GUIDED WAVE FOR DEBONDING DETECTION IN FRP-RETROFITTED CONCRETE STRUCTURES

H. Mohseni1 and C. T. Ng 1,* 1School of Civil, Environmental and Mining Engineering, The University of Adelaide, Adelaide, SA 5005,

Australia, * Email: alex.ng@adelaide.edu.au

ABSTRACT Applications of fibre-reinforced polymer (FRP) composites for retrofitting, strengthening and repairing concrete structures have been growing dramatically. FRPs have high specific strength and stiffness compared to conventional construction materials, e.g. steel. Ease of preparation and installation, resistance to corrosion, versatile fabrication and adjustable mechanical properties are other advantages of FRP composites. However, there are serious concerns about long-term performance, serviceability and durability of FRP applications on concrete structures. Therefore, structural health monitoring (SHM) in FRP-retrofitted concrete structures must be given special consideration. Proper defect detection methods are a crucial part for SHM. This paper presents a study on investigating the application of guided waves for detecting debonding between FRP and concrete structures. A three-dimensional finite element (FE) model has been developed to simulate generation and propagation of guided waves in FRP-bonded concrete elements, and scattering at debonding. Absorbing layers have been developed to provide a computationally efficient tool for investigating guided wave propagation and scattering characteristics in FRP-retrofitted concrete structures. Phase and group velocities arecalculated from FE simulations and then compared with results obtained from analytical solutions. To examine the wave scattering features at the defect, debonding between FRP and concrete issimulatedin the FE model. The FE model isthen used to investigate the feasibilityof guided waves on debonding detection. KEYWORDS FRP-retrofitted concrete structures, SHM, defect detection, debonding, guided waves, finite element simulation. INTRODUCTION Structural heath monitoring (SHM) is the implementation of a damage identification scheme to civil engineering infrastructures(Wenzel 2009; Worden et al. 2007). SHM is aimed at providing reliable data on the real conditions of structure or structural components,assessing structural integrity and ensuring serviceability and safety. Thus, the overwhelming importance of SHM is beyond question(Ng et al. 2012).Among different damage identification methods, guided wave-based approach has emerged as a promising technique(Ng 2015). Guided waves propagate in solid media, interacting with the boundaries in such a way that boundary conditions could be satisfied. Different types of guided waves can occur depending on geometrical properties and boundary conditions of the structure. For instance, Rayleigh waves propagate on the surface of a semi-infinite solid medium. Lamb waves propagate in plate-like structures and their propagation is guided by the free upper and lower surfaces of the plate. Compared to conventional bulk wave methods, guided wave–based damage identification approaches offer some advantages includingability of guided waves to travel over long distances, the active nature of guided waves, sensitivity of guided waves to small damages and capability of guided waves to inspect inaccessible, embedded and encapsulated structural components(Ng and Veidt 2012; Rose2014). Meanwhile, the use of fibre-reinforced polymer (FRP) compositesin concrete structures has been extensively expanding(Choi et al.2013; Taillade et al. 2011).FRPs are used to increase flexural or shear strength, improve ductility and repair damaged concrete elements(Teng et al. 2001; Hollaway 2010). The need for retrofitting may arise from errors in design and/or construction, changes in codes and standards or new requirements of client. Application of FRP is economical because they can be readily available and easily installed on construction site using minimum labour and equipment and with no need to temporary support. FRPs, also, offer very high specific strength and specific stiffness and they show good resistance to fatigue and corrosion(GangaRao et al. 2007). However,FRPs are susceptible to different types of defects,which can be initiated in constituent raw materials, during preparation and installation of FRP on concrete substrate and also in service life of retrofitted

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structures(Akuthota et al. 2004). If defects go undetected and untreated, effectiveness of retrofitting and performance of FRP/RC elements can be adversely affected. Thus, SHM needs to be implemented in FRP-retrofitted concrete structures using proper damage identification methods. Currently, a number of non-destructive evaluation (NDE) techniques are used for detecting defects in hybrid FRP/RC structures including visual testing, impact testing, infrared thermography and acoustic emission (Telang et al. 2006). This paper seeks to explore application of guided wave method for inspecting FRP-retrofitted concrete structures and detecting debonding at the interface of FRP and concrete. METHODOLOGY In this study, three-dimensional finite element (FE) simulations have been performed using Dynamic/Explicit module of ABAQUS version 6.12. FE analyses involved modelling of FRP-retrofitted concrete, excitation of guided waves signals and investigation of wave propagation in structural components. It is clear that for any FE simulation to yield precise results; appropriate element size must be adopted. Based on material properties of the structure, central excitation frequency and excited guided wave modes, the size of element used in this FE model is 1 mm; i.e. 1mm×1mm shell elements and 1mm×1mm×1mm solid elements. However, modelling concrete elements with real dimensions will result in a huge number of elements in the model, i.e. expensive computational cost, as the element size is usually very small compared to the size of the structure being modelled. To overcome this issue, only a section of FRP-retrofitted concrete element has been modelled in ABAQUS. That is a 40cm×5cm×8cm (L×W×H) concrete beam with 40cm×5cm CFRP attached on the top surface of the beam as shown in Figure 1. In order to avoid boundary reflections and maintain computational efficiency, absorbing regions have been applied on the extremities of the modelled slice.

