Challenges in assessing corrosion damage in reinforced concrete beams by vibration-based monitoring: literature analysis and experimental study

Abstract

Corrosion is one of the most frequently occurring problems in reinforced concrete (RC) structures. The formation of rust products results in deterioration processes that decrease the durability and structural capacity. Therefore, frequent inspection and monitoring of corrosion damage play a vital role in establishing reliable asset management of civil structures. Vibration-based monitoring (VBM) is particularly useful in studying the global response of a deteriorated structure, since a change in modal characteristics may indicate damage. Although VBM has already been studied thoroughly, a systematic understanding of how corrosion contributes to the changes in modal characteristics is still lacking. In this study, an overview and assessment of the existing literature for dynamic tests on corroded RC beams is provided, aiming to give a critical review of the current knowledge, possibilities and challenges related to this topic. Moreover, this study presents additional data from two test programmes, which enable to point out the challenges in VBM of corroding RC beams. The experimental test programmes include two locally corroded beams and three uniformly corroded beams, as well as non-corroding reference beams. For high corrosion levels, the natural frequencies of beams reported in the literature, as well as the beams of the test programmes, decreased. However, comparison with a non-corroding reference beam proved to be essential to eliminate the influence of other non-negligible factors such as creep and shrinkage. Other modal characteristics, such as the damping ratio and mode shapes, are found to be less sensitive to monitor uniform or local corrosion in RC beams.

Keywords

Vibration-based monitoring corrosion reinforced concrete damage detection natural frequency

Introduction

Chloride-induced corrosion of reinforced concrete (RC) is currently the leading cause of deterioration in concrete structures.¹ Condition monitoring of these corroding structures is crucial to decide which structures are vulnerable and need maintenance. Consequently, an effective monitoring strategy increases the safety, while the costs of repair reduce.^2,3 To assess the condition and performance of structures, non-destructive testing (NDT) and structural health monitoring (SHM) can be performed.¹ Some of the most popular NDT methods for corrosion monitoring include visual inspection, galvanostatic pulse method, half-cell potential, ultrasonic pulse velocity and acoustic emission monitoring.^4–6 These methods provide information about the deterioration of a structure on a local scale, but all have in common that upscaling their results to estimate the remaining structural capacity is challenging. With SHM, periodic inspections and analyses over time are intended to obtain information about changes in the response of the monitored structure.

Vibration-based monitoring (VBM) is a frequently used SHM technique and has been studied extensively. It was first introduced in the oil industry,⁷ but was later applied in the civil engineering industry also.^7–9 Within VBM, two different methods can be distinguished: data-based and model-based methods.¹⁰ Data-based methods focus on changes in modal characteristics over time, which are mostly extracted during operational conditions.^11,12 These modal characteristics (natural frequencies, mode shapes and modal damping ratios) can be obtained from dynamic structural response data captured by, for example, acceleration¹³ or strain sensors.^14,15 On the other hand, model-based methods use experimental data to update finite element (FE) models.¹⁶ The difference between the observed and predicted modal characteristics is minimised by updating the damage parameters of the FE model.^17,18 The model-based VBM method provides an indication of the global stiffness loss and might therefore be capable of estimating the overall behaviour of a deteriorating structure. While NDT methods typically focus on local damage assessment, model-based VBM can assess the damage on a larger, structural scale and provides useful information for assessing the remaining capacity and lifetime of a structure.^19–21

Since reinforcement corrosion may cause cracking of the concrete and a decrease in the element’s stiffness,^22,23 the dynamic properties of the structure can change. Consequently, a change in modal characteristics can be observed by VBM. Although vibration-based assessment of corroding RC structures seems promising, only few studies have investigated the effect of reinforcement corrosion in concrete on the modal characteristics. An overview of studies focusing on corrosion in RC was given by Duvnjak et al.,²⁴ which illustrates that most experimental studies are performed in laboratory conditions. Hence, the present study mainly discusses laboratory tests. Moreover, several challenges are associated with the dynamic testing of corroding RC structures, such as environmental factors, support conditions, time-dependency of concrete properties, etc. Therefore, a profound study on the vibration-based assessment of corroding RC structures is needed in light of a critical review of available data, challenges and possibilities of this SHM technique. At present, the discovered challenges in setting up experimental programmes of this kind make it hard to compare different studies. This report will therefore help in achieving more consistent results that can be more straightforwardly compared in the future. A review of literature data reported on VBM of corroding RC structures is presented in this paper, as well as new data that aim at filling knowledge gaps and investigating certain influences and challenges since the availability of reliable datasets is very limited.

Firstly, Section ‘Effects of corrosion on modal characteristics’ discusses the effects of corrosion on the properties of RC components and their expected influence on modal characteristics. Secondly, the existing literature concerning VBM of corroding RC elements is reviewed in Section ‘Discussion on experimental results reported in the literature’. Additional experimental tests are discussed in Section ‘Experimental program’, which contribute to the available data and address challenges related to dynamic testing of corroded RC structures. Finally, Section ‘Discussion’ compares the literature data with the new experimental results and focuses on recommendations to improve VBM tests on corroding RC beams.

Effects of corrosion on modal characteristics

Due to the high alkalinity of concrete, the steel reinforcement is generally protected by a passivation layer that prevents corrosion. This protective passivation layer may disappear when the pH of the concrete reaches levels below 8. The two main phenomena causing the depassivation are carbonation and chloride ingress. This paper mainly focuses on chloride-induced corrosion, which can occur because of internal (e.g. contaminated aggregates) or external (e.g. de-icing salts) sources. The chlorides locally attack the passive layer, resulting in a local section loss of the reinforcement bar (rebar), also called pit formation, which is considered a higher risk for structural safety than uniform corrosion caused by carbonation since the bearing capacity may suddenly drop without early warnings.²⁵ Carbonation will be briefly discussed when an overview of the literature is presented.

