|Structural Engineering Laboratory|
|Department of Civil Engineering|
|Indian Institute of Science|
Earthquake Engineering and Structural Dynamics Back to Top
Strong Motion during the Gujarath Earthquake
A field survey of the Gujarath earthquake of 26th January 2001, has been completed. In the absence of near field strong motion records, the level of ground motion during the devastating 26th Jan 2001 earthquake has to be found by indirect means. For the city of Bhuj a broad band velocity time history has been recorded by India Meteorological Department. This data is processed to obtain an estimate of strong ground motion at Bhuj. It is estimated that the peak ground acceleration at Bhuj was of the order of 0.38g. Ground motion in the surrounding region is indirectly found using available spectral response recorder (SRR) data. The severity of ground motion generally decreases with distance. This is usually quantified in terms of the attenuation of the peak ground acceleration (PGA) with epi-central distance. In the absence of instrumentally recorded near field ground motion for the Kutch earthquake, the attenuation of PGA has to be studied by indirect methods. For this purpose, the SRR data comes handy. In Table 1 the available SRR data at 13 stations are presented along with the place names and their epicentral distances. The highest peak acceleration response (Sa) of a simple harmonic oscillator depends strongly on the PGA value at the station. A simple empirical approach to understand this relation is to obtain a regression equation between Sa and PGA. Here this is done by considering a global sample of 295 actual strong motion accelerograms and their corresponding response spectra. This data is drawn from the website of Pacific Earthquake Engineering Research Center (URL: http:// www.peer.berkeley.edu/). These instrument based results are compared with analytical
Attenuation of Strong Ground Motion in Peninsular India
India has faced several devastating earthquakes in the past. The largest of these have originated in the Himalayan plate boundary region, which has remained a region of great scientific and engineering interest. Not surprisingly, considerable data and earthquake related literature are available about the northern part of India. On the other hand available seismological information about Peninsular India (PI), which we take here as south of 240 N latitude, is very little. This situation is changing, mainly due to three devastating events, namely, Khillari (30.9.1993), Jabalpur (22.5.1997), and Kutch (26.1.2001) shocks in recent years. But the information is so sparse, engineers presently face a daunting problem in estimating ground motion levels for future events in PI. In this respect the stable continental region (SCR) of PI shares some features of regions like the central and eastern United States. The present paper is motivated by the need to have an idea of the attenuation of ground motion in PI from the engineering point of view. In this attempt whatever data is available is made use of to arrive at a plausible attenuation formula. The study is carried out in three stages. In the first stage, events with instrumental data are considered. This set comprises of data from the Koyna-Warna region of western India. In the second stage to the above data, peak ground acceleration values estimated from spectral response recorders of the Kutch region are added. The resulting relation is expected to be well applicable to western India. However to allow for diversity of data arising from other seismogenic regions of southern India, it becomes necessary to add non-instrumental PGA estimates obtained from the observation of overturned objects and MMI values. In the sequel an empirical relation connecting PGA and MMI for Indian conditions is also developed. In the third stage the composite data set is used to arrive at an attenuation formula, expected to be useful, till new strong motion data accumulates in PI.
Earthquake Source Model and Estimation of Ground Motion
The near source region is modeled as a half-space and the source as a sequence of double couples, spread over the fault surface. An analytical approach to find the location, magnitude and orientation of the double couples by inverting available strong motion records is developed. This new method is applied to find the source of San Fernando (USA) earthquake of 1971, for which results are available from other approaches also. It is shown that the present method leads to accurate results of engineering importance. Numerical results on the geometry of the causative faults of Uttarkashi (1991) and Chamoli(1999) earthquakes are also computed. A limitation of the present method is that it can handle low frequency data such as displacements but not accelerations. Hence in simulation exercises only strong motion displacements can be found accurately. Thus, for computing attenuation of PGA in a region a reliable relation between peak displacements and accelerations is needed. Here this has been derived empirically using global strong motion data. The analytical method of simulating ground displacement and further finding attenuation of PGA is demonstrated by taking the Kutch region of Gujarath as a case study. Strong motion simulation using a half-space regional model is carried out to estimate the attenuation of PGA during the recent earthquake of January 2001. The theoretical attenuation curve is found to compare well with available observations of PGA values.
Previous work done on the seismic status of the city of Delhi (by Prof. R.N.Iyengar while at CBRI Roorkee) is being revised to improve the hazard estimation procedures to be adopted for the city of Delhi. Regional seismicity studies pertaining to the controlling region around Delhi has been completed. Microzonation of seismic hazard of Delhi city is in progress. Similar investigations are being carried out for N.E and Western regions of India.
