Imperial College London


Faculty of EngineeringDepartment of Civil and Environmental Engineering

Professor of Engineering Seismology



+44 (0)20 7594 7916p.stafford




Ms Ruth Bello +44 (0)20 7594 6040




321Skempton BuildingSouth Kensington Campus





Publication Type

133 results found

Bommer JJ, Stafford PJ, Ruigrok E, Rodriguez-Marek A, Ntinalexis M, Kruiver PP, Edwards B, Dost B, van Elk Jet al., 2022, Ground-motion prediction models for induced earthquakes in the Groningen gas field, the Netherlands, Journal of Seismology, Vol: 26, Pages: 1157-1184, ISSN: 1383-4649

Small-magnitude earthquakes induced by gas production in the Groningen field in the Netherlands have prompted the development of seismic risk models that serve both to estimate the impact of these events and to explore the efficacy of different risk mitigation strategies. A core element of the risk modelling is ground-motion prediction models (GMPM) derived from an extensive database of recordings obtained from a dense network of accelerographs installed in the field. For the verification of damage claims, an empirical GMPM for peak ground velocity (PGV) has been developed, which predicts horizontal PGV as a function of local magnitude, ML; hypocentral distance, Rhyp; and the time-averaged shear-wave velocity over the upper 30 m, VS30. For modelling the risk due to potential induced and triggered earthquakes of larger magnitude, a GMPM for response spectral accelerations has been developed from regressions on the outputs from finite-rupture simulations of motions at a deeply buried rock horizon. The GMPM for rock motions is coupled with a zonation map defining frequency-dependent non-linear amplification factors to obtain estimates of surface motions in the region of thick deposits of soft soils. The GMPM for spectral accelerations is formulated within a logic-tree framework to capture the epistemic uncertainty associated with extrapolation from recordings of events of ML ≤ 3.6 to much larger magnitudes.

Journal article

Lee RL, Bradley BA, Stafford PJ, Graves RW, Rodriguez-Marek Aet al., 2022, Hybrid broadband ground-motion simulation validation of small magnitude active shallow crustal earthquakes in New Zealand, EARTHQUAKE SPECTRA, Vol: 38, Pages: 2548-2579, ISSN: 8755-2930

Journal article

Boore DM, Youngs RR, Kottke AR, Bommer JJ, Darragh R, Silva WJ, Stafford PJ, Al Atik L, Rodriguez-Marek A, Kaklamanos Jet al., 2022, Construction of a ground-motion logic tree through host-to-target region adjustments applied to an adaptable ground-motion prediction model, Bulletin of the Seismological Society of America, Vol: 112, Pages: 3063-3080, ISSN: 0037-1106

The purpose of a median ground‐motion logic tree is to capture the center, body, and range of possible ground‐motion amplitudes for each earthquake scenario considered in a seismic hazard analysis. For site‐specific hazard analyses, the traditional approach of populating the logic tree branches with ground‐motion prediction models (GMPMs) selected and weighted on the basis of vaguely defined applicability to the target region is rapidly being abandoned in favor of the backbone GMPM approach. In this approach, the selected backbone model is first adjusted to match the earthquake source and path characteristics of the target region, and then it is separately adjusted to account for the site‐specific geotechnical profile. For a GMPM to be amenable to such host‐to‐target adjustments, the magnitude scaling of response spectral ordinates should be consistent with the theoretical scaling of Fourier amplitude spectra. In addition, the influence of individual source and path parameters should be clearly distinguished in the model to allow the adjustments to be applied individually, and reliable estimates of the source and path parameters from the host region of the GMPM should be available, as should a reference rock profile for the model. The NGA‐West2 project GMPM of Chiou and Youngs (2014; hereafter, CY14) has been identified as a very suitable backbone model. Moreover, rather than adopting generic source and path parameters and a rock site profile from the host region for CY14, which is not easily defined because the data from which it was derived came from several geographical locations, recent studies have inverted the model to obtain a CY14‐consistent reference rock profile and CY14‐compatible source and path parameters. Using these host‐region characteristics, this study illustrates the process of building a ground‐motion logic tree through the sequential application of multiple host‐to‐target‐region adjustments, each represented by a node on the logic tree to achiev

Journal article

Kruiver PP, Pefkos M, Rodriguez-Marek A, Campman X, Ooms-Asshoff K, Lavoue A, Stafford PJ, van Elk J, Chmiel Met al., 2022, Capturing spatial variability in the regional Ground Motion Model of Groningen, the Netherlands, Geologie en Mijnbouw/Netherlands Journal of Geosciences, Vol: 101, Pages: 1-16, ISSN: 0016-7746

