Observation of multiple scattering of kHz vibrations in a concrete structure and application to monitoring weak changes

Combinatorial Quantification of Multi-Features of Coda Waves in Temperature-Affected Concrete Beams

Coda waves are highly sensitive to changes in medium properties and can serve as a tool for structural health monitoring (SHM). However, high sensitivity also makes them susceptible to noise, leading to excessive dispersion of monitoring results. In this paper, a coda wave multi-feature extraction method is proposed, in which three parameters, the time shift, the time stretch, and the amplitude variation of the wave trains within the time window, are totally derived. These three parameters are each mapped to the temperature variations of concrete beams, and then combined together with their optimal weight coefficients to give a best-fitted temperature-multi-parameter relationship that has the smallest errors. Coda wave signals were collected from an ultrasonic experiment on concrete beams within an environmental temperature range of 14 °C~21 °C to verify the effectiveness of the proposed method. The results indicate that the combination of multi-features derived from coda wave signals to quantify the medium temperature is feasible. Compared to the relationship established by a single parameter, the goodness-of-fit is improved. During identification, the method effectively reduces the dispersion of identification errors and mitigates the impact of noise interference on structural state assessment. Both the identification accuracy and stability are improved by more than 50%, and the order of magnitude of the identification accuracy is improved from 1 °C to 0.1 °C.

Numerical Parametric Study of Coda Wave Interferometry Sensitivity to Microcrack Change in a Multiple Scattering Medium

The expansion of cracks in 3D printing concrete materials may lead to structural failure, so it is essential to monitor crack propagation development. Coda wave interferometry (CWI) has been proven to be sensitive to microcracks, however, the evolution pattern of ultrasonic coda waves during crack growth is still not clear. This paper reports a numerical study of the sensitivity and feasibility of CWI for monitoring microcrack growth in heterogeneous materials. A two-phase concrete model, which contains microcracks with different angles and lengths, was developed using the finite element analysis software ABAQUS. The relative velocity change (Δv/v) and the decorrelation coefficient (Kd) at different crack increments were quantitatively analyzed. The numerical simulation results show that coda waves are sensitive to microcrack length as well as the crack angle. The Δv/v increases linearly with the increase of the length of a single microcrack, and the Kd could be linked to the crack length quadratically. Furthermore, a quantitative functional relationship between the CWI observations (Kd, Δv/v) and the angle of the crack to the source/receiver and the relative length growth of the crack are established. In addition, the nonlinear relationship between slope and angle can be fitted with a sinusoidal function. The reported results quantitatively assess the coda wave variation pattern during crack propagation, which is important for the promotion and application of CWI technology.

Ultrasonic Coda Wave Experiment and Simulation of Concrete Damage Process under Uniaxial Compression

Using the coda wave interferometry (CWI) method to obtain the ultrasonic coda wave characteristics of loaded concrete is an important method to evaluate the mechanical response of concrete. In this paper, the ultrasonic coda wave characteristics of C40–C70 concrete specimens (four strengths of concrete) under uniaxial compression were tested by laboratory experiments. Furthermore, to clarify the relationship between the internal damage process of concrete and the change rate of coda wave velocity, an ultrasonic coda wave discrete element simulation model combined with digital image processing technology was established. The results show that the coda wave is very sensitive to small changes in the compressive damage to concrete, and the change in coda wave velocity can correspond to the development process of concrete damage. This research is conducive to a better understanding of the complex material behavior of compressive concrete and proves the feasibility of ultrasonic field simulation and processing by using numerical simulation images of concrete damage.

