Mainshock Aftershock Research Articles

Seismic response of RC frames under far-field mainshock and near-fault aftershock sequences

Engineered structures built in seismic-prone areas are affected by aftershocks in addition to mainshocks. Although aftershocks generally are lower in magnitude than that of the mainshocks, some aftershocks may have higher intensities; thus, structures should be able to withstand the effect of strong aftershocks as well. This seismic scenario arises for far-field mainshock along with near-field aftershocks. In this study, four 2D reinforced concrete (RC) frames with different numbers of stories were designed in accordance with the current Iranian seismic design code. As a way to evaluate the seismic response of the case-study RC frames, the inter-story drift ratio (IDR) demand, the residual inter-story drift ratio (RIDR) demand, the Park-Ang damage index, and the period elongation ratio can be useful engineering demand parameters for evaluating their seismic performance under mainshock-aftershock sequences. The frame models were analyzed under a set of far-field mainshock, near-fault aftershocks seismic sequences using nonlinear dynamic time-history analysis to investigate the relationship among IDR, RIDR, Park-Ang damage index and period ratio experienced by the frames. The results indicate that the growth of IDR, RIDR, Park-Ang damage index, and period ratio in high-rise and short structures under near-fault aftershocks were significant. It is evident that engineers should consider the effects of near-fault aftershocks on damaged frames that experience far-field mainshocks as well.

Spatiotemporal Analysis of the Foreshock–Mainshock–Aftershock Sequence of the 6 July 2017 Mw 5.8 Lincoln, Montana, Earthquake

Spatiotemporal Analysis of the Foreshock–Mainshock–Aftershock Sequence of the 6 July 2017 Mw 5.8 Lincoln, Montana, Earthquake

Damage spectra of the mainshock-aftershock ground motions at soft soil sites

The soft soil tends to amplify the damage accumulation induced by mainshock-aftershock (MSAS) sequences due to the significant amplification effect of soft soil on the ground motions. This manuscript proposes the damage spectra of MSAS ground motions at soft soil sites to quantify the accumulated damage experienced by the structures under the MSAS sequences. Artificial MSAS ground motions are firstly generated by the revised randomization method (i.e. combing two random records which belong to two different ground motion groups respectively). The effects of period normalization (i.e. the vibration period is normalized by the predominant period of mainshock ground motion) are discussed from the point of view of dispersion and mean. The effects of the aftershock ground motions at soft soil sites on the damage spectra are quantitatively studied. The results indicate that the period normalization can reduce the dispersion of damage spectra of MSAS sequences, but larger intensity of aftershock ground motion can contaminate the efficiency of period normalization. The effects of strong aftershocks at soft soil sites on the damage spectra can exceed 40%. Strong aftershock ground motions at soft soil sites tend to cause larger additional damage than those at firm soil sites. The prediction equations are finally proposed to predict the mean of damage spectra for MSAS sequences at soft soil sites.

Resilience loss factor for evaluation and design considering the effects of aftershocks

The seismic resilience of a system includes not only the consequences directly related to the intensity of earthquake but also the recovery process and time closely related to the human and government responses in the post-earthquake environment, in which many aftershocks would affect the mainshock-damaged systems. This manuscript proposes a resilience loss factor to incorporate the effects of aftershocks on the resilience loss of structures. This factor is applied on the evaluation of resilience loss for a case-study reinforced concrete (RC) frame structure under mainshock-aftershock (MSAS) sequences. The recovery time and pre-event functionality are introduced in the definition of the resilience loss factor, making this factor concentrate more on the intrinsic characteristics of structures during the recovery process. The replacement threshold based on the repair cost is incorporated into the definition of resilience loss factor to reflect the engineering application. The results indicate that the effects of considering replacement threshold and aftershocks on the resilience loss of structure can exceed 200% and 400% respectively, when the replacement threshold is reached.