Long-term exploration of the Groningen gas field in the Netherlands led to induced seismicity. Over the past nine years, an increasingly sophisticated Ground Motion Model (GMM) has been developed to assess the site response and the related seismic hazard. The GMM output strongly depends on the shear-wave velocity (VS), among other input parameters. To date, VS model data from soil profiles (Kruiver et al., Bulletin of Earthquake Engineering, 15(9): 3555–3580, 2017; Netherlands Journal of Geosciences, 96(5): s215–s233, 2017) have been used in the GMM. Recently, new VS profiles above the Groningen gas field were constructed using ambient noise surface wave tomography. These so-called field VS data, even though spatially limited, provide an independent source of VS to check whether the level of spatial variability in the GMM is sufficient. Here, we compared amplification factors (AF) for two sites (Borgsweer and Loppersum) calculated with the model VS and the field VS (Chmiel et al., Geophysical Journal International, 218(3), 1781–1795, 2019 and new data). Our AF results over periods relevant for seismic risk (0.01–1.0 s) show that model and field VS profiles agree within the uncertainty range generally accepted in geo-engineering. In addition, we compared modelled spectral accelerations using either field VS or model VS in Loppersum to the recordings of an earthquake that occurred during the monitoring period (ML 3.4 Zeerijp on 8 January 2018). The modelled spectral accelerations at the surface for both field VS and model VS are coherent with the earthquake data for the resonance periods representative of most buildings in Groningen (T = 0.2 and 0.3 s). These results confirm that the currently used VS model in the GMM captures spatial variability in the site response and represents reliable input for the site response calculations.

Journal article

Stafford P, Boore DM, Youngs RR, Bommer JJet al., 2022, Host-region parameters for an adjustable model for crustal earthquakes to facilitate the implementation of the backbone approach to building ground-motion logic trees in probabilistic seismic hazard analysis, Earthquake Spectra, Vol: 38, Pages: 917-949, ISSN: 8755-2930

he backbone approach to constructing a ground-motion logic-tree for probabilistic seismic hazard analysis (PSHA) can address shortcomings in the traditional approach of populating the branches with multiple existing, or potentially modified, ground-motion models (GMM) by rendering more transparent the relationship between branch weights and the resulting distribution of predicted accelerations. In order to capture epistemic uncertainty in a tractable manner, there are benefits in building the logic tree through the application of successive adjustments for differences in source, path and site characteristics between the host-region of the selected backbone GMM and the target region for which the PSHA is being conducted. The implementation of this approach is facilitated by selecting a backbone GMM that is amenable to such host-to-target adjustments for individual source, path, and site characteristics. The NGA-West2 GMM of Chiou and Youngs (2014, CY14) has been identified as a highly adaptable model for crustal seismicity that is well suited to such adjustments. Rather than using generic source, path and site characteristics assumed appropriate for the host region, the final suite of adjusted GMMs for the target region will be better constrained if the host-region parameters are defined specifically on the basis of their compatibility with the CY14 backbone GMM. To this end, making use of a recently developed crustal shear-wave velocity profile consistent with CY14, we present an inversion of the model to estimate the key source and path parameters, namely the stress parameter and the anelastic attenuation. With these outputs, the effort in constructing a ground-motion logic-tree for any PSHA dealing with crustal seismicity can be focused primarily on the estimation of the target-region characteristics and their associated uncertainties. The inversion procedure can also be adapted for any application in which different constraints might be relevant

Journal article

Crespo MJ, Benjumea B, Moratalla JM, Lacoma L, Macau A, Gonzalez A, Gutierrez F, Stafford PJet al., 2022, A proxy-based model for estimating V-S30 in the Iberian Peninsula, SOIL DYNAMICS AND EARTHQUAKE ENGINEERING, Vol: 155, ISSN: 0267-7261

Journal article

Hicks S, Goes S, Whittaker A, Stafford Pet al., 2021, Multivariate statistical appraisal of regional susceptibility to induced seismicity: application to the Permian Basin, SW United States, Journal of Geophysical Research. Solid Earth, Vol: 126, ISSN: 2169-9356

Induced earthquake sequences are typically interpreted through causal triggering mechanisms. However, studies of causality rarely consider large regions and why some regions experiencing similar anthropogenic activities remain largely aseismic. Therefore, it can be difficult to forecast seismic hazard at a regional scale. In contrast, multivariate statistical methods allow us to find the combinations of factors that correlate best with seismicity, which can help form the basis of hypotheses that can be subsequently tested with physical models. Whilst strong correlations do not necessarily equate to causality, such a statistical approach is particularly important for large regions with newly emergent seismicity comprising multiple distinct clusters and multi-faceted industrial operations. Recent induced seismicity in the Permian Basin provides an excellent test-bed for multivariate statistical analyses because the main causal industrial and geological factors driving earthquakes in the region remain highly debated. Here, we use logistic regression to retrospectively predict the spatial variation of seismicity across the western Permian Basin. We reproduce the broad distribution of seismicity using a combination of both industrial and geological factors. Our model shows that the proximity to neotectonic faults west of the Delaware Basin is the most important factor that contributes to induced seismicity. The second-most important factor is salt-water disposal at shallow depths, with hydraulic fracturing playing a less dominant role. The higher tectonic stressing, together with a poor correlation between seismicity and large-volume deep salt-water disposal wells indicates a very different mechanism of induced seismicity compared to that in Oklahoma.

