Sayed Mahmoud

Simulation of the response of base-isolated buildings under earthquake excitations considering soil flexibility

The accurate analysis of the seismic response of isolated structures requires incorporation of the flexibility of supporting soil. However, it is often customary to idealize the soil as rigid during the analysis of such structures. In this paper, seismic response time history analyses of base-isolated buildings modelled as linear single degree-of-freedom (SDOF) and multi degree-of-freedom (MDOF) systems with linear and nonlinear base models considering and ignoring the flexibility of supporting soil are conducted. The flexibility of supporting soil is modelled through a lumped parameter model consisting of swaying and rocking spring-dashpots. In the analysis, a large number of parametric studies for different earthquake excitations with three different peak ground acceleration (PGA) levels, different natural periods of the building models, and different shear wave velocities in the soil are considered. For the isolation system, laminated rubber bearings (LRBs) as well as high damping rubber bearings (HDRBs) are used. Responses of the isolated buildings with and without SSI are compared under different ground motions leading to the following conclusions: (1) soil flexibility may considerably influence the stiff superstructure response and may only slightly influence the response of the flexible structures; (2) the use of HDRBs for the isolation system induces higher structural peak responses with SSI compared to the system with LRBs; (3) although the peak response is affected by the incorporation of soil flexibility, it appears insensitive to the variation of shear wave velocity in the soil; (4) the response amplifications of the SDOF system become closer to unit with the increase in the natural period of the building, indicating an inverse relationship between SSI effects and natural periods for all the considered ground motions, base isolations and shear wave velocities; (5) the incorporation of SSI increases the number of significant cycles of large amplitude accelerations for all the stories, especially for earthquakes with low and moderate PGA levels; and (6) buildings with a linear LRB base-isolation system exhibit larger differences in displacement and acceleration amplifications, especially at the level of the lower stories.

Earthquake-induced structural pounding

Introduction.- Modelling of Structural Pounding.- Pounding between Buildings.- Pounding between Bridge Segments.- Mitigation of Pounding Effects.- Design of Structures Prone to Pounding.

Implicit Runge-Kutta Methods for Lipschitz Continuous Ordinary Differential Equations

Implicit Runge-Kutta (IRK) methods for solving the nonsmooth ordinary differential equation (ODE) involve a system of nonsmooth equations. We show superlinear convergence of the slanting Newton method for solving the system of nonsmooth equations. We prove the slanting differentiability and give a slanting function for the involved function. We develop a new code based on the slanting Newton method and the IRK method for nonsmooth ODEs arising from structural oscillation and pounding. We show that the new code is efficient for solving a nonsmooth ODE model for the collapse of the Tacoma Narrows suspension bridge and simulating 13 different earthquakes.

A verified inexact implicit Runge–Kutta method for nonsmooth ODEs

Structural pounding and oscillations have been extensively investigated by using ordinary differential equations (ODEs). In many applications, force functions are defined by piecewise continuously differentiable functions and the ODEs are nonsmooth. Implicit Runge–Kutta (IRK) methods for solving the nonsmooth ODEs are numerically stable, but involve systems of nonsmooth equations that cannot be solved exactly in practice. In this paper, we propose a verified inexact IRK method for nonsmooth ODEs which gives a global error bound for the inexact solution. We use the slanting Newton method to solve the systems of nonsmooth equations, and interval method to compute the set of matrices of slopes for the enclosure of solution of the systems. Numerical experiments show that the algorithm is efficient for verification of solution of systems of nonsmooth equations in the inexact IRK method. We report numerical results of nonsmooth ODEs arising from simulation of the collapse of the Tacoma Narrows suspension bridge, steel to steel impact experiment, and pounding between two adjacent structures in 27 ground motion records for 12 different earthquakes.

Linear Viscoelastic Modelling of Damage-Involved Structural Pounding during Earthquakes

Damage-involved structural pounding during earthquakes has been recently intensively studied using different impact force models. The results of the previous studies indicate that the linear viscoelastic model is relatively simple yet accurate in modelling pounding-involved behaviour of structures during earthquakes. The only shortcoming of the model is a negative value of the pounding force occurring just before separation, which does not have any physical explanation. The aim of the present paper is to verify the effectiveness of the modified linear viscoelastic model, in which damping term (related to modelling of damage effects) is activated only during the approach period of collision therefore overcoming this disadvantage. The accuracy of the model is checked in a number of comparative analyses, including the comparison with the results of impact experiments and shaking table experiments on pounding between two steel towers. The results of the study indicate that the use of the modified linear viscoelastic model leads to very similar pounding-involved responses as in the case of the linear viscoelastic model.

