Can Damage Mechanics Explain Temporal Scaling Laws in Brittle Fracture and Seismicity?

Time delays associated with processes leading to a failure or stress relaxation in materials and earthquakes are studied in terms of continuum damage mechanics. Damage mechanics is a quasi-empirical approach that describes inelastic irreversible phenomena in the deformation of solids. When a rock sample is loaded, there is generally a time delay before the rock fails. This period is characterized by the occurrence and coalescence of microcracks which radiate acoustic signals of broad amplitudes. These acoustic emission events have been shown to exhibit power-law scaling as they increase in intensity prior to a rupture. In case of seismogenic processes in the Earth's brittle crust, all earthquakes are followed by an aftershock sequence. A universal feature of aftershocks is that their rate decays in time according to the modified Omori's law, a power-law decay. In this paper a model of continuum damage mechanics in which damage (microcracking) starts to develop when the applied stress exceeds a prescribed yield stress (a material parameter) is introduced to explain both laboratory experiments and systematic temporal variations in seismicity.     

汶川地震余震活动固体潮调制的统计分析

A statistical analysis on the Wenchuan aftershock activity triggered by tidal forces is systematically studied based on Schusters test, including earthquakes triggered by tidal force, tidal stress and tidal coulomb failure stress. The results show that a group of strong aftershocks which occurred at the end of July to early August in 2008 at the north of Wenchuan were obviously triggered by earth tide, the same conclusion is drawn by Schusters smooth test of the tidal force, tidal stress and tidal coulomb failure stress. In addition, the Wenchuan aftershock activity is obviously triggered by fortnight tide. In the north, the aftershocks happened more frequently in the first and last quarters of the moon, and in the south, the aftershocks happened more frequently in the first and last quarters of the moon and during the full moon.     

Calculation of Calibration Functions and Explosive Aftershock Magnitudes in the Near Field

The current calibration function used in calculating the magnitude of natural earthquakes within 5km is a constant; a fact that causes several serious difficulties for the calculation of the magnitude of small and shallow-focus earthquakes. According to the attenuation law of explosions and the propagation theory of elastic waves, the calibration function is calculated for near field quakes from 0kin to 5kin. Magnitudes of two aftershock sequences are calculated. The magnitudes of most explosion earthquakes are small, ranging mainly from magnitude -0.5 to 1.0. The M-t chart of the explosive aftershocks is completely different from that of strong earthquake aftershocks. It not only shows positive columnar lines indieatJng large magnitudes but also short negative columnar lines indicating small magnitudes.     

Numerical Modeling of the Ston-Slano (Croatia) Aftershock Sequence

The rate of aftershock occurrence after the M6 Ston-Slano (Croatia) earthquake is modeled as the Epidemic Type Aftershock Sequence (ETAS). Increase of the modeled cumulative number of aftershocks with time was fitted to observations by the least-squares criterion using the combined grid-search and Monte-Carlo approach. This enabled not only the estimation of the most probable ETAS parameters, but also the determination of their confidence limits, as well as the estimation of the bias between them. It has been found that the bias is significant for some of the parameter pairs, regardless of the threshold magnitude assumed. Residual analyses revealed that all strong aftershocks (M _L 4.5) occurred during the periods of normal to high aftershock activity. There were two periods of quiescence in the sequence, both of which were followed by a strong aftershock.     

Aftershock seismic assessment taking into account postmainshock residual drifts

This paper introduces and evaluates a methodology for the aftershock seismic assessment of buildings taking explicitly into account residual drift demands after the mainshock (i.e., postmainshock residual interstory drifts, RIDR_o). The methodology is applied to a testbed four‐story steel moment‐resisting building designed with modern seismic design provisions when subjected to a set of near‐fault mainshock–aftershock seismic sequences that induce five levels of RIDR_o. Once the postmainshock residual drift is induced to the building model, a postmainshock incremental dynamic analysis is performed under each aftershock to obtain its collapse capacity and its capacity associated to demolition (i.e., the capacity to reach or exceed a 2% residual drift). The effect of additional sources of stiffness and strength (i.e., interior gravity frames and slab contribution) and the polarity of the aftershocks are examined in this study. Results of this investigation show that the collapse potential under aftershocks strongly depends on the modeling approach (i.e., the aftershock collapse potential is modified when additional sources of lateral stiffness and strength are included in the analytical model). Furthermore, it is demonstrated that the aftershock capacity associated to demolition (i.e., the aftershock collapse capacity associated to a residual interstory drift that leads to an imminent demolition) is lower than that of the aftershock collapse capacity, which mean that this parameter should be a better measure of the building residual capacity against aftershocks. Copyright © 2014 John Wiley & Sons, Ltd.     

