EVALUATION OF DAMAGES DUE TO ALKALI-SILICA REACTION WITH ACOUSTICS TECHNIQUES. DEVELOPMENT OF A NEW NONLINEAR METHOD.

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1 EVALUATION OF DAMAGES DUE TO ALKALI-SILICA REACTION WITH ACOUSTICS TECHNIQUES. DEVELOPMENT OF A NEW NONLINEAR METHOD. Apedovi S. Kodjo (1, 2), Patrice Rivard (1), Frederic Cohen-Tenoudji (3) and Jean-Louis Gallias (2) (1) Centre de Recherche sur les Infrastructures en Béton (CRIB), Université de Sherbrooke, Canada (2) Laboratoire de Mécanique Matériaux du Génie Civil (L2MGC), Université de Cergy- Pontoise, France (3) Laboratoire de Mécanique Physique (LMP) Université Paris 7, France Abstract Using reliable and effective nondestructive techniques (NDT) to evaluate and quantify the degree of damage in concrete structures remains challenging. Studies recently indicated that certain tools from nonlinear acoustics seem promising for the characterization of cracks or microcracks developed in concrete structures. Very few of these tools are currently applied in the field, their implementation causing various problems. This paper proposes a new method based on nonlinear acoustics to characterize the concrete deterioration, especially the damage associated with alkali-silica reaction (ASR). This method consists in quantifying the influence of an external mechanical disturbance on the propagation of an ultrasonic compression wave in the material. This influence is related to the local distortion induced by the disturbance in the structure and is closely associated with the density and specificities of the crack network in concrete. ASR damaged and non-reactive concrete specimens were submitted to various uniaxial stress levels while compression waves velocity were measured transversally. Relevant indicators of nonlinearity were highlighted in order to better assessing of the ASR effects on the structure. Measurements were also performed on concrete samples where external stress was applied in order to assess the influence of this parameter on the method. The results obtained confirm the relevance and effectiveness of this method and open up new prospects for in situ application. Keywords: Nonlinear acoustics, Damage assessment, Alkali-silica reaction, Nondestructive testing. 1. INTRODUCTION Alkali-silica reaction (ASR) causes the swelling and cracking of concrete structures. The expansion is due to the formation of a reaction product, the silica gel, which swells at moisture levels above about 85% R.H. This expansive gel induces tensile stress within

2 aggregates and cement paste, and might lead to the formation of a microcrack network through the concrete when the material tensile strength is reached. In order to rehabilitate concrete suffering from ASR, it is required to conduct a systematic assessment of the concrete condition prior to specifying any kind of repair procedure. Researchers and engineers are thus developing innovative methods for condition assessment, performance prediction, and maintenance management for the cost-effective rehabilitation of ASR-affected structures. Nondestructive methods based on nonlinear elasticity could be very effective for such task. Recent work carried out on rocks showed that the sensitivity of nonlinear elasticity for detecting various defect types is greater than the wave velocity or attenuation measurements performed in linear propagation mode [1]. This paper deals with the analysis of the nonlinear behaviour, mainly the hysteretic and slow dynamics, observed on concrete samples affected by ASR. A nonlinear technique, which can be applied in-situ, is then proposed. This technique would enable following the variation of the material elastic properties after a disturbance, such as an impact generated by a hammer. The principle consists to produce a mechanical disturbance through a specimen, while an ultrasonic compression wave is propagating in transmission mode. This disturbance creates a variation of the compression wave that is proportional to the specimen damage level. With proper analysis techniques, specific parameters, such as the standardized variation of propagation velocity, the dynamic attenuation, allowed assessing the degree of damage of the concrete. 2. THEORETICAL BACKGROUND Linear acoustic refers to low amplitude waves propagation. The elastic strains occurring are so low that the stress waves do not modify the elastic properties of the material. In nonlinear mode, the wave amplitude is much higher, and significant local deformations are created by the waves propagation. These deformations cause the modification of the material elastic properties, inducing a nonlinear behaviour. The cause of the non-linearity is related to the micro-defects within the concrete. In the specific case of ASR, the microcracks are subjected to various cycles of closing/opening due to pressure of the propagating compression waves. The behaviour of such cycles is also linked to the crack orientation with respect to the pressure direction. Depending on this orientation, the material rigidity will either reduce or increase, if cracks are opened or closed [2]. To describe some nonlinear phenomenon such as nonlinear hysteresis, the models of Priesach and Mayergosz (P-M) was used as basis in the development of some nonlinear models [3, 4]. The P-M model is based on the assumption that the macroscopic elastic properties of the tested material result from the integral response of a large number of individual elastic elements. These elements (HEU: Hysteretic Elastic Unit) are made from inter-grain boundaries, microcracks and other discontinuities. Each elastic element may or not show hysteretic behaviour between two configurations (opened or closed) depending on the stress to which it is subjected [3]. In the nonlinear mode, the Hooke s law can be written as: ^ 2 3 ε ( ε + βε + δε +...) + S ε sign σ = M, t (1)

