Construction and Building Materials 124 (2016) 1081–1089

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Construction and Building Materials

journal homepage: www.elsevier .com/locate /conbui ldmat

A new approach to estimate damage in concrete beams usingnon-linearity

http://dx.doi.org/10.1016/j.conbuildmat.2016.08.1390950-0618/� 2016 Elsevier Ltd. All rights reserved.

⇑ Corresponding authors.E-mail addresses: usmanhnf@gmail.com (M.U. Hanif), zainah@um.edu.my

(Z. Ibrahim).

Muhammad Usman Hanif ⇑, Zainah Ibrahim ⇑, Mohammed Jameel, Khaled Ghaedi, Muhammad AslamDepartment 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 2016Received in revised form 17 July 2016Accepted 28 August 2016

Keywords:DamageConcreteNonlinear analysisInverse problemImplicit dynamic analysis

a b s t r a c t

Damage detection in concrete structures has become a serious problem for engineers. Despite spanningalmost half a century, the research on this subject has proven a lack of globally applicable damage detec-tion 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 ofthe structure. This research focuses on integrating the power of commercial finite element software usingmodal dynamic analysis to detect damage in concrete structures. To achieve this goal, a simulation baseddamage detection method is used that incorporates the Concrete Damaged Plasticity model. The linearand non-linear dynamic analysis are compared and then the sensitivity of the nonlinear dynamic analysisis discussed. The results show good agreement with the previous research using different approaches. Inaddition, the proposed method shows significant sensitivity to estimate damage and that it can be inte-grated with modal testing to assess the current condition of the structure without the need for baselinedata. The mesh size effect on crack formation is also investigated.

� 2016 Elsevier Ltd. All rights reserved.

1. Introduction

Concrete as a construction material has certain advantages overother materials. It is more durable, requires less maintenance, andhas simpler and cheaper constituents. In terms of durability, differ-ent design codes specify the design life of concrete structures, asshown in Table 1.

Most concrete structural failures are either during the construc-tion phase or due to heavy environmental calamities [1]. The fail-ure or collapse during construction can be due to substandardconstruction practices. Also, the influence of environmental effectsis generally not incorporated during the design of a structure. Thatis why environmental influences magnify the deterioration process

and the structures start deteriorating before their design life [2].Structures are most affected by dynamic loads, which are frequentin bridges and high rise buildings. A survey in 2002 by the USDepartment of transportation showed that out of 5,91,707 bridgesa total of 1,62,869 (28%) were structurally deficient [3]. Significantfinancial and human resources are required to deal with thisimmense inventory of structures. This huge amount of structuralinadequacy calls for effective and efficient damage detection meth-ods that are easier, more convenient and applicable to a variety ofstructures. In addition, concrete is the most popular material incivil infrastructure and has certain merits due to self-weight, econ-omy and maintenance free construction. The currently employeddamage detection methods consist of biennial inspection by tech-nical staff who use visual aids, which requires a lot of resourcesand staff. Usually, a consultancy firm is hired to do the detailedanalysis and produce a report based on which economic rehabilita-tion measures are taken [4,5].

Table 1Service life of structures specified by different codes.

Code References Service Life

Eurocode [21] EN 1990: Basics ofstructural design

50 years forcommon structures100 years formonumental structures

AASHTO [22] AASHTO LRFD Bridgedesign specifications

75 years

American ConcreteInstitute [23]

ACI 318-14, Building coderequirements forstructural concrete

Not specified

1082 M.U. Hanif et al. / Construction and Building Materials 124 (2016) 1081–1089

Currently, inspection methods, such as visual inspection, eddycurrent, magnetic particle, ultrasonic, thermal infrared, impactecho and acoustic emission testing, are widely used for structuralhealth monitoring [6–9]. However, these methods are localizeddamage detection techniques and require the vicinity of damageto be known prior to performing the test. Engineering judgmentis used to locate the vicinity of the damage before testing, which,sometimes, is time-consuming. In addition, these methods areapplicable when both sides of the damage location are accessible,which is not always possible during the test.

