The effect of normal stress on the real area of contact during frictional sliding in rocks

The real area of contact during frictional sliding has been determined as a function of changing normal stress in triaxial experiments through the use of thermodyes. Utilizing the technique, described by Teufel and Logan in 1978, with saw-cut surfaces inclined 35° to the load axis, determinations were made for monolithologic sliding of Tennessee sandstone and Indiana limestone and dilithologic sliding of the same rocks. Confining pressures to 200 MPa were investigated at a constant shortening rate of 10^–2 mm/sec and at room temperature. Direct measurements were made of single-asperity areas and the asperity density. The product of these measurements gives the percent area of real contact across the sliding surface. Single-asperity area and density are found to remain relatively constant during the displacement. Single-asperity areas are in the ranges of 0.4 to 6×10^–2 mm² for sandstone, 0.8 to 2×10^–2 mm² for limestone, and 0.2 to 24×10^–2 mm² for sandstone sliding against limestone. These values are smaller than the grain size of either rock. The values increase with increasing normal stress for both monolithologic and dilithologic sliding. In sandstone the asperity density increases from about 0.8 to 2.75 contacts per square millimeter in a logarithmic fashion. Monolithologic limestone has values of about 0.9 contacts per square millimeter and does not show significant change with increasing normal stress. The percent area of real contact increases in all cases, with average maximum values of 16% of the apparent area at a normal stress of 374 MPa in sandstone, 18% at 25 MPa in limestone, and 22% at 123 MPa in the dilithologic specimens. The normal stress recalculated for the real area of contact approaches the unconfined compressive strength for sandstone and limestone.     

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.     

Aspects of asperity-surface interaction and surface damage of rocks during experimental frictional sliding

Summary Mechanisms for the dissipation of energy during the frictional sliding of rocks includes brittle fracture, plastic deformation, frictional heating, and elastic distortion. The first three energy sinks are manifested by surface damage during frictional sliding. Normal load, temperature, and the velocity of the sliding surfaces as well as surface roughness and hardness all influence the nature of surface damage which includes the generation of structures such as wear grooves, gouge, and welded particles.Lamont-Doherty Geological Observatory Contribution No. 2620.     

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.     

基于中速-高速摩擦实验研究含碳断层带的电导率特征

野外地质调查结果显示,断层带常富集碳质.断层带中碳的分布结构是影响断层带电导率特征的一种重要参数.本文在室温、室内湿度和2 MPa正应力条件下,对不同石墨含量（3,5,6和7 wt%）的石英-石墨混合断层泥模拟样品开展了滑动速率介于500 μm·s^-1~1 m·s^-1的摩擦实验及相应的电导率测量,以期研究断层运动对碳分布结构的影响以及断层带电性特征对碳含量及分布的响应情况.结果显示,摩擦滑动能够显著地改变样品的电性特征（电导率大小及其各向异性）.在平行滑动面方向（径向）,样品电导率随着滑动位移的增加快速增加,在滑动约数十厘米之后,其电导率基本达到稳定状态;在垂直滑动面方向（轴向）,样品电导率基本不随摩擦滑动速率和滑动距离而变化.SEM显微结构观测显示,摩擦滑动所引起的电导率各向异性直接反映了石墨分布结构的变化.该研究结果深化了对地震断裂带浅部电性特征的认识,为野外断层带大地电磁测深资料的解释提供了约束,同时对于了解含碳断层的力学性质和弱矿物相在剪切变形中的分布特征及其演化过程等方面也具有重要意义.

     

