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Marble monuments examination using the NDT method of ultrasounds I. N. Prassianakis, S. K. Kourkoulis, I. Vardoulakis National Technical University of Athens, School of Applied Sciences, Department of Mechanics, 5 Heroes of Polytechnion Avenue, Zografou Campus, Theocaris Bld., 157 73 Athens, Greece Contact

ABSTRACT:

A detailed examination of the mechanical properties of various types of marble is attempted in the present experimental study with the aid of the Non Destructive Method of ultrasounds. The anisotropy directions are first determined, the various structure imperfections are then located and finally the values of the main mechanical constants are determined. The experimental results obtained are compared with the respective ones obtained from conventional destructive tension tests. The comparison is satisfactory and the discrepancies are of minor importance. The ultimate goal of this work is to check whether it is possible or not to apply the NDT method of ultrasonics for the reliable and safe study of the present mechanical status of various ancient monuments of the cultural heritage of Greece that are constructed from this specific type of marble, since the experts working for the restoration projects demand exact knowledge of the mechanical properties of the various structural elements of the monuments. The results appear to be encouraging.

1. INTRODUCTION

For practical reasons ancient Greeks used to build their monuments using natural building stones like marble, conchyliates shellstone and various types of porolithoi, from quarries in the close vicinity of the work-site. Among these natural building stones marble was extensively used for the erection of a number of the most significant samples of west civilization. The majority of them are preserved until today only because they have been constructed from extremely durable varieties of marble. The Parthenon temple on the Acropolis of Athens, the Hermes of Praxitelis, the Niki of Samothraki and the Aphrodite of Milos are among the most characteristic examples of marble monuments of the ancient Greek civilization.

Marble is regarded as being the product of the metamorphism of limestone beds. Metamorphism takes place under the action of heat or pressure independently or of both heat and pressure simultaneously. It is a kind of rather hard rock consisting mainly of crystallized grains of calcite (CaCO₃) or dolomite (MaCO₃) or a mixture of them. Its color is mainly due to admixtures of foreign substances like muscovite and chlorite. The very good physical and mechanical properties of marble, such as its high resistance to abrasion, its translucence and its capability to be polished (as opposed to other type of rock materials), as well as its high strength and hardness render it one of the most widely used structural materials even today for the construction of both buildings and sculptures.
Unfortunately, most varieties of marble are of anisotropic nature (Corres 1993, Theocaris and Coroneos 1979, Zambas 1994) and extremely brittle and, thus, the determination of their mechanical properties becomes an extremely difficult experimental task in case ones uses the conventional destructive Strength of Materials tests (Vardoulakis et al. 1998, Kourkoulis et al. 1999, Franzini 1998). On the other hand, it is obvious that the destructive control is inapplicable at all in case one studies the behaviour of marble monuments of invaluable archaeological value.
The above mentioned inapplicability of the destructive methods for the quality chara cterization of such structures, in conjunction with the advantage of the NDT methods to maintain the integrity of the tested specimens, led to the application of the NDT method of ultrasounds for the study of marble and marble structures.
In a recent paper (Prassianakis et al. 2000) this method was applied for the mechanical characterization of prismatic specimens prepared from a specific type of marble, that is called Dionysos-Pentelikon (D-P) marble, which were subjected to three point bending. The mechanical constants were estimated and the damage evolution of the material in both the tension and the compression-regime of the bent beam was determined (Prassianakis 1994, 1997). The results obtained were in very good agreement with the respective ones obtained on the basis of a hybrid elastic-damage model, introduced recently by Exadaktylos et al. (2000) based on Hartig's approach (Hartig 1893). Motivated by the success of this work, the application of the NDT method of ultrasounds is extended in the present paper for the mechanical characterization of marble specimens that are to be subjected to direct tension.

2. THE EXPERIMENTAL PROCEDURE

A series of serious technical difficulties render the direct tension of geomaterials one of the most difficult tests in Strength of Materials. The main obstacles hard to overcome are:
• The fragmentation of the gripped region of the specimens and
• The unavoidable occurrence of a bending moment due to even the slightest non-coaxiality of gripping.
Many technical solutions for the specimen shape and the gripping configuration have been proposed. Among them the most popular ones are:
• To use flexible grips and cylindrical specimens without additional processing.
• To use a special type of "shouldered dogbone" specimens recently introduced by Vardoulakis et al. (1995).
Both alternatives were employed in the present work together with simple prismatic specimens of rectangular cross section. The shape, the geometrical characteristics and the measurement points of the types of specimens used are shown in Fig.1.