Another approach that has been frequently implemented fordamage prediction, is through investigating crack formation mech-anisms in concrete. The analytical model for crack propagation inconcrete beams was first presented by Ulfkjaer et al. [10]. A linearsoftening relation was used in the analysis. Vibration methodswere employed to examine non-linearity in concrete beamsthrough experimentation and it was established that non-linearity increased with an increase in damage and was mostpronounced at lower damage levels [11]. This was later used as adamage indicator in determining the flexural damage in reinforcedconcrete beams [12]. In spite of being a damage indicator andanalytically sound in nature, the model’s application was limitedto flexural damage detection.

Based on the above review, there are many damage detectionalgorithms being used for damage detection. Although consider-able effort is being made in modeling concrete cracking, crushingand damage mechanisms in commercial finite element softwareABAQUS [13–19], the sensitivity to damage with the aid of finiteelement software has seldom been examined. Thus, there is anecessity for a global damage detection mechanism that does notrequire data from the undamaged structure. Furthermore, thedamage detection method should be applicable to a wide rangeof structures.

Fig. 1. Response of concrete to uniaxial load

This research models the flexural response of the beam by uti-lizing the available capabilities in ABAQUS [20] to detect damage.The advantage of this technique is its convenience for engineersand the capability of inverse problem solving. The damage param-eters and detection of non-linearity were examined based onwhich the structural condition was predicted. The article com-mences by discussing the damage levels and selecting suitableconstitutive relations. Then the process of simulation is detailedand the results are discussed. Finally, conclusions are made basedon the results and discussions.

2. Damage in concrete and constitutive relations

2.1. Damage in concrete

Concrete is strong in compression and weak in tension. In mostcases, the damage starts with the initiation of cracks, which prop-agate and finally lead to collapse. Damage, in general, is defined asthe condition of the structure when it is not operating in its idealcondition but is still serviceable. A fault, on the other hand, is thestate when the structure is no longer serviceable, and a defect isan inconsistency in the material. A damaged stage is the stagewhere plans are made to detect a problem in the structure so thatit could be taken care of before the occurrence of a fault [24].Previously, the damage was artificially induced in the test speci-mens by making saw cuts or creating cavities by putting some inertmaterial during casting of the specimen. Those techniques werenot representative of the realistic damage in the specimensbecause they are not suitable for concrete cracking [25]. Recently,damage was incorporated as a function of the maximum allowableload on the specimenmaking it convenient to quantify damage as apercentage of the maximum load [11,12]. In this study, damagewas defined in 10 intervals up to the maximum load the specimencould carry.

2.2. Concrete

The compressive model used in this study translates the stress-strain behavior of concrete in agreement with most of the models[26]. However, in this study, tensile concrete modeling was thefocus, so a convenient compressive model was chosen, whichdepended on the modulus of elasticity and the compressivestrength of concrete. Martinez et al. [27] proposed a correlationbetween the modulus of elasticity of concrete and the 28-daycompressive strength in the range 21–83 MPa, as given in Eq. (1).

ing in tension (a) and compression (b).

Table 2Mechanical properties of concrete.

Density fcu fct Ec mTonne/mm3 MPa MPa MPa –

2.4E�9 36.5 3.65 26957.85 0.15

0

5

10

15

20

25

30

35

40

0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009

Yie

ld S

tres

s, M

pa

Inelastic Strain

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

0

0.5

1

1.5

2

2.5

3

3.5

4

0 0.0005 0.001 0.0015 0.002 0.0025 0.003

Yie

ld S

tres

s, M

pa

Cracking Strain

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

0

0.2

0.4

0.6

0.8

1

0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009

Dam

age

Para

met

er

Inelastic Strain

Fig. 4. Damage parameter vs. inelastic strain.

0

0.2

0.4

0.6

0.8

1

0 0.0005 0.001 0.0015 0.002 0.0025 0.003

Dam

age

Para

met

er

Cracking Strain

Fig. 5. Damage parameter vs. cracking strain.

Table 3Mechanical properties of steel reinforcement.

