PSI - Issue 10

P.A. Kakavas-Papaniaros et al. / Procedia Structural Integrity 10 (2018) 311–318 P.A. Kakavas-Papaniaros et al. / Structural Integrity Procedia 00 (2018) 000 – 000

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This implies that our initial assumption for the acoustic wave direction of propagation in the prism and masonry is accurate only when u θ ,w ≈ u θ ,m . In order to improve this fundamental assumption of the method introduced in this paper, the use of slowness curves in order to account for wave scattering is proposed and discussed in this section. To determine the number and direction of possible scattered modes, one can match the magnitude of the tangential component of the scattered modes to the tangential components of the incident wave. Assume a longitudinal wave is incident on the surface of the prism/masonry interface. The length of the arrow represents k il as given by the definition of the slowness curve. The incident angle is θ il and is measured from the interface as usual. One curve indicates the angle and the other indicates the spatial frequency. For continuity of the tangential component of the special frequency vector the directions of propagation of k sr , k rl , k ts , k tl must be θ sr , θ rl , θ ts , θ tl respectively (Nayfeh (1995)). Slowness curves for the prism/masonry and their interface were examined. Such curves were computed using an appropriate program (Duarte et al. (2004)). Indicative results for sandstone masonry units are presented in Fig.4. In anisotropic solids the wave velocity is not the same in all directions. The slowness curves trace the length (magnitude) of the spatial frequency vector k for all possible angles of incident or scattered waves. The phase of the wave travels in the direction of k with phase velocity, v, but the energy (momentum transfer) of the wave propagates in the direction normal to the curve at group velocity. For isotropic materials, these directions coincide. This theoretical approach leads to a more detailed study for the propagation of the ultrasonic waves in the prism/element interface and in non-homogeneous materials such as historical masonries. Incorporating these theoretical findings in the proposed procedure is expected to lead to a more accurate determination of the strength of large thickness elements and will allow its extension in large thickness masonries.

Fig. 4. Indicative slowness curves for sandstone masonry units.

4. Concluding remarks

Initial results from an ongoing investigation on the issue of predicting the residual strength of historic, thick masonries have been discussed in the present paper. The proposed method introduces the use of properly const ructed inserts and proper placement of the sensors as a means to “reduce” the thickness of the wall. The initial results of the ongoing experimental program aiming to validate the method are very promising. The proposed setup is easy to apply in the field using standard ultrasound measurement equipment and low cost materials for the prisms. Member strength is obtained after a simple series of calculation steps, based on properly modified, well-known equations and in-situ measurements. In its present state, due to limitations of the early experi mental results related with the use of concrete specimens, our method can be applied on thick or “blind” concrete elements, or masonries with characteristics similar to those used in the experiments discussed previously. Further calibration of the empirical coefficient n is required in order for the procedure to be widely applicable, without risking the loss of accuracy and reliability. This calibration process should include comparisons with other popular in-situ methods, e.g. flat jack tests. It should be noted that the values of n can be easily defined if results of compressive strength tests are available (even for a small number of specimens).