Mainshock Aftershock Research Articles

Prediction of damage potential in mainshock–aftershock sequences using machine learning algorithms

Prediction of damage potential in mainshock–aftershock sequences using machine learning algorithms

Mainshock–aftershock sequence simulation via latent space encoding of generative adversarial networks

AbstractAftershocks (ASs) following strong mainshocks (MSs) can exacerbate structural damage or lead to collapse. However, the scarcity of recorded data necessitates reliance on artificial sequences, which have difficulty in characterizing the time‐frequency correlation between MSs and ASs. This study innovatively converts the AS time history prediction into an image translation task, exploiting the invertible transformation between accelerograms and time‐frequency representations. An encoder–decoder neural network is developed to encode the MS information into the latent space of a pre‐trained generative adversarial network, enabling accurate AS predictions through the decoder. The integration of seismic parameters further improves the AS prediction performance. Comparative analyses demonstrate that the proposed method outperforms the traditional ones on accuracy and robustness and reproduces the non‐stationarity of ASs.

Seismic fragility analysis of girder bridges under mainshock‐aftershock sequences based on input‐output hidden Markov model

AbstractCurrent seismic design codes for bridge structures do not account for the influence of aftershock sequences, which, to some extent, overestimate the seismic performance for bridges subjected to mainshock‐aftershock (MS‐AS) scenarios. To address the great need for ground motion sequences tailored to specific research sites for fragility analysis, this study proposes a method for generating artificial MS‐AS ground motion sequences based on the evolutional bimodal Kanai–Tajimi model and the Epidemic–Type Aftershock Sequence model. We establish a framework for MS‐AS fragility analysis using an input–output Hidden Markov Model (IOHMM), where the damage states (DS) of bridge piers are considered unobservable and are inferred statistically through damage indices in an unsupervised manner. Model parameters are trained using intensity measure (IM) sequences and damage index (DI) sequences. Fragility curves for both the mainshock and state‐dependent aftershocks considering multiple aftershocks are formulated based on the initial state probability and state transition probabilities of the proposed IOHMM. The fragility analysis results reveal that as the initial seismic damage level increases, the probability of aftershocks causing higher damage levels in the structure also increases, highlighting the significant impact of aftershocks on structural damage increments. Furthermore, we extend the proposed model to a bivariate seismic intensity measure and develop fragility surfaces. The proposed framework provides a novel approach and insights for tackling seismic fragility under multiple aftershocks.

Reliquefaction behavior of sand and response of pile group subjected to repeated shaking sequence using centrifuge model experiments

A series of centrifuge model experiments were performed in this study to investigate the sand reliquefaction behavior in free field and pile group models subjected to repeated shakings. Toyoura sand was used to prepare the model ground with 50 % relative density and experimented at 50g centrifugal acceleration. A 2 × 2 pile group model was used to examine the response of piles and its effect on sand reliquefaction during repeated shakings. A seismic sequence comprising foreshocks–mainshock–aftershocks–mainshock pattern was imparted to both free field and pile group models. In addition, an independent mainshock was imparted to a free field model and compared with the seismic sequence to examine the effect of foreshocks in triggering future liquefaction. Acceleration time response, excess pore pressure (EPP), ground subsidence, bending moment and lateral displacement of the pile group were measured. Significant de-amplification and unsymmetrical response with presence of shear-induced dilatancy spikes were observed in both free field and pile group models. Results from this study indicate that foreshocks and aftershocks are not sufficient to induce liquefaction. However, liquefaction and subsequent reliquefaction were recorded in both models during mainshocks. Pile group recorded smaller EPP response and subsidence compared to free field model. Higher magnitude of reliquefaction was induced even at moderate depths during the second mainshock at a quicker time. This was primarily associated with the increase in magnitude of anisotropy due to repeated generation and dissipation of pore water which results in decrease in resistance to further reliquefaction. Hardening induced around the vicinity of the pile group due to sand densification has resulted in smaller bending moment values during second mainshock compared to the first.