Effects of pore fluid chemistry on stable sliding of Berea sandstone

Single-cycle and multiple-cycle frictional-sliding experiments were employed to evaluate the effects of pore fluid environments on yield strength, frictional-sliding dynamics, and gouge production and morphology. Circular right cylinders cored from Berea sandstone sawcut at 35° to the axes were saturated in water, an inorganic brine, and various anionic, cationic, and nonionic aqueous surface-active agents. Samples were deformed under an effective confining pressure of 50 MPa and an axial strain rate of 6×10^–5 sec^–1 until a 2% axial strain beyond yield (defined as the onset of sliding) was achieved. All samples were displaced by stable sliding. In the single-cycle tests the unsaturated and water-saturated samples displayed small stress peaks at yield. During stable sliding samples saturated with DTAB and SDS displayed slight increases in differential stress and statistically significant higher frictional coefficients than other environments (including water) but were very similar in behavior to dry, unsaturated samples. In the multiple-cycle tests, samples were loaded to 2% strain beyond yield and unloaded to a differential stress of approximately 5–10 MPa a total of four times. These results further suggest that DTAB exerts a strengthening effect on the sandstone relative to water which, to a limiting value, increased with displacement. The DTAB and SDS environments also produced a coarser grain-size distribution in the gouge relative to gouge produced in the other environments. Investigation of the gouge by scanning electron microscope revealed that these larger grains were composed of dense, apparently cemented aggregates of ultrafine, platy quartz particles.     

Effects of temperature and sliding rate on frictional strength of granite

Layers of artificial granite gouge have been deformed on saw-cut granite surfaces inclined 30° to the sample axes. Samples were deformed at a constant confining pressure of 250 MPa and temperatures of 22 to 845°C. The velocity dependence of the steady-state coefficient of friction (^ss) was determined by comparing sliding strengths at different sliding rates. The results of these measurements are consistent with those reported bySolberg andByerlee (1984) at room temperature andStesky (1975) between 300 and 400°C. Stesky found that the slip-rate dependence of (^ss) increased above 400°C. In the present study, however, the velocity dependence of (^ss) was nearly independent of temperature.     

硬石膏断层带摩擦稳定性转换与微破裂特征的实验研究

断层带摩擦稳定性转换及其对应的微破裂特征对于地震成核条件和慢地震机理研究具有重要的意义.本文利用双轴实验装置研究了硬石膏断层带摩擦稳定性的转换及其对应的应变变化、微破裂特征,并分析了实验标本的微观结构.实验结果表明,σ2和加载点速度对断层滑动稳定性具有显著影响.在低σ2条件下,硬石膏断层带出现不稳定滑动,变形以局部化的脆性破裂和摩擦为主;随σ2的增加,断层由不稳定滑动向稳定滑动转换,断层带变形方式逐渐转变为分布式的破裂.在低σ2条件下,硬石膏断层带在较低加载点速度下表现为速度强化且滑动稳定,在中等加载点速度下表现为速度弱化并伴有准周期性的黏滑,在较高加载点速度下又有转向速度强化的趋势,σ2的提高使得速度弱化的范围逐渐减少,滑动趋于稳定.上述两次转换对应不同的微破裂特征,在较高速度下从速度弱化转换为速度强化时,断层滑动伴有能量较小但频度很高的微破裂活动,而在较低速度下从速度弱化转换为速度强化时,断层滑动伴有间歇性的微破裂,这与断层带的微观结构特征有较好的对应关系,表明其转换机制是不同的.     

流体对石灰岩断层摩擦滑动影响的实验研究

在气体介质三轴高温岩石力学实验仪器上,采用意大利Scaglia Bianca石灰岩,在温度50~300℃、围压150 MPa,含50 MPa孔隙压、无孔隙压含饱和水和完全干燥三种条件下,开展摩擦滑动实验.实验力学数据和显微结构表明,完全干燥样品在120℃时出现慢滑移,实验样品中没有出现溶解与沉淀.无孔隙压含饱和水条件下,100℃、120℃、150℃条件下出现典型的慢滑移,实验样品中含有微弱的溶解与沉淀;300℃条件下出现黏滑,实验样品中出现沉淀.在含50 MPa孔隙压条件下,50℃时的实验表现为典型的稳滑,实验样品中以溶解为主;在100~150℃时,出现慢滑移,实验样品中以溶解为主,沉淀为辅;在200~300℃时,出现典型黏滑,实验样品中以沉淀为主.实验结果表明,石灰岩断层泥摩擦滑动稳定性随温度变化,受流体中碳酸钙的溶解和沉淀作用控制,因此,流体中矿物质的饱和度这一化学性质对断层带的摩擦强度和摩擦滑动稳定性具有显著影响.

