Compaction of a Rock Fracture Moderated by Competing Roles of Stress Corrosion and Pressure Solution

Unusually rapid closure of stressed fractures, observed in the initial stages of loading and at low temperatures, is examined using models for subcritical crack growth and pressure solution. The model for stress corrosion examines tensile stress concentrations induced at the Hertzian contact of propping fracture asperities, and mediates fracture growth according to a kinetic rate law. Conversely, pressure solution is described by the rate-limiting process of dissolution, resulting from the elevated stresses realized at the propping asperity contact. Both models are capable of following the observed compaction of fractures in novaculite. However, closure rates predicted for stress corrosion cracking are orders of magnitudes faster than those predicted for pressure dissolution. For consistent kinetic parameters, predictions from stress corrosion better replicate experimental observations, especially in the short-term and at low temperature when mechanical effects are anticipated to dominate. Rates and magnitudes of both stress corrosion and pressure solution are dependent on stresses exerted over propping asperities. Rates of closure due to stress corrosion cracking are shown to be always higher than for pressure solution, except where stress corrosion ceases as contact areas grow, and local stresses drop below an activation threshold. A simple rate law is apparent for the progress of fracture closure, defined in terms of a constant and an exponent applied to the test duration. For current experimental observations, this rate law is shown to replicate early progress data, and shows promise to define the evolution of transport properties of fractures over extended durations.     

A Condition for Super-shear Rupture Propagation in a Heterogeneous Stress Field

— We have used numerical simulations with the boundary integral equation method to investigate a mechanism to excite super-shear rupture velocities in a homogeneous stress field including an asperity of increased initial stress. When the rupture, with the slip-weakening distance selected to generate sub-Rayleigh speed, encounters the asperity it either accelerates to super-shear velocities or maintains the sub-Rayleigh speed, dependent on the size and amplitude of the asperity. Three classes of rupture propagation are identified: the velocity (a) for the most narrow asperities increases slowly towards the Rayleigh wave speed, (b) for intermediate width of the asperities jumps to super-shear values for a short distance but then decreases to sub-Rayleigh wave speeds, and (c) for the widest asperities jumps to super-shear values and pertains to values between the S- and P-wave velocities. The transitions between the three classes of rupture propagation are characterized by very narrow (critical) ranges of rupture resistance. If the size of the initial asperity is smaller than critical, it becomes difficult for rupture to propagate with super-shear velocities even if the initial stress level is high. Our results suggest that stress variation along the rupture path helps homogenize the rupture velocity and propagate with sub-Rayleigh wave speeds.     

An asperity model to simulate rupture along heterogeneous fault surfaces

A model has been developed to simulate the statistical and mechanical nature of rupture on a heterogeneous strike-slip fault. The model is based on the progressive failure of circular asperities of varying sizes and strengths along a fault plane subjected to a constant far-field shear displacement rate. The basis of the model is a deformation and stress intensity factory solution for a single circular asperity under a unidirectional shear stress. The individual asperities are unified through the fault stiffness and the far-field stress and displacement. During fault deformation asperities can fail and reheal, resulting in changes in the local stresses in the asperities, stress drops, and changes in the stiffness of the fault. Depending on how the stress is redistributed following asperity failure and on the strenghts of the neighboring asperities an earthquake event can be the failure of one or more asperities. Following an earthquake event seismic source parameters such as the stress drop, energy change, and moment magnitude are calculated. Results from the model show a very realistic pattern of earthquake rupture, with reasonable source parameters, the proper magnitude-frequency behavior, and the development of characteristic earthquakes. Also the progression ofb-values in the model gives some insight into the phenomenon of self-organized criticality.     

