大理岩试件中裂缝的逆向共轭剪破裂

本文介绍了以激光全息干涉法观测单轴压缩下,大理岩岩样表面的变形位移场。全息干涉图可以反映出由于岩石内部微裂隙丛集激增所导致的变形局部化,实验采用板状大理岩试件,在中心处预制了不同角度的裂缝,实验在MTS伺服压机中加载直至宏观破坏,观测了裂隙的发展过程。实验表明:当裂缝角小于45时,先在裂缝尖端处的张应力集中部位出现新裂纹,它的起裂角(与原裂缝的交角)90,裂纹弯向压力方向并趋于稳定。当>45时,在上述张裂纹稳定后,在裂缝尖端附近再次发生张裂,其起裂角60,同样弯向压力方向后稳定。在这些前期张破裂稳定后,在张裂的相反方向,也即裂缝的共轭方向上,出现内部微裂隙的丛集,并随后发生宏观的剪破坏,我们认为此逆向剪切破坏与大理岩的多晶组构有关,与应变弱化过程中变形和应力的调整有关。      

岩石裂纹附近的变形局部化与破坏——激光全息干涉法的应用

本文介绍了应用激光全息干涉法观测单轴压缩条件下裂纹附近的离面位移场和岩石的变形破坏过程。着重指出了裂纹构造活动与微裂隙丛集发育的变形局部化前兆在这种破坏过程中的相互关联,并就其所反映的震源物理本质进行了讨论。     

Modeling of strain dependency of shear modulus and damping of clayey sand

A series of cyclic triaxial tests on clayey sands was carried out and attempts were made to evaluate the strain dependency of shear modulus and damping. Strain dependencies of shear modulus and damping were simply modeled. It was shown that the change in the effective confining stress with loading cycles in the undrained shear test needed to be considered particularly in the large strain range. The consideration could be made by normalizing G with G′₀=AF(e)(σ′_m/σ_mr)ⁿ, the initial shear modulus for the effective confining stress of that particular loading cycle, instead of using G₀. G/G′₀ was expressed by a function of γ as G/G′₀=1/(1+b_gγ) which was almost stress level independent for clayey sands used in this study. The damping ratio was not much affected by the confining stress. The strain dependency of the damping ratio was modeled by h=a_hγ/(1+b_hγ). Effects of load irregularity on the shear modulus were also investigated. The excess pore pressure and the residual strain were generated especially when the major peaks in the irregular loading were applied to the specimen. However, G/G′₀ for the irregular loading could be represented reasonably well by the average curve for the uniform cyclic loading, if the excess pore water pressure and the residual strain were taken into account.     

Fault dimensions,displacements and growth

Maximum total displacement (D) is plotted against fault or thrust width(W) for 65 faults, thrusts, and groups of faults from a variety of geological environments. Displacements range from 0.4 m to 40 km and widths from 150 m to 630 km, and there is a near linear relationship betweenD andW ². The required compatibility strains (e _s) in rocks adjacent to these faults increases linearly withW and with and ranges frome _s=2×10^–4 toe _s=3×10^–1. These are permanent ductile strains, which compare with values ofe _s=2×10^–5 for the elastic strains imposed during single slip earthquake events, which are characterised by a linear relationship between slip (u) andW.The data are consisten with a simple growth model for faults and thrusts, in which the slip in successive events increases by increments of constant size, and which predicts a relationship between displacement and width of the formD=cW ². Incorporation of constant ductile strain rate into the model shows that the repreat time for slip events remains constant throughout the life of a fault, while the displacement rate increases with time. An internally consistent model withe _s=2×10^–5, giving repeat times of 160 years and instantaneous displacement rates of 0.02 cm/yr, 0.2 cm/yr, and 2.0 cm/yr when total displacement is 1 m, 100 m, and 10 km, and slip increasing by 0.5 mm with each event, gives a good approximation of the data. The model is also applicable to stable sliding, the slip rate varying with ductile strain rate and withW ².     

The chemical anomalous behaviors of water-marble rock system under action of ultrasound

By the experiment, it is confirmed that water-marble rock system shows obviously chemical anomalous behaviors: the relevant minerals which formed marble rock are resolved fast, water becomes alkaline, meanwhile H₂ emission appears under action of ultrasound; based on rock identification by microscope and chemical analysis of water and rock, the mechanism of above chemical reaction is analyzed and discussed. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,15 498–507, 1993. This study was supported by the Chinese Joint Seismological Science Foundation.     

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.     