3 where σ is the stress, ε is the deformation, M is the Young modulus, and ^ S is a function describing the hysteresis. The nonlinear behaviour of a tested sample can stem from several phenomena, such as the slow dynamical effects, the dynamic attenuation, and others. Previous research reported that the nonlinear hysteretic is strongly linked to the phenomenon of slow dynamic [2,3,5]. A simple model for the variation of the Young modulus ( M) in the nonlinear mode can be put forward to explain this phenomenon, assuming a constant time relaxation τ [2] (Fig.1): in d M τ + M = λg dt Figure 1: Slow dynamic behaviour n out Introducing a signal having the form Gθ (t), where θ (t) is Heaviside function defined by θ (t) = for t < θ (t) = 1 for t, G is displacement amplitude, λ is hysteresis coefficient. The specimen response form is then: n t /τ M ( t) = λg (1 e ) (2) However, experimental observations made on rock samples showed that the relaxation process is a time logarithmic function rather than an exponential function [3]. TenCate et al. [5] explained this effect by the statistics of bond restoration at microscopic contacts area in media after their rupture by a mechanic disturbance. The P-M model states that the nonlinear response of the tested solid stems from the integral response of a large number of individual elastic units. These elastic elements may not react to the disturbance at the same time. Actually, each elastic unit can be considered to have its own response time. Thus, the integral response of the medium depends on the average response of the whole elastic units. 3. EXPERIMENT CONFIGURATION AND RESULTS 3.1 Quasi-static experience In order to demonstrate the dependence of the velocity variation regarding the cracks dissymmetrical closing/opening cycles, quasi-static testing was carried out on two specimens. The first specimen was affected by ASR, while the second one was sound concrete. Both specimens were made with the same concrete mixture proportions, except the first one was made with reactive limestone aggregates. The experimental procedure consisted to apply, on the tested sample, different levels of compression static stress with an hydraulic press (Fig. 2). The maximum applied stress (5 MPa, which is about 2% of the concrete compressive strength) was considered to be in the elastic range of the material. The stress was applied along a single axis (uniaxial) and the waves propagate perpendicular to the direction of the applied static stress. The velocity of a compression wave was measured, which allowed following the response of the sample regarding the stress applied during a cycle of loadingunloading. Indeed, when the uniaxial load was applied on the sample, in the direction perpendicular to the load, the sample is in traction; what will cause the opening of the microscopic cracks [2]. The transducers are sensitive to the cracks that are perpendicular to

4 the direction of wave propagation. This configuration allows observing only the open cracks that are in the direction of load, thus perpendicular to the direction of wave propagation. The opening leads to a variation of the propagation velocity of compression waves. Fig. 3 shows that the velocity of the damaged specimen varies much more than that of intact: a variation of about.5 for 1MPa was observed for the damaged sample while the curves remained nearly flat the intact sample. Moreover, the damaged specimen showed a significant hysteresis compared with the intact specimen. Figure 2: Quasi-static experience,12,1 dv/v,8,6,4,2 Damaged Intact stress (MPa) Figure 3: Compression wave velocity variation versus compression stress. 3.2 New nonlinear method A series of acoustic waves was generated through the specimen with a piezoelectric transducer (Fig. 4). During this time, an impact was applied on the specimen causing mechanical disturbances; i.e. cycles of opening/closing in cracks, filled or not with silica gel. The hysteretic behaviour of the material stemming from to the mechanical dissymmetry of the opening/closing cycles increased the cracks opening with the successive impacts. The crack opening after the impact caused a temporal delay on the wave arrival. Thus, the delay and the magnitude spectrum variation of the signal enable the evaluation of the crack density per volume unit, which can be indicative of the concrete damage level. The calculation is made taking into account, as reference, the wave propagation (velocity and amplitude) when the specimen is in the relaxed state. The delay and signal spectrum magnitude variation allowed

5 calculating two nonlinear indicators, defined respectively as the disturbance rate τ V and the dynamic attenuation τ A (Fig.5). Figure 4: Experimental settings S ( f w ) amplitude (Volts) Amplitude (Volts) t P a) b) Figure 5: Ultrasonic signal; (a) time domain; (b) frequency domain VP τ = 1 V α (3) VP α Coefficient of standardization applied to avoid digits. (For our resultsα = 1 ) t p, ultrasonic wave arrival time. V, propagation velocity before impact. P S( f w ) before _ impact τ A = 1log1 (db) (4) S( f w ) after _ impact S ( f time (microseconds) ), Fourier magnitude spectrum. f w frequency (KHz)

