Introduction
Among the most difficult problems, confronted by the scientific personnel of the restoration/ conservation project of the Parthenon Temple on the Acropolis of Athens, is the restoration of the “connections” used by ancient Greeks to keep the structural members of the monument in place. The term “connection” is used to describe not only the metallic element, which was placed in a groove properly sculptured on the marble volume, but also the material that was used to cover the connector and fill the empty space of the groove and also the volume of the marble in the immediate vicinity of the metallic connector. The role of these “connections” is critical for the structural integrity of the monument given that the Parthenon is a dry-stone construction consisting of marble blocks of various size and geometry without any intermediate adhesive material between the marble blocks (Fig. 1). Under normal conditions, the “connections” are assumed to be “load-free” and it is only under excessive (unpredictable) loading schemes (as it is for example earthquake excitations) that the “connections” undertake role of load-bearing elements.
Focusing attention to the epistyles of the Parthenon Temple, it is confirmed that the ancient stonemasons used “I”-shaped metallic elements in order to keep the epistyles in place either they were placed linearly or angularly (Fig. 1(b)) with respect to each other. The original connectors of the Parthenon were made of iron and steel [
1,
2] and after they were placed in the grooves (mortises) sculptured in the marble bodies they were fully covered by pouring molten lead that completely filled the empty space. The overall design of the “connections” was based on the simple (though critical) assumption that during overloading it is the metallic element that should fail (considering the major value, both architectural and structural, of the marble elements). In other words, the metallic element should be deformed either elastically or even plastically in order to protect the marble volume.
Some decades ago, naked-eye inspection of the “connections” revealed that quite a few of them were badly damaged (Fig. 2). The damages observed for epistyles connected with “I”-shaped connectors were of two discrete modes: Fracture of the metallic connector without fracture of the surrounding marble volume and fracture of the marble volume with or without visible damage of the metallic element. The prevailing view of the scientists working for the restoration of the Parthenon Temple attributes the damages of the “connections” to the combined action of physicochemical and mechanical parameters [
3,
4]: Oxidation of the iron elements (which was accelerated due to atmospheric pollution) results to volume increase which in turn is responsible for cracking of the marble volume. Recently, an alternative theory was proposed attributing the failure of the “connections” to the fact that the load that can be undertaken by the metallic element is higher compared to the respective load that can be sustained by the marble volume itself [
5].
Independently of the chargeable event of the damage of the “connections,” fragmentation of the surrounding marble volumes was caused, which could be proven critical for the structural integrity of the Temple in case of seismic excitations. As a result, the restoration of the damaged “connections” of the epistyles became one of the most serious issues that had to be resolved by the scientific team working for the restoration of the monument. The attempt was quite challenging since a series of mutually conflicting parameters (from the archeological, architectural and engineering points of view) should be taken into account. In addition, any solution adopted should be properly validated before applied in situ, taking into account the unique cultural value of the Temple. Given that analytic validation is beyond any discussion due to insuperable difficulties (caused by the complicated geometry of the “connections” and the anisotropy and nonlinearity characterizing the materials of the connection) it appears that experimental (and in a second stage numerical) validation is the only tool that could turn on the green light for the practical application of any solution.
In this direction, an experimental protocol is here described aiming to assess the efficiency of the procedure nowadays adopted for the restoration of damaged “connections” of the Parthenon Temple. Taking into account that the mechanical response of these “connections” under pure tensile loading was recently studied both experimentally [
6] and numerically [
7], it was decided to focus attention to their mechanical response against shear loading. It is emphasized from the very beginning that the experimental study is also a challenging task mainly due to the interfaces created by the co-existence of three different materials. These interfaces are inaccessible by traditional sensing techniques used in Experimental Mechanics of Materials. As a result, novel techniques should be used that could provide data from the interior of the specimens (mainly from the hidden interfaces), since it is reasonable to assume that damage mechanisms leading to destruction of the “connections” are first activated along these interfaces. In this context, besides traditional sensing tools (electrical strain gauges, clip-gauges and dial gauges) innovative ones were also employed in the present protocol including the Acoustic Emission and the Pressure Stimulated Currents. Moreover, in the direction of obtaining data for the overall displacement field the 3D-Digital Image Correlation technique was, also, employed.
Comparative analysis of the data provided by the sensing tools used revealed valuable information about the beneficial role of the “Relieving Space,” i.e., the small portion of the web of the metallic connector that is intentionally left uncovered by the filling material. In addition, clear pre-failure indicators were detected within the data provided by the Acoustic Emission and the Pressure Stimulated Currents techniques well in advance of the macroscopic failure of the “connections,” indicating that both of them could be used as reliable Structural Health Monitoring tools of the restored “connections” of the epistyles.
The restoration of damaged “connections” of epistyles of the Parthenon Temple
The technique nowadays applied for the restoration of damaged “connections” of the Parthenon Temple was adopted after a long and painful research period that followed the revelation of the degree of damage of the authentic “connections.” Based on pioneering works by Skoulikidis [
3] and Angelides [
4], and in full accordance to the demands of the “Venice Charter” [
8], the technique suggests substitution of the damaged iron connecting elements by new ones made of pure titanium. The new connectors are placed in the grooves sculptured by ancient stonemasons (assuming that they are intact) in order to avoid additional irreversible damage of the authentic stone. Although the choice of the specific material (titanium) was initially disputed, it is nowadays adopted as an inevitable compromise balancing among a series of contradicting compatibility aspects ranging from pure chemical, to physical and mechanical. The specific choice for the metallic element excluded the use of lead as filling material (given that the “titanium-lead” pair forms strong galvanic element, which is definitely unacceptable for quite a few reasons). As a result, a suitable cementitious material was selected as filling material [
1–
4] for the restored “connections.” In other words, the “Marble-Lead-Iron” complex of the ancient stonemasons is now replaced by the “Marble-Cement-Titanium” one. The as above procedure is nowadays used, almost exclusively, not only for restoring the damaged “connections” of the epistyles of all temples of the Athenian Acropolis, but also for the restoration of any type of multi-fractured structural elements of the monuments.
