A review of rock mechanics studies in the United States pertinent to earthquake prediction

Premonitory phenomena such as dilatancy, creep, acoustic emission, and changes in seismic velocity and attenuation, electrical resistivity, magnetic moment, and gas emission, which occur before fracture of initially intact rock and before stick-slip on faults or between finely ground surfaces of rock, have been reviewed and discussed in relation to earthquake prediction. This review is restricted to the results of laboratory experiments that have been carried out in the United States of America.     

Time-dependent friction and the mechanics of stick-slip

Time-dependent increase of static friction is characteristic of rock friction undera variety of experimental circumstances. Data presented here show an analogous velocity-dependent effect. A theor of friction is proposed that establishes a common basis for static and sliding friction. Creep at points of contact causes increases in friction that are proportional to the logarithm of the time that the population of points of contact exist. For static friction that time is the time of stationary contact. For sliding friction the time of contact is determined by the critical displacement required to change the population of contacts and the slip velocity. An analysis of a one-dimensional spring and slider system shows that experimental observations establishing the transition from stable sliding to stick-slip to be a function of normal stress, stiffness and surface finish are a consequence of time-dependent friction.     

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.     

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.     

Toward a physical undenstanding of earthquake scaling relations

In seismological literature, there exist two competing theories (the so-calledW model andL model) treating earthquake scaling relations between mean slip and rupture dimension and between seismic moment and rupture dimension. The core of arguments differentiating the two theories is whether the mean slip should scale with the rupture width or with the rupture length for large earthquakes. In this paper, we apply the elastic theory of dislocation to clarify the controversy. Several static dislocation models are used to simulate strike-slip earthquakes. Our results show that the mean slip scales linearly with the rupture width for small earthquakes with a rupture length smaller than the thickness of the seismogenic layer. However, for large earthquakes with a rupture length larger than the thickness of the seismogenic layer, our models show a more complicated scaling relation between mean slip and rupture dimension. When the rupture length is smaller than a cross-over length, the mean slip scales nearly linearly with the rupture length. When the rupture length is larger than a cross-over length, the mean slip approaches asymptotically a constant value and scales approximately with the rupture width. The cross-over length is a function of the rupture width and is about 75 km for earthquakes with a saturated rupture width of 15 km. We compare our theoretical predictions with observed source parameters of some large strike-slip earthquakes, and they match up well. Our results also suggest that when large earthquakes have a fixed aspect ratio of rupture length to rupture width (which seems to be the case for most subduction earthquakes) the mean slip scales with the rupture dimension in the same way as small earthquakes.     

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.     

Mineralogy and physical nature of clay gouge

Fault gouges have been observed in the surface outcrops, in shallow excavations, and in deep (300 meters below the surface) tunnels and mines in fault zones. The 2-microns fractions in these fault gouges may compose a few percent to more than fifty percent of the total mass in the outcrops, and the mineralogy of the 2-microns fractions consists of a variety of clays (the common ones are montmorillonite, illite, kaolinite, chlorite, vermiculite and mixed-layer clays) and some quartz, feldspars, etc.Although we cannot yet conclude directly from the studies of gouges that similar gouges exist at depths where many large shallow earthquakes are generated, there is a strong possibility that they do, based on (1) available equilibrium data on various clays — for example, kaolinite has been found to exist at 4 kb and 375°C (±15°C) (Thompson, 1970) and montmorillonite + kaolite has been found to exist at 450°C and 4 kb (Velde, 1969); (2) the compatibility of laboratory velocity data in gouge (Wang et al., 1977) with those in a model for central California (Healy andPeake, 1975); (3) the capability of clays to undergo sudden earthquake-like displacements (Summers andByerlee, 1977); (4) the petrology of intrafault cataclastic rocks in old fault zones (Kasza, 1977); and (5) the compatibility of gouge mineralogy with the mineralogy of hydrothermal clay deposits.If clay gouges are indeed significant components of the fault zone at depth, then the mechanical properties of clays under confining pressures up to 4 kb are important in the behavior of faults. Very few experiments have been performed under such high pressures. But from the physical makeup of clays, we can infer that (1) the range of possible behavior includes stable sliding with vermiculite and montmorillonite (asByerlee andSummers, 1977, have proven) to stick-slip-like behavior with kaolinite, chlorite, etc.; (2) the absence or presence of water will greatly affect the strengths of gouges — it is possible that water may reduce the strength of gouge to a fairly small value.     