Nonlinear behavior of high-damping rubber bearings under horizontal bidirectional loading: full-scale tests and analytical modeling

Horizontal bidirectional loading tests are conducted for real-sized high-damping rubber (HDR) bearings with diameters of 700 mm (HDR700) and 1300 mm (HDR1300). The hysteresis loops of these bearings under bidirectional horizontal loadings are compared with those under unidirectional loadings. The results show that the bearing force measurement in the primary direction of loading increases when there is displacement in the orthogonal direction. Unusually, the maximum restoring force in the orthogonal direction to the primary loading direction occurs near zero displacement. On the basis of the observations of the restoring forces, a rate-independent model is proposed. This model simulates well the test results under both bidirectional loading and unidirectional loading. It can reproduce the irregular restoring forces characteristics around zero displacement as described above. Bidirectional loading induced twist deformation in the HDR bearings that increased local shear strains. This phenomenon results in an early failure as observed in HDR700. The additional shear strain is estimated based on the twist deformation measured by video image analysis. The comparison of the nominal total shear stress demonstrates that the increase of shear stress because of bidirectional loading occurs when the average shear strain is larger than about 200%. The larger the shear strain, the greater the bidirectional effect. It is shown that the nominal total shear stress of average strain of 350% under bidirectional circular loading pattern is approximately the same as the average shear strain of 400% under unidirectional loading. This means that the average shear strain of 350% under a bidirectional circular loading corresponds to a local shear strain of 400%. Copyright © 2012 John Wiley & Sons, Ltd.     

Intergrain contact density indices for granular mixes I： Framework

Mechanical behavior such as stress-strain response, shear strength, resistance to liquefaction, modulus, and shear wave velocity of granular mixes containing coarse and fine grains is dependent on intergrain contact density of the soil. The global void ratio e is a poor index of contact density for such soils. The contact density depends on void ratio, fine grain content （Cv）, size disparity between particles, and gradation among other factors. A simple analysis of a two-sized particle system with large size disparity is used to develop an understanding of the effects of Cv, e, and gradation of coarse and fine grained soils in the soil mix on intergrain contact density. An equivalent intergranular void ratio （ec）oq is introduced as a useful intergrain contact density for soils at fines content of less than a threshold value Crth. Beyond this value, an equivalent interfine void ratio （ef）eq is introduced as a primary intergrain contact density index. At higher values of Cv beyond a limiting value of fine grains content CVL, an interfine void ratio ef is introduced as the primary contact density index. Relevant equivalent relative density indices （Drc）eq and （Drf）eq are also presented. Experimental data show that these new indices correlate well with steady state strength, liquefaction resistance, and shear wave velocities of sands, silty sands, sandy silts, and gravelly sand mixes.     

Peak surface strains during strong earthquake motion

Peak amplitudes of surface strains during strong earthquake ground motion can be approximated by ε = Aν_max/β₁, where ν_max is the corresponding peak particle velocity, β₁ is the velocity of shear waves in the surface layer, and A is a site specific scaling function. In a 50 m thick layer with shear wave velocity β₁ 300 m/s, A 0·4 for the radial strain ε_rr, A 0·2 for the tangential strain ε_rθ, and A 1·0 for the vertical strain, ε_z. These results are site specific and representative of strike slip faulting and of soil in Westmoreland, in Imperial Valley, California. Similar equations can be derived for other sites with known shear wave velocity profile versus depth.     

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.     

Stick-slip behavior of Indian gabbro as studied using a NIED large-scale biaxial friction apparatus

This paper reports stick-slip behaviors of Indian gabbro as studied using a new large-scale biaxial friction apparatus, built in the National Research Institute for Earth Science and Disaster Prevention (NIED), Tsukuba, Japan. The apparatus consists of the existing shaking table as the shear-loading device up to 3, 600 kN, the main frame for holding two large rectangular prismatic specimens with a sliding area of 0.75 m² and for applying normal stresses σ_n up to 1.33 MPa, and a reaction force unit holding the stationary specimen to the ground. The shaking table can produce loading rates v up to 1.0 m/s, accelerations up to 9.4 m/s², and displacements d up to 0.44 m, using four servocontrolled actuators. We report results from eight preliminary experiments conducted with room humidity on the same gabbro specimens at v = 0.1-100 mm/s and σ_n = 0.66-1.33 MPa, and with d of about 0.39 m. The peak and steady-state friction coefficients were about 0.8 and 0.6, respectively, consistent with the Byerlee friction. The axial force drop or shear stress drop during an abrupt slip is linearly proportional to the amount of displacement, and the slope of this relationship determines the stiffness of the apparatus as 1.15×10⁸ N/m or 153 MPa/m for the specimens we used. This low stiffness makes fault motion very unstable and the overshooting of shear stress to a negative value was recognized in some violent stick-slip events. An abrupt slip occurred in a constant rise time of 16-18 ms despite wide variation of the stress drop, and an average velocity during an abrupt slip is linearly proportional to the stress drop. The use of a large-scale shaking table has a great potential in increasing the slip rate and total displacement in biaxial friction experiments with large specimens.     

