A new approach to estimate damage in concrete beams using non-linearity

Construction and Building Materials 124 (2016) 1081–1089

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A new approach to estimate damage in concrete beams using non-linearity Muhammad Usman Hanif ⇑, Zainah Ibrahim ⇑, Mohammed Jameel, Khaled Ghaedi, Muhammad Aslam Department of Civil Engineering, Faculty of Engineering, University of Malaya, 50603 Kuala Lumpur, Malaysia

h i g h l i g h t s
Lack of globally applicable damage detection method in RC beams.
Constitutive relations for damage in concrete beams.
Method proposed for damage detection without requiring undamaged state.
Nonlinear damage detection in RC beams through simulations.
This model is capable of detecting damage in inverse problem solving.

a r t i c l e

i n f o

Article history: Received 13 May 2016 Received in revised form 17 July 2016 Accepted 28 August 2016

Keywords: Damage Concrete Nonlinear analysis Inverse problem Implicit dynamic analysis

a b s t r a c t Damage detection in concrete structures has become a serious problem for engineers. Despite spanning almost half a century, the research on this subject has proven a lack of globally applicable damage detection methodology that can detect damage without the use of parameters from the undamaged state. Therefore, there is a vital need to detect damage without the use of data from the undamaged state of the structure. This research focuses on integrating the power of commercial finite element software using modal dynamic analysis to detect damage in concrete structures. To achieve this goal, a simulation based damage detection method is used that incorporates the Concrete Damaged Plasticity model. The linear and non-linear dynamic analysis are compared and then the sensitivity of the nonlinear dynamic analysis is discussed. The results show good agreement with the previous research using different approaches. In addition, the proposed method shows significant sensitivity to estimate damage and that it can be integrated with modal testing to assess the current condition of the structure without the need for baseline data. The mesh size effect on crack formation is also investigated. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction Concrete as a construction material has certain advantages over other materials. It is more durable, requires less maintenance, and has simpler and cheaper constituents. In terms of durability, different design codes specify the design life of concrete structures, as shown in Table 1. Most concrete structural failures are either during the construction phase or due to heavy environmental calamities [1]. The failure or collapse during construction can be due to substandard construction practices. Also, the influence of environmental effects is generally not incorporated during the design of a structure. That is why environmental influences magnify the deterioration process ⇑ Corresponding authors. E-mail addresses: [email protected] (M.U. Hanif), [email protected] (Z. Ibrahim). http://dx.doi.org/10.1016/j.conbuildmat.2016.08.139 0950-0618/Ó 2016 Elsevier Ltd. All rights reserved.

and the structures start deteriorating before their design life [2]. Structures are most affected by dynamic loads, which are frequent in bridges and high rise buildings. A survey in 2002 by the US Department of transportation showed that out of 5,91,707 bridges a total of 1,62,869 (28%) were structurally deficient [3]. Significant financial and human resources are required to deal with this immense inventory of structures. This huge amount of structural inadequacy calls for effective and efficient damage detection methods that are easier, more convenient and applicable to a variety of structures. In addition, concrete is the most popular material in civil infrastructure and has certain merits due to self-weight, economy and maintenance free construction. The currently employed damage detection methods consist of biennial inspection by technical staff who use visual aids, which requires a lot of resources and staff. Usually, a consultancy firm is hired to do the detailed analysis and produce a report based on which economic rehabilitation measures are taken [4,5].

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Table 1 Service life of structures specified by different codes. Code

References

Service Life

Eurocode [21]

EN 1990: Basics of structural design

AASHTO [22]

AASHTO LRFD Bridge design specifications ACI 318-14, Building code requirements for structural concrete

50 years for common structures 100 years for monumental structures 75 years

American Concrete Institute [23]

Not specified

This research models the flexural response of the beam by utilizing the available capabilities in ABAQUS [20] to detect damage. The advantage of this technique is its convenience for engineers and the capability of inverse problem solving. The damage parameters and detection of non-linearity were examined based on which the structural condition was predicted. The article commences by discussing the damage levels and selecting suitable constitutive relations. Then the process of simulation is detailed and the results are discussed. Finally, conclusions are made based on the results and discussions. 2. Damage in concrete and constitutive relations