Correlation of Load-Bearing Behavior of Reinforced Concrete Members and Velocity Changes of Coda Waves

The integral collection of information such as strains, cracks, or temperatures by ultrasound offers the best prerequisites to monitor structures during their lifetime. In this paper, a novel approach is proposed which uses the collected information in the coda of ultrasonic signals to infer the condition of a structure. This approach is derived from component tests on a reinforced concrete beam subjected to four-point bending in the lab at Ruhr University Bochum. In addition to ultrasonic measurements, strain of the reinforcement is measured with fiber optic sensors. Approached by the methods of moment-curvature relations, the steel strains serve as a reference for velocity changes of the coda waves. In particular, a correlation between the relative velocity change and the average steel strain in the reinforcement is derived that covers 90 % of the total bearing capacity. The purely empirical model yields a linear function with a high level of accuracy (R2=0.99, RMSE≈90μstrain).

An improved ultrasonic coda wave method for concrete behavior monitoring under various loading conditions

Monitoring of concrete behavior is an important task to evaluate the safety of concrete structures. This paper proposes a new stretching factor accumulation method based on the stepwise coda wave interference (CWI) to accurately calculate the relative velocity change Δv/v. The Δv/v and residual decorrelation coefficient Kd are used to study the concrete behavior in step loading experiment and short-time fixed loading experiment. The results show that: (1) In the loading stage of step loading experiments, both Δv/v and Kd can be used to monitor the load and the microcrack development; (2) In the relaxation stage of step loading experiments, the slow dynamics effect of concrete specimens can be characterized by Δv/v and Kd; (3) In the short-time fixed loading experiments, both Δv/v and Kd increase with the time of fixed loading, and the increasing rate of Δv/v decreases with the increase of concrete strength. This work can be used to promote the development of ultrasonic testing techniques that aid in concrete behavior monitoring.

Locating structural changes in a multiple scattering domain with an irregular shape

Locadiff is a method for imaging local structural changes in a random, heterogeneous medium. It relies on the combination of a forward model to calculate the sensitivity kernel of the source-receiver pairs, with an inversion method to determine the position of the changes. So far, the sensitivity kernel has been evaluated based on an analytical solution of the diffusion equation, which lacks the flexibility to handle problems where the domain has boundaries with an irregular shape. Moreover, the accuracy of the previous inversion method, based on linear algebra tools, was very sensitive to the values of the inversion parameters. This paper introduces a more generic approach to solve both these issues. The first problem is tackled by the implementation of a numerical method as an alternative for solving the diffusion equation. The second problem is tackled by the introduction of enhanced optimization algorithms to improve the stability of the inversion. This improved version of Locadiff is validated via both numerical examples and experimental data from an actual civil engineering problem.

Thermal modulation of nonlinear ultrasonic wave for concrete damage evaluation

A nonlinear ultrasonic test is proposed for material damage evaluation using thermal modulation. Temperature change excites and modulates nonlinear behavior of ultrasonic waves in concrete. Coda wave interferometry was used to analyze the relative velocity change of ultrasonic wave with temperature variations. On concrete samples with different levels of thermal damage, experimental results indicate that the samples with a higher damage level demonstrated higher sensitivity to temperature variations. In addition, a slow dynamics nonlinear behavior was observed. When the temperature changed and then remained constant, the wave velocity gradually approached to its equilibrium value.

Correlation between Coda Wave and Stresses in Uni-Axial Compression Concrete

Stresses in structures are usually converted by measured strains based on corresponding constitutive relations of materials. However, it is difficult to determine the constitutive relation of the material accurately, which leads to significant uncertainty of the converted stresses. This paper proposed a method to estimate the stresses in concrete by using the coda wave interference technique and established a model to describe the relation between the deformation of microcracks and the sound velocity. Based on the experiments, the development law of the coda waves with different frequencies of sound signal propagating in concrete was verified and discussed, and the change of the coda wave velocity during the loading and unloading of the specimen was tested. Parameters involved in the established model were regressed according to the experimental data. The analysis results show that the method can be used to test concrete stress and has a desirable accuracy.

