5. Application to nonlinear characterization of concrete

Consolidated granular media and in particular concrete exhibit a strong nonlinear hysteretic elastic behavior when excited by ultrasonic wave perturbations [23–28]. The nonlinear behavior is strongly enhanced when the concrete is damaged [29]. A significant enhancement of the nonlinear response can be created by one of the numerous damages that might occur within concrete structures via quasi-static loading [30, 31], thermal stresses [8, 32, 33], carbonation [34], corrosion [35], and salt expansion [36]. Here, we show how different damage types affect the nonlinear observations derived from the scaling subtraction method, thus suggesting SSM to be a suitable method to monitor damage evolution in time. We also wish to highlight how nonlinear indicators defined using the SSM approach (particularly the slope b) allow to discriminate between different types of damage.

### 5.1 Load effects on discontinuities in concrete

One of the major effects that create damage in concrete is the application of mechanical loads in the presence of discontinuities. Indeed, discontinuity surfaces are very often the place from where damage may begin its progression. The effects could be the increase in crack density [37] and/or the crack openings [38, 39], depending on the nature of discontinuity such as existing cracks [40] or weak layers [41–43].

In [25], one specimen with an internal discontinuity surface was produced by piling up two concrete cubes (measuring 10 cm on each side). The two pieces were joined using a thin layer of cement paste. Concrete cubes were produced using a concrete mix with CEM II A-L 42.5 R cement, ordinary aggregates (max. size = 16 mm) and a water to cement ratio equal to 0.74, with no admixtures. Their age at the date of testing was approximately 6 months. The evaluation of the mechanical characteristics of the concrete was performed using mono-axial static compression tests that resulted in a compressive strength of 24 N/mm<sup>2</sup> . The longitudinal wave speed in the cube was measured to be V ¼ 3850m=s and the density of the cubes <sup>ρ</sup> <sup>¼</sup> <sup>2330</sup> kg=m3. For this experiment, one emitter (T1) and three receivers (R2, R3, and R4) were used, as schematized in Figure 3. Two receivers (R2 and R3) performed direct transmission measurements; whereas, the third (R4) was used in indirect transmission mode. It is important to note that the direct path from the emitter to R2 and R4 crosses the discontinuity of the concrete, while the path to receiver R3 does not (See Figure 3). Only the results obtained from receiver R4 will be shown here for the sake of conciseness.

As explained above, the evolution of damage as a function of the applied load can be followed using different nonlinear indicators. However, in these experiments, it is important to note that the frequency analysis (using FFT for instance) was not efficient, since the nonlinear indicators related to the possible generated frequencies (higher order harmonics) were below the noise level. Therefore, the application of the traditional nonlinear elastic wave spectroscopy is not expected to be efficient in detecting the presence of nonlinearity during these experiments.

F is the transfer function, u denotes the output signal, and A is the amplification

Consider an elastic wave propagating in a microdamaged medium. In such a case, one might expect that if the propagation excites the nonlinearity of the system, it will consequently break the superposition property. Therefore, if the exciting wave is generated at amplitude A0, small enough so that nonlinearity of the medium is negligible, the system will behave linearly and its response is u0ð Þt . At a larger excitation amplitude A, the response u tð Þ of the same system is no longer equal to

> A A<sup>0</sup>

which would be the response of that system if it remains linear even at large amplitudes. Therefore, the difference between the two responses can be taken as an indicator of nonlinearity. The nonlinear scaled subtracted signal w tð Þ, termed SSM

This time domain analysis of elastic nonlinearity, called scaling subtraction method (SSM), has proved to be sensitive to damage detection and easy to set [16]. From the quantitative point of view, if exciting signals are in the form of monochromatic continuous waves and measurements are taken in standing wave conditions, the SSM signal w(t) is also a continuous wave. Thus, a parameter could be introduced either as the maximum or the "energy" of the nonlinear signal w(t) as

> ðT 0 w2

where T is the wave period. The parameter could then be shown as a function of

where x is the maximum of the output amplitude. Thus, experimental data could be fitted to derive the coefficient a and the parameter b, normally called slope, since

From the point of view of damage monitoring, for a given sample state, a quantitative nonlinear indicator must be defined. To this purpose, we observe that

θ<sup>0</sup> ¼ 1=T

excitation amplitude in order to highlight nonlinearity.

