Constitutive behavior and stability of frictional sliding of granite

An understanding of the frictional sliding on faults that can lead to earthquakes requires a knowledge of both constitutive behavior of the sliding surfaces and its mechanical interaction with the loading system. We have determined the constitutive parameters for frictional sliding of initially bare surfaces of Westerly granite, using a recently developed high pressure rotary shear apparatus that allows long distances of sliding and therefore a greater assurance of attaining steady state behavior. From experiments conducted at room temperature and normal stresses of 27–84 MPa several important results have been found. (1) A gouge layer 100 to 200 m thick was developed from the initially bare rock surfaces after 18 to 70 mm of sliding. (2) The steady state frictional resistance, attained after about 10 mm of sliding, is proportional to the negative of the logarithm of the sliding velocity. (3) Abrup changes in the velocity of sliding result in initial changes in the frictional resistance, which have the same sign as the velocity change, and are followed by a gradual decay to a new steady state value over a characteristic distance of sliding. This velocity weakening behavior is essentially identical with that found by several previous workers on the same material at lower normal stress. (4) Our results are well described by a two state variable constitutive law. The values of the constitutive parameters are quite similar to those found previously at low normal stress, but the characteristic distance is about an order of magnitude smaller than that found at 10 MPa normal stress with thicker layers of coarser gouge. (5) We have approximated our results with a one state variable constitutive law and compared the results with the predictions of existing nonlinear stability analysis; in addition, we have extended the stability analysis to systems possessing two state variables. With such formulations good agreement is found between the experimentally observed and theoretically predicted transitions between stable and unstable sliding. These results allow a better understanding of the instabilities that lead to earthquakes.     

The effects of sliding velocity on the frictional and physical properties of heated fault gouge

The frictional properties of a crushed granite gouge and of gouges rich in montmorillonite, illite, and serpentine minerals have been investigated at temperatures as high as 600°C, confining pressures as high as 2.5 kbar, a pore pressure of 30 bar, and sliding velocities of 4.8 and 4.8×10^–2 m/sec. The gouges showed nearly identical strength behaviors at the two sliding velocities; all four gouges, however, showed a greater tendency to stick-slip movement and somewhat higher stress drops in the experiments at 4.8×10^–2 m/sec. Varying the sliding velocity also had an effect on the mineral assemblages and deformation textures developed in the heated gouges. The principal mineralogical difference was that at 400°C and 1 kbar confining pressure a serpentine breakdown reaction occurred in the experiments at 4.8×10^–2 m/sec but not in those at 4.8 m/sec. The textures developed in the gouge layers were in part functions of the gouge type and the temperature, but changes in the sliding velocity affected, among other features, the degree of mineral deformation and the orientation of some fractures.     

Complexities of rock fracture and rock friction from deformation of Westerly granite

A series of rock friction experiments has been carried out to study the complexities in rock fracture and rock friction. Intact Westerly granite samples were loaded to shear failure in a laboratory polyaxial loading apparatus. The resultant fractured samples were reloaded to cause frictional sliding. Both polyaxial loading (₁ > ₂ > ₃ > 0) and equal confining condition (₁ > ₂ = ₃ > 0) were used. The deformation processes were monitored by macroscopic axial stress-strain, optical holography, and ultrasonic velocity measurements.Intense localized deformation along the fracture occurred very early in the loading of fractured samples. Contacts on the fracture surfaces continuously broke during loading. No acoustic velocity anomaly was observed for the fractured sample, in contrast to a 25% drop in the velocity before the failure of the corresponding intact sample. The current study and previous research suggest that the deformation localization is an important process in governing the instability of rock friction. Instability analysis of rock friction needs to include not only the deformation processes along the sliding surfaces, but also those adjacent to the fractures such as the localized deformation along the fractures observed in the current study. The instability analysis of rock friction with rate- and state-dependent friction laws does not specifically include the deformation localization adjacent to the faults and thus ignores an important class of instability as described byRudnicki (1977).A dependence of frictional strengths on the stress components normal to the sliding and in the plane of the fracture surface was observed. This dependence can be understood by considering the loading of the irregular fracture surface under polyaxial loading conditions. This observation requires the friction laws in the macroscopic scale to be modified for those cases where the three principal stresses (₁, ₂, and ₃) are significantly different.     