Especially for the restoration of the “connections” of the epistyles a slightly modified version of the as above technique was proposed a few years ago by Zambas [
6]: Part of the connector’s web is left uncovered by the filling material in order to increase the deformation capability of the connector. The empty space left in the groove is usually denoted as “Relieving Space” and its role is not as yet assessed experimentally or numerically.
In fact (and in spite of its wide acceptance and adoption), the mechanical response of the restored “connections” to mechanical loads is not in-depth studied from the structural point of view. A possible explanation of this scarce of studies is the fact that, in their initial position, the “connections” are assumed load free: The only loading expected, i.e. the own weight of the epistyles and of the structural members superimposed to the epistyles, is carried by the epistyles themselves. However, it is quite possible that in case of excessive loading (for example due to seismic excitations) the epistyles tend to be displaced with respect to each other and as a result the “connections” are mechanically stressed.
The mechanical response of “connections” with “I”-shaped metallic elements was until now studied only under pure tensile load by Zambas [
6] (scientific responsible of the Parthenon restoration project from 1984 until 1994). In his milestone work Zambas used a personally improvised experimental set-up (Fig. 3(a)) to impose tensile loading on specimens consisting of two identical marble blocks (Fig. 3(b)) connected together with two “I”-shaped steel connectors (Fig. 3(c)) (ensuring symmetry and axial loading). Following the ancient technique molten lead was poured until the connectors were covered and the grooves filled (Fig. 3(d)). In all experiments it was the connector that failed while the marble blocks remained intact.
Zambas’ protocol was not repeated for blocks connected according to the technique used nowadays. In this direction, and taking into account the critical role of the connections for the integrity of the monument, it was decided to thoroughly study the response of the “connections” used today, in order for definite conclusions to be drawn about their efficiency against mechanical excitations in the form of shear loading. The specific protocol, which is still in progress, is conducted in close collaboration with the scientific personnel of the Parthenon restoration project. Their assistance in the design of the specimens of the protocol was invaluable and it is gratefully acknowledged. The specimens were in situ prepared by highly qualified and experienced technicians of the Parthenon’s work-site.
During the preliminary stages of that protocol attention was paid to detect and quantify the parasitic moments (bending and torsional) prohibiting the implementation of pure shear loading. These parasitic moments are due to the fact that the metallic connector is placed asymmetrically with respect to the geometric center of the marble blocks. In this direction, specimens of various geometries were prepared and tested [
9,
10] before the geometry considered as optimum was finalized.
The experimental protocol
The materials
The materials used for the construction of the specimens were: Dionysos marble for the epistyles, commercially pure titanium for the “I”-shaped connectors and a cement-based material to fill the grooves and cover the connectors.
Dionysos marble is nowadays used, almost exclusively, to cover the needs of the Parthenon restoration project for copies of destroyed or lost structural elements or patches for partially destroyed ones. It exhibits physical and mechanical properties almost identical to those of the Pentelic marble, used by ancient Greeks for the construction of all monuments of the Acropolis hill. An analytic description of its physical properties can be found in an earlier work by Tassogiannopoulos [
11]. From the Strength of Materials point of view, the data published vary within broad limits [
6,
12,
13] given that the mechanical properties of rocks and rock-like materials strongly depend on the exact quarrying location. An additional scattering reason is the anisotropy characterizing Dionysos marble, which, according to Vardoulakis and Kourkoulis [
13,
14], is of the transverse isotropy mode.
Concerning the metallic connectors ancient technicians used a variety of steel consisting of successive layers of “soft” pure iron and “hard” steel of increased carbon content [
15]. Based on arguments related to optimum resistance to corrosion, suitable mechanical strength and coefficient of thermal expansion similar to the respective one of marble, Skoulikidis [
3] and Angelides [
4] suggested pure titanium as the best choice for the construction of the restored “connections.” Pure titanium has approximately the same Poisson’s ratio and thermal expansion coefficient as Dionysos and Pentelic marbles. Therefore the restored structural members of the monument are protected from fracture due to differential lateral shrinkage and differential thermal expansion, respectively. The type of titanium used for the restoration project is characterized by a relatively high modulus of elasticity (exceeding 100 GPa) which is combined with increased ductility (approaching 40%) enabling the metallic element of the “connections” to absorb a significant amount of strain energy and bear high deformations before fracture.. The mechanical properties of the titanium used in the present experimental protocol were obtained from a series of preliminary direct tension tests with cylindrical bars of various diameters (covering the whole range of diameters used in the Acropolis work-sites) and are recapitulated in Table 1.
As already mentioned, the as above choice for the metallic element of the “connection” renders the use of lead as filling material of the groove (after placing the connector in it) inapplicable, since it is incompatible to titanium. Therefore it was substituted by a cement based material according to the conclusions drawn by Skoulikidis [
3] who studied the pair of materials used by Balanos [
16] for the restoration of the Erechtheion temple (i.e. a cement-based filling material and the marble which was in contact with it) and found no mechanical or chemical decay at all. Based on this observation, Skoulikidis [
3] proposed a mix of one part white cement and three parts silica sand as the most suitable filling material for the restored “connections” [
1–
4]. Marinelli et al. [
17] and Kourkoulis and Pasiou [
18] quantified experimentally the mechanical properties of this material.
