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

472.4.3.1. Pile modelPile Dynamics, Inc. (2000) described that a typical uniform cross section pile inCAPWAP is divided into N p segments of pile masses (M) with each has approximate 1 m(3.3 ft) equal length (∆L) and each pile mass is connected with a series of elasto-plasticsprings. The sum of all ∆L equals to the total pile length (L) and the sum of all wave traveltime ∆t equals the total wave travel time L/C. A pile can be divided into different lengths asaccording to their material properties. For piles with variable cross section, force reflectionhappens between segments with different geometries. Thus, based on the wave propagationconcept, reflected waves traveling upward will superimpose with the downward waves.CAPWAP assumes that all pile segments are unstressed before driving; however, in reality,residual forces could develop in pile segments during driving when unbalanced pile forcesoccur before coming to rest. Hannigan and Webster (1987) stated that the summation of pileforces must be in equilibrium at which pile segments with residual compressive forces arebalanced by segments with residual tension forces.2.4.3.2. Soil modelThe CAPWAP soil model at each pile mass is represented by an elasto-plastic springand a linear dashpot as shown in Figure 2.9. Generally, the soil model can be described bythree parameters: soil resistance (R), quake (q), and viscous damping coefficient (C v ) at a soilsegment k and pile segment i with a relationship given by Eq. (2.22), which is equal to thesummation of soil static and dynamic resistances. The static soil resistance (R sk ) representedby a spring is equal to the product of the spring constant or soil stiffness (k) and the piledisplacement (u). Whereas, the dynamic soil resistance (R dk ) represented by a linear dashpotis presented by a product of the viscous damping coefficient (C v ) and the instantaneousvelocity ( ̇ ).̇ (2.22)where,R k= total soil resistance force at soil segment k, kN or kip,