S - Kam Ng PhD Dissertation Final.pdf - Digital Repository of CCEE ...

27RTLR sC vJ cv b= total soil resistance, kN or kip,= static soil resistance, kN or kip,= linear viscous damping coefficient ≈ J c (EA/C), kN-s/m or kip-s/ft,= Case damping factor, dimensionless, and= velocity of pile toe at time T1+L/C, m/s or ft/s.The pile toe velocity is expressed using Eq. (2.7), which is equal to the summation ofthe initial pile top velocity (v T ) and the net velocity, induced by the difference in pile forceand soil resistance. Substituting Eq. (2.7) into Eq. (2.6) and replacing the C v with J c andEA/C, the static soil resistance can be rearranged as Eq. (2.8). Furthermore, the maximumstatic soil resistance can be determined by replacing the time t* with t m , the time whenmaximum total resistance occurs, and by substituting RTL(t*) with Eq. (2.5). Hannigan et al.(1998) noted that Eq. (2.8) is best used for displacement piles and piles with large shaftresistance. Also, they noted that Eq. (2.9) is more appropriately used for piles with large toeresistances, piles with large toe quakes, and piles with delay in toe resistances.( ) ( ) , ( ) ( )- (2.7)( ) ( ) [ ( ) ( ) ( )] (2.8)( ){( ) [ ( ) ( )](2.9)( ) [ ( ) ( )]}where,RTL(t*) = total soil resistance at time t*, kN or kip,R s (t*) = static soil resistance at time t*, kN or kip,R s (t m ) = maximum static soil resistance at time t m , kN or kip,F T (t*) = measured force at pile top at time t*, kN or kip,v T (t*) = measured velocity at pile top at time t*, m/s or ft/s,