An application of reliability-based robustness assessment of steel moment resisting frame structures under post-mainshock cascading events

The paper presented herein proposes a reliability-based framework for quantifying the structural robustness considering the occurrence of a major earthquake (mainshock) and subsequent cascading hazard events, such as aftershocks that are triggered by the mainshock. These events can significantly increase the probability of failure of buildings, especially for structures that are damaged during the mainshock. The application of the proposed framework is exemplified through three numerical case studies. The case studies correspond to three SAC steel moment frame buildings of 3-, 9-, and 20- stories, which were designed to pre-Northridge codes and standards. Twodimensional nonlinear finite element models of the buildings are developed using the Open System for Earthquake Engineering Simulation framework (OpenSees), using a finite-length plastic hinge beam model and a bilinear constitutive law with deterioration, and are subjected to multiple mainshock-aftershock seismic sequences. For the three buildings analyzed herein, it is shown that the structural reliability under a single seismic event can be significantly different from that under a sequence of seismic events. The reliability-based robustness indicator used shows that the structural robustness is influenced by the extent by which a structure can distribute damage.

Statistical similarity between the compression of a porous material and earthquakes

It has been long stated that there are profound analogies between fracture experiments and earthquakes; however, few works attempt a complete characterization of the parallelisms between these so separate phenomena. We study the Acoustic Emission events produced during the compression of Vycor (SiO&sub&2&/sub&). The Gutenberg-Richter law, the modified Omori's law, and the law of aftershock productivity hold for a minimum of 5 decades, are independent of the compression rate, and keep stationary for all the duration of the experiments. The waiting-time distribution fulfills a unified scaling law with a power-law exponent close to 2.45 for long times, which is explained in terms of the temporal variations of the activity rate.

Average White Band poster, ca. 2000

The Average White Band's debut album, Show your hand, was released in 1973. The "classic funk and R & B" band included members Alan Gorrie, Owen "Onnie" McIntyre, Malcolm "Mollie" Duncan, Roger Ball, Robbie McIntosh, and Mike Rosen. Rosen was quickly replaced by Hamish Stuart. The band, comprised of Scotsmen, released a second album in 1974 that featured the US number 1/UK Top 10 single "Pick up the Pieces". That same year, Robbie McIntosh died of a heroin overdose and was replaced by Steve Ferrone. The song "Cut the Cake" from their third album made the US top 10, and subsequent releases in the late 1970s and early 1980s proved successful. The members largely pursued individual projects in the years that followed, but re-formed in 1989 (with original members Gorrie, Ball and McIntyre, and new members Alex Ligertwood and Eliot Lewis) and released the album Aftershock. Over the years, the band's members have changed, and the band is currently comprised of Onnie McIntyre, Rocky Bryant, Alan Gorrie, Fred "Freddy V" Vigdor and Klyde Jones. Their most recent album, Times Squared, was released in 2009.

The intracratonic Caraibas-Itacarambi earthquake of December 09, 2007 (4.9 m(b)), Minas Gerais State, Brazil

On December 9, 2007, a 4.9 m(b) earthquake occurred in the middle of the Sao Francisco Craton, in a region with no known previous activity larger than 4 m(b). This event reached intensity VII MM (Modified Mercalli) causing the first fatal victim in Brazil. The activity had started in May 25, 2007 with a 3.5 magnitude event and continued for several months, motivating the deployment of a local 6-station network. A three week seismic quiescence was observed before the mainshock. Initial absolute hypocenters were calculated with best fitting velocity models and then relative locations were determined with hypoDD. The aftershock distribution indicates a 3 km long rupture for the mainshock. The fault plane solution, based on P-wave polarities and hypocentral trend, indicates a reverse faulting mechanism on a N30 degrees E striking plane dipping about 40 degrees to the SE. The rupture depth extends from about 0.3 to 1.2 km only. Despite the shallow depth of the mainshock, no surface feature could be correlated with the fault plane. Aeromagnetic data in the epicentral area show short-wavelength lineaments trending NNE-SSW to NE-SW which we interpret as faults and fractures in the craton basement beneath the surface limestone layer. We propose that the Caraibas-Itacarambi seismicity is probably associated with reactivation of these basement fractures and faults under the present E-W compressional stress field in this region of the South American Plate. (c) 2009 Elsevier B.V. All rights reserved.