Journal article

Stafford P, 2021, Constraints on near-source saturation models for avoiding over-saturation of response spectral ordinates in RVT-based stochastic ground-motion simulations, Journal of Seismology, Vol: 26, Pages: 1-13, ISSN: 1383-4649

Inversions of empirical data and ground-motionmodels to find Fourier spectral parameters can result in parameter combinations that produce over-saturation of shortperiod response spectral ordinates. While some evidence forover-saturation in empirical data exists, most ground-motionmodellers do not permit this scaling within their models.Host-to-target adjustmentsthat are made to published groundmotion models for use in site-specific seismic hazard analyses frequently require the identification of an equivalentset of Fourier spectral parameters. In this context, when inverting response spectral models that do not exhibit oversaturation effects, it is desirable impose constraints upon theFourier parameters to match the scaling of the host-regionmodel. The key parameters that determine whether oversaturation arises are the geometric spreading rate (γ) and theexponential rate within near-source saturation models (hβ ).The article presents the derivation of simple nonlinear constraints that can be imposed to prevent over-saturation whenundertaking Fourier spectral inversions.

Journal article

Baker JW, Bradley BA, Stafford P, 2021, Seismic Hazard and Risk Analysis, Seismological Research Letters, Vol: 92(5), Pages: 3248-3250, ISSN: 0895-0695

Journal article

Hicks S, Goes S, Whittaker A, Stafford Pet al., 2021, Multivariate statistical appraisal of regional susceptibility to induced seismicity: application to the Permian Basin, SW United States, Publisher: Earth ArXiv

Induced earthquake sequences are typically interpreted through causal triggering mechanisms. However, studies of causality rarely consider large regions and why some regions experiencing similar anthropogenic activities remain largely aseismic. Therefore, it can be difficult to forecast seismic hazard at a regional scale. In contrast, multivariate statistical methods allow us to find the combinations of factors that correlate best with seismicity, which can help form the basis of hypotheses that can be subsequently tested with physical models. Such a statistical approach is particularly important for large regions with newly-emergent seismicity comprising multiple distinct clusters and multi-faceted industrial operations. Recent induced seismicity in the Permian Basin provides an excellent test-bed for multivariate statistical analyses because the main causal industrial and geological factors driving earthquakes in the region remain highly debated. Here, we use logistic regression to retrospectively predict the spatial variation of seismicity across the western Permian Basin. We reproduce the broad distribution of seismicity using a combination of both industrial and geological factors. Our model shows that hydraulic fracturing and/or hydrocarbon production from the Wolfcamp Shale is the strongest predictor of seismicity, although the physical triggering process is unclear due to uncertain earthquake depths. We also find that the proximity to neotectonic faults west of the Delaware Basin is another important factor that contributes to induced seismicity. This higher tectonic stressing, together with a poor correlation between seismicity and large-volume deep salt-water disposal wells indicates a very different mechanism of induced seismicity compared to that in Oklahoma.

Working paper

Stafford P, 2021, Risk oriented earthquake hazard assessment: influence of spatial discretisation and non-ergodic ground-motion models, Advances in Assessment and Modeling of Earthquake Loss, Editors: Akkar, Ilki, Goksu, Erdik, Publisher: Springer, Pages: 169-187

Three important aspects of ground-motion modelling for regional or portfolio risk analyses are discussed. The first issue is the treatment of discretisation of continuous ground-motion fields for generating spatially correlated discrete fields. Shortcomings of the present approach in which correlation models based upon point estimates of ground motions are used to represent correlations within and between spatial regions are highlighted. It is shown that risk results will be dependent upon the chosen spatial resolution if the effects of discretisation are not adequately treated. Two aspects of non-ergodic groundmotion modelling are then discussed. Correlation models generally used within risk modelling are traditionally based upon very simple partitioning of ground-motion residuals. As regional risk analyses move to non-ergodic applications where systematic site effects are considered, these correlation models (both inter-period and spatial models) need to be revised. The nature of these revisions are shown herein. Finally, evidence for significantly reduced between-event variability within earthquake sequences is presented. The ability to progressively constrain location and sequence-dependent systematic offsets from ergodic models as earthquake sequences develop can have significant implications for aftershock risk assessments.