震源体破裂行为的重整化群方法研究

应用重整化群方法对一维、二维和三维震源体的破裂问题进行了研究，得到了一维、二维和三辰原体破裂的临界概率值分别国０．２０６３、０．１７０７和０．１５９９，相关长度指数分别为１．４３８８、０．８０８４和０．５７５７。进而由此揭示了临界概率和相关长度指数随维数增大而减少的变化规律。     

Global survey of aftershock area expansion patterns

We developed an objective method to define the aftershock areas of large earthquakes as a function of time after the main shock. The definition is based upon the amount of energy released by aftershocks, the spatial distribution of the energy release is first determined and is contoured. The 1-day aftershock area is defined by a contour line corresponding to the energy release level of 10^15.6 ergs/(100 km² · day). The 10-day, 100-day and 1-y aftershock areas are similarly defined by contour lines corresponding to 10^14.8, 10^14.0, and 10^13.5 ergs/(100 km² · day), respectively. We also define the expansion ratios at time t by the ratio of the aftershock area at t to that at 1 day.Using this method we study the aftershock area expansion patterns of 44 large (M_s ? 7.5) and five moderate shallow earthquakes which occurred from 1963 to 1980. Each aftershock sequence is examined at four different times, i.e., 1 day, 10 days, 100 days, and 1 y after the main event. We define the aftershock area expansion ratios η and η_e by $\text{S(100)/S(}\text{1}\text{)}\text{and}\text{L(100)/L(1)}$, respectively: here S(t) and L(t) are the area and the length of the aftershock area, respectively, at time t. Our study suggests that a distinct regional variation of aftershock area expansion patterns is present; it is strongly correlated with the tectonic environment. In general, the subduction zones of the “Mariana” type have large expansion ratios, and those of the “Chilean” type have small expansion ratios. Some earthquakes that occurred in the areas of complex bathymetry such as aseismic ridges tend to have large expansion ratios.These results can be explained in terms of an asperity model of fault zones in which a fault plane is represented by a distribution of strong spots, called the asperities, and weak zones surrounding the asperities. The rupture immediately after the main shock mostly involves asperities. After the main rupture is completed, the stress change caused by the main shock gradually propagates outward into the surrounding weak zones. This stress propagation manifests itself as expansion of aftershock activity. In this simple picture, if the fault zone is represented by relatively large asperities separated by small weak zones (“Chilean” type), then little expansion of aftershock activity would be expected. On the other hand, if relatively small asperities are sparsely distributed (“Mariana” type), significant expansion occurs. The actual distribution of asperities is likely to be more complex than the two cases described above. However, we would expect that the expansion ratio is in general proportional to the spatial ratio of the total asperity area to the fault area.     

Characterization of Stress Drops on Asperities Estimated from the Heterogeneous Kinematic Slip Model for Strong Motion Prediction for Inland Crustal Earthquakes in Japan

Dense strong motion observation networks provided us with valuable data for studying strong motion generation from large earthquakes. From kinematic waveform inversion of seismic data, the slip distribution on the fault surface of large earthquakes is known to be spatially heterogeneous. Because heterogeneities in the slip and stress drop distributions control the generation of near-source ground motion, it is important to characterize these heterogeneities for past earthquakes in constructing a source model for reliable prediction of strong ground motion. The stress changes during large earthquakes on the faults recently occurring in Japan are estimated from the detailed slip models obtained by the kinematic waveform inversion. The stress drops on and off asperities are summarized on the basis of the stress change distributions obtained here. In this paper, we define the asperity to be a rectangular area whose slip is 1.5 or more times larger than the average slip over the fault according to the previous study for inland crustal earthquakes. The average static stress drops on the asperities of the earthquakes studied here are in the range 6?C23?MPa, whereas those off the asperities are below 3?MPa. We compiled the stress drop on the asperities together with a data set from previous studies of other inland earthquakes in Japan and elsewhere. The static stress drop on the asperity depends on its depth, and we obtained an empirical relationship between the static stress drop and the asperity??s depth. Moreover, surface-breaking asperities seemed to have smaller stress drops than buried asperities. Simple ground motion simulations using the characterized asperity source models reveal that deep asperities generate larger ground motion than shallow asperities, because of the different stress drops of the asperities. These characteristics can be used for advanced source modeling in strong ground motion prediction for inland crustal earthquakes.     

