*2.2. Experimental Measurements*

For each river sand and pier, experimental measurements of the instantaneous velocity have been carried out along four vertical sections, set upstream (U), downstream (D), and laterally against (S1 and S2) the pier; each section was 6 cm away from the face of the pier, with five discharges, and, for each one, having three seepage percentages, that is, 0%, 10%, and 15%, respectively. Such percentages were selected so as to obtain a seepage velocity less or equal to 1% of the mean velocity in the channel [28]. The combinations resulted in 15 test runs, as specified in Table 1.



The instantaneous velocity was measured using an Acoustic Doppler Velocimeter (ADV), with an acoustic frequency of 10 MHz and a sampling rate of 200 Hz for 5 min at each of the data points. Each test run duration was 24 h. The duration of the experimental runs was set depending upon the criteria of the equilibrium state for the scour depth, given by Kumar et. al. [29]. During the experimental measurements, the signal-to-noise ratio (SNR) was kept at 15 or above, and the average correlation coefficient between the transmitted and received signal was less than 70%. The ADV uncertainty was evaluated by collecting 10 pulses over 5 min near the bed (*z* ≈ 5 mm). The results are shown in Table 2, where *U*, *V*, and *W* are the mean time velocities in an *x* (longitudinal), *y* (transverse), and *z* (vertical) direction, respectively, and *<sup>u</sup>*, *<sup>v</sup>*, and *w* are the corresponding fluctuating velocities, respectively.


**Table 2.** Uncertainty associated with Acoustic Doppler Velocimeter (ADV) data.

The ADV data were contaminated with spikes because of interference between the transmitted and received signals. Acceleration threshold methods [30] were applied in order to remove the spikes, by fitting velocity power spectra with Kolmogorov's −5/3 scaling law in the inertial subrange, with threshold values ranging between 1–1.5.

The measurement of bed deformations under water typically utilizes high-frequency sound wave (ultrasonic) technology. The bed profiles around the pier were measured using Sea Tech 5 MHz Ultrasonic Ranging System (URS), with four pairs of transducers fixed to a mechanical trolley moving at a constant speed. The sound waves transmitted from the sensors were reflected by a solid object, the time for the sound waves to travel from the sensor to the object and back to the sensor was recorded, and the distance from the sensor to the reflective object was obtained. The URS uncertainty was evaluated collecting 15 measurements near the bed (*z* ≈ 5mm). The results are in Table 3.

**Table 3.** Uncertainty associated with Ultrasonic Ranging System (URS) data.