A two degree-of-freedom earthquake model with static/dynamic friction

Can a simple multi-block-spring model with total symmetry make interesting predictions for fault behaviour? Our model consists of a symmetric, slowly driven, two degree-of-freedom block-spring system with static/dynamic friction. The simple friction law and slow driving rate allow the state of this fourth order system to be described between slip events by a single variable, the difference in the stretch of the driving springs. This stretch difference measures the locked-in stress and is closely related to fault stress inhomogeneity. In general,smoothing is not observed. A spatially homogeneous stress state is found to almost always be unstable, in that the system tends toward an inhomogeneous state after many slip events. The system evolves either to a cycle that alternates between two types of earthquakes, or to a cycle with repeating but identical asymmetric earthquakes. One type of alternating earthquake solution is structurally unstable, which implies a great sensitivity to model perturbations. For this simple model, spatial asymmetry necessarily occurs, despite the symmetry in the model, thus suggesting that spatial structure in seismicity patterns may be a consequence of earthquake dynamics, not just fault heterogeneity.     

Earthquake parameters affecting the performance of an RC frame with friction damper

In this paper, correlation between the ground motion parameters and the peak displacement demand of a reinforced concrete single degree of freedom system retrofitted by friction dampers is investigated. The aim is to reveal the best parameters that are used in selecting earthquake records for nonlinear dynamic analysis of the system. Performing numerous nonlinear time history analyses, it is observed that different earthquake parameters play role in peak displacement demand related to the ranges formed by the different periods of a reinforced concrete frame, the strength ratio of total system at slip displacement and the stiff/soft soil profiles. For the both soil types, out of sixteen ground motion parameters, the eight, Spectral Response Acceleration, Peak Ground Acceleration, Effective Peak Acceleration, Maximum Incremental Velocity, Peak Ground Velocity, Arias Intensity, Arias Intensity-based Parameter and Effective Peak Velocity correlate better with peak displacement demand.     

On the physical essence of the b value for AE of rock tests and natural earthquakes in terms of fracture mechanics

The problem of physical essence of theb value forAE of rock tests and natural earthquakes has been a controversial topic during the past two decades. In the present paper the order and energy of each microfracturing of the microcrack system existing in a rock specimen is discussed from the viewpoint of fracture mechanics, then the whole series ofAE and subsequently the value ofb are determined. The order of microfracturing depends on the parametersKei/Kci whereKei is the effective stress intensity factor of thei-th microcrack andKci is the fracture toughness in the site of thei-th crack. The energy of eachAE can be expressed asηi ∫ loili Gids whereG is the energy release rate of microcarck,loi andli are the original and final crack lengths respectively andηi is the emanating efficiency for thei-th crack. If we assume that the distribution density function of microcrack lengthl isp(l)=Bl−v whereB andγ are constants, then the expressionb=3γ/2 can be deduced. Hence, we have come to the conclusion that the value ofb mirrors essentially the “crack-system-configuration” of the material, which means the distribution of the sizes, shapes and orientations of microcracks over space as well as the distribution of the other relevant physical parameters such as fracture toughness, friction coefficient, etc. Our conclusion is somewhat similar in character to Mogi’s. He concluded thet the heterogeneity of the material plays the most important role in determining the value ofb. The term heterogeneity of course covers the idea of “crack-system-configuration, but we think that our view has a little bit deeper insight to the problem than that of Mogi. This subject is supported by Chinese Joint Seismological Science Foundation.     

Seismicity gap near Oaxaca,southern Mexico as a probable precursor to a large earthquake

Summary An area of significant seismic quiescence is found near Oaxaca, southern Mexico. The anomalous area may be the site of a future large earthquake as many cases so far reported were. This conjecture is justified by study of past seismicity changes in the Oaxaca region. An interval of reduced seismicity, followed by a renewal of activity, preceded both the recent large events of 1965 and 1968. Those past earthquakes have ruptured the eastern and western portions of the present seismicity gap, respectively, so that the central part remaining is considered to be of the highest risk of the pending earthquake.The most probable estimates are: 7 1/2±1/4 for the magnitude and =16.5°±0.5°N, =96.5°±0.5W for the epicenter location. A firm prediction of the occurrence time is not attempted. However, a resumption of seismic activity in the Oaxaca region may precede a main shock.On leave from the Marine Science Institute, University of Texas, USA.     