Currently, inspection methods, such as visual inspection, eddy current, magnetic particle, ultrasonic, thermal infrared, impact echo and acoustic emission testing, are widely used for structural health monitoring [6–9]. However, these methods are localized damage detection techniques and require the vicinity of damage to be known prior to performing the test. Engineering judgment is used to locate the vicinity of the damage before testing, which, sometimes, is time-consuming. In addition, these methods are applicable when both sides of the damage location are accessible, which is not always possible during the test. Another approach that has been frequently implemented for damage prediction, is through investigating crack formation mechanisms in concrete. The analytical model for crack propagation in concrete beams was first presented by Ulfkjaer et al. [10]. A linear softening relation was used in the analysis. Vibration methods were employed to examine non-linearity in concrete beams through experimentation and it was established that nonlinearity increased with an increase in damage and was most pronounced at lower damage levels [11]. This was later used as a damage indicator in determining the flexural damage in reinforced concrete beams [12]. In spite of being a damage indicator and analytically sound in nature, the model’s application was limited to flexural damage detection. Based on the above review, there are many damage detection algorithms being used for damage detection. Although considerable effort is being made in modeling concrete cracking, crushing and damage mechanisms in commercial finite element software ABAQUS [13–19], the sensitivity to damage with the aid of finite element software has seldom been examined. Thus, there is a necessity for a global damage detection mechanism that does not require data from the undamaged structure. Furthermore, the damage detection method should be applicable to a wide range of structures.

2.1. Damage in concrete Concrete is strong in compression and weak in tension. In most cases, the damage starts with the initiation of cracks, which propagate and finally lead to collapse. Damage, in general, is defined as the condition of the structure when it is not operating in its ideal condition but is still serviceable. A fault, on the other hand, is the state when the structure is no longer serviceable, and a defect is an inconsistency in the material. A damaged stage is the stage where plans are made to detect a problem in the structure so that it could be taken care of before the occurrence of a fault [24]. Previously, the damage was artificially induced in the test specimens by making saw cuts or creating cavities by putting some inert material during casting of the specimen. Those techniques were not representative of the realistic damage in the specimens because they are not suitable for concrete cracking [25]. Recently, damage was incorporated as a function of the maximum allowable load on the specimen making it convenient to quantify damage as a percentage of the maximum load [11,12]. In this study, damage was defined in 10 intervals up to the maximum load the specimen could carry. 2.2. Concrete The compressive model used in this study translates the stressstrain behavior of concrete in agreement with most of the models [26]. However, in this study, tensile concrete modeling was the focus, so a convenient compressive model was chosen, which depended on the modulus of elasticity and the compressive strength of concrete. Martinez et al. [27] proposed a correlation between the modulus of elasticity of concrete and the 28-day compressive strength in the range 21–83 MPa, as given in Eq. (1).

Fig. 1. Response of concrete to uniaxial loading in tension (a) and compression (b).

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M.U. Hanif et al. / Construction and Building Materials 124 (2016) 1081–1089 Table 2 Mechanical properties of concrete.

Table 3 Mechanical properties of steel reinforcement.

m

Density Tonne/mm3

fcu MPa

fct MPa

Ec MPa

–

2.4E9

36.5

3.65

26957.85

0.15

40

Yield Stress, Mpa

Plain bars Main bars

Diameter (mm)

fy (MPa)

Es (MPa)

es

m

q

6 10

393.600 540.800

208,000 199,200

0.25 0.32

0.3 0.3

7850 7850

qffiffiffiffi 0 Ec ¼ 3320 f c þ 6900

35

kg/m3

ð1Þ

30 25 20 15 10 5 0

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

0.009

Inelastic Strain Fig. 2. Compressive yield stress vs. inelastic strain.

4 3.5

Yield Stress, Mpa

Bar type

3 2.5 2 1.5 1

2.3. Steel reinforcement

0.5 0

The model used for the compressive strength of concrete was the concrete damaged plasticity (CDP) model proposed in the paper [26]. The CDP model was chosen in the finite element software ABAQUS [28]. The concrete damaged plasticity model is capable of carrying out the static and dynamic analysis of RC members with bars embedded. The model includes isotropic material, which accounts for tensile cracking and the compressive crushing modes. Most importantly, the model is also capable of stiffness degradation with irreversible damage that occurs during the fracture process [29]. The response of concrete to uniaxial tension and uniaxial compression is shown in Fig. 1(a) and (b), respectively. For the CDP model, the default values of the dilation angle, eccentricity, fb0/fc0, K and viscosity parameter were used as 35, 0.1, 1.16, 0.667 and 0.01, respectively. These parameters were also used with slight variations in other models [16,19]. The mechanical properties of concrete are summarized in Table 2, while the input constitutive relations and the damage parameters as a function of the compressive and tensile strengths are shown in Figs. 2–5.

