Dynamic characteristics of shear buildings on laminated rubber bearings

Analytical solutions are derived for the dynamic characteristics of base-isolated shear buildings supported on laminated rubber bearings. The solution process takes into account the combined effects of the superstructure flexibility and the base raft inertia on the dynamic characteristics. A series of parametric studies is carried out and the effects of varying the stiffness and mass of the base-isolation system on the frequencies and mode shapes are identified. Approximate solutions for the fundamental base-isolated frequency and mode shape are obtained, which are suitable for use in the preliminary design of non-rigid base-isolated buildings.     

Seismic response of torsionally coupled base isolated structures

An analytical study of the seismic response of typical base isolated structures mounted on rubber bearings is presented. Isolated buildings are liable to have closely spaced lower modes of vibration with small eccentricity between centres of mass and rigidity. The isolated structure is modelled as a rigid deck with lumped masses supported on axially inextensible elastomeric rubber bearings. This simplified system has three degrees of freedom (dof), two translations and one rotation in the horizontal plane. The Green's functions for the displacement response of the 3 dof system are derived for both undamped and damped cases with small and large eccentricities. The small eccentricity case is taken from a specific isolated building, while the large eccentricity case arises from the 5 per cent accidental eccentricity which is required by various seismic codes. An interaction equation for normalized displacements is established for an idealized flat velocity spectrum or hyperbolic acceleration spectrum. An isolated building on rubber bearings would have its fundamental period fall into this range of a design spectrum. Numerical results for the specific building subjected to the El Centro earthquake of 1940 are presented. Both the time history and the response spectrum modal superposition analysis were performed. In the response spectrum analysis, the Complete Quadratic Combination (CQC) showed superiority over the Square Root of the Sum of Squares (SRSS) in estimating maximum responses. It is concluded that the effect of torsional coupling on the transient response of base isolated structures is insignificant, due to the combined effect of the time lag between the maximum translational and torsional responses and the influence of damping in the isolation system which for elastomeric bearings can be as high as 8 to 10 per cent.     

Methodology for estimating human perception to tremors in high-rise buildings

Human perception to tremors during earthquakes in high-rise buildings is usually associated with psychological discomfort such as fear and anxiety. This paper presents a methodology for estimating the level of perception to tremors for occupants living in high-rise buildings subjected to ground motion excitations. Unlike other approaches based on empirical or historical data, the proposed methodology performs a regression analysis using the analytical results of two generic models of 15 and 30 stories. The recorded ground motions in Singapore are collected and modified for structural response analyses. Simple predictive models are then developed to estimate the perception level to tremors based on a proposed ground motion intensity parameter—the average response spectrum intensity in the period range between 0.1 and 2.0 s. These models can be used to predict the percentage of occupants in high-rise buildings who may perceive the tremors at a given ground motion intensity. Furthermore, the models are validated with two recent tremor events reportedly felt in Singapore. It is found that the estimated results match reasonably well with the reports in the local newspapers and from the authorities. The proposed methodology is applicable to urban regions where people living in high-rise buildings might feel tremors during earthquakes.     

Response spectral attenuation relationships for Sumatran-subduction earthquakes and the seismic hazard implications to Singapore and Kuala Lumpur

Singapore and Kuala Lumpur, the capital of Malaysia, may well represent the classic examples of area with low seismic hazard but with high consequence. Both cities are located in a low-seismicity region of Southeast Asia, where active seismic sources are located more than 300 km away. Seismic designs have not been implemented in this seemingly low-hazard region though distant earthquakes in Sumatra had frequently shaken high-rise structures in the two cities. Several studies have been conducted to systematically assess the seismic hazards of Singapore and the Malay Peninsula. The present research particularly addresses issues in deriving a new set of attenuation relationships of peak ground acceleration (PGA), peak ground velocity (PGV) and response spectral acceleration (RSA) for the Sumatran-subduction earthquakes. To be relevant for the seismic hazard assessment of the remote metropolises, the derived attenuation relationships cover a long distance range from 150 to 1500 km. The attenuation relationships are derived using synthetic seismograms that account for source and path effects. The uncertainties in rupture parameters, such as stress drop, strike, dip and rake angles, have been defined according to the regional geological and tectonic settings as well as the ruptures of previous earthquakes. The seismic potential of the Sumatran subduction zone are high in the region from 2°N to 5°S as there has been no recurrence of great thrust events since 1861. A large event with M_w greater than 7.8 in this particular subduction zone may be capable of generating destructive ground motions in Singapore and Kuala Lumpur, even at a distance of 700 km.     