Multiasperity fault model and the nature of short-period subsources

We suggest to consider the breaking of an asperity,i.e., a small contact patch between fault walls, as a typical subsource producing an elementary short-period radiation pulse from a source of a large earthquake. Based on the results ofDas andKostrov we propose formulas to describe amplitudes and spectra of acceleration for a multiasperity fault/source model. The stress drop over an asperity is determined in several ways; the estimates agree to give the average value of several hundred bar. Theoretical acceleration spectral shapes for the case of similar asperities agree with the observed ones, they reproduce such features as lower-frequencyf ¹ slope, peak, and high-frequency cutoff. The statistical stress-drop distribution over the population of asperities, and also the related distribution of peak accelerations are discussed. There distributions are found to be the power-law ones with exponent near to 2. This means that acceleration peaks are formed normally by breaking of individual asperities. We consider small earthquakes as produced by breaking of single asperities, this idea explains the observed correlation between the upper cutoff frequency of acceleration spectrum and the typical characteristic frequency of small earthquakes.     

A statistical damage model with implications for precursory seismicity

Acoustic emissions prior to rupture indicate precursory damage. Laboratory studies of frictional sliding on model faults feature accelerating rates of acoustic emissions prior to rupture. Precursory seismic emissions are not generally observed prior to earthquakes. To address the problem of precursory damage, we consider failure in a fiber-bundle model. We observe a clearly defined nucleation phase followed by a catastrophic rupture. The fibers are hypothesized to represent asperities on a fault. Two limiting behaviors are the equal load sharing p = 0 (stress from a failed fiber is transferred equally to all surviving fibers) and the local load sharing p = 1 (stress from a failed fiber is transferred to adjacent fibers). We show that precursory damage in the nucleation phase is greatly reduced in the local-load sharing limit. The local transfer of stress from an asperity concentrates nucleation, restricting precursory acoustic emissions (seismic activity).     

Asperity Distribution of the 1952 Great Kamchatka Earthquake and its Relation to Future Earthquake Potential in Kamchatka

—The 1952 Kamchatka earthquake is among the largest earthquakes of this century, with an estimated magnitude of M _w = 9.0. We inverted tide gauge records from Japan, North America, the Aleutians, and Hawaii for the asperity distribution. The results show two areas of high slip. The average slip is over 3 m, giving a seismic moment estimate of 155×10²⁰Nm, or M _w = 8.8. The 20th century seismicity of the 1952 rupture zone shows a strong correlation to the asperity distribution, which suggests that the large earthquakes (M > 7) are controlled by the locations of the asperities and that future large earthquakes will also recur in the asperity regions.     

The rupture process and asperity distribution of three great earthquakes from long-period diffracted P-waves

Maximum earthquake size varies considerably amongst the subduction zones. This has been interpreted as a variation in the seismic coupling, which is presumably related to the mechanical conditions of the fault zone. The rupture process of a great earthquake indicates the distribution of strong (asperities) and weak regions of the fault. The rupture process of three great earthquakes (1963 Kurile Islands, M_W = 8.5; 1965 Rat Islands, M_W = 8.7; 1964 Alaska, M_W = 9.2) are studied by using WWSSN stations in the core shadow zone. Diffraction around the core attenuates the P-wave amplitudes such that on-scale long-period P-waves are recorded. There are striking differences between the seismograms of the great earthquakes; the Alaskan earthquake has the largest amplitude and a very long-period nature, while the Kurile Islands earthquake appears to be a sequence of magnitude 7.5 events.The source time functions are deconvolved from the observed records. The Kurile Islands rupture process is characterized by the breaking of asperities with a length scale of 40–60 km, and for the Alaskan earthquake the dominant length scale in the epicentral region is 140–200 km. The variation of length scale and M_W suggests that larger asperities cause larger earthquakes. The source time function of the 1979 Colombia earthquake (M_W = 8.3) is also deconvolved. This earthquake is characterized by a single asperity of length scale 100–120 km, which is consistent with the above pattern, as the Colombia subduction zone was previously ruptured by a great (M_W = 8.8) earthquake in 1906.The main result is that maximum earthquake size is related to the asperity distribution on the fault. The subduction zones with the largest earthquakes have very large asperities (e.g. the Alaskan earthquake), while the zones with the smaller great earthquakes (e.g. Kurile Islands) have smaller scattered asperities.     