The present source mechanism models are not efficient in computation of ground accelerograms, which contain high frequencies. New engineering source models that are seismologically consistent and amenable for computation of surface acceleration are under development. These are capable of incorporating fault details such as dip, strike, rupture length etc. as random variables.
There are many practical problems wherein the system is nonlinear and/or the excitation is non-gaussian. Special types of non-gaussian excitations for which exact solutions are possible at least with linear systems are being explored. Higher order linearization technique previously developed for approximate analysis of single degree nonlinear systems, is being improved to include multi degree of freedom systems.
Structural dynamics with parameter uncertainties & structural reliability analysis
The problem of determining the statistics of transient response of randomly inhomogeneous beams is formulated. This is based on the use of stochastic dynamic stiffness coefficients in conjunction with fast Fourier transform algorithm. The dynamic stiffness coefficients, in turn, are determined using stochastic finite element formulation, which employs frequency dependent shape functions. The approach is illustrated by analyzing the response of a random rod subject to a box car type of axial impact and, also, by considering the flexural response of a randomly inhomogeneous beam resting on randomly varying Winkler's foundation and subjected to the action of a moving force. Discussion on the treatment of system property random fields as being non-Gaussian in nature is presented. Also discussed are the methods for handling non-zero initial conditions within the framework of the frequency domain response analysis employed in the study. Satisfactory comparisons between the analytical results and simulation results is demonstrated.
The problem of characterizing response variability and assessing reliability of vibrating skeletal structures made up of randomly inhomogeneous, curved/straight Timoshenko beams is considered. The excitation is taken to be random in nature. A frequency domain stochastic finite element method is developed in terms of dynamic stiffness coefficients of the constituent stochastic beam elements. The displacement fields are discretized by using frequency and damping dependent shape functions. Questions related to discretizing the inherently non-Gaussian random fields that characterize beam elastic, mass and damping properties are considered. Analytical methods, combined analytical and simulation based methods, direct Monte Carlo simulations and simulation procedures that employ importance-sampling strategies are brought to bear on analyzing dynamic response variability and assessment of reliability. Satisfactory performance of approximate solution procedures outlined in the study is demonstrated sing limited Monte Carlo simulations.
The problem of response surface modeling of a limit surface lying within two hyperspheres of prescribed radii is considered. The relevance of this problem in structural reliability analysis involving performance functions with multiple design points and/or multiple regions that make significant contributions to failure probability is discussed. The paper also proposes global measures of sensitivity of failure probability with respect to the basic random variables. The performance of the proposed improvements is examined by comparing simulation-based results with results from the proposed procedure with reference to a set of nonlinear performance functions.
Critical stochastic earthquake load models
Studies dealing with the determination of critical earthquake load models for linear structures subjected to single-point seismic inputs have been conducted. The primary objective of this study is to examine the realism in critical excitations and critical responses vis a vis the framework adopted for the study and constraints that these excitations are taken to satisfy. Two alternative approaches are investigated. In the first approach, the critical earthquake is expressed in terms of a Fourier series that is modulated by an enveloping function that imparts transient nature to the inputs. The Fourier coefficients are taken to be deterministic and are constrained to satisfy specified upper and lower bounds. Estimates on these bounds, for a given site, are obtained by analyzing past earthquake records from the same site or similar sites. The unknown Fourier coefficients are determined such that the response of a given structure is maximized subjected to these bounds and additional constraints on intensity, peak ground acceleration, peak ground velocity and peak ground displacement. In the second approach, the critical earthquake is modeled as a partially specified non-stationary Gaussian random process which is defined in terms of a stationary random process of unknown power spectral density (PSD) function modulated by a deterministic envelope function. The input is constrained to possess specified variance and average zero crossing rate. Additionally, a new constraint in terms of entropy rate representing the expected level of disorder in the excitation is also imposed. The unknown PSD function of the stationary part of the input is determined so that the response of a given structure is maximized. The optimization problem in both these approaches is solved by using sequential quadratic programming method. The procedures developed are illustrated by considering seismic response of a tall chimney and an earth dam. It is concluded that the imposition of lower and upper bounds on Fourier coefficients in the first approach and constraints on amount of disorder in the second approach are crucial in arriving at realistic critical excitations.