Frequency selection for coda wave interferometry in concrete structures

This study contributes to the establishment of frequency recommendations for use in coda wave interferometry structural health monitoring (SHM) systems for concrete structures. To this end, codas with widely different central frequencies were used to detect boreholes with different diameters in a large concrete floor slab, and to track increasing damage in a small concrete beam subjected to bending loads. SHM results were obtained for damage that can be simulated by drilled holes on the scale of a few mm or microcracks due to bending. These results suggest that signals in the range of 50-150kHz are suitable in large concrete structures where it is necessary to account for the high attenuation of high-frequency signals.

Diffuse ultrasound monitoring of stress and damage development on a 15-ton concrete beam

This paper describes the use of an ultrasonic imaging technique (Locadiff) for the Non-Destructive Testing & Evaluation of a concrete structure. By combining coda wave interferometry and a sensitivity kernel for diffuse waves, Locadiff can monitor the elastic and structural properties of a heterogeneous material with a high sensitivity, and can map changes of these properties over time when a perturbation occurs in the bulk of the material. The applicability of the technique to life-size concrete structures is demonstrated through the monitoring of a 15-ton reinforced concrete beam subject to a four-point bending test causing cracking. The experimental results show that Locadiff achieved to (1) detect and locate the cracking zones in the core of the concrete beam at an early stage by mapping the changes in the concrete's micro-structure; (2) monitor the internal stress level in both temporal and spatial domains by mapping the variation in velocity caused by the acousto-elastic effect. The mechanical behavior of the concrete structure is also studied using conventional techniques such as acoustic emission, vibrating wire extensometers, and digital image correlation. The performances of the Locadiff technique in the detection of early stage cracking are assessed and discussed.

Structural monitoring of a highway bridge using passive noise recordings from street traffic

Structural damage on bridges presents a hazard to public safety and can lead to fatalities. This article contributes to the development of an alternative monitoring system for civil structures, based on passive measurements of seismic elastic waves. Cross-correlations of traffic noise recorded at geophone receiver pairs were found to be sufficiently stable for comparison and sensitive to velocity changes in the medium. As such velocity variations could be caused by damage, their detection would be valuable in structural health monitoring systems. A method, originally introduced for seismological applications and named Passive Image Interferometry, was used to quantify small velocity fluctuations in the medium and thereby observe structural changes. Evaluation of more than 2 months of continuous geophone recordings at a reinforced concrete bridge yielded velocity variations Δv/v in the range of -1.5% to +2.1%. The observed fluctuations correlate with associated temperature time series with a striking resemblance which is remarkable for two completely independent data sets. Using a linear regression approach, a relationship between temperature and velocity variations of on average 0.064% °C(-1) can be identified. This value corresponds well to other studies on concrete structures.

Locating and characterizing a crack in concrete with diffuse ultrasound: A four-point bending test

This paper describes an original imaging technique, named Locadiff, that benefits from the diffuse effect of ultrasound waves in concrete to detect and locate mechanical changes associated with the opening of pre-existing cracks, and/or to the development of diffuse damage at the tip of the crack. After giving a brief overview of the theoretical model to describe the decorrelation of diffuse waveforms induced by a local change, the article introduces the inversion procedure that produces the three dimensional maps of density of changes. These maps are interpreted in terms of mechanical changes, fracture opening, and damage development. In addition, each fracture is characterized by its effective scattering cross section.

Automatic identification of multiply diffracted waves and their ordered scattering paths

An automated algorithm uses recordings of acoustic energy across a spatially-distributed array to derive information about multiply scattered acoustic waves in heterogeneous media. The arrival time and scattering-order of each recorded diffracted acoustic wave, and the exact sequence of diffractors encountered by that wave, are estimated without requiring an explicit model of the medium through which the wave propagated. Individual diffractors are identified on the basis of their unique single-scattering relative travel-time curves (move-outs) across the array, and secondary (twice-scattered) waves are detected using semblance analysis along temporally offset primary move-outs. This information is sufficient to estimate travel times and scattering paths of all multiply diffracted waves of any order, and for these events to be identified in recorded data. The algorithm is applied to synthetic acoustic data sets from a variety of media, including different numbers of point-diffractors and a medium with strong heterogeneity and non-hyperbolic move-outs.