The specimens and the gripping/loading fixture
Two types of specimens were used in the present experimental protocol, designated as CF (Completely Filled connectors) and RS (specimens with “Relieving Space”). Both types of specimens consisted of two independent marble blocks, the geometry and dimensions of which are shown in Fig. 4(a). The two blocks were joined together with the aid of one “I”-shaped titanium connector (Fig. 4(b)) and suitable cement-based filling material. The construction of the specimens was realized according to a lengthy and laborious procedure as follows: As a first step suitable marble volumes had to be selected paying every effort for them to be free from inhomogeneities and defects and also for their bedding planes to be properly oriented with respect to the expected loading scheme (recall that Dionysos marble is a transversely isotropic material). Then the volumes were cut and blocks were formed according to the geometry of Fig. 4(a). Two holes were drilled on the one marble block in order to exert the shear force (Fig. 4(a)). The holes were drilled on the block which is expected to be movable with respect to the other block that is expected to be totally immobilized. The position of the holes was determined based on preliminary calculations in order to avoid local marble fracture around the holes due to the increased stress concentrations in the immediate vicinity of the load application points. As a next step the grooves (mortises) were sculptured on both blocks (Fig. 4(a)). Their depth was equal to 7 cm while their boundary followed the shape of the connector. After sculpturing the grooves the connector was placed in them and the cement-based material was prepared, according to the proportion of ingredients used at the work-site of the Parthenon Temple. The groove was then saturated with water and the filling material was poured in the volume between the connector and the marble blocks.
For the first type of specimens the connector was completely covered Fig. 4(c) and the groove was completely filled (CF specimens). For the second type of specimens a portion of the groove (on either side of the common contact plane of the two blocks) was left uncovered (Fig. 4(d)), leaving an empty space, which permits easier deformation of the connector (RS specimens). It is exactly the role of this empty space that, among others, will be assessed in the present study, taking into account that its efficiency is not as yet studied.
The specimens were cured for more than a month (for the filling material to attain its maximum strength) before they were transferred to the Laboratory of Testing and Materials of the National Technical University of Athens for the implementation of the experiments.
In the mean time the loading fixture was designed and constructed, taking advantage of the experience gathered during previous attempts to conduct pure shear loading of the “connections” [
9,
10]. In general, improvising a set-up for pure shear experiments is a difficult task. Various solutions are mentioned in the literature for concrete and soils however studies related to the shear of marble structural elements joined together with metallic connectors are scarce. The additional difficulty in this case is that besides the parasitic bending moments (almost inevitably appearing in shear tests) torsional ones are, also, generated while testing the interconnected marble blocks. As already mentioned, this is due to the inherent asymmetry of the specimens which is imposed by the fact that the metallic connector is placed relatively close to the surface rather than at the center of the specimens. Attempts to completely restrict these moments using complementary constraints could influence the failure mode and shadow the conclusions drawn and therefore they were avoided in the present protocol. This decision was dictated, also, by the fact that when the epistyles of the monument are in situ connected there are not additional restrictions and therefore the laboratory tests would not properly simulate the actual loading scheme.
In this direction, non-commercial gripping and loading fixtures were improvised, minimizing parasitic moments without influencing the failure mode. The solution finally favored, shown in Fig. 5(a) (together with the experimental set-up), consisted of an extremely stiff rigid plate and two “G”-shaped metallic elements restricting the motion of the one block of the specimens with the aid of six rigid tie rods. In addition a “T”-shaped loading platen was designed in such a way that the load was exerted at the vertical plane containing the metallic connector in the direction of further reducing parasitic torsional moments. Furthermore, two “P”-shaped metallic elements were used to keep the loading platen in contact with the loaded volume of the specimen while two titanium bars were used to transfer the load from the movable traverse of the loading frame to the movable block of the specimens.
The sensing techniques used in the protocol
It is generally accepted, nowadays, that failure mechanisms leading to the fracture of the “connections” of marble epistyles are first activated along the internal (hidden) material interfaces (marble-to-cement and cement-to-titanium). This is supported by both naked-eye observations of in situ epistyles of the Parthenon Temple [
19] and, also, by previous laboratory experimental studies [
20]. As a result, collecting raw data from these interfaces becomes a crucial demand. Given that traditional sensing techniques (like for example, photoelasticity, electrical strain gauges, caustics etc.) record data mainly from the external surface of the specimens, the internal events (local failures, micro-fractures…), preceding the macroscopic observable failures, can only be detected using innovative sensing techniques. In the present protocol two sensing techniques were used: A mature and well established one, widely used worldwide, i.e. the Acoustic Emission (AE) technique, and a recently introduced one, known as the Pressure Stimulated Currents [
21] technique.
The AE technique detects acoustic events taking place within the material during mechanical loading. The technique was applied in geomaterials already since 1938 by Obert [
22]. The main advantages of the AE technique is that it monitors internal failure processes during the whole loading procedure of either a specimen or a structure by just attaching a number of sensors on it. In addition, taking into account that acoustic emissions depend mainly on irreversible deformations, it becomes evident that the AE technique is, also, useful for Structural Health Monitoring [
23]. Further applications include the quantification of the fracture process zone by means of the source location of the acoustic emissions in concrete as well as in situ inspection of vessels, leak detection etc. For the needs of the present protocol eight R15
a acoustic emission sensors with 150 kHz resonant (Physical Acoustics) were attached at the positions shown in Fig. 5(a), with the aid of silicone. Preamplifiers with 40 dB gain were used. The specimens tested consist of three different materials, however, a uniform wave velocity vector was considered. This velocity was determined equal to about 1000 m/s and 500 m/s along the connector’s axis (
x-axis) and normal to it in the xy plane (
y-axis), respectively, based on the results of a series of preliminary breakings of a pencil lead pressed against the specimen. The equipment and software used were by Mistras Group, Inc.
