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

25When a uniform free end rod is impacted by a mass, a compressive force pulse iscreated and travels down the rod at its material wave speed. Referred to Eq. (2.3), theparticle velocity is directly proportional to the force and it moves in the same direction of thecompressive force. At time L/C after the impact, the compressive force pulse arrives the freeend of the rod. Since there are no resistance effects acting at the end of the rod, a samemagnitude tensile stress wave occurs and reflects from the rod tip back toward the top.Thus, the compressive and tensile forces at the free end cancel each other and the net forcebecomes zero. However, the particle velocities from both the downward compressive forceand the upward tensile force are moving in the same direction and thus, the particle velocityterm doubles in magnitude.On the other hand, for a uniform rod with a fixed end, the particle velocity at thefixed end is prevented from moving and becomes zero. However, the compressive force thattravels down the rod at its wave speed reflects and superimposes at the fixed end. As aresult, the net force doubles and the particle velocity becomes zero during reflection at thefixed end. By relating the above wave mechanics of a rod to a pile, the increase in soilresistance acting on a pile decreases the velocity record relatively more than the force record.This phenomenon can be seen from a typical force-velocity record collected from a PDA testas shown in Figure 2.2. The separation of the force and velocity records between the time ofa hammer impact (T1) and the time for a complete wave propagation (T2) indicates thepresence of soil resistance alongside of a pile. The extent of separation qualitativelydescribes the magnitude of the soil shaft resistance. For a primarily frictional pile with arelative small end bearing resistance as shown in Figure 2.2, the force approaches zero whilethe velocity increases immediately near time T2.2.3.4. Case method2.3.4.1. Soil resistanceCase method is a numerical technique used in the PDA to determine the static soilresistance (i.e., pile resistance), which is developed from the principles of wave mechanics.