Seismic response of segmental buildings

This paper proposes an aseismic design concept in which the superstructure of a base-isolated building is divided into several segments. Each segment may comprise a few storeys and is interconnected by additional vibrational isolation systems. The dynamic characteristics of the segmental buildings are investigated. The optimum parameters of the vibration isolation systems are determined by minimizing the mean square acceleration response. The seismic response of a typical segmental building subjected to the N—S component of the 1940 El Centro earthquake input is evaluated and compared with the responses of the corresponding fixed-base and conventional base-isolated buildings. The comparisons show that, when the superstructure is segmented, while the acceleration response in the superstructure remains as small as that in the conventional base-isolated building, the displacement across the base isolation system at foundation level is substantially reduced.     

Evaluating pluvial flood hazard for highly urbanised cities: a case study of the Pearl River Delta Region in China

Natural Hazards - Rapid urbanisation and economic growth in developing Asian countries have exacerbated their exposure to flood hazards, particularly evident in low-lying urban cities that are...     

When the doorbell rings–a case of building response to a long distance earthquake

Responding to ground tremors caused by the magnitude 7–0 Liwa earthquake in Sumatra on 16 February 1994, a doorbell system on the 15th floor of a 17-storey building in Singapore rang repeatedly at an epicentral distance of more than 750 km. This paper first reviews briefly the regional seismicity, surface geology and effects of local soil amplification for Singapore. It then estimates the building response through the linear and non-linear analyses of impact conditions for the double-pendulum doorbell system. Based on the impact analysis results, it is shown that the acceleration response at the 15th floor reached at least 0–02 g and that the base shear coefficient was no less than 1–0 per cent. The response was comparable to the notional horizontal load which usually governs the design of most buildings in Singapore. In view of the fast growing economy and the rapid urbanization of Singapore, it is prudent to re-evaluate systematically the effects of a long distance, large Sumatra earthquake on Singapore.     

Seismic response of base-isolated structures with vertical-rocking coupling

A base-isolated building is liable to have a small horizontal eccentricity between the centre of mass of the superstructure and the centre of rigidity of the supporting bearings. In seismic analysis, the structure is modelled as a rigid block with tributary masses supported on massless elastomeric rubber bearings placed at a constant elevation below the centre of mass. This simplified system has three degrees of freedom: two translations and one rotation in the vertical plane. The investigation of the dynamic behaviour of a base-isolated building is carried out for both the detuned and the perfectly tuned cases. In the detuned case, the natural frequencies of the system are assumed to be well separated. In the perfectly tuned case, the uncoupled rocking frequency is assumed to be identical to the vertical translational frequency, which may result from an unusual mass distribution and/or an extreme aspect ratio of the superstructure. Perturbation methods are implemented in finding the dynamic characteristics for both cases. However, the dynamic response of the perfectly tuned case is the major concern in this investigation. The Green's functions for the displacement response of the three-degree-of-freedom system are derived for both the undamped and damped conditions. The response spectrum modal superposition method is used in estimating the maximum acceleration response. A simple method, accounting for the effect of closely spaced modes, is proposed for combining modal maxima and results in an approximate solution corresponding to a single-degree-of-freedom system. This approximate solution may be used for the preliminary design of a base-isolated structure. Numerical results for a base-isolated building subjected to the vertical component of the El Centro earthquake of 1940 were carried out for comparison with these analytical results. The proposed modal combination method showed superiority over the conventional Square Root of the Sum of the Squares method in estimating maximum responses. The results also indicated that the approximate single-degree-of-freedom system yields accurate estimations. It is shown that the effect of rocking coupling on the vertical response of base-isolated structures subjected to transient loadings, such as earthquake motions, can generally be neglected as a result of the combined effects of the time lag between the maximum translational and rotational responses and the influence of damping in the isolation system, which for elastomeric bearings can be as high as 8 to 10 per cent of critical.