The intraplate Porto dos Gauchos seismic zone in the Amazon craton - Brazil

The largest earthquake observed in the stable continental interior of the South American plate occurred in Serra do Tombador, Mato Grosso state - Brazil, on January 31,1955 with a magnitude of 6.2 m(b). Since then no other earthquake has been located near the 1955 epicentre. However, in Porto dos Gauchos, 100 km northeast of Serra do Tombador, a recurrent seismicity has been observed since 1959. Both Serra do Tombador and Porto dos Gauchos are located in the Phanerozoic Parecis basin. Two magnitude 5 earthquakes occurred in Porto dos Gauchos, in 1998 and 2005, with intensities up to VI and V, respectively. These two main shocks were followed by aftershock sequences lasting more than three years each. Local seismic stations have been deployed by the Seismological Observatory of the University of Brasilia since 1998 to study the ""Porto dos Gauchos"" seismic zone (PGSZ). A local seismic refraction survey was carried out with two explosions to help define the seismic velocity model. Both the 1998 and 2005 earthquake sequences occurred in the same WSW-ENE oriented fault zone with right-lateral strike-slip mechanisms. The epicentral zone is in the Parecis basin, near its northern border where there are buried grabens, generally trending WNW-ESE, such as the deep Mesoproterozoic Caiabis graben which lies partly beneath the Parecis basin. However, the epicentral distribution indicates that the 1998 and 2005 sequences are related to a N60 degrees E fault which probably crosses the entire Caiabis graben. The 1955 earthquake, despite the uncertainty in its epicentre, does not seem to be directly related to any buried graben either. The seismicity in the Porto dos Gauchos seismic zone, therefore, is not directly related to rifted crust. The probable direction of the maximum horizontal stress near Porto dos Gauchos is roughly E-W, consistent with other focal mechanisms further south in the Pantanal basin and Paraguay. but seems to be different from the NW-SE direction observed further north in the Amazon basin. The recurrent seismicity observed in Porto dos Gauchos, and the large 1955 earthquake nearby, make this area of the Parecis basin one of the most important seismic zones of Brazil. (C) 2009 Elsevier B.V. All rights reserved.

Coda wave attenuation in the Parecis Basin, Amazon Craton, Brazil: sensitivity to basement depth

Small local earthquakes from two aftershock sequences in Porto dos GaA(0)chos, Amazon craton-Brazil, were used to estimate the coda wave attenuation in the frequency band of 1 to 24 Hz. The time-domain coda-decay method of a single backscattering model is employed to estimate frequency dependence of the quality factor (Q (c)) of coda waves modeled usingwhere Q (0) is the coda quality factor at frequency of 1 Hz and eta is the frequency parameter. We also used the independent frequency model approach (Morozov, Geophys J Int, 175:239-252, 2008), based in the temporal attenuation coefficient, chi(f) instead of Q(f), given by the equation for the calculation of the geometrical attenuation (gamma) and effective attenuation Q (c) values have been computed at central frequencies (and band) of 1.5 (1-2), 3.0 (2-4), 6.0 (4-8), 9.0 (6-12), 12 (8-16), and 18 (12-24) Hz for five different datasets selected according to the geotectonic environment as well as the ability to sample shallow or deeper structures, particularly the sediments of the Parecis basin and the crystalline basement of the Amazon craton. For the Parecis basin for the surrounding shield and for the whole region of Porto dos GaA(0)chos Using the independent frequency model, we found: for the cratonic zone, gamma = 0.014 s (-aEuro parts per thousand 1), nu a parts per thousand 1.12; for the basin zone with sediments of similar to 500 m, gamma = 0.031 s (-aEuro parts per thousand 1), nu a parts per thousand 1.27; and for the Parecis basin with sediments of similar to 1,000 m, gamma = 0.047 s (-aEuro parts per thousand 1), nu a parts per thousand 1.42. Analysis of the attenuation factor (Q (c)) for different values of the geometrical spreading parameter (nu) indicated that an increase of nu generally causes an increase in Q (c), both in the basin as well as in the craton. But the differences in the attenuation between different geological environments are maintained for different models of geometrical spreading. It was shown that the energy of coda waves is attenuated more strongly in the sediments, (in the deepest part of the basin), than in the basement, (in the craton). Thus, the coda wave analysis can contribute to studies of geological structures in the upper crust, as the average coda quality factor is dependent on the thickness of sedimentary layer.