Fragility Analysis of a Concrete Gravity Dam under Mainshock–Aftershock Sequences considering Sliding and Cracking

Fragility Analysis of a Concrete Gravity Dam under Mainshock–Aftershock Sequences considering Sliding and Cracking

Optimal design of chevron braced friction damper for mainshock–aftershock vulnerability control

This study proposes the optimum design of chevron braced friction dampers (CBFDs) for the vulnerability control of steel moment–resisting frames (SMRFs) under mainshock-aftershock (MS-AS) sequences. First, the optimum parameters of the CBFD systems installed in the stories of an inelastic SMRF are found through minimizing the maximum damage index of stories averaged over seven scaled earthquake excitations. The uniform distribution of the story damage along the height of the controlled SMRF is adopted as constraint in the optimization procedure. The damage index is calculated based on the Park-Ang damage model which is expressed based on a linear combination of deformation, moment, and absorbed hysteretic energy of structural elements imposed by an earthquake excitation. Results reveal that the optimized CBFDs-equipped SMRF exhibits better distribution of the story damage than that of the uncontrolled SMRF. Finally, the vulnerability assessment of the optimized CBFDs-equipped SMRF under MS and MS-AS ground motions is investigated by the fragility curves. The fragility assessment emphasize that the optimized CBFDs effectively mitigate the seismic vulnerability of the controlled SMRF under MS-AS sequences at different damage states.

Multi-metric evaluation of the optimal intensity measure for mainshock-aftershock fragility analysis of transmission towers

Identifying the optimal intensity measure (IM) contributes to reducing uncertainties in probabilistic seismic demand models (PSDM) and enhancing confidence of their results. Although many studies have discussed appropriate IMs for mainshocks, relatively less attention is paid to the potential aftershock effect. In particularly, the optimal IMs for developing PSDM of transmission towers subjected to sequential earthquakes has not been well studied previously. Therefore, this paper conducts a multi-metric evaluation to identify the optimal IM in the context of mainshock-aftershock (MSAS) fragility analysis of transmission towers. This evaluation process includes collecting a set of ground motions recorded with varying magnitudes and fault distances to construct MSAS sequences, followed by comprehensive discussions on their seismic characteristics by comparing thirty-six potential IMs candidates. Additionally, a finite element model of a transmission tower is established to numerically investigate different engineering demand parameters (EDP) of the tower under the selected MSAS sequences. The optimal PSDM of the transmission tower is determined by evaluating each couple of IM−EDP on a logarithmic space using multiple evaluation metrics. Through this analysis, the first-mode spectral acceleration Sa(T1,ξ) is identified as the optimal IM as it exhibits excellent correlation, efficiency, practicality and proficiency with the EDPs of the transmission tower, especially with the inter-segment displacement ratio. Consequently, seismic fragility curves of the transmission tower are developed using the optimal IM. The research outcome can contribute to improving the understanding of the probabilistic assessment of transmission towers in the MSAS scenario.

Endurance time analysis for seismic performance of underground structures subjected to mainshock–aftershock sequences

The seismic response analysis of subway underground structures only considers the impact of a single mainshock, ignoring the aftershocks, which may cause more serious secondary damage within a short time after strong earthquakes. To investigate the seismic performance of underground structures under sequential earthquakes and improve the understanding of aftershocks, we analyzed the dynamic response of subway station structures under mainshock–aftershock sequences. A typical two-story and three-span subway station was selected as the prototype, and a finite element model of a soil–underground structure interaction was established. Based on the basic concept of endurance time and design response spectrum of relevant seismic standards in China, an endurance time acceleration function was generated, and nine mainshock–aftershock sequences were constructed. Thereafter, the seismic responses of subway stations under the action of mainshock–aftershock sequences, such as lateral deformation characteristics and damage failure law, were discussed and analyzed. The results show that the endurance time method can be used as a new and efficient method to study the seismic performance of underground structures subjected to mainshock–aftershock sequences. The effects of aftershocks on the damage and lateral displacement of underground structures were preliminarily revealed. The structural deformation response of each layer varies greatly due to the different damage states of the mainshock. The maximum story drift θ of the structure increases with the increase of loading seismic intensity. From the perspective of seismic damage and relative deformation, the structural dynamic response, considering the effect of sequential earthquakes, is greater than that of the mainshock alone, which reflects the disadvantage of aftershocks in seismic design. The results provide a reference for seismic analysis and damage assessment of structures under sequential earthquakes.

