## 3 Low-Strain Integrity Testing
### The IR Method  
IR testing, developed in the 1960s in France, represents a low-strain, low-frequency nondestructive evaluation method based on elastic stress wave propagation for pile in tegrity assessment [68]. The schematic diagram of IR is shown in Figure 5[69]. The IR testing employs a controlled impact at the pile head to generate stress waves that propagate downward and reflect from defects or the pile toe. Unlike SE testing, IR testing requires simultaneous acquisition of both force-time and velocity-time histories, which are subsequently transformed into the frequency domain via fast Fourier transform (FFT). Obtain the defect location or pile length based on the mobility curve characteristics [70; 71; 72]. The mobility curves for the IR test of the characteristics are shown in Figure 6. The formula for calculating the pile length in the IR test is shown in Equation (2).  
\[L=\frac{\text{c}}{2\times df} \tag{2}\]  
where \(df\) is the frequency of repeated patterns in the mobility curve.  
Since the 1990s, IR testing has become widely adopted for PIT. [PERSON] et al. [73] systematically documented the methodology and advantages of the IR test. [PERSON] and [PERSON] [74] demonstrated its effectiveness for assessing cast-in-place bored piles supporting transmission towers, including quantifying alkali-aggregate reaction damage in underground pile structures. [PERSON] and [PERSON] [37] verified the capability of IR testing for drilled wellbore integrity assessment. The assessment results were mainly limited by the L/D ratio, the ratio of soil shear wave velocity to concrete propagation velocity, and the shear wave velocity of the soil layer under layered soil conditions. [PERSON] et al. [75] proposed an estimation formula for assessing the dimensions of defects in drilled piles using impulse response testing based on finite element simulations.  
Figure 5: Impulse response test method: (**a**) the concept; (**b**) example of using in practice [69].  
Figure 6: Mobility curve from an IR test [42].  
PIT becomes significantly more challenging because the top of the pile is covered by the structure. [PERSON] et al. [76] conducted finite element analyses to systematically evaluate testing effectiveness with and without pile caps, finding that signal interpretation was substantially complicated by both boundary reflections from the pile cap and its asymmetric geometry. [PERSON] et al. [42] compared the feasibility of SE and IR in detecting pile defects with pile caps. The results showed that the pile cap had a significant effect on the signal. Both methods were unable to detect minor defects in piles with pile caps.  
Above all, the IR testing exhibits notable limitations when pile head accessibility is constrained. Furthermore, two critical scenarios significantly compromise data quality: (1) piles with L/D ratios exceeding 30, and (2) piles embedded in rigid soil formations. Under these conditions, the test typically yields only initial dynamic stiffness parameters while failing to capture subsequent toe reflections, resulting in incomplete datasets [77]. This limitation stems from excessive stress wave attenuation and energy dissipation into the surrounding soil matrix, which effectively masks the reflected wave signals from deeper pile sections.