In the conventional dynamic test, the imparted stress-wave has a steep rise and an intensity that changes along the pile length. That is, when the impact peak reaches the pile toe and the entire pile is engaged by the blow, force from the pile hammer transmitted to the pile varies and is superimposed by numerous reflections. The force in the pile varies considerable between the pile head and the pile toe. The steep rise of the stress-wave and the reflections are indeed the condition for the analysis. When the impact is
"soft" and the rise, therefore, is less steep, it becomes difficult to determine in the analysis just from where the reflections originate and how large they are. However, in the 1990s, an alternative dynamic method of testing was developed, called Statnamic, here denoted "long duration impulse method"
consisting of giving the pile just this soft-rising, almost constant force. The method is usually called
“rapid loading test” and consists of impacting the pile in a way where the rise of force is much softer than in the pile driving impact, and the impulse (a better word than "impact") was of a much longer duration.
The long duration impulse usually makes the pile move as a rigid body, that is, the pile velocity at the pile head is the same as the velocity at the pile toe. This aspect made possible an analysis method, called the
"unloading point method" for determining the pile capacity (Middendorp et al. 1992).
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The long duration impulse method is a dynamic method. However, the transfer of the force to the piles, the impulse, can take 100 to 200 milliseconds, i.e., five to twenty times longer time than the time for a pile driving impact. The stress-wave velocity in the pile is the same, however. This means that the sharp changes of force experienced in the pile driving are absent and that the pile moves more or less as a rigid body. Although the ram travel is long, the peak force is reduced by that the impact velocity has been reduced. As a large ram mass is used, a large energy is still transferred to the pile. The key to the long duration impulse method lies in this slowing down of the transfer of the force from the impacting hammer to the pile. In method employed by a Dutch company, Fundex, this is achieved by letting the ram impact a series of plate springs which compression requires the hammer to move much more than required in case of the ordinary hammer and pile cushions, and thus reduce the kinetic energy in the transfer to the pile. The Statnamic method, developed by Berminghammer in Canada, achieves the effect in the pile in a radically different way, using a propellant to send a weight up in the air above the pile, in the process creating a downward force on the pile according to Newton's third law.
The measurements consist of force, movement, acceleration, and time. The most important display of the results consists of a load-movement curve, as illustrated in Fig. 9.19.
Fig. 9.19 Load-movement curve from Statnamic test (Bermingham et al. 1993)
Load, movement, velocity, and acceleration versus time are important records of the test. An example of these records are presented in Fig. 9.20 (same test as in Fig. 9.19). The maximum movement (about 4 mm in the example case) is where the pile direction changes from downward to upward, i.e., the pile rebounds, is called the "Unloading Point", "P-point" for short. The maximum load applied to the pile by the ram impulse (about 4.5 KN in the example case) occurs a short while (about 3 ms in the example case) before the pile reaches the maximum movement. Most important to realize is that the pile velocity is zero at the unloading point, while the acceleration (upward) is at its maximum. Shortly before and after the maximum force imposed, the velocity of the pile head and the pile toe are considered to be essentially equal, that is, no wave action occurs in the pile. This is assumed true beyond the point of maximum movement of the pile.
In the pile-driving dynamic test, the methods of analysis of the force and velocity measured in a dynamic test includes a separation of the damping portion (the velocity dependent portion) of the dynamic resistance. Inertia forces are considered negligible. In contrast, in the long duration impulse method, the velocity of the pile is zero at the unloading point, which means that damping is not present. However, the acceleration is large at this point and, therefore, inertia is a significant portion of the measured force.
MAXIMUM
MOVEMENT — UNLOADING POINT
Movement (mm)
The equilibrium between the measured force and the other forces acting on the pile at any time is described by the following equation (Middendorp et al. 1992).
Eq. 9.24 F = ma + cv + ku
where F = measured force (downward) m = mass of pile
a = acceleration (upward) c = damping factor v = velocity
k = modulus
u = movement
The two unknowns in Eq. 9.24 are the damping factor, c, and the modulus, k. The other values are either known or measured. As mentioned, at the unloading point, the velocity is zero along the full length of the pile. This becomes less true as the pile length increases, but for piles shorter than about 40 m, observations and research have shown the statement to be valid (Middendorp et al. 1995; Nishimura et al.
1998).
At the time of zero velocity, the damping component of Eq. 9.24 is zero, because the velocity is zero.
This determines the static resistance at the unloading point, because the force and acceleration are measured quantities and the mass is known. Thus, the static resistance acting on the pile at the unloading point is obtained according to Eq. 9.25 as the value of measured force plus the inertia (note acceleration is upward—negative).
Eq. 9.25 RP = (FP - maP)
where RP = static resistance at the UPM-point FP = force measured force at the UPM-point m = mass of pile
aP = acceleration measured at the UPM-Point
In the range between the maximum measured force and the unloading point, the load is decreasing (the pile decelerates; acceleration is negative) while the movement is still increasing, and the pile has a velocity (downward and reducing toward zero at the unloading point, which means that damping is present). These quantities are measured. Moreover, it is assumed that at the maximum force, the pile has mobilized the ultimate shaft resistance and that the continued soil response is plastic until the unloading point is reached. That is, the static resistance is known and equal to the value determined by Eq. 9.25.
This is the primary assumption of the Unloading Point Method for determining the pile capacity using the UPM (Middendorp et al. 1992).
Fig. 9.20 Load, movement, velocity, and acceleration
versus time from Statnamic test (Bermingham et al. 1993) Eq. 9.24 can be rearranged to Eq. 9.26 indicating the solution for the damping factor.
9.26
v R ma c= F− − P
where c = damping factor
F = measured force (downward) m = mass of pile
a = acceleration (upward)
RP = static resistance at the UPM-point v = velocity
TIME (ms) Movement (mm) | Load (KN)
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The value of the damping factor, c, in Eq. 9.26 is calculated for each instant in time between the maximum measured force and the unloading point. For the Statnamic test, the number of data points depends on the magnitude of movement of the pile after the maximum Statnamic force is reached.
Typically, the number of data points collected in this range is 50 to 200. The c values are averaged and taken to represent the damping factor acting on the pile throughout the test. The measured force and acceleration plus the pile mass then determine the static load-movement curve according to Eq. 9.27.
9.27 RP = F - ma - cavg v
where RP = static resistance at the UPM-point F = measured force (downward) m = mass of pile
a = acceleration (upward)
cavg = average damping factor between the maximum force and the P-point v = velocity
Fig. 9.21 illustrates the results of the analysis for a 9 m long, 910 mm diameter bored pile in clay (Justason and Fellenius 2001).
Fig. 9.21 Example of measured force-movement curve and simulated static load-movement curve Data from Justason and Fellenius (2001)
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Lately, several papers have been published showing case histories where the capacity determined in a Statnamic test according to the Unloading Point Method (UPM) to considerably overestimate the capacity determined on the same pile in a static loading test. (e.g., Middendorp et al. 2008; Brown et al. 2006;
Brown and Hyde 2008). In clay, the overestimation has been as large as close to a factor of two. The referenced papers hypothesize that the capacity overestimation is a result of the velocity of the pile and associated dynamic effects, notwithstanding that the UPM capacity is determined at zero velocity—non- dynamic condition—, and recommend that a correction factor be applied to the UPM-determined capacity. Such correction factors can never be general factors associated with the method, and it appears necessary to calibrate the Long Duration Impulse Testing Methods to a static loading test before relying on a UPM-determined capacity value for a specific site and project.