Assessment of wave modulus of elasticity of concrete with surface-bonded piezoelectric transducers

https://doi.org/10.1016/j.conbuildmat.2020.118033Get rights and content

Highlights

  • Systematic study for assessment of WMoE of concrete by surface-bonded PZT transducers is conducted.

  • The physical relationship between Rayleigh wave and WMoE is applied in signal processing.

  • Comprehensive recommendations for effective assessment of WMoE of concrete are provided.

  • Piezoelectric and infinite elements are utilized in the numerical model.

Abstract

Measurement of the modulus of elasticity of concrete based on wave propagation technique is a critical method to assess condition and performance of concrete materials and structures. In this study, a combined numerical and experimental study is conducted for assessment of wave modulus of elasticity (WMoE) of the fully-cured concrete using surface-bonded PZT (lead zirconate titanate) transducers, also so called smart piezoelectric modules (SPMs). Rayleigh wave (R-wave) acquired from the surface-bonded PZT transducers is selected as the main target signal, and the explicit physical relationship between R-wave and WMoE is applied in signal processing. Piezoelectric solid element and electric load are applied to model the PZT transducers and actuate stress waves in numerical simulation, respectively. The numerical analysis provides a better understanding of surface wave propagation in concrete and sheds light on physical experiment. Effects of excitation frequency, excitation waveform, and size of PZT transducers are first examined in numerical simulation and then validated by physical experiment. Good agreements between the numerical and experimental results show that the Hanning windowed 5-peak or 7-peak sinusoidal tone burst at the frequency range of 40 kHz to 100 kHz is recommended as the excitation signals; while the width-to-thickness ratio of square transducers ranging from 10 to 15 is suggested for selection and design of surface-bonded PZT transducers. Effective measurement of WMoE using the surface-bonded PZT transducers shows great potential for nondestructive evaluation of concrete, and it can be used for condition assessment and health monitoring of concrete structures.

Introduction

Concrete structures are widely used in civil engineering and construction industry, such as bridges, building, dams, high-speed railways, etc. However, insufficient curing, long term aging, or deterioration during service life, and unforeseen failure make structural safety an important and ubiquitous problem to be solved. In condition assessment and health monitoring of concrete structures, the modulus of elasticity (MOE) measured using wave propagation (WP) technique is a critical parameter to assess performance of structural concrete. Therefore, systematic, feasible and cost-efficient concrete material property assessment techniques need to be further investigated.

To date, assessment techniques for the MOE of concrete can be generally divided into two categories: destructive testing and non-destructive testing (NDT) techniques. Compression test is still a commonly used destructive testing technique due to its reliability and popularity. Nevertheless, for complex concrete structures, this method requires a large number of standard cube or cylindrical samples, which may not be available after many years. But the extraction of the samples for compression test from the original structure is often undesirable.

Nondestructive testing (NDT) techniques can be classified as magnetic particle inspection (MPI), infrared thermography, X-radiographic detection [1], resonant frequency technique, ultrasonic pulse velocity (UPV) test [2], [3], rebound hammer (RH) test [4], etc. Some of these techniques extremely depend on the inspection equipment, testing environment, material type, and skill of operators; while others are cost-intensive, time- and labor-consuming. These limitations thus promptly hinder the application of conventional NDT techniques in condition assessment and health monitoring of concrete structures.

Piezoelectric transducers, fabricated by smart material, such as PZT (lead zirconate titanate), have been extensively applied in smart structural systems [5], [6]. Under high temperature and strong electric field, piezoceramics are poled. Due to this special characteristic, PZT transducers will generate linear electric displacements in response to applied mechanical stress, which is called direct piezoelectric effect. Conversely, they will produce linear mechanical strain when subjected to electric field, which is called converse piezoelectric effect. Hence, PZT transducers can be used as both actuators and sensors. Due to its low power consumptions, ease of fabrication and installation, suitability for in situ application, etc., condition assessment methods based on PZT transducers will overcome the shortcomings of conventional monitoring techniques. Moreover, condition assessment methods based on PZT transducers possess significant advantages, such as real-time and in situ monitoring, high linearity, wide frequency excitation and response, and potential integration for smart structures.