地震统计力学—几个非线性地震模型的相互关系及其物理含义

近年来地震统计力学研究的进展已经使我们有可能以一种简洁的方式将一些非线性地震模型物理地联系起来,并从地震学角度阐明这些模型的意义和限度。本文结合逾渗模型、热力学弹性回跳模型及弹簧滑块模型,系统地评述了这方面研究的进展。     

城市地震灾害与防震减灾对策

综合有关资料显示,地震灾害造成城市人员重大伤亡,经济损失惨重,是毁城之首。城市震灾具有许多特点,是防震减灾的重中之重,提出了城市的综合防震减灾对策,可减轻未来震灾损失,促进社会的稳定和可持续发展。     

一次地震预测的案例

2001年11月14日昆仑山8.1级地震后, 川滇地区的震情引起了地震学者的普遍关注。 文中详细阐述了针对当时川滇地区的多种地震与地震前兆观测项的观测异常形成的综合预测意见及预测三要素的判定, 并探讨了8.1级地震对这一预测意见的影响及对经验性地震预报的认识。     

地震信息分类与编码研究

回顾了我国地震信息分类与编码研究的现状,分析了地震信息分类与编码研究中存在的问题,指出加强地震信息分类与编码体系研究,优先制定基础性地震信息分类与编码标准的重要性,分类时除应遵守分类基本原则,还应发掘信息本身特性,提出分类的个性原则.     

Real time test of the long-range aftershock algorithm as a tool for mid-term earthquake prediction in Southern California

Result of the algorithm of earthquake prediction, published in 1982, is examined in this paper. The algorithm is based on the hypothesis of long-range interaction between strong and moderate earthquakes in a region. It has been applied to the prediction of earthquakes withM6.4 in Southern California for the time interval 1932–1979. The retrospective results were as follows: 9 out of 10 strong earthquakes were predicted with average spatial accuracy of 58 km and average delay time (the time interval between a strong earthquake and its best precursor) 9.4 years varying from 0.8 to 27.9 years. During the time interval following the period studied in that publication, namely in 1980–1988, four earthquakes occurred in the region which had a magnitude ofM6.4 at least in one of the catalogs: Caltech or NOAA. Three earthquakes—Coalinga of May, 1983, Chalfant Valley of July, 1985 and Superstition Hills of November, 1987—were successfully predicted by the published algorithm.The missed event is a couple of two Mammoth Lake earthquakes of May, 1980 which we consider as one event due to their time-space closeness. This event occurred near the northern boundary of the region, and it also would have been predicted if we had moved the northern boundary from 38°N to the 39°N; the precision of the prediction in this case would be 30 km.The average area declared by the algorithm as the area of increased probability of strong earthquake, e.g., the area within 111-km distance of all long-range aftershocks currently present on the map of the region during 1980–1988 is equal to 47% of the total area of the region if the latter is measured in accordance with the density distribution of earthquakes in California, approximated by the catalog of earthquakes withM5. In geometrical terms it is approximately equal to 17% of the total area.Thus the result of the real time test shows a 1.6 times increase of the occurrence ofC-events in the alarmed area relative to the normal rate of seismicity. Due to the small size of the sample, it is of course, beyond the statistically significant value. We adjust the parameters of the algorithm in accordance with the new material and publish them here for further real-time testing.     

Response of base‐isolated nuclear structures for design and beyond‐design basis earthquake shaking

The American Society of Civil Engineers (ASCE) 43‐05 presents two performance objectives for the design of nuclear structures, systems and components in nuclear facilities: (1) 1% probability of unacceptable performance for 100% design basis earthquake (DBE) shaking and (2) 10% probability of unacceptable performance for 150% DBE shaking. To aid in the revision of the ASCE 4‐98 procedures for the analysis and design of base‐isolated nuclear power plants and meet the intent of ASCE 43‐05, a series of nonlinear response‐history analyses was performed to study the impact of the variability in both earthquake ground motion and mechanical properties of isolation systems on the seismic responses of base‐isolated nuclear power plants. Computations were performed for three representative sites (rock and soil sites in the Central and Eastern United States and a rock site in the Western United States) and three types of isolators (lead rubber, Friction Pendulum and low‐damping rubber bearings) using realistic mechanical properties for the isolators. Estimates were made of (1) the ratio of the 99th percentile (90th percentile) response of isolation systems computed using a distribution of spectral demands and distributions of isolator mechanical properties to the median response of isolation systems computed using best‐estimate properties and 100% (150%) spectrum‐compatible DBE ground motions; (2) the number of sets of three‐component ground motions to be used for response‐history analysis to develop a reliable estimate of the median response of isolation systems. The results of this study provide the technical basis for the revision of ASCE Standard 4‐98. Copyright © 2012 John Wiley & Sons, Ltd.     

Nonuniform earthquake input for arch dam–foundation interaction

Wave scattering and dam–foundation interaction are important aspects of a realistic earthquake analysis of arch dams. In the first part of this paper it is shown how the motion obtained from a two-dimensional scattering analysis can be used as an input for a three-dimensional dam–foundation analysis. In the second part, a method for calculating the scattered motion is explained. The scattered motion is obtained via the two-dimensional dynamic stiffness matrix. The dynamic stiffness matrix for an out-of-plane motion is calculated by the Complementary-Domain Method (CDM). Some examples are presented to verify the method and to show the influence of the scattering of the seismic ground motion.