     

正应力扰动对断层滑动失稳影响的实验研究

利用双轴伺服控制加载装置,采用三块花岗闪长岩标本组成的含有两个滑动面的直剪结构,开展了摩擦滑动实验.实验中通过在垂直滑动面的载荷上叠加正弦波状和方波状的扰动,研究了正应力扰动对断层黏滑失稳的影响.研究表明,在恒定的正应力和位移速率下,标本表现为规则的黏滑,叠加正应力扰动后,随扰动振幅的增加黏滑发生时间与扰动的相关性增大,黏滑应力降和时间间隔的分布趋于离散.黏滑应力降和时间间隔的平均值随平均正应力的增加呈线性增长,扰动叠加后黏滑应力降的离散度随平均正应力的增加而增大;黏滑应力降和时间间隔主要受应力变化幅度的影响,而与应力变化的速率关系不大.剪应力和正应力扰动都会对断层黏滑失稳产生影响,而正应力扰动的影响更明显.这两种扰动对断层黏滑失稳影响的机制存在差异,剪应力扰动只是改变断层滑动的推动力,而正应力扰动则改变了断层面上凹凸体的接触状态.     

摩擦状态-速率依从的区域地震触发模型研究

设计一个具有摩擦状态-速率依从机制模拟大地震后区域触发地震的模型, 该模型由一定数量表示地震成核断层的函数组成。 大震对区域静应力场的影响由应力阶跃载荷表现, 利用摩擦状态-速率依从的一维自由度弹簧滑块模型结果计算地震发生时间提前。 结果表明, 施加幅度为地震应力降几十分之一至百分之一的应力阶跃, 可以引起地震发生速率的明显变化, 该变化通过统计检验, 与大地震后的区域触发地震活动相似。     

长白山天池火山西南麓水压致裂法地应力测量及其实测数据在断裂稳定性分析中的应用

长白山天池火山是一座新生代多成因复合火山, 其活动性一直受到地学界的高度重视.而地应力测量数据对于了解火山的活动情况等具有重要意义, 但目前长白山天池火山地区实测地应力资料较少.为了更准确地了解长白山天池火山地区现今地应力状态及断裂稳定性, 在长白山天池火山西南麓MJZ测点0~300 m孔深开展了水压致裂法地应力测量.利用此次实测地应力数据, 本文首先分析了该地区地壳浅表层应力状态, 结果表明: ①测区以水平构造应力为主导, 应力值与其他地区相比, 相对较低; ②S_H(最大水平主应力)、S_h(最小水平主应力)和S_v(垂向主应力)均随深度增加而基本呈线性增大趋势; 在60~180 m深度, 三者展现为逆断层应力状态, 即S_H＞S_h＞S_v; 在180~300 m, 则表现为S_H＞S_v＞S_h, 该应力关系有利于走滑断层活动; ③钻孔上部S_H方向为N38°E, 与东北地区构造应力场方向基本一致.钻孔下部由于受区内NW向断裂和其他因素影响, 存在与区域主应力方向有偏差的局部应力场.其次, 基于实测应力数据, 应用库仑摩擦滑动准则, 并取摩擦系数为0.6和1.0, 初步评价了区域断裂的稳定性.结果显示, 研究区现今应力状态尚未达到断裂失稳滑动水平, 推测测区断裂目前相对稳定.结合其较低的应力积累水平, 一定程度上反映出长白山天池火山区目前没有明显活动, 地壳总体是稳定的.本文的研究结果可为长白山天池火山的活动性、地震地质等研究提供地应力方面的基础数据, 同时也为测区地质环境安全评价提供参考依据.

     

考虑支座摩擦滑移及结构碰撞的非规则人字形桥梁地震响应分析

针对非规则人字形桥梁在地震作用下灾变严重的问题,以一座非规则人字形桥梁为研究对象,建立其空间分析模型,研究综合考虑支座摩擦滑移、结构碰撞对非规则人字形桥梁地震响应的影响。结果表明:邻梁间的碰撞作用可使得桥梁墩顶位移及内力相比不考虑时有所减小,但同时也使梁体产生了较大的加速度脉冲效应;当考虑支座摩擦滑移和结构碰撞时,固定墩墩顶位移和邻梁相对位移峰值有一定程度增大,然而对梁体加速度脉冲效应结果影响并无统一规律;纵向地震波作用下,非规则人字形桥梁不仅存在顺桥向的碰撞,横桥向的碰撞响应也不容忽视。非规则人字形桥梁进行抗震设计计算时应选取符合实际情况的计算模型,考虑支座摩擦滑移及结构间的碰撞。     