Fig 1: Shape and dimensions of the three types of specimens.

The exact dimensions of the "dogbone" specimens are described analytically by Vardoulakis et al. (1995). Specimens were prepared that were cut along all different anisotropy directions of the materials studied. Indeed, as it can be seen in Fig.2, marble has three distinct anisotropy directions (one parallel to the material layers, a second one along the width of the web and a third one along the thickness of the web) and thus it appears to be an orthotropic material (Corres 1993). After a long series of direct tension tests (Vardoulakis and Kourkoulis, 1997) it has been concluded that the mechanical properties along the first two anisotropy directions are very similar to each other. Thus, the material can be considered as transversely isotropic and it can be described with the aid of five elastic constants: the two elastic moduli in the plane of transverse isotropy and normal to it, the two Poisson's ratios characterizing the lateral strain response in the plane of transverse isotropy to a tensile stress acting parallel and normal to it, and the shear modulus in planes normal to the plane of isotropy (Lekhnitskii 1977).

Fig 2: Anisotropy of Dionysos-Pendelikon marble and specimen sampling. Both 'beams' and 'architraves'have been employed in the present experimental analysis

The destructive tension tests were carried out using a very stiff INSTRON loading frame with maximum loading capacity 250 kN. On the other hand, the non destructive measurements were performed using the ultrasonic device USIP-11 of Krautkramer. The probes used were the K2G ones of Krautkramer again and the frequency of both the longitudinal and the transverse waves produced by the respective probes were 2 MHz.
Using the values of the velocities, c_l and c_t, of the longitudinal and transverse elastic stress waves, respectively, propagating within the mass of marble specimens, as they were determined with the aid of ultrasonic measurements, and knowing that the density of D-P marble varies around the value of r=2730 gr/cm³, one can proceed to the estimation of the values of the elastic constants, i.e. of the modulus of elasticity, E, of the modulus of rigidity, G, and Poisson's ratio, n, using the familiar formulae (Prassianakis 1994, 1997):

(1)

3. EXPERIMENTAL RESULTS

All results of both the destructive and non-destructive testing are recapitulated in Tables I, II, III and IV. Analytically, Table I contains the average values of the modulus of elasticity, E, Poisson's ratio, n, and fracture tensile strength, s_f, of a long series of conventional destructive direct tension tests, with D-P marble specimens cut along all three anisotropy directions.

Direction of anisotropy ¯	E (GPa)	n (-)	sf(MPa)
Strong	84.5	0.26	10.8
Intermediate	79.5	0.26	9.5
Weak	50.0	0.11	5.3
Table I: The mechanical properties of D-P marble loaded statically in direct tension

It is clear from this table that the assumption concerning the transversally isotropic nature of D-P marble is fully justified, since the constants along the strong and the intermediate anisotropy direction are very close to each other.
On the other hand all information that has been obtained from the NDT method of ultrasounds using the prismatic type of specimens are included in Table II. The code indicates the order and the relative direction of the material layers of each individual specimen.

Specimen		cl (cm/sec)	ct|| (m/sec)	ct^ (m/sec)	E" GPa	E^ GPa	G" GPa	G^ GPa	n" (-)	n^ (-)
1a	1 1'	6204,1 5776,2	3380 3196,8	3250 3107,8	80,3 71,3	75,4 68,2	31,2 27,9	28,8 26,4	0,28 0,28	0,31 0,29
1b	1 1'	5248,6 5202,2	3380 3196,9	3250 3107,8	71,2 66,7	68,5 64,5	31,2 27,9	28,8 26,4	0,15 0,19	0,19 0,22
2a	1 1'	5343,1 5264,8	3078,2 3085,4	2933,3 2983,5	64,7 63,5	59,9 61,3	25,9 26,0	23,5 24,0	0,25 0,22	0,28 0,26
2b	1 1'	5611,3 5388,1	3153,1 3114,6	2976,8 3034,3	68,8 66,1	62,9 64,2	27,1 26,5	24,2 26,0	0,27 0,25	0,30 0,28
3a	1 1'	5674,9 5076,7	3072,1 3067,6	2983,4 2888,1	66,3 62,2	63,8 57,6	25,7 25,7	24,3 22,8	0,29 0,21	0,30 0,27
3b	1 1'	5921,3 5787	3193,8 3177,1	3079,8 3077,7	71,5 70,8	67,4 67,4	27,9 27,6	25,9 25,9	0,29 0,28	0,31 0,30
3c	1 1'	5907,4 5437,7	3458 3308,4	3623,5 3174,6	80,7 71,8	76,6 68,7	32,6 29,9	30,2 27,5	0,24 0,21	0,27 0,25
Table II: Elastic constants of the prismatic marble specimens obtained with the aid of the NDT method of ultrasounds.

