The effects of geometry and material properties on instability, on the history of the surface deformation, and on the earthquake recurrence time are studied. The results are presented in terms of variations of ground-surface shear strain and shear strain rate, and velocity of points within the fault at various times during the earthquake cycle.It is found that the location of rupture initiation, the possibility of a sudden rupture as opposed to stable creep, and also the ground deformation pattern and its history, all critically depend on the mechanical response of the material within the fault zone, especially that of the brittle section. Shorter earthquake recurrence times are obtained for shallower brittle zones and for a stiffer lithosphere. Lower viscosities of the aseismic zone and the absence of asthenospheric coupling tend to suppress instability and promote stable creep. The model results thus suggest that the overall viscosity of the ductile creeping zone must exceed a minimum value for a sudden upward propagating rupture to take place within the seismic section.     

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.     

Constitutive relations for fault slip and earthquake instabilities

Constitutive relations for fault slip are described and adopted as a basis for analyzing slip motion and its instability in the form of earthquakes on crustal faults. The constitutive relations discussed include simple rate-independent slip-weakening models, in which shear strength degrades with ongoing slip to a residual frictional strength, and also more realistic but as yet less extensively applied slip-rate and surface-state-dependent relations. For the latter the state of the surface is characterized by one or more variables that evolve with ongoing slip, seeking values consistent with the current slip rate. Models of crustal faults range from simple, single-degree-of-freedom spring-slider systems to more complex continuous systems that incorporate nonuniform slip and locked patches on faults of depth-dependent constitutive properties within elastic lithospheric plates that may be coupled to a viscoelastic asthenosphere. Most progress for the rate and state-dependent constitutive relations is at present limited to single-degree-of-freedom systems. Results for stable and unstable slip with the various constitutive models are summarized. Instability conditions are compared for spatially uniform versus nonuniform slip, including the elastic — brittle crack limit of the nonuniform mode. Inferences of constitutive and fracture parameters are discussed, based on earthquake data for large ruptures that begin with slip at depth, concentrating stress on locked regions within a brittle upper crust. Results of nonlinear stability theory, including regimes of complex sustained stress and slip rate oscillations, are outlined for rate and state-dependent constitutive relations, and the manner in which these allow phenomena like time-dependent failure, restrengthening in nearly stationary contact, and weakening in rapidly accelerated slip, is discussed.     

三维脆性破裂的拉应力判据

用线弹性断裂力学对连续介质中三维裂纹(K_Ⅲ≠0)破裂的拉应力断裂准则提出了补充性假说和相应的计算方法（第一主微分面定点法）。对于给定应力强度因子K_i（i=Ⅰ,Ⅱ,Ⅲ）的裂纹问题,从理论上给出了初始破裂面完整形式的解析表示或数值计算结果。推导结果是,三维拉张破裂的初始破裂面是以破裂点为顶点的广角锥面,跨在原始裂纹面的前缘,它的外缘为螺旋线,锥面的每一条母线都与过该线的第一主微分面重合。大量的这样的初始破裂面叠错密接,互不相交。推算的结果与已有的三锥破裂实验结果基本符合。把补充后的拉应力判据和最大拉应力理论相比较,发现在应力分量只保留奇异项的情况下,这两种判据是等价的;但如果对应力分量作零阶项修正,则两种判据只在三维(K_Ⅲ≠0)问题中等价,在二维(K_Ⅲ=0)问题中不完全等价。     

不同距离力源作用下脆性破裂的稳定性和止裂

根据断裂力学的原理, 提出了脆性破裂的止裂准则, 给出了最小止裂方程. 利用Erdogan的集中力的零频Green函数解, 分析了点力和简单分布力的位置对脆性破裂的稳定性和止裂的作用, 给出了若干典型条件下临界载荷、 失稳边界线、 止裂点的计算结果. 近距离力源引起的稳定性破裂, 对于解释一些蠕裂和构造的形成是有意义的; 不同距离力源引起的失稳破裂, 对于解释不同震级地震的发生和停止是有意义的. 强地震的发生有可能是远场力与近场力各种复合作用的结果. 本文的结果对于认识诱发地震的力学机制也有重要意义.      

Steadiness and stop of brittle fracture driven by the forces in different distances

Introduction The problem of crack stop of fault is of special importance in geosciences. This is because the risk of rupture of large scale fault is taken as the object of investigation in the geosciences. In some meaning, the stop of earthquake rupture is more important than initial because of its influ-ence on the prediction of energy releasing during the earthquake. There are quite a few of factors that cause stop of the fault. For example, the effect of barriers, the rapid healing of shea…     

Failure Mode and Spatial Distribution of Damage in Rothbach Sandstone in the Brittle-ductile Transition

— To elucidate the spatial complexity of damage and evolution of localized failure in the transitional regime from brittle faulting to cataclastic ductile flow in a porous sandstone, we performed a series of triaxial compression experiments on Rothbach sandstone (20% porosity). Quantitative microstructural analysis and X-ray computed tomography (CT) imaging were conducted on deformed samples. Localized failure was observed in samples at effective pressures ranging from 5 MPa to 130 MPa. In the brittle faulting regime, dilating shear bands were observed. The CT images and stereological measurements reveal the geometric complexity and spatial heterogeneity of damage in the failed samples. In the transitional regime (at effective pressures between 45 MPa and 130 MPa), compacting shear bands at high angles and compaction bands perpendicular to the maximum compression direction were observed. The laboratory results suggest that these complex localized features can be pervasive in sandstone formations, not just limited to the very porous aeolian sandstone in which they were first documented. The microstructural observations are in qualitative agreement with theoretical predictions of bifurcation analyses, except for the occurrence of compaction bands in the sample deformed at effective pressure of 130 MPa. The bifurcation analysis with the constitutive model used in this paper is nonadequate to predict compaction band formation, may be due to the neglect of bedding anisotropy of the rock and multiple yield mechanisms in the constitutive model.     