Crustal heterogeneities and complexities of fault processes

In this work we study the relation between crustal heterogeneities and complexities in fault processes. The first kind of heterogeneity considered involves the concept of asperity. The presence of an asperity in the hypocentral region of the M = 6.5 earthquake of June 17-th, 2000 in the South Iceland Seismic Zone was invoked to explain the change of seismicity pattern before and after the mainshock: in particular, the spatial distribution of foreshock epicentres trends NW while the strike of the main fault is N 7◦ E and aftershocks trend accordingly; the foreshock depths were typically deeper than average aftershock depths. A model is devised which simulates the presence of an asperity in terms of a spherical inclusion, within a softer elastic medium in a transform domain with a deviatoric stress field imposed at remote distances (compressive NE − SW, tensile NW − SE). An isotropic compressive stress component is induced outside the asperity, in the direction of the compressive stress axis, and a tensile component in the direction of the tensile axis; as a consequence, fluid flow is inhibited in the compressive quadrants while it is favoured in tensile quadrants. Within the asperity the isotropic stress vanishes but the deviatoric stress increases substantially, without any significant change in the principal stress directions. Hydrofracture processes in the tensile quadrants and viscoelastic relaxation at depth may contribute to lower the effective rigidity of the medium surrounding the asperity. According to the present model, foreshocks may be interpreted as induced, close to the brittle-ductile transition, by high pressure fluids migrating upwards within the tensile quadrants; this process increases the deviatoric stress within the asperity which eventually fails, becoming the hypocenter of the mainshock, on the optimally oriented fault plane. In the second part of our work we study the complexities induced in fault processes by the layered structure of the crust. In the first model proposed we study the case in which fault bending takes place in a shallow layer. The problem can be addressed in terms of a deep vertical planar crack, interacting with a shallower inclined planar crack. An asymptotic study of the singular behaviour of the dislocation density at the interface reveals that the density distribution has an algebraic singularity at the interface of degree ω between -1 and 0, depending on the dip angle of the upper crack section and on the rigidity contrast between the two media. From the welded boundary condition at the interface between medium 1 and 2, a stress drop discontinuity condition is obtained which can be fulfilled if the stress drop in the upper medium is lower than required for a planar trough-going surface: as a corollary, a vertically dipping strike-slip fault at depth may cross the interface with a sedimentary layer, provided that the shallower section is suitably inclined (fault "refraction"); this results has important implications for our understanding of the complexity of the fault system in the SISZ; in particular, we may understand the observed offset of secondary surface fractures with respect to the strike direction of the seismic fault. The results of this model also suggest that further fractures can develop in the opposite quadrant and so a second model describing fault branching in the upper layer is proposed. As the previous model, this model can be applied only when the stress drop in the shallow layer is lower than the value prescribed for a vertical planar crack surface. Alternative solutions must be considered if the stress drop in the upper layer is higher than in the other layer, which may be the case when anelastic processes relax deviatoric stress in layer 2. In such a case one through-going crack cannot fulfil the welded boundary conditions and unwelding of the interface may take place. We have solved this problem within the theory of fracture mechanics, employing the boundary element method. The fault terminates against the interface in a T-shaped configuration, whose segments interact among each other: the lateral extent of the unwelded surface can be computed in terms of the main fault parameters and the stress field resulting in the shallower layer can be modelled. A wide stripe of high and nearly uniform shear stress develops above the unwelded surface, whose width is controlled by the lateral extension of unwelding. Secondary shear fractures may then open within this stripe, according to the Coulomb failure criterion, and the depth of open fractures opening in mixed mode may be computed and compared with the well studied fault complexities observed in the field. In absence of the T-shaped decollement structure, stress concentration above the seismic fault would be difficult to reconcile with observations, being much higher and narrower.

InSAR deformation measurements of the earthquake cycle in transcurrent tectonic domains, analytical and analog modeling

I applied the SBAS-DInSAR method to the Mattinata Fault (MF) (Southern Italy) and to the Doruneh Fault System (DFS) (Central Iran). In the first case, I observed limited internal deformation and determined the right lateral kinematic pattern with a compressional pattern in the northern sector of the fault. Using the Okada model I inverted the observed velocities defining a right lateral strike slip solution for the MF. Even if it fits the data within the uncertainties, the modeled slip rate of 13-15 mm yr-1 seems too high with respect to the geological record. Concerning the Western termination of DFS, SAR data confirms the main left lateral transcurrent kinematics of this fault segment, but reveal a compressional component. My analytical model fits successfully the observed data and quantifies the slip in ~4 mm yr-1 and ~2.5 mm yr-1 of pure horizontal and vertical displacement respectively. The horizontal velocity is compatible with geological record. I applied classic SAR interferometry to the October–December 2008 Balochistan (Central Pakistan) seismic swarm; I discerned the different contributions of the three Mw > 5.7 earthquakes determining fault positions, lengths, widths, depths and slip distributions, constraining the other source parameters using different Global CMT solutions. A well constrained solution has been obtained for the 09/12/2008 aftershock, whereas I tested two possible fault solutions for the 28-29/10/08 mainshocks. It is not possible to favor one of the solutions without independent constraints derived from geological data. Finally I approached the study of the earthquake-cycle in transcurrent tectonic domains using analog modeling, with alimentary gelatins like crust analog material. I successfully joined the study of finite deformation with the earthquake cycle study and sudden dislocation. A lot of seismic cycles were reproduced in which a characteristic earthquake is recognizable in terms of displacement, coseismic velocity and recurrence time.