While condition assessment methods based on PZT transducers can be generally classified as the electro-mechanical impedance (EMI)-based and the WP-based techniques. For the EMI technique, a single PZT transducer is bonded onto or embedded into concrete to actively provide local excitation at high frequency and simultaneously sense local dynamic response. Damage had been characterized using PZT transducers on aluminum and concrete specimens [7], [8], [9]. The experimental results showed that the EMI technique was highly sensitive to incipient damage. Moreover, the root mean square deviation (RMSD), mean absolute percentage deviation (MAPD), and covariance and correlation coefficient (CC) were proved to be good damage indices in different cases. Presence of damage [10], [11] and stress changes [12], [13] were found to induce a variation in structural impedance, which could be analyzed and compared with a pristine measurement. Over the last couple of decades, monitoring structure itself attracted attention of many researchers. However, the strength of structural adhesives and the effect of corrosion during curing process and service life are also crucial to health of structures. Therefore, adhesive debonding and corrosion monitoring based on the EMI technique [14], [15], [16], [17], [18], [19], [20] were recently investigated. The EMI method based on thickness mode resonance was applied for assessment of the adhesive bonds of carbon fiber–reinforced polymer [18]. The results showed that the weak bond level could be detected based on the RMSD value and then the change of conductance peak frequency. Lim et al. [19] conducted an experimental study to monitor the curing process of structural adhesives based on the EMI technique. The results illustrated that both the EMI and WP techniques were correlated well with the physical changes of structural adhesive during the curing process and the tensile tests. Li et al. [20] proposed a corrosion monitoring method for smart corrosion coupon based on the EMI technique using PZT transducers. The results showed that the peaks in the conductance signatures present a leftward shift and the peak frequencies decrease linearly with increase of the corrosion amount, which makes a contribution to quantitative assessment of corrosion amount. Successful numerical and experimental applications revealed the potential of the EMI technique for in situ structural health monitoring (SHM).

The WP technique, on the other hand, has been successfully applied to condition assessment and health monitoring of metallic and composite structures. Usually, two or more PZT transducers are employed in the WP technique. Beard and Chang [21] proposed a concept for active damage detection in a composite tube. The experimental results showed that the location of damage could be found by measuring the arrival time of waves. Giurgiutiu et al. [22] thoroughly investigated wave functions of longitudinal wave (L-wave), shear wave (S-wave), flexural wave, Rayleigh wave (R-wave), and Lamb wave. They proved that PZT transducers could replace the traditional bulky ultrasonic transducers in some cases. Furthermore, some damage indices were verified to have a good correlation with the crack growth by conducting a crack propagation test [23], [24]. The proposed damage index increases as the crack expands, and it approaches a value of 1.0 as the crack propagates a sufficient distance away from the detecting paths.

The WP technique based on the PZT transducers is also broadly applied to health monitoring and damage detection of concrete structures. PZT transducers can be embedded into or surface-bonded onto the host structures. Song et al. [25] proposed a method using PZT transducers embedded in the reinforced concrete bent-cap to detect the existence and severity of cracks. The proposed method was proved to be more sensitive than the traditional method based on Linear Variable Differential Transformer (LVDT) and microscopy. Then, this technique was applied to early-age strength monitoring, crack detection, and debond detection for concrete structures [26], [27], [28], [29], [30]. Kong et al. [27] conducted a research on very early age (0–20 h) concrete hydration characterization monitoring by using piezoceramic-based smart aggregates. The amplitude and frequency response of the electrical signal were proven reliable to classify and verify the three hydration stages (i.e., the fluid, transition, and hardened stages). Feng et al. [28] proposed an active sensing approach based on smart aggregates to detect the cracks and the further leakage of concrete pipelines. The results of time domain analysis and frequency domain-based wavelet analysis showed that the stress wave energy attenuation could be used to distinguish the type of cracks and determine the further leakage. Wu and Chang [29], [30] conducted both numerical and experimental studies to detect debond in reinforced concrete structures. The results indicated that the amplitude of signal and the time of flight (TOF) were sensitive to the extent of debond and the elongation of rebar, respectively. In addition, different kinds of stress waves were also used in SHM of concrete [31], [32]. Qin and Li [31] monitored the cement paste hydration process using L-wave propagating across the specimens. The results showed that concrete hydration process could be divided into four stages. Qiao et al. [32] developed the technique for material property assessment and crack identification of recycled concrete using the embedded PZT transducers. The first S-wave was proved capable of indicating the existence and roughly the extent of the damage. Nevertheless, the PZT transducers embedded into concrete still have some disadvantages, such as infeasible to be replaced when they are out of work, difficult to be implemented nondestructively in existing concrete structures, etc.

