Pounding response of adjacent buildings with non-equal height under near-fault strong ground motion

In this paper a simple model of one and two-storey adjacent buildings excited by the horizontal and vertical components of fault-normal pulse and fault-parallel displacement with different magnitudes and time lags has been considered. In the considered model each storey consist of a rigid beam connected to two axially rigid mass-less columns by nonlinear rotational springs and linear rotational dashpots. For determination of the pounding force the non-linear viscoelastic model has been chosen. In this model، a non-linear spring following the Hertz law of contact is applied together with an additional non-linear damper، which is activated during the approach period of collision in order to simulate the process of energy loss taking place mainly during that period. The ground motion is described by fault-normal pulse and fault-parallel permanent displacement، and their amplitudes and duration are selected consistent with the variables that describe near-fault motions. An important physical characteristic of the selected pulse and displacement is large initial velocity associated with onset of these motions and it is proportional to the stress drop on the fault. It is assumed that the buildings are near the fault and that the longitudinal axis of the buildings (x-axis) coincides with the radial direction (r-axis) of the propagation of waves from the earthquake source so that the absolute displacements of the bases of columns because of the wave passage are different. It is further assumed that the ground motion can be described approximately by linear-wave motion. It is assumed that the excitations at all bases have the same amplitude but differ in terms of phase. The phase difference (or time delay) between the input ground motions depends on the length of the buildings and the horizontal phase velocity of the incident waves. The system of equations of motion has been solved by the fourth-order Runge-Kutta method because of its self-starting feature and the long-range stability. For the considered models the results indicate: (1) for nonlinear behavior of material the impact force tends to increase of maximum relative displacement and permanent deformation specially in the second storey (2) the maximum impact force and the minimum distance required to avoid pounding of adjacent buildings under fault-normal pulse are many times larger than those induced by fault-parallel displacement (3) material nonlinearity reduces the maximum impact force and the minimum distance required to avoid pounding significantly، respect to the linear case. Also in nonlinear case the maximum impact force occurs at d>0، while for linear case it happens at d=0 (4) the time delay in ground motion can increase 1. 5 to 2 times the maximum impact force and the minimum distance required to avoid collision. The horizontal component of the ground motion is predominant in this magnification and the effects of the vertical and rocking components of ground motion are negligible.