Experimental model updating of slope considering spatially varying soil properties and dynamic loading

AbstractThe widespread threat posed by slope structure failures to human lives and property safety is widely acknowledged. Additionally, natural soil often displays spatial variability due to geological deposition and other factors. Therefore, predicting the seismic response of slopes subjected to ground motions and inversely analyzing the spatial distribution of soils remains an unresolved issue. In the present work, a shaking table experimental test is first designed and carried out, in which a soft‐soil slope dynamic system is established. To capture the seismic response of the soft‐soil slope, specifically the experimental characteristic of acceleration and soil pressure response in both spatial domain and time domain, a series of sensors were pre‐embedded in the slope. Subsequently, a model updating approach is proposed for slope seismic analysis that incorporates spatial variability of soil. In addition, to enhance computational efficiency, the dimensionality reduction of Karhunen–Loève expansion method is introduced to reduce inverse analysis parameters. On the basis of 34 samples collected from experimental data, it is shown that near‐fault pulse‐like ground motions deliver greater concentrated energy, causing more severe damage to slope structures, especially the topsoil layer. Furthermore, using data obtained from a shaking table test subjected to ground motion Recorded Sequence Number 158H1 from the Pacific Earthquake Engineering Research Center NGA‐West2 database as an example, it is also shown that the proposed approach demonstrates high accuracy in predicting the spatial distribution of the maximum shear modulus in soil slope dynamic systems. The present work not only addresses the challenges posed by mainshock–aftershock effects but also highlights the potential of model updating approaches to enhance the understanding of slope behavior under seismic loading conditions.

Seismic Performance of Buildings Equipped with Four-Joint Rotational Friction Dampers in Mainshock–Aftershock Sequences

Seismic Performance of Buildings Equipped with Four-Joint Rotational Friction Dampers in Mainshock–Aftershock Sequences

Characteristics of Micro-Seismic Events Induced by Ground Collapse-A Case Study in the Rongxing Gypsum Mine in Hubei Province, China.

Mining activities can damage rock masses and easily induce ground collapse, which seriously threatens safe production in mining areas. Micro-seismic systems can monitor rock mass deformation signals in real time and provide more accurate data for rock mass deformation analysis. Therefore, in this study, the waveform characteristics of micro-seismic events induced by ground collapse in the Rongxing gypsum mine were analyzed; the occurrence of these events was introduced on the basis of Fast Fourier Transform, an established Frequency-Time-Amplitude model, in order to put forward the index of energy proportion of the main band. The results showed the following. (1) The seismic sequence type of ground collapse was foreshock-mainshock-aftershocks. The interval between the foreshock and mainshock was longer than that between the mainshock and aftershocks. (2) The deformation corresponding to the foreshock micro-seismic events was mainly that of a small-scale crack. The deformation corresponding to the micro-seismic events during the mainshock was characterized by the gradual development of small-scale cracks, and the development of large-scale cracks accelerated, accompanied by slight rock collapse. The deformation corresponding to the micro-seismic events during the aftershocks showed that almost no small-scale cracks developed, and the large-scale crack development was intense, and accompanied by numerous rock and soil mass collapses. (3) The observed decreasing frequency distribution and energy dispersion can be used as possible precursors of ground collapse.