Book chapter

Ramos-Moreno C, Ruiz-Teran AM, Stafford PJ, 2021, Impact of stochastic representations of pedestrian actions on serviceability response, Proceedings of the Institution of Civil Engineers: Bridge Engineering, Vol: 174, Pages: 113-128, ISSN: 1478-4637

Over the past 15 years, there have been some research outcomes in other disciplines that could be used to produce new, more accurate and realistic numerical models to characterise pedestrian loads and to significantly improve predictions of response for multiple-pedestrian scenarios. However, the disconnection between fields has not facilitated this further research. Using this, the paper presents (a) a new sophisticated load model that includes a description of vertical and lateral loads, including pedestrian–structure interaction, (b) the numerical description of relationships to describe the key parameters of the proposed model and (c) the evaluation of the effects of pedestrian characteristics that are relevant for serviceability response of footbridges. The proposed new load model allows for the inherent variability of individual pedestrian actions (intra-subject variability), a probabilistic description of how pedestrian characteristics vary among subjects (inter-subject variability) and collective human behaviour (pedestrian–pedestrian interaction). Some of these characteristics are not currently considered in design approaches and can have a substantial impact on structural response assessments. Finally, recommendations are made for many of these characteristics to be introduced in analyses to evaluate the vibration serviceability limit state of footbridges in a more accurate and realistic manner.

Journal article

Rodriguez-Marek A, Bommer J, Youngs RR, Crespo MJ, Stafford PJ, Bahrampouri Met al., 2021, Capturing epistemic uncertainty in site response, Earthquake Spectra, Vol: 37, Pages: 921-936, ISSN: 8755-2930

The incorporation of local amplification factors determined through site response analyses has become standard practice in site-specific probabilistic seismic hazard analysis (PSHA). Another indispensable feature of the current state-of-practice in site-specific PSHA is the identification and quantification of all epistemic uncertainties that influence the final hazard estimates. Consequently, logic trees are constructed not only for seismic source characteristics and ground-motion models (GMMs) but also for the site amplification factors, the latter generally characterized by branches for alternative shear-wave velocity (VS) profiles. However, in the same way that branch weights on alternative GMMs can give rise to unintentionally narrow distributions of predicted ground-motion amplitudes, the distribution of amplification factors obtained from a small number of weighted VS profiles will often be quite narrow at some oscillator frequencies. We propose an alternative approach to capturing epistemic uncertainty in site response in order to avoid such unintentionally constricted distributions of amplification factors using more complete logic-trees for site response analyses. Nodes are included for all the factors that influence the calculated amplification factors, which may include shallow VS profiles, deeper VS profiles, depth of impedance contrasts, low-strain soil damping, and choice of modulus reduction and damping curves. Site response analyses are then executed for all branch combinations to generate a large number 2 of frequency-dependent amplification factors. Finally, these are re-sampled as a discrete distribution with enough branches to capture the underlying distribution of amplification factors (AFs). While this approach improves the representation of epistemic uncertainty in the dynamic site response characteristics, modeling uncertainty in the AFs is not automatically captured in this way, for which reason it is also proposed that a minimum level of e

Journal article

Garcia-Troncoso N, Ruiz-Teran A, Stafford PJ, 2020, Attenuation of pedestrian-induced vibrations in girder footbridges using tuned-mass dampers, Advances in Bridge Engineering, Vol: 1, Pages: 1-26, ISSN: 2662-5407

This article presents a numerical assessment of pedestrian-induced vibrations for a wide range of girder footbridges before and after the installation of tuned-mass dampers (TMD). Realistic pedestrian loads are defined using a stochastic model that represents the key characteristics of pedestrians and their intra- and inter-subject variability with the aim of ensuring an accurate estimation of the dynamic response. A comprehensive set of numerical analyses have been performed considering different cross sections, structural materials, span lengths (up to 100 m), and pedestrian flows. The optimal TMD characteristics, number and location, required to reduce the accelerations, down to a level that fulfils serviceability criteria, are identified. Design recommendations for girder footbridges implementing damping devices at the design stage are also included.

Journal article

Ramos-Moreno C, Ruiz-Teran AM, Stafford PJ, 2020, Guidance for footbridge design: a new simplified method for the accurate evaluation of the structural response in serviceability conditions, Advances in Bridge Engineering, Vol: 1, Pages: 1-21, ISSN: 2662-5407

This paper proposes a simplified hand-calculation methodology that permits a fast response assessment (both in vertical and lateral direction) under different pedestrian scenarios. This simplified method has the same accuracy than that of very sophisticated numerical nonlinear finite element models including pedestrian inter-variability, interaction among pedestrians in flows, and pedestrian-structure interaction. The method can capture the effects of pedestrian loads in and out of resonance. This methodology is based on a new, and experimentally contrasted, stochastic pedestrian load model derived by the authors implementing a multi-disciplinary state-of-the-art research, and on a large set of sophisticated finite element analyses.There is a significant gap in the literature available for bridge designers. Some current codes do not indicate how the performance for serviceability limit-states should be assessed, in particular for lateral direction. Others define methods that are not based on the latest research in this field and that require the use of dynamic structural analysis software. A very sophisticated load model, such as that described above, and recently proposed by the authors, may not be accessible for most of the design offices, due to time and software constraints. However, an accurate assessment of the serviceability limit state of vibrations during the design stages is paramount. This paper aims to provide designers with an additional simple tool for both preliminary and detailed design for the most typical structural configurations.First, the paper presents the methodology, followed by an evaluation of the impact of its simplifications on the response appraisal. Second, the paper evaluates the validity of the methodology by comparing responses predicted by the method to those experimentally measured at real footbridges. Finally, the paper includes a parametric analysis defining the maximum accelerations expected from pedestrian streams crossing mult

