parameters and, consequently, the test results resemble more closely those of a static load test. To ensure this is the case, both the ISO and ASTM standards specify a minimum load duration of 10 L/c where L is the pile length and c is the speed at which the stress wave propagates through the pile. and is the pile velocity. The inertial resistance is represented bym∙a where m is the pile mass and is the pile acceleration. a [Eq. 1] F soil static dynamic inertia =F +F +F =(k∙u)+(C∙v)+(m∙a) Given the extended load duration during rapid load testing, the pile can be assumed to behave as a rigid body, where the velocity and acceleration are the same along the length of the entire pile. On that basis, in the late 1980s, Middendorp developed the Unloading Point Method (UPM), which is the commonly used method to analyze data obtained from a rapid load test. The UPM is straightforward and, more importantly, is independent of the person performing the analysis, and centers around the point on the measured load- displacement curve where the displacement of the pile is maximal Rapid Load Test Analysis When a pile is subjected to a load test, the total pile resistance can be split into three components: static, dynamic and inertial. As shown in [Eq. 1], the static resistance is represented by the term where is the soil stiffness and is the pile displacement. The dynamic resistance is represented by where v k∙u u C∙v C is the soil damping constant and the velocity of the pile equals zero, at which point the pile is assumed to behave quasi-statically. Therefore, from [Eq. 1], only the static and inertia terms remain (F =0). dynamic [Eq. 2] F ) can be expressed as shown in [Eq. 2]. FRLT soil static inertia RLT k [Eq. 3] F static RLT inertia RLT RLT =F -F =F -(m∙a) Measuring acceleration (using accelerometers), displacement (using an optical sensor) and F (using load cells), the unloading point can be defined. Using the load and acceleration at the instant the unloading point occurs (t UPM), the static resistance Fstatic can be determined. As an additional check, the measured displacement can be compared with the computed displacement determined from double-integrating the acceleration signal. By comparing the results determined using the UPM with results from top-down static load testing, it became clear that the effect of the induced pore water pressures cause the mobilized resistance of a pile to be overestimated. Therefore, the value of F static determined using [Eq. 3] must be corrected to take these effects (i.e., loading rate effects) into account, as shown in [Eq. 4] where η represents the loading rate effects based on soil type. Typical values for η are 1 for rock, 0.94 for sand and 0.66 for clay. [Eq. 4] F static,corrected=η∙Fstatic Test Device The StatRapid test device used on the Barcelona project consisted of a main frame, a modular hammer and a system of specially- designed springs, and was capable of generating a test load up to 12 MN (2,700 kip). The entire system was transported to the site on three trucks. Once the trucks arrived on site, the test device was assembled in about three hours due to its modular design. equilibrium of forces, the measured force from the rapid load test ( =F =F +F =(k∙u)+(m∙a) Rearranging [Eq. 2], the static resistance ( F ) can be computed using [Eq. 3]. static Furthermore, given the Measurements used to determine needed to determine static resistance using the Unloading Point Method (UPM) 16 • DEEP FOUNDATIONS • MAY/JUNE 2019 Offloading components of the testing device