Model updating of highway slope under seismic intensity conditions considering spatially varying soils

Abstract Understanding the mechanisms underlying earthquake-induced landslides and assessing seismic responses are crucial for effective mitigation strategies. Earthquakes typically involve a mainshock followed by aftershocks, posing challenges to structures weakened by the mainshock. Highway slope structures, especially those in unsaturated soft-soil slopes, are vulnerable to aftershocks, amplifying the damage caused by the mainshock-aftershock (MSAS) sequence. While existing research primarily focuses on the effects of mainshocks on certain structures, there is a notable gap regarding the damage sustained by unsaturated slope structures under MSAS conditions. Addressing this gap is vital for comprehensive risk assessment and mitigation. To address these challenges, we propose a stochastic model updating approach for seismic reliability analysis. This approach integrates subset simulation with adaptive Bayesian updating and dimensionality reduction using the Karhunen–Lòeve expansion. Shaking table tests on a slope structure with unsaturated red clay soil are conducted to investigate the effects of matrix suction on performance degradation and failure mechanisms. The results reveal spatial variability in soil property parameters, underscoring the need to incorporate this variability into inverse analyses. Traditional deterministic methods or probability-based approaches may overlook such variability. Also, the results indicated our proposed approach enables effective prediction of seismic responses for unsaturated slopes subjected to MSAS sequences. By considering spatial variability and the effects of matrix suction, our method offers a comprehensive framework for seismic reliability analysis of unsaturated slope structures.

Seismic behaviour of self-centring hybrid steel frames equipped with SMA plates under mainshock–aftershock sequences

This paper focuses on the mechanical behaviour, seismic application in steel frame connections and steel structure of shape memory alloy (SMA) plates. This study commenced by examining the hysteretic response of SMA plates subjected to cyclic tension tests, considering two different loading paths. Subsequently, a self-centring steel frame connection equipped with SMA plates and washers (SC-PW) was examined via quasi-static cyclic loading tests, and comparatively satisfactory self-centring behaviour was observed. However, the degradation of the initial stiffness of the SC-PW due to an initial imperfection was observed. An improvement strategy was proposed to overcome the degradation of the hysteretic behaviour (e.g., initial stiffness) of the SC-PW. Disc springs with a larger stiffness and preloads were introduced to overcome the degradation of the initial stiffness of the SC-PW, and the validation was confirmed via detailed finite element (FE) analyses. To improve the computation efficiency, a simplified FE model was developed to reproduce the hysteretic responses of the connection. Based on the simplified FE model, a six-storey prototype structure, i.e., a self-centring hybrid steel frame (SCHSF), equipped with the improved connection was developed, and the structural dynamic responses were investigated via nonlinear response history analyses, where mainshock–aftershock sequences were considered. The influence of the SMA material properties on the seismic behaviour of the prototype structure was investigated.

Performance-based plastic design and seismic fragility assessment for chevron braced steel frames considering aftershock effects

Observations from past earthquakes demonstrated that buildings in high seismic regions might be exposed to several aftershocks following the mainshock which can significantly increase the damage level. Since aftershocks have the potential to increase the vulnerability of buildings damaged under mainshocks, it is crucial to consider aftershock effects in the structural design phase. Performance-based Plastic Design (PBPD) method is an innovative seismic design method in which the building designed by this method shows a desirable performance under severe ground motions. PBPD allows the designer to avoid time-consuming trial and error process of analyses that are usually done in Performance-based Design method to reach a desirable performance. However, this efficient method is only valid for mainshocks only and does not consider aftershock effects in the structural design process. In this study, initially, the seismic performance (interstory drift and plastic hinges distribution) of the three 3-, 6-, and 9- story PBPD designed Chevron-braced Steel frames (CBSF) are compared under mainshocks (MS) and mainshock-aftershock (MS-AS) sequences. Subsequently, a PBPD method is developed for CBSFs considering the aftershock effects in the structural design process. Incremental dynamic analysis (IDA) has been performed using a suite of mainshocks and aftershock ground motions to develop a design base shear modification factor. Using the developed method, the performance of CBSFs under MS and MS-AS sequences is evaluated and compared with the existing PBPD method. Fragility curves are developed to compare the seismic vulnerability of the frames designed based on PBPD and proposed PBPD methods under MS-AS sequences. The outcomes of this study provide a practical design approach for CBSFs under MS-AS sequences and shows that the structures designed using developed PBPD method show more desirable behavior under MS-AS sequences compared with the structures designed using the conventional PBPD method.

