MODAL-ANALYSIS OF SOFT-SOIL SITES INCLUDING RADIATION DAMPING

For the one-dimensional analysis of soft-soil layers on an elastic hal f-space, a general form of analytical solution is developed for conver ting radiation damping due to energy leaking back to the half-space in to equivalent modal damping, allowing the modal analysis technique to be extended to a site where radiation damping has to be accounted for. Closed-form solutions for equivalent modal damping ratios and effecti ve modal participation factors are developed for a single layer with a shear wave velocity distribution varying from constant to linearly in creasing with depth. Compact and recursive forms of solutions for equi valent modal damping ratios are developed for a system with an arbitra ry number of homogeneous layers on an elastic half-space. Comparisons with numerical solutions show that the modal solutions are accurate. T he nominal frequency of a site, i.e. the inverse of four times the tot al shear wave travel time through the layers, is an important paramete r for estimating the high mode frequencies. A parameter study shows th at for the same impedance ratio of the bottom layer to the elastic hal f-space, a system of soil layers with an increasing soil rigidity with depth has, in general, larger peak modal amplifications at the ground surface than does a single homogeneous layer on an elastic half-space , while a system with a decreasing soil rigidity with depth has smalle r modal peak amplifications.