Identification of High Frequency Pulses from Earthquake Asperities Along Chilean Subduction Zone Using Strong Motion

The Chilean subduction zone is one of the most active of the world with M?=?8 or larger interplate thrust earthquakes occurring every 10?years or so on the average. The identification and characterization of pulses propagated from dominant asperities that control the rupture of these earthquakes is an important problem for seismology and especially for seismic hazard assessment since it can reduce the earthquake destructiveness potential. A number of studies of large Chilean earthquakes have revealed that the source time functions of these events are composed of a number of distinct energy arrivals. In this paper, we identify and characterize the high frequency pulses of dominant asperities using near source strong motion records. Two very well recorded interplate earthquakes, the 1985 Central Chile (Ms?=?7.8) and the 2007 Tocopilla (Mw?=?7.7), are considered. In particular, the 2007 Tocopilla earthquake was recorded by a network with absolute time and continuos recording. From the study of these strong motion data it is possible to identify the arrival of large pulses coming from different dominant asperities. The recognition of the key role of dominant asperities in seismic hazard assessment can reduce overestimations due to scattering of attenuation formulas that consider epicentral distance or shortest distance to the fault rather than the asperity distance. The location and number of dominant asperities, their shape, the amplitude and arrival time of pulses can be one of the principal factors influencing Chilean seismic hazard assessment and seismic design. The high frequency pulses identified in this paper have permitted us to extend the range of frequency in which the 1985 Central Chile and 2007 Tocopilla earthquakes were studied. This should allow in the future the introduction of this seismological result in the seismic design of earthquake engineering.     

Study on Potential Strong Earthquake Risks Around the Mabian Area,Southern Sichuan

Based on seismic data from the regional network for the last 34 years,we analyzed the present fault behavior of major fault zones around the Mabian area,southern Sichuan,and identified the risky fault-segments for potential strong and large earthquakes in the future.The method of analysis is a combination of spatial distribution of b-values with activity background of historical strong earthquakes and current seismicity.Our results mainly show:(1) The spatial distribution of b-values indicates significant heterogeneity in the studied area,which reflects the spatial difference of cumulative stress levels along various fault zones and segments.(2) Three anomalously low b-value areas with different dimensions were identified along the Mabian-Yanjin fault zone.These anomalies can be asperities under relatively high cumulated stress levels.Two asperities are located in the north of Mabian county,in Lidian town in western Muchuan county,and near Yanjin at the south end of the fault zone.These two areas represent potential large earthquake seismogenic sites around the Mabian area in the near future.Besides them,the third relatively smaller asperity is identified at southern Suijiang,as another potential strongearthquake source.(3) An asperity along the southwestern segment of the Longquanshan fault zone indicates the site of potential moderate-to-strong earthquakes.(4) The asperity along the segment between Huangmu town in Hanyuan county and Longchi town in Emeishan city on Jinkouhe-Meigu fault has potential for a moderate-strong earthquake.     