Figure 2.

146

Basic principle of SSM analysis.

in materials exhibiting hysteresis, a power law holds in the form

u0ð Þt (17)

w tðÞ¼ u tðÞ� urefð Þt (18)

θ ¼ maxð Þ w tð Þ (19)

<sup>θ</sup> <sup>¼</sup> ax<sup>b</sup> (21)

ð Þt dt (20)

urefðÞ¼ t

factor. Here, u0 is the response at the excitation amplitude v0.

signal, is introduced as (see Figure 2)

Acoustics of Materials

#### Figure 3.

Experimental set-up based on the use of four identical transducers, one transmitter (T1), and three receivers (R2, R3, and R4).

In general, when comparing different signals at different load levels, even if we observe a change in the signal shape, we should keep in mind that the change might not be due only to the damage of the interface, but also due to the other effects such as a change in the coupling quality or in the transducers arrangement especially when detaching and reattaching transducers. In that sense, it is important to note that the nonlinearity indication provided by the SSM represents an absolute measure since the reference signal is contained in the measurement itself.

In [35], ultrasonic tests were performed on one reinforced concrete sample

Evolution of the SSM indicator θ as a function of energy of the output signal in the case of the low-quality layer

Time Domain Analysis of Elastic Nonlinearity in Concrete Using Continuous Waves

DOI: http://dx.doi.org/10.5772/intechopen.82621

located approximately in its center, making a reinforcement ratio corresponding to 0.19% (see Figure 5). Ultrasonic measurements consisted in exciting the sample using sinusoidal bursts at increasing amplitudes (10 cycles of 55.5 kHz frequency). Ultrasonic measurements were performed at different corrosion steps, as induced by an accelerated corrosion set-up, and data analysis was made on the basis of linear and nonlinear indicators. Linear indicators were the ultrasonic phase velocity (compression mode) and attenuation. Linear wave velocity was determined using the lowest excitation amplitude. Since transducers were removed before the beginning of each accelerated corrosion step, it was preliminarily verified that effects due to small differences in coupling were negligible compared to the ones induced by corrosion. Transducer positioning was made in such a way to be able to detect the direct transmission of the traveling ultrasonic wave. Furthermore, another transducer was put on the same side as the transmitter (at 15 cm) in order to estimate the sensitivity of the proposed techniques when the access to the opposite face is not

Reinforced concrete samples affected by an important corrosion (left); ultrasonic transmitters and receivers

), which contained a steel bar (14 mm of diameter)

sizing (90 <sup>90</sup> 500 mm<sup>3</sup>

possible.

Figure 5.

149

placed on the concrete sample (right).

Figure 4.

discontinuity.

Experimental results from [25] are shown in Figure 4. As anticipated above, the latter refers to signals recorded by the receiver R4. The SSM indicator ð Þθ shows that the increase of load does not immediately cause a raise of nonlinearity, which starts to increase slightly only from 10 to 50 kN. However, we notice a clear increase in θ for higher loads, when the specimen is close to collapse, where fractures close to the bonding layer become evident around 90 kN. The log-log scale of θ on the same figure shows that θ changes linearly as a function of the amplitude. The slope of this logarithm evolution, which is around �2 at low loading steps, becomes �3 for higher load levels. Therefore, the evolution of nonlinearity as a function of damage progression can be appreciated, for a fixed value of the input energy, by analyzing the nonlinear indicator as a function of the applied load. This is done by extrapolating θ from the fitting function in order to obtain (θð ÞÞ x<sup>0</sup> at each loading step.