Concerning the PSC technique its founding principle is that electrical signals are produced during mechanical loading of some brittle materials like marble, amphibolite and cement-based materials [
24–
26]. These signals are usually recorded in the form of very weak electric current using sensitive electrometers. The sensors used to collect these currents consist of pairs of gold plated electrodes. They are simple to be constructed and their cost is low compared to competitive sensing sensors. In the present study, the pairs of electrodes were attached on either the front (Fig. 5(a)) or on both the front and rear surfaces of the specimen very close to the region where fracture of marble is expected, according to the results of previous preliminary tests [
20] and in situ observations [
19]. The data recording and acquisition system consisted of extremely sensitive programmable electrometers (Keithley, 6517A), resolving currents in the 0.1 fA to 2.0 mA range.
Taking now into account that the data recorded by both these techniques are of qualitative rather than quantitative nature it is crucial for their outcomes to be properly calibrated and compared against quantitative ones. For this purpose the Digital Image Correlation (DIC) technique was, also, used in the present protocol permitting recording of the 3D displacement field developed. The DIC technique was theoretically founded and experimentally applied almost 30 years ago [
27]. It is a non-destructive, contactless technique the application of which necessitates a random pattern of dots on the specimen’s surface which is captured successively by two cameras during the whole duration of the experiment. The basic principle behind DIC is the correlation of the position of each dot in the undeformed state of the specimen to its respective position in the deformed state. The technique is widely used nowadays worldwide for the three dimensional full-field representation of displacement and strain fields. Additional applications include the monitoring of crack propagation, determination of the crack opening displacement, calculation of stress intensity factors etc. In the protocol here described a 3D-DIC system (LIMESS Messtechnik & Software GmbH, Germany) was used. The resolution of the cameras is equal to 1624×1234 pixels with an accuracy for displacements equal to 0.01 pixel. Since the full field displacement field on the front surface of the specimen was to be determined the active field was a rectangle of dimensions 53.0×37.5 cm
2 and the size of the pattern’s dots was calculated equal to about 1 mm. The sampling rate was set equal to 1 photo per 7 s.
Moreover, two clip gauges were also used, to measure the relative displacement of the marble blocks composing the specimens. They were properly attached on the side of the specimens opposite from that on which the dots pattern of the DIC technique was drawn. The first one (lower level) was placed close to the working table (lower edge of the specimen) and the second one (upper level) close to the upper edge of the moving block (Fig. 5(a)).
Finally, in order to measure the axial strains developed along the web of the metallic connector, three electrical strain gauges were properly glued along its longitudinal axis. One of them was glued exactly at the mid-section of the connector (interface of the two marble blocks). The remaining two strain gauges were glued on either side of the connector, i.e., on the connector’s part placed in the groove from the side of the immovable block and on the connector’s part placed in the groove from the side of the movable block (Fig. 5(b)).
The experimental procedure
All experiments were carried out with the aid of a servo-hydraulic loading frame (INSTRON 1126, 250 kN). The frame was chosen because it is equipped with an extremely rigid working table permitting stable fixing of the specimens on it. Before the experiments the load cell was calibrated using certified weights (for the lower scales) and certified load-rings for the high load scales. It was found that the maximum error was well below 0.15%. In addition, the displacement of the frame’s traverse was checked using a certified micrometer and the error determined was insignificant.
The target of the experimental procedure was to impose parallel sliding of the one marble block with respect to the other, normally to the longitudinal axis of the titanium connector. In this context, the specimens were placed on the table of the frame and one of its two constituent parts (marble blocks) was rigidly clamped on the frame’s table with the aid of the fixture previously described. The load was exerted on the movable block under displacement-control conditions at a rate equal to 0.2 mm/min (quasi-static loading conditions) using the set-up described in Section 3.2. During the tests the following quantities were recorded as functions of time: The load imposed by the frame, the displacement of the frame’s traverse, the PSC produced, the AE activity, the 3D displacement field, the opening of the “connection” (distance between the marble blocks along the axis of the connector), the elongation of the tie rods, the displacement of the (theoretically) immovable metallic plate restricting the motion of the immovable marble block, and finally the strains on the web of the “I”-shaped connector.
Comparative analysis of these data permitted gaining insight of the succession of damage mechanisms and the assessment of the efficiency of the RS specimens against the CF ones.
The mechanical response of the “connections”
For both types of specimens it can be safely concluded that the experiments were successfully implemented concerning, at least, the realization of shear loading. Although parasitic moments were not totally suppressed they were significantly reduced in comparison to previous attempts [
9,
10]. The marble block assumed to be totally immobilized was indeed kept in-place by the custom-made metallic devices while the block on which the forces were exerted appeared translating almost parallel to the fixed one.
CF-specimens
Macroscopic observation of the specimen during and after loading indicated clearly that the moving block was the only one that was fractured and the fracture started from the middle point of the groove’s flange (Fig. 6 (a)). Moreover, the overall final deformation of the metallic connector does not appear severe at least by naked-eye inspection (Fig. 6(b)).
The maximum force sustained by the specimen was equal to about 27.5 kN as it can be seen from Fig. 7 in which the raw data concerning the force induced are plotted against the displacement of the loading frame’s moving traverse (it is here recalled that this is not the actual displacement of the moving block, which will be determined accurately in Section 6 using the data of the 3D-DIC system). The overall plot appears consisting of three clearly distinguishable parts, i.e., OA, AB and BC (ignoring some minor nonlinearities observed at the very early loading steps due to inevitable bedding errors). The two slope changes dividing the plot into parts appear at load levels equal to about 60% of the maximum force applied (i.e., at about ~17.0 kN) and 85% of the maximum force (~23.0 kN).
The relative position of the two constituent blocks of the specimen (i.e. the normal distance between them), was recorded by the two traditional clip gauges and is plotted in Fig. 8(a) with respect to the load level. The upper-level clip recorded a monotonously increasing distance between the two marble blocks the maximum value of which did not exceed 1 mm. On the contrary, the indications of the lower-level clip appear oscillating around their initial position (zero opening) and the maximum values attained did not exceed 0.016 mm, indicating that the target of almost parallel vertical displacement of the moving block with respect to the immovable one was achieved at a very satisfactory degree.