Bar type Diameter(mm)

fy(MPa)

Es(MPa)

es m qkg/m3

Plain bars 6 393.600 208,000 0.25 0.3 7850Main bars 10 540.800 199,200 0.32 0.3 7850

M.U. Hanif et al. / Construction and Building Materials 124 (2016) 1081–1089 1083

Ec ¼ 3320ffiffiffiffif 0c

qþ 6900 ð1Þ

The model used for the compressive strength of concrete wasthe concrete damaged plasticity (CDP) model proposed in thepaper [26]. The CDP model was chosen in the finite elementsoftware ABAQUS [28]. The concrete damaged plasticity model iscapable of carrying out the static and dynamic analysis of RC mem-bers with bars embedded. The model includes isotropic material,which accounts for tensile cracking and the compressive crushingmodes. Most importantly, the model is also capable of stiffnessdegradation with irreversible damage that occurs during thefracture process [29]. The response of concrete to uniaxial tensionand uniaxial compression is shown in Fig. 1(a) and (b), respec-tively. 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 alsoused with slight variations in other models [16,19]. The mechanicalproperties of concrete are summarized in Table 2, while the inputconstitutive relations and the damage parameters as a function ofthe compressive and tensile strengths are shown in Figs. 2–5.

2.3. Steel reinforcement

The constitutive relationship adopted by Bai et al. [30] wasused. Two types of steel reinforcement were used. Plain bars with6 mm diameter were used for the top reinforcement and trans-verse reinforcement while 10 mm bars were used as the maintension reinforcement. The properties of the steel reinforcementare shown in Table 3.

3. Finite element simulation

Commercial software subroutine ABAQUS 6.14 was used for theanalysis. The reference test data used were taken from recentresearch [12]. The selected experimental setup is shown in Fig. 6.The beam was applied with four-point loading. The accelerationsand displacements for dynamic loading were recorded at thenodes, as shown in the test setup. Roller and hinge boundaryconditions were found suitable for matching the modal frequencieswith the test data. Two types of meshing were used; 25 mmelement size for the analysis and 10 mm element size for the crackvisualization. The summary of the mesh details is shown in Table 4.Convergence was achieved in meshing and the analysis resultswere reasonably similar for both meshing sizes.

Static analysis was performed with the incremental static loadas a percentage of damage. The approximate maximum load thatthe beam can take was 45 kN. The total load was incrementallyapplied in increments of approximately 10–15% of the maximumload and was specified as the percentage of damage. The load stepcan be seen in Fig. 7.

After every loading and unloading, dynamic analysis wasperformed with harmonic excitation, which was less than the firstnatural frequency, for 5 s. A harmonic excitation of 30 Hz (less thanthe first natural frequency) was applied at a point below the load-ing point. The response of the harmonic excitation was recordedvia software using the linear perturbation procedure. A linearperturbation step of the system provides the linear response of

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

Table 4Meshing Details for the Analysis.

Meshsize

Types of analysis run Number ofnodes

Number ofelements

Static Modaldynamic

Dynamicimplicit

25 mm U U U 6534 480010 mm U – – 6,97,761 6,55,200

1084 M.U. Hanif et al. / Construction and Building Materials 124 (2016) 1081–1089

the system about the last non-linear step (base state) prior to thelinear perturbation. Modal dynamic analysis was performed afterthat with the same harmonic input excitation of 30 Hz. The modaldynamic procedure provides time history analysis of linear sys-tems. The excitation is given as a function of time. It was assumedthat the amplitude curve was specified so that the magnitude ofthe excitation varied linearly within each increment [31]. Theresponse of the modal dynamic analysis is detailed in Section 4.5.1.

Non-linear dynamic analysis was performed with the sameinput excitation, i.e. harmonic excitation with a frequency of30 Hz. Implicit dynamic analysis procedure was chosen for thispurpose because of its stability for larger time steps. The responseof the system was calculated using the implicit time integration

Fig. 7. Load step configuration (with percentage o

scheme [28]. The flow chart for the procedure explained above isshown in Fig. 8. Raleigh damping was used for the model withthe damping ratio taken as 5 percent [32]. The results of implicitdynamic analysis are detailed in Section 4.5.2.

4. Results and discussion

The results of the simulation of a reinforced concrete beam infinite element software ABAQUS are stated and discussed in thissection.

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 mid-span of the beam. The load-deflection response was recorded forcomparison with the experimental data. The load deflectionresponse was compared with the model proposed by Hamadet al. [33] for a 50% damage load. The load-deflection response ofthe current model agrees well with the model reference model.The current model shows slightly less stiff behavior compared tothe comparison model, which can be attributed to the support

f maximum static load shown in data labels).

