sensitivity

The French national research project SENSO aims at providing a methodology combining several non destructive testing methods to evaluate indicators required for assessing the durability of concrete cover. A large set of 0.5m x 0.25m x 0.12m slabs has been built for various water/cement ratios, aggregate sizes and type. Those slabs have been subsequently studied under controlled water saturation level, chloride content and carbonation depth. To perform the numerous surface wave phase velocity dispersion curve measurements required for the data base, LCPC has designed a small size portable robot that records seismograms with a laser interferometer as a receiver. In this paper we describe the robot, the experimental protocol together with the signal processing technique used. Surface wave phase velocity is sensitive to shear and Young moduli (controlled by destructive tests) and to water content that are not necessarily uniform with depth and dispersion of surface wave is observed. Preliminary results of dispersion curves inversion illustrate these variations.


Introduction
Within the scope of the French National Agency project SENSO several non destructive methods have been studied with the aim of characterizing concrete mixes of various compositions including variation of aggregate type and size, porosity, water content, chloride content and carbonation depth. The objective of this paper is to present the underlying developments carried out by LCPC to perform efficient surface waves measurements within this context. In this paper we will illustrate the methodology developed to extract results that are presented more fully in a companion paper [1].
Surface Waves (SW) are a good candidate to evaluate non destructively the mechanical properties of cover concrete [2] and thus to tackle the problem of assessing in situ, non destructively, some durability indicators [6]. Surface Waves (SW) can be easily generated and represent the more energetic wave train recorded at the surface. In the case of a semiinfinite, homogeneous, isotropic and elastic medium the SW (Rayleigh wave), has a velocity C r that is independent of frequency equal to: C r = 0,871,12 ν 1 +ν V S where ν is the Poisson coefficient and V S is the shear wave velocity directly linked to the shear modulus G and the density  through V S =  G  . Surface wave investigation depth is roughly equal to half their wavelength, so that, their velocity varies with frequency as soon as the material presents some mechanical characteristics varying with depth [8]. The phase velocity dispersion curve, namely the phase velocity as a function of frequency, becomes the input to an inverse problem which aim is to recover as a function of depth the shear wave velocity V S [5].
In the SENSO project, 9 concrete mixes have been studied. For each concrete mix 8 slabs, of 0.5 m x 0.25 m x 0.12 m size, are available to perform the parametric study. For dry and fully saturated concrete the 8 slabs are available. For subsequent water content (20 %, 40 %, 80 %), carbonation depth and chloride content, this number is reduced.
For cover concrete investigation, wavelengths between 0.01 m up to 0.06 m are good candidate to investigate shallow concrete (the first 0.03 m). Considering an average SW velocity of 2200 m/s the frequency range required is between 35 kHz up to 220 kHz. As the appropriate wavelengths have a size similar to that of the aggregates, concrete cannot be considered as an homogeneous material with regards to SW propagation. Averaging of SW measurements is required to recover the so-called coherent SW wave field that has traveled in the homogeneous equivalent concrete [3]. It is important to note that it is the mechanical properties of the equivalent homogeneous concrete that are pertinent information for durability assessment of given structure. Furthermore, this is required if quantitative measurements are expected and would make it possible to follow, for instance, the evolution of porosity with time.
In [3] it is shown that to recover a good estimate of SW attenuation and phase velocity dispersion curves up to 180 kHz, for a given mix in a given state, several dozen of independent seismograms have to be recorded to compute the coherent SW train. Such numerous measurements were not possible in the SENSO project : it would have required more slabs than available together with a measurement time not feasible with the duration of the project. Indeed, even if the robot we designed dramatically accelerate the measurement compared to sensors in contact, it takes around 15 minutes to measure one complete seismogram made of 86 measurements points. Consequently each seismogram will be used independently and the coherent wave field is not computed. The results obtained hereafter are thus relevant to follow general trends. We will show results on phase velocity dispersion curves only as attenuation measurements are unsatisfactory within this context.
We will first describe the robot that has been designed to perform the measurements. We will then show signals and explain the general interpretation procedure. We will finish by some results and give some perspectives. Figure 1 shows the robot lying on top of one slab. This robot can also be used on a wall thanks to a dedicated frame onto which it can be clamped.

Source
Surface waves (SW) are generated with a sensor in contact (Fig.1 left). This source has been designed especially for this purpose by the French society IMASONIC. It is made of a matrix of piezoelectric components. Its is a large band transducer with a central frequency at 110 kHz [50 kHz -300 kHz at -3 dB]. A wedge adapted for a Rayleigh wave speed around 2100 m/s is used to favor the generation of SW. All the measurements have been made with this wedge with no difficulty whatever the actual true SW wave velocity. The source signal is a Ricker wavelet (the second derivative of a Gaussian function) whose energy is centered at 120 kHz. The coupling is ensure with water. As concrete is porous, a plastic film (common tape) is glued onto the surface before applying the source to prevent the penetration of the coupling agent within the material. The source is amplified by a Ritec RAM500 amplifier.

Receiver
The receiver is a laser interferometer from Polythec PI (OFV-505 sensor and OFV-5000 controller) with a VD-02 demodulator that has a sensitivity of 25 mm.s -1 .V -1 and a bandwidth from 0 to 1.5 MHz. The measurements points are aligned with the source. An aluminum tape is glued onto the line to improve the reflectivity of the surface. The laser interferometer is moved automatically every 0.005 m, from 0.01 m to the source up to 0.43 m, the largest offset.