Time-dependent and spatio-temporal statistical analysis of seismicity: application on the complete data set of the 2010 Beni–Ilmane earthquake sequence

SUMMARY The Beni–Ilmane (BI) seismic sequence, situated in the north-central region of Algeria, began on 2010 May 14 with a main shock of ML 5.4 followed by two other shocks on May 16 and 23 of ML 5.3 for both. Using the complete data set from May 14 to August 31 and the Epidemic Type Aftershock Sequences (ETAS) model to separate background from aftershocks contribution gave a first insight around the uncertainty that surrounds the causes and mechanisms of the seismicity. According to our findings, two phases have been determined, the first one, beginning from May 14, shows low b- and p-values with most of the seismicity being self-triggered. In contrast, the second phase, beginning from May 23, demonstrates an increase of both the b- and p-values with a high number of background events. In the second phase, the background contribution involves 53 per cent of all seismic activity after May 23’s peak which is high compared to typical main shock–aftershocks sequences. A possible explanation is that the main shocks began or assisted aseismic processes in addition to causing aftershocks. A sealed source at depth may have been broken by the third main shock, opening the way for the following incursion of highly pressurized fluids (hydrocarbures) confirmed by a high Vp/Vs ratios.

Seismotectonics of the Querétaro Region (Central Mexico) and the 1934 MI 4.8 Earthquake North of Celaya

Abstract The Querétaro region (central Mexico) is located in the trans-Mexican volcanic belt, an active volcanic arc related to the subduction of oceanic plates along the Pacific margin of Mexico. It is characterized by north–south-striking normal faults of the southern Basin and Range Province, up to 40 km long and with morphologically pronounced scarps, such as the San Miguel de Allende fault and the faults forming the Querétaro graben. These faults are located directly north of a major regional-scale system of east–west striking, seismically active intra-arc normal faults that are oriented parallel to the axis of the volcanic arc. Where the two orthogonal normal fault systems interfere, the outcrop-scale observations show that the east–west intra-arc fault system overprints the Basin and Range Province structures. Here we document a 1934 earthquake in a region previously not known for seismic activity. Our study is mostly based on an unpublished contemporary dossier preserved at Archivo Histórico del Instituto de Geología de la Universidad Nacional Autónoma de México, a recently inventoried archive that also preserves several unpublished macroseismic and instrumental studies of major Mexican subduction zone earthquakes between 1911 and 1954. A mainshock–aftershock sequence that initiated 14 July 1934 is documented by instrumental recordings at the Tacubaya observatory and by macroseismic observations at ten population centers, ranging in intensity between five and seven on the modified Mercalli scale. Based on the size of the damage area, the intensity magnitude of the mainshock is estimated at 4.8 ± 0.5. Based on the intensity distribution, the epicenter was located in the Laja River valley north-northeast of the town of Celaya, in the south-southwestern extrapolated continuation of the San Miguel de Allende normal fault scarp, which suggests that this fault extends to the epicentral region of the 1934 earthquake and is characterized by recurrent Quaternary tectonic activity.

