Abstract

Non Destructive Testing of concrete structure to assess their condition is a tool particularly adapted to on site investigations. Unfortunately, methods are sometimes limited by their sensitivity to several parameters which cannot be separately controlled. Coupling of techniques might help solving this problem.

Electrical resistivity measurement and acoustic methods are both sensitive to cracks parameters. Electrical measurement enables to accede to depth and equivalent resistivity of the crack (linked to opening and moisture condition of the defect). Acoustic methods are sensitive to the crack depth and to its eventual partial closure. We propose to use both methods to reach a better characterisation of crack. A rough draft of abacus is built to deduce parameters from various datasets.

Works are still in progress but the tests carried out on an experimental slab will drive further works on this way, to propose an original response to engineers.

1 Introduction

In civil engineering, importance of structural management is increasing according to economical pressure. New needs of damage characterisation are appearing in order to forecast and plan rehabilitation works. In this frame, Non Destructive Techniques are appearing as efficient tools for on site study. They are more and more included in the assessment strategy of structure owners. Today, new methods are under development in view of more complete structure characterisations than before.

Cracks are defects whose description can provide engineers a better assessment of structural condition. To date the usual characterisation performed on a structure are: the description of the crack profiles on the surface (eventually their quantification through image analysis), and the follow up of the crack opening in time. This information is not sufficient to a complete assessment of structural condition.

Electrical resistivity and acoustic measurements devoted to crack characterization are two NDT still in progress. They show a promising sensitivity to concrete damage, but their dependence to a lot of uncontrolled parameters prevents a deeper data analysis.

Combination of measurements seems to be a solution to exploit more completely information drawn from electrical and acoustic techniques. Works presented in this paper show the ability of both techniques, and the interest of a coupled approach for further works.

2 Electrical resistivity measurement for cracks characterisation

2.1 Electrical resistivity technique
Electrical resistivity of concrete is mainly conditioned by the electrolytic conductivity through porosity of material. Today the technique is only used to study reinforcement corrosion (detecting humidity and ionic ingress which promotes rebar alteration) [POL 00]. But cracks in concrete must appear as preferential ways for fluids, and we propose to use this effect to study cracks with electrical measurement.

In that aim, we have developed a device (figure 1) which enables to characterise the upper layer concrete of the structure (location of main alterations), by on site resistivity measurement. The four-probe square device injects electrical current between two lateral probes, and measures the potential difference between the two others. The apparent resistivity is deduced reporting the potential on the intensity, in function of the set geometrical characteristics. Measurements are performed for two investigation orthogonal directions, at each sounded point. Resistivity variations are linked to cracks presence and dependant on their properties. Results are exploited by drawing isoresistivity maps or profiles. The calculation of material electrical anisotropy (defined as the ratio between resistivity obtained for the two injection orientations), is also an indicator of local behaviour of the material.

Fig 1: Measurement device.

Electrical characteristics of concrete obtained depend on material properties around probes and is named apparent resistivity. The crack presence leads to various signal disturbances according its characteristics.

2.2 Sensitivity of electrical resistivity to equivalent resistivity of cracks
The equivalent resistivity of crack is a parameter which can describe the overall influence of a given crack, described as an homogenous defect. This ideal picture simplifies the influence of various parameters and allows numerical study in first approach. The equivalent resistivity of the crack mainly depends on the electrical resistance of the filling material of the crack. Distinction can be made between an insulating crack, which can be considered as dry (then passive, in first approach), and a conductive crack, considered as moistened (then with an active alteration). Experimental works [LAT 03] show that the crack opening is also a factor conditioning the equivalent resistivity of the crack (since its changes the bridging in the crack).

Numerical works have been made with a 3D finite element software (CESAR LCPC), to study the influence of the equivalent resistivity of crack. Computations are made for various resistivities of crack, and considering two orientations for electrical current injection directions (indicated with the double arrows on figures). Figures 2 and 3 show results for conductive and resistive cracks (relatively to the concrete) and for the electrical injection in parallel with the crack (PL) and perpendicularly to it (PP); the device being located right to the crack.