障碍体和凹凸体对地震矩的影响

本文利用具有非均匀剪切应力分布的圆盘状裂缝问题的解,定量计算了障碍体和凹凸体对地震矩的影响.我们发现,除非障碍体的尺寸很小或很接近于整个断层的尺寸,含有障碍体的断层的地震矩,大致为具有均匀应力降的等面积断层的地震矩的40%.由此可以推知,在障碍体的这种尺寸范围内,视应力降大致也是△Af=SA-f的40%.这里SA是远场应力,f是残余摩擦应力.另外,已存在滑动带对于凹凸体破坏的地震矩有明显的放大作用,这种作用在凹凸体尺寸较小时特别显著.例如,当凹凸体半径是整个断层半径的2/10时,凹凸体上的矩被放大7倍多;当其半径为整个断层半径的1/10时,凹凸体的矩将被放大约30倍. 文中还比较了三维效应和二维效应的差异.我们发现,Mx0/M0c在三维情形对障碍体尺寸的变化并不敏感,这是与二维情形很不相同的.这里,Mx0是具有障碍体的断层破裂所产生的地震矩,M0c是相应的均匀断层破裂的矩.所以,二维分析不适用于具有障碍体的三维断层.然而,在分析已存在滑动带对凹凸体破裂的矩的影响时,平面应变结果与三维结果差异并不很大.      

The characteristic displacement in rate and state-dependent friction from a micromechanical point of view

The physical meaning of the characteristic displacement that has been observed in velocity-stepping friction experiments was investigated based on the micromechanics of asperity contact. It has been empirically found for bare rock surfaces that the magnitude of the characteristic displacement is dependent only on surface roughness and insensitive to both slip velocity and normal stress. Thus the characteristic displacement has been interpreted as the displacement required to change the population of contact points completely. Here arises a question about the physical mechanism by which the contact population changes. Because individual asperity contacts form, grow and are eliminated with displacement, there are at least two possible interpretations for the characteristic displacement: (1) it is the distance over which the contacts existing at the moment of the velocity change all fade away, being replaced by new asperity contacts, or (2) it is the distance required for a complete replacement in the real contact area that existed at the moment of the velocity change. In order to test these possibilities, theoretical models were developed based on the statistics of distributed asperity summits. A computer simulation was also performed to check the validity of the theoretical models using three-dimensional surface topography data with various surface roughnesses. The deformation was assumed to be elastic at each asperity contact. The results of both the simulation and the theoretical models show that the characteristic displacement in (1) is about three times longer than that in (2). Comparison of the results with the experimental observations obtained by others indicates that the possibility (2) is the correct interpretation. This means that the state in the rate and state variable friction law is memorized in a very confined area of real contact. Further, our results explain why the characteristic displacement is insensitive to normal stress: this comes from the fact that the microscopic properties such as the mean contact diameter are insensitive to normal stress. The approach based on the micromechanics of asperity contact is useful to investigate the underlying mechanism of various phenomena in rock friction.     

2011年M_W9.0东日本大地震动力学破裂过程的数值模拟

力学上,地震可以看作在应力场作用下由于断层带介质的突然损伤或软化导致的断层带失稳事件.本文基于这个地震动力学模型,利用一种可以模拟断层大位错的有限元方法,研究了2011年MW9.0东日本大地震(Tohoku-Oki)的动力学破裂过程.比较了无障碍体和具有不同刚度障碍体的断层带模型产生的断层位移、位错和应力降.主要结果表明,障碍体的存在并不明显地改变障碍体区域的初始构造应力场.对有障碍体情形,准静态结果显示断层上盘最大逆冲位移和最大剪切位错分别为51m和58m,均发生在海底表面海沟处,与无障碍体的结果(最大剪切位错约55m)相比差别不大;下盘最大倾向位移(-10m)并不与上盘最大值出现在同一位置,而是在障碍体处.障碍体处剪应力降(约11 MPa)大于周围非障碍体区域.障碍体处正应力降的最大值约为3 MPa.模拟结果似乎不支持海山是导致本次地震异乎寻常大位错的原因,而倾向于断层带剪切刚度在地震过程中极度损伤或软化.     