0

0.0005

0.001

0.0015

0.002

0.0025

0.003

Cracking Strain Fig. 3. Concrete tensile softening model, yield stress vs. cracking strain.

The constitutive relationship adopted by Bai et al. [30] was used. Two types of steel reinforcement were used. Plain bars with 6 mm diameter were used for the top reinforcement and transverse reinforcement while 10 mm bars were used as the main tension reinforcement. The properties of the steel reinforcement are shown in Table 3.

Damage Parameter

1 0.8

3. Finite element simulation

0.6

Commercial software subroutine ABAQUS 6.14 was used for the analysis. The reference test data used were taken from recent research [12]. The selected experimental setup is shown in Fig. 6. The beam was applied with four-point loading. The accelerations and displacements for dynamic loading were recorded at the nodes, as shown in the test setup. Roller and hinge boundary conditions were found suitable for matching the modal frequencies with the test data. Two types of meshing were used; 25 mm element size for the analysis and 10 mm element size for the crack visualization. The summary of the mesh details is shown in Table 4. Convergence was achieved in meshing and the analysis results were reasonably similar for both meshing sizes. Static analysis was performed with the incremental static load as a percentage of damage. The approximate maximum load that the beam can take was 45 kN. The total load was incrementally applied in increments of approximately 10–15% of the maximum load and was specified as the percentage of damage. The load step can be seen in Fig. 7. After every loading and unloading, dynamic analysis was performed with harmonic excitation, which was less than the first natural frequency, for 5 s. A harmonic excitation of 30 Hz (less than the first natural frequency) was applied at a point below the loading point. The response of the harmonic excitation was recorded via software using the linear perturbation procedure. A linear perturbation step of the system provides the linear response of

0.4 0.2 0

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

0.009

Inelastic Strain Fig. 4. Damage parameter vs. inelastic strain.

Damage Parameter

1 0.8 0.6 0.4 0.2 0

0

0.0005

0.001

0.0015

0.002

0.0025

Cracking Strain Fig. 5. Damage parameter vs. cracking strain.

0.003

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M.U. Hanif et al. / Construction and Building Materials 124 (2016) 1081–1089

Fig. 6. Beam setup (from previous experimental data [12]).

Table 4 Meshing Details for the Analysis. Mesh size

25 mm 10 mm

Types of analysis run Static

Modal dynamic

Dynamic implicit

U U

U –

U –

Number of nodes

Number of elements

6534 6,97,761

4800 6,55,200

the system about the last non-linear step (base state) prior to the linear perturbation. Modal dynamic analysis was performed after that with the same harmonic input excitation of 30 Hz. The modal dynamic procedure provides time history analysis of linear systems. The excitation is given as a function of time. It was assumed that the amplitude curve was specified so that the magnitude of the excitation varied linearly within each increment [31]. The response of the modal dynamic analysis is detailed in Section 4.5.1. Non-linear dynamic analysis was performed with the same input excitation, i.e. harmonic excitation with a frequency of 30 Hz. Implicit dynamic analysis procedure was chosen for this purpose because of its stability for larger time steps. The response of the system was calculated using the implicit time integration

scheme [28]. The flow chart for the procedure explained above is shown in Fig. 8. Raleigh damping was used for the model with the damping ratio taken as 5 percent [32]. The results of implicit dynamic analysis are detailed in Section 4.5.2. 4. Results and discussion The results of the simulation of a reinforced concrete beam in finite element software ABAQUS are stated and discussed in this section. 4.1. Static simulation load-deflection results The load-deflection response of the static test is shown in Fig. 9. For four-point loading, the deflections were recorded at the midspan of the beam. The load-deflection response was recorded for comparison with the experimental data. The load deflection response was compared with the model proposed by Hamad et al. [33] for a 50% damage load. The load-deflection response of the current model agrees well with the model reference model. The current model shows slightly less stiff behavior compared to the comparison model, which can be attributed to the support

Fig. 7. Load step configuration (with percentage of maximum static load shown in data labels).

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30

Constitutive Relation Applied Load, kN

25

Boundary Conditions

Apply Load

20 15 10 Present Study 5 Hamad et al. 0

Unloading no

Determination of Natural frequencies

0

2

4 6 Midpoint Deflection, mm

8

10

Fig. 9. Static load-deflection plot of the beam up to 50% damaged load.