When the passive layer is destroyed and the RC starts to corrode, rust products are formed in an electro-chemical process that requires water and oxygen. A constant supply of iron atoms is necessary to continue the corrosion process, which causes a reduction of the rebar’s cross-section, and consequently the tensile capacity of the rebar reduces. The ductility of the rebar decreases due to a reduction in steel elongation at maximum load.^26–28 Since rust products occupy a larger volume than the initial steel, internal stresses in the concrete increase and can cause concrete cracking or spalling. Furthermore, the bond strength between highly corroded rebars and concrete decreases, which is most significant for higher corrosion levels (CLs) because of the reduced confinement of the cracked concrete.^29–31 The effects of corrosion on RC beams are illustrated in Figure 1. The damage mechanisms caused by corrosion of RC can be divided into three categories related to (1) concrete (cracking and spalling), (2) steel reinforcement (section loss, tensile capacity and ductility reduction) and (3) bond deterioration.²⁶

For VBM, it is important to understand how the micro- and macrocracks caused by corrosion damage affect the stiffness of the structure. Corrosion damage in an RC beam may cause a reduction in bending stiffness (EI), which combines the second moment of area (I) and Young’s modulus (E) of the RC beam. Firstly, concrete cracking (Figure 1(a)) causes a reduction of the beam’s stiffness since the cracks alter the stress–strain relation of the undamaged material. Additionally, when spalling occurs, the element’s second moment of area reduces.^29,32 Because of these effects, concrete cracking and spalling are the main contributors to the loss in bending stiffness of a corroded element. Herein, transversal cracking caused by corrosion of the stirrups is expected to have a larger impact on the bending stiffness than longitudinal cracks. Secondly, the steel reinforcement mainly becomes important after flexural cracking of the concrete, when the reinforcement bridges the cracks and partly compensates for the stiffness loss caused by the cracked concrete (i.e. tension stiffening).³³ The reduction of the rebar’s cross-section due to corrosion (Figure 1(b)) therefore has an influence on the stiffness and second moment of area of RC. Thirdly, also the bond between steel and concrete is affected by corrosion due to both the concrete cracking and the steel section loss,³⁰ which causes a reduction in composite interaction between steel and concrete, and hence a reduction in I. Finally, other effects of corrosion damage include the reduced ductility and tensile capacity of the rebars. Yet, these forms of damage do not influence the bending stiffness of the beam.

However, it should be noted that for low CLs, before cracking of the concrete cover, the bending stiffness might initially increase. This can occur because of the internal pressure build-up and added roughness of the rebar which both cause an increase in friction. The increase in stiffness occurs until reaching a critical point and afterwards the bond strength decreases rapidly due to the reduced mechanical interaction and loss of confinement due to concrete cracking. Critical CLs typically vary between 0.3% and 4.81%.³⁰

Dynamic tests have been used in the past to assess damage in concrete structures.^7,34,35 It was found that a significant decrease in natural frequencies is a clear indicator of deterioration.³² The natural frequencies ( $f_{n}$ ) of a beam with free-free boundary conditions can be derived from the partial differential equation of motion for an Euler-Bernoulli beam,³⁶ resulting in Equations (1) and (2), based on the length (L), dynamic Young’s modulus (E), second moment of area (I) and mass per unit length (m). This equation is only valid for bending modes and most accurate for slender beams and low order modes.^35,37 The parameter $k_{n}$ depends on the mode number n and is found as the solution of the transcendental Equation (2). The displacement mode shapes which belong to the natural frequencies of the first three bending modes of a beam with free-free boundary conditions are illustrated in Figure 2.

f_{n} = \frac{{(k_{n} L)}^{2}}{2 π} \sqrt{\frac{EI}{m L^{4}}}

(1)

\cosh (k_{n} L) \cdot \cos (k_{n} L) = 1

(2)

As can be seen from Equation (1), the natural frequency $f_{n}$ decreases if the Young’s modulus (E) of the beam decreases. E will decrease when the stress–strain relation of a material is modified, which can happen because of damage. In model-based VBM, E is the material property which is most often adapted to capture the effects of concrete cracking.¹⁶ However, the natural frequencies change with the square root of E, so a large stiffness change is needed before damage can be detected. Additionally, according to Equation (1), the frequency $f_{n}$ also decreases with decreasing I. The causes of a reduction in the element’s second moment of area due to rebar corrosion were shown in Figure 1. Finally, also the mass (m) influences the natural frequencies. Severe concrete spalling will cause a reduced mass, which results in an increase of the frequency $f_{n}$ , and has therefore an opposite influence compared to the other corrosion effects. However, this influence of reduced mass might have a limited effect in comparison with the bending stiffness.

Care should be taken when analysing the changes of natural frequencies of structures exposed to changing environmental conditions, since these can also have a large influence on the dynamic properties of RC elements and possibly mask the effects from damage. It was reported by Salawu³² that a decrease in natural frequency of 5% should be achieved during on-site monitoring to assure that the change in natural frequencies is not only caused by environmental factors. This implies that the effect of regular environmental factors such as temperature and loading conditions needs to be filtered out from the time series of natural frequencies if early damage detection is targeted. This filtering process is termed data normalization. It requires continuous monitoring of the natural frequencies and typically involves machine-learning techniques³⁸ that do not necessarily need the environmental factors to be measured.³⁹

Local damage may affect the mode shapes of a structure, so this type of damage could be identified from a change in the displacement mode shapes. This requires a sufficiently dense mesh of well-positioned accelerometers.^9,35 It is noted here that a uniform change in stiffness will not result in a change of mode shape, but only in a change of natural frequency. Damage which is of a more global nature will therefore be more easily picked up from changes in natural frequency. Consequently, mode shapes are generally found to be less influenced by environmental effects than natural frequencies.^9,35,40 A change in mode shapes, and therefore identification of local damage, can, for example, be quantified by the Modal Assurance Criterion (MAC),⁴¹ which equals 1 for identical mode shapes and takes a low value for dissimilar mode shapes. Previous studies have also explored the effect of damage on strain mode shapes and curvatures, which appear more sensitive to local damage and less sensitive to temperature changes.^42–45

A third modal parameter, next to the natural frequencies and mode shapes, is the modal damping. This parameter represents all possible forms of energy dissipation. These forms of energy dissipation may be affected differently by damage or environmental factors, causing possible deviations in results. Previous research has found that changes in modal damping are inconsistent when assessing damage in RC structures.^46,47

Discussion on experimental results reported in the literature

Most research on the modal characteristics of corroding RC structures has been done on the basis of tests on beams in laboratory conditions. To corrode the RC beams, accelerated corrosion processes were performed, mainly based on chloride ingress. An overview of experiments reported in the literature is presented in Table 1. The research on modal characteristics was mostly limited to natural frequencies because of the challenges related to mode shapes and modal damping mentioned in Section ‘Effects of corrosion on modal characteristics’. The third column of Table 1 shows the change in first natural frequency ( $f_{1}$ ) for different studies. When no detailed information was available about the orientation of the mode, it is assumed that $f_{1}$ is the natural frequency associated with the first vertical bending mode. This is the case for all but one study, which all refer to mode 1 or the first natural frequency. Only Shahid et al.⁴⁸ specifically mention that their reported results originate from the first vertical bending mode.

Table 1.

Overview of experimental results regarding monitoring of the natural frequencies of corroded beams reported in the literature. (The results by Zhang et al.⁴⁹ are the average of four beams with similar CLs.)