The as above conclusions, concerning the minimization of parasitic bending and torsional moments, were, also, verified by taking advantage of the data provided by the 3D-DIC system. The respective plots for the upper and lower levels of the immovable block are plotted in Fig. 8(b). It is here recalled that the DIC system provides data gathered from the opposite side of the specimen with respect to that on which the clip-gauges are attached, i.e., from the side painted with the random pattern of black dots (Fig. 5). As a result, it should not be expected for the data of the DIC system and the clip gauges to be identical, since micro-rotational motions are not totally suppressed due to inherent (and inevitable) asymmetries of the specimens, as it was earlier explained. Keeping this in mind, it is very encouraging to observe from Fig. 8(b) that the two blocks behave as a single body up to a load level equal to about one third of the maximum force attained. From this point on the distance between them starts increasing smoothly but it does not exceed 300 mm even at the moment of fracture, definitely proving that the test realized corresponds to an almost pure shear one. It is, also, mentioned that the relative distance between the two blocks starts increasing faster at a load level of about 19 kN, shortly after the first slope change of the load-displacement curve (point A in Fig. 7).
The data of the DIC technique were used, also, for the study of the deformation of the cement-based filling material. In this direction, two elementary areas of this material, located on either side of the interfacial plane (the plane of contact of the two blocks), were isolated, as it is shown in Fig. 9(a). Their displacements ux along the axis of the connector (horizontal or x-axis) and uy along the loading axis (vertical or y-axis) were determined and are plotted in Fig. 9(b) against the load applied. It is definitely proven from both plots of Fig. 9(b) that the two elementary areas, although located on different marble blocks, exhibit almost identical displacement components, both horizontally and vertically, during the whole loading procedure. It is thus safely concluded that, at least for the specific type of specimens, the filling material is not fatally cracked at its free surface. Obviously, internal damage accumulation within the mass of the filling material does develop, however it seems that it does not reach critical levels that could cause macroscopically visible cracking.
The axial strains developed along the web of the metallic connector, as recorded by the electrical strain gauges, are plotted in Fig. 10, again versus the load applied. It is interesting to note that the strain gauge glued from the side of the immovable (fixed) block, appears almost insensitive up to a load level equal to about 60% (~17.0 kN) of the maximum load applied (it is recalled that this load level corresponds to the first slope change of the load-displacement plot). Then the specific portion of the connector’s web becomes under tension up to a load-level equal to about 70% of the maximum one (~19.0 kN). From this load level on the absolute values of the strains start decreasing and at a load-level equal to about 23.0 kN (almost 85% of the respective maximum value, corresponding to the second slope change of the load-displacement plot) the specific portion of the connector becomes under compression.
The strain gauge at the opposite portion of the connector’s web (i.e., in the movable block) indicates compressive deformation of the specific portion for the whole loading procedure. The compressive strain increases monotonically until about 60% of the fracture load, coinciding again to point A of Fig. 7 (i.e., the first slope change of the load-displacement plot). Then a local extremum appears (accompanied by a slight decrease of the magnitude of the strain equal to about 10%) and then it starts increasing again almost until the fracture of the moving block.
Concerning the central section of the connector, its behavior (as recorded by the respective strain gauge) appears similar to that of the movable block until about 35% of the fracture load. In other words up to a load level in the range between 0.0 and 11.0 kN the central section of the connector is under compression of gradually increasing intensity. Then the value of the compressive strains is almost stabilized up to about 60% of the fracture load. From this load level on the values of the axial strain start decreasing, they are zeroed (at about 77% of the fracture load) and turn to positive values indicating tension of the connector’s central section until the final fracture of the moving block.
RS-specimens
Naked-eye observation indicates that the failure of the specimen was again due to fracture of the movable marble block. The crack initiated again form the middle section of the groove’s flange (Fig. 11(a)). The connector was now severely damaged plastically (Fig. 11(b)).
Concerning the failure load it is very interesting to observe that the specimen fractured at exactly the same load level as the CF type of specimen, i.e., at about 27.5 kN. This is a very encouraging indication concerning the repeatability of the experiments which is always under question in case of tests influenced by a long series of uncertainty factors (inhomogeneity of marble [
11], difficulties in the determination of its mechanical properties either by direct tension or using the Brazilian-disc test [
28,
29], quality of interfaces, exact placement of the connector, quality of grooving etc.).
The loading history for the specific type of specimens is represented by the typical load-displacement curve, plotted in Fig. 12 (it is again emphasized that the actual displacement of the moving block is not identical to the displacement of the traverse of the loading frame, as it will be discussed in the “Discussion and Conclusions” section). The differences between the specific plot and the respective one of the CF type of specimens are striking: It starts with an almost linear portion (OA in Fig. 12) up to about 20% of the maximum load attained (~5.0 kN) which is followed by a second almost linear portion of considerable lower slope (AB in Fig. 12) up to about 25% of the fracture load (~7.0 kN). Then the curve becomes gradually steeper with an intermediate slope change at about 65% of the maximum force induced (17.5 kN). Another interesting characteristic of the specific plot is the fact that two load drops were recorded, one at about 55% of the maximum load (~15.0 kN) and a second one at about 97% of the maximum force (~26.5 kN). The reason of these drops will be discussed in next section taking advantage, also, of the data of the innovative sensing techniques used (AE and PSC).
