Marble Samples Research Articles

Statistical Volume Elements for the Characterization of Angle-Dependent Fracture Strengths in Anisotropic Microcracked Materials

Abstract Statistical volume elements (SVEs) are used to homogenize fracture strength of rock, based on the microcrack statistics of a real-world Yuen-Long marble sample. The small size of SVEs enables maintaining inhomogeneities in fracture properties with lower computational cost compared to methods that explicitly model microcracks at macroscale. Maintaining inhomogeneity is important to capture realistic fracture patterns in rock as a quasi-brittle material. Uniaxial tensile, uniaxial compressive, and shear strengths are derived for arbitrary angle for loading and orientation of a single crack by using the linear elastic fracture mechanics (LEFM) method and incorporating frictional effects. Mesoscopic fracture strength fields are generated for different strengths and angle of loading by traversing the spatial domain with circular SVEs. Increasing the SVE size smoothens the spatial inhomogeneity and angular anisotropy of homogenized strengths. Spatial and angular covariance functions of the random fields are obtained to demonstrate how fracture strength varies in space and by changing the angle of loading. Two isotropic and anisotropic rock domains are studied and shown to have very different single- and two-point statistics. Macroscopic fracture simulations by an asynchronous spacetime discontinuous Galerkin (aSDG) method demonstrate that most macroscopic cracks for the anisotropic domain are aligned with the weakest strength planes.

Provenance of White Marbles from the Roman City of Tauriana (Palmi, Reggio Calabria, Italy)

The work shows the results of an archaeometric study performed on fourteen white marble samples from the Roman city of Tauriana (Palmi, Reggio Calabria, Italy), belonging to different architectural elements of the Municipal Museum Complex and artifacts reused in the modern town. Samples were studied by optical microscopy (OM), x-ray powder diffraction (XRPD), and isotope ratio mass spectrometry (IRMS) of 13C and 18O with the aim to identify their provenance. The comparison between the collected data and the historical ones, concerning the ancient quarries of white marble of the Mediterranean area, allowed us to prove that most of the marbles used in the city of Tauriana were from the Apuan Alps Basin (Carrara) and, in few cases, from Minor Asia (Proconnesos, Aphrodisias, Docimium) and Greek (Thasos and Pentelic) quarries.

White and some colored marbles as alternative radiation shielding materials for applications

ABSTRACT In this paper, the radiation shielding parameters such as linear attenuation coefficients (LAC, µ), mass attenuation coefficients (MAC, µ/ρ), effective atomic numbers (Zeff), effective electron densities (Neff), half value of layers (HVL), mean free paths (MFP) and buildup factors (exposure (EBF) and energy absorption (EABF)) were investigated for cream (M1), pink (M2), white (M3), maroon (M4) and green (M5) marbles. Attenuation coefficients were measured in the energy region 31.18–661.66 keV photon energies. The values of Zeff and Neff were then calculated using these coefficients with logarithmic interpolation method, and HVLs and MFPs were calculated using the values of LAC of marble samples at the same photon energies. The experimental results were compared with the theoretical values obtained from WinXCom program, and good agreements were observed between the experimental and theoretical results. HVLs and MFPs of all marble samples were compared with those of some concretes, glasses and commercial radiation shielding glasses (SCHOTT Co.). The studied marbles were better radiation shielding materials than standard shielding concretes due to lower HVL and MFP values lower than the ordinary concrete. Finally, EBFs and EABFs of the marbles were calculated in the energy region 0.015–1 MeV up to penetration depths of 40 mfps by Geometric Progression method (G-P), and the results were discussed in terms of photon energies and chemical compositions of the marbles.

Thermoluminescence dating of calcite – Alpha effectiveness and measurement protocols

Alpha irradiation is less efficient in inducing the thermoluminescence (TL) signal compared to beta and gamma irradiation. Although TL dating has been applied to calcite from various geological contexts, studies of the alpha effectiveness (a-values) of calcite are relatively scarce, and the reported a-values are focused on the 280 °C TL peak of speleothem calcite. In this study, three single-aliquot regenerative-dose (SAR) protocols were applied to measure the a-values of the 280 °C TL peak, the 350 °C TL peak, and the isothermal thermoluminescence at 240 °C (ITL240) of calcite from travertine, limestone and marble samples. The performances of the three SAR protocols were compared and the ITL240 signal was generally equivalent to the 280 °C TL peak TL. The a-values of the 280 °C TL peak of the samples range from 0.19 to 0.24, with a mean value of 0.20 ± 0.01, which are within the range of a-values previously reported for speleothems. The a-values of the ITL240 signal are slightly higher, and the mean value is 0.23 ± 0.01. However, the 350 °C TL peak has a lower mean a-value of 0.15 ± 0.01. The dose response curves for the 280 °C TL peak, 350 °C TL peak and ITL240 signal of the samples have characteristic saturation doses (D0) of 3000–5000 Gy, showing great potential for dating samples millions of years old.

