Figure 9. Probability density function of direct ultrasonic velocity of Metellino palace.

Figure 10. Indirect ultrasonic test setup.

dynamic Young's modulus that turns out to be around 30,000 MPa (mean value) with modest variability. Indirect ultrasonic tests Indirect ultrasonic tests were performed on every single step of the two stairways, in order to obtain a wide set of values that may represent a significant statistical sample.

The "time of flight" was obtained placing the receiver on the "first column" (the black one in Figure 10) and moving the emitter in the other three different positions on each step.

The processing phase of these tests is a little more complex then the direct ultrasonic ones, due to difficulty in the estimation of the wave path. For this reason, it was decided to divide the data in three different sets, one for each horizontal distance between the sensor (i.e. 70 cm, 140 cm, 210 cm). In this way, the possible error in the path estimation was minimized.

Figure 11. Probability density function of indirect ultrasonic velocity, sensor distance 140 cm, of Caffa palace.

For each distance, the p.d.f. of the velocity was obtained (Fig. 11) and the extreme values were analyzed in detail. It results that the state of preservation of the stair is essentially homogeneous.

Thanks to this wide experimental campaign, the results of the following numerical analyses can be reasonably extended to the whole stairways of both the palaces.

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