In reinforced concrete (RC) structures, an evidence of damage is the presence of cracking. In order to evaluate the effect of damage on cracking pattern and natural frequency in RC slabs, two of such structures with different dimensions and reinforcement ratios were tested, in which cracks were induced through application of static load, followed by modal tests using impact excitation. The paper aims to discuss this issue.
The gradient of the fundamental natural frequency along the decay, the crack opening rate and also a global damage index based on changes of the fundamental natural frequency were evaluated.
The behaviour of the aforementioned gradient was distinct for both slabs, increasing monotonically with the cracking level for the slab with lowest reinforcement ratio, and increasing until 33 per cent of the collapse load and then decreasing afterwards for the slab with the highest ratio. Changes of the gradient were consistent with changes of the crack opening rate. Both results of gradient changes and cracking pattern brought evidence that the balance between open (old) and breathing (new) cracks differed between the slabs, and may be responsible for such differences.
Damage assessment in RC structures using vibration tests is mostly concentrated on beams. In this work, an advance is made by investigating slabs. The lack of a unique pattern of changes of the gradient implies that its absolute value is not generally suitable for the association with the damage level. However, the impact tests can be effectively used to detect early damage on slabs using this proposed parameter.
Ferreira, G.S., Guedes, T.O., Melo, L.F., Gonçalves, M.S. and Pimentel, R. (2019), "Damage assessment of reinforced concrete flat slabs through modal tests using impact excitation", International Journal of Structural Integrity, Vol. 10 No. 2, pp. 265-275. https://doi.org/10.1108/IJSI-08-2018-0049Download as .RIS
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A variety of pathologies can affect reinforced concrete (RC) structures, such as voids during casting of concrete, excessive load, consequences of design errors, among others. One of the signs of problems is the presence of cracks. Since cracking changes the structure’s stiffness, it is possible to associate the detection, localisation and quantification of damage with changes in vibratory properties, such as natural frequencies, mode shapes or damping ratios. Applications regarding this in different structures and employing different techniques can be cited (Zanuy et al., 2014; Capozucca and Magagnini, 2017; Xu et al., 2018; Cao et al., 2017). The choice of the damage evaluation technique depends on the level of information that can be extracted from data as well as on the structural behaviour after damage.
By considering the structural behaviour, two groups of techniques can be specified. The first one is the group of linear techniques, which considers that the structure is approximately linear after damage, within a certain range of excitation, and, consequently, a direct relationship is assumed between changes in vibratory properties (natural frequencies, mode shapes and damping ratios) and changes in physical properties (mass, stiffness and damping). Fan and Quiao (2010) made a classification of these techniques into four categories: based on mode shape, based on curvature mode shape changes, based on natural frequencies, and on a combination of natural frequencies and mode shapes. Dawari and Vesmawala (2013) employed modal curvature and modal flexibility to detect concrete voids in RC beams. Rucevskis et al. (2016), in turn, employed modal curvature to detect damage on metal plates, but without the need of a baseline for the undamaged state, and successfully detected the existing damage. In another approach, Reynders and De Roeck (2010) employed the local flexibility method to evaluate stiffness changes on beams that had different levels of damage and were excited by impact load.
The second group of techniques considers nonlinear behaviour, which, in principle, tends to be more realistic, since non-linearity is an intrinsic condition of RC cracked structures. Therefore, the crack pattern during the excitation stage or immediately after it is relevant, and there are two major cracking models: the models that consider the cracks remaining open (called open crack models), and the models considering cracks opening and closing (called breathing cracks models) (Nguyen, 2013; Andreaus et al., 2007; Chondros et al., 2001). Breathing cracks, in special, are sources of non-linearity because they change the stiffness of the structure during the process of vibration. The majority of the works explored this feature of breathing cracks through use of cyclic excitation (Cheng et al., 1999; Andreaus and Baragatti, 2011; Bovsunovsky and Surace, 2005; Xu and Castel, 2016).
