Elsevier

Ultrasonics

Volume 117, December 2021, 106540
Ultrasonics

Evaluation of stiffness loss of reinforced concrete beams using the diffuse ultrasound method

https://doi.org/10.1016/j.ultras.2021.106540Get rights and content

Highlights

  • Ultrasonic energy transferring is influenced by cracking.

  • Diffuse ultrasound parameters can be used to determine cracking bending moment.

  • Diffusivity and ATME showed to be highly correlated to the stiffness loss of beams.

Abstract

Flexural cracks are common in reinforced concrete (RC) beams. At service loads, the tensile stresses induced by the bending moments cause beam sections to crack, leading to loss of stiffness and a consequent increase in beam deflections. Serviceability limit states in RC beam design include maximum deflection and maximum crack widths. Cracks affect the propagation of ultrasound by disrupting its travel path, which leads to a strongly scattering of the ultrasonic waves. As a result, there is a delay in the arrival of the ultrasonic energy flux, which can be observed by the increasing formation of coda waves. This resultant incoherent wavefield can be approximated by the diffuse ultrasound method. The diffuse ultrasound method can better describe the cracking effects over a larger region of the RC element compared to the ultrasonic pulse velocity, the most used ultrasound parameter in concrete applications. Changes in the diffuse ultrasound parameters (diffusivity, dissipation and ATME) can be related to the extent of cracking in a RC element. The objective of this research was to apply the diffuse ultrasound method to evaluate the stiffness loss due to flexural cracking of RC beams. Beams with different longitudinal flexural reinforcement ratios were cast and submitted to a bending test. The deflection at mid-span, and thus beam stiffness, was monitored during the test. Ultrasound transducers were installed in the central region of the beams with ultrasound readings performed during the tests in order to acquire the waveforms at various loading stages. For each waveform, the diffuse ultrasound parameters were recovered using a time–frequency analysis. The behavior of the diffuse parameters with increasing progressive damage caused by flexural cracking was analyzed and correlated to the stiffness loss of the beams. As a result, it was observed that diffusivity and ATME were the most sensitive parameters to identify the onset of cracking and also were seen to be related to beam stiffness variation at early cracking stage. When correlated with stiffness loss values up to 70%, diffusivity and ATME presented high mean correlation coefficients, allowing to conclude that it is possible to estimate the stiffness loss through the diffuse ultrasound parameters in the interval following the beginning of the cracking process.

Introduction

Flexural reinforced concrete elements are subjected to cracking. Although the extent of cracking is not an issue at the design stage, it impacts deeply serviceability limit states, either by increasing deflections as a result of the reduction of the effective stiffness, or by excessive crack widths, which has a negative effect on the durability of the structure. Therefore, there is a need for the development and improvement of techniques that qualitatively and quantitatively assess the extent and the effect caused by cracks in the performance of concrete structures in service.

The use of stress wave propagation methods such as ultrasound allows one to indirectly evaluate the cracking process in a convenient and fast approach. The ultrasonic pulse velocity (UPV) is the most used ultrasonic parameter in the inspection of a concrete structure [6]. It has been successfully applied to detect internal non-uniformities [17], to measure the depth of surface opening cracks [19], among other applications. However, by only relying on UPV, one may not be able to acquire important information on the changes in concrete microstructure due to cracking [28], [18], [1].

Concrete is a heterogeneous material, where aggregates, voids and internal microcracks, of various sizes and with different elastic properties, act as scatterers for ultrasonic waves propagating through this multi-phase medium. These mechanical waves suffer repeated reflections, intensified according to the relative size of the wavelength to the scatterers. These reflective (or dispersive) effects are prevalent in the stochastic frequency range, in which the wavelength is on the same order of magnitude as the size of the scatterers, and also when the volume fraction of the scatterers is very high [24], [16]. As a consequence, multiple scattering occurs, with energy being translated to a later random arrival of waveforms (called coda waves). Coda waves travel a path much longer than the direct path and, therefore, are more sensitive to small changes that occur in the medium [20].

