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A laser interferometer robot for the study of surface wave

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A laser interferometer robot for the study of surface wave Powered By Docstoc
					                       NDTCE’09, Non-Destructive Testing in Civil Engineering
                           Nantes, France, June 30th – July 3rd, 2009



A laser interferometer robot for the study of surface wave
sensitivity to various concrete mixes
Odile ABRAHAM1, Géraldine VILLAIN1, Laiyu LU1 ,Louis-Marie COTTINEAU1,
Olivier DURAND1
1
    LCPC, Bouguenais, France, odile.abraham@lcpc.fr

Abstract
   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.

Résumé
   Le projet national SENSO a pour objectif de définir une méthodologie qui combine
plusieurs méthodes non destructives pour évaluer des indicateurs nécessaires à l'étude de la
durabilité des bétons. Un jeu de plus de 100 dalles de 0,5 m x 0, 25 m x 0,12 m a ainsi été
réalisé avec différents rapports eau/ciment, tailles et types de granulats. Pour mener à bien les
nombreux essais à différentes teneurs en eau, teneurs en Cl- et profondeurs de carbonatation
le LCPC a conçu un robot portable qui enregistre des sismogrammes avec un interféromètre
laser en réception pour étudier les courbes de dispersion de vitesse de phase des ondes de
surface. Dans cet article nous décrivons le robot, le protocole expérimental et la procédure de
traitement du signal utilisée. La vitesse de phase des ondes de surface est sensible au module
d'Young (mesuré par essais destructif) et à la teneur en eau qui peuvent varier avec la
profondeur. Des résultats préliminaires obtenus avec un algorithme d'inversion des courbes de
dispersion en milieu continument variable (par opposition à un milieu multicouche) en cours
de validation sont discutés.

Keywords
     Concrete, Surface wave, inversion, dispersion curve

     1   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
                     NDTCE’09, Non-Destructive Testing in Civil Engineering
                         Nantes, France, June 30th – July 3rd, 2009


and represent the more energetic wave train recorded at the surface. In the case of a semi-
infinite, homogeneous, isotropic and elastic medium the SW (Rayleigh wave), has a velocity
                                                             0,871,12 ν
  C r that is independent of frequency equal to: C r =                   V S where ν is the
                                                                 1 +ν
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.

  2    Description of the laser interferometer robot
   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.

   2.1 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
                       NDTCE’09, Non-Destructive Testing in Civil Engineering
                           Nantes, France, June 30th – July 3rd, 2009


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.




        Figure 1. Left : picture of the piezoelectric source. Right : Picture of the robot; the
                                receiver is a laser interferometer

   2.2 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.




      Figure 2. Measurement set-up. The signal are recorded from 0.01 m from the source to
                        0.43 m with an inter-trace equal to 0.005 m

   2.3 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.

  3     Measurement of the dispersion curve
   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.
                     NDTCE’09, Non-Destructive Testing in Civil Engineering
                         Nantes, France, June 30th – July 3rd, 2009


   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.




         Figure 3. Left : one seismogram. Right : one signal at 0.2 m from the source.

   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
                     NDTCE’09, Non-Destructive Testing in Civil Engineering
                         Nantes, France, June 30th – July 3rd, 2009


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).

   4   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.

   5   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
                     NDTCE’09, Non-Destructive Testing in Civil Engineering
                         Nantes, France, June 30th – July 3rd, 2009


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.

Acknowledgements
   We would like to thank the French National Agency for Research (ANR) for funding this
research project. We would like to thank Fabrice Blaineau (LCPC) for the design of the robot
and Alain Grosseau (LCPC) for its realization.

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