The problem of modeling probabilistic critical earthquake load models for linear structures is considered. The new formulations developed in this study, for determining critical seismic excitations, integrate methods of structural reliability, nonlinear optimization programming and random vibration analysis. The ground acceleration is modeled as a partially specified stationary Gaussian random process. The known information on the excitation involve bounds on total average energy, zero crossing rate and the amount of disorder represented in terms of entropy rate. The power spectral density function of the earthquake acceleration is taken to be unknown and is computed such that the probability of failure of a given structure is maximized or the reliability index of the structure is minimized. The critical earthquake excitations, as envisaged in both these two approaches, require results on extreme value distribution of the structure response over a specified duration of time. The constrained nonlinear optimization problems are tackled using the sequential quadratic programming (SQP) method. The illustrative examples include modeling of critical seismic inputs for a steel frame and a tall chimney. The results indicate that the two approaches lead to the same critical inputs as by maximizing the structure response variance. The second approach is promising since it can be extended to handle nonlinear and/or parametrically excited structures.
The problem of modeling probabilistic critical earthquake excitations for nonlinear structures is considered. The formulation developed in this study integrates methods of structural reliability, response surface fitting and nonlinear optimization programming. The proposed algorithm, thus, is capable of handling a wide class of problems including structures nonlinearity and temporal variation of excitations as well. The ground accelerations are modeled as a vector of partially specified non-stationary Gaussian random processes. Each of these random processes is obtained by modulating a stationary Gaussian random process with a deterministic envelope function. The envelope functions are taken to be known while the power spectral density function/matrix of the stationary part is kept unknown. The excitations are taken to satisfy constraints on total average energy, zero crossing rate, entropy rate and other positivity and bounding requirements that are of mathematical nature. The unknown PSD function/matrix of the stationary accelerations is computed such that the structure reliability index is minimized. Since, the performance functions involved in the reliability analysis are given implicitly in terms of a set of random variables, these functions are approximated with quadratic surfaces at the failure point. The constrained nonlinear optimization problems are tackled using the sequential quadratic programming (SQP) method. The formulation is illustrated by computing the critical seismic inputs for singly-supported and multiply-supported oscillators that have cubic force-displacement relations.
The earthquake response of stack like structures subjected to simultaneous action of random horizontal and vertical earthquake acceleration components is considered. The governing equation of motion in this case is approximated by a set of randomly time varying ordinary differential equations. The components of earthquake accelerations are modeled as non-stationary Gaussian random processes that are obtained by multiplying deterministic modulating functions with partially specified stationary random processes. Specifically it is assumed that the matrix of power spectral density (psd) functions of the stationary components are not known while the variance, average rate of zero crossings, entropy rate and frequency range of interest are taken to be known. The unknown input psd matrix is determined such that the reliability index associated with a specified structure performance function is minimized. The solution procedure employed combines theory of Hasofer-Lind reliability indices, response surface modeling and constrained nonlinear optimization tools. The critical input psd matrix so obtained leads to the definition of excitation models that produce the least favorable response which at the same time possess a few of the well known properties of earthquake loads. The study also reports on an approach to solve the analogous problem within deterministic framework. This facilitates a comparison to be made on probabilistic and deterministic solutions to the same problem. A numerical example that illustrates the concepts developed with reference to a chimney structure is provided.
Structural damage detection using vibration data
The problem of detecting local/distributed change of stiffness in bridge structures using ambient vibration data is considered. The vibration induced by a vehicle moving on the bridge is taken to be the excitation source. A validated finite element model for the bridge structure in its undamaged state is assumed to be available. Alterations to be made to this initial model, to reflect the changes in bridge behavior due to occurrence of damage, are determined using a time domain approach. The study takes into account complicating features arising out of dynamic interactions between vehicle and the bridge, bridge deck unevenness, spatial incompleteness of measured data and presence of measurement noise. The inclusion of vehicle inertia, stiffness and damping characteristics into the analysis makes the system time variant, which, in turn, necessitates treatment of the damage detection problem in time domain. The efficacy of the procedures developed is demonstrated by considering detection of localized/distributed damages in a beam-moving oscillator model using synthetically generated vibration data.
The problem of detecting local and/or distributed loss of stiffness in bridge girders using vibration data generated by passage of a moving vehicle is considered. A time domain structural damage detection scheme within finite element modeling framework, that takes into account time varying structural matrices, structural non-linearities and spatial incompleteness of measured data, is developed. The damage parameters associated with changes in structural stiffness are shown to be governed by a set of overdetermined non-linear equations, which are solved iteratively. Illustrative examples on a geometrically non-linear Euler-Bernoulli beam carrying a moving single degree of freedom oscillator are provided.
