## 3 Low-Strain Integrity Testing  
Low-strain integrity testing is performed by using a low-energy transient or steady-state excitation at the top of the pile. The resulting velocity-time response at the pile head is measured, with simultaneous recording of the force-time history when applicable. Pile integrity is assessed through time-domain or frequency-domain analysis of wave propagation characteristics based on fluctuation theory [14]. As the predominant reflection-based techniques, sonic-echo (SE) and impulse-response (IR) methods have been extensively employed in both academic research and field applications to evaluate pile integrity, whether for newly constructed piles or existing structures with accessible pile heads [24; 36; 37]. [PERSON] et al. [38] summarized the integrity testing results of nine piles. In this paper, the SE and IR inspection data were summarized and processed. Tables 2 and 3 show the pile length and defect type testing results, respectively. From Tables 2 and 3, it can be seen that the testing results may be related to a variety of factors. This will be discussed in detail in the following section. Advancements in sensor technology and associated instrumentation have facilitated the development of numerous testing methodologies derived from low-strain testing principles. This section comprehensively reviews established low-strain integrity testing approaches and their recent technological advancements. Figure 2: Flow chart of article selection process in the review. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**File No.** & **Total Length** & **Embed Length** & **File Cross-Sectional** & _L/D Ratio_ & \(L\) of SE Testing_ & \(L\) of IR Testing_ \\  & **(m)** & **(m)** & **Area (m\({}^{2}\))** & & & & \\ \hline  & & & & & & & 16.7 (0.6) \({}^{*}\) & 17.0 (2.4) \\
1 & 16.6 & 15.7 & 0.66 & 18.1 & 16.2 (\(-\)2.4) & 21.6 (30.1) \\  & & & & & & 16.0 (\(-\)3.6) & 16.8 (1.2) \\ \hline  & & & & & & 11.8 (1.7) & 11.3 (\(-\)2.6) \\
2 & 11.6 & 10.9 & 0.66 & 12.7 & 11.0 (\(-\)5.2) & 10.7 (\(-\)7.8) \\  & & & & & 11.1 (\(-\)4.3) & 11.1 (\(-\)4.3) \\ \hline  & & & & & & 11.1 (\(-\)2.4) & 15.8 (\(-\)4.2) \\
3 & 16.5 & 15.6 & 0.66 & 18.0 & 16.5 (\(0\)) & 16.5 (\(0\)) \\  & & & & & 16.0 (\(-\)3.0) & 16.7 (1.2) \\ \hline  & & & & & & 11.2 (\(-\)1.8) & 10.3 (\(-\)9.6) \\
4 & 11.4 & 10.6 & 0.66 & 12.4 & 11.3 (\(-\)0.9) & 10.7 (\(-\)6.1) \\  & & & & & 11.0 (\(-\)12.3) & 11.3 (\(-\)0.9) \\ \hline  & & & & & & 16.5 (\(-\)1.8) \\
5 & 16.8 & 15.9 & 0.66 & 18.3 & 8.4 (\(-\)50.0) & 18.6 (10.7) \\  & & & & & & 2 (\(-\)5.4) & 8.5 (\(-\)49.4) \\ \hline  & & & & & & 21.8 (\(-\)9.5) & 22.3 (\(-\)7.5) \\
6 & 24.1 & 23 & 0.66 & 26.3 &? (\(\)) & 17.7 (\(-\)26.6) \\  & & & & &? (\(\)) & 22.0 (\(-\)8.7) \\ \hline  & & & & & & 10.7 (0) & 10.0 (\(-\)6.5) \\
7 & 10.7 & 9.6 & 0.66 & 11.7 & 10.4 (\(-\)2.8) & 10.7 (0) \\  & & & & & 9.5 (\(-\)11.2) & 11.0 (2.8) \\ \hline  & & & & & & 12.8 (4.9) & 11.6 (\(-\)4.9) \\
8 & 12.2 & 11.1 & 0.66 & 13.3 & 12.6 (3.3) & 12.2 (0) \\  & & & & & 12.0 (\(-\)1.6) & 12.4 (1.6) \\  & & & & & 13.7 (12.3) \\ \hline  & & & & & 9.2 (\(-\)11.5) & 9.9 (\(-\)4.8) \\
9 & 10.4 & 9.3 & 0.66 & 11.3 & 10.4 (\(0\)) & 9.4 (\(-\)9.6) \\  & & & & & 9.3 (\(-\)10.6) & 10.7 (2.9) \\ \hline  & & & & & & \\ \end{tabular} * a (b): a means pile length, b means accuracy. b = (\(L_{\text{test}}-L_{\text{true}}\))/\(L_{\text{test}}\times\)00%;? means no test result.  
\end{table} 
Table 2: Testing results of pile lengths [38].