Comprehensive study on stability of deep crust and unstable behavior of earthquake source by both failure mechanism and frictional sliding mechanism

In this paper the relation between fault movement and stress state in deep crust is discussed, based on synthetic analysis of the crustal stresses measured over the world and the concerned data of focal mechanism. Using Coulomb criterion for shear failure and frictional slip, analytical expressions for estimating stabilities of intact rock and existing fault in the crust and for identifying the type of faulting (normal, strike-slip or thrust fault) are derived. By defining the Failure FunctionF _m and the Fraction FunctionF _f, which may describe steadiness of crustal rock and existing fault, respectively, a synthetic model is set up to consider both fracturing mechanism and the sliding mechanism. By this model, a method to study stability and unstable behavior of crustal rock and fault at different depths is given. According to the above model, quantitative study on the crustal stability in the North China plain is made in terms of the measured data of hydraulic fracturing stress, pore-fluid pressure, terrestrical heat flow in this region. The functionsF _m andF _f and the shear stresses on faults with different strike angle and dip angle at various depths in this region are calculated. In the calculation the constraint condition of fault movement obeys Byerlee’s Law, and the depth-dependent nonlinear change in the vertical stress due to inhomogeneity of crustal density and the high anomalous pore-fluid pressure in deep crust of this region are considered. The conclusions are: the unstable behavior of the crust in the North China plain is not failure of crustal rock but slip on existing fault; the depth range where stick-slip of fault may happen is about from 8 to 20 km or more; stability of steep fault is lower than that of gentle sloping fault; the shear stresses in the range where may occur stick-slip are nearly horizontal; the steep faults trending from NNE to NE in this region are liable to produce strong earthquakes, whose co-seismic faultings are, for the most part, right lateral slip; the change in pore-fluid pressure in depth remarkably affects the stability of the crust and the increase in pore-fluid pressure, therefore, would be an important factor exciting strong earthquake in this region. The above theoretical inferences are consistent with the data measured in this region. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologia Sinica,13, 450–461, 1991. This work is supported by Chinese Joint Seismological Science Foundation.     

村镇滑移隔震建筑瞬时摩擦耗能的参数敏感性分析

给出了村镇滑移隔震建筑瞬时摩擦耗能的概念,并以此概念为响应指标。通过极差大小的对比,分析了该响应指标对刚度比、第二阶段刚度系数、隔震层屈服位移、隔震层摩擦系数、系统质量比和上部结构自振周期六个参数变化的敏感程度,阐述了上述系统参数对瞬时摩擦耗能这一响应指标的影响规律。研究表明:场地条件和地震动幅值大小对瞬时摩擦耗能均有显著影响;在所考虑的参数范围内,上部结构自振周期总是对瞬时摩擦耗能有较为显著的影响,摩擦系数对瞬时摩擦耗能的影响跟场地条件有关,Ⅰ类场地条件中摩擦系数对瞬时摩擦耗能影响不显著,而Ⅱ、Ⅲ和Ⅳ类场地条件中,摩擦系数对瞬时摩擦耗能的影响则非常显著;隔震层屈服位移、刚度比和第二阶段刚度系数总得来讲对瞬时摩擦耗能影响不显著,质量比对瞬时摩擦耗能影响居中。     

