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

49Pile Segment iSoil Segment kJ kR dkVelocity, u iMassStaticResistance(Spring)R skDynamicResistance(Dashpot)CJ kvkk skq kR ukDisplacement, u iFigure 2.9: CAPWAP soil model (after Pile Dynamic, Inc. 2000)An extended CAPWAP soil model shown in Figure 2.10 includes a radiationdamping model that simulates the surrounding soil motion. It provides an improved modelfor a better correlation with static load tests by limiting the maximum Smith’s shaft dampingfactor to 1.3 s/m (0.4 s/ft) (Likins et al. 1992). For the shaft radiation damping model, a soilmass (M s ) and a dashpot with damping coefficient (C sk ) are used to replace the rigid soilsupport of the traditional Smith model. Similarly, the toe radiation model uses a soil mass(M t ) and a dashpot with a damping coefficient (C BT ). The model allows the energydissipation in the soil-pile interface and prevents interface failures. Likins et al. (1992)suggested that the radiation damping model is used only when the Smith damping factorsexceed 0.79 s/m (0.24 s/ft). Furthermore, a toe gap is included in the extended CAPWAPmodel. A gap (g) between the pile toe and the soil happens when the pile is driven on a veryhard soil layer. The static toe resistance is developed when the toe displacement exceeds thegap. For a full activation of soil toe resistance, the sum of the toe gap and the quake must beless than the maximum pile toe displacement, and the static soil resistance can be revised aswhere,R sk( ) (2.25)= static soil resistance force at soil segment k = N s +1, kN or kip,