		Change in $f_{1}$ (%)	Correctedwithreferencebeam?	Directlytaken fromreported data?	CL (%)	Directlytaken fromreporteddata?	Size(w × h × l) [mm³]	Corroded area	Exposure
Chloride-induced corrosion of the tensilezone of RC beams	Razak andChoi⁵⁰	−1.04	✓	✓	7.65 (Moderate cracking)	✓	Not reported	Uniform	Not reported
	Razak andChoi⁵⁰	−4.06	✓	✓	7.77 (Slight spalling)	✓	Not reported	Uniform
	Maalej et al⁵¹	+3.9	✓	✗	4.2	✓	235 × 324 × 2500	Uniform	First cracking by bending and then cyclic accelerated corrosion with NaCl (3%) and constant current
	Maalej et al⁵¹	+3.1	✓	✗	15	✓	235 × 324 × 2500	Uniform
	Shahzad et al⁴⁸	−0.67	✓	✓	1.03	✓	100 × 70 × 600	Uniform	Accelerated corrosion with NaCl (5%) and constant current
	Shahzad et al⁴⁸	−2.6	✓	✓	6.18	✓	100 × 70 × 600	Uniform
	Ortega and Robles²¹	−1	✗	✗	6.00	✗	80 × 160 × 1100	Local (500 mm)	Accelerated corrosion with constant current
		−6			11.82
		−12			22.89
		−23			28.15
	Zhang et al⁴⁹	−3.5	✗	✗	1.19	✓	150 × 120 × 3200	Uniform	Accelerated corrosion through salt chamber
Other corrosion set-ups on RC beams	Capozucca and Cerri⁵²	−3.5	✗	✗	Not reported	✓	100 × 150 × 2000	Local(300 mm)	Cyclic accelerated corrosion of compression rebars with NaCl (10%)
	Capozucca and Cerri⁵²	−3.3	✗	✗	Not reported	✓	100 × 150 × 2000	Local(300 mm)
	Zhang and Sun⁵³	−2.46 to −6.67	✗	✓	Not reported	✓	150 × 120 × 3200	Uniform	Concrete carbonation-induced reinforcement corrosion

RC: reinforced concrete; CL: corrosion level. Remarkable deviations in exposure are indicated in bold.

Some experimental programmes displayed in Table 1 include a reference or a control beam. This beam has been tested similarly to the corroded beam, but without inducing corrosion, with the aim of separating the changes in modal characteristics caused by effects that are not related to corrosion. If data from such non-corroding reference beam were available in the literature, the results for the change in $f_{1}$ reported in Table 1 were corrected accordingly, as will be explained further. Whether a correction with a reference beam is applied or not is indicated in the fourth column of Table 1. Furthermore, the change in $f_{1}$ is either directly taken from the reported data or calculated based on the results reported in the referred literature, as indicated in the fifth column of Table 1.

Additionally, the CLs related to these changes in natural frequency are presented in Table 1. If these values were not provided in the cited studies, and therefore not directly taken from the reported data, they were calculated based on the duration of the current-driven corrosion process and estimated penetration depth, according to Faraday’s law.^54,55 The seventh column of Table 1 indicates for which study this is the case. Furthermore, the size of the specimens, the corroded area and information about the corrosion conditions are indicated in Table 1 as well. Because of the large variation in experimental set-ups, the changes in natural frequencies should be compared carefully. When some information is not available, the cell is marked as not reported.

The first group in Table 1 considers chloride-induced corrosion of the tensile rebars of RC beams and consists of five studies. The results all show a decrease of the natural frequencies for corroded beams, except for the study of Maalej et al.⁵¹ They performed corrosion tests, but first introduced cracks into the RC beams by executing four-point bending tests. The bending cracks clearly led to a decrease of the natural frequencies. However, considerably large increases of the first natural frequencies were found after corrosion in comparison to the non-corroding reference beam. The authors explain these unexpected results by the continuous hydration process of the young concrete and the enhanced bond caused by corrosion products.

Each row in Table 1 presents results derived from different test specimens, except for the results of Ortega and Robles.²¹ Here, Table 1 shows the result of a single beam (labelled ‘beam I’ in the study of Ortega and Robles²¹) which was tested at several CLs. Ortega and Robles²¹ tested twelve beams with varying curing processes and concrete mixtures. However, the beam which is closest to the ones considered in the other test programmes described in the literature (beam I) is reported here. Ortega and Robles²¹ found a large decrease of $f_{1}$ in comparison with the other reported studies. On one hand, this can be explained by the high CL which reduces the bending stiffness. On the other hand, there was no reference beam to correct the results so other factors besides corrosion might also have contributed to the decrease in dynamic parameters.

Figure 3 displays the changes in $f_{1}$ in relation to the CL of several VBM tests on RC beams reported in the literature. A distinction is made between results corrected with a reference beam (black markers) and results without correction based on a reference beam (open markers). For the corrected results, the stiffness changes that are not related to corrosion are omitted according to Equations (3) and (4), taking into account the quadratic relation between E and f (Equation (1)) and assuming a uniform Young’s modulus:

Δ E_{X, corrected} = \frac{E_{X, cor} - E_{0, cor}}{E_{0, cor}} \cdot 100 - \frac{E_{X, ref} - E_{0, ref}}{E_{0, ref}} \cdot 100

(3)

\begin{matrix} Δ f_{X, corrected} = \sqrt{| \frac{f_{X, cor}^{2} - f_{0, cor}^{2}}{f_{0, cor}^{2}} \cdot 100 - \frac{f_{X, ref}^{2} - f_{0, ref}^{2}}{f_{0, ref}^{2}} \cdot 100 |} \\ * sign (\frac{f_{X, cor}^{2} - f_{0, cor}^{2}}{f_{0, cor}^{2}} - \frac{f_{X, ref}^{2} - f_{0, ref}^{2}}{f_{0, ref}^{2}}) \end{matrix}

(4)

In Equations (3) and (4), the natural frequencies at the start of the testing procedure are indicated with 0 and after a certain period of testing with X. Furthermore, the values of the reference beam are marked with ref and those of the corroding beam with cor. In Table 1 and Figure 3, corrected values are calculated with Equation (4) when possible, which is only the case for the results of Maalej et al.⁵¹ Uncorrected results are shown in Figure 3 when available. When corrected results were directly reported in the literature,^48,50 it was not explicitly specified how the correction was made. However, assuming a simple linear correction between the natural frequencies and the Young’s modulus only results in minor differences with Equation (4) for small changes in natural frequencies. Figure 3 illustrates that the change in $f_{1}$ is less strong when corrections are applied, indicating the importance of a reference beam. This reference beam reduces disturbances of the results caused by factors which are independent of the corrosion process. Furthermore, a decreasing trend of natural frequencies can be observed with increasing CL, assuming that both corroded and reference beam are tested in the same conditions and at the same age.