Patterns of Reservoir‐Triggered Seismicity in a Low‐Seismicity Region of France

We analyzed the impact of the 26 largest impounded reservoirs on reservoir‐triggered seismicity (RTS) patterns in the low‐seismicity region of continental France. We treat reservoir‐triggered earthquakes as tectonic earthquakes and apply similar concepts in our analysis. Generally, the spatial extent of an aftershock zone is controlled by the mainshock rupture length. In a similar manner, we use reservoir length as an equivalent length to the rupture length to assess the spatial extent of reservoir‐triggering earthquakes and one to three reservoir lengths as a proxy for the near‐field distance where the stress change induced by reservoir impoundment may trigger seismicity. Accordingly, we define the 1Lr distance as the near‐field reservoir effect on seismicity and the 10Lr distance as the far field, null effect of reservoir stress change on background seismicity. We find that (1) about a quarter of the reservoirs trigger Mmax=2.5–4.7 within the 1Lr distance in a 15 yr space time window, and (2) as tested against a randomized series, superposed epoch analysis demonstrates a robust increase in the average seismicity rate within 2 yrs for the 1–3Lr distance from reservoirs. The reservoirs that trigger in the (⁠ 1Lr ⁠) near‐field distance are significantly larger than the nontriggering ones. While considering the distance of triggering of earthquakes from the reservoir, it is more appropriate to consider the normalized distance (the distance normalized by the reservoir length) to identify earthquake triggering reservoirs at a 1Lr distance. While considering reservoir dimensions, the reservoir length appears to be a more important parameter than the reservoir depth, as the length is proportional to the area of significant stress change. Our results suggest that the RTS mimics the aftershock sequence of a slow reservoir‐impoundment loading, with a corresponding M∗reservoir=M(Lr) mainshock magnitude. Further, when considering mainshock–aftershock interactions, our analysis and observations support that the Mmax for RTS for a given reservoir remains, on average, smaller than the reservoir magnitude equivalent.

Advanced two-step integrated optimization of actively controlled nonlinear structure under mainshock–aftershock sequences

In this paper, an attempt is made to examine a new method for designing and applying the active vibration control system to improve building performance under mainshock–aftershock sequences. In this regard, three different structures are considered; 5-, 10-, and 15-story buildings. Seven mainshock–aftershock sequences are selected from the Iranian accelerogram database for analyzing the structures. By implementing an advanced two-step optimization method, buildings equipped with the active vibration control system (linear–quadratic regulator (LQR) algorithm) are designed to withstand all events of mainshock–aftershock sequences. In the first optimization step, a multi-objective optimization with the genetic algorithm is performed and a set of optimal Pareto front results is obtained. In the next step, the life-cycle cost of each optimal design sample of the Pareto front is calculated by considering the cumulative damage and the design sample with the minimum cost is selected as a final optimal property. The results prove that the active vibration control system is capable of reducing structural responses, including acceleration, drift, and residual drift under mainshock–aftershock sequences, and consequently the life-cycle cost of buildings, especially the taller ones. In addition, obtaining the building design variables (story stiffness and yielding force) and active LQR algorithm properties simultaneously leads to a slightly softer final building model than the conventional structure designed by the common building design code. Moreover, it is revealed that, by considering the aftershocks, the building life-cycle cost increases significantly.

3D seismogenic model of the 2015 Gorkha earthquake and subsequent seismic risk

On April 25th, 2015, the moment magnitude (M-w) 7. 8 Gorkha earthquake, Nepal occurred in Himalaya orogenic belt, which seems insufficient to release the accumulated energy as suggested previously. The following seismic risk assessments are mostly based on the two dimensional or pseudo-three dimensional inversions of tectonic deformation. Here we analyze the relationship between the main shock and biggest aftershock of the 2015 Gorkha earthquake sequence, and its unevenness in time and space. Combining focal mechanism solutions, crustal velocity structure, relocated aftershocks, and inversion results from InSAR, we construct a three dimensional model which changes along both the strike and dip directions of the Main Himalayan Thrust. The finite element method with nonlinear friction is used to calculate the fault behavior and block deformation in one earthquake recurrence period. Comparison between the forward calculation results and the co-seismic deformation observed from InSAR, and co-seismic slip inverted from deformation observations, and time-space evolution of historical earthquakes revealed that the three dimension model is close to the reality. The results suggest two potential seismic risk regions in the future: a big earthquake might be located in the east of the 1934 Bihar-Nepal M-w similar to 8. 1 earthquake, and a moderate to major event might take place to the southeast of the aftershock M(w)7. 3 earthquake.

