Monument Future. Siegfried Siegesmund

in different mediums. The velocity and the attenuation are the two most important parameters in ultrasonic testing.

      For the ultrasonic testing of stone, the favourable frequency range is 20 kHz–1000 kHz. The velocity and attenuation of ultrasonic waves in stone depend among other factors on the density, water content and cracks. The amplitude and velocity of the first wave received are positively correlated to the mechanical strength of the stone, and the mechanical strength directly responds to the weathering condition of the stone.

      Therefore ultrasonic testing is an appropriate method to detect the position and trend of weathered zones and cracks inside a stone.

      There are many situations for cracks, crazings, and splits on the surface and in the interior of stone sculptures. Ultrasonic waves may go directly through a crack if the fracture surfaces are still in contact with each other with little effect on the velocity but with a distinct attenuation of the amplitude. For the situation that the fracture surfaces are completely apart from each other, the waves bypass the crack and the transit time increases. Due to the open split that runs through the stone, the wave will not be received on the other side.

      For evaluating the stone weathering level, we use the P-wave velocity V normalized with respect to the velocity of an unweathered sample V₀ as shown in table 1, which is normally used by conservators. For the Fangshan Hanbaiyu marble V₀ is about 4,500 m/s.

175Table 1: Normalized velocity ratios for the definition of stone weathering levels.

Weathering Level	Vi / V0
Not Weathered	≥ 0.9
Void ratio increased	0.75–0.9
Floor level of weathering	0.75
Slightly waethered	0.5–0.75
Moderately weathered	0.25–0.5
Severly weathered	≤ 0.25

       Crack depth detection

      In case of open cracks the ultrasonic waves run from the emitting probe to the end of a crack, and then back to the receiving probe. Assuming that the crack is perpendicular to the surface and the ultrasonic waves propagate with constant velocity, the depth can be easily calculated.

      We measure the ultrasonic transit times between points A and B for the path ACB and between points D and F for the path DCF, and also the distances AE and DE for mode A. For mode B, the respective transit times are for the paths ACB and ACE and the distances AD and DB as shown in Fig. 5. The choice of mode A or B depends on the field situation. The data is evaluated with respect to the crack depth by Equation 1 (mode A) or Equation 2 (mode B). Both equations can be deduced by geometrical reasoning from the sketches in Fig. 3.

      Figure 3: Crack depth detection modes.

       Ultrasonic CT method

      The principle of ultrasonic CT is shown in Fig. 4. Abundant data of wave time are collected by fanshaped testing. S₁–S_n are the emitting points, R₁₁, R₁₂…R_ni, R_nj are the corresponding receiving points.

      Hypothesize that there are N testing line in the section plane, and the section plane may be separated to M grids on request of calculating accuracy.

      Equation 1: Crack depth equation of mode A T₁ – ultrasound wave time DCF; T₂ – ultrasound wave time ACB L₁ – distance DE; L₂ – distance AE H – height of the triangle, depth of the crack

      Equation 2: Crack depth equation of mode B T₁ – ultrasound wave time ACE; T₂ – ultrasound wave time ACB L₁ – distance AD; L₂ – distance BD H – height of the triangle, depth of the crack

      The result will be got by solving the matrix equation below:

      Equation 3: USCT matrix equation l_ij – length of path i in unit j; S_j=1/ V_j – slowness of unit j; t_i – wave time of path i.

      The velocity V_j of ultrasonic wave in each unit of the section is given by the reciprocal of each S_j.

       Detecting of the statue

       Detecting for the depth of the cracks

      There were 77 micro cracks observed on the surface of the statue and 15 of them were chosen for testing with either mode A or B, depending on the position of the crack.

      The ultrasonic device used was a Proceq PunditLab+, with the precision of 0.1 µs on wavetime reading and the probes were Proceq 40 17-B 54 KHz conical probes (Fig. 5), with the contact area of diameter 4 mm, that ensures the precision of the contact points and the accurcy of testing results. Fig. 6 shows examples of cracks detected. Table 2 shows the calculated depth results of fifteen cracks and the depth ranged from 0 to 68 mm.

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      Figure 4: Principle of ultrasonic CT.

       USCT testing of the head

      The authors have developed a USCT system that can be used for testing wood and stone structures. It comprises a Proceq Pundit Lab+ non-metal ultrasonic device, an amplifier between the receiving probe and the detector, a sensor diameter convertor, a multi sensor fixator and the USCT analysis software. We have 20 Sonotec L40 54 kHz sensors of diameter 50 mm, and the convertors transmit the diameter to 10 mm when contacted the tested object. That makes the coordinates of each contacting points more precise. Non couplant is used for testing thus avoiding the penetration of couplants into the object through open cracks.

      Laboratory tests were made with several wood and limestone samples, and the USCT images correspond very well with the visible appearance of the samples commendably. Fig. 7 shows four of them. All the equipment can be packed into one suitcase and easily transported for on-site testing.

      For the on-site testing of the statue, a section of the cranial region of the statue was chosen as shown in Fig. 8, and sixteen probes were used. Fig. 9 shows the USCT detecting array and USCT image.

      Figure 5: Probe for crack depth detection.