Report - PEER - University of California, Berkeley

4. EARTHQUAKE GROUND MOTION INPUT AND UNCERTAINTIES OFITS PARAMETERSThe earthquake ground motion input used in this analysis is the artificial groundmotion (Jiang 1984). The earthquake acceleration time history is expressed as:a(t)= ψ(t)as(t)(2)where a s (t) is a stationary Gaussian process with zero mean value and ψ(t)is anenvelope function describing the nonstationary process.⎧(t/ t1)⎪2ψ ( t) = ⎨ 1⎪⎪−c(t−⎩e2t2 )where c is an attenuation constant.when t < twhen t11when t > t≤ t ≤ t22(3)N−1a s (t) = 2 ∑ G( ωk) ∆ω cos( ωkt − φ k )k=1(4)where φkare random phase angles of uniform distribution and are independent ofeach other during ( 0 ,2π). G( ω k ) is a density function of the power spectrum, and isobtained by transformation of the mean response spectrum R(ω , ξ)with the powerspectrum G(ω ) .The acceleration time history a(t) is normalized using its maximum amplitudea max . The normalized nonstationary acceleration time history is as follows:amψ(t)a(t) =asmax(t)(5)So, the nonstationary acceleration time history is:a g (t) = Apam(t)(6)where, A p is a given peak ground acceleration.The artificial wave as mentioned above is obtained by transforming the meanresponse spectrum into the power spectrum. So the parameters of the earthquakemodel include the mean response spectrum, the duration of earthquake ground motionand the damping ratio. We take the standard response spectrum in the Chinese “Codefor seismic design of buildings” (GBJ11-89) as the mean response spectrum. Theformer is obtained by simply averaging a large number of strong earthquake412