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.     

安宁河断层地震成核条件研究——来自天然花岗岩断层泥摩擦实验的启示

安宁河断层历史上发生过多次强震,现存的地震空区反映了其断层中部近30年来的断层闭锁和应变积累情况,是潜在的大地震危险区.本研究采用断层带内的新鲜花岗岩断层泥样品,在水热条件下开展了摩擦滑动实验,以研究安宁河断层摩擦特性和地震成核条件.实验有效正应力200 MPa,孔隙水压30 MPa,温度25~600℃,剪切滑移速率在1 μm·s^-1,0.2 μm·s^-1,0.04 μm·s^-1之间切换.实验结果显示,在100~400℃,摩擦系数随着温度的增加而增大（约0.663~0.704）,温度高于400℃时略有降低.从200℃开始,花岗岩断层泥的摩擦滑动表现出由速度强化向速度弱化转变,并随温度升高速度弱化程度增强,在600℃时仍然具有显著的速度弱化,具备地震成核条件.本研究获得的花岗岩断层发生不稳定滑动的温度范围为200~600℃,远大于已有研究中给出的350~400℃这一不稳定滑动的温度上限.本实验首次发现,在相同温度条件下花岗岩断层滑动稳定性与加载速率转变方向有关,向慢速切换或低速下（0.04 μm·s^-1）可以促进花岗岩断层由稳定滑动向不稳定滑动转变.基于本实验结果,结合川滇地区的地温梯度,推测得出安宁河断层中北段的地震成核深度为10~30 km,该断层的地震空区是断层闭锁的具体表现.

     

On a model of frictional sliding

A model of frictional sliding with anN-shaped curve for the sliding velocity dependence of the coefficient of friction is considered. This type of friction law is shown to be related to dynamic i.e., velocity dependent ageing of asperity junctions. Mechanisms of ageing for ductile (Bowden-Tabor) and brittle (Byerlee) materials, though different in nature, lead to qualitatively similarN-shaped velocity dependencies of the coefficient of friction. Estimates for the velocities limiting the range of negative velocity sensitivity of the coefficient of friction are obtained for the ductile case and—albeit with a lesser degree of reliability—for the brittle one. It is shown by linear stability analysis that discontinuous sliding (stick-slip) is associated with thedescending portion of theN-shaped curve. An instability criterion is obtained. An expression for the period of the attendant relaxation oscillations of the sliding velocity is given in terms of the calculated velocity dependence of the coefficient of friction. It is suggested that the micromechanically motivated friction law proposed should be used in models of earthquakes due to discontinuous frictional sliding on a crustal fault.     

Rupture and particle velocity during frictional sliding

Summary Laboratory measurements of rupture and particle velocity are in surprisingly good agreement with seismic values, providing further evidence that stick-slip friction is a suitable mechanism for shallow earthquakes. A simple theory is developed to explain the linear relationship observed between average particle velocity and stress drop for stick-slip events. Both stick-slip ruptures and cracks in brittle material commonly propagate at velocities roughly comparable to theS wave velocity of the material. Rupture normally begins relatively slowly and accelerates to a steady velocity in a few centimeters. Observations suggest that stick-slip ruptures can propagate atS wave speeds or occasionally greater and that cracks in pre-stressed glass can also propagate faster than theS waves. Fracture and thus rupture velocity of intact rock specimens is greatly influenced by the inhomogeneous structure of rock. Fracture may be modeled by coalescence of many cracks rather than growth of a single crack.Lamont-Doherty Geological Observatory Contribution No. 2627.     