Still in the group of non-linear damage detection techniques, the use of impact excitation in concrete structures remains less explored, although it is a quick assessment technique, with data being promptly acquired by few sensors positioned on the structure. The majority of works using this technique are devoted to beams. Neild et al. (2003) carried out tests with impact excitation on beams for increasing damage levels produced by static load intercalated by modal tests, and explored the changes of natural frequency along the decay as a nonlinear assessment method. An addition to the previous research line was made by Zhu and Law (2007) who applied the Hilbert–Huang transform on cracked RC beams to evaluate the changes in natural frequency along the decay. Wang et al. (2012), in turn, tested RC beams and proposed a window width to evaluate the natural frequencies after the impact.
Different from beams, RC slabs have a crack pattern in which the existing cracks tend to spread on the surface of the structure. Still, a factor that can affect the crack pattern is the reinforcement ratio. Han (2011) observed that the transverse reinforcement in one-way slabs can restrain flexural crack opening, indicating that this reinforcement can modify the cracking pattern, as was also observed by Lantsoght et al. (2013) in slabs under concentrated load. The influence of reinforcement ratio in RC slabs was also noticed when they were subjected to blast loads because the deformation and damage degree decreased with the increase in this ratio (Yao et al., 2016).
In this paper, which is a follow-up of a previous investigation (Pimentel et al., 2017), this phenomenon was explored in two RC slabs with different dimensions and reinforcement ratios, subjected to increasing static loads applied in stages and intercalated by modal tests. The change in natural frequency along the decay for various load levels was explored, and its gradient was related to a global damage index based on the first natural frequency for undamaged and damaged scenarios. The crack opening rate of both slabs was used to evaluate the behaviour of the gradient of frequency with crack level.
2. Description of the prototype structures and tests
Two RC slabs were tested in laboratory. The first one, named S1, had a length of 3.0 m and a width of 1.35 m, with rebars of 5.0 mm diameter spaced 9.0 cm along the width and 22.0 cm along the length. The properties of the materials employed were steel with yielding stress 500 MPa and concrete with 25 MPa of compression strength. The second slab, named S2, had a length of 2.50 m and was 1.65 m wide, using rebars of 6.3 mm spaced 7.0 cm along the width and 7.5 cm along the length, and a concrete of 30 MPa of compression strength. The longitudinal and transverse reinforcement ratio in the slabs were, respectively, 2.15 and 0.98 cm2/m for slab S1, and 4,36 cm2/m and 4,05 cm2/m for slab S2. Both slabs were 0.08 m thick and simply supported along all their width (Figure 1). A test mesh was marked on top of the slab surface, for use during the modal tests (Figure 2). An identical mesh was marked at the bottom surface so as to locate the cracks.
In slab S1, the test points were 28.75 cm apart along the width and 48.33 cm apart along the length. In addition, intermediate points along the length were marked in the central line. This way, slab S1 had a total of 42 test points (see Figure 3(a)). In slab S2, due to its different dimensions in comparison with slab S1, an approximately square mesh was employed, being 25 cm by 25.6 cm apart along the width and length, respectively, with a total of 77 test points (see Figure 3(b)). The mesh dimensions were selected bearing in mind that good resolution is attained for the mode shapes to be obtained, in particular for the first mode. Due to the way the slabs are supported, the first mode has the shape of a beam-like mode. This way, more than ten test points were marked along the central line of each slab, in the direction of the length. This was considered to be sufficient to follow adequately the expected sinusoidal shape of the first mode. The remaining test points were equally distributed along each slab surface, so as mode shape alterations due to cracking could be followed.
For the modal test, the choice of the driving point position was made after preliminary tests and numerical modelling, in order to identify the mode shapes of interest, including the first mode. In slab S1, a single driving point was adopted (test point 12), whereas in slab S2, two driving points were used (points 18 and 62). The use of more test and driving points in the second slab was due to the experience acquired after the tests in the first slab, in particular for obtaining accurate mode shapes.