Journal article

Rood AH, Rood DH, Stirling MW, Madugo CM, Abrahamson NA, Wilcken KM, Gonzalez T, Kottke A, Whittaker AC, Page WD, Stafford PJet al., 2020, Earthquake hazard uncertainties improved using precariously balanced rocks, AGU Advances, Vol: 1, Pages: 1-24, ISSN: 2576-604X

Probabilistic seismic hazard analysis (PSHA) is the state‐of‐the‐art method to estimate ground motions exceeded by large, infrequent, and potentially damaging earthquakes; however, a fundamental problem is the lack of an accepted method for both quantitatively validating and refining the hazard estimates using empirical geological data. In this study, to reduce uncertainties in such hazard estimates, we present a new method that uses empirical data from precariously balanced rocks (PBRs) in coastal Central California. We calculate the probability of toppling of each PBR at defined ground‐motion levels and determine the age at which the PBRs obtained their current fragile geometries using a novel implementation of cosmogenic 10Be exposure dating. By eliminating the PSHA estimates inconsistent with at least a 5% probability of PBR survival, the mean ground‐motion estimate corresponding to the hazard level of 10−4 yr−1 (10,000 yr mean return period) is significantly reduced by 27%, and the range of estimated 5th–95th fractile ground motions is reduced by 49%. Such significant reductions in uncertainties make it possible to more reliably assess the safety and security of critical infrastructure in earthquake‐prone regions worldwide.

Journal article

Bommer J, Stafford PJ, 2020, Selecting ground-motion models for site-specific PSHA: adaptability vs applicability, Bulletin of the Seismological Society of America, Vol: 110, Pages: 2801-2815, ISSN: 0037-1106

Capturing the center, the body and the range of ground-motion predictions is an indispensableelement of site-specific probabilistic seismic hazard analyses (PSHA), for which the logic tree isthe ubiquitous tool in current practice. The criteria for selecting the ground-motion models (GMMs)used in such studies have generally been focused on their potential applicability to the region andsite for which the PSHA is being conducted. However, except for applications within the fewregions with abundant ground-motion databases, it will rarely be the case that GMMs can beidentified which are perfectly calibrated to the characteristics of the target study region in termsof source and path properties. A good match between the generic site amplification model withinthe GMM and the site-specific dynamic response characteristics is equally, if not more, unlikely.Consequently, adjustments are likely to be made to the selected GMMs to render them moreapplicable to the target region and site. Empirical adjustments for host-to-target region sourcedifferences using local recordings are unlikely to be robust unless these have been generated byearthquakes from a wide range of magnitudes. Empirical adjustments for site characteristics areimpossible unless there are recordings from the target site. Therefore, the preferred approachmakes parametric adjustments to empirical GMMs, isolating each host-to-target difference to mapthe individual contributions to the epistemic uncertainty. For such an approach to be applied, theemphasis moves from selecting GMMs on the basis of their applicability to focusing on theiramenability to being adjusted to the target region and site. An adaptable equation is characterizedby well constrained host-region source, path and site characteristics and a functional form inwhich response spectral accelerations scale with source, path and site characteristics in a mannersimilar to the scaling implicit in stochastic simulations based on Fourier amplitude spectra.

Journal article

Bommer J, Green RA, Stafford PJ, Maurer BW, Kruiver PP, Edwards B, Rodriguez-Marek A, de Lange G, Oates SJ, Storck T, Omidi P, Bourne SJ, van Elk JFet al., 2020, Liquefaction hazard of the Groningen region of the Netherlands due to induced seismicity, Journal of Geotechnical and Geoenvironmental Engineering, Vol: 146, Pages: 04020068-1-04020068-15, ISSN: 0733-9410

The operator of the Groningen gas field is leading an effort to quantify the seismic hazard and riskof the region due to induced earthquakes, includingoverseeing one of the most comprehensive liquefaction hazard studies performedgloballyto date. Due tothe unique characteristics of the seismic hazard and the geologic deposits in Groningen, efforts first focused on developing relationships for a Groningen-specific liquefaction triggering model. The liquefaction hazard was then assessedusing a Monte Carlo method, wherein a range of credibleevent scenarios were considered in computingliquefaction damage-potentialhazard curves. Thiseffort entailed the use of a regional stochastic seismic source model,ground motion prediction equation,site response model,and geologic model that were developed as part of the broader regional seismic hazardassessment.“No-to-Minor Surficial Liquefaction Manifestations”arepredicted for mostsites across the study areafor a 75-year return period. The only sites where “Moderate Surficial Liquefaction Manifestations” are predicted are in the town of Zandeweer, with only some of the sites in the townbeing predicted to experience this severityof liquefactionfor thisreturn period.