Experimental examination on the heterogeneity parameter C v of earthquake precursors

Two rock samples with different structures and materials were deformed under a biaxial loading system, and multipoint strain measurements were performed for each sample. The distribution of strain anomalies during the deformation and the instability process were analyzed by using C _v value put forward by WANG Xiao-qing and CHEN Xue-zhong, et al, a parameter to describe the heterogeneous distribution of earthquake precursors, so as to examine the method of C _v value and to explore its physical meaning experimentally. The result shows that the change of C _v value is correlated to the change of deformation characteristics and is an effective parameter to describe the heterogeneity of precursor distribution. C _v value increases firstly and then decreases before the instability, and the instability occurs when C _v value decreases to the level before increasing. This indicates that C _v value may be a useful parameter for earthquake prediction. Foundation item: Chinese Joint Earthquake Sciences Foundation (9507435).     

九寨沟M_s7.0地震前地应变LURR异常演化特征

从岩石应力-应变的本构关系出发,以能够反映岩石应变变化的地应变观测数据作为"响应量",通过库伦应力触发模型的加卸载响应比计算方法,计算2017年8月8日九寨沟M_S7.0地震前震中及周边500km范围内应变观测的加卸载响应比结果。结果显示,基于应变观测的加卸载响应比方法能够较好地从潮汐频段提取地震前LURR异常,九寨沟地震前,300km范围内的多个应变观测台站出现LURR异常,其中相距96km的两水台EW分量Y值最大达到3.27;LURR空间演化特征显示,在震前约9个月内震中及周边地区陆续出现异常"集中—增强—减弱"过程,证明该地区在长期应力累积的背景下,应力的不断累积增强导致震中及附近区域的岩石出现不断损伤或弱化,最终位于树正断裂上的应变能积累超过了介质强度而引发了此次地震。     

大理石板中心受压时的破裂形式及破裂传播速度的实验研究

本文叙述大理石板中心受压时的破裂形式及破裂传播速度:1.主破裂走向与大理石纹理多数成45°角,少数近似平行,破裂时总是一侧先断通;破裂前存在剪应变,主破裂方向不一定与最弱张裂面一致;2.1gV—L图表明:始发段,刚出现裂纹时,V较大(约10毫米/秒),随L增大,V急剧减小(约0.05毫米/秒);缓裂段,随L增大,V起伏式缓慢增长(0.1—2毫米/秒);速裂段,过一明显转折点后,随L增大,V急剧增长(约1米/秒),破裂发生     

Development of faults as zones of deformation bands and as slip surfaces in sandstone

Three forms of fault are recognized in Entrada and Navajo Sandstones in the San Rafael Desert, southeastern Utah; deformation bands, zones of deformation bands, and slip surfaces. Small faults occur asdeformation bands, about one millimeter thick, in which pores collapse and sand grains fracture, and along which there are shear displacements on the order of a few millimeters or centimeters. Two or more deformation bands adjacent to each other, which share the same average strike and dip, form azone of deformation bands. A zone becomes thicker by addition of new bands, side by side. Displacement across a zone is the sum of displacements on each individual band. The thickest zones are about 0.5 m and total displacement across a thick zone rarely exceeds 30 cm. Finally,slip surfaces, which are through-going surfaces of discontinuity in displacement, form at either edge of zones of highly concentrated deformation bands. In contrast with individual deformation bands and zones of deformation bands, slip surfaces accommodate large displacements, on the order of several meters in the San Rafael Desert.The sequence of development is from individual deformation bands, to zones, to slip surfaces, and each type of faulting apparently is controlled by somewhat different processes. The formation of zones apparently involves strain hardening, whereas the formation of slip surfaces probably involves strain softening of crushed sandstone.     

Cyclic shear response of channel-fill Fraser River Delta silt

The cyclic shear response of a channel-fill, low-plastic silt was investigated using constant-volume direct simple shear testing. Silt specimens, initially consolidated to stress levels at or above the preconsolidation stress, displayed cyclic-mobility-type strain development during cyclic loading without static shear stress bias. Liquefaction in the form of strain softening accompanied by loss of shear strength did not manifest regardless of the applied cyclic stress ratio, or the level of induced excess pore water pressure, suggesting that the silt is unlikely to experience flow failure under cyclic loading. The cyclic shear resistance of the silt increased with increasing overconsolidation ratio (OCR) for OCR>1.3. The silt specimens that experienced high equivalent excess cyclic pore water pressure ratios (r_u>80%) resulted in considerable volumetric strains (2.5%–5%) during post-cyclic reconsolidation implying potentially significant changes to the particle fabric under cyclic loading.     