Boundary Conditions

Apply Load

Unloading

Determination of Natural frequencies

Harmonic Excitation(less than first natural frequency)

Frequency Response

Next Load Step

yes

Natural frequency matcheswith test data?

no

Constitutive Relation

Record displacements and accelerations

Fig. 8. Flow chart for finite element simulation.

0

5

10

15

20

25

30

0 2 4 6 8 10

App

lied

Load

, kN

Midpoint Deflection, mm

Present Study

Hamad et al.

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

M.U. Hanif et al. / Construction and Building Materials 124 (2016) 1081–1089 1085

conditions and the inclusion of compression reinforcement, as wellas the contribution of the stirrups, which, as explained by Aslamet al. [34], increases the ductility of the beam model.

4.2. Crack propagation

The software was capable of indicating the inclined crack prop-agation. The cracking pattern was compared with the analyticallydeveloped flexural model, which is capable of detecting damagethrough non-linearity [12]. The reason for crack investigating crackpropagation was to validate the capability of the present study formixed-mode crack formation. The major cracks seemed to besignificantly vertical to match the cracking pattern predicted by

Fig. 10. Comparison of simulated cracking patte

similar research [12], which assumed the initiation of the cracksalong the stirrup lines and was verified experimentally. The slightdifferences in the crack formation were refined using a finer mesh.Hamad et al. [33] assumed the cracks form along the stirrups atequal distance. The present study validates the initiation of forma-tion cracks by the flexural damage model at lower damage levels,as shown in Fig. 10. The dotted lines are overlain along the initia-tion of the cracks in similar research, which gives an idea of thecrack formation in the simulated model. The onset of the verticalcracks was inclined, which indicates the capability of the presentstudy for mixed-mode cracking as well, which can be separatelyinvestigated by applying a three-point loading. The mixed-modecracking in the cracking is a combination of flexural and shear(or torsion) cracking, which is the practical case scenario fordamage being induced in structures.

4.3. Relation of mesh size and crack pattern

To see the crack patterns with high accuracy, an attempt wasmade 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 meshingwas further refined to thoroughly investigate the inclined crackformation in the beam for each damage level, as shown inFig. 11. There was a shear span of 1000 mm on both sides andthe cracks were supposed to be inclined in the shear span. Fromthis figure, it can be seen that at the 46% damage level, the cracksstarted to become oblique. The onset of oblique cracking can be setas 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 isillustrated in Fig. 12. In the figure, first, five normalized modalfrequencies were plotted against the damage levels to see the trendof each mode. In the elastic range, there was no degradation in the

rn (below) with Hamad et al., (above) [12].

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

0.75

0.8

0.85

0.9

0.95

1

0 10 20 30 40 50 60 70 80 90 100

Nor

mal

ized

nat

ural

Fre

quen

cy

% of Damage

Mode 1

Mode 2

Mode 3

Mode 4

Mode 5

Hamad et al.

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

1086 M.U. Hanif et al. / Construction and Building Materials 124 (2016) 1081–1089

natural frequency. The reason for discussing the modal frequencydeterioration is to make a comparison of intensively used pastmethods [35] with the current study in terms of sensitivity to dam-age. As the stiffness of the beam reduced with increasing damage,there was a reduction in the natural modal frequency but notsignificant enough even at complete failure. In field conditions, this

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

1E-10

1E-09

1E-08

1E-07

1E-06

1E-05

1E-04

1E-03

1E-02

1E-01

1E+00

0906030

Pow

er S

pect

ral D

ensi

ty (m

m/H

z)

Frequency (Hz)

15%Damage 23%Damage

28%Damage 35%Damage

46%Damage 59%Damage

70%Damage 82%Damage

95%Damage 100%Damage

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.

M.U. Hanif et al. / Construction and Building Materials 124 (2016) 1081–1089 1087

sensitive enough to detect damage without the influence ofenvironmental effects.

4.5. Sensitivity to damage

In the present simulation, two types of dynamic analysis wereperformed separately, as explained in Section 3. The modaldynamics and implicit dynamic analysis were used as linear andnon-linear analysis, respectively. Both systems were evaluatedbased on the presence of non-linearity and compared with eachother in detail. The nonlinear dynamic analysis was said to besensitive to damage through the formation of super-harmonics[36]. A comparison was made between modal dynamic analysisand dynamic implicit analysis, as explained below.

