Elsevier

Cement and Concrete Research

Volume 53, November 2013, Pages 248-255
Cement and Concrete Research

A review of ultrasonic Coda Wave Interferometry in concrete

https://doi.org/10.1016/j.cemconres.2013.07.009Get rights and content

Highlights

  • CWI evaluates relative velocity changes (dV/V) of ultrasonic sound speed.

  • CWI zoom in the tiny changes of concrete acousto-elasticity properties

  • CWI allows to track thermal, mechanical and chemical damage.

  • CWI has an incredible sensitivity as low as 2.10 5in dV/V.

  • dV/V greater than 2.10 3/MPa indicates a level of significant damage.

Abstract

Concrete is a multicomposite material with heterogeneities ranging in size from micrometers to centimeters. At low frequency (below 50 kHz), ultrasound propagates through concrete without suffering scattering and absorption. On the contrary, above ≈ 100 kHz, the waves strongly interact with all the heterogeneities and enter a multiple scattering regime. This regime induces 1) substantial attenuation of coherent waves (direct waves and ballistic echoes), a feature that disables most conventional imaging techniques; and 2) the onset of late arrival signals that form the ultrasonic coda. An important feature of coda waves is their very high sensitivity to weak changes in the medium. Over the last years Coda Wave Interferometry (CWI) applied to ultrasound in concrete has been widely adopted in the non-destructive testing community. This article reviews several applications based on the precise processing of ultrasonic coda, in the case of thermal and/or stress and/or damage changes.

Introduction

Of all the available techniques for evaluating and testing engineered materials, especially concrete, those employing mechanical waves, either sonic or ultrasonic (US), are particularly attractive (see for instance the review of Mc Cann [1]). US techniques are non-destructive, non-hazardous, they can be used on site, and they are naturally highly sensitive to the mechanical properties of the material tested. In a pitch-catch configuration, the velocity associated with compressional (longitudinal) or shear (transverse) waves is easily deduced from the distance separating the transducers, and from the time-of-flight of the ultrasonic pulse propagating between them. As compressional and shear velocities directly depend on the elastic moduli (Lamé coefficients), estimating the velocity of ultrasound gives many indications on the mechanical properties of the material [2], [3], including (among others) its rigidity [4], its state of stress [5], its level of chemical damage [6] or mechanical damage [7]. In pulse-echo configurations, it is possible to visualize major discontinuities associated with a significant impedance contrast (or mismatch) in the concrete, including large cracks, cavities, large pieces of steel, etc.

The general idea with US techniques is that a better spatial resolution is obtained by increasing the frequency. However, attenuation also increases considerably with frequency, to the extent that the effective range allowed for US inspection is limited [8]. Attenuation relates to two distinct physical phenomena: 1) scattering, and 2) intrinsic absorption. In the first case, the information contained in the ultrasonic pulse response is transformed into a complex collection of late waveforms. In the latter it is simply canceled. The present article focuses on the first phenomenon that occurs in the so-called mesoscopic regime of US in concrete. The different mechanical wave propagation regimes in concrete are reviewed first of all. There are basically four different regimes that are defined for four consecutive frequency ranges.

In most concrete samples, the wave speed corresponding to compressional (resp. shear) waves is of the order of Vp  4300 m/s (resp. Vs  2500 m/s. Some significant fluctuations can be observed, mainly depending on the chemical and physical formulation of the concrete. Given that the interest here lies only in the comparison of different frequency domains, only the order of magnitude matters. In relation to the frequency f, the wavelength can be simply expressed as λp,s = Vp,s/f, in other words, the higher the frequency, the smaller the wavelength.

At frequencies lower than 20 kHz, in the seismic and audible range, the wavelength λ is greater than or of the order of the macroscopic size of the structure L:λ>L.

In this case, only stationary waves are excited, corresponding to the vibrational eigenmodes of the structure. This is the frequency range of structural health monitoring and modal analysis, techniques that are easy to implement but have limited sensitivity to local and/or microscopic features and poor resolution for locating defects.

The next frequency range is the standard range for ultrasonic testing of concrete. In this domain, the wavelength λ is smaller than the structure, but larger than the size of the heterogeneities d. Concrete is effectively a multicomposite material made of a micrometric cement paste aggregating millimetric sand and centimetric gravel. When the ultrasonic wavelength λ is much larger than these lengths, the sound interacts weakly with the heterogeneities and propagation takes place according to the Born (or simple scattering) approximation. Also, if absorption is weak, which means that the intrinsic absorption characteristic length a is larger than the size L of the specimen being tested, then this is the regime where most conventional imaging procedure can be operated:d<λ<L<la.