Dependence of reaction rate of pyrite oxidation on temperature, pH and oxidant concentration

Pyrite is a common sulfide mineral, particularly abundant in mining waste. It is a focus of mine envi-ronmental concern because the oxidation of exposed pyrite may lead to acid drainage and poisonous mate-rials (like As and heavy metals) release. In the United States, approximately $1000000 per day is spent in alleviating acid mine drainage[1], while the Canadian mining community has environmental liabilities that exceed $2 billion for disposal, management, and rec-lamation of mine waste[2]. …     

Effect of displacement rate on the real area of contact and temperatures generated during frictional sliding of Tennessee sandstone

Summary The real area of contact has been determined, and measurements of the maximum and average surface temperatures generated during frictional sliding along precut surfaces in Tennessee sand-stone have been made, through the use of thermodyes. Triaxial tests have been made at 50 MPa confining pressure and constant displacement rates of 10^–2 to 10^–6 cm/sec, and displacements up to 0.4 om. At 0.2 cm of stable sliding, the maximum temperature decreases with decreasing nominal displacement rate from between 1150° to 1175°C at 10^–2 cm/sec to between 75° to 115°C at 10^–3 cm/sec. The average temperature of the surface is between 75 and 115°C at 10^–2 cm/sec, but shows no rise from room temperature at 10^–3 cm/sec. At 0.4 cm displacement, and in the stick-slip mode, as the nominal displacement rate decreases from 10^–3 to 10^–6 cm/sec, the maximum temperature decreases from between 1120° to 1150°C to between 1040° to 1065°C. The average surface temperature is 115° to 135°C at displacement rates from 2.6×10^–3 to 10^–4 cm/sec.With a decrease in the displacement rate from 10^–2 to 10^–6 cm/sec, the real area of contact increases from about 5 to 14 percent of the apparent area; the avergge area of asperity contact increases from 2.5 to 7.5×10^–4 cm². Although fracture is the dominate mechanism during stick-up thermal softening and creep may also contribute to the unstable sliding process.     

镜质体反射率与最高温度及其附近温度变化率的关系——几种镜质体反射率计算模型的比较

对常用的Waples、Middleton及Easy%Ro模型,通过蒙特卡罗方法,得到了相应的简化模型.所有简化模型均表明镜质体反射率(Ro)主要受控于最高温度(Tmax),并且与最高温度附近的温度变化率(Hr)有关.通过对简化模型的比较发现：(1)相对于Easy%Ro模型而言,Waples、Middleton模型对Hr的变化更为敏感;(2)总的来讲,达到相同的Ro值Middleton模型需要的温度最高,Easy%Ro模型其次,Waples模型需要的温度最低.在一定条件下,根据简化模型,利用实测的lnRo-H数据可以求取地层经历的最高温度及相应的地温梯度、热流和时间.实例分析表明岩石热导率等数据的准确性直接影响Ro解释的结果,但这种影响容易分析,而Hr的不确定性则导致多解性.     

Wall building stiffness and strength effect on content sliding in Wellington seismic conditions

A numerical study of unobstructed content sliding within several low‐to‐midrise reinforced concrete cantilever wall buildings designed to Wellington conditions in New Zealand is performed to validate the belief that increasing a building's strength and/or stiffness would result in more severe sliding response. It was shown that contents within stronger buildings experienced larger sliding response. If the building was designed to be strong, the sliding response of contents with a friction coefficient of 0.1 was smaller in stiffer buildings compared with those in flexible buildings. However, the trends start reversing with an increase in friction coefficient or a decrease in building strength. Overall, content sliding is not necessarily more severe in stiffer buildings, and in many cases, the opposite is true. This study's findings were compared against an existing parametric equation for estimating the maximum sliding displacement. This equation, which was originally derived for contents located within elastic frame buildings, was found to be more efficient than considering total floor accelerations alone but was underconservative by a mean of 17% for yielding multistorey buildings. A design procedure considering content sliding using the parametric equation and an example are provided. Copyright © 2016 John Wiley & Sons, Ltd.     

