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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–Sn are the emitting points, R11, R12…Rni, Rnj 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 lij – length of path i in unit j; Sj=1/ Vj – slowness of unit j; ti – wave time of path i.
The velocity Vj of ultrasonic wave in each unit of the section is given by the reciprocal of each Sj.
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.
Figure 6: Cracks in the marble of the Soong Ching-ling statue.
The ultrasonic velocity in fresh marble similar to 177the material of the statue is about 4,500 m/s, and the measured velocities shown in the result image range between 1,000–4,500 m/s.
According to the USCT results no penetrative severe cracks were found. The depth of the superficial cracks on the top of the head was not more than 50 mm. However, a clearly deteriorated zone with a thickness from 10 to 50 mm, caused by the disintegration of the crystal fabric, was found around the head.
Conclusion
According to the observation, almost all of the 77 cracks should be developed from the stone interlayers. The depth of 15 cracks has been detected and the results are between 0–68 mm. By USCT, a loosened zone with thickness up to 50 mm has also been found.
Table 2: Crack depth data.
For the reason of the statue has just been exposed to the natural environment for only 35 years, the marble should be in the early stage of deterioration, that is surface crystal fabric loosing and surface cracks developing.
The main factors that cause crystal fabric loose on marble surface, development of spalls and cracks should be sharp drop in temperature caused by sudden rain in summer, repeated uneven expansion and contraction, scouring and dissolution of 178acid rain, ice splitting action and growth of lower organisms such as mosses and lichens, etc.
If no effective measures are taken, the deterioration level of the statue may increase quickly, perhaps even seriously in the next 50 years producing a similar state as the marble railing of Tian’anmen-Qing Dynasty monument (Fig. 10).
Figure 7 : Laboratory samples and corresponding USCT images. a. Ø 22 cm wood sample and corresponding USCT image. b. Ø 28 cm wood sample and corresponding USCT image. c. Ø 22 cm wood sample and the corresponding USCT image. d. Ø 55 cm limestone sample and corresponding USCT image.
Figure 8: USCT testing section.
Figure 9: USCT testing. a. USCT testing array b. USCT image