Fig 2: Apparent resistivity depending on resistivity of the crack. Numerical results on dry crack.

Fig 3: Apparent resistivity depending on resistivity of the crack. Numerical results on wet crack.

In terms of electrical resistivity variations, graphs show that for an injection in parallel with defect (configuration PL) is leading to qualitatively the same result for resistive and conductive crack. For an injection with the configuration PP, crack increases the apparent resistivity only for the resistive case. Thus, measurements combined in two orthogonal axis enable to characterise the equivalent resistivity of crack whatever it is dry or wet.

2.3 Sensitivity of electrical resistivity to crack depth
Following the same approach than above, the influence of crack depth is assessed. The numerical modelling considers several depths of crack, for both configurations of the set (PP and PL), and for an insulating and a conductive crack (figure 4 and 5). Results show that depth and apparent resistivity variations are linked: the more the crack is deep, the more the resistivity is disturbed. As previously, we can observe for the PL configuration, that effects of crack on electrical response are equivalent with a resistive or an insulator disorder. For PP configuration, apparent resistivity is sensitive to crack depth only for resistive cracks.

Fig 4: Apparent resistivity depending on the crack depth. Numerical results on dry crack.

Fig 5: Apparent resistivity depending on the crack depth. Numerical results on wet crack.

2.4 Expression of damage with the electrical anisotropy.
The electrical anisotropy (expressed in terms of decimal logarithm), is defined as the ratio between resistivities for configuration PP and PL measured at the same point. This indicator does not depend on the resistivity value of the concrete, and allows to generalise results. Influence of equivalent resistivity of crack (expressed relatively to resistivities contrasts), and of depth (reported to the set size), are drawn (Figure 6 et 7).

Fig 6: Apparent anisotropy depending on the resistivity contrast - Numerical results.

Fig 7: Apparent anisotropy depending on the crack depth (dry and wet cracks).

Numerical computations help to understand that influences of equivalent resistivity of crack, and crack depth, independently leads to same electrical apparent resistivity disturbances (qualitatively). So, at this stage, we cannot make the part between effects of these two parameters. From an electrical point of view, we treat about a crack intensity corresponding indistinctively to influence of equivalent resistivity and depth of the crack.

3 Acoustic methods

In order to determine the crack depth of an opening crack at least two acoustic methods exists. The first one relies on compression wave the second one on surface waves.

3.1 Compression wave technique
The use of compression wave propagation to characterise crack depth is well known [BS96]. It relies on travel time measurements between a source located on one side of the crack and a receiver that is either on the same side or on the opposite side (Figure 8). When the receiver is on the same side, the travel time as a function of the source-receiver distance is a straight line with a slope equal to the inverse of the compression wave velocity. When the receiver crosses the crack there is a characteristic travel time jump that is linked to the depth of the crack. To improve the reliability of the measurement signal stacking is recommend. Furthermore work should be carried out on the signals themselves rather than using black box devices. Indeed in the later equipment, the trigger level may significantly corrupt the quality of the data with no possible control of the operator.

Fig 8: Principe of crack depth determination with compression waves.

3.2 Surface waves technique
The use of surface waves to determine crack depth has also been proposed [HEV98a]. The physical principal relies on the penetration depth of the surface waves that is of the order of the wavelength. Small wavelengths will be reflected by the crack whereas long wavelengths will pass below the crack (Figure 9). The crack can be seen as a filter to surface waves whose cut-off frequency is related to its depth. This filter frequency is obtained by averaging in the frequency domain ratios of the amplitude of two receivers located on either side of the crack. This spectral ratio is denoted Ut/Ui in the following. For each pair of receivers Ut/Ui is calculated for two sources points on each side of the crack. The objective of this experimental procedure is to remove the source function itself as well as the coupling of the receivers. Several pairs of receivers are used to remove modulation noise coming from the fact that the reflected and the transmitted surface wave have not been separated. This procedure, that requires a multi channel acquisition system, has been preferred to a complex signal processing technique for robustness. Work is now going on to incorporate wave separation to the multi-channel procedure.