Figure 1 Schematic of FRP/RC model

Accuracy and efficiency of finite element simulations are highly dependent on the successful implementation of absorbing regions. Absorbing Layers by Increasing Damping (ALID) is one of commonly used methods in guided wave problems(Pettit et al. 2014). It involves adding successive layers to the main structure with gradual increase in damping values while other elastic properties are the same as main structure. To keep explicit analyses computationally efficient, only mass-proportional damping has been applied as it has small effect on stable time increment. Mass-proportional damping across absorbing regions can be formulated as(Rajagopal et al.2012):

𝐶𝑀(𝑥) = 𝐶𝑀𝑚𝑎𝑥𝑋(𝑥)𝑃 (1) where X(x) ranges from 0 at the beginning of absorbing layer and 1 at the end of absorbing layer, and CMmax has a real positive value.

X

Y

Z

Measurement points

Wave actuator

Concrete

CFRP Slice modelled in

ABAQUS

232

Analytical verification of FE simulation has been carried out by DISPERSE computer program. DISPERSE has been designed to obtain dispersion curves, helping study of guided wave propagation in multi-layered media. DISPERSEapplies global matrix method to create dispersion curves. In this method, the propagation of waves in a bulk material should be described and related to displacements and stresses in the material. Then, individual layers would be assembled to create the global matrix representing a complete system(Pavlakovic and Lowe 2003). RESULTS AND DISCUSSIONS To study guided waves scattering characteristics due to debonding at FRP/RC interface, wave propagation modelin FRP-retrofitted concrete structure needs to be verified the in different media.To do so, absorbing regions have been applied to FRP, RC and FRP/RC models. For this study, absorbing layer has been considered acceptable if the ratio of amplitude of reflected wave to incident wave is smaller than -46 dB. Considering Eq. 1, a value of P equal to 3 has been used based on the practice of Rajagopal et al. (2012). Also, the width of absorbing region for all models is 40 mmand CMmax = 2.5×10+06.Guided waves were simulated using a Hanning windowed tone burst pulse as:

wherea, N, fcdenote the wave amplitude, number of cycles and central frequency respectively. It has been assumed that a=10-7 m, N=5 and fc=150 kHz as shown in Figure 2:

Figure 2 Excitation signal

Mechanical properties of reinforced concrete are assumedas: Ec=25 GPa, Uc=2400 kg/m3, Qc= 0.16 CFRP composite is comprised of 4 plies with reference orientation angle of 0o, 90o, 90o and 0o. It is assumed that each FRP ply is made up of carbon fibre and epoxy matrix with a fibre weight fraction (Wf) of 80%. Table 1 displays mechanical properties of carbon fibre and epoxy matrix:

Table 1 Properties of CFRP constituent materials

Elastic properties of fibre Ef11 (GPa) Ef22 (GPa) Gf12 (GPa) Gf23 (GPa) Uf (kg/m3) Qf12

231 14.48 22.75 4.83 1760 0.27

Elastic properties of matrix

Em (GPa) Gm (GPa) Um (kg/m3) Qm 3.77 1.35 1220 0.40

Chamis (1984) formulated mechanical properties of a composite ply based on the properties of fibre and matrix:

0 0.5 1 1.5 2 2.5 3x 10-5

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Time (sec)

Nor

mal

ised

Am

plitu

de

𝑢(𝑡) = 𝑎2 (1 − 𝑐𝑜𝑠 2𝜋𝑓𝑐𝑡𝑁 ) 𝑐𝑜𝑠2𝜋𝑓𝑐𝑡 (2)

233

𝜌 = 𝑉𝑓𝜌𝑓 + 𝑉𝑚𝜌𝑚 = 1𝑊𝑓𝜌𝑓

+ 𝑊𝑚𝜌𝑚

(3)

𝐸11 = 𝑉𝑓𝐸𝑓11 + 𝑉𝑚𝐸𝑚 (4)

𝐸22 = 𝐸33 =𝐸𝑚

1 − √𝑉𝑓(1 − 𝐸𝑚𝐸𝑓22

) (5)

𝐺12 = 𝐺13 =𝐺𝑚

1 − √𝑉𝑓(1 − 𝐺𝑚𝐺𝑓12

) (6)

𝐺23 =𝐺𝑚

1 − √𝑉𝑓(1 − 𝐺𝑚𝐺𝑓23

) (7)

𝜈12 = 𝜈13 = 𝑉𝑓𝜈𝑓12 + 𝑉𝑚𝜈𝑚 (8)

𝜈23 =𝐸222𝐺23

− 1 (9)

where V, W, E, G, U and Q represent the volume fraction, weight fraction, modulus of elasticity, shear modulus, density and Poisson's ratio of constituent materials respectively. Also, subscripts f and m denote properties of fibre and matrix respectively. Based on the elastic properties of carbon fibre and epoxy matrix and also carbon fibre weight fraction, elastic properties of CFRP composite can be calculated as shown in Table 2.

