*3.2. Guided Wave Testing*

Many guided wave modes exist in a cylindrical rod, and each mode travels at a different velocity. These wave modes are often categorized into three different types: longitudinal (L), torsional (T) and flexural (F). Figure 4 shows the dispersion curves of the phase velocity for the first few modes in the 6.35 mm aluminum rod. The fundamental L (0, 1) mode was identified as most suitable for this study for several reasons. First of all, at the testing point (see Figure 4), there is mainly axial surface displacement and little radial

displacement in the rod, which makes the attenuation very sensitive to the shear wave velocity of the surrounding mortar or concrete. Furthermore, most importantly, the L (0, 1) mode could be easily excited by the piezo discs adopted in this study and is non-dispersive at low frequency. The attenuation caused by the surrounding mortar or concrete could be calculated from:

$$\alpha = -\frac{1}{\mathbf{D}} \ln f\_0(\frac{\mathbf{A\_{emb}}}{\mathbf{A\_0}}) \tag{1}$$

where D is the embedded depth, A<sup>0</sup> is the signal amplitude before the rod was embedded, and Aemb is the signal amplitude after the rod was embedded.

**Figure 4.** Phase velocity dispersion curves for an aluminum rod of 6.35 mm diameter.

Figure 5 shows two sets of representative waveforms for a mortar sample with w/c of 0.40 using different rods, and only the first two reflection echoes were shown. As shown in Figure 5, amplitudes of the signals getting from the steel rod of 3.17 mm diameter decrease very slowly in the first 4 h. In contrast, the amplitudes of the signals getting from the aluminum rod of 3.17 mm diameter decrease much faster in the first 4 h. This is probably due to the reason that acoustic impedance mismatch between early age mortar and aluminum is much smaller than the mismatch between early age mortar and steel. Thus, more energy is leaked to the surrounding mortar sample in the aluminum rod. This also implies that the aluminum rod is probably more sensitive and suitable to monitor the evolution of early age properties of cementitious samples.

The amplitude of the reflected guided waves was then normalized to the amplitudes of the waves obtained when the rods were not embedded. Figure 6a shows the normalized peak amplitudes getting from four different rods as a function of mortar age. It was noticed that during the first 3 h, the peak amplitudes of both the 6.35 and 3.17 mm steel rods decrease very slowly. As a result, the guided wave attenuation in these two rods does not increase significantly in the first 3 h (see Figure 6b).

**Figure 5.** Waveforms at 0.5, 2.0, 4.0, and 6.0 h for a mortar sample with w/c = 0.40 using: (**a**) a steel rod of 3.17 mm diameter; (**b**) an aluminum rod of 3.17 mm diameter.

**Figure 6.** Four different rods in mortar sample with w/c = 0.40. (**a**) normalized wave amplitude and (**b**) attenuation.

Another phenomenon noticed is that the attenuation trends in both steel rods are almost the same, especially after 5 h of setting. The reason was further investigated, and wavelet analysis was adopted to see the time-frequency domain difference between the signals obtained from the 6.35 mm and 3.17 mm diameter steel rods, respectively. As seen in Figure 7a, the central frequency of the reflected echoes obtained from the 6.35 mm diameter steel rod is 135 kHz, corresponding to a frequency-radius product of 428.63 kHz-mm. Sun [34] has proposed an improved approach to calculate the group velocity dispersion curve of rebar embedded into concrete, based on the PCDISP package [35]. By using Sun's approach, the theoretical group velocity in steel rod with a frequency-radius product of 428.63 kHz-mm was found to be 4989 m/s. While the group velocity calculated using the experimental data in this study was 2 × 304.8 mm/(0.2623–0.1403) ms = 4997 m/s, this agrees well with the theoretical group velocity.

×

**Figure 7.** The wavelet of signals obtained from mortar sample with w/c = 0.40 at the age of 0.5 h. (**a**) steel rod with a diameter of 6.35 mm and (**b**) steel rod with a diameter of 3.17 mm.

In the reflected echoes obtained from the 3.17 mm diameter steel rod, two dominant central frequencies, 135 kHz and 270 kHz could be observed. Note that the frequencyradius product of the 270 kHz signal is 428.63 kHz-mm in the 3.17 mm rod, and this product is the same as the one obtained from the 6.35 mm rod. As the hardening process develops, the 428.63 kHz-mm product will gradually become the dominant one in the 3.17 mm rod. Thus, the attenuation trends in both the 6.35 mm and 3.17 mm diameter steel rods are almost the same after 5 h of setting.