In general, it can be observed from Figure 3 that a higher CL causes a larger reduction in natural frequencies. The results by Maalej et al.⁵¹ are clearly deviating from the other results, which is probably due to the mechanical pre-cracking of the beams and differences in the set-up of the experiments. Therefore, the uncorrected results will not be discussed further. Razak and Choi⁵⁰ demonstrated that changes in natural frequencies are not only dependent on the difference in CL, but also on the difference in crack pattern. A transition from moderate cracking to slight spalling caused a strong decrease in natural frequencies, even though the CL remained similar. The results of Shazad et al.⁴⁸ appear to be in accordance with other datasets. Ortega and Robles²¹ obtained large changes in $f_{1}$ , most likely related to the high CL and lack of a reference beam. Furthermore, the results show a clear decreasing trend since all values are derived from a single beam which was tested at different CLs. Finally, Zhang et al.⁴⁹ reported a relatively large decrease in $f_{1}$ with respect to the low CL. However, Figure 3 only shows the CL of the main reinforcement while the stirrups of the beams tested by Zhang et al.⁴⁹ reached more than double the CLs of the main reinforcement. Furthermore, it should be noted that the change in $f_{1}$ for the experiments of Zhang et al.⁴⁹ is calculated relative to the natural frequency after 20 days of corrosion since no initial reference value was obtained from a non-corroded beam. Figure 3 shows the results for four different specimens tested by Zhang et al.,⁴⁹ while Table 1 contains an average value since the CLs of all four beams are very similar.

Next to the natural frequencies, also the modal damping ratio was studied by Razak and Choi⁵⁰ and Shahzad et al.⁴⁸ Razak and Choi⁵⁰ reported an increase in modal damping ratio with an increase in CL for modes 2 and 3. However, a decrease of the modal damping ratio was found for mode 1, resulting in inconsistencies in the modal damping ratio for different mode shapes. On the other hand, Shahzad et al.⁴⁸ observed significant increases of the modal damping ratio with an increase in CL. In relative terms, these increases in modal damping ratio were far higher than the observed decreases in natural frequency. The authors therefore claim that the change in modal damping ratio is much more sensitive to corrosion damage than the change in natural frequencies. However, the results were less stable for locally corroded beams than for uniformly corroded beams, since the response changed with every repetition of the dynamic test. Too little data is reported in the literature to conclude on the effectiveness of the modal damping ratio as a damage indicator for corrosion in RC. Aside from the need for more data, also more information regarding the boundary conditions during experimental tests is necessary because of the energy loss through the supports to the environment.

The second group of Table 1 shows results of dynamic tests on corroding beams, but with different corrosion set-ups than the first group. Capozucca and Cerri⁵² studied the effect of corrosion of compression rebars subjected to four or eight corrosive cycles, while Zhang and Sun⁵³ investigated the influence of accelerated carbonation-induced corrosion on the natural frequencies of RC beams, making both studies not directly comparable to the previously discussed ones. Capozucca and Cerri⁵² noticed that increases in corrosion of the compression rebars also resulted in larger decreases in natural frequencies. The changes in $f_{1}$ reported for Capozucca and Cerri⁵² in Table 1 are calculated based on the first available data point.

The influence of carbonation-induced corrosion on the natural frequencies of RC beams with different strength grades was investigated by Zhang and Sun.⁵³ Carbonation-induced corrosion was also found to lead to a decrease in natural frequencies in this study. However, it was found that a mass increase due to the infiltration of carbon dioxide into the concrete is the main reason for the reduction in natural frequencies. Additionally, they observed that increasing the concrete strength from strength grade 30 to 40 significantly reduced the change in natural frequencies since the increase in mass is lower. A possible strength increase due to pore filling by corrosion products is not discussed. The results of Zhang and Sun⁵³ were not compared to reference values of a non-corroding reference beam.

Next to corrosion of RC beams, previous research has also studied corroding prestressed concrete (PC) elements. Capozucca,⁵⁶ Rashetnia et al.,⁵⁷ Lee and Kang⁵⁸ and Zuccarino et al.⁵⁹ performed dynamic tests on corroding PC beams. It was observed that the decrease in natural frequencies becomes stronger when the level of corrosion damage is higher.^56,58 The loss of prestressing force due to corrosion is the main cause for changes in modal characteristics.⁵⁸ Rashetnia et al.⁵⁷ successfully estimated this prestressing force reduction with inverse identification analysis techniques based on changes in modal characteristics. Overall, the detection of damage in prestressed elements is challenging because typically either extensive prestress losses need to have occurred or the concrete section needs to be severely cracked^58,59 to induce detectable changes in natural frequency. Moreover, the bending cracks caused by the reduced prestress need to remain open during dynamic testing to observe decreases in natural frequency.^56,60 Zuccarino et al.⁵⁹ observed changes in natural frequencies, mode shapes and modal damping ratios and stated that modal damping ratios are more sensitive to corrosion-induced damage than natural frequencies. Additionally, Zuccarino et al.⁵⁹ confirmed that changes in mode shapes are not suitable to indicate uniform corrosion damage of PC.

In addition to the testing of beams, the modal characteristics of corroding containment vessels were studied by Lin et al.,⁶¹ concrete frames by Zou et al.,⁶² columns by Ge et al.⁶³ and plates by Zhang et al.⁶⁴ The natural frequencies of containment vessels⁶¹ and columns⁶³ were found to decrease because of corrosion damage. However, Zou et al.⁶² found inconsistencies in the frequency change. After corrosion, the first natural frequency unexpectedly increased. This is possible at initial corrosion stages, as seen before by Maalej et al.⁵¹ Furthermore, the modal damping ratio did not consistently increase with an increase in CL.⁶² Zhang et al.⁶⁴ observed large decreases in the first three natural frequencies of around 30% for RC plates with a CL of 15%. These large decreases can be related to the small height of the specimen. Because of this, the damaged concrete cover takes up a large area of the cross-section and its cracking and spalling may cause a severe decrease in bending stiffness.

In situ investigation of VBM on corroding structures has only been performed to a limited extent. A main challenge for in situ monitoring is the large influence of environmental factors such as temperature fluctuations, air humidity, rain and wind.^13,14,34 It has been shown that the natural frequencies of structural components decrease with a temperature or humidity increase.⁴⁰ The Tilff bridge in Belgium is an example where VBM was used to assess the structural condition after corrosion was observed.^15,65 A combined set-up with optical fibres and accelerometers was used to find modal characteristics of the damaged bridge. Damage was localised by the updating of a FE model of the undamaged structure based on the experimentally obtained modal characteristics.

Although VBM campaigns focused on corrosion are rare, in situ research on damage monitoring in general is more extensive.⁶⁶ For example, the dynamics of the Z24 bridge in Switzerland were monitored continuously during 1 year and later progressive damage tests were performed to observe changes in modal characteristics.^67–69 Local corrosion was simulated by cutting prestressing strands and spalling was simulated by removing part of the concrete cover. During long-term monitoring, the environmental conditions also were recorded. These results were used to filter out the influence of the environment on the natural frequencies.