Table 2 Elastic properties of CFRP lamina

E11 (GPa) E22 (GPa) E33 (GPa) G12 (GPa) G13 (GPa) G23 (GPa) 169.6 10.24 10.24 6.88 6.88 3.51

Q12 Q13 Q23 U (kg/m3)

0.31 0.31 0.46 1616 Generation and propagation of guided waves were simulated in ABAQUS and results were then used to calculate group velocity and phase velocity denoted by Cg and Cp respectively:

𝐶𝑔 =Δ𝑥Δ𝑡 (10)

𝐶𝑝 =2𝜋𝑓𝑐Δ𝑥Δ𝜑 (11)

where∆x is distance between measurement points, ∆tis difference of wave arrival time, fc is the excitation frequency, and ∆M indicates phase difference between measurement points. Next, group and phase velocities for all FRP, RC and FRP/RC models were obtained from FE simulations and then compared with DISPERSE results.

Figure 3Dispersion curves obtained from DISPERSE of a 4-ply CFRP for fundamental asymmetric mode of

guided waves

0.1 0.2 0.3 0.4 0.5 0.6 0.70

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Frequency (MHz)

Vel

ocity

(m/m

s)

Group velocityPhase velocity

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Table 3 displays values of phase and group velocities for fundamental asymmetric and symmetric modes (denoted by Aand S respectively) for FRP, RC and FRP/RC models.It can be seen that FE simulation results have been verified by DISPERSE.

Table 3 Comparison between FE and DISPERSE results

FE DISPERSE

A S A S

Cg(m/s) Cp(m/s) Cg(m/s) Cp(m/s) Cg(m/s) Cp(m/s) Cg(m/s) Cp(m/s)

FRP 1517 1138 7478 7553 1630 1152 7439 7467 RC 1892 1898 1882 1904 1896 1896 1896 1896

FRP/RC 2020 2047 2021 2047 2038 2038 2038 2038 To localize the damage, time-of-flight (ToF) method has been used. ToF-based damage localization has been widely used in guided Lamb wave damage detection schemes(Harri et al. 2008; Diamantia et al. 2005).Basically, ToFcan be defined as the time difference between the incident wave and damage-scattered wave captured by the same sensor. A simple example is when damage is located exactly on the projection of actuator and sensor. As shown in Figure 4, the sensor captures the incident wave first and then the wave reflected back from the damage. Difference of ToF between thescattered wave from the damage and incident wave (∆t) can be obtained from the measured data. Since the material properties of the structures are known in advance, and hence, the group velocity of the wave (Cg) is known, damage location can be determined as:

𝐿_𝑑 = 12 (𝐶𝑔. ∆𝑡) (12)

Figure 4 Schematic of one-dimensional damage localization in FRP/RC using ToF

To deploy ToF method in FE model, debonding at FRP/RC interface was added to the model. Two cases were studied with debonding located between x=0.250–0.255m and x=0.280–0.285 m. Guided waves were generated at x=0 and then incident waves and scattered waves were sensed at x=0.150 m.In order to obtain signal envelopes, Hilbert transform (Ng 2014)wasthen applied to process the measured wave signals. Figure 5 displays normalised out-of-plane displacements at the measurement point and signal envelope for two cases of debonding:

0 1 2 3x 10-4

-1

-0.8

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-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Time (sec)

Nor

mal

ised

dis

plac

emen

t

Sensor Actuator

Debonding Guided waves

L_d

Concrete

FRP

a

Y

X

Incident wave

Reflections from debonding

235

Figure 5Normalised out-of-plane displacements at measurement point in model with debonding at

a)x=0.250–0.255 m; and b)x=0.280–0.285 m

Considering Eq. 12 and the group velocity value from Table 3 for FRP/RC model (2020 m/s), we can estimate the damage location using ToF information of the scattered wave. For example, the debonding area in second case begins at x=0.280 m and debonding location is estimated at x=0.285 m.

As seen above, the estimated debonding location using the ToF information hasa good agreement with the real debonding location. CONCLUSIONS A three-dimensional computationally efficient FE model was developed to simulate propagation and scattering of guided waves at debondings in FRP-retrofitted concrete elements. Absorbing regions were successfully implemented in FE model to avoid unwanted wave reflections from boundaries, and hence, to improve the computational efficiency of the FE simulation. FE results were verified by analytical methods. The study shows that guided wave is sensitive to debonding and ToF information can be used to determine the debonding location in FRP/RC structures. ACKNOWLEDGEMENTS The research described in this paper was financially supported by the Australian Research Council under grant number DE130100261. The support is greatly appreciated. REFERENCES Akuthota, B., Hughes, D., Zoughi, R., Myers, J. and Nanni, A. (2004). "Near-field microwave detection of

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