The trend presented in Figure 4 leads to the following conclusions. The low compressive loads create a rearrangement of the internal structure (e.g., pores closing) where the damage in the discontinuity is expected to be minor. When loads are increased (up to �50% of the failure load), the nonlinearity increases slightly, and early damage (microdamage) is expected in the discontinuity. Finally, macrodamage is created at loads larger than �50% of the failure load, where a clear change of the slope is observed.

#### 5.2 Corrosion effect on elastic properties of reinforced concrete

Steel corrosion in reinforced concrete elements has negative effects on their load carrying capacity [44]. Furthermore, the expansion of the oxidation products creates cracking [45, 46] and deteriorates the bond between steel and concrete [47]. The overall weakening of the concrete structures by reinforcement corrosion is then expected [48].

Time Domain Analysis of Elastic Nonlinearity in Concrete Using Continuous Waves DOI: http://dx.doi.org/10.5772/intechopen.82621

#### Figure 4.

In general, when comparing different signals at different load levels, even if we observe a change in the signal shape, we should keep in mind that the change might not be due only to the damage of the interface, but also due to the other effects such as a change in the coupling quality or in the transducers arrangement especially when detaching and reattaching transducers. In that sense, it is important to note that the nonlinearity indication provided by the SSM represents an absolute mea-

Experimental set-up based on the use of four identical transducers, one transmitter (T1), and three receivers

Experimental results from [25] are shown in Figure 4. As anticipated above, the latter refers to signals recorded by the receiver R4. The SSM indicator ð Þθ shows that the increase of load does not immediately cause a raise of nonlinearity, which starts to increase slightly only from 10 to 50 kN. However, we notice a clear increase in θ for higher loads, when the specimen is close to collapse, where fractures close to the bonding layer become evident around 90 kN. The log-log scale of θ on the same figure shows that θ changes linearly as a function of the amplitude. The slope of this logarithm evolution, which is around �2 at low loading steps, becomes �3 for higher load levels. Therefore, the evolution of nonlinearity as a function of damage progression can be appreciated, for a fixed value of the input energy, by analyzing the nonlinear indicator as a function of the applied load. This is done by extrapolating θ from the fitting function in order to obtain (θð ÞÞ x<sup>0</sup> at each loading step. The trend presented in Figure 4 leads to the following conclusions. The low compressive loads create a rearrangement of the internal structure (e.g., pores closing) where the damage in the discontinuity is expected to be minor. When loads are increased (up to �50% of the failure load), the nonlinearity increases slightly, and early damage (microdamage) is expected in the discontinuity. Finally,

macrodamage is created at loads larger than �50% of the failure load, where a clear

Steel corrosion in reinforced concrete elements has negative effects on their load carrying capacity [44]. Furthermore, the expansion of the oxidation products creates cracking [45, 46] and deteriorates the bond between steel and concrete [47]. The overall weakening of the concrete structures by reinforcement corrosion is then

5.2 Corrosion effect on elastic properties of reinforced concrete

change of the slope is observed.

expected [48].

148

Figure 3.

(R2, R3, and R4).

Acoustics of Materials

sure since the reference signal is contained in the measurement itself.

Evolution of the SSM indicator θ as a function of energy of the output signal in the case of the low-quality layer discontinuity.