Journal article

Lee RL, Bradley BA, Stafford P, Graves RW, Rodriguez-Marek Aet al., 2020, Hybrid broadband ground motion simulation validation of small magnitude earthquakes in Canterbury, New Zealand, Earthquake Spectra, Vol: 36, Pages: 673-699, ISSN: 8755-2930

Ground motion simulation validation is an important and necessary task towards establishing the efficacy of physics-based ground motion simulations for seismic hazard analysis and earthquake engineering applications. This paper presents a comprehensive validation of the commonly used Graves and Pitarka (2010, 2015) hybrid broadband ground motion simulation methodology with a recently developed 3D Canterbury Velocity Model. This is done through simulation of 148 small magnitude earthquake events in the Canterbury, New Zealand, region in order to supplement prior validation efforts directed at several larger magnitude events. Recent empirical ground motion models are also considered to benchmark the simulation predictive capability, which is examined by partitioning the prediction residuals into the various components of ground motion variability. Biases identified in source, path and site components suggest that improvements to the predictive capabilities of the simulation methodology can be made by using a longer high frequency path duration model, reducing empirical Vs30-based low frequency site amplification, and utilizing site-specific velocity models in the high frequency simulations.

Journal article

Xu B, Bompa DV, Elghazouli AY, Ruiz-Teran AM, Stafford PJet al., 2020, Numerical assessment of reinforced concrete members incorporating recycled rubber materials, Engineering Structures, Vol: 204, ISSN: 0141-0296

This paper is concerned with the inelastic behaviour of reinforced concrete beam-column members incorporating rubber from recycled tyres. Detailed three-dimensional nonlinear numerical simulations and parametric assessmentsare carried out using finite element analysis in conjunction with concrete damage plasticity models. Validationsof the adopted nonlinear finite element procedures arecarried out against experimental results from a series of tests involvingconventional and rubberised concrete flexural members and varying levels of axial load. The influence of key parameters, such as the concrete strength, rubber content, reinforcement ratio and level of axial load, on the performance of such members, is then examined in detail.Based on the results, analytical models are proposed for predicting the strength interaction as well as the ductility characteristicsof rubberised reinforced concrete members. The findings permit the development ofdesignexpressionsfor determiningthe ultimate rotation capacityof members,usinga rotation ductility parameter, or through a suggestedplastic hinge assessment procedure. Theproposedexpressionsare shown to offer reliable estimates of strength and ductilityof reinforced rubberised concrete members,whichare suitable for practical application and implementation in codified guidance.

Journal article

Georgiadis K, Ruiz-Teran AM, Stafford PJ, 2020, Comparison of the structural behaviour between under-deck cable-stayed and under-deck suspension footbridges under pedestrian action, Pages: 765-772

Under-deck cable-stayed (UDCS) and under-deck suspension (UDS) footbridges are slender structures supported by cables located below the deck and, despite the similarities in their appearance, they represent two different engineering concepts. In the present work, their structural behaviour has been investigated in detail and their response under static and dynamic pedestrian loading has been compared. A static analysis has been conducted first. Then a modal analysis has been performed, followed by a full time-history dynamic analysis under the action of a stochastic pedestrian load model. The influence of geometric non-linearity in both static and dynamic analyses has been examined. Results show that although the bending moments and deflections in UDS footbridges are smaller compared to UDCS footbridges, the level of accelerations, which is the governing design criterion for the bridge deck in order to satisfy comfort, is similar.

Conference paper

Ntinalexis M, Bommer JJ, Ruigrok E, Edwards B, Pinho R, Dost B, Correia AA, Uilenreef J, Stafford PJ, van Elk Jet al., 2019, Ground-motion networks in the Groningen field: usability and consistency of surface recordings, JOURNAL OF SEISMOLOGY, Vol: 23, Pages: 1233-1253, ISSN: 1383-4649

Several strong-motion networks have been installed in the Groningen gas field in the Netherlands to record ground motions associated with induced earthquakes. There are now more than 450 permanent surface accelerographs plus a mobile array of 450 instruments, which, in addition to many instrumented boreholes, yield a wealth of data. The database of recordings has been of fundamental importance to the development of ground-motion models that form a key element of the seismic hazard and risk estimations for the field. In order to maximise the benefit that can be derived from these recordings, this study evaluates the usability of the recordings from the different networks, in general terms and specifically with regards to the frequency ranges with acceptable signal-to-noise ratios. The study also explores the consistency among the recordings from the different networks, highlighting in particular how a configuration error was identified and resolved. The largest accelerograph network consists of instruments housed in buildings around the field, frequently installed on the lower parts of walls rather than on the floor. A series of experiments were conducted, using additional instruments installed adjacent to these buildings and replicating the installation configuration in full-scale shake table tests, to identify the degree to which structural response contaminated the recordings. The general finding of these efforts was that for PGV and oscillator periods above 0.1 s, the response spectral ordinates from these recordings can be used with confidence.

