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

̇50k sku ig i= soil stiffness of the k-th segment resistance, kN or kip,= pile displacement at segment i = N p , m or ft, and= pile gap beneath pile toe, m or ft.Pile Segment, N pToe Soil Segment, N s +1Toe Soil Segment, NS+1Toe Gap, g tPlug Plug Mass, Mass, M p M pToe Radiation RediationDamping ModelMassBottom Skin Friction, Segment N sPile Segment Npq Quake , R Shaft, , C , RNs u,Ns Sq S /Ultimate Shaft Resistance, RLSusShaft J v,nLinear Viscous Damping Coefficient, C vsSoil Mass, M s SShaft J sk Damping Coefficient ofSupport Soil Mass (M S ), C SKShaftSkin RediationDamping Radiation Model Damping ModelToe J v,n+1Linear ,O p viscous damping, C vT / Toe damping option, O pSoil Mass, M t Quake q , R , C , Rt utToe, tq T /Ultimate Lt Toe Resistance, R utToe Damping Coefficient of Support Soil Mass (M t ), C BTJ BTFigure 2.10: The extended CAPWAP soil resistance model includes toe gap, plug mass, andradiation damping (after Pile Dynamic, Inc. 2000)Another consideration is the pile plug which is modeled with a soil mass (M p ) asshown in Figure 2.10. The soil mass exerts an external resistance force (R M ) on pile toe attime j. The additional external resistance due to pile plug force can be expressed as. ̇ ̇ /(2.26)where,R MjM p= external resistance force due to pile plug at time j, kN or kip,= soil mass in pile plug, kN-s 2 /m or kip-s 2 /ft,= pile bottom velocity at time j, m/s or ft/s,