Next Load Step

Natural frequency matches with test data?

yes

Harmonic Excitation (less than first natural frequency)

Frequency Response

similar research [12], which assumed the initiation of the cracks along the stirrup lines and was verified experimentally. The slight differences in the crack formation were refined using a finer mesh. Hamad et al. [33] assumed the cracks form along the stirrups at equal distance. The present study validates the initiation of formation cracks by the flexural damage model at lower damage levels, as shown in Fig. 10. The dotted lines are overlain along the initiation of the cracks in similar research, which gives an idea of the crack formation in the simulated model. The onset of the vertical cracks was inclined, which indicates the capability of the present study for mixed-mode cracking as well, which can be separately investigated by applying a three-point loading. The mixed-mode cracking in the cracking is a combination of flexural and shear (or torsion) cracking, which is the practical case scenario for damage being induced in structures. 4.3. Relation of mesh size and crack pattern

Record displacements and accelerations Fig. 8. Flow chart for finite element simulation.

conditions and the inclusion of compression reinforcement, as well as the contribution of the stirrups, which, as explained by Aslam et al. [34], increases the ductility of the beam model. 4.2. Crack propagation The software was capable of indicating the inclined crack propagation. The cracking pattern was compared with the analytically developed flexural model, which is capable of detecting damage through non-linearity [12]. The reason for crack investigating crack propagation was to validate the capability of the present study for mixed-mode crack formation. The major cracks seemed to be significantly vertical to match the cracking pattern predicted by

To see the crack patterns with high accuracy, an attempt was made to reduce the mesh size of the concrete beam from 25 mm (see Fig. 10) to 10 mm, as depicted in Fig. 11. Likewise, the meshing was further refined to thoroughly investigate the inclined crack formation in the beam for each damage level, as shown in Fig. 11. There was a shear span of 1000 mm on both sides and the cracks were supposed to be inclined in the shear span. From this figure, it can be seen that at the 46% damage level, the cracks started to become oblique. The onset of oblique cracking can be set as a reference point for damage to predict the shear behavior, which can aid in mixed-mode crack formation. 4.4. Modal frequency deterioration The modal frequency response of the modal analysis is illustrated in Fig. 12. In the figure, first, five normalized modal frequencies were plotted against the damage levels to see the trend of each mode. In the elastic range, there was no degradation in the

Fig. 10. Comparison of simulated cracking pattern (below) with Hamad et al., (above) [12].

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Fig. 11. Crack formation for 10 mm mesh at different load levels.

1

Normalized natural Frequency

0.95

0.9 Mode 1 Mode 2

0.85

Mode 3 Mode 4 Mode 5

0.8

Hamad et al.

0.75

0

10

20

30

40

50

60

70

80

90

100

% of Damage Fig. 12. Reduction in normalized frequency against the percentage of damage.

natural frequency. The reason for discussing the modal frequency deterioration is to make a comparison of intensively used past methods [35] with the current study in terms of sensitivity to damage. As the stiffness of the beam reduced with increasing damage, there was a reduction in the natural modal frequency but not significant enough even at complete failure. In field conditions, this

small difference in response can be easily influenced by environmental conditions. Herein, the study attempted to analyze the deterioration of the system with the use of a few lower modes. The decline in the first modal frequency by non-linear analysis was performed by Hamad et al. [36], as illustrated in Fig. 12, which also showed degradation in natural frequency but was not

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1E+00

Power Spectral Density (mm/Hz)

1E-01 1E-02 1E-03

15%Damage

23%Damage

28%Damage

35%Damage

46%Damage

59%Damage

70%Damage

82%Damage

95%Damage

100%Damage

1E-04 1E-05 1E-06 1E-07 1E-08 1E-09 1E-10

0

30

60

90

Frequency (Hz) Fig. 13. Response of harmonic excitation at 30 Hz for modal dynamic analysis.

Fig. 14. Response of harmonic excitation at 30 Hz for dynamic implicit analysis.

