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Torsional vibration technique for the acoustoelastic characterization of concrete

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Abstract

There is no nondestructive evaluation method capable of determining stresses in concrete structural members in situ. Here, we propose and evaluate a torsional-vibration testing technique that offers an approach to estimate the stress state in concrete specimens by means of characterizing the material nonlinearity. We axially load three prismatic specimens comprising different concrete mixtures and measure their torsional vibration frequencies during four loading cycles. The fundamental torsional frequency shows a positive correlation with applied compressive stress for both loading and unloading stages after correcting for the effects of non-uniform torsion, geometric nonlinearity and changing boundary conditions. To quantify this behavior, we define the nonlinear parameter \(\beta_{G}\) to characterize the material nonlinearity (acoustoelasticity). The values of \(\beta_{G}\) of the initial loading cycle are lower than those of the subsequent loading cycles. However, the latter values of our concrete mixtures are consistent and similar to the values computed from previously published results. An estimate of the \(\beta_{G}\) parameter of a concrete structural member provides a pathway for nondestructive assessment of in situ compressive stress in the member.

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Funding

This study was funded by Centro de Innovación en Ingeniería CII and Schmidt Premoldeados S.A. through research project Udelar-T2-2017, and CAP-Udelar.

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Correspondence to Agustin Spalvier.

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Appendices

Appendix 1

This appendix contains the raw measurement data and calculated values for specimen 1. These are organized in Table 6, where columns 1 through 8 represent, respectively: 1: loading stage and cycle, 2: measured uniaxial compressive strain, 3: measured torsional frequency of vibration (\(\hat{f}_{1}\)), 4: applied compressive stress, 5: calculated k using Eq. (15), 6: torsional fundamental frequency of vibration corrected to decouple the effect of boundary conditions (unrestrained free–free bar) calculated using Eq. (14), 7: measured (and interpolated) fundamental torsional frequency of vibration of the control prism, and 8: fundamental torsional frequency corrected for the effect of changing boundary conditions and temperature.

Table 6 Data measured and calculated from tests of specimen 1

Appendix 2

Figure 9 shows the results of the FEM model carried out using the geometry of our prisms, where a/L = 1/4, superimposed onto models with a/L = 1/8 and a/L = 1/16.

Fig. 9
figure 9

Results of FEM simulation frequency increments for three different aspect-ratio geometries

The numerical results shown in Fig. 9 confirm the fact that warping and geometric nonlinearity can be neglected with respect to the acoustoelastic effect of the Saint–Venant torsional term in Eq. (7) where a/L < 2.

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Spalvier, A., Domenech, L.D., Cetrangolo, G. et al. Torsional vibration technique for the acoustoelastic characterization of concrete. Mater Struct 53, 7 (2020). https://doi.org/10.1617/s11527-020-1438-6

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