Inferences on earthquake kinematic properties from data inversion: two different approaches

During my PhD, starting from the original formulations proposed by Bertrand et al., 2000 and Emolo & Zollo 2005, I developed inversion methods and applied then at different earthquakes. In particular large efforts have been devoted to the study of the model resolution and to the estimation of the model parameter errors. To study the source kinematic characteristics of the Christchurch earthquake we performed a joint inversion of strong-motion, GPS and InSAR data using a non-linear inversion method. Considering the complexity highlighted by superficial deformation data, we adopted a fault model consisting of two partially overlapping segments, with dimensions 15x11 and 7x7 km2, having different faulting styles. This two-fault model allows to better reconstruct the complex shape of the superficial deformation data. The total seismic moment resulting from the joint inversion is 3.0x1025 dyne.cm (Mw = 6.2) with an average rupture velocity of 2.0 km/s. Errors associated with the kinematic model have been estimated of around 20-30 %. The 2009 Aquila sequence was characterized by an intense aftershocks sequence that lasted several months. In this study we applied an inversion method that assumes as data the apparent Source Time Functions (aSTFs), to a Mw 4.0 aftershock of the Aquila sequence. The estimation of aSTFs was obtained using the deconvolution method proposed by Vallée et al., 2004. The inversion results show a heterogeneous slip distribution, characterized by two main slip patches located NW of the hypocenter, and a variable rupture velocity distribution (mean value of 2.5 km/s), showing a rupture front acceleration in between the two high slip zones. Errors of about 20% characterize the final estimated parameters.

Risk analysis of light-frame wood construction due to multiple hazards

Light-frame wood buildings are widely built in the United States (U.S.). Natural hazards cause huge losses to light-frame wood construction. This study proposes methodologies and a framework to evaluate the performance and risk of light-frame wood construction. Performance-based engineering (PBE) aims to ensure that a building achieves the desired performance objectives when subjected to hazard loads. In this study, the collapse risk of a typical one-story light-frame wood building is determined using the Incremental Dynamic Analysis method. The collapse risks of buildings at four sites in the Eastern, Western, and Central regions of U.S. are evaluated. Various sources of uncertainties are considered in the collapse risk assessment so that the influence of uncertainties on the collapse risk of lightframe wood construction is evaluated. The collapse risks of the same building subjected to maximum considered earthquakes at different seismic zones are found to be non-uniform. In certain areas in the U.S., the snow accumulation is significant and causes huge economic losses and threatens life safety. Limited study has been performed to investigate the snow hazard when combined with a seismic hazard. A Filtered Poisson Process (FPP) model is developed in this study, overcoming the shortcomings of the typically used Bernoulli model. The FPP model is validated by comparing the simulation results to weather records obtained from the National Climatic Data Center. The FPP model is applied in the proposed framework to assess the risk of a light-frame wood building subjected to combined snow and earthquake loads. The snow accumulation has a significant influence on the seismic losses of the building. The Bernoulli snow model underestimates the seismic loss of buildings in areas with snow accumulation. An object-oriented framework is proposed in this study to performrisk assessment for lightframe wood construction. For home owners and stake holders, risks in terms of economic losses is much easier to understand than engineering parameters (e.g., inter story drift). The proposed framework is used in two applications. One is to assess the loss of the building subjected to mainshock-aftershock sequences. Aftershock and downtime costs are found to be important factors in the assessment of seismic losses. The framework is also applied to a wood building in the state of Washington to assess the loss of the building subjected to combined earthquake and snow loads. The proposed framework is proven to be an appropriate tool for risk assessment of buildings subjected to multiple hazards. Limitations and future works are also identified.