Experimental programme

To extend the available experimental data and investigate conflicting results reported in the literature, two new test programmes were set up in a collaboration between KU Leuven and Ghent University. The test set-ups were already briefly discussed in the studies of Vandecruys et al.^70–72 Both test programmes make use of non-corroding reference beams. The first programme consists of two RC beams with a length of 3 m which are corroded locally, while the second programme focuses on three larger beams with a length of 5 m which are uniformly corroded. An accelerated corrosion process with a chloride solution and direct current are used in both test programmes. An overview of the test samples is given in Table 2. The label of the beams is composed by a number, followed by the type of corrosion (Reference specimens without corrosion, Local symmetrical corrosion, Local asymmetrical corrosion, Uniform corrosion), for which 1 or 2 is added if two beams with the same properties are tested, and the CL. The CL is calculated after cleaning the corroded rebars and determining their remaining mass. The relative mass loss is directly related to the CL.

Table 2.

Overview of the tested beams.

	Beam label	Corrosion time (days)	CL (%)	Corroded area
Program 1	1.1_R1-0	0	0	No corrosion
	1.2_Ls-5.6	70	5.6	Local (1300 to 1700 mm), symmetrical
	1.3_R2-0	0	0	No corrosion
	1.4_La-9.2	70	9.2	Local (1800 to 2200 mm), asymmetrical
Program 2	2.1_R-0	0	0	No corrosion
	2.2_U-2.7	35	2.7	Uniform
	2.3_U-5.2	154	5.2	Uniform
	2.4_U-6.2	302	6.2	Uniform

CL: corrosion level.

All beams, including the non-corroded reference beams, are inspected with the VBM technique. During dynamic testing, the beams are supported by flexible, inflated tyres to simulate free-free boundary conditions. The assumption of dynamic free-free boundary conditions is confirmed when the identified natural frequency of the highest rigid-body mode of the beam (test programme 1: ±20 Hz/test programme 2: ±30 Hz) is much lower than the identified natural frequency of the lowest vibration mode of the beam (test programme 1: ±105 Hz/test programme 2: ±61 Hz). This requirement was met for both test programmes so the assumption of dynamic free-free boundary conditions could be made. The beams are dynamically excited by an impact hammer. The dynamic response is measured by uniaxial accelerometers placed on the surface of the beams. Different types of accelerometers are used, with frequency ranges starting at 0.5–2.5 Hz and reaching 1000–4000 Hz, thus all covering the frequency range 2.5–1000 Hz. Moreover, since only vertical bending modes are reported here, only the accelerometers at the top surface of the beams are of importance, which all cover the frequency range $2.5 - 2000 Hz$ . The sensitivities of all sensors are sufficient for the level of acceleration in the test and range from $100 mV / g - 1 V / g$ . The output-only modal analysis is performed with MACEC,⁷³ an in-house developed Matlab toolbox, and the stochastic subspace identification method is applied.⁷⁴

Test programme 1: locally corroded beams

The corrosion set-up of the first test programme is shown in Figure 4. Two concrete beams with dimensions $150 \times 220 \times 3000 m m^{3}$ are locally corroded over a length of $400 mm$ . The remaining part of the tensile rebars is treated with a protective coating as well as the compressive rebars across from the corrosion zone, as indicated in red on Figure 4. All beams are created with a concrete composition of $350 kg / m^{3}$ CEM I 52.5N, $620 kg / m^{3}$ sand 0/4, $1270 kg / m^{3}$ aggregates 4/14, $164 kg / m^{3}$ water and $7 kg / m^{3}$ NaCl. The local area is corroded by rotating the beams so that their tensile reinforcement is located on top and placing a bottomless tank filled with 5% sodium nitrate (NaCl) over a part of the beam. The first 3 weeks, both beams were corroded with a current density of $50 μ A / c m^{2}$ . The following 7 weeks, the current was increased to 100 or $250 μ A / c m^{2}$ , depending on the set-up (see Figure 4). For each corroding beam, a non-corroding reference beam was tested simultaneously to compare the measurements. All beams were continuously supported at both ends and in the middle of the beam, except during dynamic testing when they were positioned on two tyres. After 70 days of corrosion, both beams mainly had longitudinal cracks at the corroded surface and some small transverse cracks at the side of the beam. Beam 1.4_La-9.2 also showed a longitudinal crack at the side (e.g. Figure 5).

During dynamic testing, the beams are flipped over, so the corroded tensile rebars are at the bottom of the beam. Accelerometers are placed in four rows of seven sensors on the surface of the beam, with a spacing of $500 mm$ in the middle and $450 mm$ at the sides of the beam. Two rows are placed at the front of the beam, and two rows are placed on top (Figure 6), so that vertical as well as horizontal bending and torsional modes can be identified. Due to this dense grid of accelerometers, not only the natural frequencies and modal damping can be extracted from the data, but also detailed displacement mode shapes. The beam is excited by a series of hammer impacts on a corner of the top surface, followed by a series of impacts on a corner of the side surface. These impact locations ensure that every mode of the beam is excited. In Figure 2, you can clearly see that the modal displacement is the highest at the outer ends of the beam for the first three bending modes, which makes this the ideal location for excitation.³²

The results of the natural frequencies of the first three vertical bending modes (B1, B2 and B3) are reported in Table 3. The identification results of the torsional modes and horizontal bending modes are not discussed here as they are rarely reported in the literature and therefore cannot be compared to previous studies. The initial values of the natural frequencies of modes B1, B2 and B3 are presented, together with the change in natural frequency after 70 days of corrosion and after correction with the values of the reference beam (Equation (4)). The natural frequencies clearly decrease when damage is induced in the specimens. However, also the reference beams show significant decreases in natural frequencies, as shown by the large corrections. These are most likely caused by the development of micro-cracks in young concrete due to time-dependent processes such as creep and shrinkage. The concrete age was 28 days at the initial dynamic tests and subsequent start of the corrosion process. Since the reference beams compensate for the factors unrelated to corrosion (shrinkage and creep), the final corrected percentages are assumed to be caused by the corrosion process itself. It should however be emphasized that this also introduced an additional uncertainty.

Table 3.

Change in natural frequencies for beams 1.2 and 1.4, and the corrected changes in natural frequencies compared to their respective reference beams.