砾石掺量及侧限压力对黏土类土石混合体动力特性的影响分析

黏土类土石混合体常作为路基填料在工程中广泛应用,然而其在交通荷载作用下的动力特性方面研究较少。为此,本文以0.05 Lc(Lc为圆柱试样直径)为土体、块石分类阈值,根据土石混合体中砾石掺量、侧限压力的不同,采用自振柱仪对其在小应变(10^-6~10^-4)下的动剪切模量和阻尼比进行研究。结果表明:土石混合体最大动剪切模量随砾石掺量的增加而不断增大,且在20%~40%掺量区间内增幅最大,随侧限压力的增加而增大,且增幅逐渐变小;在应变幅值相同的条件下,动剪切模量衰变程度随砾石掺量的增加而不断减少,且在20%~40%掺量区间内减幅最大,随侧限压力的增加而减小,且减幅逐渐变小;最小、最大阻尼比随砾石掺量和侧限压力的增加而减少。结合试验结果分别从颗粒“骨架”结构性、动态结构稳定性、材料密实度、能量耗散等方面阐述块石掺量和侧限压力对土石混合体动剪切模量和阻尼比的影响机理。最后采用优化Hardin-Drnevich模型建立砾石掺量、侧限压力与土石混合体动力特性参数(最大动剪切模量、参考剪应变、最大阻尼比、最小阻尼比)之间的估算公式,以期为土石混合路基的动力设计和施工提供指导。     

Geomagnetic diurnal-variation anomalies and their relation to strong earthquakes

The diurnal-variation anomalies of the vertical-component in geomagnetic field are mainly the changes of phase and amplitude before strong earthquakes. On the basis of data recorded by the network of geomagnetic observatories in China for many years, the anomalous features of appearance time of the minima of diurnal variations (i.e, low-point time) of the geomagnetic vertical components and the variation of their spatial distribution (i.e, phenomena of low-point displacement) have been studied before over 30 strong earthquakes with M _S≥6.6 such as Kunlunshan M _S=8.1 earthquake on November 14, 2001; Bachu-Jashi M _S=6.8 earthquake on February 24, 2003; Xiaojin M _S=6.6 earthquake on September 22, 1989, etc. There are good relations between such rare phenomena of geomagnetic anomalies and the occurrence of earthquakes. It has been found that most earthquakes occur in the vicinity of the boundary line of sudden change of the low-point displacement and generally within four days before and after the 27th or 41st day counting from the day of appearance of the anomaly. In addition, the anomalies of diurnal-variation amplitude near the epicentral area have been also studied before Kunlunshan M _S=8.1 earthquake and Bachu-Jiashi M _S=6.8 earthquake. Foundation item: National Science Technology Tackle Key Project during the Tenth Five-year Plan (2001BA601B01-05-04)     

Coulomb constitutive laws for friction: Contrasts in frictional behavior for distributed and localized shear

We describe slip-rate dependent friction laws based on the Coulomb failure criteria. Frictional rate dependence is attributed to a rate dependence of cohesionc and friction angle . We show that differences in the stress states developed during sliding result in different Coulomb friction laws for distributed shear within a thick gouge layer versus localized shear within a narrow shear band or between bare rock surfaces. For shear within gouge, shear strength is given by =c cos + _n sin, whereas for shear between bare rock surfaces the shear strength is =c cos + _n tan, where and _n are shear and normal stress, respectively. In the context of rate-dependent Coulomb friction laws, these differences mean that for a given material and rate dependence of the Coulomb parameters, pervasive shear may exhibit velocity strengthening frictional behavior while localized shear exhibits velocity weakening behavior. We derive from experimental data the slip-rate dependence and evolution ofc and for distributed and localized shear. The data show a positive rate dependence for distributed shear and a negative rate dependence for localized shear, indicating that the rate dependence ofc and are not the same for distributed and localized shear, even after accounting for differences in stress state. Our analysis is consistent with the well-known association of instability with shear localization in simulated fault gouge and the observation that bare rock surfaces exhibit predominantly velocity weakening frictional behavior whereas simulated fault gouge exhibits velocity strengthening followed by a transition to velocity weakening with increasing displacement. Natural faults also exhibit displacement dependent frictional behavior and thus the results may prove useful in understanding the seismic evolution of faulting.