On the other hand, the surface-bonded PZT transducers can be easily installed and replaced. Due to surface installation method, surface wave (i.e., R-wave) becomes the main concerned signals. Song et al. [33] conducted both numerical and experimental studies on concrete structures using surface-bonded PZT transducers and obtained the group velocity dispersion curves of surface wave. Recently, experimental studies aiming at further verifying the effectiveness of surface-bonded PZT transducers were conducted, and various practical issues were investigated [34], [35]. Soon afterwards, some numerical studies on monitoring of concrete curing and predicting the mechanical properties of structural adhesives under curing were further conducted using the PZT-based WP technique [36], [37].

So far, most of the researches on SHM of concrete based on the WP technique with the PZT transducers have mainly focused on experimental studies, and they rarely focused on theoretical or numerical studies. The lack of understanding on physical behavior of both the PZT transducers and host structures in the WP technique impedes effective design and placement of PZT transducers and makes physical experiments out of guidance. In addition, statistical methods are mainly adopted to assess performance of concrete structures. Direct physical relationship between the wave modulus of elasticity (WMoE) of concrete and R-wave acquired from the PZT transducers is rarely applied to signal processing.

In this study, the WMoE of the fully-cured concrete is numerically and experimentally evaluated by the surface-bonded PZT transducers. Physical relationship between R-wave and WMoE of concrete is directly applied in signal processing. In the numerical simulation, the piezoelectric solid element and electric load are employed to model PZT transducers and actuate stress waves, respectively. The corresponding physical experiment is then conducted to compare with the numerical results. Some key parameters influencing measurement accuracy, such as excitation frequency, excitation waveform, size of PZT transducers, are evaluated. Good agreement between the numerical and experimental results provides some feasible recommendations for assessment of WMoE of concrete with the surface-bonded PZT transducers. Effective measurement of WMoE using R-wave acquired from the surface-bonded PZT transducers in the form of smart piezoelectric modules (SPMs) shows great potential for NDT of concrete.

Section snippets

Principle of the WP technique

In this section, the principle of the WP technique based on the physical relationship between the R-wave velocity and the WMoE of propagating medium is introduced [38].

Based on the classical theory of elasticity, the Navier governing equations are:λ+μ·u+μ2u=ρu¨where λ and μ are the Lamé constants.

The detailed deriving processes for the solution to the Navier governing equations are presented in Appendix A. The relationship between the bulk wave velocity and the WMoE of propagating medium

Numerical simulation model

In this section, the commercial finite element (FE) software ABAQUS is used to establish a three-dimensional (3D) FE model of concrete with piezoelectric solid element for simulating the piezoelectric transducers (sensors and actuators) and infinite element for dealing with the boundary condition.

The wavelength of most excitation signals employed in this study is about 50 mm (40 kHz). To avoid the overlaps of the signals due to the near-field effect, the dimensions of concrete sample and the

Experimental setup

In this section, the physical experiment corresponding to those set up in the numerical models is conducted, and their results of R-wave velocity and WMoE are compared. All the material parameters of concrete and PZT transducers are same as those used in the numerical FE simulation (see Table 1, Table 2).

The concrete specimen with dimensions of 1000 mm × 500 mm × 100 mm was cast. The maximum size of aggregate is 16 mm, the water-to-cement cement ratio is 0.4, and the concrete grade is C30. As

Results and discussions

In this section, three key parameters, i.e., excitation frequency, excitation waveform and size of the surface-bonded PZT transducers, are investigated numerically and experimentally. The first two parameters are about choice of excitation signals, while the last one is about design of the PZT transducers. The effects of the three parameters on the assessment of WMoE of concrete are discussed, and some feasible recommendations are reached. It should be noted that the R-wave collected from the

Conclusions

In this paper, a comprehensive numerical and experimental study is conducted for assessment of WMoE of the fully-cured concrete using the surface-bonded PZT transducers. The explicit physical relationship between the WMoE of concrete and R-wave velocity acquired from the surface-bonded PZT transducers is applied in signal processing. In the numerical simulation, the piezoelectric solid element and infinite element are used to model the PZT transducers and weaken wave reflection and scattering

CRediT authorship contribution statement

Haifan Yu: Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Software, Validation, Visualization, Writing - original draft. Linjun Lu: Conceptualization, Funding acquisition, Project administration, Resources, Supervision, Writing - review & editing. Pizhong Qiao: Conceptualization, Methodology, Writing - review & editing.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

The authors would like to acknowledge the support from the National Natural Science Foundation of China (NSFC Grant nos. 51678360 and 51679136).

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