Report - PEER - University of California, Berkeley

the mean and standard deviation of sliding relative to a rigid base considering anensemble of 75 real earthquake motions. This work also considered the probability ofover turning and rocking for rigid bodies. Similarly, Choi and Tung (2002) studiedthe sliding behavior of a freestanding rigid body under the action of base excitation.The objective of this study was to estimate the amount of sliding when a rigid body issubjected to real earthquake motion. In this context, Choi and Tung (2002) apply anextension of Newmark’s (1965) work, using absolute base spectral displacementrather than maximum velocity, as was done by Newmark (1965).Studies have reported the effect of sliding response due to both verticalacceleration and base frictional coefficient [e.g., Taniguchi (2002), Garcia and Soong(2003)]. Taniguchi (2002), for example, investigated the nonlinear seismic responseof free-standing rectangular rigid bodies on horizontally and vertically acceleratingrigid foundations. The equations of motion and associated boundary conditionscorresponding to commencement and termination of liftoff, slip and liftoff-slipinteraction motions are provided. Applying a large number of time historiesTaniguchi (2002) found that the response of the body is sensitive to small changes inthe friction coefficient and slenderness of the body, and to the wave properties andintensity of ground motions. It was also observed that vertical excitation addsirregularities to the behavior, as it excites or dampens the response depending uponthe direction. Recent work by Garcia and Soong (2003) provide analyticallydeveloped seismic sliding fragility curves using design spectrum compatible timehistories. Two different damage measures (DMs) are considered for development ofsliding fragility in the study of Garcia and Soong (2003): (i) excessive relativedisplacement and (ii) excessive absolute acceleration. This study concluded that thesliding response is very sensitive to the coefficient of friction. It was also observedthat neglecting vertical acceleration might lead to unconservative estimates of sliding.Although previous studies have contributed to determining sliding responseestimation, both in a deterministic and probabilistic sense, consideration of uncertainparameters in this estimation has not been provided. For sliding bodies in a realisticbuilding setting, even small environmental changes (e.g., moisture, dust, etc.), canchange the interface resistance characteristics. Furthermore, from the aforementioneddiscussion, it is clearly that considering the supporting structure (bench and building)is important. These two uncertain issues are the focus of this paper.2. ANALYTICAL FORMULATION2.1 Pure Sliding under Horizontal ExcitationConsidering the free body diagram of the rigid equipment shown resting on the top ofa bench in Figure 2, the condition describing the onset of the movement of the bodymay be expressed as:m& x&(t)≥ µ mg(1)s199