Dynamic Response of Block Foundations Resting on Soil–Rock and Rock–Rock System Under Vertical Excitation

Abstract

In the present study, the effect of various soil–rock and rock–rock foundation systems on dynamic response of block foundations of different mass and equivalent radius under vertical mode of vibration is investigated. The frequency dependent stiffness and damping of foundation resting on homogeneous soil and rocks are determined using the half-space theory. The dynamic response characteristics of foundation resting on the layered system considering soil–rock and rock–rock combinations are evaluated using finite element program with transmitting boundaries. The procedure to determine the frequency amplitude response of soil–rock and weathered rock–rock systems is discussed in detail and the equations are proposed for the same. The variation of natural frequency and resonant amplitude with shear wave velocity are investigated for different top layer thickness. The dynamic behaviour of foundation is also determined for different rock–rock systems by considering sandstone, shale and limestone underlain by basalt rock. The variation of the stiffness, damping and amplitudes of foundation with frequency are shown in this study for various rock–rock combinations. It has been observed that the natural frequency increases and the peak displacement amplitude decreases with increase in shear wave velocity ratio. The variation of natural frequency and peak displacement amplitude are also studied for different top layer thickness and eccentric moments. Finally the parametric study is carried out to determine the natural frequency and resonant amplitude for block foundations of size 4 m × 3 m × 2 m and 8 m × 5 m × 2 m using generalized relations proposed in the present study.