	1.2_Ls-5.6			1.4_La-9.2
	Initial $f_{n}$ (Hz)	Changein $f_{n}$ (%)	Corrected changein $f_{n}$ with referencebeam (%)	Initial $f_{n}$ (Hz)	Change in $f_{n}$ (%)	Corrected change in $f_{n}$ with reference beam (%)
B1	104.75	−2.22	−0.99	106.23	−2.94	−1.49
B2	280.93	−3.66	−1.57	284.66	−3.23	−1.75
B3	529.79	−3.40	−0.92	533.91	−2.01	−0.58

The displacement mode shapes of the beams before and after corrosion were compared by computing the MAC values which showed that these did not consistently decrease when the CL increased. Moreover, the MAC values of the first three bending modes remained higher than 0.99 throughout the entire test, indicating that the displacement mode shapes did not significantly change during the corrosion process. An investigation of the modal damping ratios for different levels of corrosion did not reveal a correlation of the damping ratios with the CL. The modal damping ratios were found to fluctuate between 0.5% and 2.0% for the reference beams as well as for the corroded beams.

Test programme 2: uniformly corroded beams

The corrosion set-up of the second test programme is shown in Figure 7. Three beams with dimensions $300 \times 400 \times 5000 m m^{3}$ are corroded over the entire length. The concrete is the same for all beams and composed of $270 kg / m^{3}$ CEM I 52.5N, $518 kg / m^{3}$ sea sand, $427 kg / m^{3}$ sand 0/4, $955 kg / m^{3}$ aggregates 6.3/14, $174 kg / m^{3}$ water and $1.9 kg / m^{3}$ superplasticizer. Similar as in the first test programme, the beams are corroded by rotating them so that their tensile reinforcement is located on top during corrosion, and by placing a bottomless tank filled with 5% NaCl over the beam. All three beams were corroded with a current density of $100 μ A / c m^{2}$ . Also a non-corroding reference beam was tested each time at the same age of the corroding beams to compare the measurements. In between measurements, the beams were all supported at both ends. After corrosion, all beams mainly had longitudinal corrosion cracks at the corroded surface and some longitudinal corrosion cracks at the side of the beam (e.g. Figure 8).

Accelerometers were placed in three rows of 10 sensors on the surface of the beam, according to Figure 9. The sensors are not equally distributed over the length of the beam because of obstacles (e.g. other sensors which are unrelated to the current paper) which put restrictions on the available surface. During dynamic testing, the beams were rotated again and supported by three tyres (one at each end and one in the middle) to simulate free-free conditions. The beams were excited by vertical strokes of an impact hammer at a corner of the top surface and horizontal strokes at a corner of the side surface. Similar to test programme 1, these excitation locations were selected as they allow for the adequate excitation of all relevant modes.

Table 4 summarises the natural frequencies for the corroded beams before corrosion (at an age of 28 days), the change in natural frequencies after corrosion and the corrected change in frequencies after comparison with the reference beam (Equation (4)). The first three bending modes are reported, which are the most accurately detected. Mode B1 is not reported for beams 2.2 and 2.4 because of measurement errors due to a technical issue. For beams 2.3 and 2.4, corrosion leads to a reduction in natural frequency. Nevertheless, also the reference beam 2.1 shows a reduction in frequency over time. Hence, the frequency changes of the corroded beams are corrected with those of the reference beam at the corresponding age to determine the influence of corrosion on the natural frequencies. It can be seen that for beam 2.2 with the lowest corrosion degree (CL = 2.7%), there is a positive influence of corrosion on the natural frequencies. This increase of the natural frequencies is most likely caused by the continuous hydration process of the young concrete and the increased bond between the rebar and the concrete caused by corrosion products. For low CLs, the pressure build-up before cracking enhances the confinement of the rebars and the corrosion products add to the roughness of the rebar’s surface. For beam 2.3 (CL = 5.2%), there is a negative influence of corrosion on the natural frequencies, except for mode B2. For beam 2.4 with the longest exposure to corrosion (CL = 6.2%), the largest decreases in natural frequency are found.

Table 4.

Change in natural frequencies for beams 2.2, 2.3 and 2.4, and the corrected changes in natural frequencies compared to the reference beam.

	2.2_U-2.7			2.3_U-5.2			2.4_U-6.2
	Initial $f_{n}$ (Hz)	Change in $f_{n}$ (%)	Corrected change in $f_{n}$ (%)	Initial $f_{n}$ (Hz)	Changein $f_{n}$ (%)	Correctedchangein $f_{n}$ (%)	Initial $f_{n}$ (Hz)	Changein $f_{n}$ (%)	Corrected change in $f_{n}$ (%)
B1	–	–	–	60.66	−7.85	−2.01	–	–	–
B2	164.70	+1.41	+2.05	162.76	−3.50	+1.84	169.16	−13.50	−3.28
B3	303.97	+0.15	+1.83	300.54	−4.98	−1.03	306.48	−10.54	−2.78

Discussion

The literature data reported in Section ‘Discussion on experimental results reported in the literature’ can now be compared with the experimental test results as described in Section ‘Experimental program’. First, the new datasets will be combined and compared with the literature data, and influencing factors are discussed. Hereafter, challenges are highlighted and recommendations for future tests will be given.

Comparison between the literature and experimental results

The experimental tests as described in Section ‘Experimental program’ confirmed that natural frequencies decrease due to corrosion damage. However, this decrease in natural frequencies needs to be corrected with results of a non-corroded reference beam of equal concrete composition and age, as the effect of ageing is significant. After the correction, a smaller reduction in natural frequencies is found. Additionally, young beams with low damage degrees (e.g. beam 2.2) can show an increase of $f_{n}$ .

Figure 10 shows a comparison between the literature and the additional experimental test programmes. The change in natural frequency for mode B1 is shown for most beams. For beams 2.2 and 2.4 from test programme 2, the average change in natural frequency of B2 and B3 is shown, since mode B1 was not identified. It can be seen that observed trends and the resulting changes in $f_{1}$ agree fairly well with the literature. Even though the accelerated corrosion process varies among all experimental programmes, the results demonstrate that the natural frequencies generally decrease with an increase of the CL. Especially when looking at different beams of the same study, which have a similar experimental set-up, a decreasing trend of $f_{1}$ can be found.

The effect of correcting the results with a non-corroding reference beam is also illustrated in Figure 10. Other factors besides corrosion which can influence the modal characteristics might remain unknown when no reference beam is tested and important information might be left unnoticed. Furthermore, the analysis of uncorrected results might lead to an overestimation of the corrosion damage. Although the corrected results are more reliable, their magnitude decreases and changes in natural frequencies due to corrosion are harder to distinguish.

