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E0-190-2008_(10)1D_Shear_Propagation(SHAKE)

# j fj n in eq40 eo denotes the incident

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Unformatted text preview: EO denotes the incident wave amplitude at the engineering bedrock. Ej En En+1 =Eo Fn Fn+1 Engineering Bedrock Because the shear stress at the soil surface (z1=0) must be null, τ1(z1=0)=0 ( 1) 1-th stratum E1 Z1 F1=E1 dj (2) 2-nd stratum Z2 the shear stress amplitude given by Eq.(17): (17) becomes zero at the soil surface j=1 and z1=0. (42) (43) Substituting Eq.(43) into Eq.(16): (43) (16) the displacement amplitude for the first stratum (j=1) becomes: (44) and the displacement amplitude Us at the soil surface z1=0 becomes: (45) Substituting Eq.(43): (43) into Eq.(40)： (40) then, (46) ∴ Eo = (b11 + b12 )E1 (47) Eq.(47) gives: (48) Finally, (49) Putting: (50) then, Eq.(49) can be rewritten by: (51) In Eq.(29)： (29) putting j=1, then: (52) where, (53) Concerning the j-th stratum, (54) (55) the displacement amplitude Uj at the j-th interface is: (56) The shear strain amplitude Γj in the j-th stratum is: Γj = Γj ( z j = 0.5d j ) (57) where, (58) (59) (4) Time Domain Response Analy...
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