## 3 Low-Strain Integrity Testing
### The SE Method  
The SE method is a widely adopted low-strain integrity testing technique grounded in time-domain wave propagation theory [39]. Figure 3 illustrates the test schematic and typical instrumentation configuration. During testing, an impact hammer or force bar delivers a transient excitation at the pile head, inducing a low-frequency stress wave that propagates longitudinally through the pile shaft. Upon encountering defects or the pile toe, the resulting wave impedance variations cause partial stress wave reflections that return to the pile head, where a transducer records the reflected signals. Time-domain waveform analysis serves as the primary diagnostic tool, where pile length and defect locations are determined through a comprehensive evaluation of three key waveform characteristics: reflected wave arrival time, amplitude, and phase direction. When the stress wave encounters necking, pile breakage, segregation, honeycomb, and secondary casting surfaces, the wave impedance increases, and the reflected wave has the same initial phase as the incident wave. When the stress wave encounters neck expansion, bottom expansion, or pile bottom, the wave impedance increases, and the reflected wave is in the opposite initial phase to the incident wave [40]. Since the impedance of a pile is a function of its density, stiffness, and cross-sectional area, impedance variations due to inconsistencies in the quality of the concrete along the pile body can cause similar reflections [41]. Pile length and integrity assessment requires a comprehensive analysis of multiple data sources, including processed signal characteristics (particularly relative velocity variations following the initial impact pulse), field records, and soil profile data. Figure 4 displays representative velocity waveforms obtained from SE testing. The distance to a defect (or pile length) \(L\) can be determined using Equation (1):  
\[L=\frac{\text{c}\times dt}{2} \tag{1}\]  
* The number means the depth from top of pile to defect (m);? means the test results are doubtful. \end{table}
Table 3: _Cont._where \(c\) denotes the wave velocity, which is usually 3000-4500 m/s for concrete piles [42]; \(dt\) is the time required for the wave to propagate from the pile tip to the reflector and back. Clear reflections from the pile tip and a sufficiently stable signal usually indicate that the pile is free of defects. Figure 4 demonstrates that signal resolution and sensitivity constitute critical parameters for reliable pile integrity assessment. However, the pile integrity signals received by the signal receiver at the pile head are more complex and accompanied by background noise, which interferes with the signal recognition. Signals and noise typically exhibit distinct frequency characteristics. Time-domain analysis normally fails to eliminate noise entirely. Signal processing originates from an interdisciplinary convergence of mathematics, physics, and engineering [45]. In particular, in the field of transportation infrastructure diagnostics, methods for processing noise and vibration signals share technical similarities with PIT research. The Fourier transform (FT) is commonly employed for noise reduction in pile integrity assessment. The FT effectively filters out stationary noise at a fixed frequency by  
Figure 4: Velocity waveform from a SE test [42]. Figure 3: Sonic echo test of pile and test equipment [43; 44]. decomposing the signal into single-frequency components. However, its assumption of signal stationarity and inherent lack of time resolution preclude precise temporal localization of noise or defect-related signals [46]. In non-stationary field conditions where sudden construction impacts superimpose with defect reflection wave spectra, critical signals may be erroneously filtered. Moreover, the distinctive characteristics of transient defect reflections are often insufficiently resolved [47]. Therefore, traditional FT has limited effectiveness in analyzing non-stationary signals.