Journal article

Green RA, Bommer JJ, Rodriguez-Marek A, Maurer BW, Stafford PJ, Edwards B, Kruiver PP, de Lange G, van Elk Jet al., 2019, Addressing limitations in existing ‘simplified’ liquefaction triggering evaluation procedures: application to induced seismicity in the Groningen gas field, Bulletin of Earthquake Engineering, Vol: 17, Pages: 4539-4557, ISSN: 1570-761X

The Groningen gas field is one of the largest in the world and has produced over 2000 billion m3 of natural gas since the start of production in 1963. The first earthquakes linked to gas production in the Groningen field occurred in 1991, with the largest event to date being a local magnitude (ML) 3.6. As a result, the field operator is leading an effort to quantify the seismic hazard and risk resulting from the gas production operations, including the assessment of liquefaction hazard. However, due to the unique characteristics of both the seismic hazard and the geological subsurface, particularly the unconsolidated sediments, direct application of existing liquefaction evaluation procedures is deemed inappropriate in Groningen. Specifically, the depth-stress reduction factor (rd) and the magnitude scaling factor relationships inherent to existing variants of the simplified liquefaction evaluation procedure are considered unsuitable for use. Accordingly, efforts have first focused on developing a framework for evaluating the liquefaction potential of the region for moment magnitudes (M) ranging from 3.5 to 7.0. The limitations of existing liquefaction procedures for use in Groningen and the path being followed to overcome these shortcomings are presented in detail herein.

Journal article

Edwards B, Zurek B, van Dedem E, Stafford PJ, Oates S, van Elk J, DeMartin B, Bommer Jet al., 2019, Simulations for the development of a ground motion model for induced seismicity in the Groningen gas field, the Netherlands, Bulletin of Earthquake Engineering, Vol: 17, Pages: 4441-4456, ISSN: 1570-761X

We present simulations performed for the development of a ground motion model for induced earthquakes in the Groningen gas field. The largest recorded event, with M3.5, occurred in 2012 and, more recently, a M3.4 event in 2018 led to recorded ground accelerations exceeding 0.1 g. As part of an extensive hazard and risk study, it has been necessary to predict ground motions for scenario earthquakes up to M7. In order to achieve this, while accounting for the unique local geology, a range of simulations have been performed using both stochastic and full-waveform finite-difference simulations. Due to frequency limitations and lack of empirical calibration of the latter approach, input simulations for the ground motion model used in the hazard and risk analyses have been performed with a finite-fault stochastic method. However, in parallel, extensive studies using the finite-difference simulations have guided inputs and modelling considerations for these simulations. Three approaches are used: (1) the finite-fault stochastic method, (2) elastic point- and (3) finite-source 3D finite-difference simulations. We present a summary of the methods and their synthesis, including both amplitudes and durations within the context of the hazard and risk model. A unique form of wave-propagation with strong lateral focusing and defocusing is evident in both peak amplitudes and durations. The results clearly demonstrate the need for a locally derived ground motion model and the potential for reduction in aleatory variability in moving toward a path-specific fully non-ergodic model.

Journal article

Stafford PJ, Zurek BD, Ntinalexis M, Bommer JJet al., 2019, Extensions to the Groningen ground-motion model for seismic risk calculations: component-to-component variability and spatial correlation, Bulletin of Earthquake Engineering, Vol: 17, Pages: 4417-4439, ISSN: 1573-1456

A bespoke ground-motion model has been developed for the prediction of response spectral accelerations, peak ground velocity and significant duration due to induced earthquakes in the Groningen gas field in the Netherlands. For applications to the calculation of risk to the exposed building stock, extensions to the model are required. The use of the geometric mean horizontal component in the ground-motion predictions and the arbitrary horizontal component for the building fragility functions requires the addition of component-to-component variability. A model for this variability has been developed that both reflects the strong horizontal polarisation of motions observed in many Groningen records obtained at short distances and the fact that the strong polarisation is unlikely to persist at larger magnitudes. The other extension of the model is the spatial correlation of ground motions for the calculation of aggregated risk, which can be approximated through simple rules for sampling the variance within site response zones. Making use of ground-motion recordings from several networks in the field and the results of finite difference waveform simulations, a Groningen-specific spatial correlation model has been developed. The new model also combines results from traditional variogram fitting approaches with a new method to infer spatial correlation lengths from observed variance reduction. The development of the new spatial correlation model relaxes the need to approximate spatial correlation through the sampling of site response, although the results obtained herein suggest that similar results could be obtained using either approach. The preliminary consideration of the numerical waveform modelling results in this study paves the way for significant extensions to be made for the modelling of spatial correlations and the decomposition of apparent spatial variability into systematic and random components within a fully non-ergodic framework .