Revealing the structure of a granular medium through ballistic sound propagation

We study the propagation of sound through a bidimensional granular medium consisting of photoelastic disks, which are packed into different crystalline and disordered structures. Acoustic sensors placed at the boundaries of the system capture the acoustic signal produced by a local and well-controlled mechanical excitation. By compressing the system, we find that the speed of the ballistic part of the acoustic wave behaves as a power law of the applied force with both exponent and prefactor sensitive to the internal geometry of the contact network. This information, which we are able to link to the force-deformation relation of single grains under different contact geometries, provides enough information to reveal the structure of the granular medium.

Mode-converted diffuse ultrasonic backscatter

Diffuse ultrasonic backscatter describes the scattering of elastic waves from interfaces within heterogeneous materials. Previously, theoretical models have been developed for the diffuse backscatter of longitudinal-to-longitudinal (L-L) wave scattering within polycrystalline materials. Following a similar formalism, a mode-conversion scattering model is presented here to quantify the component of an incident longitudinal wave that scatters and is converted to a transverse (shear) wave within a polycrystalline sample. The model is then used to fit experimental measurements associated with a pitch-catch transducer configuration performed using a sample of 1040 steel. From these measurements, an average material correlation length is determined. This value is found to be in agreement with results from L-L scattering measurements and is on the order of the grain size as determined from optical micrographs. Mode-converted ultrasonic backscatter is influenced much less by the front-wall reflection than an L-L measurement and it provides additional microstructural information that is not accessible in any other manner.

Validation of a thermal bias control technique for Coda Wave Interferometry (CWI)

The Coda Wave Interferometry (CWI) analysis serves to monitor the variation of propagation velocity in a heterogeneous medium with high precision (10(-3)% in relative terms). In combination with acoustoelastic theory, this type of analysis offers an NDT method for stress evaluation and/or damage detection. Since the CWI method is intended to evaluate extreme levels of accuracy, the presence of bias under certain circumstances can undermine evaluation results and/or test repeatability. In this paper, we offer a bias control technique involving the use of a second (reference) specimen for CWI analysis that is designed to compensate: (1) the thermally-induced velocity variation due to environmental temperature fluctuations; and (2) bias originating from experimental procedures. The presentation of this technique contains both a theoretical analysis and experimental protocol for the purpose of implementation. Furthermore, comparisons of experimental results have been included in order to demonstrate the utility of this bias control technique under laboratory conditions.

Study of stress-induced velocity variation in concrete under direct tensile force and monitoring of the damage level by using thermally-compensated Coda Wave Interferometry

In this paper, we describe an experimental study of concrete behavior under a uniaxial tensile load by use of the thermally-compensated Coda Wave Interferometry (CWI) analysis. Under laboratory conditions, uniaxial tensile load cycles are imposed on a cylindrical concrete specimen, with continuous ultrasonic measurements being recorded within the scope of bias control protocols. A thermally-compensated CWI analysis of multiple scattering waves is performed in order to evaluate the stress-induced velocity variation. Concrete behavior under a tensile load can then be studied, along with CWI results from both its elastic performance (acoustoelasticity) and plastic performance (microcracking corresponding to the Kaiser effect). This work program includes a creep test with a sustained, high tensile load; the acoustoelastic coefficients are estimated before and after conducting the creep test and then used to demonstrate the effect of creep load.

