Applications

The experimental work performed to date has been largely qualitative in manner where microstructural damage is introduced in an unquantifiable manner, such as ASR or stress corrosion cracking in concrete [Planes & Larose 2013, Shokouhi & Lorenz 2014]. Most studies merely detect a change in coda wave differencing parameters without correlating the changes to a specific change in the material or damage state. This is to be expected given the distributed nature of the damage of interest and the difficulty in quantifying the damage growth. The majority of quantitative work in detecting damage deals with measuring the relative velocity due to either thermal or homogeneous loading [Weaver & Lobkis 2000, Zhang et al. 2012, Larose & Hall 2009, Niederleithinger & Wunderlich 2013], though a few papers discuss quantifiable amounts of defects/damage [Seher et al. 2013, Michaels & Micheals 2005]. Some of the earlier work for coda

wave NDE has been reviewed by Planes & Larose with a focus on concrete applications [Planes

& Larose 2013].

As noted earlier, several approaches to detecting damage have been applied to concrete;

most notably the diffusion fit parameters and the relative velocity change. Diffusion fitting provides three parameters by which damage can be detected/characterized and the material can be evaluated. The diffusion parameters have been used to characterize several cement specimens with various sizes and distributions [Becker et al. 2003], where qualitative trends and some ability to distinguish microstructure were observed. It was noted that better models are needed to analyze scatterer size and distribution. Self-healing concrete was monitored and evaluated in a similar qualitative manner [In et al. 2013]. The qualitative detection of micro damage (damage with a length scale on the order of or smaller than the largest aggregate) in concrete has also been explored with diffusion fitting [Deroo et al. 2010], where it was demonstrated that the diffusivity parameter is sensitive to damage density while the dissipation parameter remained constant. The quantitative applications of diffusion fitting to damage characterization in concrete to date have largely involved measuring the depth of surface breaking macro-cracks. Several publications have demonstrated that the time lag of the peak diffusive energy is well correlated to crack depth [Ramamoorthy et al. 2004, In et al. 2012, Quiviger et al. 2012, Seher et al. 2013]. Payan et al.

(2013) were able to improve the characterization by applying dynamic loading to the specimen in the form of a low frequency shaker. The limitation with the macro-crack depth measurements is that the crack is surface penetrating and the transducers have to be on the opposite side of the crack. Several things become clear from these studies: 1) the diffusivity and dissipation parameters can partially but not fully characterize a cementious material, 2) micro damage is detectable with the diffusivity parameter with some potential for characterization, 3) surface breaking

macro-cracks can be sized, and 4) the sensitivity to damage has not been established and it is unlikely that small amounts of damage (a few micro-cracks) can be detected in samples that are cubic meters in volume.

Relative velocity change is the most popular coda wave differencing parameter and can be used to directly measure thermal and structural loads, the acoustoelastic parameter, as well as micro-crack density [Planes & Larose 2013]. One of the first application of relative velocity measurements for NDE purposes correlated structural and thermal loading on Berea sandstone to the change in coda wave relative velocity [Gret et al. 2006]. Parallel and subsequent publications applied relative velocity extraction methods to concrete in order to measure thermal induced velocity variation [Larose et al. 2006, Niederleithinger & Wunderlich 2013, Zhang et al. 2013b].

These studies confirmed the linear phase shift with temperature for concrete materials that was previously demonstrated by Roberts et al. (1992) for acrylic plates and Weaver & Lobkis (2001) for aluminum billets. Several publications also examine the relative velocity variations due to structural loading [Larose & Hall 2009, Stahler & Sens-Schönfelder 2011, Zhang et (2011, 2012)], which confirmed the linear relation of the phase lag with time predicted by Snieder (2006). Zhang et al. (2013a) attempted to examine relative velocity variation due to the heterogeneous stress field generated by 4-point-bending on a concrete specimen, but the research yielded inconclusive results. The linear relation between applied homogeneous stress (or strain) and the coda wave relative velocity indicates the appropriateness of measuring the acoustoelastic parameter with coda waves. The acoustoelastic parameter, first derived by Hughes & Kelly (1953) based on Murnaghan’s theory [Murnaghan 1951], is the ratio of the relative velocity change to the change in applied strain. Payan et al. were able to use coda waves to measure the third order elastic constants from Murnaghan’s theory in addition to the acoustoelastic parameter in a concrete

specimen. Additionally, several authors have demonstrated the potential capability of the acoustoelastic parameter to detect micro damage and fatigue in concrete [Schurr 2010, Schur et al.

2011a, Schurr et al. 2011b, Zhang et al. 2011]. Coda wave relative velocity has also been qualitatively used by several authors to directly estimate damage (typically stress induced micro-cracking) [Masera et al. 2011, Neiderleithinger et al. 2010, Shokouhi & Neiderleithinger 2012, Shokouhi 2013, Shokoui & Lorenz 2014, Frojd & Ulriksen 2016]. Each of these studies demonstrated an increasing magnitude for the relative velocity change with increasing amounts of damage. While it is true that an increase in the number of micro-cracks should theoretically increase the mean travel time, this will only become apparent for large numbers of micro-cracks.

Improvements in detecting micro-cracks in cementious materials have been observed by several authors when a lower frequency pump wave is included [Toumi et al. 2011, Zhang et al.

2013, Zhang 2013c, Hilloulin et al. 2014a, Hilloulin et al. 2014b, Moradi-Marani et al. 2014]. The lower frequency pump wave opens and closes the micro-cracks, which allows for greater interaction with the coda wave components. The nonlinear mixing between the pump and coda waves also allows for the improved measurements of the nonlinear parameters

Coda wave NDE is a volumetric method and as such no information regarding the location of the damage is extractable using the previously mentioned methods. In order to address this shortcoming, several authors have attempted to locate damage and applied stresses using theoretical spaciotemporal decorrelation kernals to predict the coda wave for an undamaged sample for a given transmitter-receive pair and solving the inverse problem [Planes et al. 2013, Niederleithinger et al. 2014]. Damage and point loads have been located to within several centimeters for large concrete samples.

The two primary methods of analyzing differences in coda waves caused by damage or other subtle changes are based on time dependent phase lag or total waveform energy. While these differencing parameters are useful they only compare global coda wave parameters. An alternative method, first proposed by Michaels & Michaels (2005) for the analysis of coda waves, is to examine the parameters of the residual signal left over after a point-by-point subtraction of two coda waves (e.g. the signal energy contained in the residual). Michaels’ have utilized/developed at total of five such features (henceforth referred to as differential features) to characterize changes present in the coda wave due to the introduction of damage and variations in environmental conditions [Michaels & Michaels 2005, Michaels et al. 2005, Lu 2007, Michaels 2008]. These investigations demonstrated that the differential features are sensitive to damage and environmental effects in aluminum plates. They also demonstrated that the environmental effects can be separated from damage and that thermal changes can be compensated for.