滑坡的摩擦力与正压力力偶的地震波场模拟

滑坡的地震波反演是确定滑坡动力学过程的有效途径.然而,目前的滑坡地震波反演大多基于点源模型,将滑坡面近似为点源,仅考虑滑体作用于滑床的摩擦力及其变化.但实际滑坡过程中,由于重力和滑动距离的存在,滑床还受到一个逐渐增加的正压力力偶作用.为定量探讨这一正压力力偶对滑坡地震波场的贡献,我们基于有限滑坡面模型,分别正演模拟了滑坡过程中摩擦力和正压力力偶的地震波场,得到了正压力力偶地震波场在整个滑坡地震波场中的能量比例及其随距离的变化.研究发现,正压力力偶地震波场具备近场项衰减特征,相较于摩擦力波场随距离衰减更快.正演模拟显示,正压力力偶地震波场在滑坡尺度2~3倍距离范围内较为显著;但在更远距离上,由于其幅度大致随距离的平方衰减,其贡献几可忽略.此外,正压力力偶波场在波形特征上与摩擦力波场也存在明显区别,二者的相对大小与摩擦系数和坡度等参数密切相关.本文模拟分析表明,完整的滑坡近场地震波场应该同时考虑摩擦力和正压力力偶的贡献;滑坡动力学参数反演中,利用近场地震波记录,考虑有限尺度的滑坡面,原则上我们不仅可以确定传统滑坡动力学参数,还有可能确定摩擦系数和流体压力等参数在空间上的变化分布.

     

竖向地震动对滑动摩擦隔震桥梁结构地震反应的影响

利用接触摩擦单元建立了滑动摩擦隔震桥梁支座在竖向地震动作用下的有限元模型,通过算例讨论了竖向地震动对不同支座摩擦系数和不同刚度(墩径)滑动摩擦隔震桥梁地震反应的影响,初步探讨了竖向地震动的激励方向对分析结果的影响,分析结果表明,竖向地震动对滑动摩擦隔震桥梁结构的地震反应有较大的影响,在竖向地震动较为明显地区的滑动摩擦隔震桥梁结构设计时,应予以考虑。     

摩擦生热对断层演化过程的影响:Ruina-和Chester-Higgs-模型的对比分析

利用速率-状态摩擦定律（Rate-and State-Dependent Friction Law：简称RSF定律）,结合McKenzie-Brune摩擦生热模型,本文分别从Ruina提出的RSF定律和Chester-Higgs提出的RSF定律出发,通过一维弹簧-滑块模型,采用四阶变步长的Dormand-Prince算法,对断层演化过程进行了数值模拟,探讨了摩擦生热对断层演化进程的影响.模拟结果显示,与Ruina-模型相比,Chester-Higgs-模型在断层高速滑动时存有更大的摩擦强度,表明摩擦生热对断层具有一定的强化作用,且同临界滑移距离的取值相关.而且,Chester-Higgs-模型在失稳时的断层面温度远远低于Ruina-模型,表明摩擦生热在断层演化过程中能抑制断层面温度的剧烈升高,且正应力和临界滑移距离越大,两种模型的温差越为明显,而断层的刚度和尺度则对温度的影响很小.模拟两种模型周期演化过程的结果表明,在相同的初始条件下,Chester-Higgs-模型给出的断层失稳周期明显比Ruina-模型更短,说明摩擦生热对断层自身演化最显著的影响是较大地缩短了地震重复发生周期.当断层进入周期性演化后,Chester-Higgs-模型给出的摩擦强度大于Ruina-模型,且对第一次非周期性失稳的摩擦强度和剩余应力的继承性更好.另外,由Chester-Higgs-模型给出的静态应力降远小于Ruina-模型给出的结果,所对应的单个事件的滑移量也小于Ruina-模型.

     

岩盐断层带黏滑及稳滑过程中声发射活动特征的初步分析

本文利用双轴摩擦实验对含水条件下岩盐断层带摩擦滑动性状进行了实验研究, 观测和分析了摩擦滑动过程中的声发射活动, 并利用扫描电镜分析了断层带的微观变形结构.结果表明, 含水岩盐断层带在伴随黏滑的速度弱化域和伴随稳定滑动的速度强化域, 摩擦过程中均产生了大量声发射事件; 黏滑过程与稳滑过程中的小声发射事件存在共同之处, 即两者均表现为能级低; 但黏滑过程中的小声发射事件的优势频率既有低频(10 kHz左右)和中频(100 kHz左右), 也有高频(370 kHz左右), 而在稳定滑动过程中, 小声发射事件的优势频率仅有低频和中频, 缺少高频事件.这种差异与两者变形主导机制的不同密切相关.在断层黏滑循环中, 接近摩擦峰值时声发射发生率明显增加, 但高频事件减少、中频和低频事件增加; 进入亚失稳阶段后, 声发射只有低频和中频信号, 几乎不再出现高频信号.这种差异与断层带变形方式的变化密切相关.

     

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.