The absorption length is the length beyond which the intensity of the ultrasonic beam is decreased by a factor er/la. This decay is only due to dissipation effects, which must be differentiated from scattering phenomena. At microscopic scale, ultrasonic intrinsic absorption is due to viscous effects and corresponds to a loss of wave information. Scattering attenuation reduces the amplitude of the direct wave, but also induces the onset of late arrival constituting the so-called ultrasonic coda: the wave information is not canceled but transformed. The absorption length also defines the ultrasound penetration depth, and is well known to depend on frequency: the higher the frequency, the greater the attenuation. On the one hand, higher frequencies are required to improve sensitivity and resolution. On the other hand, high frequencies must be avoided in order to obtain a good signal-to-noise ratio in the waveforms and limited attenuation. Both trends tend to balance out in the 20 kHz–150 kHz frequency range, as defined in many standards (see for instance the International Organization for Standardization 1920-7).

For ultrasonic wavelengths shorter than the size of the heterogeneities, the wave can interact with the heterogeneities several times before reaching the detector. The distance between two scattering events is defined as the scattering mean free path . If the intrinsic absorption a is large enough, wave propagation falls into the multiple scattering regime:λ<dl<L<la.

Assuming that heterogeneities in concrete are dominated by centimetric gravel, this regime is attained for wavelengths shorter than or of the order of a centimeter, at frequencies higher than about 100 kHz. In most practical cases, intrinsic absorption starts to have a major effect above roughly 1 MHz, thus the frequency range of 150 kHz–1 MHz defines the multiple scattering regime. It is important to note that the frequencies limiting the different domains are given with a wide range of uncertainty, since the transition from one regime to another is smooth. In the multiple scattering regime, the waves bounce randomly off several heterogeneities before reaching the receiver, and wave trajectories show random characteristics to the extent that conventional imaging procedures fail. Nevertheless, the so-called US coda waves, corresponding to multiply scattered paths, are perfectly reproducible and deterministic. Transforming the random-like waveforms of the US coda into pieces of information relevant to non-destructive testing is a real challenge. This regime will be further developed in this paper.

At frequencies higher than 1 MHz, US waves are very hard to observe on large length scales. This is due to the combination of scattering attenuation and intrinsic absorption. In this latter domain, US techniques might be implemented on small size laboratory samples but hardly on-site.

As scattering strongly affects the amplitude of direct (or ballistic) waves, scattering is often considered to reduce the penetration depth of ultrasound. Nevertheless, scattering effects have to be differentiated from intrinsic absorption: energy here is not dissipated (and converted into heat) but translated in later, randomly arriving waveforms. The diffusion (or multiple scattering) regime that occurs above 100 kHz can be characterized by the following features [9] (see Fig. 1):

  • The direct wave is highly attenuated (to the extent that it is sometimes no longer visible).

  • Conventional imaging techniques, based on direct or simple scattering assumptions fail.

  • Onset of late arrivals constituting the so-called US coda.

The word coda has been inherited from the seismological community, where it refers to the tail of the seismograms after an earthquake [10]. These late arrivals are formed from the interference of various wave trajectories (see inset of Fig. 1). Because of the complexity of the material, it is hardly possible to describe in detail the phase and amplitude of coda waves, which might appear as the result of a random process. Nevertheless, coda waves are perfectly reproducible. Also, contrary to the unpredictability of the waveforms, the average intensity I (r, t) of the wave can be easily modeled, for instance by the diffusion equation (Fig. 2). In 3D infinite space, the solution of the diffusion equation, assuming a constant and isotropic diffusivity, takes the simple form of:Irt=14πDt3/2er24Dt,where D is the diffusivity and r is the source–sensor distance. The diffusion equation does not describe the wave propagation, but the propagation of the average intensity of the wave (or, in other words, the envelope of the waveform). Similarly to the random walk of a Brownian particle, the diffusion equation describes the probability of a wave pacquet being present at a given position after a given propagation time. This diffusion process is similar to heat transfer: the size of the diffuse halo where the waves are mostly concentrated (higher probability of presence, higher ultrasonic intensity) at a time t after the source pulse, is of the order of Dt. The diffusion constant describes how fast the ultrasonic intensity is transferred in the material. A high value of D means that the transfer is fast, which corresponds to a weak level of scattering. A low value of D means a slow transfer and a very high degree of multiple scattering.

The first work to present quantitative estimations of the multiple scattering process in concrete [9], [11] reported diffusivities ranging from ≈ 40 mm2/μs at 100 kHz, ≈ 20 mm2/μs at 200 kHz to ≈ 5–≈ 10 mm2/μs at 1 MHz. Since the diffusivity depends on the grain size, on the grain concentration and on the impedance contrast between the grains and the cement paste, the diffusion constant can significantly vary from one composition of concrete to another. Nevertheless, a large number of independent experiments have reported US diffusivity values of a similar order of magnitude [12], [13], [14], [15], [16], [17].