In [35], ultrasonic tests were performed on one reinforced concrete sample sizing (90 <sup>90</sup> 500 mm<sup>3</sup> ), which contained a steel bar (14 mm of diameter) located approximately in its center, making a reinforcement ratio corresponding to 0.19% (see Figure 5). Ultrasonic measurements consisted in exciting the sample using sinusoidal bursts at increasing amplitudes (10 cycles of 55.5 kHz frequency). Ultrasonic measurements were performed at different corrosion steps, as induced by an accelerated corrosion set-up, and data analysis was made on the basis of linear and nonlinear indicators. Linear indicators were the ultrasonic phase velocity (compression mode) and attenuation. Linear wave velocity was determined using the lowest excitation amplitude. Since transducers were removed before the beginning of each accelerated corrosion step, it was preliminarily verified that effects due to small differences in coupling were negligible compared to the ones induced by corrosion. Transducer positioning was made in such a way to be able to detect the direct transmission of the traveling ultrasonic wave. Furthermore, another transducer was put on the same side as the transmitter (at 15 cm) in order to estimate the sensitivity of the proposed techniques when the access to the opposite face is not possible.

#### Figure 5.

Reinforced concrete samples affected by an important corrosion (left); ultrasonic transmitters and receivers placed on the concrete sample (right).

At the time when linear indicators, namely ultrasonic velocity and attenuation, manifested a weak sensitivity to corrosion (the velocity regularly but slightly decreases and the attenuation increases), the nonlinear indicator showed an important evolution. Indeed, the relative variations corresponding to velocity and attenuation as a function of the corrosion step were determined as 4 and 70% at most, respectively. However, larger effects were observed for the relative variation of the nonlinear indicator by changing up to 350%. Here, it should be pointed out that when comparing the first and the last corrosion steps (instead of considering as reference the intact sample), the relative change of the velocity and attenuation were 1.5 and 30%, respectively, while the nonlinear indicator was 250%. This evolution shows the high sensitivity of nonlinear methods to the microstructure modifications due to corrosion. Finally, the nonlinear indicator remains sensitive to corrosion creation and evolution even when the access to the opposite side of the corroded concrete samples is not possible. Indeed, Figure 6 shows that the nonlinear indicator extracted from data of receivers 1 and 2 was almost the same at the first two stages of corrosion. For the last two corrosion states, a difference can be noticed between both results, but the increase of sensitivity to corrosion is clearly visible for both sensors.

flight, but it proved to be only slightly sensitive to the increase of damage and without any difference in the behavior of samples with small and large aggregates

Time Domain Analysis of Elastic Nonlinearity in Concrete Using Continuous Waves

Thus, in order to appreciate the different behaviors expected for the different samples, the SSM technique was applied as discussed previously, with ultrasonic sensors attached on the bases of the sample prisms. Results are reported in Figure 7, where the nonlinear parameter is shown vs. the output amplitude. It is possible to observe that damage starts earlier in the sample with large aggregates, as expected. Macrocracks are more rapidly formed and at the largest thermal excitation, the

Furthermore, it is also possible to observe a change in slope (nonlinear indicator b) when macrocracks start appearing (large aggregates case only). This is similar to what observed for the case of quasi-static loadings. Indeed, in both quasi-static and thermal cases, the situation is similar: microcracking (first) and coalescence into macrocracks (later) is due to the presence of localized mechanical stresses (due to load or local gradients of thermal expansion), without the formation of any reaction products, as in the cases of corrosion and salt expansion (see next subsection).

The presence of soluble salts into capillary water is one of the major problems affecting masonry structures. Numerous works pointed out the potential noxiousness of water-transported salts (which might happen during repeated wet-dry cycles). Indeed, due to crystallization of some salts in the form of expansive compounds, progressive cracking and detachment phenomena happen especially at the interfaces between different material layers. In that sense, there is a clear need to develop an effective and reliable diagnosis of the onset of such damage phenomena in order to make corrective actions, in terms of repair and maintenance optimization, possible [49–53]. The close interaction between the ultrasonic wave and the material mechanical/elastic properties made ultrasonic methods widely used for

Nonlinear parameter vs. output amplitude for samples with small and large aggregates at different levels of

sizes.

Figure 7.

151

thermal damage.

increase in nonlinearity is noticeable.

DOI: http://dx.doi.org/10.5772/intechopen.82621

5.4 Degradation by expansive salts in masonry systems
