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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(a) (b) Fig. 1. (a) Optimum setup; (b) “corner” setup for ultrasound measurements on masonry elements.

Fig. 2. The proposed setup for ultrasound measurements on thick masonry elements.

When layered anisotropic materials such as wood are used for the wedges, the velocity u θ of an acoustic wave for a given direction of propagation defined by the angle, θ , can be calculated using the classical formula provided in Hankinson (1921) and Armstrong et al. (1991):

u u

u

(3)



0 90



  n

n

u

u

sin

cos



0

90

In the previous equations, u 0 and u 90 are the wave velocities for two principal directions, namely the direction parallel and normal to the layers when applied for layered anisotropic media, i.e. wooden inserts or several types of masonry. The values of the empirical coefficient, n , for wood range from 1.5 to 2.5, with 2.0 being the obvious option when aiming for an average value for u θ . The definition of n for different types of masonries was one of the aims of the experimental investigation presented herein. In order to calculate u θ for the wedges using Eq.(3), u 0 and u 90 should be directly measured for the material of the wedges using proper specimens (Fig.3a). With u θ known, the “ travel-time ” of the ultrasound in the prisms, t w , can be obtained from the following expression:

(4)

, / w w w t d u  

with d w as shown in Fig. 2. Considering a symmetric placement of the inserts, the total “travel - time” of the ultrasonic wave, t tot , which is directly measured using the proposed setup, can be related to t w as follows: 2 tot w m t t t   (5)