Aftershock collapse vulnerability assessment of reinforced concrete frame structures

In a seismically active region, structures may be subjected to multiple earthquakes, due to mainshock–aftershock phenomena or other sequences, leaving no time for repair or retrofit between the events. This study quantifies the aftershock vulnerability of four modern ductile reinforced concrete (RC) framed buildings in California by conducting incremental dynamic analysis of nonlinear MDOF analytical models. Based on the nonlinear dynamic analysis results, collapse and damage fragility curves are generated for intact and damaged buildings. If the building is not severely damaged in the mainshock, its collapse capacity is unaffected in the aftershock. However, if the building is extensively damaged in the mainshock, there is a significant reduction in its collapse capacity in the aftershock. For example, if an RC frame experiences 4% or more interstory drift in the mainshock, the median capacity to resist aftershock shaking is reduced by about 40%. The study also evaluates the effectiveness of different measures of physical damage observed in the mainshock‐damaged buildings for predicting the reduction in collapse capacity of the damaged building in subsequent aftershocks. These physical damage indicators for the building are chosen such that they quantify the qualitative red tagging (unsafe for occupation) criteria employed in post‐earthquake evaluation of RC frames. The results indicated that damage indicators related to the drift experienced by the damaged building best predicted the reduced aftershock collapse capacities for these ductile structures. Copyright © 2014 John Wiley & Sons, Ltd.     

A closing Ligurian Sea?

Two earthquakes occurred in the Ligurian Sea in December 1989 and April 1990. Both were widely felt along the French and Italian Rivieras, thus reminding us of the seismic risk in this region. The significant increase in the number of seismic stations in the area facilitated the study of these two shocks and their related aftershocks. Using different techniques (absolute and relative hypocentral locations, doublet analysis and waveform modeling), we computed accurate hypocentral locations and estimated the location-error range for earthquakes in this area. We also computed the focal mechanisms for both mainshocks, and we present here a synthesis that integrates previous data. The reactivation in compression of the Ligurian Sea sphenochasm is confirmed, which would eventually result in the closing of an aborted oceanic domain. As the seismic activity is clearly restricted to the northern margin, we suggest it locally results from the lateral expulsion of the south-western Alps along the Apulian indenter.     

针对应急救援的强余震特征统计

大地震后强余震活跃,震后快速判断最大余震震级和强余震发生可能性对提高应急救援效率有重大意义。针对震后应急救援,本文根据救援存活率将震后救援期分为8个时段:震后12 h、震后24 h、震后48 h、震后72 h、震后96 h、震后120 h、震后144 h和震后168 h。对我国大陆地区1966年以来6级及以上地震强余震资料进行分时段统计,分别拟合出8个时段的最大余震震级和主震震级的经验公式;并提出震后强余震发生可能性的经验判断方法,通过本文提出的可能性指数a,依据主震震级,震后可以快速判定强余震发生的可能性。     

汶川地震余震区波速比与强余震的关系

利用2008年5月12日汶川地震余震的P波和S波到时数据,对龙门山地区波速比进行了计算。结果表明,该地区的强余震全部发生在波速比相对较高的地区,这应该是地下介质的破碎原因造成的。     

Spatial distribution of aftershocks and background seismicity in central California