The excitation was applied in each point using an instrumented impact hammer B&K model 8210. At the driving points, an Endevco accelerometer model 752A13 was placed, having a sensitivity of 1 V/g. A spectrum analyser Dataphysics Quattro was employed to acquire the excitation and response signals, and was connected to a PC Notebook. Each acquired signal lasted 4 s and had 4,096 points for the tests in slab S1, and 8 s with 8,192 points for the tests in slab S2, using, in both cases, five impacts in each test point so as to obtain average frequency response functions (FRFs) with minimised noise effects. Modal parameters were obtained using StarModal software (Spectral Dynamics, 2001). The software employs a special hybrid algorithm that uses least-squares complex exponential and polynomial techniques to extract the modal properties from the whole set of input FRFs. The operation is interactive and requires user intervention in defining frequency bands and number of modes to be identified in each frequency band. As for the first mode, it was clearly identified as an isolated first peak at the FRFs. This way, in this case, a frequency band was defined to include the first mode alone.
The responses in time domain were filtered later on, to isolate the component of response at the fundamental natural frequency of the tested slab. The band-pass filter employed was a basic house-made application running in Matlab software. The isolation of the frequency component of interest was carried out in the frequency domain after applying a Fourier transform to the time domain signal. An inverse Fourier transform returned the filtered time domain signal, and frequency spectra of the original and filtered signals were compared to assure the filtering procedure was successful. Then, the variation of the fundamental frequency along the decay of the signal after impact was obtained for each level of induced damage, and is discussed in the following section. It should be mentioned that not all the data acquired during the modal tests were employed in this paper; this is just a general description of the whole test setup.
After the modal test was performed in the uncracked slab, which was used as a reference, the next step was the application of static load (see Figure 1). The static load apparatus consisted of two metallic beams positioned at 1/3 and 2/3 of slab’s main span and parallel to the supports, with the load being measured by a load cell of 1 MN capacity connected to an Ahlborn data logger model Almemo 2890-9.
Static loads were applied in both slabs, in stages. In slab S1, three stages were applied, which were 8, 16 and 22 kN, corresponding, respectively, to 33.3, 66.6 and 91.7 per cent of the collapse load. In slab S2, the stages were 3, 6, 9, 12, 15, 18, 21, 24, 27 and 42.5 kN, and the collapse was reached for a load of 62.5 kN. After each load stage and disassembling of the static load apparatus, modal tests were performed as previously described, with the aim of evaluating the changes on modal properties and the crack rise, the cracks being marked at the bottom surface of the slab.
3. Results and discussion
3.1 Cracking and natural frequency
The pattern of cracking for both slabs are shown in Figures 4 and 5, until near or at the collapse. A difference is observed in the crack intensity in early load levels (33 per cent of the collapse load), in which slab S2 showed a much severe crack rise. A change on reinforcement is a factor that can cause variation in cracking pattern (Han, 2011; Lantsoght et al., 2013; Gurutzeaga et al., 2015; Han et al., 2011).
The fundamental natural frequency of uncracked and cracked slabs is shown in Figure 6 as a function of the percentage of the collapse load and, thus, the crack level. There is a decrease in the first natural frequency of slab S1, as observed in several tested RC elements (Pesic et al., 2015). The behaviour of slab S2 is similar to slab S1 up to 40 per cent of the collapse load; after that, it showed an almost steady value of natural frequency until 70 per cent of the collapse load. It was not possible to carry on measurements at high levels of load for this slab due to a logistic problem. However, since cracking reduces the stiffness of the slab and thus its natural frequency, it can be seen that the changes of natural frequency in each slab are consistent with its respective cracking pattern. This is because the cracking intensity is much higher in slab S2 than in slab S1 for low percentage levels of the applied load. Slab S2 also has a variation of natural frequency to damage that resembles the behaviour observed in Hamad et al. (2014), in which the fundamental natural frequency stabilized after 60 per cent of the collapse load.
