Thermal modulation of nonlinear ultrasonic wave for concrete damage evaluation

Concrete damage usually manifests as cracks and microcracks. Nonlinear ultrasonic techniques have attracted considerable attention due to their high sensitivity to microcracking damage in concrete. Nonlinear resonance acoustic spectroscopy (NRAS) and nonlinear wave modulation spectroscopy (NWMS) are two common test methods. The NRAS method¹ measures the resonance frequency shift when a concrete sample is excited at different strain levels. Frequency shift is caused by material softening at high strain levels. This method is usually only applied on small samples. The NWMS method mixes a low frequency (f₁) wave and a high frequency (f₂) probing wave and measures the sideband energy at frequencies f₂ ± f₁.² The relationship between the sideband energy and the low frequency energy level represents the material nonlinearity. High amplitude vibration or impact modulation are used to drive nonlinear movement of microcracks in the concrete. Some researchers proposed a modified NWMS method, where the coda wave interferometry (CWI) is used to examine the relative velocity change of the high frequency diffuse ultrasonic wave instead of calculating the sideband energy.³ Both NWMS methods require either a high amplitude impact source or a low frequency pumping wave source to excite nonlinear response of materials, which is often challenging for large concrete structures.

Coda wave represents the noisy part of an elastic wave after the wave travels through a complex medium and experiences multiple scattering. Scattering happens when the wavelength of elastic wave is smaller than or comparable to the size of scatters (aggregates, cracks). Coda wave can be used to monitor very small changes in material, such as stress change, initiation and development of microcracks. Coda wave is also very sensitive to temperature variation, and the temperature effect often overshadows other effects due to material change. Therefore, temperature variation is usually treated as a pollution to the CWI results. Many studies indicate that the temperature induced velocity change is linearly related to the temperature variation.^4,5 Therefore, a bias control technique with a reference sample has been used to compensate the temperature effect. However, as presented in this paper, the relationship between the relative velocity change and temperature variation depends on the damage level of materials. The measurement on a reference concrete sample cannot fully compensate the temperature effect on the test samples.

The authors investigated the relative velocity change with temperature on concrete samples with different levels of damage and proposed a nonlinear ultrasonic wave method based on thermal modulation. The ambient temperature variation is used as the driving force to excite nonlinear response and modulate the high frequency ultrasonic waves in concrete. Thermal-modulation coefficient, which represents the thermal dependence of the relative velocity changes, is a new nonlinear parameter to evaluate concrete damage levels. The proposed thermal modulation method is easy to perform, and applicable to most concrete structures exposed in the ambient environment.

Four concrete prisms (76 mm × 76 mm × 305 mm) were cast and tested in the study [see Fig. 1(a)]. Prism 1 was kept at room temperature (23 °C) and used as the reference sample. The other three samples were heated in an oven to induce thermal damages. The water evaporation during the heating period would generate thermal cracks and pores in the concrete micro-structure. The heating procedure is shown in Fig. 1(b). Prisms 2, 3, and 4 were heated at 120 °C for 3 h. After cooling down for 6 h, prism 3 and 4 were heated again at 160 °C for 3 h. Finally, prism 4 was cooled down and then heated at 200 °C for 3 h. All samples were fully cooled down before the ultrasonic test. After heating, three different damage levels were generated on prisms 2, 3, and 4. Before the thermal damage, the resonance frequencies of all prisms were measured: 3223, 3240, 3244, and 3286 Hz for prisms 1 to 4. It is seen that all samples had similar resonance frequencies at the initial state. After the thermal damage, all samples went through multiple thermal cycles (23 °C–50 °C) in an environmental chamber for conditioning. The purpose of conditioning is to reduce the initial nonlinear response of concrete materials due to hysteresis, similar to low strain pre-loading cycles in loading tests. Then we measured the resonance frequencies again: 3116, 2854, 2645, and 2459 Hz for prism 1 to 4. All samples show different degrees of frequency drop, in which prism 4 had the largest drop. Although the reference sample (prism 1) did not experience the thermal damage, it still showed slight frequency drop. It could be caused by water evaporation during the conditioning cycles.