ESTIMATION OF STATIC COULOMB STRESS CHANGE AND STRONG MOTION SIMULATION FOR JIUZHAIGOU 7.0 EARTHQUAKE BASE ON SENTINEL-1 INSAR DATA INVERSION

Abstract. On August 8, 2017, an earthquake of M 7.0 occurred at Jiuzhaigou. Based on the Sentinel-1 satellite InSAR data, we obtained coseismic deformation field and inverted the source slip model. Results show that this event is dominated by strike slip, and the total released seismic moment is 8.06 × 1018 Nm, equivalent to an earthquake of Mw ~ 6.57. We calculated static stress changes along strike and dip direction, and the static stress analysis show that the average stress drop are at low level, which may be responsible for the low level of ground motion during Jiuzhaigou earthquake. The coseismic Coulomb stress changes are calculated base on the inverted slip model, which revealed that 82.59 % of aftershocks are located in the Coulomb stress increasing area, 78.42 % of total aftershocks may be triggered by the mainshock aftershock, indicating that the mainshock has a significant triggering effect on the subsequent aftershocks. Based on stochastic finite fault model, we simulated regional peak ground acceleration (PGA), peak ground velocity (PGV) and the intensity, and results could capture basic features associated with the ground motion patterns. Moreover, the simulated results reflect the obvious rupture directivity effect.

Hysteretic energy prediction method for mainshock-aftershock sequences

Structures located in seismically active regions may be subjected to mainshock-aftershock (MSAS) sequences. Strong aftershocks significantly affect the hysteretic energy demand of structures. The hysteretic energy, EH,seq, is normalized by mass m and expressed in terms of the equivalent velocity, VD,seq, to quantitatively investigate aftershock effects on the hysteretic energy of structures. The equivalent velocity, VD,seq, is computed by analyzing the response time-history of an inelastic single-degree-of-freedom (SDOF) system with a varying vibration period subjected to 309 MSAS sequences. The present study selected two kinds of MSAS sequences, with one aftershock and two aftershocks, respectively. The aftershocks are scaled to maintain different relative intensities. The variation of the equivalent velocity, VD,seq, is studied for consideration of the ductility values, site conditions, relative intensities, number of aftershocks, hysteretic models, and damping ratios. The MSAS sequence with one aftershock exhibited a 10% to 30% hysteretic energy increase, whereas the MSAS sequence with two aftershocks presented a 20% to 40% hysteretic energy increase. Finally, a hysteretic energy prediction equation is proposed as a function of the vibration period, ductility value, and damping ratio to estimate hysteretic energy for mainshock-aftershock sequences.

Earthquake Direction Effects on Seismic Performance of Concrete Gravity Dams to Mainshock–Aftershock Sequences

The aim of the present study was to examine the effects of earthquake direction on seismic performance of concrete gravity dams subjected to seismic sequences. For these purposes, two seismic incident directions are applied along horizontal axes to assess the maximum structural demands. Nonlinear dynamic analyses of the dam-reservoir-foundation system subjected to as-recorded mainshock–aftershock sequences are conducted to investigate the effects: 1) direction of single earthquake events; 2) direction of seismic sequences; 3) aftershock polarity; and 4) earthquake intensity. The results indicate that earthquake direction can significantly change the damage propagation processes of concrete gravity dams.

New Data on Aftershocks of the December 7, 1988, Spitak Earthquake

The paper addresses the collection and analysis of new data on aftershocks that occurred within 20 days of the main shock of the December 7, 1988, Spitak earthquake, Mw = 6.8. The data were used to improve the location of aftershock hypocenters and magnitudes. Available data concerning this 20-day period were the least reliable in terms of completeness, representativeness, and the accuracy of hypocenter location and, in particular, estimation of energy classes and magnitudes. New data were retrieved from the records and bulletins of the seismic stations of the regional and global networks. Hypocenter parameters were determined by means of the minimization of wave travel-time residuals and subsequent double-difference hypocenter relocation. Digital records of the Obninsk and Arti seismic stations (Δ = 15°–18°) and five more distant stations (Δ = 34°–53°) were used to more accurately estimate the surface-wave magnitude of the main shock and strongest aftershock. The aftershock catalog of the Spitak earthquake was substantially revised. First, the previous hypocenter locations (Aref’ev et al., 1991) were improved using the double-difference method; second, new data were retrieved from the bulletins of Caucasian seismic stations. The minimum magnitude of completeness (M c = 1.9) of the new catalog for the first 20 days after the main shock (when there were no epicentral observations) is the same as that for the period from December 7, 1988, to December 31, 1989. The new catalog contains information on 2090 aftershocks with magnitude M = 1.9 and more for the period from December 7, 1988, to December 31, 1989. The double-difference method allowed the location of the epicenters of clustered earthquakes to be reliably estimated with a longitude error of no more than 4.6 km, a latitude error of 4 km, and a depth error of 5 km. The new spatial distribution of the aftershock hypocenters is better correlated with the tectonic setting than the old data. The new catalog can be used to assess seismic hazard after strong earthquakes in the region.