诱发前震预报方法的检验——1981—992年中国大陆地震活动图象

大强固区之间的相互作用和震后运动可以引起触发,强固区破裂引起相邻强固区加载。震后运动可以在大范围内发生并引起相邻区域的不均匀应变积累。观测表明大震后首先发生中等地震的地点正好是下次大震的位置,所以任何一个大地震发生都提供了一个探寻临界破裂区的良好时机。依据1960—1980年资料总结的中期地震危险性估测方法称为“诱发前震图象”,1981—1992年的地震资料完全证实了该方法的可靠性。     

Study on the characteristics of rock failure strain and acoustic emission field for two parallelling faults with the same slip direction including asperities

Introduction Concerning about research on grouped-earthquake seismogenic and occurrence, at present it is only limited on the stage of the theoretical analysis and numerical model. For instance, ZHANG (1987) simulated the grouped-earthquake generation and physical mechanism making use of spring-block principle. Applying for non-linear dynamic model, referring to Chinese continental plate as object, LI, et al (1997) performed the numerical simulation on the seismogenic and occurring of group…     

Slip- and Time-dependent Fault Constitutive Law and its Significance in Earthquake Generation Cycles

-- By integrating effects of microscopic interactions between statistically self-similar fault surfaces, we succeeded in deriving a slip- and time-dependent fault constitutive law that rationally unifies the slip-dependent law and the rate- and state-dependent law. In this constitutive law the slip-weakening results from the abrasion of surface asperities that proceeds irreversibly with fault slip. On the other hand, the restoration of shear strength after the arrest of faulting results from the adhesion of surface asperities that proceeds with contact time. At the limit of high slip-rate the unified constitutive law is reduced to the slip-weakening law. At the limit of low slip-rate it shows the well-known log t strengthening of faults over the wide range of contact time t. In the steady state with a constant slip-rate V the shear strength has the negative log V dependence, known as the velocity-weakening. Another important property expected from the unified constitutive law is the gradual increase of the critical weakening displacement D_c with stationary contact time. We numerically examined behavior of a single degree of freedom elastic system following the slip- and time-dependent constitutive law, and found that the periodic stick-slip motion is realized when the adhesion rate is high in comparison with the loading rate. If the adhesion rate is very low, behavior of the system gradually changes from stick-slip motion to steady sliding with time.     

岩石突发失稳序列的实验研究

根据三轴压缩条件下岩石试件变形过程中多次重复发生的粘滑失稳事件，着重研究了突发失稳序列的演变特征及其影响因素。研究表明，随着错动量的增大，突发失稳的临界差应力和应力降呈现“正坡”、“负坡”和“平缓跳动”等阶段性变化，而应力降比率则渐趋减小；其变化原因主要与错动面的密接和凹凸程度、碎屑厚度、粒度、以及试件受力和刚度约束条件的改变等因素有关。突发失稳序列的变化特征，有可能为预测后续地震强弱变化的趋势提供依据     

A Rupture Model for the 1999 Chi-Chi Earthquake from Inversion of Teleseismic Data Using the Hybrid Homomorphic Deconvolution Method

This study investigates the kinematics of the rupture process of the M _L 7.3 Chi–Chi, Taiwan, earthquake on September 21, 1999. By applying the proposed hybrid homomorphic deconvolution method to deconvolve teleseismic broadband P-wave displacement recordings of the earthquake, this study derives the apparent source time functions (ASTFs) at ten stations located around the epicenter. To further characterize the fault, the kinematic history of the rupture was inverted from ASTFs using a genetic algorithm, coupled with nonlinear iterative technique. The calculated ASFTs reveal that the total rupture event lasted for approximately 27 s. Static slip distribution images indicate that most slip occurred at shallower portions of the fault plane, especially 20–55 km north of the epicenter. The maximum slip reached 20 m at 45 km north of the epicenter, and the average slip throughout the observed rupture area was approximately 2 m. Large asperities on the fault appeared at 25–35 km and 40–50 km north of the hypocenter, and coincided with relatively high rupture velocity. This suggests that the earthquake’s energy may have been released quickly. The rupture velocity decreased upon encountering an asperity, and increased again after passing the asperity. This implies that the rupture required more time to overcome the resistances of the asperities. The maximum rupture velocity was 3.8 km/s, while the average rupture velocity was approximately 2.2 km/s. The rise time distribution suggests that larger slip amplitudes generally correspond to shorter rise times on the subfaults.