Mode-resolved travel-time statistics for elastic rays in three-dimensional billiards

We consider the ray limit of propagating ultrasound waves in three-dimensional bodies made from a homogeneous, isotropic, elastic material. Using a Monte Carlo approach, we simulate the propagation and proliferation of elastic rays using realistic angle-dependent reflection coefficients, taking into account mode conversion and ray splitting. For a few simple geometries, we analyze the long-time equilibrium distribution, focusing on the energy ratio between compressional and shear waves. Finally, we study the travel time statistics, i.e., the distribution of the amount of time a given trajectory spends as a compressional wave, as compared to the total travel time. These results are intimately related to recent elastodynamics experiments on Coda-wave interferometry by Lobkis and Weaver [Phys. Rev. E 78, 066212 (2008)].

Monitoring stress changes in a concrete bridge with coda wave interferometry

Coda wave interferometry is a recent analysis method now widely used in seismology. It uses the increased sensitivity of multiply scattered elastic waves with long travel-times for monitoring weak changes in a medium. While its application for structural monitoring has been shown to work under laboratory conditions, the usability on a real structure with known material changes had yet to be proven. This article presents experiments on a concrete bridge during construction. The results show that small velocity perturbations induced by a changing stress state in the structure can be determined even under adverse conditions. Theoretical estimations based on the stress calculations by the structural engineers are in good agreement with the measured velocity variations.

Probing slow dynamics of consolidated granular multicomposite materials by diffuse acoustic wave spectroscopy

The stiffness of a consolidated granular medium experiences a drop immediately after a moderate mechanical solicitation. Then the stiffness rises back toward its initial value, following a logarithmic time evolution called slow dynamics. In the literature, slow dynamics has been probed by macroscopic quantities averaged over the sample volume, for instance, by the resonant frequency of vibrational eigenmodes. This article presents a different approach based on diffuse acoustic wave spectroscopy, a technique that is directly sensitive to the details of the sample structure. The parameters of the dynamics are found to depend on the damage of the medium. Results confirm that slow dynamics is, at least in part, due to tiny structural rearrangements at the microscopic scale, such as inter-grain contacts.

Varying the effective refractive index to measure optical transport in random media

We introduce a new approach for measuring both the effective medium and the transport properties of light propagation in heterogeneous media. Our method utilizes the conceptual equivalence of frequency variation with a change in the effective index of refraction. Experimentally, we measure intensity correlations via spectrally resolved refractive index tuning, controlling the latter via changes in the ambient pressure. Our experimental results perfectly match a generalized transport theory that incorporates the effective medium and predicts a precise value for the diffusion constant. Thus, we directly confirm the applicability of the effective medium concept in strongly scattering materials.

Monitoring stress related velocity variation in concrete with a 2 x 10(-5) relative resolution using diffuse ultrasound

Ultrasonic waves propagating in solids have stress-dependent velocities. The relation between stress (or strain) and velocity forms the basis of non-linear acoustics. In homogeneous solids, conventional time-of-flight techniques have measured this dependence with spectacular precision. In heterogeneous media such as concrete, the direct (ballistic) wave around 500 kHz is strongly attenuated and conventional techniques are less efficient. In this manuscript, the effect of weak stress changes on the late arrivals constituting the acoustic diffuse coda is tracked. A resolution of 2 x 10(-5) in relative velocity change is attained which corresponds to a sensitivity to stress change of better than 50 kPa. Therefore, the technique described here provides an original way to measure the non-linear parameter with stress variations on the order of tens of kPa.

Diffusive transport of light in a two-dimensional disordered packing of disks: analytical approach to transport mean free path

We study photon diffusion in a two-dimensional random packing of monodisperse disks as a simple model of granular media and wet foams. We assume that the intensity reflectance of disks is a constant r . We present an analytic expression for the transport mean free path l;{*} in terms of the velocity of light in the disks and host medium, radius R and packing fraction of the disks, and the intensity reflectance. For glass beads immersed in air or water, we estimate transport mean free paths about half the experimental ones. For air bubbles immersed in water, l;{*}R is a linear function of 1epsilon , where epsilon is the liquid volume fraction of the model wet foam. This throws light on the empirical law of Vera [Appl. Opt. 40, 4210 (2001)] and promotes more realistic models.