Testing for the ‘predictability’ of dynamically triggered earthquakes in The Geysers geothermal field

The Geysers geothermal field is well known for being susceptible to dynamic triggering of earthquakes by large distant earthquakes, owing to the introduction of fluids for energy production. Yet, it is unknown if dynamic triggering of earthquakes is ‘predictable’ or whether dynamic triggering could lead to a potential hazard for energy production. In this paper, our goal is to investigate the characteristics of triggering and the physical conditions that promote triggering to determine whether or not triggering is in anyway foreseeable. We find that, at present, triggering in The Geysers is not easily ‘predictable’ in terms of when and where based on observable physical conditions. However, triggered earthquake magnitude positively correlates with peak imparted dynamic stress, and larger dynamic stresses tend to trigger sequences similar to mainshock–aftershock sequences. Thus, we may be able to ‘predict’ what size earthquakes to expect at The Geysers following a large distant earthquake.

Seismic Evaluation of Steel Moment Frames Under Mainshock–Aftershock Sequence Designed by Elastic Design and PBPD Methods

ABSTRACTAftershocks can increase building vulnerability and decrease life-safety of the residents; nevertheless, no practical design method has yet been considered the seismic risk of aftershock. In this study, a new design method known as performance-based plastic design (PBPD) has been utilized instead of conventional elastic design (ED) for steel moment frames which considers nonlinear behavior of structures directly in the design process. Result of time-history analysis shows that drift increase due to aftershock for ED-frame is more than PBPD-frame. In addition, plastic hinge and hysteretic energy distributions for PBPD-frame when subjected to mainshock–aftershock sequence is more desirable than ED-frame.

Seismic Damage Assessment of SMA-Retrofitted Multiple-Frame Bridge Subjected to Strong Main Shock–Aftershock Excitations

Seismic Damage Assessment of SMA-Retrofitted Multiple-Frame Bridge Subjected to Strong Main Shock–Aftershock Excitations

Constraining the magnitude of the largest event in a foreshock–main shock–aftershock sequence

Constraining the magnitude of the largest event in a foreshock–main shock–aftershock sequence

Probabilistic Assessment and Cost-Benefit Analysis of Nonductile Reinforced Concrete Buildings Retrofitted with Base Isolation: Considering Mainshock–Aftershock Hazards

AbstractNonductile reinforced concrete (RC) frame buildings were found to be vulnerable to earthquakes. Thus retrofitting of these buildings is necessary, as addressed in the recent retrofit progra...

Forecasting the (Un)Productivity of the 2014 M 6.0 South Napa Aftershock Sequence

ABSTRACT The 24 August 2014 M w 6.0 South Napa mainshock produced fewer aftershocks than expected for a California earthquake of its magnitude. In the first 4.5 days, only 59 M ≥1.8 aftershocks occurred, the largest of which was an M 3.9 that happened a little over two days after the mainshock. We investigate the aftershock productivity of the South Napa sequence and compare it with other M ≥5.5 California strike‐slip mainshock–aftershock sequences. While the productivity of the South Napa sequence is among the lowest, northern California mainshocks generally have fewer aftershocks than mainshocks further south, although the productivities vary widely in both regions. An epidemic‐type aftershock sequence (ETAS) model (Ogata, 1988) fit to Napa seismicity from 1980 to 23 August 2014 fits the sequence well and suggests that low‐productivity sequences are typical of this area. Utilizing regional variations in productivity could improve operational earthquake forecasting (OEF) by improving the model used immediately after the mainshock. We show this by comparing the daily rate of M ≥2 aftershocks to forecasts made with the generic California model (Reasenberg and Jones, 1989; hereafter, RJ89), RJ89 models with productivity updated daily, a generic California ETAS model, an ETAS model based on premainshock seismicity, and ETAS models updated daily following the mainshock. RJ89 models for which only the productivity is updated provide better forecasts than the generic RJ89 California model, and the Napa‐specific ETAS models forecast the aftershock rates more accurately than either generic model. Therefore, forecasts that use localized initial parameters and that rapidly update the productivity may be better for OEF than using a generic model and/or updating all parameters.