The concrete prisms were monitored using ultrasonic wave when subject to ambient temperature changes. Two piezoceramic disks were installed on the left and right surfaces of each prism as the transmitter and receiver [see Fig. 1(b)]. There was a longitudinal offset distance between the transmitter and receiver, which was designed to reduce the direct wave amplitude and increase coda wave amplitude. An ultrasonic pulser/receiver emitted square wave pulses to drive the transmitter at the frequency of 100 kHz. The received signals were amplified by 20 dB and digitized by an oscilloscope with a sampling rate of 20 MHz. Meanwhile, the internal and surface temperature of the prisms were monitored using thermocouple sensors on another sample (prism 0) cast with the same batch of concrete. Prism 0 was placed right next to the four test prisms and all prisms were assumed to have the same surface and internal temperature during the test.

The concrete prisms were moved outdoors during a winter day and continuously monitored for 22 h. The air temperature was −3.7 °C at beginning of the test and 1.6 °C at the end, with the high of 5.5 °C and low of −8.5 °C during the period. The temperature of the prisms dropped from 19 °C to −4.5 °C in the first 11 h. The histories of air and concrete temperatures are shown in Fig. 2(a). Moisture effect is neglected in this work since the humidity level was very low (<10%) during the testing.

CWI analysis uses cross-correlation between the unperturbed signal s₀(t) and perturbed signal s₁(t) to calculate the relative velocity change. Lobkis and Weaver⁶ proposed the stretching technique which allows processing the full waveform by applying a stretching factor ε to the perturbed signal s₁(t). Using the stretching technique, the cross-correlation coefficient is evaluated as

The stretching factor ε_max which maximizes the cross-correlation coefficient represents the relative velocity change dV/V. The stretching technique works well for uniform material changes caused by temperature.

Figure 2(a) shows the temperature histories of the concrete prisms and ambient air. The internal and surface temperature readings on concrete prisms are very close with difference less than 2 °C. Therefore, we use their average to represent the concrete temperature. Figure 2(b) presents the relative velocity changes for the four prisms from the CWI analysis. For each sample, its first signal was used as the reference in the CWI analysis; therefore, the relative velocity changes started from zero. It is seen that the damage levels affect the relative velocity changes, where prism 4 shows the highest dV/V while the control sample has the lowest dV/V when experiencing the same temperature changes. Based on the temperature changing rates, the entire monitoring process can be divided into four segments: fast cooling, slow cooling, slow warming, and stable. Ultrasonic wave velocity changes will be discussed for each segment.

Comparing Figs. 2(a) and 2(b), we notice the temperature and relative velocity change curves have an opposite and almost mirror relationship. This relationship is validated when the relative velocity changes are plotted vs temperature for all prisms. Figure 2(c) shows the correlation curves during segment 1, where the linear fits for all four curves have coefficients of determination R² above 0.989. These results indicate there is a strong linear relationship between the relative velocity change and the temperature change. The slope of the linear relationship, which represents the sensitivity of the relative velocity change to the temperature variation, is denoted as the thermal-modulation coefficient α_th. The absolute values of α_th(/ °C) are 1.3 × 10⁻⁴, 3.8 × 10⁻⁴, 6.5 × 10⁻⁴, and 9.2 × 10⁻⁴ for prisms 1–4, respectively. These values are much larger than the thermal expansion coefficient of concrete 10⁻⁵/ °C. This phenomenon was also observed by Weaver and Lobkis^6,7 on aluminum samples. It is believed that α_th is mainly affected by variation of elastic moduli rather than the thermal expansion. Therefore, the thermal-modulation coefficient α_th describes material's nonlinear elastic property under thermal effect.

The magnitudes of α_th increase with the damage levels of the concrete samples. This phenomenon can be explained by nonlinear behaviors of concrete with microcracks under temperature change. Microcracks in concrete will open/close during the heating/cooling process, which will decrease/increase the ultrasonic wave velocity and elastic moduli, and induce strong nonlinear response of materials. Therefore, for a sample with a higher level of microcracking damage, the relative velocity change will be more sensitive to temperature changes than a sample with less damage.

