The main goal of any pile loading test is to determine the ultimate resistance of an isolated pile foundation.
The reaction force is equal to the active load only in the case of static loading and until the system starts to fail.
In soil mechanics limit analysis (Chen & Liu 1990) the first collapse load is determined by the force's equilibrium condition obeying Newton's law (lower bound theorem), and the second by energy and work done transformation considerations (upper bound theorem), satisfying Hamilton's principle of energy conservation.
The lower bound corresponds to the start of permanent material deformations and the upper bound to the start of system displacement, as a rigid body, along a defined rupture surface.
In a static test, force and displacement are measured at increasing loading stages, and the system response is the load settlement curve.
There are many interpretations for a given curve, each one leading to a particular ultimate resistance value (Terzaghi 1942, Vesic 1975, de Beer 1988).
Therefore the ultimate resistance for static loading condition is a matter of discussion in foundation engineering practice (Reese 1972, Vesic 1975, Fellenius 1980).
So, what can be understood by ultimate resistance: is the limit load given by the lower or by the upper bound theorems? Engineers' opinions vary, but most Brazilian engineers accept the latter.
In the case of hammer impacts of constant energy, ultimate resistance can be predicted by the pile dynamic formulae or by application of stress wave theory to the impact (Whitaker & Bullen 1981, Goble et al 1975).
The force history and displacements are obtained from deformation and acceleration measurements. The total kinetic energy is evaluated by integration of force and displacement curves.
The dynamic or total resistance (J = 0) is evaluated from measured forces and velocities curves. The static ultimate resistance is evaluated by using Smith's model (Smith 1960) or the derived model of CASE and CAPWAP methods (Goble et al 1981, Rausche et al 1985, Goble & Likins 1996).
In this analysis the static ultimate resistance is defined by the Davisson's criterion (Davisson 1972).
One can also ask: is this ultimate resistance the limit load given by the lower or by the upper bound theorem? This can be clarified by the dynamic increasing energy test (DIET).
For increasing applied energy (Aoki, 1997) the system mobilises increasing dynamic resistances and displacements, as shown by the curve in Figure 1. For each increasing energy hammer blow, D is the total, K is the elastic and S is the permanent displacements.
From point E on the curve, the system starts to show permanent displacement (lower bound) and from point F the curve shows linear behaviour, ie the excess of deformation energy equals the excess of work done (upper bound).
The corresponding static CASE resistance - displacement curve is presented in Figure 2.
Figure 3 shows the same curve obtained from CAPWAP analysis for a blow of maximum applied energy (point A in figure 1).
In this context the dynamic constant energy test always gives the same point on the curve. It is not possible to define the shape of the curve and its consequences.
The definition of the ultimate resistance is therefore unclear in both static and dynamic loading tests and DIET is a promising tool to understand better the behaviour of an isolated pile foundation system at the rupture.
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