4.5.1. Modal dynamicsThe dynamic response of the structure for each damage level is

shown in Fig. 13. The structure was loaded and unloaded monoton-ically for each damage level. Modal dynamic analysis was

performed after each loading cycle. A harmonic excitation wasapplied for a frequency of 30 Hz for a time of 5 s. The response ofthe system was analyzed through Fast Fourier Transform (FFT) toachieve power spectral density to investigate the formation ofsuper-harmonics. There was no indication of super-harmonics atany damage level, as shown in Fig. 13. Hence modal dynamicanalysis, as previously used, is not necessarily sensitive todamage.

4.5.2. Dynamic implicit analysisThe dynamic implicit analysis was done through a significantly

lower time step (0.0001 s). Again a harmonic excitation wasapplied at a frequency of 30 Hz for 5 s. The response, as powerspectral density, is illustrated in Fig. 14. The super-harmonics wereformed at integer multiples of the excitation frequency. The ampli-tude of the super-harmonics was studied for all damage levels anda comparison was made. The magnified depictions of super-harmonics at 60 Hz and 90 Hz are shown in Figs. 15 and 16,respectively.

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0 10 20 30 40 50 60 70 80 90 Diff

eren

ce in

supe

rhar

mon

ics a

nd c

urve

fit

% of Damage

1st Superharmonic 2nd Superharmonic

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

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

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

1088 M.U. Hanif et al. / Construction and Building Materials 124 (2016) 1081–1089

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

According to the aforementioned interpretations from Figs. 14–16,the trend of amplitude of super-harmonics with increasingdamage was plotted in Fig. 17. The super-harmonics reflect thepresence of nonlinearity [33] and it can be seen that the non-linearity increases up to the 35% damage level and then startsdecreasing after the 46% damage level. This implies that thepresence 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 lowerdamage levels. A similar trend of non-linearity with damage hasalso been observed elsewhere [11,12].

5. Conclusions

A sensitive damage detection method was presented in thisstudy. The investigation of damage sensitive parameters wasundertaken through computer-aided simulations. The ConcreteDamaged Plasticity (CDP) model was implemented to simulate areinforced concrete beam to detect damage globally via the exis-tence of non-linearity. The model formulation makes it convenientfor engineers and researchers to investigate the damage ofconcrete in more detail and gain more insights incorporating theexisting simplified research. Based on the aforesaid explanations,the following conclusions can be drawn.

1. The concrete damaged plasticity (CDP) model is capable ofdetecting damage without the use of baseline data of the struc-ture, which is very useful for detecting damage in existinginfrastructure where there is a lack of data for the undamagedstructure.

2. As damage is detected through the presence of non-linearity,which increases with increasing damage and is more pronouncedat lower damage levels, the method proposed in the current studycan be very useful in detecting damage in its initial stages.

3. The non-linear dynamic analysis (Implicit Dynamic Analysis) ismore sensitive to damage compared to the linear dynamicanalysis (Modal Dynamic Analysis). Unlike linear dynamicanalysis, the modal parameters of non-linear dynamic analysisare more sensitive to damage and are less influenced byenvironmental conditions.

4. Reasonable crack formation can be predicted using the damageparameters at reasonably coarser meshing.

5. The present study offers promising insights into mixed-modecrack formation, as cracks in visualization get inclined at higherdamage levels. Mixed-mode crack formation is the practicalcase scenario for damage in concrete beams.

Finally, the currently applied procedure can provide a majorbreakthrough in damage detection in realistic damage scenarios(e.g. mix mode crack formation) without the need of baselinestructural data. Improved tension and compression damageparameters, together with efficient computing can be used toenhance the damage efficiency in the future.

Acknowledgements

This research was supported by University Malaya ResearchGrant (UMRG – Project No. RP004A/13AET), University MalayaPostgraduate Research Fund (PPP – Project No. PG187-2014B)and Fundamental Research Grant Scheme, Ministry of Education,Malaysia (FRGS – Project No. FP028/2013A).

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