Statistical energy analysis of engineering structures
The problem of characterizing stochastic variability in energy flow characteristics predicted using statistical energy analysis (SEA) formalisms is considered. In the present study, the application of the SEA procedure to a given problem is considered to be successful if the sample fluctuations in subsystem energy levels do not differ from the predicted averages by a prescribed amount. Methods that are well developed in the field of structural reliability analysis are brought to bear on examining this issue. Accordingly, the notion of a reliability index that qualifies successful performance of SEA procedure is introduced. This index is shown to depend upon, not only the modal characteristics of the subsystems, but also, on uncertainty parameters, coupling characteristics and over all structural geometry and connectivity. The determination of this index requires the solution of a constrained nonlinear optimization problem. The computation of this index also leads to three other failure descriptors, namely, the point of maximum probability of failure, a vector of sensitivity factors relating system uncertain parameters to reliability index and a notional probability of failure that serves as an approximation to the failure probability. Numerical examples on vibration flow in spring coupled rods and plate structures are used to illustrate the features of proposed performance index.
The behavior of suspension bridges under seismic loading depends on several nonlinearities present in the structure. A special purpose finite element code has been developed which simulates the self weight condition of the cable-deck-tower structure taking in to account the exact erection process followed at the construction site. An incremental nonlinear self -weight analysis has been employed to arrive at the stresses in the structure and the cable profile. The cable has been modeled using an equivalent modulus that accounts for geometric nonlinear effects. The equivalent modulus has been derived from the basic cable equation accounting for the sequence of the bridge erection process. The study indicates that the inclusion of the actual sequence of bridge construction results in a modification of the dynamics of the structural system (natural frequencies and mode shape) significantly.
An optimal design of a hybrid mass damper (HMD) system, consisting of a tuned mass damper (TMD) and an active mass driver (AMD), as its passive and active control system components respectively, for wind induced or seismically excited building structures, has been studied. Genetic algorithm has been used for the optimization of the hybrid mass damper parameters, as the optimization problem is not necessarily convex. In view of seeking a more realistic model, hardware related constraints have been considered in the model. Numerical examples for the optimum parameters of the hybrid mass damper for multi degree freedom structures has been studied to show the effectiveness of the design process. The hybrid mass damper (HMD) control system strategy for three-dimensional building models, incorporating torsionally coupled modes, under wind induced or seismic excitations has also been studied. As an extension of this study, an assessment of the performance of the control formulation in a damaged structure has also been studied.
In the initial phase, a LQG control algorithm was designed for the pre-earthquake model and its performance evaluated for a given set of earthquake excitations. As the evaluation model of the building remained unchanged during this evaluation, no change was made in the control algorithm by the supervisory control system. After evaluating performance of the control system for the pre-earthquake evaluation model for all the given earthquake excitation, the evaluation model of the building was changed to represent a post-earthquake model keeping the control algorithm unchanged, i.e., same as that designed for the pre-earthquake evaluation model. The performance of the control system was evaluated again for the post-earthquake evaluation model for all given earthquake excitations. As the evaluation model changed, online system identification of the supervisory controller identified the changes in the system. A new LQG control algorithm was designed for the identified system and subsequently the control algorithm was tuned. The performance of the tuned controller was evaluated for the same set of earthquakes. Performance of the control system was evaluated using the evaluation criteria defined in the 20 storey benchmark building model (http://www.nd.edu/~quake /). The comparisons of the different performance indices (e.g. peak and r.m.s. displacement and acceleration levels, number of control devices, sensors, energy supplied to drive the active masses, etc.) for the pre and post earthquake case is shown in table 2. It is seen that adaptive control leads to a comparable performance level of the control system in the damaged building as observed in the undamaged building.
Fuzzy logic control systems have been applied as an effective control system in various fields, including vibration control of structures because of its inherent robustness and ability to handle non-linearity and uncertainties in the structural behavior and loading. A multi-objective optimal fuzzy controlled seismically excited nonlinear building structure has been studied. Acceleration and velocity information has been used as feedback to the fuzzy logic controller. As an extension, a supervisor model has been constructed and trained on an artificial neuro-fuzzy inference system ANFIS platform so that it can detect changes in the system dynamics of the primary structure and tune the parameters of the fuzzy logic controller. This adaptive control system has been studied to assess its performance and has been found to yield vibration control to the same degree that was available in the undamaged structure.
Inelastic Response to Earthquakes
Influence of shape of a building in plan on the inelastic earthquake response was determined numerically. Further work is underway to obtain the response of tall buildings of different plan shapes subjected to earthquakes. It is proposed to try soft top storey (Expendable top storey) concept for building taller than 2 storeys and of different plan shapes. 11 M.E a theses in addition to 2 PhD�s mentioned already above were completed during the process of the above investigations.