Inelastic Damage-Involved Response of Colliding Buildings during Earthquakes

Interactions between adjacent, insufficiently separated buildings have been repeatedly observed during major earthquakes. This phenomenon, known as the earthquake-induced structural pounding, may be the reason of local damage at the contact points as well as may lead to the extensive damage at the base of the colliding structure or even initiate its total collapse. In this paper, we examine the importance of inelastic modelling of structural behaviour as the result of damage due to earthquake excitation and structural pounding. The study concerns two adjacent four-storey buildings with different dynamic properties. In the numerical simulations, the nonlinear viscoelastic model is used to model the pounding force during collisions at different storey levels of the structures. The model allows us to take into consideration the dissipation of energy due to damage taking place at the time of collision. Three different ground motion records with different peak ground acceleration levels are used in the study. The comparison between elastic and inelastic damage-involved structural behaviour is investigated. The results of the study show significant changes in the dynamic responses of the inelastic systems as compared to those of elastic ones. The results clearly indicate that modelling the colliding buildings to behave inelastically is really essential in order to obtain accurate damage-involved structural response under earthquake excitation.

Behaviour of Colliding Multi-Storey Buildings under Earthquake Excitation Considering Soil-Structure Interaction

This paper investigates the coupled effect of the supporting soil flexibility and pounding between neighbouring, insufficiently separated buildings under earthquake excitation. Two adjacent three-storey structures, modelled as inelastic lumped mass systems with different structural characteristics, have been considered in the study. The models have been excited using the time history of the Kobe earthquake of 1995. A nonlinear viscoelastic pounding force model has been employed in order to effectively capture the impact forces during collisions. A discrete element model has been incorporated to simulate the horizontal and rotational movements of the supporting soil. Numerical simulations have been performed using developed software based on the Matlab code. The variation in storeys peak displacements, peak accelerations and peak impact forces for various gap sizes is presented in the paper and comparisons are made with the results obtained for colliding buildings with fixed-base supports. The results of the study indicate that the incorporation of the soil-structure interaction decreases both storey peak displacements and peak impact forces during collisions, whereas increase the peak accelerations at each floor level.

Non-Linear Behaviour of Base-Isolated Building Supported on Flexible Soil under Damaging Earthquakes

Seismic isolation is a strategy to reduce damage of structures exposed to devastating earthquake excitations. Isolation systems, applied at the base of buildings, lower the fundamental frequency of the structure below the range of dominant frequencies of the ground motion as well as allow to dissipate more energy during structural vibrations. The effectiveness of the base-isolated buildings in damage reduction has been confirmed numerically for the models of structures with fixed supports. The aim of the present paper is to show the results of the non-linear analysis of the response of a base-isolated building supported on soft soil incorporating soil-structure interaction. The detailed study has been conducted for the building equipped with high damping rubber bearings used as isolation devices. The results of numerical simulations demonstrate that soil flexibility has a significant influence on the behaviour of isolated base of the structure. Considering the flexibility of soil significantly affects the rigid superstructure response lowering its potential to reduce structural damage.

Seismic Response Evaluation of Buildings Considering Soil Flexibility

This research attempts to investigate the effect of soil-structure interaction (SSI) on the seismic response of buildings. Computational simulation of a one storey building having different natural periods is performed using time history analysis. Different earthquake motions with different peak ground accelerations (PGA) levels are used as excitations. The ground motion records have been selected in order to ensure low, moderate, and high PGA levels. Moreover, sandy soil with several values of shear wave velocities is used in order to investigate the sensitivity of the seismic response to the velocity variation. An efficient discrete-element model which represents the rotational and horizontal degrees of freedom of the soil mass is considered in the analysis. The coupled equations of motion for the building model with SSI are presented and solved in incremental form using the Newmarks step by step iteration method. In general, the results of the study in terms of response, peak response and peak response amplification show significant changes in considering and ignoring SSI effect. In particular, the numbers of significant cycles of large response amplitude for the building have been increased due to the inclusion of SSI. Moreover, considering the soil flexibility amplifies the peak response of buildings with low natural periods. Furthermore, it has been found that, shear wave velocity variation shows appreciable changes in the peak dynamic response amplification and seems to be insignificant at high natural periods for all levels of earthquake excitations considered.