Quantification of the Uncertainty in Ultrasonic Wave Speed in Concrete: Application to Temperature Monitoring with Embedded Transducers

Abstract

This article presents an overall examination of how small temperature fluctuations affect P-wave velocity (V_p) measurements and their uncertainties in concrete using embedded piezoelectric transducers. This study highlights the fabrication of custom transducers tailored for long-term concrete monitoring. Accurate and reliable estimation of ultrasonic wave velocities is challenging, since they can be impacted by multiple experimental and environmental factors. In this work, a reliable methodology incorporating correction models is introduced for the quantification of uncertainties in ultrasonic absolute and relative velocity measurements. The study identifies significant influence quantities and suggests uncertainty estimation laws, enhancing measurement accuracy. Determining the onset time of the signal is very time-consuming if the onset is picked manually. After testing various methods to pinpoint the onset time, we selected the Akaike Information Criterion (AIC) due to its ability to produce sufficiently reliable results. Then, signal correlation was used to determine the influence of temperature (20 °C to 40 °C) on V_p in different concrete samples. This technique proved effective in evaluating velocity changes, revealing a persistent velocity decrease with temperature increases for various concrete compositions. The study demonstrated the capability of ultrasonic measurements to detect small variations in the state of concrete under the influence of environmental variables like temperature, underlining the importance of incorporating all influencing factors.

Keywords: concrete properties; embedded piezoelectric transducer; monitoring; ultrasound; uncertainty.

Figure 1

Piezoelectric transducers designed for concrete embedding. Features include a piezoelectric patch, a rear backing layer for support, a resin front layer for protection during casting, and a coaxial cable connection. The piezoelectric patch is a disk with an outside diameter of 10 mm and a thickness of 10 mm made of piezoelectric material PIC255 and a screen-printed Ag electrode [PI France SAS].

Figure 2

Piezoelectric transducers designed and manufactured for embedding in concrete. (a) The piezoelectric patch and the welded cables are set in an aluminum tube made of conductive material. (b) The piezoelectric patch is insulated with layers of epoxy material. (c) All transducers are manufactured using a digital milling machine to provide the same size for all transducers and a smooth surface to ensure good contact with concrete.

Figure 3

Recording of source and received signals. The blue waveform represents the source signal from the first transducer consisting of six cycles, while the orange waveform shows the signal received by the second transducer. The onset times are measured in both signals, allowing for the determination of the time of flight (TOF) by calculating the difference between the onset times. Following the P wave, subsequent wave packets containing other wave types, such as the S wave, and multiple reflections of them are observable in the received signal.

Figure 4

A reference material, namely marble, was used to calibrate the piezoelectric transducers. By measuring ultrasonic wave velocity at two different propagation distances d1 in (a) and d2 in (b) we can estimate the propagation time of the wave within the transducers. Note: The two depicted transducers are identical in function, although their external appearance differs slightly due to variations in the application of waterproof coating for technical purposes.

Figure 5

Images of the setup before concrete pouring. (a) Two pairs of embedded ultrasonic transducers set at the center of a concrete specimen next to an embedded electrical capacitive transducer. (b) Zoomed-in view of the embedded transducers (commercial ultrasonic transducers and the developed piezoelectric transducers).

Figure 6

Ultrasonic monitoring system. (a) An eight-channel ultrasonic measurement setup for continuous real-time monitoring of concrete properties. (b) Presentation of coaxial cables extending from the embedded transmitter and receiver transducers to the measurement system (concrete specimens during the hardening phase). This setup is equipped with eight channels to facilitate simultaneous viewing of multiple acquisitions from the receivers.

Figure 7

Climate chamber setup, comprising concrete blocks cast with embedded transducers protected by an aluminum foil covering to preserve moisture content.

Figure 8

The AIC is used to determine the onset of a specific portion of the signal (solid black line). The AIC function is illustrated in blue. The intersection between the AIC’s minimum value and the signal (dashed black line) illustrates the signal’s onset time ($t_p$).

Figure 9

(a) Full cross-correlation function between two signals (at ti and To1). The points of interest around the maximum peak are marked in red, and the purple curve shows a degree 2 polynomial fitted to these points. (b) Zoomed-in view of the area around the peak of the cross-correlation function where the red points of interest are used to fit the 2-degree polynomial.

Figure 10

Signal recording from the transducer embedded in concrete block B30 (black). (a) Colored functions represent Tukey windows applied to the center of the first occurrence of the signal alternation with different alpha values. (b) A Tukey window with $\alpha$ = 0.1 is applied to the center of the first occurrence of the signal alternation (between the start point (1) and the end point (2)) with alpha = 0.1 (green).

Figure 11

Evolution of recorded signals in time and amplitude. (a) Superposition of signals recorded on the piezoelectric transducer embedded in concrete block B30 during monitoring of temperature changes. The different colors represent signals captured at various time intervals or under varying conditions, highlighting the changes in signal characteristics over time. (b) Zoomed-in view of the start of the signal, where the variation of time ($\mathsf{\Delta }{t}_p$) and amplitude ($\mathsf{\Delta }a$) is detected upon the first arrival of the signal.

Figure 12

Significant influence quantities presented with and Ishikawa diagram (5M Methods) [43] for ultrasonic measurements performed using transducers embedded in concrete.

Figure 13

Hourly monitored wave velocity variation (absolute value) with temperature changes in concrete block B60, displaying recorded and corrected values alongside hourly data with associated error bars.

Figure 14

Study of V_p with temperature changes in three different concrete blocks using embedded ultrasonic transducers. Errors bars are computed using Equation (9) (Section 2.6).

Figure 15

Velocity variation (percentage of reference value) for temperature changes of three samples with different concrete properties (Table 2). The solid lines with error bars represent the variation of velocity (dV/V), and the dashed lines represent temperature variations in each concrete block.

Figure 16

Velocity variation (percentage of reference value) obtained using cross-correlation for temperature changes in concrete block B30. The black line represents temperature variations recorded inside the concrete using an embedded transducer. Tukey windows with different alpha values are applied to the first arrivals of the recorded signals (The size of the Tukey window is kept constant, and the endpoint of the window is always positioned on the 3rd zero (point (1) in Figure 10b)). For each Tukey window (depending on the alpha value), the variation of wave velocity (dV/V[%]) is presented.

Figure 17

Analysis of factors influencing the measurement of wave propagation time measurement. Transducer calibration uncertainty is identified as the dominant influence.