In addition, in two test programmes an increase in $f_{1}$ was noticed. In the tests of Maalej et al.,⁵¹ this was probably due to pre-cracking as discussed before. In the current test programme 2, this was observed for some modes of beams with low CL, and this might be explained by the previously mentioned hydration process and enhanced bond.^51,62

It can be concluded that for low CLs, the stiffness decrease of a structure remains small, while large decreases in stiffness are necessary to obtain changes in modal characteristics. The sensitivity of natural frequencies to detect corrosion is therefore relatively limited for low CLs and with the set-ups and data-processing techniques applied in the studies included in this overview. As a result, it is advised to use higher CLs (>5%) in order to ensure changes in modal characteristics and to prevent the initial increase in bond due to corrosion. Furthermore, a comparison between different studies must be done carefully since the set-up and exposure to corrosion may vary considerably.

The change in mode shapes was not discussed in the literature references, possibly because mostly uniform corrosion damage was induced, which is expected to have a minor effect on the mode shapes, or because of an insufficient amount of accelerometers. A change in modal damping ratio might also indicate corrosion,^24,48,50 even though some of the previous studies have found the modal damping ratio to be less reliable for damage quantification.^46,47,62 The tests in Section ‘Experimental program’ confirmed the latter statement, as no correlation was found between the CL and modal damping ratio.

Besides the CL, other parameters such as the (a)symmetry, crack formation and mode number may have an influence on the changes in natural frequency as well. These influencing factors will be discussed in the following paragraphs.

Influence of (a)symmetry of local corrosion

A comparison is made between beam 1.2_Ls-5.6 and 1.4_La-9.2 of Section ‘Test program 1: locally corroded beams’. Here it is to be noted that both the CL and location of damage were different for both beams. Beam 1.4 has an overall larger decrease in natural frequencies after correction with a reference beam (Table 3), which is in line with its higher CL. Yet, when the different mode shapes are studied, some interesting observations can be made in relation to the location of corrosion. For mode B3, the decrease in natural frequency is larger for symmetrically corroded beam 1.2, even though the CL is lower. This can be explained by the fact that this is an odd mode number. Figure 11 shows that for odd numbered mode shapes (B1 and B3), the zone with the highest curvature is located in the middle of the beam. When the beam is damaged at a location where the curvature is largest, a larger effect on the modal characteristics is expected. Furthermore, beam 1.4 shows a significant difference in natural frequency decrease when comparing mode B2 (−1.75%) with mode B3 (−0.58%). Figure 11 shows that the position of the highest curvature for B2 agrees with the location of the asymmetrically corroded zone of beam 1.4, which may explain the higher decrease in the natural frequency of mode B2 compared to B3. Since the curvature for mode B1 is very similar at the symmetrically and asymmetrically corroded zone, the effect of (a)symmetry may be lower compared to the other modes.

Ndambi et al.⁷⁵ studied the influence of symmetrical and asymmetrical damage induced by mechanical loading and primarily found that asymmetrical damage had a larger influence on the change in mode shapes than symmetrical damage. Additionally, it was noticed that odd numbered modes were more influenced by symmetrical damage while even modes were more influenced by asymmetrical damage.⁷⁶ This is in agreement with the results reported here.

Influence of the crack pattern

Corrosion damage is mainly manifested by longitudinal cracking of the concrete cover at the location of the rebars. During the experimental programmes, no relation was found between the formation of surface cracks and sudden decreases in the natural frequencies. Furthermore, since the crack pattern of all tested beams was similar, no distinction could be made between the results of the beams based on their crack patterns. However, it can be assumed that transverse cracks caused by corrosion of the stirrups have a larger influence on the bending modes than longitudinal cracks. Additionally, more cracks will obviously result in a larger decrease of the bending stiffness and will therefore have a larger influence on the natural frequencies.

The results reported in the literature are not very conclusive when it comes to the influence of cracks. The dissimilarity between experimental set-ups is too large to compare the effects of the crack patterns. Nevertheless, the effect of concrete spalling on dynamic results has been observed by Razak and Choi.⁵⁰ They noticed that spalling of the concrete cover had a large effect on the natural frequencies. Spalling reduced the natural frequencies up to 75% more than moderate cracking. Additionally, Zhang et al.⁴⁹ observed relatively large changes in $f_{1}$ , which were likely related to corrosion of the stirrups, causing transverse cracking of the concrete. However, more research is needed on beams with various crack patterns to further investigate this topic.

Influence of the mode number

The influence of the mode number on the changes in natural frequency caused by damage is a highly discussed topic.⁷⁷ Several researchers investigating corrosion damage^47,50,58,61 claim that the relative change in natural frequencies increases with higher modes, or in other words that higher modes are more sensitive to corrosion damage.

For uniform corrosion, no influence of mode number would be expected since the beam’s stiffness uniformly decreases. According to Equation (1), the natural frequency decreases proportionally to the square root of the Young’s modulus E. On the other hand, when corrosion occurs locally, the change in natural frequency is expected to be influenced by the mode number, as seen in Figure 11. However, the mode shape itself, and hence the location of the highest curvature, could be more dominant than the mode number. Therefore, a clear relation between the relative decrease in natural frequency and the mode number is hard to obtain.

The increasing trend of relative change in natural frequency with increasing mode number is not confirmed by either of the experimental test programmes reported in this paper. Tables 3 and 4 do not show a larger decrease in natural frequency for higher mode shapes. Moreover, also higher order mode shapes (up to 2500 Hz) were investigated for both test programmes and no correlation was found between the decrease in $f_{n}$ and the mode number. Also Capozucca and Cerri⁵² did not find a clear trend in their work. To verify these findings, simulations were performed with varying lengths and locations of the damaged zone. For sake of brevity, these simulations are not further discussed in this paper. The results showed no influence of the mode number on the change in natural frequencies. Instead, the location of the damaged area with regard to the curvature of the mode shape had a greater impact on the decrease in natural frequency. Thus, the influence of the mode number remains unclear and should be part of further investigations.

Challenges and recommendations

General challenges within data-based VBM of structures in the field are the noise effects caused by environmental influences and measurement uncertainties.^34,78 However, different techniques have been developed to cope with these issues and VBM has been used successfully in experimental testing and on-site.^34,67 This section focuses on specific challenges encountered during dynamic testing of corroding samples in laboratory conditions. Noise is therefore limited and the temperature and humidity have a negligibly small impact on the results since they will not vary significantly. However, measurement uncertainties remain an issue during the testing of corroded samples in the laboratory, next to other set-up-related challenges which have until now remained unexplored.

First of all, not all experimental programmes discussed in Section ‘Discussion on experimental results reported in the literature’ have used an uncorroded reference beam, although proven valuable in previous research.^25–27 The tests which were performed within the framework of this paper confirm the need for a reference beam during experimental testing, since creep and shrinkage can reduce the natural frequencies of young concrete beams. To further study these effects, reference beams 1.3 and 2.1 have been monitored for a longer period until the ages of 208 and 330 days, respectively (Figure 12). The evolution of $f_{n}$ for the non-corroding beams shows that the reduction in natural frequencies is stronger when the beams are younger, confirming the hypothesis that time-dependent concrete properties may have a significant influence on the modal characteristics of young concrete. Therefore, the use of an undamaged reference beam is highly recommended, especially during laboratory testing at relatively young age. The reduction in natural frequencies seems to become less significant at an age of 4 to 10 months, for test programmes 1 and 2, respectively.