Integrated transnational macroseismic data set for the strongest earthquakes of Vrancea

A unique macroseismic data set for the strongest earthquakes occurred since 1940 in Vrancea region, is constructed by a thorough review of all available sources. Inconsistencies and errors in the reported data and in their use are analyzed as well. The final data set, free from inconsistencies, including those at the political borders, contains 9822 observations for the strong intermediate-depth earthquakes: 1940, Mw=7.7; 1977, Mw=7.4; 1986, Mw=7.1; 1990, May 30, Mw=6.9 and 1990, May 31, Mw=6.4; 2004, Mw=6.0. This data set is available electronically as supplementary data for the present paper. From the discrete macroseismic data the continuous macroseismic field is generated using the methodology developed by Molchan et al. (2002) that, along with the unconventional smoothing method Modified Polynomial Filtering (MPF), uses the Diffused Boundary (DB) method, which visualizes the uncertainty in the isoseismal's boundaries. The comparison of DBs with previous isoseismals maps represents a good evaluation criterion of the reliability of earlier published maps. The produced isoseismals can be used not only for the formal comparison between observed and theoretical isoseismals, but also for the retrieval of source properties and the assessment of local responses (Molchan et al., 2011).

Experience and lessons learnt from the SMART 2013 Benchmark

The French CEA, together with EDF and the IAEA, recently organised an international benchmark to evaluate the ability to model the mechanical behaviour of a typical nuclear reinforced concrete structure subjected to seismic demands. The participants were provided with descriptions of the structure and the testing campaign; they had to propose the numerical model and the material laws for the concrete (stage #1). A mesh of beam and shell elements was generated; for modelling the concrete a damaged plasticity model was used, but a smeared crack model was also investigated. Some of the initial experimental results, with the mock-up remaining in the elastic range, were provided to the participants for calibrating their models (stage #2). Predictions had to be produced in terms of eigen-frequencies and motion time histories. The calculated frequencies reproduced reasonably the experimental ones; the time histories, calculated by modal response analysis, also reproduced adequately the observed amplifications. The participants were then expected to predict the structural response under strong ground motions (stage #3), which increased progressively up to a history recorded during the 1994 Northridge earthquake, followed by an aftershock. These results were produced using an explicit solver and a damaged plasticity model for the concrete, although an implicit solver with a smeared crack model was also investigated. The paper presents the conclusions of the pre-test exercise, as well as some observations from additional simulations conducted after the experimental results were made available.

Implications of fault constitutive properties for earthquake prediction.

The rate- and state-dependent constitutive formulation for fault slip characterizes an exceptional variety of materials over a wide range of sliding conditions. This formulation provides a unified representation of diverse sliding phenomena including slip weakening over a characteristic sliding distance Dc, apparent fracture energy at a rupture front, time-dependent healing after rapid slip, and various other transient and slip rate effects. Laboratory observations and theoretical models both indicate that earthquake nucleation is accompanied by long intervals of accelerating slip. Strains from the nucleation process on buried faults generally could not be detected if laboratory values of Dc apply to faults in nature. However, scaling of Dc is presently an open question and the possibility exists that measurable premonitory creep may precede some earthquakes. Earthquake activity is modeled as a sequence of earthquake nucleation events. In this model, earthquake clustering arises from sensitivity of nucleation times to the stress changes induced by prior earthquakes. The model gives the characteristic Omori aftershock decay law and assigns physical interpretation to aftershock parameters. The seismicity formulation predicts large changes of earthquake probabilities result from stress changes. Two mechanisms for foreshocks are proposed that describe observed frequency of occurrence of foreshock-mainshock pairs by time and magnitude. With the first mechanism, foreshocks represent a manifestation of earthquake clustering in which the stress change at the time of the foreshock increases the probability of earthquakes at all magnitudes including the eventual mainshock. With the second model, accelerating fault slip on the mainshock nucleation zone triggers foreshocks.

Natural Disaster and Intangible Heritage: Beyond the Horizon

When 7.8-magnitude earthquake struck Nepal in 2015, many monuments, temples and houses turned into rubbles killing more than 8,000 people and injuring above 21,000. This unfortunate and tragic natural disaster brought international attention to Nepal. But in this time of despair and pain there was a sign of hope that should be acknowledged well, the spirit of community facing the disaster. This paper is about the indigenous community of Kathmandu on how they organized an important traditional festival just four months after the disaster when most the people were still living in the makeshifts, along with the smaller aftershock continuing almost everyday. In the country like Nepal with numerous intangible heritages, which is, still living is not taken seriously by the concerned authorities and mostly been neglected. It is the indigenous community who has been carrying out those heritages, as they are inseparable aspect of the social life. With this paper it tries look at the community involvement and intangible heritage of Kathmandu Valley, which is a part of my PhD research thesis.