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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of elasticity of masonry units is also relatively high when compared with the rnodulus of elasticity of typical mortar that is used in the structure. When a typical masonry element is built, the masons combine the masonry units with mortar to form that structural element. When these two different materials with vastly different properties are combined to form the structural element, the properties of the combined element are not readily identifiable. In this study, before the properties related to the compressive strength of the masonry are experimentally examined, we will test our approach in a concrete made masonry, thus avoiding such difficulties. When the ultrasound “travels” through a material, the velocity, u , in the direction of the maximum energy, namely that of the longitudinal wave which will be referred in the following sections as the “principal” direction, can be related with the material properties using the following, well-known equation:

(1)

1/ 2 ( / )   u E

where E represents t he Young’s modulus of the material and ρ its density. Eq.(1) provides the basis for the calculation of the dynamic modulus of elasticity, E d , of the material, which can be linked with its compressive strength, f c , using the following relations (Kakavas and Lemis (2016)):

2 (1 )(1 2 ) (1 )       

 d E u

(2a)

(2b)

0.83  st d E E

(2c)

2 ( / 4.73)  E

f

c

st

with E st being the material’s static modulus of elasticity and ν the Poisson’s ratio. For typical masonries, the latter’s values range from about 0.2 to 0.3; hence Eq.(2a) can be further simplified to:

(2d)

2 0.9  

d E u

Ultrasound velocity in the principal direction of propagation is obtained by in-situ measurements of the respective “travel” times through masonry elements of known thickness. The previous equations imply that the receiver is placed opposite to the transmitter as shown in Fig. 1a. This is the “classical” application of the method, which, as previously discussed, fails in cases of very thick masonries commonly encountered in historical buildings. In these cases, alternative setups are usually employed in praxis, e.g. by placing the transmitter and receiver on an accessible corner of the masonry (Fig. 1b). However, in this case, the measured “travel” time s are not representative of the longitudinal wave as shown in Fig.1b; hence Eqs.2(a-d) yield results of questionable accuracy. Placing the transmitter and receiver on an accessible corner of the masonry is a rather intuitive method in order to technically “reduce” its thickness and achieve measurements of ultrasonic wave propagation velocities using standard equipment. Hence, the proposed procedure was based on this setup, modified as presented in Fig.2. The orientation of both the transmitter and the receiver with respect to the face of the masonry is altered using wedge-type inserts, thus allowing the measurement of longitudinal wave “travel” times. As a result, Eqs.2 (a-d) are in this case applicable, as the proposed setup agrees with their inherent assumptions. However, the proposed setup introduces a number of parameters that should carefully be considered as they may affect the reliability of the measurements. Obviously, in the proposed setup, the signal emitted from the transmitter passes through the prism for a certain time, travels through the masonry, and next travels through the second prism before arriving to the receiver. One parameter that may affect the velocity of the ultrasonic wave is the angle, θ , that defines its principal direction of propagation. The effect of θ is expected to be more significant when using non-homogeneous material for the inserts (e.g. wood), since historical masonries are by principle non-homogenous (although in many cases, equivalent isotropic materials are used in structural analyses in order to represent masonry). Apparently, in isotropic materials such as Plexiglas, sound is travelling with the same velocity in all directions; such materials should be preferred for constructing the prisms.