A considerable advantage of coda waves is their very high sensitivity to weak perturbations in the medium. Imagine, for instance, an experiment where sources and receivers have fixed locations, while a small mechanical change occurs inside the complex material being tested. Since multiply scattered waves spend a much longer time in the material than direct waves, they accumulate the signature of the very small changes encountered along their propagation. Thus, a change that is undetected by first arrivals becomes visible in the coda. G. Poupinet and co-authors [18] first investigated the effect of a small velocity change on seismic coda waves. They used seismic doublets, which are earthquakes occurring at the same place but at different dates, to demonstrate that small variations occurring in the earth's crust between the two seismic events are detectable. The main effect of a limited velocity change is to stretch the time axis of the record. In the coda, the time-delay between the initial and the final record is greater than around the first arrival.

A few years later, this “doublet” technique was transposed to ultrasound [19], [20]. Thanks to their seminal paper in 2002, Snieder and co-authors [21] gave a strong push to the use of seismic and US coda waves to monitor weak velocity changes in solids. The simple theoretical picture behind their processing is that any signal including multiply scattered waves φ(t) is the superposition of wave pacquets arriving with random time ti and random amplitude Ai. Thus, the effect of a global relative velocity change dV/V is to delay each wave pacquet by an amount of time proportional to the relative velocity change:φt=iAisttiφt=iAistti+dVVtwhere s(t) is the pulse initially sent by the source. Note that the travel time change along each wave path is independent of the wave trajectory but only depends linearly on the time in the coda. This simple model assumes that 1) the relative velocity change is homogeneous in the medium, and 2) the amplitude of the wave pacquets Ai does not change. The second assumption is actually a first order approximation that has been studied in depth by Weaver and Lobkis [22].

As a simple illustration, Fig. 3 shows two synthetic US coda obtained in a concrete-like medium after a 500 kHz broadband US pulse source. To mimic the gravel, a myriad of rigid scatters is placed in the simulation. Between the two acquisitions, the background velocity has increased by only dV/V = 0.02%. Such a tiny change is not visible with direct waves (inset (a) of Fig. 3) but clearly measurable in the late coda (inset (b) of Fig. 3).

Since 2002, many applications of CWI have been developed, including monitoring of the earth's crust with ambient seismic noise [23], [24], [25]. This paper focuses more specifically on developments in non-destructive testing and evaluation of concrete. The next section presents data processing procedures adapted to the high precision requested for CWI. Recent applications of CWI in concrete will then be reviewed.

Section snippets

CWI data processing

There are several ways to measure a relative velocity change dV/V in the coda. The first method, introduced in [18], [19], and further developed in [21], involves evaluating the time delays in consecutive small time-windows of length T at different times t in the coda, after the following cross-correlation:CCtδt=tT/2t+T/2φtφt+δtdttT/2t+T/2φ2dttT/2t+T/2φ2dt.

The cross-correlation can be made either in the frequency domain [26] or in the time domain. The time delay that maximizes CC is the

Application of CWI to thermal changes

The simplest physical effect that results in a relative velocity change is probably temperature. Thermal variations result in variations in the material acoustic velocity and dilation. Given that the former effect is in general one order of magnitude greater than the latter, an apparent velocity change in the US coda can be attributed to an actual velocity change in the material. The effect of temperature in concrete is well known, but the measurement of thermal CWI is relatively recent. In

Application of CWI to acousto-elasticity

When motion equations include non-linear elastic laws, ultrasonic velocities and strain are found to depend on one another. The relative velocity change of a material can be written, in the first order, as dV/V = 1  βϵ, where β is the non-linear elastic parameter and ϵ the strain. The non-linear elastic parameter β is a dimensionless parameter. This parameter can vary over several orders of magnitude: from about 5–10 for simple homogeneous materials like water, to more than 103 for rocks. Changes

Ultrasound depth penetration

The question of penetration depth, or volume of investigation of US in concrete is of primary interest. As the diffusion equation properly describes the propagation of the US intensity, the diffusion equation can be used as a basis for assessing the penetration depth. For instance, for collocated source and receiver, the investigated volume grows as a function of Dt, where D is the US diffusivity of concrete, and t the time in the coda. For instance, around 200 kHz and for a concrete formulation

Future work and prospects: heterogeneous changes

In some practical applications and geometries, such as bending tests, the stress is not evenly distributed. This results in an uneven distribution of local relative velocity change. CWI performed on the whole coda gives an estimation of the velocity change averaged over the volume of investigation of the ultrasound. Recent studies have demonstrated that the apparent relative velocity change in the coda is actually the superimposition of all contributions originating from all local volumes where

Conclusions

Ultrasonic CWI is a very efficient tool for quantifying tiny mechanical changes in concrete. A stress-induced CWI test consists of a series of US measurements for frequencies typically within the 150–1000 kHz range. Between two consecutive acquisitions, the state of stress is varied (temperature can also be varied instead of stress, but is harder to control). The quantity derived from CWI is the relative velocity change, for which a relative precision of the order of 10 5 can be easily attained.

Acknowledgments

This work is supported by the VOR program from the University of Grenoble, the ANR SISDIF grant.

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