Luis Esteva

Optimal instrumentation of uncertain structural systems subject to earthquake ground motions

A criterion is proposed for making decisions regarding the optimal location of a given number of sensors to record the seismic response of a structure for identification purposes. The optimal location of the sensors is selected so that the expected value of a Bayesian loss function, expressed in terms of the Fisher information in the recordings, is minimized. The criterion is applied to the case of multi-degree-of-freedom systems with uncertain structural properties subjected to earthquake ground motions modelled as stationary stochastic processes. The use and capabilities of the criterion are thoroughly illustrated by means of an example. Results are used to assess the influence of record duration, recording noise, and ground motion frequency content and amplitude, on the optimal location of accelerometers as well as on the reduction of prior uncertainty about the structural parameters.

Life-cycle optimization in the establishment of performance-acceptance parameters for seismic design

A life-cycle formulation is presented for the determination of optimum values of the mechanical properties of a structural system exposed to seismic risk. The resulting values are intended for providing support for the establishment of performance-acceptance criteria and parameters for seismic design. A method is developed for the determination of expected damage functions in terms of simplified reference models of the complex nonlinear systems that are typical of engineering practice. The uncertainties associated with the use of the simplified model to estimate peak dynamic responses of the system of interest are accounted for by means of first-order second-moment probabilistic criteria. An illustrative application of the criteria proposed is presented, together with a discussion about the translation of the results of the optimization studies into engineering criteria and methods expressed in conventional design formats.

Optimal instrumentation of structures on flexible base for system identification

A criterion previously developed by Heredia-Zavoni and Esteva for selecting optimal sensor locations is used to analyse the optimal instrumentation of structures on soft soils. The stochastic response of a linear structural system on a flexible base is formulated for use of the criterion. The case of MDOF shear systems on flexible base, with uncertain lateral stiffness and subjected to random earthquake ground motions, is studied. The optimal location of accelerometers, the reduction of prior uncertainty on the lateral stiffness, the effects of the base flexibility, the relative influence of translation and rocking of the base, and the influence of recording noise are assessed and discussed. Copyright

Evolutionary properties of stochastic models of earthquake accelerograms : Their dependence on magnitude and distance

An approach to generate artificial earthquakeaccelerograms on hard soil sites is presented. Eachtime-history of accelerations is considered as arealization of a non-stationary gaussian stochasticprocess, with statistical parameters depending onmagnitude and source-to-site distance. In order tolink the values of these parameters for each groundmotion record with the corresponding magnitude andsource-to-site distance, semi-empirical functionalrelations called generalized attenuationfunctions are determined. The set of realground-motion time histories used to obtain thesefunctions correspond to shocks generated at differentsources and recorded at different sites in thevicinity of the southern coast of Mexico. The resultsshow significant dispersion in the parameters of themodel adopted, which reflect that associated with thereal earthquakes included in the sample employed.The problem of conditional simulation of artificialacceleration time histories for prescribed intensitiesis briefly presented, but its detailed study is leftfor a companion paper. The criteria and modelsproposed are applied to generate two families ofartificial acceleration records for recurrenceintervals of 100 and 200 years at a specific sitelocated in the region under study. The results shownin this article correspond to acceleration timehistories recorded on firm ground for earthquakesgenerated at the subduction zone that runs along thesouthern coast of Mexico, and cannot be generalized tocases of earthquakes generated at other sources orrecorded at other types of local conditions. Thismeans that the methods and functional forms presentedhere are applicable to these other cases, but thevalues of the parameters that characterize thosefunctions may differ from those presented here.

Reliability functions for earthquake resistant design

Abstract A unified approach is presented for the establishment of design conditions and acceptance criteria for performance objectives associated with different return intervals. A life-cycle optimization analysis is adopted for this purpose. Reliability and expected damage functions are defined both for individual seismic events and for a long-term framework. System reliability functions are determined by Monte Carlo simulation for a number of multistory frames, designed for different base-shear ratios and subjected to earthquakes of different intensities. Systematic trends are identified about the variation of the reliability index with the natural logarithm of the expected ductility demand of a reference system. These trends lead to the definition of seismic reliability functions that can easily be adapted for applications to reliability-based design. The problem of transforming the results of the optimization studies into codified rules for practical design is briefly discussed.

