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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5

(a) (b) Fig. 3. (a) Ultrasonic wave velocity measurements on wood specimens; (b) Application of the proposed method using wooden inserts. For the setup considered (Fig.2), the “travel - time”, t m , of the ultrasound in the masonry element is connected to the velocity of the wave transferring the maximum energy, i.e. the longitudinal wave as follows:

(6)

t

, d u  

/ m c

m

In the previous equation, u θ ,m is the velocity of the ultrasonic wave transferring the maximum energy. The principal direction of this wave is defined by a (generally unknown) angle θ (m) with respect to the face of the masonry at the point of entry. The accurate calculation of θ requires the consideration of wave refraction, reflection and scattering, which are mostly affected by the material properties of the prisms and masonry and the condition of the masonry/ prism interface. However, considering the fact that the prisms’ sections are isosceles right triangles and ar e placed symmetrically on the wall faces, we can assume for the sake of simplicity that θ (m) = θ (w) ; hence, d c can be easily defined by measuring d 1 as shown in Fig.2. As a result, Eq. (6) leads to the calculation of u θ ,m ( t m is obtained from Eq.5). As it has already been discussed, u θ ,m should not be used in Eq. (2a) or (2d) since it does not represent the longitudinal ultrasonic wave propagation velocity in the masonry, u m . However, these two values of velocity can be related using the Hankinson (1921) formula (Eq. (3)). Two basic assumptions were adopted in order to further simplify the formula: • An equivalent isotropic material is considered for the masonry; hence sound is travelling with the same velocity in all directions leading to u 0 = u 90 = u m . • θ = 45 ο , which is acceptable given the geometry and locations of the prisms.

Considering the above, the following expression can be derived from Eq. (3):

(7)

, n m m u u  

/ 2 1 

Eqs. (3) to (7) represent the calculation steps of the proposed procedure for the prediction of residual strength of thick structural elements utilizing ultrasonics. The last step provides a value of u m which can be used in Eqs.2(a-d) in order to obtaine the compressive strength of masonry, as long as an estimation for the value of the empirical coefficient n is available. The calibration of n for selected types of masonries was the aim of the experimental measurements discussed in the following section.

2.2. Experimental investigation of the ultrasound “travel - times” and calibration of the empirical coefficient

A series of laboratory tests were used in order to verify the proposed procedure for ultrasound measurements in thick masonries, as well as calibrate the value of the empirical coefficient, n . Typical cubic concrete specimens of 150 mm edge were used in order to represent masonry. Concrete strength, f c , was directly calculated by performing