sensitive enough to detect damage without the influence of environmental effects. 4.5. Sensitivity to damage In the present simulation, two types of dynamic analysis were performed separately, as explained in Section 3. The modal dynamics and implicit dynamic analysis were used as linear and non-linear analysis, respectively. Both systems were evaluated based on the presence of non-linearity and compared with each other in detail. The nonlinear dynamic analysis was said to be sensitive to damage through the formation of super-harmonics [36]. A comparison was made between modal dynamic analysis and dynamic implicit analysis, as explained below. 4.5.1. Modal dynamics The dynamic response of the structure for each damage level is shown in Fig. 13. The structure was loaded and unloaded monotonically for each damage level. Modal dynamic analysis was

performed after each loading cycle. A harmonic excitation was applied for a frequency of 30 Hz for a time of 5 s. The response of the system was analyzed through Fast Fourier Transform (FFT) to achieve power spectral density to investigate the formation of super-harmonics. There was no indication of super-harmonics at any damage level, as shown in Fig. 13. Hence modal dynamic analysis, as previously used, is not necessarily sensitive to damage. 4.5.2. Dynamic implicit analysis The dynamic implicit analysis was done through a significantly lower time step (0.0001 s). Again a harmonic excitation was applied at a frequency of 30 Hz for 5 s. The response, as power spectral density, is illustrated in Fig. 14. The super-harmonics were formed at integer multiples of the excitation frequency. The amplitude of the super-harmonics was studied for all damage levels and a comparison was made. The magnified depictions of superharmonics at 60 Hz and 90 Hz are shown in Figs. 15 and 16, respectively.

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According to the aforementioned interpretations from Figs. 14–16, the trend of amplitude of super-harmonics with increasing damage was plotted in Fig. 17. The super-harmonics reflect the presence of nonlinearity [33] and it can be seen that the nonlinearity increases up to the 35% damage level and then starts decreasing after the 46% damage level. This implies that the presence of nonlinearity is at its maximum at lower damage levels, and starts reducing when the damage is further increased. Therefore, the nonlinearity can be a damage indicator at lower damage levels. A similar trend of non-linearity with damage has also been observed elsewhere [11,12]. 5. Conclusions A sensitive damage detection method was presented in this study. The investigation of damage sensitive parameters was undertaken through computer-aided simulations. The Concrete Damaged Plasticity (CDP) model was implemented to simulate a reinforced concrete beam to detect damage globally via the existence of non-linearity. The model formulation makes it convenient for engineers and researchers to investigate the damage of concrete in more detail and gain more insights incorporating the existing simplified research. Based on the aforesaid explanations, the following conclusions can be drawn.

Fig. 15. First super-harmonics at 60 Hz (magnified view).

1. The concrete damaged plasticity (CDP) model is capable of detecting damage without the use of baseline data of the structure, which is very useful for detecting damage in existing infrastructure where there is a lack of data for the undamaged structure. 2. As damage is detected through the presence of non-linearity, which increases with increasing damage and is more pronounced at lower damage levels, the method proposed in the current study can be very useful in detecting damage in its initial stages. 3. The non-linear dynamic analysis (Implicit Dynamic Analysis) is more sensitive to damage compared to the linear dynamic analysis (Modal Dynamic Analysis). Unlike linear dynamic analysis, the modal parameters of non-linear dynamic analysis are more sensitive to damage and are less influenced by environmental conditions. 4. Reasonable crack formation can be predicted using the damage parameters at reasonably coarser meshing. 5. The present study offers promising insights into mixed-mode crack formation, as cracks in visualization get inclined at higher damage levels. Mixed-mode crack formation is the practical case scenario for damage in concrete beams.

Difference in superharmonics and curve fit

Fig. 16. Second super-harmonics at 90 Hz (Magnified View).

0.35 1st Superharmonic

0.3

2nd Superharmonic

Finally, the currently applied procedure can provide a major breakthrough in damage detection in realistic damage scenarios (e.g. mix mode crack formation) without the need of baseline structural data. Improved tension and compression damage parameters, together with efficient computing can be used to enhance the damage efficiency in the future.

0.25 0.2 0.15 0.1 0.05

Acknowledgements

0 0

10

20

30

40 50 % of Damage

60

70

80

90

Fig. 17. Trend of super-harmonics as nonlinearity against increasing damage.

The formation of super-harmonics indicated the presence of nonlinearity. The super-harmonics amplitude was compared with each damage level to investigate the trend of increase in damage to the nonlinearity. It can be seen that the non-linearity increased up to 35% of damage and then decreased, and after a damage level of 50% it showed a different behavior.

This research was supported by University Malaya Research Grant (UMRG – Project No. RP004A/13AET), University Malaya Postgraduate Research Fund (PPP – Project No. PG187-2014B) and Fundamental Research Grant Scheme, Ministry of Education, Malaysia (FRGS – Project No. FP028/2013A). References [1] M.A. Khan, Accelerated bridge construction, Accel. Bridg. Constr., Elsevier, 2015, pp. 257–308, http://dx.doi.org/10.1016/B978-0-12-407224-4.00006-X.

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