6 With an attempt to demonstrate the slow dynamic relaxation processes before disturbance, tests were carried out on two concrete specimens (one made with sound concrete, the second affected by ASR). Figure 6 shows that the dynamic attenuation of the intact specimen decreased before the damaged specimen. Others tests were carried out on four concrete cores, referred to as E1, E2, E3, and E4. These cores were taken from the same hydraulic structure and they exhibited different degrees of damage associated with ASR [6]. The visual examination of cores E1, E2, E3 pointed out the presence of several cracks partially or totally filled with gel. No significant damage was observed on core E4. Figures 7a to 7d show the disturbance rate measurements for various samples during a serie of 1 impacts. Figure 8 shows the comparative results for the 4 cores. Two kinds of behaviour can be observed. A higher disturbance rate was measured for cores E1, E2 and E3 compared with core E4. The disturbance rate of the undamaged core varied little during the impacts and quickly reached a limit value of about 15. On the other hand, the disturbance rate increased significantly after each impact for the damaged cores, and reached an asymptotic trend, which is about 5 for the most deteriorated core (Fig. 8). Regarding the damaged cores, the first impact, transmitted to the specimen some energy, which produced a partial opening of the cracks. With the following impact, due to the relaxation process in time logarithmic "phenomenon of slow dynamics", the specimen was not allowed to relax (i.e. the cracks did not have time to close up). Therefore, additional energy was provided from successive impacts, increasing the opening of the cracks until the maximum opening has been reached. With the same impact energy, the specimen E4 reached its maximum opening prior to the damaged samples. Results showed that the presence of cracks in concrete leads to an increasing disturbance rate with the successive impacts. Without significant damage level, the disturbance rate remained low and did not increase much. This conclusion was confirmed with a Plexiglas specimen, an homogeneous material that does not present any damage (Fig. 8). Results indicated that the Plexiglas specimen does not present any disturbance due to the impacts. 7 5 attenuation (db) 3 1 damaged intact -1 Impact time (s) Figure 6: Dynamic attenuation

7 6 Impact 1 disturbance rate 4 2 Impact Impacts time (s) Figure 7a: Disturbance rate of specimen E1 6 disturbance rate 4 2 Impact 1 Impact Impacts time (s) Figure 7b: Disturbance rate of core E2

8 6 disturbance rate 4 2 Impact 1 Impact Impacts time (s) Figure 7c: Disturbance rate of core E3 6 disturbance rate 4 2 Impact 1 Impact Impacts time (s) Figure 7d: Disturbance rate of core E4

9 disturbance rate E3 E4 E1 E2 Plexiglas Number of impacts Figure 8: Disturbance rate variations with impacts number 4. CONCLUSION A new non-destructive technique for assessing concrete damage was developed. This technique is based on the theory of non-linearity according to the model proposed by Priesach-Mayergosz and uses the material response to a mechanical disturbance. The specimen response to this disturbance shows its slow dynamic relaxation, which allowed evaluating the concrete damage level. It was initially showed by a quasi-static test the nonlinear behaviour of samples affected by ASR. The results showed the relevance of the technique to discerning sound concrete from concrete damaged by ASR. Compression wave velocity was measured. For the damaged concrete, the velocity was 436 m/s, while it was 422 m/s for the sound concrete; the velocities were about the same. The new technique indicated that the damaged concrete showed a disturbance rate 3 times higher than that sound concrete. However, on a field structure, two factors may impede the application of this technique: - confinement stress within structure due to its own mass and to the swelling gel; - accessibility of the structure members for transmission mode. Work is currently being conducted in order to improve the technique for in situ applications. Furthermore, research will be carried out to assess other deterioration processes, such as freeze/thaw cycles, with the attempt to characterize the damage typically associated with ASR. ACKNOWLEDGEMENTS The authors wish to thanks CRIB technical staff. Financial support has been provided by the Natural Science and Engineering Research Council of Canada (NSERC) and by the Fonds québécois de recherche sur la nature et les technologies (FQRNT).

10 REFERENCES [1] Koen Van Den Abeele, A. Sutin, J. Carmeliet, P. Johnson, Micro-damage diagnostics using nonlinear elastic wave spectroscopy, NDT&E International 34 (21) [2] P. Rasolofosaon, B. Zinszner et P. Johnson, Propagation des ondes élastiques dans les matériaux non linéaires, Revue de l Institut Française du Pétrole, 52, (6) (1997) [3] L. A. Ostrovsky and P. Johnson, Dynamic nonlinear elasticity in geomaterials, La Rivista del Nuovo Cimento, 24 (7) (21). [4] K.R. Mc Call, and R.A. Guyer, Equation of state and wave propagation in hysteretic non linear elastic material, Geophysical Research Letters, 99, (23) (1994) [5] J. TenCate, E. Smith, R. A. Guyer, Universal Slow Dynamics in Granular Solids, Physical Review Letters, 85, (5) (2) [6] P. Rivard, G. Ballivy, S. Rousseau, Relationships between physical and mechanical properties of concrete affected by alkali-silica reaction: application in field, 7 th CANMET/ACI Conference on durability of concrete, Montréal, May 26.