In this multiple scattering range, the displacement field of an elastic wave is no longer coherent with its original phase, due to the loss of its temporal and spatial correlation in relation to the incident wave. It behaves randomly, with zero mean. These combined factors characterize a stochastic process that can be described as an approximation of the diffusion equation [33]. Thus, an approach in terms of mean wave energy may be used, since it remains a significant parameter. The temporal evolution of the average density of the ultrasonic energy can be approximately modeled by the diffusion equation, being called the diffuse ultrasound method [32], [20].

This method has attracted a lot of attention, especially for its ability to quantitatively assess small-scale damage in the concrete microstructure that is not amenable to identification through more common ultrasound parameters, such as UPV. The diffuse ultrasound parameters, such as diffusivity, dissipation and arrival time of the maximum energy (ATME), have shown great potential in assessing concrete integrity conditions. Deroo et al. [8] successfully evaluated microcrack damage in concrete caused by the alkali-aggregate reaction and by thermal effects, using the diffusivity and dissipation parameters; Becker et al. [5], Schurr et al. [25] and Ahn et al. [2] showed that diffusivity is sensitive to microcracks and to the microstructural behavior of concrete; Quiviger et al. [22] evaluated the ability to detect, locate and characterize real cracks in the first layer of concrete; Ramamoorthy et al. [23], Seher et al. [27] and In et al. [10] performed numerical and experimental analyzes to determine the depth of surface cracks in both concrete specimens and beams under bending using the ATME parameter; Jiang et al. [11] showed that in full size concrete beams, loading stresses influence the diffusivity parameter, proving the method's potential in determining internal material changes due to cracking. More recently, Landis et al. [12] showed the relation between diffuse ultrasound parameters to the microstructure of concrete specimens through X-ray computed tomography. Other techniques based on the theory of diffuse ultrasound, as is the case with the coda wave interferometry, coda wave decorrelation and Locadiff, were able to detect, locate and characterize pre-existing and also flexural cracks from smaller specimens to full size concrete beams [13], [34], [35].

Based on the aforementioned research, it can be observed that parameters related to the diffuse ultrasound method may be able to characterize the stiffness loss of reinforced concrete beams due to flexural cracking. In addition to be able to detect cracking, it is important to quantify its influence on the structural behavior of the element. Detecting damage at an early stage of degradation can significantly reduce maintenance costs and prevent catastrophic failure of concrete structures.

The diffuse ultrasound method has been successfully applied in detecting damage in a laboratory environment, both in small specimens with controlled damage and full-scale concrete beams, showing a high potential of the method for field measurements of real concrete structures. Therefore, as a step towards a more practical application, the objective of this study was to evaluate the behavior of the diffuse ultrasound parameters in a situation of spontaneous appearance and propagation of flexural cracks, similar to that observed in field applications.

Six reinforced concrete (RC) beams with two levels of reinforcement ratio were cast. The beams were subjected to a four-point bending test up to failure. During the test, ultrasonic readings were taken in the central region of the beams. The diffuse ultrasound method was then applied with the diffusivity, dissipation and ATME parameters being correlated with the continuous loss of stiffness of the beams. The results indicated that the diffusion method can be applied to evaluate the stiffness loss in reinforced concrete beams, specially at the early stage of cracking.

