Quantitative assessment of bonding between steel plate and reinforced concrete structure using dispersive characteristics of lamb waves
Introduction
Steel and concrete are the most widely used construction materials. Structures consisting of reinforced concrete structure covered with steel plate are widely used for infrastructures and buildings. High-rise structures and long span bridges can be concrete-filled steel tubular member (CFST member) [1], dry cask storage facilities shield high-level radioactive spent fuel are made by thick concrete cylinder with inner and outer steel liner [2], steel jacket is used for retrofits reinforced concrete bridge columns [3], reinforced concrete member strengthened by adhering steel plate with bolts and epoxy [[4], [5], [6]], and factory floor or dame surfaces cover with steel plate to increase the abrasion resistance.
To achieve the designed capacity for these composite members, fully bond between concrete and steel is most essential. Shrinkage and creep behaviors are different for well bonded and debonding CFST member [7,8]. Corrosion on the exterior steel tube may reduce the composite action between steel and concrete [9,10]. For nuclear concrete containment structure, degraded coatings and moisture barrier seals lead to corrosion of the interior surface of steel liners [11]. For steel plate strengthened concrete member, infillings must be fully casted inside the gap between steel plate and concrete to assure the compatibility of displacement on the steel-concrete boundary [[4], [5], [6]].
The defects which are hidden underneath the steel plate may not be observed by visual inspection. The RC structure strengthened by steel plate with epoxy as the adhesives can be considered as three-layered structure. The RC column strengthened by steel jacket with non-shrinkage mortar filling the gap can be considered as two-layered structure as the infill has the acoustic impedance similar to concrete. CFST member is also included in this category.
The air voids at the bounding layer can be assessed by A-scan methods such as normalized impact-echo method and low-frequency ultrasound [12,13]. Shen et al. use the dispersive characteristics of ultrasonic surface waves to evaluate the property of the bonding layer in a steel-epoxy-concrete layered structure [14]. Wu and Chen use dispersion of laser generated surface wave to evaluate the unbound ratio for epoxy bonded layered medium [15,16]. Both groups used spectral analysis of surface wave (SASW) to analyze the phase differences. Zhang and Lu study the dispersive characteristic of Rayleigh Wave in a Stratified Half-Space [17]. The zigzag dispersion curve corresponds to variated modes at different frequencies for the case with a soft layer between two almost equally stiff layers. Park et al. obtained the phase velocity spectrum in three-layered pavement structure using MASW method with 100 equally spaced stations. The main response follows the dispersion curve of the fundamental anti-symmetric (A0) Lamb wave mode of the top stiffer layer except for low frequency region [18]. Ryden and Lowe found the discrepancy in the low frequency region corresponds to the branches of interaction of leaky Lamb waves in the first two layers [19]. Song and Popovics demonstrate the attenuation of S0 modal response of the steel plate is sensitive to interface bonding condition [20].
In present study, bonding condition between steel plate and substrates is assessed by the dispersion of A0-Lamb wave mode of the top steel layer. Instead of using two receivers or multiple receivers to extract the dispersion of phase velocity, single test is performed using a sensor placed 0.4 m away from an impact source to obtain the dispersion of group slowness spectrogram. The test scheme has at least three benefits. First, large area can be covered in shorter period of time comparing to conventional A-scan and MASW methods. Secondly, as no unwrapping the phase angle as SASW method, the jump of velocity caused by different dominant modes for layer structures would not be confused with the jump caused by wrapping of phase. Thirdly, with only one receiver needed, the instrumentation has the benefits of cost efficiency and has potential to develop affordable automated test system.
Both numerical and experimental studies were performed. A simple index to qualitatively evaluate the bonding condition was developed. Two and three layered concrete plate specimens containing debonding crack with different lateral size were designed. The effects on type of impact-source, the positions of the impactor and receiver and the length of defect passing the test line were studied.
Section snippets
Theoretical backgrounds
The signal obtained by the receiver 0.4 m away from the impactor is analyzed using Short-Time Fourier Transformation (STFT). The resolution of the dispersion modal images is enhanced by reassignment method [21,22]. The results are represented in the slowness-frequency domain. The slowness is calculated by time divided by the impact-receiver distance.
For STFT, the recorded signal (s(t)) is separated into a series of overlapping sections. Each section is multiplied by a select window function
Numerical simulation
Numerical models of a steel plate, a fully bonded steel and concrete composite plate, a fully bonded steel-epoxy-concrete composite plate as well as two and three layered plates with different lateral size of gaps underneath the steel layer were constructed. Different sizes of void gap in the epoxy or cementitious layers were modeled to simulate the cases with partially unfilled or debonding situations.
Explicit 2-D axisymmetric models were constructed using ANSYS-LS-DYNA. Fig. 1 shows the three
Specimen preparation
Two concrete plate specimens with dimensions of 1 m× 1 m × 0.2 m were cast. For three layered specimen, after concrete hardening, the Styrofoam sheets with lateral dimensions 0.1 × 0.1 m, 0.2 × 0.2 m and 0.3 × 0.3 m and a thickness of 3 mm were patched onto the surface of the concrete specimen as shown in the Layout of Fig. 2(a). Fill the epoxy resin onto the concrete until reaching the same height as the Styrofoam sheet. A steel plate with thickness of 12 mm was then placed above the epoxy
Results
In this section, the analysis procedures to obtain the key parameter for assessing the bonding condition for two-layered and three layered structures are shown first. The effects of different impact-sources, location of the impact, as well as the length passing defect were investigated. Test parameters are listed at Table 2.
The numerical and experimental results obtained from different test situation are labeled by following rules. There are five segments in a label: In the first segment, “n”
Discussion
Although Fig. 14 shows limit variation of A0-slope for defect length about 10–15 cm in 2-layered specimen and about 10–20 cm for 3-layered specimen, the proposed method can still provide valuable information using gridded arrangement of test lines. Smaller defect would be reflected in the contour map as fewer test lines pass by.
The experimental results show that the presence of the epoxy layer affects the linearity at the low-wavelength region. For steel-concrete composite plate, the near
Conclusion
The study provides a new technique to quantitatively evaluate the range of interfacial debonding between steel plate and substrates. Test is carried out by a small hammer which records the initial tapping time by embedded piezoelectric element and the displacement receiver located at 0.4 m from the hammer. An enhanced image of group slowness spectrogram can be obtained from the displacement waveform through STFT and reassigned method. Both numerical and experimental methods were conducted in
Acknowledgments
The authors would like to thank the Ministry of Science and Technology, Republic of China, Taiwan, for financially supporting this research under contract No. MOST 104-2221-E-324 -022 -MY3.
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