Conditional Mean Spectrum of Aftershocks

Abstract This study proposes a pragmatic method to generate the conditional mean spectrum of aftershocks (CMS A ), which reasonably considers the dependence of the spectral shapes (epsilons) between mainshocks and aftershocks using the copula technique. To obtain the CMS A , the conditional mean epsilons of aftershocks are computed, conditioned on the corresponding values of mainshocks, and then these conditional mean epsilons are further used to modify the predicted response spectra of aftershocks estimated by a specific ground‐motion prediction equation. To validate the presented method, a suite of 662 real mainshock–aftershock ground‐motion sequences from 13 earthquake sequences are selected to form the database for this study. The Abrahamson et al. (2014, hereafter, ASK14) model is selected to predict the response spectra of aftershocks. This study builds the joint probability distributions between mainshock epsilons and aftershock epsilons with copula functions. The CMS A values are calculated for all the selected mainshock ground motions according to the procedures of generating CMS A . The results show that, compared with the predicted response spectra estimated by the ASK14 model, the CMS A matches the as‐recorded response spectrum of aftershocks better, especially for long periods. This result validates the presented method of generating the CMS A . Electronic Supplement: Detailed information of a set of 674 mainshock–aftershock (MS–AS) ground‐motion sequences.

Damage demand assessment of mainshock-damaged concrete gravity dams subjected to aftershocks

In China, the current seismic codes specify a single earthquake event as the design seismic load for concrete gravity dams. However, a large mainshock usually triggers numerous aftershocks in a short period. This paper assesses the effects of aftershocks on concrete gravity dam–reservoir–foundation systems and provides a quantitative description of the damage demands prior to and following the aftershocks. For this purpose, a set of 20 as-recorded mainshock–aftershock seismic sequences is considered in this study. The correlation between the ground motion characteristics of the as-recorded mainshocks and those of the aftershocks is examined. In order to identify the influence of the ground motion characteristics of aftershocks on the damage demands of the mainshock-damaged dams, the nonlinear behavior of the concrete gravity dams that are subjected to single seismic events and typical as-recorded seismic sequences is compared in terms of the structural damage, displacement response, and damage dissipated energy. A series of nonlinear dynamic analyses is performed to quantify the influence of aftershocks, which are selected by using different methods, on the damage demands of concrete gravity dam–reservoir–foundation systems in terms of the local and global damage indices. The results show that the aftershocks lead to an increase in the damage demands of the dam at the end of the seismic sequence when the concrete gravity dam is already damaged during the first individual seismic event and has not been repaired. In addition, the results also reveal that the repeated seismic sequences tend to underestimate the level of damage demands.

Aftershock collapse fragility curves for non‐ductile RC buildings: a scenario‐based assessment

SummaryRecent studies have addressed the computation of fragility curves for mainshock (MS)‐damaged buildings. However, aftershock (AS) fragilities are generally conditioned on a range of potential post‐MS damage states that are simulated via static or dynamic analyses performed on an intact building. Moreover, there are very few cases where the behavior of non‐ductile reinforced concrete buildings is analyzed.This paper presents an evaluation of AS collapse fragility conditioned on various return periods of MSs, allowing for the rapid assessment of post‐earthquake safety variations based solely on the intensity of the damaging earthquake event. A refined multi‐degree‐of‐freedom model of a seven‐storey non‐ductile building, which includes brittle failure simulations and the evaluation of a system level collapse, is adopted. Aftershock fragilities are obtained by performing an incremental dynamic analysis for a number of MS–AS ground motion sequences and a variety of MS intensities.The AS fragilities show that the probability of collapse significantly increases for higher return periods for the MS. However, this result is mainly ascribable to collapses occurred during MSs. When collapse cases that occur during a MS are not considered in the assessment of AS collapse probability, a smaller shift in the fragility curves is observed as the MS intensity increases. This result is justified considering the type of model and collapse modes introduced, which strongly depend on the brittle behavior of columns failing in shear or due to axial loads. The analysis of damage that is due to MSs when varying the return period confirms this observation. Copyright © 2017 John Wiley & Sons, Ltd.