The ultrasonic measurements have been performed at three different points (one at the middle section and two close to the edges) on each one of the sides (1) and (1') see Figure 2a) of the prismatic type specimens. The values of the above Table II have been determined as the average value of the three measurements on each side of the specimen and for each one of the three anisotropy direction. The symbol (||) characterizes quantities obtained from measurements that have been performed along a direction parallel to the material layers of the specimens, while the symbol (^ ) characterizes quantities obtained from measurements that have been performed along a direction perpendicular to the material layers of the specimens.
In next Table III the values of the velocities, c_l and c_t, of the longitudinal and transverse elastic waves, respectively are recapitulated, as well as the corresponding values of the elastic constants, as they have been determined with the aid of Eqs.(1), again as the average of the ultrasonic measurements performed at two points of each specimen (see Fig.2b). In this case all measurements were exclusively performed along the direction parallel to the longitudinal axis of each cylindrical specimen. Both the individual measurements and their average value have been included in the table. It is mentioned at this point that the specimens of this type were cut along directions forming angles 0^o, 45^o and 90^o with the direction perpendicular to the material layers of the marble.

Specimen, Direction	Measurement	cl (m/sec)	ct (m/sec)	E(GPa)	G(GPa)	n(-)
1st , 45o	1	5722,7	3141,7	69,5	27,0	0,29
	2	6132,5	3282,5	75,9	29,4	0,29
	Average			72,7	28,2	0,29
1st, 90o	1	6104,5	3395,4	79,9	31,4	0,27
	2	5775,6	3333,4	75,8	30,3	0,25
	Average			77,8	30,8	0,26
2nd, 0o	1	6023,6	3149,4	70,9	27,1	0,31
	2	6068,0	3135,3	70,4	27,7	0,31
	Average			70,6	27,4	0,31
2nd, 90o	1	6082,8	3381,6	79,8	31,2	0,28
	2	6238,7	3298,1	77,2	29,7	0,30
	Average			78,5	30,4	0,29
3rd, 0o	1	6446,2	3352,6	80,3	30,6	0,31
	2	6462,7	3361,2	80,8	30,8	0,31
	Average			80,5	30,7	0,31
3rd, 45o	1	5946,6	3186,6	71,5	27,7	0,29
	2	5804,5	3266,2	73,4	29,1	0,27
	Average			72,4	28,4	0,28
3rd, 90o	1	5994,0	3375,0	78,9	31,1	0,27
	2	5994,0	3290,6	75,7	29,6	0,28
	Average			77,3	30,3	0,275
4th, 0o	1	6162,9	3298,7	77,2	29,7	0,30
	2	6068,0	3250,0	74,9	28,8	0,30
	Average			76	26,2	0,30
Table III: Elastic constants of the cylindrical marble specimens obtained with the aid of the NDT method of ultrasounds.

Finally, in Table IV the results have been summarized from the study of the specimens of the third type (Fig.2c). The specimens of this category were subjected to direct tensile loading for the parallel destructive determination of the values of the elastic constants E, G, and n, after having been tested with the aid of the NDT method of ultrasonics All specimens were cut along a direction parallel to the material layers. The values of the same constants were, also, determined using the respective values of the elastic waves velocities and Eqs.(1) using the results of two measurements performed at two points of each specimen (Fig.3c). Again both the individual measurements and their average value have been included in Table IV. The measurements were performed at points (1) along directions parallel to the longitudinal axis of each specimen, while at points (2) they were performed along directions perpendicular to the bases of the specimens.