3.2 Gradient of natural frequency
Natural frequencies grew along the decay of response after impact excitation, as the cracks initially opened tend to close with the reduction of the vibration level. This made it possible to obtain curves of variation of natural frequency along the decay. For a given modal test, since the level of vibration differed among different test points, first, each response signal had a decay interval selected for further processing in order to keep constant the amplitude of the first cycle of vibration among the signals. In sequence, the natural frequency was calculated for each vibration cycle; a curve was then obtained when plotting the natural frequency against the cycle number. Linear regression was then applied, and a gradient was obtained from the curve. This procedure was repeated for several test points in each cracking stage, and then an average regression line was produced for that stage of induced cracking. Finally, in order to better compare frequency regression lines from different cracking conditions, each average regression line was re-plotted employing relative frequency values, which were obtained by taking the ratio of the instantaneous natural frequency and the maximum natural frequency observed in that respective regression line. The value of the gradient of each final average regression line representative of a cracking condition was calculated and plotted in Figure 7, against the percentage of ultimate load applied to induce cracking in the respective slab.
The pattern of changes of the gradient in slab S2 is in accordance with results obtained for beams tested in similar conditions by Neild et al. (2003) and Wang et al. (2012), who observed that the gradient grew until an intermediate level of damage and then decreased. Herein, the growth of the gradient occurred for slab S2 until 33 per cent of the collapse load, and then reduced for the following load levels. However, for slab S1, there is growth of the gradient until near the collapse. A possible explanation for this difference would be a distinct balance between the existing breathing and open cracks in both slabs for a given percentage of the collapse load, reminding that it is the breathing crack that causes the variation of natural frequency along the decay. Still regarding this, it could be argued that amplitude dependent material behaviour would lead to changes in natural frequencies along the decay, independent of the cracking condition and even for the uncracked state. This was already investigated (Pimentel et al., 2017) and it was shown that the gradient of time–frequency curves due to damage could be distinguished from other causes related to non-linear behaviour of the tested slabs.
RC slabs can present a residual deflection after unloading and some of the cracks remain open, as noticed by Mahowald et al. (2010). However, it was not possible to quantify the number of open and breathing cracks for each cracking stage. On the other hand, a clue regarding the cracking behaviour could be made by plotting the total length of existing cracks vs the percentage of the collapse load. For a given load stage, the total crack length is the summation of the length of all cracks (visible by naked eye) present on the slab after the removal of the load. First, cracks were marked and differentiated among the crack stages. Then, photos of the bottom of the slab were taken after each load stage and a sketch was drawn from each photo using an image-processing software. It should be noted that the grid of test points were marked at the bottom surface of the slab. Thus, a scale could be defined in the sketches, in order to calculate the actual length of the cracks.
The result is shown in Figure 8(a) and it is possible to notice a difference in the behaviour of the crack opening rate between the two slabs, from the slope of the curves. While slab S1 shows a reasonably constant slope (i.e. crack rate) with the damage level, slab S2 shows a decrease in the crack rate. A probable cause of this difference in the crack rate is that the slab S2 had more cracks for a lower percentage of the collapse load when compared to slab S1. This can be visually confirmed (Figures 4 and 5) from the different crack evolution patterns in both slabs. By considering that old cracks are wider than new cracks, the former tended to be of the open type, as opposite to new cracks that tended to be more of the breathing type. This way, slab S2 would have a greater incidence of open cracks for higher cracking levels than slab S1. This leads to a difference in nonlinear behaviour between the two slabs, implying different behaviour of the gradients of frequency, as seen in Figure 7. It should be noted that the behaviour of the gradient depicted in Figure 7 is consistent with the difference in cracking evolution between the two slabs shown in Figure 8(a).
A similar conclusion could be inferred if crack density is employed instead of crack length. Crack density is defined by the ratio between the crack length and the surface area of the respective slab (Short et al., 2002; Litorowicz, 2006; Torrijos et al., 2010). Since both slabs had similar surface area, the shape of the curves obtained (shown in Figure 8(b)) is similar to those, respectively, obtained in Figure 8(a).