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.     

岩石破裂强度的温度和应变率效应及其对岩石圈流变结构的影响

研究了温度和应变率对岩石破裂强度的影响,得到了岩石圈中一些典型岩石破裂强度的新的经验规律.新的经验规律除考虑围压和标本尺度的影响外,还考虑了温度和应变率的影响,并增加了新岩石的结果,所以更能反映岩石圈内岩石破裂的真实状态.通过对鄂尔多斯平均流变结构的计算和对比研究表明：传统的忽略脆性破裂的流变模型过高地估计了流变强度,流变机制的分布也不尽合理.而考虑了脆性破裂机制的流变模型的结果表明脆性区分为两部分,浅部以摩擦滑动机制控制,深部以脆性破裂机制控制.由于新的经验规律考虑的代表性岩石更全面,并考虑了应变率的影响,得到的脆性区的范围进一步增大,流变强度进一步降低.     

True Triaxial Stresses and the Brittle Fracture of Rock

This paper reviews the efforts made in the last 100 years to characterize the effect of the intermediate principal stress σ ₂ on brittle fracture of rocks, and on their strength criteria. The most common theories of failure in geomechanics, such as those of Coulomb, and Mohr, disregard σ ₂ and are typically based on triaxial testing of cylindrical rock samples subjected to equal minimum and intermediate principal stresses (σ ₃=σ ₂). However, as early as 1915 Böker conducted conventional triaxial extension tests (σ ₁=σ ₂) on the same Carrara marble tested earlier in conventional triaxial compression by von Kármán that showed a different strength behavior. Efforts to incorporate the effect of σ ₂ on rock strength continued in the second half of the last century through the work of Nadai, Drucker and Prager, Murrell, Handin, Wiebols and Cook, and others. In 1971 Mogi designed a high-capacity true triaxial testing machine, and was the first to obtain complete true triaxial strength criteria for several rocks based on experimental data. Following his pioneering work, several other laboratories developed equipment and conducted true triaxial tests revealing the extent of σ ₂ effect on rock strength (e.g., Takahashi and Koide, Michelis, Smart, Wawersik). Testing equipment emulating Mogi's but considerably more compact was developed at the University of Wisconsin and used for true triaxial testing of some very strong crystalline rocks. Test results revealed three distinct compressive failure mechanisms, depending on loading mode and rock type: shear faulting resulting from extensile microcrack localization, multiple splitting along the σ ₁ axis, and nondilatant shear failure. The true triaxial strength criterion for the KTB amphibolite derived from such tests was used in conjunction with logged breakout dimensions to estimate the maximum horizontal in situ stress in the KTB ultra deep scientific hole.     

受压岩石裂隙相互作用导致破裂的机理

应用伪张力法，研究了在压应力状态下岩石内部任意多条随机微裂隙的相互作用和扩展聚集机理．即在受载岩石裂隙的相互作用下，形成一个裂隙较易聚集的方向，岩石的宏观破裂与此方向有关．给出了岩石宏观破裂判据，并确定了破裂面的方位．指出库仑准则所确定的初始剪切破裂方向仅为本文的一个特例．作为实例分析了雁形裂纹的形成和扩展机制．     

The micromechanics of friction in a granular layer

A grain bridge model is used to provide a physical interpretation of the rate- and state-dependent friction parameters for the simple shear of a granular layer. This model differs from the simpler asperity model in that it recognizes the difference between the fracture of a grain and the fracture of an adhesion between grains, and it explicitly accounts for dilation in the granular layer. The model provides an explanation for the observed differences in the friction of granular layers deformed between rough surfaces and those deformed between smooth surfaces and for the evolution of the friction parameters with displacement. The observed evolution from velocity strengthening to velocity weakening with displacement is interpreted as being due to the change in the micromechanics of strain accommodation from grain crushing to slip between adjacent grains; this change is associated with the observed evolution of a fractal grain structure.     

Failure Potential Evaluation in Engineering Experiments Using Load/Unload Response Ratio Method

The Load/Unload Response Ratio (LURR) method is proposed for prediction of the failure of brittle heterogeneous materials. Application of the method typically involves evaluating the external load on materials or structures, differentiating between loading and unloading periods, determining the failure response during both periods from data input, and calculating the ratio between the two response rates. According to the method, the LURR time series usually climbs to an anomalously high peak prior to the macro-fracture. To show the validity of the approach in engineering practice, we applied it to the loading and unloading experimental data associated with a two-floor concrete-brick structure. Results show that the LURR time series of the two floors consists of the damage evolution of the structure: they are at low level for most of the time, and reach the maxima prior to the final fracture. We then attempt to combine the LURR values with damage variable (D) to provide the health assessment of the structure. The relationship between LURR and D, defined as a function of Weibull stochastic distribution, is set up to provide more detailed underlying physical means to study damage evolution of the structure. The fact that the damage evolution of the structure correlates well with the variation of LURR time series may suggest that the LURR approach can be severed as a useful tool to provide the health assessment to big scale structures or ancient buildings.     

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。