The relative (horizontal) distance between the two constituent marble blocks of the specimen was again recorded with the aid of two traditional clip-gauges and the respective data are plotted in Fig. 13(a) against the load level. Contrary to what happened in the CF type of specimen (Fig. 8(a)) the two clip-gauges provided almost identical data (at least from a quantitative point of view) up to a load level equal to about two thirds of the maximum load attained. At the upper level the two blocks were moving apart from each other up to about 23% of the maximum force (~6.0 kN) and this distance was kept constant almost up to 57% of the maximum force (15.5 kN). Then the distance between the two blocks decreased slightly and remained almost constant up to a load level equal to about 80% of the maximum force attained (~21.5 kN). From this point one the blocks started moving apart from each other until the fracture of the movable marble volume. The initial mutual displacement of the two blocks was recorded also by the lower level clip gauge. Moreover, the magnitude of the recordings were almost identical to those of the upper level clip indicating that the two blocks were moving apart from each other according to an almost translational mode up to a load level equal to about 23% of the maximum force induced (~6.0 kN). From this load level on the two blocks started approaching each other (however without coming into contact).
It is very interesting to note that the recordings of both clip-gauges were not only of the same order of magnitude but also that the maximum values attained did not exceed 550 mm, indicating the test is an almost pure shear one. Moreover it is emphasized that the overall relative displacement of the two marble blocks is quite close to that of the CF type specimen, indicating that the “Relieving Space” does not impose additional parasitic motions.
The conclusions concerning the minimization of parasitic bending and torsional moments were again supported further by the data provided by the 3D-DIC technique for the displacement field of the two marble blocks. Keeping again in mind that the DIC system provides data from the opposite side of the specimen with respect to that of the clip-gauges (and therefore no identity between the respective data are to be expected) the relative distance between the two constituent blocks of the specimen is plotted in Fig. 13(b). The similarity between this plot and the respective one of Fig. 8(b) is obvious, both from the qualitative and quantitative points of view. At the upper level the distance between the two marble blocks is almost zero until about two thirds of the maximum load level attained (the specific load level corresponds to the final slope change of the load-displacement curve, Fig. 12). From this load level on the distance starts increasing until the macroscopic fracture of the specimen. At the lower level the distance between the two blocks increases smoothly from relatively low load levels, however its rate of increase changes significantly at the same load level as that of the lower level (two thirds of the maximum one). Again the maximum relative displacement between the two marble blocks does not exceed 250 mm for the whole loading procedure definitely verifying the minimization of both torsional and bending motion trends.
As far as it concerns the straining of the metallic connector, it was again recorded with the aid of electrical strain gauges glued on its web at the same positions as those for the CF specimen (i.e., at the interfacial section and at either side of this section). The respective data are plotted in Fig. 14. Direct comparison to the respective data of the CF specimen (Fig. 10) reveals a huge quantitative difference. The strains recorded for the RS specimen approach 4×103mstrain (in fact the specific value could be much higher in case the respective strain gauge kept recording until the final fracture of the specimen) while those of the CF specimen did not exceed 0.9×103mstrain. Although this difference should be expected taking into account that the connector is now free to deform (at least in the immediate vicinity of its central portion due to the presence of the “Relieving Space”), it is the very first time that this difference is experimentally quantified. Moreover, it is concluded from Fig. 14 that the connector’s web placed on the side of the fixed marble block is under tension until about 15% of the fracture force (~5.0 kN). At that load level an abrupt unloading is observed and the specific portion of the connector remains almost strain free up to about 50% of the fracture force (~14.0 kN). From this load level on the specific strain gauge indicates very slight compression of the specific portion of the connector’s web which is continued with slight disturbances up to the fracture of the specimen. Again the difference between the RS and the CF specimens is remarkable. The respective strain gauge for the CF specimen recorded continuously increasing compression of the specific portion of the connector until the final fracture of the specimen (Fig. 10). The strain gauge located at the central section of the connector provided data only up to about 50% of the fracture load indicating that the central area of the connector’s web is initially under increasing tensile strain (up to about 15% of the fracture force or about (~5.0 kN). Then the stain starts decreasing constantly and the central section of the connector becomes under compression straining mode which increases almost linearly up to about 50% of the fracture force (~14.0 kN), a load level at which the strain gauge ceased recording (obviously due to interruption of the electric circuit). Similar conclusions were drawn by an auxiliary electrical strain gauge glued at the central section of the connector (red line in Fig. 14), which unfortunately ceased recording at about 15% of the fracture load. The strain gauge glued at the portion of the connector placed in the groove of the movable block was destroyed during the preparation of the specimen.
Electric- versus acoustic-activity during the loading procedure
The weak electric currents produced during the whole loading procedure were recorded by the extremely sensitive electrometers of the experimental set-up. Their time evolution is plotted in Fig. 15 for both the CF and RS types of specimens, in juxtaposition to the respective variation of the load induced.
As it can be seen from Fig. 15(a), in which the PSC evolution for the CF type of specimen is plotted, the electric current produced is almost negligible until about a time instant of about 300 s where a first peak is observed and the electric activity starts being amplified (with some time fluctuations) until a time instant equal to about 450 s which corresponds to the first slope change of the load-displacement curve. At this time instant a second strong peak is recorded, which according to literature corresponds to increased degree of internal damage, mainly in the form of micro-cracking [
21,
24–
26]. It is interesting to be noted, that this peak precedes well the appearance of the slope change of the load-displacement curve. Then the electric activity returns to its previous level and is almost constant up to a time instant equal to about 700 s, which corresponds to the second slope change of the load-displacement plot (again well in advance). At the specific time instant the PSC exhibits a third, extremely strong, peak indicating again serious internal damage in the form of micro-cracking. The electric activity is again restored to much lower levels, however, with increasing tendency. It is thus concluded that the PSC follows closely even the slightest changes of the load-displacement curve locating clearly the time instants (or equivalently load-levels) at which internal damage mechanisms are activated or their action is strongly amplified. Moreover the respective electric signals appear before the respective changes of the load-displacement plots.
Finally the electric activity starts increasing rapidly a little before the macroscopic crack propagation providing clear warning indications of upcoming catastrophic failure. According to literature this abrupt increase of the PSC-values corresponds to the initiation of the propagation of the macroscopic cracks which eventually lead to fracture.