We examine the spatial distribution of earthquake hypocenters in four central California areas: the aftershock zones of the (1) 1984 Morgan Hill (2) 1979 Coyote Lake, and (3) 1983 Coalinga earthquakes, as well as (4) the aseismically creeping area around Hollister. The basic tool we use to analyze these data are frequency distributions of interevent distances between earthquakes. These distributions are evaluated on the basis of their deviation from what would be expected if earthquakes occurred randomly in the study areas. We find that both background seismic activity and aftershocks in the study areas exhibit nonrandom spatial distribution. Two major spatial patterns, clustering at small distances and anomalies at larger distances, are observed depending on tectonic setting. While both patterns are seen in the strike-slip environments along the Calaveras fault (Morgan Hill, Coyote Lake, and Hollister), aftershocks of the Coalinga event (a thrust earthquake) seem to be characterized by clustering only. The spatial distribution of earthquakes in areas gradually decreasing in size does not seem to support the hypothesis of a self-similar distribution over the range of scales studied here, regardless of tectonic setting. Spatial distributions are independent of magnitude for the Coalinga aftershocks, but events in strike-slip environments show increasing clustering with increasing magnitude. Finally, earthquake spatial distributions vary in time showing different patterns before, during, and following the end of aftershock sequences.     

Recurrence Interval Statistics of Cellular Automaton Seismicity Models

The recurrence interval statistics for regional seismicity follows a universal distribution function, independent of the tectonic setting or average rate of activity (Corral, 2004). The universal function is a modified gamma distribution with power-law scaling of recurrence intervals shorter than the average rate of activity and exponential decay for larger intervals. We employ the method of Corral (2004) to examine the recurrence statistics of a range of cellular automaton earthquake models. The majority of models has an exponential distribution of recurrence intervals, the same as that of a Poisson process. One model, the Olami-Feder-Christensen automaton, has recurrence statistics consistent with regional seismicity for a certain range of the conservation parameter of that model. For conservation parameters in this range, the event size statistics are also consistent with regional seismicity. Models whose dynamics are dominated by characteristic earthquakes do not appear to display universality of recurrence statistics.     

Magnitude scaling factors in liquefaction triggering procedures

A revised magnitude scaling factor (MSF) relationship for CPT-based and SPT-based liquefaction triggering analyses is presented in this paper. The revised MSF relationship incorporates functional dependency on the soil characteristics [represented by clean sand equivalent penetration resistances in the present form] as well as on earthquake magnitude. The revisions in MSF are based on the examination of cyclic testing results for a broad range of soil types and densities, analyses of strong ground motion records to develop relationships for the equivalent number of loading cycles for different soil properties, and the synthesis of those results into an MSF relationship suitable for implementation in practice. A separate study [2] showed that use of the revised MSF relationship in CPT-based and SPT-based liquefaction triggering procedures is well-supported by the case history databases. Other factors known to fundamentally influence the MSF are discussed.     

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.     

Power-law Distributions of Offspring and Generation Numbers in Branching Models of Earthquake Triggering

We consider a general stochastic branching process,which is relevant to earthquakes as well as to many other systems, and we study the distributions of the total number of offsprings (direct and indirect aftershocks in seismicity) and of the total number of generations before extinction. We apply our results to a branching model of triggered seismicity, the ETAS (epidemic-type aftershock sequence) model. The ETAS model assumes that each earthquake can trigger other earthquakes (aftershocks). An aftershock sequence results in this model from the cascade of aftershocks of each past earthquake. Due to the large fluctuations of the number of aftershocks triggered directly by any earthquake (fertility), there is a large variability of the total number of aftershocks from one sequence to another, for the same mainshock magnitude. We study the regime in which the distribution of fertilities is characterized by a power law ~1/¹⁺. For earthquakes we expect such a power-distribution of fertilities with =b/ based on the Gutenberg-Richter magnitude distribution ~ 10^–bm and on the increase ~ 10^–m of the number of aftershocks with the mainshock magnitude m. We derive the asymptotic distributions p_r(r) and p_g(g) of the total number r of offsprings and of the total number g of generations until extinction following a mainshock. In the regime < 2 for which the distribution of fertilities has an infinite variance, we find This should be compared with the distributions obtained for standard branching processes with finite variance. These predictions are checked by numerical simulations. Our results apply directly to the ETAS model whose preferred values =0.8–1 and b=1 puts it in the regime where the distribution of fertilities has an infinite variance. More generally, our results apply to any stochastic branching process with a power-law distribution of offsprings per mother     

2011年日本东北大地震特低频地磁信号的分形标度特征研究

本文选择2011年3月11日M9.0日本东北大地震震中附近三个地磁台站16个月(2010/01/01—2011/04/30)的特低频地磁观测资料,采用去倾扰动分析方法,得到了这三个台站地磁记录的非均匀标度特征随时间的变化,提出了一种能反映地磁三分量非均匀标度特征同步变化的指标,并据此探讨了特低频地磁信号分形标度特征变化与日本东北大地震之间的可能关联性,初步结果表明,这三个台站的特低频地磁信号分形标度特征指标在日本东北大地震前25~50天左右呈现出同步的异常增加,基于磁静日观测资料的随机合成地磁数据的统计检验结果可知前述异常并非随机异常,而是一种具有统计显著性的异常,可能反映了日本东北大地震对周边地磁信号内在的非线性系统特征产生了有统计意义的影响.     