Seismic collapse assessment of intermediate RC moment frames subjected to mainshock-aftershock sequences

This paper assessed the effects of mainshock-aftershock (MS-AS) sequences on the seismic vulnerability of intermediate reinforced concrete moment frames (IRCFs), considering various mainshock intensity scenarios. Moreover, given the limited library of real MS-AS ground motion sequences in the Iran plateau, a MS-AS sequence-selection method is proposed to generate artificial sequences that incorporate the magnitude, seismotectonic region, fault mechanism, and site condition of a target area. Three 4-, 7-, and 10-story IRCFs, modeled in OpenSees software, are subjected to real as well as artificial MS-AS sequences and collapse fragility curves are derived using the incremental dynamic analysis (IDA) results. The results show that the occurrence of mainshock can significantly increase the vulnerability of buildings during the aftershock. For various mainshock intensity scenarios, a general decrease in the collapse capacity is observed across all mainshock-damaged buildings, with a more significant decrease for taller buildings. Hence, it is essential to consider the effects of aftershock in the seismic design of IRCFs to mitigate the risk of collapse. Furthermore, by comparing the seismic responses caused by artificial sequences with those caused by real sequences, the validity of artificial sequence-selection method is confirmed; thus, artificial sequences can be used as a substitute for real sequences. Regression equations are also presented to predict the collapse capacity reduction of frames with different story numbers in presence of various mainshock intensity scenarios.

Permissible Scale Factors for Various Intensity Measures in Aftershock Ground Motion Scaling

This manuscript investigates the bias introduced by scaling aftershock ground motions when evaluating the performance of structures subjected to earthquake sequences. The study focuses on different hysteretic behaviors exhibited by structures and selects eight intensity measures as scale indicators. A benchmark database comprising 274 recorded mainshock–aftershock ground motions is utilized for analysis. The findings reveal that scaling aftershock records using intensity measures such as SI (seismic intensity), PGV (peak ground velocity), IC (Arias intensity), and Sa (spectral acceleration) relative to mainshock records effectively controls the mean bias within 30% throughout the entire period range, given a maximum scale factor of 10.0. However, it is observed that the additional damage in systems exhibiting un-degrading hysteretic behavior is more significantly affected by aftershock ground motion scaling compared to systems with degrading hysteretic behavior. Furthermore, scaling aftershock ground motions upwards using relative Sa tends to overestimate the additional damage incurred by structures. These results emphasize the importance of considering the specific hysteretic behavior of structures when applying aftershock ground motion scaling, as well as selecting appropriate intensity measures for accurate evaluation of structural performance.

Study on the Performance of Mountain Tunnel Against Mainshock–Aftershock based on Resilience Evaluation Framework

Study on the Performance of Mountain Tunnel Against Mainshock–Aftershock based on Resilience Evaluation Framework

Probabilistic framework for seismic resilience assessment of transmission tower-line systems subjected to mainshock-aftershock sequences

Immediate damage to electricity transmission systems after strong earthquakes can significantly cause widespread power outages and impede maintenance activities. Whereas previous seismic resilience assessments have investigated comprehensively the recovery capability of structures under isolated mainshocks, the effect of aftershocks has received less attention. This paper introduces a probabilistic framework for resilience assessment incorporating the effect of aftershocks and utilizes it to investigate the seismic performance of a transmission tower-line system (TTLS) under mainshock-aftershock (MSAS) sequences. Exceedance probabilities for different damage states of the TTLS are analyzed using fragility curves. Multiple decision variables (including functionality loss, recovery time, recovery function and resilience indicator) are subsequently calculated to quantify the effect of aftershocks. Meanwhile, the seismic resilience of the TTLS is further assessed by considering the uncertainties associated with those decision variables. The results reveal that aftershocks exert a significant influence on the seismic resilience of the TTLS, particularly when it experiences minor or moderate damage following the mainshocks. However, as the damage to the TTLS worsens due to larger mainshocks, the role of subsequent aftershocks becomes comparatively less influential. The proposed framework provides valuable insights for infrastructure systems before and after earthquake, effectively mitigating the adverse effects of sequential earthquakes.