When observing Figure 12, for the reference beams some fluctuations are noticeable in the change of natural frequencies in function of time; the frequencies do not decrease monotonically. Since the standard deviations of the natural frequencies are mostly below $1 Hz$ and do never reach over $2.5 Hz$ , large fluctuations are assumed to be mostly caused by other factors than the measurement accuracy. Environmental factors were also excluded as beams were tested in a laboratory with constant temperature and relative humidity.

Therefore, the influence of the support conditions is checked, as presented in Figure 13. Previously, it was confirmed that the test set-up with inflated tyres can approximate dynamic free-free boundary conditions since the beam is vibration isolated from its environment in the frequency range of interest. However, small deviations in the results can occur due to changes in the support conditions. During test programme 1, the tyres were roughly placed with their centre at a distance of $275 mm$ from the edge of the beam (Figure 6). A change of the tyres’ position will change the natural frequencies, based on the location of the tyre with respect to the displacement of the mode shape (Figure 13(left)). Furthermore, also the pressure inside the tyres has an effect on the natural frequencies (Figure 13(right)). It is expected that a higher pressure difference causes larger changes in $f_{n}$ .

Based on the results presented in Figure 13, the small influences due to changes in boundary conditions are expected to have been lower than approximately 0.25% for plausible deviations of tyre position (±10 cm) and pressure (±20 kPa), which is not negligible for the lower CLs.

Another challenging aspect of VBM is the global assessment of stiffness variations by the technique. VBM based on natural frequencies captures global and significant changes in stiffness due to damage, but lacks sensitivity to small-scale local damage.^34,35 Strain mode shapes can be used to increase the sensitivity of VBM to local damage.⁴⁵ Furthermore, the underlying damage process remains unknown when applying dynamic testing. Therefore, it is recommended to add a second, local technique to the test set-up. For several beams described in Section ‘Experimental program’, early damage detection and damage localization was achieved by applying acoustic emission (AE) monitoring.⁷² Also Lacidogna et al.⁷⁹ coupled AE and VBM during bending tests on small concrete beams, although damage was mechanically induced and not related to corrosion. In the study of Vereecken et al.,⁸⁰ it was shown that information on local strains allows updating of model-based VBM information by means of a Bayesian approach. Further research will focus on efficiently combining local and global monitoring techniques, in combination with dedicated filtering, to reduce uncertainties and increase the sensitivity of VBM towards corrosion monitoring in RC structures.

The aforementioned challenges in laboratory conditions might also impact in situ monitoring campaigns. Firstly, although reference beams are necessary in laboratory conditions, the effects of creep and shrinkage will be relatively unimportant in situ since the material is much older than the beams tested in the laboratory. This alleviates the need for a reference structure, which would typically not be available in practice. Instead, a FE model can be used to compare and check the results. Reynders et al.^15,65 have used this model-based approach to localise damage on the Tilff bridge. Secondly, the boundary conditions in situ are mostly unknown and might experience influences of environmental factors. Therefore, the results of VBM on real-life structures should be interpreted with caution and the support conditions should be thoroughly inspected. Finally, the global aspect of natural frequency monitoring can be resolved by adding local NDT methods to the monitoring campaign.

Conclusions

This paper presented a review on data from dynamic tests on corroded RC beams reported in the literature, providing an overview and critical review of the current knowledge, possibilities and challenges. As the literature review showed a lack of coherent datasets, experimental tests were performed to extend the limited available data and to enable a more thorough validation of the VBM method for corroded RC beams. Two test programmes were performed and included both local and uniform corrosion.

Based on the analysis of literature data and experimental results, following main conclusions were drawn:

High CLs will decrease the natural frequencies of an RC beam. However, due to scatter, this trend is best observed when comparing specimens with different CLs from the same test programme.

Beams with low CLs might show an insignificant decrease in natural frequencies, or even have slightly increased frequencies, which is attributed to the enhanced bond.

Comparison between different experimental programmes should be done carefully since corrosion set-ups vary significantly, and test set-up variations may have a larger effect on the results than the CLs.

No reliable results in changes of mode shapes and modal damping ratios were found in relation to the CL for corroding RC beams.

The careful execution of two test programmes and comparison with literature data allowed to identify additional factors that influence the natural frequencies as well. The effect of corrosion damage on the bending modes will be largest when the damage appears in the zones with highest modal curvature. Furthermore, transverse cracking and spalling have a larger effect on the parameters of the flexural mode shapes than longitudinal cracking. The influence of the mode number remains unclear as the literature does not agree on this point, and no clear trend was observed in the additional experimental results. Yet, the location with the greatest curvature may be more influential than the mode number.

Finally, several unexplored challenges in dynamic testing of corroded RC beams were identified, and recommendations were formulated:

The sensitivity of natural frequencies may not be sufficient for low CLs and local damage. Low CLs might even increase the bond strength between the rebar and concrete. Therefore, it is advised to assume CLs of at least 5% for significant results.

During the laboratory tests, comparing the results to a non-corroded reference beam is essential to reduce influences of time-dependent concrete properties on the modal characteristics, especially for relatively young RC samples.

Neglecting the effects of creep and shrinkage might lead to an overestimation of the corrosion damage. For the uncorroded reference beams in our experiments, changes in natural frequencies up to −2.5% (beams of 3 m length) and −8% (beams of 5 m length) were found. These decreases in natural frequencies appeared to reduce significantly when using beams at an age of 4–10 months.

The results appear to be strongly influenced by the beams’ support conditions. Hence, it is important to maintain appropriate and consistent support conditions for all tests. It was shown that changes up to 0.25% in natural frequencies might be expected for small deviations of the position (±10 cm) and pressure (±20 kPa) of the supporting tyres.

Obtaining information about the underlying damage processes is challenging. These challenges should be elaborated in future work by dedicated filtering and combining local and global monitoring techniques. Additionally, to draw accurate conclusions from the modal damping ratios, more information about the boundary conditions is required. And finally, as the analysis has shown that displacement mode shapes and modal damping ratios are less reliable, the use of strain mode shapes could increase the sensitivity of VBM to local damage.

Footnotes

Acknowledgements

The authors acknowledge the collaborations with the FWO-SBO project LifeMACS (project no. S001021N).

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work has been funded by the Research Foundation Flanders (FWO PhD-grands no. 1SC1921N and FWO project no. G013317N).

ORCID iD

Eline Vandecruys

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