Investigation of block foundations resting on soil-rock and rock-rock media under coupled vibrations

In the present study,the dynamic response of block foundations of different equivalent radius to mass（R;/m） ratios under coupled vibrations is investigated for various homogeneous and layered systems.The frequency-dependent stiffness and damping of foundation resting on homogeneous soils and rocks are determined using the half-space theory.The dynamic response characteristics of foundation resting on the layered system considering rock-rock combination are evaluated using finite element program with transmitting boundaries.Frequencies versus amplitude responses of block foundation are obtained for both translational and rotational motion.A new methodology is proposed for determination of dynamic response of block foundations resting on soil-rock and weathered rock-rock system in the form of equations and graphs.The variations of dimensionless natural frequency and dimensionless resonant amplitude with shear wave velocity ratio are investigated for different thicknesses of top soil/weathered rock layer.The dynamic behaviors of block foundations are also analyzed for different rock-rock systems by considering sandstone,shale and limestone underlain by basalt.The variations of stiffness,damping and amplitudes of block foundations with frequency are shown in this study for various rock—rock combinations.In the analysis,two resonant peaks are observed at two different frequencies for both translational and rotational motion.It is observed that the dimensionless resonant amplitudes decrease and natural frequencies increase with increase in shear wave velocity ratio.Finally,the parametric study is performed for block foundations with dimensions of 4 m × 3 m × 2 m and 8m×5m×2m by using generalized graphs.The variations of natural frequency and peak displacement amplitude are also studied for different top layer thicknesses and eccentric moments.

Development of design charts to predict the dynamic response of pile supported machine foundations

This paper proposes design charts for estimating imperative input parameters for continuum approach analysis of the nonlinear dynamic response of piles.Experimental and analytical studies using continuum approach have been conducted on single and 2×2 grouped piles under coupled and vertical modes of vibration,for different dynamic forces and pile depth.As these design charts are derived from model piles,the charts have been validated for prototype pile foundations using scaling law.The experimental responses of model piles are scaled up and these responses exhibit good agreement with analytical results.This study also extends to estimation of the errors in computing frequency–amplitude responses with an increase in pile length.It is found that,with an increase in pile length,the errors also increase.The effectiveness of the proposed design charts is also checked with data based on different field setups given in existing literature,and these charts are found to be valid.Thus,the developed design charts can be beneficial in estimating the input parameters for continuum approach analysis for determining the nonlinear responses of pile supported machine foundations.