Spatial Scaling of Effective Modulus and Correlation of Deformation Near the Critical Point of Fracturing

Many observations point to the lithosphere being metastable and close to a critical mechanical point. Exercises in modelling deformation, past or present, across subsurface reservoirs need to take account of this criticality in an efficient way. Using a renormalization technique, the spatial scaling of effective elastic modulus is derived for 2-D and 3-D bodies close to the critical point of through-going fracturing. The resulting exponent, d_μ, of spatial scaling of effective modulus with size, , takes the values ~ −2.5 and −4.2 in two- and three-dimensional space, respectively. The exponents are compatible with those for scaling of effective modulus with fracture density near the percolation threshold determined by other workers from numerical experiments; the high absolute values are also approximately consistent with empirical data from a) fluctuations in depth of a seismic surface; b) `1/k' scaling of heterogeneities observed in one-dimensional well-log samples; c) spatial correlation of slip displacements induced by water injection. The effective modulus scaling modifies the spatial correlation of components of displacement or strain for a domain close to the critical point of fracturing. This correlation function has been used to geostatistically interpolate components of the strain tensor across subsurface reservoirs with the prime purpose of predicting fracture densities between drilled wells. Simulations of strain distributions appear realistic and can be conditioned to surface depths and observations at wells of fracture-related information such as densities and orientations, welltest permeabilities, changes in well-test permeabilities, etc.     

Relocation of Early and Late Aftershocks of the 2001 Bhuj Earthquake Using Joint Hypocentral Determination (JHD) Technique: Implication toward the Continued Aftershock Activity for more than Four Years

We employed layered model joint hypocentral determination (JHD) with station corrections to improve location identification for the 26 January, 2001 M_w 7.7 Bhuj early and late aftershock sequence. We relocated 999 early aftershocks using the data from a close combined network (National Geophysical Research Institute, India and Center for Earthquake Research Institute, USA) of 8–18 digital seismographs during 12–28 February, 2001. Additionally, 350 late aftershocks were also relocated using the data from 4–10 digital seismographs/accelerographs during August 2002 to December 2004. These precisely relocated aftershocks (error in the epicentral location<30 meter, error in the focal depth estimation < 50 meter) delineate an east-west trending blind thrust (North Wagad Fault, NWF) dipping (~ 45°) southward, about 25 km north of Kachchh main land fault (KMF), as the causative fault for the 2001 Bhuj earthquake. The aftershock zone is confined to a 60-km long and 40-km wide region lying between the KMF to the south and NWF to the north, extending from 2 to 45 km depth. Estimated focal depths suggest that the aftershock zone became deeper with the passage of time. The P- and S-wave station corrections determined from the JHD technique indicate that the larger values (both +ve and -ve) characterize the central aftershock zone, which is surrounded by the zones of smaller values. The station corrections vary from −0.9 to +1.1 sec for the P waves and from −0.7 to +1.4 sec for the S waves. The b-value and p-value of the whole aftershock (2001–2004) sequences of M_w ≥ 3 are estimated to be 0.77 ± 0.02 and 0.99 ± 0.02, respectively. The p-value indicates a smaller value than the global median of 1.1, suggesting a relatively slow decay of aftershocks, whereas, the relatively lower b-value (less than the average b-value of 1.0 for stable continental region earthquakes of India) suggests a relatively higher probability for larger earthquakes in Kachchh in comparison to other stable continental regions of the Indian Peninsula. Further, based on the b-value, mainshock magnitude and maximum aftershock magnitude, the Bhuj aftershock sequence is categorized as the Mogi's type II sequence, indicating the region to be of intermediate level of stresses and heterogeneous rocks. It is inferred that the decrease in p-value and increase in aftershock zone, both spatially as well as depth over the passage of time, suggests that the decay of aftershocks perhaps could be controlled by visco-elastic creep in the lower crust.     