Acquisition parameters
The sampling frequency is equal to 10MHz. 256 signals are average to improve the signal to noise ratio at a given receiver position. This number, never changed hereafter, can be reduced in the case of low porosity concrete but remains necessary for porous concretes that attenuate strongly the SW wave train. A home designed computer software in LabWindows CVI drives a motor to automatically move the laser interferometer and pilot the generation and acquisition of the signals. Figure 3 shows one recorded seismogram and a zoom on one signal situated at 0.2 m from the source. All signals are windowed automatically based on an automatic procedure that picks the maximum amplitude of each trace to center the window. We will see hereafter that the SW is slightly dispersive: consequently the velocity deduced from the time picking, that would be an "average SW group velocity", is not used hereafter. Furthermore, the SW dispersion is increased in case of carbonation and the window size for this case is enlarged.

Measurement of the dispersion curve
We have decided to follow within the SENSO project the phase wave velocity Vφ at given wavelengths. Our aim was to always investigate the slabs at given depths range: six values Vφ, called observables, corresponding to wavelengths from 0.01 m to 0.06 m, were extracted from the dispersion curves. The observable that has proven to be the more relevant, on the basis of statistical studies carried out by other partners of the project [6] was Vφ having a wavelength equal to 0.03 m. Obviously smaller wavelengths are more sensitive to the heterogeneousness of concrete, while larger wavelengths could be perturbed by the thickness of the slab here equal to 0.12 m. Finally this wavelength was in the frequency region where our source was the more energetic so that signal to noise ratio was optimal. The phase velocity dispersion curves are computed with the slant stack method in the frequency domain as proposed by [4] (also called p-ω transform). Apart from some of the carbonated slabs, only the fundamental mode is visible in our p-ω diagrams.

Figure 4. Phase velocity dispersion curves for G8 (W/C=0.9) and G1 (W/C=0.3)] for the [saturated case -100%] and [dry case -0%]
The maximum of the p-ω diagram is automatically picked. Previous studies have shown [7] that, to measure a SW phase velocity at a given wavelength, the set-up spread should at least equal twice the wavelength. To provide, as requested by the project, our observables at the center of the slab, and 0.05 m away on both sides of the center, we selected a spread length equal to 0.26 m centered on each point. Those spreads are overlapping but the conditions given by [7], for subsequent use (inverse problem), are respected. Figure 4 shows examples of phase velocity dispersion curves obtained for the more (G8) and less (G1) porous concrete in the fully saturated (100%) and dry (0%) cases. The water to cement ratio respectively equals to 0.9 for G8 and 0.3 for G1 (see [1] for more details). Full saturation is favorable to seismic measurement, as it corresponds to the lowest attenuation level compared to partially saturated cases. Considering one concrete mix, we see that, even though the slabs comes from the same mixture, their phase velocity varies one from the other. We observe as well that for wavelength lower than 0.02 m the computation of the phase velocity is perturbed by the heterogeneity of concrete (for both concretes the largest aggregate size is equal to 0.014 m). Full saturation always corresponds to the highest phase velocities, but, as the synthesis of our result shows in a companion paper [villain], the dry case does not correspond to the lowest velocity. SW phase velocity cannot be considered as a linear function of water saturation level. Finally we can observe a slight dispersion of the result which could be explained by: 1) a skin effect corresponding to a porosity in the first millimeters that differs from that of inner concrete due to curing condition 2) the distribution of aggregate size with depth that stabilizes only after half the size of the lager aggregate and scattering of SW wave 3) a water content gradient. Even if 1) and 2) should not be disregarded (some comments can be found in [3,5]), the existence of a moisture gradient is definitely present for G1 (E/C=0.3) in the dry case (Fig.4b).

Towards the solution of the inverse problem
To solve the inverse problem, that is to recover the shear wave velocity as a function of depth from the dispersion curve, a forward model is required. In the case of cover concrete two majors difficulty exist: the influence of the aggregate may produce a dispersion that some kind of homogenization model should forecast, and, second, the variations are continuous function of depth (like water saturation level, porosity, etc) rather than a given succession of homogeneous layers. This is illustrated here with concrete G1.

Figure 5. Left -Shear wave velocity profile as a function of depth for Phase velocity dispersion curves for G1 (W/C=0.3) Right -Dispersion curves (measured and model)
At this stage the influence of the heterogeneity of concrete is disregarded, and the inversion is processed with a forward model that considers that material properties varies continuously with depth [5]. Figure 5 shows the result for concrete G1. To comment this result one must keep in mind that the dependency of the velocity with water content is not a linear function increasing with water content (the curve has a U shape). In the case of the wet concrete the shear velocity V S is almost constant with depth. In the case of the dry concrete V S is increasing with depth. This can be explain by the fact that this concrete with a low W/C ratio is indeed not fully dry, the inner part still having a high water content (typically a volumic water content higher than 10%), whereas the near-surface is dry.

Conclusions
A robot using an interferometer laser as a receiver has been designed to perform efficient and repetitive measurement of surface wave phase velocity dispersion curves. In a first step, a robust observable for cover concrete mechanical characterization is the phase velocity associated to the wavelength equal to 0.03 m. This observable is sensitive to water content, bulk modulus and porosity and can be used for data fusion with other methods. In a second step surface wave dispersion curves can inform on variation with depth of a given property. We show here that inversion of surface wave dispersion curves inform on the homogeneity of the water content with depth.