In the context of a growing need for safety and reliability in Civil Engineering, acoustic methods of nondestructive testing provide answers to a real industrial need. Linear indicators (wave speed and attenuation) exhibit a limited sensitivity, unlike nonlinear ones which usually have a far greater dynamic range. This paper illustrates the potential of these indicators, and evaluates its potential for in situ applications. Concrete, a structurally heterogeneous and volumetrically, mechanicallydamaged material, is an example of a class of materials that exhibit strong multiple scattering as well as significant elastic nonlinear response. In the context of stress monitoring in pre-stressed structures, we show that intense scattering can be applied to robustly determine velocity changes at progressively increasing applied stress using coda wave interferometry and thereby extract nonlinear coefficients. In a second part, we demonstrate the high sensitivity of nonlinear parameters to thermal damage as regard with linear ones. Then, the influence of water content and porosity on these indicators is quantified allowing to uncouple the effect of damage from environmental or structural parameters.

The present paper is devoted to the study of the potential applications of techniques derived from nonlinear acoustics, applied to the nondestructive testing of concrete. Nonlinear methods have been considered, because nonlinearity indicators exhibit large dynamic ranges, which can be used in homogenous media [

One of the major challenges for non-destructive evaluation in civil engineering is the need for indicators which can faithfully provide relevant

With respect to wave propagation, the term

As a result, these materials present a resonant frequency shift when increasing excitation amplitude. Under two harmonic sources (frequencies

These indicators have already been used for the Non Destructive Testing (NDT) of concrete. Mechanical damage has been widely discussed. Fatigue damage as been monitored by nonlinear resonance methods using flexural [

In the present study, we propose to investigate several aspects of the problems currently encountered in civil engineering.

The first of these is related to the evaluation of stress in the inaccessible, pre-stressed cables embedded in concrete structures. Because of the inaccessible nature of these cables, we have concentrated our efforts on the influence of stress on concrete, the outer surface of which remains accessible. For that purpose, we study the classical nonlinear properties of concrete, the parameter

The second aspect is related to reduce the threshold damage detection. In this context, the sensitivity analysis of the non-classical nonlinear parameter

Having demonstrated the strong sensitivity of this indicator to damage, the third aspect is related to the study of the influence of concrete’s environmental and structural parameters (water content porosity) on its nonlinear non classical response. The aim of this analysis is to separate the influence of these two effects with the ultimate goal to apply this method on real concrete structures.

The variation of the velocity of ultrasonic waves resulting from static loading has been well understood in isotropic homogeneous materials since the 1960’s. Described by classical expressions of the 2nd order (linear elasticity) as a function of

We have studied a promising method which enables the scattering properties of concrete to be put to advantage, thereby avoiding the need for reference state measurements (velocity and distance). Inspired from geophysics, this method, based on the analysis of the coda of transmitted signals, is found to have considerable potential for

The term

Implementation of the CWI method. Solid line: reference signal. Dotted line: signal under stressed conditions. (a) Typical signals recorded on our sample. (b) Early part of the signal. (c) Portion of the coda. (d) Cross-correlation function.

Velocity variations are not apparent at the beginning of the signal (Figure

We used a hydraulic press (MTS 318.25), into which we introduced a concrete sample with a diameter of 75 mm and a length of 160 mm (Figure

Third order elastic constants and nonlinear parameter determined for concrete and some other materials from literature.

Iron [ | −348 | −1 030 | 1 100 | −7.3 |

Pyrex glass [ | 14 | 92 | 420 | 4.4 |

Granite [ | −3 371 | −6 742 | −6 600 | −441 |

Sandstone [ | −97 800 | −99 400 | −84 900 | −9 600 |

Concrete from [ | −139 | |||

Concrete (present) | −3 007 | −2 283 | −1 813 | −157 |

Experimental setup

Relative velocity variations as a function of strain.

The following section is devoted at studying the sensitivity of the nonlinear non classical parameter

In civil engineering, the problem of monitoring tunnels after a fire, or of drums of stored radioactive waste, is currently debated. Following the study of classical nonlinearity, we now focus on the non-classical nonlinearity (

We used four identical samples, of parallelepiped geometry with dimensions

For the linear method, a flight-time measurement is carried out in order to evaluate the velocity

We observe that there is a visible shift in resonance frequency (Figure

NRUS experiment for the

Relative variation of the nonlinear parameter

The next section is aimed at quantifying the contribution of environmental and structural concrete parameters on the nonlinear

In order to study the influence of water content and porosity on the nonlinear response of concrete, we used 5 series of 6 parallelepiped samples (

The wave interaction method is used to extract the nonlinear parameter

In the case of the present study (Figure

Experimenatl setup. FFT (C1) and FFT (C2) are respectively the typical frequency spectrums of LF and HF obtained in experiments. FFT (C2) illustrates the interaction of HF with LF.

The first measurement campaigns dealt with the saturation states of 0% and 100%. The results are presented in Figure

Nonlinear parameter measured at 0% and 100% saturation, as a function of the water to cement ratio.

Dependence of the nonlinear parameter on the degree of water saturation

To the best of our knowledge, no former studies have derived the dependence of the nonlinear

In this paper, we demonstrate the high potential of nonlinear acoustic techniques, applied to the

We propose a robust and accurate method for monitoring the stressed state of concrete, thereby removing the need to measure a distance. The

The high sensitivity of the nonlinear

In the last section, we have quantified the influence of water content and porosity on the nonlinear

These studies were conducted in the context of two French national projects (ACTENA and SENSO) supported by the French Research National Agency, funded by Electricité De France (EDF) with the technical support of the Laboratoire de Mécanique et d’Acoustique (CNRS, UPR-7051). Authors would thank Paul Johnson (Los Alamos National Laboratory, USA) for comments and discussions. C. Payan gratefully thank Julie Baret for helpful technical support.