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

60v xiusing Figure 5 in Rausche (1994), (s/ft) 1/N , and= maximum pile velocity, m/s or ft/s.2.5.7. WEAP computation and analysisAs described in Section 2.4.2, the time increment adapted in WEAP is chosen as thesmallest of the wave travel time increment through any hammer and pile segments. Toensure stability in WEAP computation, the minimum time is divided by a factor given by( √ ) (2.37)where,∆t = time increment, s,L iC im ik i= pile length at segment i, mor ft,= wave speed at pile segment i, m/s or ft/s,= a lump segment mass, kN-s 2 /m or kip-s 2 /ft,= hammer or driving system stiffness, kN/m or kip/ft, and= a reduction factor greater than 1, WEAP default value is 1.6.WEAP performs a pre-integration for velocity from acceleration and for displacementfrom velocity. The initial acceleration is taken as the gravitational acceleration of thehammer. WEAP computed the spring force by multiplying spring stiffness to relativedisplacements of the neighboring pile segments. Also, the dashpot force is calculated bymultiplying pile damping factor to relative velocities of neighboring pile segments. UsingNewton’s Second law, the acceleration of a pile segment i at time step j is revised using theexternal resistance forces given by Eq. (2.38). Thereafter, the velocity and displacement arerefined and all forces are recalculated. The computation will repeat until either the requirediteration steps have exceeded or the convergence of top and bottom velocities are achieved.( )(2.38)