Section snippets

Ultrasonic diffusion theory

The diffusion equation describes the evolution over time of the spectral energy density (energy per frequency, per volume) of an ultrasonic wave field, after it has been strongly scattered. Thereby, at the limit of multiple scattering events in a highly heterogeneous medium, the energy density of a diffuse ultrasonic field, in an elastic-linear body β, develops according to the diffusion equation described by Weaver and Sachse [33] and Weaver [32], as shown in Equation (1):E(r,t,f)t-D2E(r,t,f

Specimen preparation

In order to evaluate the cracking process in structures subjected to bending, six reinforced concrete beams were cast. The RC beams, with 1700 mm in length and 150 mm × 220 mm cross section, were divided into two batches with three beams each. Each batch corresponded to a different longitudinal reinforcement ratio: 0.48% for beams of batch B1 and 1.22% for beams of batch B2. The different reinforcement ratios were adopted to produce different stress distributions and, thus, different cracking

Bending test

The bending tests of batches B1 and B2 were performed at 102 and 89 days of concrete age, respectively. The average concrete strengths on the day of the tests were 47.7 MPa and 49.0 MPa for batches B1 and B2, respectively, determined according to the Brazilian Standard ABNT NBR 5739:2018 [4]. During the four-point bending test, the RC beams from batch B1 showed a ductile behavior with failure due to yielding of the longitudinal reinforcement steel without concrete crushing in the compression

Conclusion

The present work investigated the feasibility of the diffuse ultrasound method to evaluate stiffness loss of reinforced concrete beams subjected to four-point bending tests. From the experimental results, the following conclusions can be drawn:

  • -

    The diffusivity and the ATME parameters were able to detect the onset of flexural cracking, and thus determine the cracking bending moment. While there was a sharp decrease in diffusivity, there was a pronounced increase in ATME. The dissipation

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.

Acknowledgement

The authors would like to acknowledge Fundação de Amparo à Pesquisa e Extensão Universitária (FAPEU) for financial assistance and to GPEND/LEE/UFSC where the research was developed. This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001.

References (35)

  • Aggelis, Dimitrios G.; Shiotani, Tomoki. Experimental study of surface wave propagation in strongly heterogeneous...
  • Ahn, Eunjong et al. Effectiveness of diffuse ultrasound for evaluation of micro-cracking damage in concrete. Cement And...
  • Anugonda, Phanidhar et al. Diffusion of ultrasound in concrete. Ultrasonics, [s.l.], v. 39, n. 6, p.429-435, out. 2001....
  • Associação Brasileira De Normas Técnicas. NBR 5739: Concreto – Ensaio de compressão de corpos de prova cilíndricos. Rio...
  • Becker, Jens et al. Characterization of Cement-Based Materials Using Diffuse Ultrasound. Journal Of Engineering...
  • Bungey, John H. et al. Testing of Concrete in Structures. 4. ed. New York: Taylor & Francis,...
  • Deroo, Frederik. Damage detection in concrete using diffuse ultrasound measurements and an effective medium theory for...
  • Deroo, Frederik et al. Detection of damage in concrete using diffuse ultrasound. The Journal Of The Acoustical Society...
  • In, Chi-won et al. Monitoring and evaluation of self-healing in concrete using diffuse ultrasound. Ndt & e...
  • In, Chi-won et al. Estimation of Crack Depth in Concrete Using Diffuse Ultrasound: Validation in Cracked Concrete...
  • Jiang, Hanwan et al. Diffusion Coefficient Estimation and Its Application in Interior Change Evaluation of Full-Size...
  • Landis, Eric N. et al. Relating ultrasonic signals to concrete microstructure using X-ray computed tomography....
  • Larose, Eric et al. Locating and characterizing a crack in concrete with diffuse ultrasound: A four-point bending test....
  • Page, J. H. et al. Experimental test of the diffusion approximation for multiply scattered sound. Physical Review E, v....
  • Page, John H. et al. Classical wave propagation in strongly scattering media. Physica A: Statistical Mechanics and its...
  • Payan, Cédric et al. Ultrasonic Methods. In: Balayssac, Jean-Paul; Garnier, Vincent. Non-destructive testing and...
  • Perlin, L. P.; Pinto, R.C.A. Ultrasonic tomography in concrete. IBRACON Structures and Materials Journal. São Paulo, v....
  • Cited by (0)

    View full text