Life-cycle optimisation in earthquake engineering

An overview is presented of life-cycle optimisation in the establishment of reliability- and performance-based seismic design requirements for multi-storey systems. Alternative approaches are presented for the development of seismic vulnerability functions that do not require the determination of lateral deformation capacities. The influence of damage accumulation on the evolution of the seismic reliability functions is discussed, and some results are presented about the sensitivity of the seismic reliability and performance functions to the contribution of energy-dissipating devices to the lateral strength and stiffness of multi-storey frames. The process of structural damage accumulation resulting from the action of sequences of seismic excitations is taken into account in the assessment of life-cycle system reliability and performance, and in the formulation of reliability and optimisation criteria and methods for the establishment of structural design requirements and for the adoption of repair and maintenance strategies. Problems related to the transformation of research results into practically applicable seismic design criteria are briefly discussed. Several illustrative examples are presented.

Seismic vulnerability functions of multi-storey buildings: estimation and applications

Seismic vulnerability functions of structural systems are presented as expressions relating earthquake intensities with quantitative measures of their probable consequences on the performance of those systems. The consequences considered include direct and indirect costs of structural and non-structural damage, either for the condition of system survival or for the possibilities of partial or total collapse. A review is presented of recent efforts towards the development of these functions for multi-storey building systems and for their application in life-cycle optimization studies for the establishment of target safety levels and the corresponding seismic design criteria. Special attention is given to the evaluation of system reliability with respect to the ultimate capacity (collapse) failure mode. Results are presented of some studies about the time-dependent process of damage accumulation and reliability evolution in building frames, as well as of the optimum design criteria and maintenance strategies for structural frames with hysteretic energy-dissipating devices.

Simulating earthquake ground motion at a site, for given intensity and uncertain source location

Following a companion article, ground motion acceleration time historiesduring earthquakes can be described as realizations of non-stationarystochastic processes with evolutionary frequency content and instantaneousintensity. The parameters characterizing those processes can be handled asuncertain variables with probabilistic distributions that depend on themagnitude of each seismic event and the corresponding source-to-sitedistance. Accordingly, the generation of finite samples of artificial groundmotion acceleration time histories for earthquakes of given intensities isformulated as a two-stage Monte Carlo simulation process. The first stageincludes the simulation of samples of sets of the parameters of thestochastic process models of earthquake ground motion. The second stageincludes the simulation of the time histories themselves, given theparameters of the associated stochastic process model. In order to accountfor the dependence of the probability distribution of the latter parameterson magnitude and source-to-site distance, the joint conditional probabilitydistribution of these variables must be obtained for a given value of theground motion intensity. This is achieved by resorting to Bayes Theoremabout the probabilities of alternate assumptions.Two options for the conditional simulation of ground motion time historiesare presented. The more refined option makes use of all the informationabout the conditional distribution of magnitude and distance for thepurpose of simulating values of the statistical parameters of the groundmotion stochastic process models. The second option considers allprobabilities concentrated at the most likely combination of magnitude anddistance for each of the seismic sources that contribute significantly to theseismic hazard at the site of interest.

Seismic Vulnerability of an Inventory of Overturning Objects

A methodology is presented for assessing the probability of overturning under the action of ground motions of given intensities, and the expected values and standard deviations of damage produced by overturning of objects in a group or inventory exposed to the same seismic event. We apply this methodology to one example of the typical contents located on the base (i.e., free-field) of a middle-class house or apartment. A detailed inventory was gathered, and recent well-recorded accelerograms at the site were used to compute the rocking response of every object. Vulnerability functions for the whole inventory computed at four different sites in terms of epicentral distance and site effects show large differences between them.

Seismicity assessment using earthquake catalogues with uncertain and incomplete data: probabilistic formulation

A novel generalized probabilistic formulation is proposed to assess seismicity using earthquake catalogues with uncertain and incomplete data. The seismicity, described by the complete exceedance rate of magnitudes, is estimated starting from a consistent incomplete exceedance rate which is rationally linked to the catalogue data. Complete and incomplete exceedance rates are represented by similar functional forms and they are related by a completeness function, which expresses the probability that an event is included in a data set. Completeness is considered uncertain and it is defined by a suitable, continuous, analytical, magnitude dependent function. The importance of this work lies on its applicability because it can be useful in seismic zones where information about seismic activity is scarce or simply when the catalogue is incomplete in a range of magnitudes that can have a significant influence on the seismic hazard analysis and on the resulting seismic risk assessment. Moreover, it can also be applied in the common case when the catalogue is considered complete above a given magnitude threshold. Numerical examples are presented to illustrate the influence of catalogue incompleteness on the complete exceedance rate estimations. In companion papers, attention is focused on the estimation of completeness probabilities of available catalogues and on parameter estimation of the exceedance rate functions.