As seen in Figure 6, both the 6.35 mm and 3.17 mm aluminum rods show a rapid decrease in peak amplitudes in the first 4 h. Note that from around four hours, the decrease rate of the peak amplitude of the 6.35 mm aluminum rod becomes very slow. While the decrease rate of the peak amplitude of the 3.17 mm aluminum rod remains pretty high, this continuous rapid change makes the 3.17 mm aluminum rod the best choice within the four rods for monitoring the setting of cementitious materials. For simplicity, only the results obtained from the 3.17 mm aluminum rod will be shown in the following sections.

Since there is mainly axial surface displacement and little radial displacement under the low- frequency L (0,1) mode [36], shear leakage will control the attenuation caused by the embedded materials. Therefore, this mode is particularly sensitive to the shear properties of the embedded materials. Note that the shear wave velocity was

obtained during the test as well, it would be very interesting to correlate it with the guided wave attenuation.

Figure 8 shows the correlation formed by shear wave velocity versus the guided wave attenuation. As seen in the figure, despite some variations in the very early age, shear wave velocity still correlates strongly with the guided wave attenuation. Specially, after the very early age, there is an approximately linear relationship between these two measurements. Similar relationships, obtained by using steel rod for guide wave propagation, were also found in the hardening process monitoring of epoxy resins [33] and cement pastes [34].

**Figure 8.** Correlation between shear wave velocity and attenuation.

To find out the influence of coarse aggregates on this technique, a w/c = 0.50 concrete sample was tested in this study. The normalized amplitude and attenuation change during hydration of a concrete sample, and the mortar sample sieved from concrete are shown in Figure 9. As shown in the figure, the developing trends in both materials are almost identical. This is probably because the rod is very thin compared to the size of coarse aggregates, and the rod is still mainly surrounded by mortar when embedded in the concrete sample. This implies that this technique is able to eliminate the effects of coarse aggregates, which makes it of great potential to be applied to the fresh concrete in the field after a standard setup is established. Another thing that needs to be noted is that an increasing practice in concrete engineering is the use of additives to reduce the water dosage, and the rheological properties of concrete samples using additives may be quite different. Thus, extensive attention should be paid when applying this approach to concrete samples using additives.

In order to find out whether coarse aggregates affect the development and the evolution of shear waves in concrete, shear wave velocity change during the setting process is also shown here (see Figure 10). As seen in the figure, the shear wave velocity in concrete is around 860 m/s at the initial setting time, and it is about 450 m/s higher than the shear wave velocity in mortar sieved from the same batch of concrete. This is understandable, because when taking shear wave velocity measurement on concrete samples, the shear wave has to propagate through the coarse aggregates, whose mechanical properties are very different from the surrounding mortar. In other words, the effects of coarse aggregates could not be ignored when taking shear wave velocity measurements.

**Figure 9.** Guided waves in concrete and mortar sieved from concrete: (**a**) normalized amplitude and (**b**) attenuation.

**Figure 10.** Shear wave velocities in concrete and mortar sieved from concrete.

#### 500 **4. Conclusions**

Age (h) 1234567 0 In this study, an embedded guided wave technique has been adopted to monitor the setting process of cementitious samples. Specially, four different kinds of rods have been tested simultaneously to find out the optimal guided wave setup. Shear wave velocities of the mortar and concrete have been monitored and the time of setting has also been measured on these samples, and the relationship between these measurements has been discussed. The following conclusions could be drawn from this study.

Within the four rods tested in this study, the aluminum rod with a diameter of 3.17 mm performs the best. It could be adopted to characterize the whole setting process of cementitious samples with standard water to cement ratios.

By using an aluminum rod in the fundamental mode, a strong correlation between the attenuation and the shear wave velocity has been shown in mortar samples. This trend agrees well with the previous embedded guide wave monitoring studies, which used a steel rod to guide wave propagation.

This technique worked equally well in concrete samples and mortar samples sieved from the same batch of concrete. This implies that this technique is able to eliminate the effects of coarse aggregates, and is of great potential for field setting monitoring of cementitious materials with standard water to cement ratios.

**Author Contributions:** Methodology, G.Y. and S.L.; analysis, D.W. and S.L.; validation, D.W. and P.S.; writing—original draft preparation, S.L.; writing—review and editing, G.Y., D.W. and P.S.; funding acquisition, G.Y. and S.L. All authors have read and agreed to the published version of the manuscript.

**Funding:** National Key Research and Development Project (2019YFE0118500) and Academic Frontier Project of China University of Mining and Technology (2017XKQY050) are greatly appreciated for their generous funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Data available on request due to their size properties. The data presented in this study are available on request from the corresponding author.

**Conflicts of Interest:** The authors declare no conflict of interest.