Saving lives in earthquakes: successes and failures in seismic protection since 1960

This paper will look at what we have and have not achieved in reducing the risks to human life from earthquakes in the last 50 years. It will review how success has been achieved in a few parts of the world, and consider what needs to be done by the scientific and engineering community globally to assist in the future task of bringing earthquake risks under control. The first part of the talk will re-examine what we know about the casualties from earthquakes in the last 50 years. Almost 80% of about 1 million deaths turn out to have been caused by just ten great earthquakes, together affecting a tiny proportion of the territory at risk from heavy ground shaking. The disparity between richer and poorer countries is also evident, not only in fatality rates, but also in their rates of change. But the existing casualty database turns out to be a very poor basis for observing such differences, not only because of the small number of lethal events, but also because of the very limited data on causes of death, types and causes of injury. These have been examined in detail in only a few, recent events. All that can be said with certainty is that a few wealthier earthquake-prone countries or regions have made impressive progress in reducing the risk of death from earthquakes, while most of the rest of the world has achieved comparatively little, and in some areas the problem has become much worse. The second part of the paper looks in more detail at what has been achieved country-by-country. Based on a new expert-group survey of key individuals involved in earthquake risk mitigation, it will examine what are perceived to be the successes and failures of risk mitigation in each country or group of countries. This survey will be used to highlight the achievements of those countries which have successfully tackled their earthquake risk; it will examine the processes of earthquake risk mitigation, from campaigning to retrofitting, and it will consider to what extent the achievement is the result of affluence, scientific and technical activity, political advocacy, public awareness, or the experience of destructive events. It will ask to what extent the approaches pioneered by the global leaders can be adopted by the rest. The final section of the talk will argue that it can be useful to view earthquake protection activity as a public health matter to be advanced in a manner similar to globally successful disease-control measures: it will be argued that the key components of such programmes—building in protection; harnessing new technology and creating a safety culture—must be the key components of earthquake protection strategies also. It will consider the contribution which the scientific and engineering community can make to bringing down today’s unacceptably high global earthquake risk. It will be suggested that this role is wider than commonly understood and needs to include: Building-in protection

基于损伤性能并考虑主余震作用的消能减震结构抗震设计

综合考虑余震影响和结构损伤,提出一种基于损伤性能的消能减震结构抗震设计方法。为满足结构抵抗余震的性能要求,提出结合主余震的损伤性能目标。以Park-Ang双参数损伤模型为基础建立了结构层间损伤计算公式,通过损伤程度评估结构抗震性能,给出消能减震结构基于损伤性能的抗震设计流程。     

Wavelet‐based simulation of spectrum‐compatible aftershock accelerograms

In damage‐based seismic design it is desirable to account for the ability of aftershocks to cause further damage to an already damaged structure due to the main shock. Availability of recorded or simulated aftershock accelerograms is a critical component in the non‐linear time‐history analyses required for this purpose, and simulation of realistic accelerograms is therefore going to be the need of the profession for a long time to come. This paper attempts wavelet‐based simulation of aftershock accelerograms for two scenarios. In the first scenario, recorded main shock and aftershock accelerograms are available along with the pseudo‐spectral acceleration (PSA) spectrum of the anticipated main shock motion, and an accelerogram has been simulated for the anticipated aftershock motion such that it incorporates temporal features of the recorded aftershock accelerogram. In the second scenario, a recorded main shock accelerogram is available along with the PSA spectrum of the anticipated main shock motion and PSA spectrum and strong motion duration of the anticipated aftershock motion. Here, the accelerogram for the anticipated aftershock motion has been simulated assuming that temporal features of the main shock accelerogram are replicated in the aftershock accelerograms at the same site. The proposed algorithms have been illustrated with the help of the main shock and aftershock accelerograms recorded for the 1999 Chi–Chi earthquake. It has been shown that the proposed algorithm for the second scenario leads to useful results even when the main shock and aftershock accelerograms do not share the same temporal features, as long as strong motion duration of the anticipated aftershock motion is properly estimated. Copyright © 2008 John Wiley & Sons, Ltd.