3.3 Gradient vs global damage index
It is possible to relate the gradient of the frequency-decay curves and a global damage index based on the variation of the fundamental natural frequency. Rodríguez-Gómez and Cakmak (1990) proposed a damage index based on the relationship between the changes of natural frequency at the beginning and ending of the decay. Pimentel et al. (2017) introduced a modification of this index (DIm), shown in Equation (1), to make a comparison of the structural condition when cracked with its respective uncracked stage, by adopting the initial natural frequency wo for the undamaged state, and the final natural frequency wn as the natural frequency of the damaged stage. These frequencies where obtained from processing the signals for each load stage, using StarModal software:
The plot between the damage index DIm and the gradient for both slabs is shown in Figure 9. It can be seen that while the index grows steadily with the increase in the damage level for slab S1, the pattern on slab S2 is similar to slab S1 until a certain load level (corresponding to 33.6 per cent of the collapse load), and after that, the damage index stabilizes. Since natural frequencies did not show expressive change in slab S2 for higher levels of damage, there is no significant change of its damage index, as expected. On the other hand, for initial damage levels, the curves obtained for both slabs are very similar until a damage index DIm around 0.3.
Two reinforced simply supported concrete slabs, named S1 and S2, were tested. Although they had the same support conditions, dimensions and reinforcement ratios were distinct between them, highlighting that the reinforcement ratio of slab S2 was the highest. After each stage of static load was applied, modal testing was carried out, aiming to get vibratory properties and follow their change with the damage level. Visually, it was possible to notice a different crack pattern between the slabs, where the slab with the highest reinforcement ratio (S2) showed a much high crack density in the central part of span for lower percentage levels of the collapse load.
Different behaviour was observed from the results of the modal test between the slabs, which could be related to the differences in the cracking pattern. First, the variation of the first natural frequency for different damage levels was evaluated. Slab S1 presented monotonic decrease of the fundamental frequency as the static load increased (and so the induced crack). On the contrary, slab S2 presented a decrease of natural frequency until about 40 per cent of the collapse load and then it became steady until the last load level tested.
While evaluating the slope of the natural frequency curve along decay produced by impact excitation (i.e. the gradient of frequency) vs percentage of ultimate load curve, it was noticed that there was a growth of the gradient until 33.6 per cent of the collapse load in slab S2 and then it reduced for higher levels of the applied load. Conversely, in slab S1, the gradient grew steadily until the last load level near the collapse. When the cracking opening rate was evaluated by the slope of the curve of the total crack length vs percentage of ultimate load, it was possible to notice a distinct evolution of cracking between the slabs. Slab S1 presented a constant crack rate, while in slab S2, the crack rate reduced while increasing the applied load.
Differences of the gradient of frequency between the slabs can be related to the changes in the crack opening rate. The distinct behaviour of the crack rate is possibly associated to a different balance between open (old) and breathing (new) cracks in each slab, and slab S1 would present much of the latter type for high levels of percentage of ultimate load. Since the breathing cracks are a major contributor for nonlinear effects during decay, the gradient behaved accordingly.
A global damage index based on a relationship between the fundamental natural frequency of each slab with respect to the natural frequency of the uncracked state was plotted against the gradient of the frequency, for each slab. Again, slab S2 presented a distinct behaviour in comparison to slab S1. Both slabs showed a variation of the damage index in a very similar fashion up to a value of such index of 0.3. After this point, the damage index stabilized in slab S2, while in slab S1, it presented increasing values until near the collapse.
This pattern of changes of the damage index followed the pattern of variation of the natural frequencies in both slabs, since the damage index was based on changes of the natural frequency. However, the rise of nonlinear effects for high levels of damage might make use of natural frequency not suitable in terms of identifying the level of damage, as it occurred in slab S2. On the other hand, the correlation between the damage index and the gradient was significant for low levels of damage, making it possible to relate the gradient to the intensity of damage.
Overall, it can be concluded that a lack of a pattern for the variation of the gradient of natural frequency and damage index for both test structures indicates an impossibility of the use of impact tests as a method to quantify the damage level on RC slabs for all damage levels using this non-linear feature. However, for low damage levels, the use of gradient is suitable and presented a strong correlation with a global damage index based on the variation of the natural frequencies between cracked and uncracked conditions.
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Conflict of interest: the authors declare that there are no conflicts of interest regarding the publication of this paper.
Financial support from Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) and Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (Capes) is acknowledged. Thanks are due to R. Finotti, C. Theodoro, G. Medeiros, L. Silva, J. Carvalho and L. Pereira for their help during the tests. The data sets generated and/or analysed during the current study are available from the corresponding author on reasonable request.