A Semi-empirical method for estimation of maximum seismic shear strain in imperforated ground excited by vertically propagating shear waves

Dehghanian, Kaveh
Seismic design of underground structures requires calculation of the deformation in surrounding geological formations. The seismic hazard on a site is usually expressed as a function of amplitude parameters of free-field motion. Therefore, simplified relations between depth and parameters of ground motion are necessary for preliminary designs. The objective of this study is to employ random vibration theory to develop a simple relationship between maximum shear strain (γmax), depth, and ground-motion intensity parameters related to seismic hazard. The ground motion on surface, which is assumed as a stationary random process in the wide sense, is represented by a power spectral density function. Considering one-dimensional shear-wave propagation, transfer functions between ground motion and γmax amplitude at any arbitrary depth is formulated. The theoretical results are compared with the dynamic response of horizontally layered formations to seismic motions defined by accelerograms recorded on ground surface. The effect of material nonlinearity on peak strains is simply modeled by the method of equivalent linearization. It was concluded that the transition from PGA-sensitiveness of max to its PGV sensitiveness in uniformly elastic half-space occurs around the depth of (PGV·Vs)/(2·PGA). max is proportional to d and PGA in very shallow ranges of d, whereas it reaches to figures around (PGV/Vs)/2 by increasing d. max is also related to the amplitudes of a pseudo-spectral acceleration. Both relationships can be used as a reasonable first-order estimator for max in horizontally layered geological formations if the travel time of vertically incident shear waves to reach from free boundary to the depth of interest is substituted for the parameter d/Vs. The concept of equivalent travel time may yield overestimation of max if Vs is increasing by depth. However it leads severe underestimation of max in relatively soft layers embedded in stiffer geological formations. The method of equivalent linearization can be used for estimation of max if the response of geological layers to shearing is nonlinear. 


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Citation Formats
K. Dehghanian, “A Semi-empirical method for estimation of maximum seismic shear strain in imperforated ground excited by vertically propagating shear waves,” Ph.D. - Doctoral Program, Middle East Technical University, 2016.