Seismic velocity changes during fracture and frictional sliding

Fracture and frictional sliding are considered as phenomena involving brittle failure. Brittle failure is preceded by the formation of small (subcritical) cracks. In non-water-saturated rock, the distribution, shape and size of these suberitical cracks determine the change in the physical properties prior to failure. A model is proposed which suggests that the spatial and temporal distribution, shape and size of subcritical cracks within a stressed rock depend upon the rate of deformation and the volatile content.As a rock is stressed beyond about 50 percent of its ultimate failure stress, dilatancy is initiated. With increasing stress a broad zone of cracks develops within the dilatant region. The seismic velocities through this zone decrease markedly and the cracks grow more numerous., changing in size and shape. Before brittle failure of the rock occurs, the subcritical cracks interact, leading to a concentration of the zone. During the stage when the zone narrows, the seismic velocities in crease in the surrounding volume due to local rotation of stresses and consequent closure of some cracks. In most laboratory experiments the stage during which the velocity increases and the now intense deformation zone becomes narrow is very short and difficult to observe experimentally. At very low strain rates and with volatiles present, the crack growth and subsequent interaction lead to the narrowing of the intense deformation zone and therefore to an observable increase in velocity.The above is based upon an interpretation of a number of experiments. Using optical holography we have observed the development and subsequent intensification of a deformation zone. Ultrasonic velocity measurements showed a distinct anomaly (decrease followed by an increase) before failure. The anomaly was only detectable at our lowest experimental strain rates (3×10^–8/sec).     

上地幔剪切波各向异性约束下的中国大陆岩石圈底部的剪切拖曳力和应变率

地幔对流在岩石圈底部产生的剪切拖曳力和应变率的估计有助于理解和认识板块构造运动、岩石圈变形特征和应力分布格局、地壳长期运动状态和克拉通演化的深部动力学环境,但准确地估计它们是一个挑战.本文利用核相剪切波分裂各向异性约束下获得的全球和区域地震速度结构"耦合"的地幔对流模型计算了中国大陆岩石圈底部的剪切拖曳力和应变率.结果...     

应变率对钢筋混凝土柱动态特性的影响

文中以OPENSEES有限元软件为工具,利用基于柔度法的钢筋混凝土柱纤维单元,考虑钢筋与混凝土材料的应变率效应,对钢筋混凝土柱进行了动态响应分析,并用试验结果验证了文中方法的正确性.通过数值模拟,研究了钢筋混凝土柱在不同轴压比、不同混凝土强度、不同纵筋率条件下的动态力学特性.结果表明,随着轴压比的提高,钢筋混凝土柱的应...     

断层形变趋势变化研究--垂直形变趋势累积率Dc值

通过对跨断层测量特点的分析,提出断层运动中趋势性成分具有反映区域地壳形变及应变能累积程度的意义。据此建立形变趋势累积率的概念,推导了相应的计算公式并对其性质及物理意义作了初步解释。震例计算表明,该指标能够反映区域地壳的背景活动强度,对中强地震亦具有较强的敏感性。具有一定的实用价值     

Application of the Pi theorem to the wear rate of gouge formation in frictional sliding of rocks

A simple law of wear rate is examined for the process of gouge generation during the frictional sliding of simulated faults in rocks, by use of the Pi theorem method (dimensional analysis) and existing experimental data. The relationship between wear rate (t/d) and the applied stress can be expressed by the power-law relations $$\frac{t}{d} = C_\sigma \sigma ^{m\sigma } ,\frac{t}{d} = C_\tau \tau ^{m\tau }$$ wheret is the thickness of the gouge generated on the frictional surfaces,d is the fault displacement, σ and τ are normal stress and shear stress, respectively, andC _σ,C _τ,m _σ andm _τ are constants. These results indicate that the exponent coefficientsm _σ andm _τ and the coefficientsC _σ andC _τ depend on the material hardness of the frictional surfaces. By using the wear rates of natural faults, these power-law relationships may prove to be an acceptable palaeopiezometer of natural faults and the lithosphere.     