The concrete prisms were also tested by the nonlinear resonance acoustic spectroscopy. The frequency shift and the spectral amplitude are plotted in Fig. 3 with the fitted line slopes as the nonlinear parameters α. The nonlinear parameters α for the four prisms are −3.17 × 10⁻⁴, −6.7 × 10⁻⁴, −12.72 × 10⁻⁴, −32.51 × 10⁻⁴. By normalizing the parameters with respect to prism 1, the parameters α have ratios of 1 : 2 : 3.8 : 10.3 for the four samples, while the thermal-modulation coefficients have ratios of 1 : 2.9 : 5 : 7.1. Although these two test methods are very different in terms of the excitation sources (thermal effect vs impact) and measurements (velocity vs frequency), the thermal-modulation coefficients α_th and the nonlinear resonance parameters α show good agreement in general.

In Fig. 2(b), velocities in all samples first decreased due to temperature rise in segment 3, and then steadily increased with time in segment 4 (constant temperature). Figure 4(a) presents a detailed view of temperature change in segments 3 and 4, when the sample temperature increased from −4.0 °C to 1.0 °C during 13.5 to 18.5 h, and then maintained at this temperature for about 3.25 h. The relative velocity changes for all samples during this constant temperature period (segment 4) are shown in Fig. 4(b). During the process, prism 4 (highest damage) has the largest velocity change rate while the control sample (prism 1) has the slowest rate. The velocity increase for prism 4 in segment 4 was about 0.8%, which is quite significant when comparing with the relative velocity change 1.5% in segment 1 with 19 °C temperature change. Such large velocity change in segment 4 could not be attributed to the temperature fluctuation which was only about 0.2 °C during this monitoring period. This phenomenon is similar to the velocity recovery after an impact, which is usually called slow dynamics.⁸ When an impact or a thermal shock is applied on a concrete sample and removed later, the velocity will slowly approach towards an equilibrium value. In this test, the recovery process was only monitored for 3.25 h. The velocity change curves still show a clear trend of increase with time. Full velocity recovery may take many hours or even days when the samples are placed back in the original temperature condition.

Temperature slowly decreased in segments 2 and increased in segment 3, and the relative velocities also slowly increased and decreased accordingly. However, the velocity vs temperature relationships in these two segments are more complex than in segment 1 because both effects, thermal modulation and slow recovery, affected the velocity change. When the recovery mechanism dominates, the velocity may increase even with slow temperature rise in the later part of segment 3 [Fig. 2(b)].

In this work, we propose a new nonlinear ultrasonic test method to evaluate concrete damage using thermal modulation of ultrasonic waves. We observed linear relationships between the relative velocity changes and temperature variations on four concrete prisms. The prism with a higher damage level shows higher sensitivity to temperature changes. Therefore, the slope of the linear relationship, thermal-modulation coefficient, can be used as a nonlinear parameter to characterize concrete damages. In addition, we observed that the temperature changing rate may affect the velocity change, probably due to the slow dynamics mechanism. When a concrete sample experienced temperature variation and then was kept at a constant temperature for a long time, the velocity will gradually approach to the equilibrium velocity at the constant temperature. This recovery process is a form of creep, as discussed by TenCate et al.⁸ It is found that the recovery rate also depends on the damage level of samples. The concrete samples with higher damage levels also show higher recovery rate under a constant temperature. Therefore, thermal-modulation coefficient and recovery rate, both nonlinear parameters related to temperature change, may be used to evaluate the damage level of concrete materials.

Compared to other nonlinear acoustic test methods, the presented method is applicable to large scale concrete structures by using passive temperature change of structures. In this study, we only investigated the velocity change below room temperature. The thermal-modulation coefficient and recovery behavior in different temperature ranges and the effects of temperature changing rate will be studied in the future.

This research was supported by the U.S. Department of Energy–Nuclear Energy University Program (NEUP) under Contract No. DE-NE0008544.