Estimation of site amplification functions in Gujarat region, India

Site response in the Gujarat region is studied using local earthquake data recorded at 32 sites spread all over Gujarat region, India. Out of these 32 sites, 15 sites are located in Kachchh region, 8 in Saurashtra and 9 in mainland Gujarat region. These sites are underlain by different types of rocks/sediments of different ages. Out of 32 stations, 7 stations are on Quaternary deposits, 6 on Tertiary, 11 on Deccan, 3 on Jurassic, 3 on Cretaceous and 2 on Proterozoic rocks. The predominant frequencies at these sites depend strongly on the local geology. The average predominant frequencies of the sites on Quaternary sediments are 2.4?Hz, 5.3?Hz on Tertiary, 7.5?Hz on Jurassic, 7.2?Hz on Deccan, 4.6?Hz on Cretaceous and 7.5?Hz on Proterozoic formations. The average site amplification values at predominant frequencies are 3.7 for the sites of Quaternary deposits, 3.3 for Tertiary, 3.3 for Cretaceous rock, 4.2 for Deccan trap, 4.1 for Jurassic sites and 4.6 for Proterozoic. The damage to the houses during 2001 Bhuj earthquake is compared with the amplification at predominant frequencies at those sites. The spatial variation of predominant frequencies and the site amplifications at different frequencies corresponding to the natural frequencies of different storey buildings are studied, which will be useful in the evaluation of seismic hazard in the region.     

Estimation of Strong Ground Motion from a Great Earthquake Mw 8.5 in Central Seismic Gap Region, Himalaya (India) Using Empirical Green’s Function Technique

In the present study ground motions for a Mw 8.5 scenario earthquake are estimated at 13 sites in Kumaun-Garhwal region using the empirical Green’s function technique. The recordings of 1991 Uttarkashi earthquake of Mw 6.8 at these sites are used as an element earthquake. A heterogeneous source model consisting of two asperities is considered for simulating the ground motions. The entire central seismic gap (CSG) can expect acceleration in excess of 100 cm/s² with NW portion in excess of 400 cm/s² and SE between 100 and 200 cm/s². The central portion can expect peak ground acceleration (PGA) between 200 and 400 cm/s². It has been observed from simulation of strong ground motion that sites located near the rupture initiation point can expect accelerations in excess of 1g. In the present analysis, Bhatwari and Uttarkashi can expect ground accelerations in excess of 1g. The estimates of the PGA are compared with earlier studies in the same region using different methodologies and it was found that the results are comparable. This has put constrains on the expected PGAs in this region. The obtained PGA values can be used in identifying the vulnerable areas in the central Himalaya, thereby facilitating the planning, design and construction of new structures and strengthening of the existing structures in the region.     

Modeling viscous damping in nonlinear response history analysis of buildings for earthquake excitation

The Rayleigh damping model, which is pervasive in nonlinear response history analysis (RHA) of buildings, is shown to develop ‘spurious’ damping forces and lead to inaccurate response results. We prove that a viscous damping matrix constructed by superposition of modal damping matrices—irrespective of the number of modes included or values assigned to modal damping ratios—completely eliminates the ‘spurious’ damping forces. This is the damping model recommended for nonlinear RHA. Replacing the stiffness‐proportional part of Rayleigh damping by the tangent stiffness matrix is shown to improve response results. However, this model is not recommended because it lacks a physical basis and has conceptual implications that are troubling: hysteresis in damping force–velocity relationship and negative damping at large displacements. Furthermore, the model conflicts with the constant‐damping model that has been the basis for fundamental concepts and accumulated experience about the inelastic response of structures. With a distributed plasticity model, the structural response is not sensitive to the damping model; even the Rayleigh damping model leads to acceptable results. This perspective on damping provides yet another reason to employ the superior distributed plasticity models in nonlinear RHA. OpenSees software has been extended to include a damping matrix defined as the superposition of modal damping matrices. Although this model leads to a full populated damping matrix, the additional computational demands are demonstrated to be minimal. Copyright © 2015 John Wiley & Sons, Ltd.     

Elastic earthquake analysis of torsionally coupled multistorey buildings

With the aid of perturbation analysis of vibration frequencies and mode shapes it is shown that any lower vibration mode of a torsionally coupled building may be approximated as a linear combination of three vibration modes of the corresponding torsionally uncoupled system (a system with coincident centres of mass and resistance but all other properties are identical to the actual system): one translational mode along each of the two principal axes of resistance and one mode in torsional vibration. This result provides the motivation for a simpler—relative to the standard—procedure for analysing the response of torsionally coupled multistorey buildings to earthquake ground motion. To illustrate the application and accuracy of this procedure two numerical examples are presented.     

Rocking response of rigid blocks to earthquakes

This investigation deals with the rocking response of rigid blocks subjected to earthquake ground motion. A numerical procedure and computer program are developed to solve the non-linear equations of motion governing the rocking motion of rigid blocks on a rigid base subjected to horizontal and vertical ground motion. The response results presented show that the response of the block is very sensitive to small changes in its size and slenderness ratio and to the details of ground motion. Systematic trends are not apparent: The stability of a block subjected to a particular ground motion does not necessarily increase monotonically with increasing size or decreasing slenderness ratio. Overturning of a block by a ground motion of particular intensity does not imply that the block will necessarily overturn under the action of more intense ground motion. In contrast, systematic trends are observed when the problem is studied from a probabilistic point of view with the ground motion modelled as a random process. The probability of a block exceeding any response level, as well as the probability that a block overturns, increases with increase in ground motion intensity, increase in slenderness ratio of the block and decrease in its size. It is concluded that probabilistic estimates of the intensity of ground shaking may be obtained from its observed effects on monuments, minarets, tombstones and other similar objects provided suitable data in sufficient quantity is available, and the estimates are based on probabilistic analyses of the rocking response of rigid blocks, considering their non-linear dynamic behaviour.     

Earthquake analysis of concrete gravity dams including dam-water-foundation rock interaction

A general procedure for analysis of the response of concrete gravity dams, including the dynamic effects of impounded water and flexible foundation rock, to the transverse (horizontal) and vertical components of earthquake ground motion is presented. The problem is reduced to one in two dimensions, considering the transverse vibration of a monolith of the dam. The system is analysed under the assumption of linear behaviour for the concrete, foundation rock and water. The complete system is considered as composed of three substructures—the dam, represented as a finite element system, the fluid domain, as a continuum of infinite length in the upstream direction, and the foundation rock region as a viscoelastic half-plane. The structural displacements of the dam are expressed as a linear combination of Ritz vectors, chosen as normal modes of an associated undamped dam-rock system. The effectiveness of this analytical formulation lies in its being able to produce excellent results by considering only a few Ritz vectors. The generalized displacements due to earthquake motion are computed by synthesizing their complex frequency responses using Fast Fourier Transform procedures. The stress responses are calculated from the displacements. An example analysis is presented to illustrate results obtained from this analytical procedure. Computation times for several analyses are presented to illustrate the effectiveness of the procedure.