Journal article

Dong W, Stafford P, Ruiz-Teran A, 2019, Inverse form-finding for tensegrity structures, Computers and Structures, Vol: 215, Pages: 27-42, ISSN: 0045-7949

In this study we examine the topic of inverse form-finding, also referred to as topology finding, for tensegrity structures. Specifically, the problem addressed is given the specification of final nodal positions for a tensegrity, we seek to find appropriate connectivities, or topologies, that satisfy stability and connectivity constraints. Two new algorithms are presented in the paper. The first may be applied for generating prestress-stable tensegrity structures, while the second can be used to generate super-stable tensegrities. Numerical examples for both 2D and 3D tensegrities are provided to demonstrate that these new algorithms can produce desirable structures with nodal positions being the only prescribed piece of information. We also show that inverse form-finding of a specific Class k tensegrity can be formulated into a graph factorization problem. This is the first time that both the stability property and class can be specified among the few existing inverse form-finding methods. These new methods facilitate the design process in which a desired nodal geometry is prescribed, and viable structural configurations consistent with this geometry can be obtained.

Journal article

Stafford PJ, 2019, Continuous integration of data into ground-motion models using Bayesian updating, Journal of Seismology, Vol: 23, Pages: 39-57, ISSN: 1383-4649

The development of empirically constrained ground-motion models has historically followed a cyclic process in which every few years, existing models are updated to reflect new data and knowledge that has become available. Ground-motion developers make use of their prior knowledge to identify appropriate functional forms for the models, but the actual regression analysis and model calibration is effectively performed from a fresh start with each update. With the anticipated increase in data availability coming in the future, this traditional approach will become increasingly cumbersome. The present article presents a framework in which Bayesian updating is used to continuously update existing ground-motion models as new data becomes available. This new approach is shown to provide similar results to the more traditional approach, but is far less data-intensive and will scale well into the future. The approach is demonstrated through an example in which an initial regression analysis is conducted on a portion of the NGA-West2 dataset representative of the information available in 1995. Model parameters, variance components and crossed random effects are then updated with data from every other event in the NGA-West2 dataset and the results from Bayesian updating and traditional regression analysis are compared. The two methods are shown to provide similar results, but the advantages of the Bayesian approach are subsequently highlighted. For the first time, the article also demonstrates how prior distributions of model parameters can be obtained for existing ground-motion models that have been derived using both classical, as well as more elaborate multi-stage, procedures with and without constrained parameters.

Journal article

Teslim-Balogun A, Malaga-Chuquitaype C, Stafford PJ, 2019, A Numerical Study on the Structural Response of Steel Structures under Post-Blast Travelling Fires, Structures Congress - Blast, Impact Loading, and Research and Education, Publisher: AMER SOC CIVIL ENGINEERS, Pages: 59-69

Conference paper

Georgiadis K, Ruiz-Teran AM, Stafford PJ, 2019, Investigation of under-deck cable-stayed footbridges under dynamic pedestrian loading, Pages: 1655-1662

Under-deck cable-stayed (UDCS) footbridges are slender structures that promote the axial behaviour. This allows designers to take advantage of the entire sectional areas and reduce the required construction materials. Besides their high structural efficiency and sustainability, they also possess a number of other advantages such as multiple construction possibilities and strong aesthetic characteristics, therefore becoming an attractive solution in urban infrastructure. However, due to their slenderness, they are more prone to vibrations. Recent closures of footbridges of this typology, indicate that fundamental aspects of their structural response still remained unclear. This paper presents a set of example bridges built with this typology and a detailed investigation of a benchmark case under the dynamic action of pedestrians. Results show that, although ULS is satisfied using a very high deck slenderness (1/100), the SLS of vibrations is the critical design criterion that governs the slenderness of the deck (leading to values of 1/60).

Conference paper

Shi Y, Stafford PJ, 2018, Markov-chain Monte Carlo ground-motion selection algorithms for conditional intensity measure targets, Earthquake Engineering and Structural Dynamics, Vol: 47, Pages: 1468-1489, ISSN: 0098-8847

Two new algorithms are presented for efficiently selecting suites of ground motions that match a target multivariate distribution - or conditional intensity measure target.The first algorithm is a Markov-chain Monte Carlo (MCMC) approach in which records are sequentially added to a selected set such that the joint probability density function (PDF) of the target distribution is progressively approximated by the discrete distribution of the selected records.The second algorithm derives from the concept of the acceptance ratio within MCMC but does not involve any sampling.The first method takes advantage of MCMC's ability to efficiently explore a sampling distribution through the implementation of a traditional MCMC algorithm.This method is shown to enable very good matches to multivariate targets to be obtained when the numbers of records to be selected is relatively large.A weaker performance for fewer records can be circumvented by the second method which uses greedy optimization to impose additional constraints upon properties of the target distribution.A preselection approach based upon values of the multivariate PDF is proposed that enables near-optimal record sets to be identified with a very close match to the target.Both methods are applied for a number response analyses associated with different sizes of record sets and rupture scenarios.Comparisons are made throughout with the Generalized Conditional Intensity Measure (GCIM) approach.The first method provides similar results to GCIM, but with slightly worse performance for small record sets, while the second method outperforms method one and GCIM for all considered cases.

Journal article

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