For the RS type of specimen two electric sensors (instead of one) were used attached on the front and rear surfaces of the marble blocks, taking into consideration the increased degrees of freedom of the specimen due to the presence of the “Relieving Space.” Their recordings during the whole loading procedure are plotted in Fig. 15(b), again in juxtaposition to the respective time evolution of the load induced. It is observed from this figure that the PSC follows again the variation of the load according to a quite satisfactory manner. The recordings of the two sensors are quite similar to each other up to a time instant equal to about 2700 s corresponding to a load level of about 15.0 kN or equivalently 50% of the fracture load. It is quite remarkable that the specific time instant corresponds to the first load drop (point C in Fig. 15(b)). Moreover, both electric sensors exhibit increase of their recordings slightly before the load drop. From this time instant on the sensor attached at the rear surface of the specimen starts recording systematically higher PSC values indicating that damage mechanisms are more active at this area of the specimen. The diversification between the data of the two electric sensors starts slightly before the final slope change of the load-time plot (see the intermediate ellipse in Fig. 15(b)). The PSC recorded from this sensor exhibits again an abrupt increase during the second load drop (at about 97% of the maximum force) indicating again that the system entered to its critical stage and catastrophic failure is impending.
The fact that the two electric sensors provided different recordings after a specific load level indicates the need to carefully consider the points at which the sensors are attached, especially in case of specimens made of inhomogeneous materials (like marble) and also in case of complicated geometry and combined loading schemes. Clearly the specific issue needs further study for additional geometries and different degrees of material inhomogeneity.
The acoustic activity recorded is plotted for both types of specimens in Fig. 16, in which the normalized cumulative number of acoustic events is plotted versus time, in juxtaposition to the respective load-time plot. Taking into account the size and the complicated geometry of the specimens, it was decided to split the volume into sub-volumes given that the acoustic activity at the central part of the specimens is extremely intensive (compared to the respective activity at the remaining portions of the specimens) and therefore plotting the data for the whole volume as a single unity could perhaps shadow crucial details of the damage processes. The five sub-volumes were: A central one, corresponding to the portions of both blocks at the immediate vicinity of their interfacial section at the mid-point of the web of the connector and four additional ones corresponding to the upper and lower part of each marble block, as it is seen in the photo embedded in Fig. 16. The color code of the embedded photo corresponds to the color of the curves of each sub-volume. Normalization was achieved by assigning each event to one of the five sub-volumes, according to its coordinates (which are given by the software). Then the cumulative number of the acoustic events was calculated for each sub-volume versus time. Finally, this number (at any time instant) was divided by the respective maximum one, i.e., by the total number of events assigned to the specific sub-volume until fracture.
For the CF type of specimen the acoustic activity (Fig. 16(a)) for all five volumes is almost negligible up to about half of the maximum load attained for all five sub-volumes including the central one. From this point on, which corresponds clearly to the first slope change of the load-displacement curve, the number of acoustic events recorded starts increasing according to more or less the same rate for all five sub-volumes. The main difference is that the slope of the two curves corresponding to the two sub-volumes of the moving block is steadily increasing while that of the plots of the remaining other sub-volumes appears rather constant. Especially during the very last loading steps the acoustic activity in the two sub-volumes of the moving marble block (the one that eventually was fractured) is amplified according to an almost explosive manner and the respective plots become almost vertical.
The respective activity for the RS type of specimen is shown in Fig. 16(b). The same division of the volume of the specimen into sub-volumes and the same color code were adopted in order for a direct comparison between the two specimen types to be possible. The main difference is that now the acoustic activity starts from significantly lower load levels. All five plots (corresponding to each sub-volume) follow, according to a quite satisfactory manner, the time evolution of the load imposed. What is to be emphasized is that now the slope of the plot corresponding to the lower sub-volume of the moving block (where fracture eventually happened) is continuously increasing from relatively low load levels while the slope of the other four plots is either constant or gradually decreasing. This increase for the slope change of the plot of the critical sub-volume is perhaps an interesting indicator of upcoming failure which is clearly detected well in advance of the fatal crack propagation.
The spatial distribution of the acoustic events for both the CF- and the RS-specimens is plotted in Fig. 17. The same color-code as that in Fig. 16 is adopted to distinguish between the acoustic events recorded in each sub-volume. The duration of the tests was split into two time intervals: The first one takes into account the events recorded from the initiation of the loading procedure up to a load level equal to about 17 kN, which corresponds to a slope change of the load-displacement plot of the CF-type of specimens and to a slope change and the first load drop of the load-displacement curve of the RS-type of specimens (Figs. 17(a1) and 17(b1)). The second time interval takes into account the acoustic events recorded from the load level of 17 kN to the end of the loading procedure (i.e., to the fracture of the specimens) (Figs. 17(a2) and 17(b2)). Finally, the spatial distribution of the total number of acoustic events is, also, plotted (Figs. 17(a3) and 17(b3)).
An alternative way for taking advantage of the data concerning the acoustic activity is based on the relation between the average frequency (AF) of the signals and the respective Rise Time (RT) or the respective Rise Time per Amplitude (RA). More specifically, it is considered that the relation between these parameters provides valuable information concerning the nature of the source of acoustic signals permitting classification of the cracks formed during loading to Mode-I and/or Mode-II [
30,
31]. According to this approach, acoustic signals of high AF and low RT or RA are attributed to “tensile” (mode-I) cracking while on the contrary AE signals of low AF and high RT or RA are attributed to other crack modes (mode-II crack or mixed-mode cracks) or to shear phenomena. Following this approach, an attempt is now described to classify the micro-cracks detected during the present experimental protocol. In this direction, the AF of the acoustic signals recorded during the whole duration of the tests by two sensors attached on the “movable” epistyle (the one finally fractured) is plotted versus the respective RA parameter in Fig. 18. One of the two sensors is attached close to the flange of the groove (i.e., close to the area at which macroscopic fracture propagation started) while the second one is attached relatively far away from this critical region (see the sketch of Fig. 18(c)). It is evident from Figs. 18(a) and 18(b) that the sensor far from the critical region of the “movable” epistyle records signals due to both tensile and non-tensile micro-cracking while the respective sensor close to the critical region records significantly higher number of signals due to tensile micro-cracking for both the CF- and the RS-types of specimens.