Fig 9: Principe of crack depth determination with surfaces waves.

3.3 Sensitivity to crack depth
The compression wave method will give the depth of the first contact between the two sides of the crack. The precision of this depth determination can be estimated to be 10%. Note that it will be inefficient if the crack is filled with water.

The interaction of surface waves with a crack either fully open or partially open has been investigated numerically with an Indirect Boundary Element Method (IBEM) [PED94]. In the case of a crack in a semi-infinite medium the average spectral ratio of the transmitted signal to the incident signal is shown figure 10. The cut-off frequency f_c is determined by derivation of these curves. f_c has been empirically set to the lowest frequency at which the slope of the curve shown figure 10 is equal to 0.075. The relation between fc and the crack depth h is given by:

Fig 10: Average spectral ratio calculated for several crack depths indicated in centimetre of the graph.

where V_R is the Rayleigh wave velocity (homogeneous isotropic half space). It should be noted that this result is only valid if the concrete medium can be considered as non dispersive with regards to surface waves propagation (i.e. surface waves velocity do not depend on frequency). It has been verified that the presence of water does not change this result.

3.4 Sensitivity to partial closure
When the crack is partially closed it can be shown that the compression wave method will give the depth of the first contact. If this contact is longer than 2cm, surface waves as well "will not see" the crack below [HEV98b]. If the contact is shorter, the crack depth estimated with the surface waves method will be larger than the depth of the first contact but not equal to the total depth of the crack (except if the contacts are smaller than 1/100 of the total depth of the crack). Both methods are thus complementary. As discussed above, the sensitivity of both acoustic methods has been assessed with regard to water filling. In case of other kind of filling as far as mechanical energy is transmitted through the crack it is expected that the same conclusion as for water can be drawn for the compression wave method: a filling will prevent its use. For surface waves, the important physical parameter is the transmission rate of shear stress trough the filling. If, like in water, it is very small, the surface waves method will not be influenced by the filling. In other instances, it can be expected that only qualitative information could be expected, if no information at all.

4 Coupling of techniques

4.1 Synthesis of theoretical ability of techniques
The two non Destructive Techniques discussed here make it possible to assess some characteristics of cracks.

Electrical resistivity measurements are sensitive to various crack parameters. Previous works prove the link between two main characteristics called as the depth, and the equivalent resistivity of crack (which combines effects of crack opening, resistivity of the filling and crack bridging). Theses two factors lead to anisotropy variations, but at this stage no distinction can be made between their effects, without additional assumptions. It is thus expected that the determination of the crack depth with the acoustic method will constrain the interpretation of the electrical resistivity measurements.

4.2 Coupling of techniques
Methods built on two distinct physical principles (electrical and mechanical) make it possible to determine more reliable crack characteristics: the assessment of crack profile, based on two measurement ways, guarantee the independence of results.

We can propose to assess the crack depth by acoustic measurements, and then use electrical measurements to obtain the intensity of crack (linked to depth and equivalent resistivity of crack). Combination of results leads to distinguish effects of depth and of equivalent resistivity on electrical measurements, then to characterise geometrical profile of the damage.

5 Experimental test on a damage slab

5.1 Presentation of the experimental study
The experimental study is carried out on a concrete test slab 5mx6m x 0.6m (Figure 11). There is no rebar (plastic fibers have been used). Three 5mm wide saw cuts have been introduced in order to model three (ideal) crack depths (4cm, 9cm, 16cm). The aggregate size varies from 0 to 14mm.

Fig 11: Schematic presentation of the test slab with one acoustic set-up drawn.

Electrical and acoustic measurements are realised along three profiles, perpendicularly to each crack.

The electrical measurement sessions are led with two square devices: 5 and 10 cm size, with the both orientations of the set (injection in parallel or perpendicularly to the crack - that is to say respectively PL or PP configuration). We consider in succession three crack conditions - crack filled in by air, by water, and by wet sand - to compare results for various equivalent resistivities for the nine (3 x 3) depth / fillin combinations.