No	Measurement	Non-destructive testing					Destructive testing
		cl (m/sec)	ct (m/sec)	E (GPa)	G (GPa)	n	E (GPa)	G (GPa)	n
0202	1	3025,7	3368,2	78,7	30.9	0.270	79,5	31,3	0,27
	2	6038,4	3429,3	80,9	32,1	0,260
	Average			79,8	31,5	0,265
1201	1	6000,3	3409,7	80,0	31,7	0,260	81,0	32,0	0,26
	2	6001,6	3412,5	80,2	31,8	0,260
	Average			80,1	31,8	0,265
1202	1	5764,7	3164,7	70,0	27,3	0,280	73,1	28,9	0,26
	2	5587	3166,1	69,0	27,4	0,260
	Average			69,5	27,4	0.270
1203	1	5920	3305,1	75,8	29,8	0,280	76,2	30,1	0,26
	2	5863,6	3324,6	76,1	30,2	0,260
	Average			76,0	30,2	0,265
1206	1	6273,1	3384,5	80,7	31,2	0,290	82,3	32,4	0,27
	2	5805,4	3187,1	71,0	27,7	0,280
	Average			72,4	28,3	0,280
1213	1	5920	3250	73,8	28,8	0,280	72,3	28,5	0,27
	2	5805,4	3187,1	71,0	27,7	0,280
	Average			72,4	28,3	0,280
1303	1	5934,8	3258,1	74,2	29,0	0,280	74,0	29,1	0,27
	2	5846,9	3170,7	70,8	27,5	0,290
	Average			72,5	28,3	0,285
Table IV: Comparison of the values of the elastic constants of :dogbone" cylindrical marble specimens obtained with the aid of the NDT method of ultrasounds and the destructive tension experiment

Concerning the code of the specimens of this category, the first number indicates whether their surface was artificially polished (1) or not (0), the second one indicates the diameter of the specimens measured in cm, while the last two numbers indicate the order of the specimen. For example the code 1206 indicates the sixth specimen surface polished specimen of diameter two centimeters. It is mentioned, also, that all specimens in all three cases were obtained from the same batch of marble.

4. CONCLUSIONS

Based on the destructive and non-destructive experimental procedure described in the previous paragraph and the results obtained one can safely draw the following conclusions:
Although marble is a material of strongly anisotropic nature and of layered structure, it can be relatively easily studied using the NDT method of ultrasounds than using conventional destructive testing methods. Depending on the quality of marble and the frequency of the ultrasonic wave used, one can test marble specimens of thickness varying from a few centimeters to almost one meter and higher. Thus, the specific NDT method used in the present study is very flexible and suitable for the examination and quality characterization of the present state of ancient marble monuments and sculptures, the archaeological value of which does not permit conventional destructive testing.
Concerning the numerical results for the elastic constants it has been concluded that the values of the elasticity and rigidity moduli, E and G respectively, are considerably higher along directions parallel to the material layers of marble compared to the respective values along directions perpendicular to the layers. The opposite is true for the results concerning the values of Poisson's ratio. This observation is verified by considering the results obtained from the destructive tensile testing of the specimens, which have, also, been included in Table IV for comparison reasons. In fact, all values obtained from the NDT method of ultrasonics and the destructive tensile test are in very good agreement to each other and the maximum determined discrepancy is of the order of 10 % and lower.
The last observation is extremely encouraging for further application of NDT testing of marble and marble structures, since beyond the values of the elastic constants along an arbitrary direction one can, also, determine safely and reliably the principal anisotropy directions, the locations of various invisible by naked eye imperfections and impurities diminishing the strength of specific marble specimens (called "kommoi" at the era of the Parthenon builders) and of course the dimensions of the specimens.
The above conclusions indicate once again the value of the NDT method of ultrasounds rendering it one of the most reliable tools available for the study of marble monuments.

Acknowledgements

The financial support of the European Union in the frame of the "Standards Measurements and Testing" program, under the contract SMT4-CT96-2130 is gratefully acknowledged. The assistance of Mrs. Konte Georgia, graduate student of the Civil Engineering Department of National Technical University of Athens, in the execution of the experimental part of this work is, also, gratefully acknowledged by the authors.

REFERENCES

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