Volume changes during fracture and frictional sliding: A review

Summary Volume changes in geologic materials have been measured with strain gauges, cantilever displacement gauges, or through observation of either pore or total volume. When porosity is less than 0.05, compaction is small or absent; apart from elastic strains in the minerals, dilatancy predominates, beginning at 50 to 75 percent of the fracture stress difference. When initial porosity exceeds about 0.05, compaction and dilatancy may overlap. The onset of dilatancy has not been identified, but most of the dilatancy occurs within about 10 percent of the fracture stress difference. In low porosity rocks, dilatancy increases initial porosity by a factor of 2 or more; in porous rocks or granular aggregates the increase is only 20 to 50 percent. However, the actual pore volume increase is larger in rocks of high initial porosity. Hence, earthquake precursors which depend on the magnitude of dilatancy should be more pronounced in porous rocks or in fault gouge. In contrast, precursors which are based on fractional changes in some porosity-related property may be more pronounced in rocks of low initial porosity. Future work is particularly needed on constitutive relations suitable for major classes of rocks, on the effects of stress cycling in porous rocks, on the effects of high temperature and pore fluids on dilatancy and compaction, and on the degree of localization of strain prior to fracture.     

Electrical resistivity changes in rocks during frictional sliding and fracture

Significant changes of electrical resistivity of saturated rocks and water pressure along sliding surface occurred during stick-slips in our direct shear experiment. Two types of changes of electrical resistivity occurred. In the first, resistivity decreased with increasing shear stress, reached minimum together with a sudden release of shear stress and returned to a higher value immediately afterwards. In the second, resistivity again decreased with increasing stress but, in contrast to the first type of changes, it decreased further upon the sudden drop of shear stress. The magnitude and the direction of the changes of water pressure on the sliding surface during stick-slip were not uniform, indicating local variations of surface deformation.     

First passage of a sliding rigid structure on a frictional foundation

The first passage problem for a sliding rigid block on a frictional foundation, subjected to Gaussian white noise through the foundation, is studied. A well-posed boundary value problem is formulated from Markov process theory and solved for the ordinary moments of time to first passage by the finite element method. A range of parameters is studied representing a simple seismic base isolation system. Results of Monte Carlo simulation are given for comparison.     

Mantle tomography and its relation to temperature and composition

We propose a new method to constrain lateral variations of temperature and composition in the lower mantle from global tomographic models of shear- and compressional-wave speed. We assume that the mantle consists of a mixture of perovskite and magnesio-wüstite. In a first stage, we directly invert V_P and V_S anomalies for variations of temperature and composition, using the appropriate partial derivatives (or sensitivities) of velocities to temperature and composition. However, uncertainties in the tomographic models and in the sensitivities are such that variations in composition are completely unconstrained. Inferring deterministic distributions of temperature and composition being currently not possible, we turn to a statistical approach, which allows to infer several robust features. Comparison between synthetic and predicted ratios of the relative shear- to compressional-velocity anomalies indicates that the origin of seismic anomalies cannot be purely thermal, but do not constrain the amplitude of the variations of temperature and composition. We show that we can estimate these variations using histograms of the relative V_P and V_S anomalies at a given depth. We computed histograms for a large variety of cases and found that at the bottom of the mantle, variations in the volumic fraction of perovskite from −14 to 10% are essential to explain seismic tomography. In the mid-mantle, anomalies of perovskite are not required, but moderate variations (up to 6%) can explain the observed distributions equally well. These trade-offs between anomalies of temperature and composition cannot be resolved by relative velocity anomalies alone. An accurate determination of temperature and composition requires the knowledge of density variations as well. We show that anomalies of iron can then also be resolved.