The acoustic set-up consist is 12 sensors located on both side of the cracks. The distance between sensors is 2cm. The sources are steel balls located at the far ends of the slab (in order to be in the far field as in the numerical modelling study). The surface waves velocity is equal to V_R=2400±220m/s. It has been check that it is independent on the frequency for frequency larger than 8 kHz.

5.2 Results
Resistivity profiles are drawn for each case considered (for each depth, for each filling in, and for each device size). The case of a sand filled crack (9 cm depth, 10 cm device) is given as an example on figure 12. We can observe disturbances of electrical resistivity right to the crack, and its expression in term of anisotropy (figure 13).

Fig 12: Apparent resistivity profile (PP and PL) a=10cm - d=9 cm - filled with sand.

Fig 13: Anisotropy profile a=10cm - d=9 cm - filled with sand.

The spectral amplitude ratio for the surface waves method are given on figure 14. The dark zones on the left of each graph correspond to wavelengths that are influenced by the thickness of the slab and thus must not be taken into account. It can be seen that as the crack depth increases the low frequencies are more and more filtered. The experimental curve and corresponding numerical one are matching well. Estimations of the crack depth for the two deeper cracks (9cm and 16cm) are easily obtained with the slope of the curve procedure described above. It is not the case for the shallowest crack even though the filtering effect is still visible and concerned higher frequencies than for the 9cm crack. This might come from the fact that for small wavelengths the concrete cannot be considered as a homogenous material (typically wavelength shorter than 7.5 times the nominal size of the aggregates [CHA02]).

5.3 Coupling
All the electrical measurements, expressed as the log₁₀An, lead to linked depth (p, reported on a, the size of device) and equivalent resistivity (r) of crack (figure 15). The graph is proposed as an abacus allowing to deduce one of the two parameters, the second being given. For example, on figure 15, the equivalent resistivity of crack (r) can be assessed based on the hypothesis on depth (p/a), and the calculation of log₁₀An.

Based on the study of the slope of the curves given Figure 14, the surface wave method give the following depth estimation for the two deeper cracks : 9,7±1,9cm, 16,0 ± 3,4 cm.

Fig 14: Experimental spectral ratio Ut/Ui for the three crack depth (from left to right: 4 cm, 9 cm and 16 cm).

For example, for a blind study of the crack with 9 cm in depth and filled with sand, the assessment by acoustic method of its depth, with its uncertainty, leads to estimate the ratio d/a (depth / size of the set) to be equal to 0,97 ± 0,19. The measurement of electrical anisotropy right to the defect (here Log₁₀An = -1, see on figure 13), should lead to the determination of the equivalent resistivity of crack, as the result of data issued from both techniques (grey arrows on figure 15).

Fig 15: Abacus linking anisotropy (measured), resistivity of the filling and crack depth (two device sizes merged).

At this stage of progress we cannot estimate the accuracy on equivalent resistivity of crack determination. Experimental works have been realised only on three different cracks. We have not enough values with electrical method to be able to choose the corresponding equivalent resistivity of the crack. Works are in progress to complete the abacus (based on numerical modelling).

Even if, results are not complete enough to use the coupling of theses techniques (acoustic and electrical) to assess crack internal characteristics, the proposed approach proves its potential concerning the described problematic.

6 Conclusion

The interest of combining electrical and acoustic methods to characterise cracks has been tested. These two Non Destructive Techniques give complementary information on the defect, since they are based on different physical phenomena. Their coupling leads to clear and to enrich measurements. As information is obtained separately, they are not redundant and they give solutions to exploit more completely measurements.

Though each technique is still in progress, this way is innovating, by the approach, and by the type of results. A lot of parameters are still to study to understand all their influence (bridges, opening ...) but the present results are encouraging and further works are planned.

Besides solutions proposed by each technique independently, the coupling of methods opens on new perspectives for the characterisation of concrete cracks on site.

Bibliographie

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