Discussion and conclusions
The technique adopted nowadays for restoring damaged “connections” of structural elements of the Acropolis monuments was experimentally assessed assuming that the “connections” are subjected to pure shear loading. Following a long series of preliminary attempts a proper geometry of the specimens was designed, which, in combination to a carefully improvised system for gripping the specimens and applying the load, permitted implementation of almost pure shear experiments. Indeed the data gathered for the full-field displacement field by the 3D-DIC system and the clip-gauges verified that parasitic bending and torsional moments (which inevitably tend to appear due to inherent asymmetries of the specimens) were minimized for both types of specimens.
The comparative assessment of the mechanical response of the two types of specimens was unexpectedly surprising and the role of the “Relieving Space” was proven of catalytic nature. For this conclusion to become evident the load-time curves for the two specimens are plotted in juxtaposition to each other in Fig. 19. In this figure the displacement was measured either directly from the system of the loading frame or taking advantage of the data provided by the DIC system. It is seen from this figure that while the overall strength of the specimens is not influenced at all by the existence of the “Relieving Space” (the fracture force in both cases was almost the same, i.e., around 27.5 kN) the respective “overall stiffness” of the RS specimen (as it is expressed by the slope of the load-displacement curve) is dramatically reduced: The displacement of the moving marble block exceeds 12 mm (if measured by the frame’s system) or it approaches 10 mm (if measured by the DIC system). In both cases it is about ten times higher compared to the respective value for the CF type of specimen. Given that the final load attained is the same for both specimens it is concluded that the CF specimen is ten times “stiffer” compared to the RS specimen. Taking into account that the role of properly designated “connection” is, among others, to protect the marble volumes by permitting deformation of the metallic connecting element it is evident that the presence of “Relieving Space” is “sine qua non” for the proper implementation of the restoration of damaged “connections” of the Acropolis monuments.
Another conclusion drawn from Fig. 19 is the crucial role of the system used to quantify the displacement of the specimens. Although it is quite familiar for people working experimentally that the “grip-to-grip” data provided by systems incorporated in loading frames are not reliable it is here quantitatively indicated that the “error” is by no means acceptable even as a rough approximation of the actual displacement of the specimen. Especially for the “stiff” CF specimen the actual displacement measured by the DIC is about four times smaller compared to the value measured by the frame resulting to errors exceeding even 400% in case absolute values of the displacement are required.
The catalytic role of the “Relieving Space” was, also, revealed by the axial straining of the web of the metallic element of the “connections.” The quantitative differences between the strains of the connectors for the CF and RS types of specimens were huge, verifying that the connector in the design with “Relieving Space” is indeed free to deform, or in other words to absorb strain energy protecting the surrounding marble in case of excessive loading.
Besides assessing the efficiency of the “Relieving Space” it was among the targets of the present study to quantify the potentiality of novel sensing techniques to provide data from the interior of the specimens concerning the nature and the spatiotemporal evolution of the damage mechanisms activated and, also, their potentiality to be used as structural Health Monitoring tools. Both techniques employed (i.e., the Acoustic Emissions and the Pressure Stimulated Currents) were found to provide data following, according to a very satisfactory manner, the mechanical response of the specimens and moreover both of them provided clear pre-failure indicators which, in some cases, were well in advance of the respective phenomena observed at the external surface of the specimens.
It is also worth noticing that the data of the two techniques are in excellent qualitative mutual agreement. To further support the specific conclusion, the time evolution of the cumulative energy of the acoustic signals and of the Pressure Stimulated Currents is plotted in Fig. 20 in juxtaposition to the time evolution of the load level. It is observed that for both specimen types the time evolution of the cumulative energy is qualitative the same for the acoustic signals and the PSC. Especially for the RS type of specimen the similarity is quite striking: The plots exhibit two clearly distinguishable portions, i.e. one for which the energy increases almost linearly following the initial linear portion of the load-time plot and one with considerably reduced slope for the remaining duration of the test. The specific similarity between the energies of the acoustic events and the PSC is also revealed and quantitative described in recent studies with completely different experimental protocols [
32]. The same conclusions about the qualitative agreement of the AE and PSC data can be drawn from Fig. 21 in which the PSC is plotted versus time in juxtaposition to the number of hits per second recorded by the two sensors attached on the “movable” epistyle (the one finally fractured) in the positions described in Fig. 18(c), for both types of specimens. It is observed that the peaks of the PSC plots are accompanied by strongly increased acoustic activity (Fig. 21(a)), while the high gradient of the PSC-time plots corresponds to amplified acoustic activity which is reduced as the slope of the PSC-time plot decreases (Fig. 21(b)).
Before concluding it is to be mentioned that, in spite of the small number of experiments, the conclusions drawn from the present protocol may be proven of utmost importance for scientists working in situ for the restoration of stone monuments, since it is the first time that the role of “Relieving Space” was assessed experimentally and, also, the two sensing techniques (AE and PSC) were considered in juxtaposition concerning their efficiency in experiments with specimens of complex geometry under an almost pure shear loading scheme. As a next step, in the direction of optimum exploitation, the data gathered from the protocol here described, will be used to validate and calibrate a numerical model which will permit parametric study of the role of the (quite a few) factors that influence the mechanical response of mutually interconnected marble structural members under pure shear loading mode.
Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature
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