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

39computation is stable only when the time increment is shorter than the critical wave traveltime of any pile segment (Pile Dynamic Inc. 2005). Because a fairly long wave is usuallyinduced during pile driving, a division of pile lengths from 1.5 m (5 ft) to 3m (10 ft) willusually produce a stable computation with an acceptable accuracy. The hammer ram asshown in Figure 2.6, is represented by a rigid, heavy and short single weight W1 without anyelasticity. The cap block is represented by a spring K1 that can only transmit compressionbut not tension. The pile cap likes the ram is represented by a single weight W2 without anyelasticity. The cushion is used under the pile cap to protect the piles from damaging and it isrepresented by a non-tensional spring K2. The pile is divided in ten sectional weights fromW3 to W12 and they are connected with springs from K3 to K11.Smith adapted Chellis’s concept of soil mechanics, which soil compresses elasticallyto a displacement called quake (q) and fails plastically with a constant ultimate static soilresistance (R u ) as illustrated with a black solid line OABC shown in Figure 2.7. Smithdeveloped a mathematical equation which accounts for both static and dynamic soilbehaviors as illustrated with a dash line OA′BC shown in Figure 2.7. The total soil resistanceat any point x′ with x deformation on the line OA′BC is given by( ) (2.16)where,RR sR dJ sv pKx= total soil resistance, kN or kip,= static soil resistance, kN or kip,= dynamic soil resistance, kN or kip,= Smith damping constant, s/m or s/ft,= instantaneous velocity of a pile segment, m/s or ft/s,= spring constant for soil model, kN/m or kip/ft, and= soil deformation, m or ft.