Full-field strain evolution and characteristic stress levels of rocks containing a single pre-existing flaw under uniaxial compression

In this study, full-field strain evolution and characteristic stress levels of marble samples containing a single pre-existing flaw were comprehensively studied. The full-field strain was performed by digital image correlation (DIC) method, and the variations of characteristic stress levels with respect to inclination angle were discussed. To compare the experimental results, discrete element method was adopted, and the full-field stress evolution was reproduced to reappraise the localization zones. The results indicate that the presence of pre-existing flaws induces strain localization and degradation of mechanical properties for pre-cracked samples. When the strain localization firstly appeared surrounding pre-existing flaws, the axial stress levels at this moment increase with regard to inclination angle, leading to the increase of peak strength, crack initiation stress, crack damage stress, and normalized crack initiation stress. The normalized crack damage stress obtained by experiments shows flaw independency, and the results were verified by simulation results. Based on the full-field stress evolution, the tensile stress in x direction concentrates around pre-existing flaw and its location moves towards flaw tips with the increase of inclination angle. The compressive stress in y direction around pre-existing flaw is lower than other zones, revealing the upper and bottom surfaces of pre-existing flaw deform to each other. When the numerical models are subjected to same axial loading, the full-field stress around pre-existing flaw decrease as the inclination angle increases, which confirmed the results of full-field strain evolution and elucidated the pre-existing flaw with large inclination angle has less effect on degrading the mechanical properties.

Physical-Chemical Characteristics of South Aceh Marble and Its Suitability for Tiles Application


 
 
 
 Marble is a metamorphic rock that is widely distributed in the Earth�s continental layer. Regarding its antiquity and aesthetic appeal, it has been widely used as a construction material such as flooring tiles in buildings and monument. Physical and chemical properties of natural stones play an important role on deciding their application area as a building stone. This study reports the physicochemical analysis of marble stones from the Gunung Kerambil (GK), Alur Kering (AK) and Meukek (M) area in South Aceh District. Density, water absorption and chemical analyses of the marble samples were determined. Physical properties of samples were determined through laboratory measurements. Chemical characterizations were made using X-ray Fluorescence (XRF) method. Based on,water absorption test results, the marbles from South Aceh are applicable for tile application.
 
 
 

Radiochemical Assessment of Uranium in Locally Used Marbles

A sensitive method is used for the extraction and determination of soluble uranium in locally used marble has been developed. Isobutyl Methyl Ketone (IBMK) was used as extractant and 0.02 % (w/v) Arsenazo (III) as a chromogenic reagent. The present study assesses the gross radioactivity and extractable uranium in marble samples. A Multichannel Analyzer (MCA) coupled with NaI (Tl) crystal detector was used for the measurement of gross radioactivity whereas spectrophotometer was used to estimate the uranium contained in sample with the help of Arsenazo (III). The extraction involved the adjustment of pH at 0.9. The efficient extraction was achieved by the addition of at least 10 g of Al (NO3)3. This method involved the reduction of UO2 (+2) to U (IV) by using granulated Zinc in concentrated hydrochloric acid. The physical measurements showed the presence of gross radioactivity in the range 266.19 Bq/kg to 644.268 Bq/Kg while the chemical analysis showed the uranium concentration in the range of 0.02ppm to 0.06 ppm.

On anisotropic fracture and energy evolution of marble subjected to triaxial fatigue cyclic-confining pressure unloading conditions

To exam the anisotropic deformation and energy evolution characteristics of interbedded marble, cylindrical marble samples cored along angles of 0°, 30°, 60°, and 90° with respect to interbeds were subjected to a triaxial compression experiencing disturbance of the fatigue cyclic-confining pressure unloading (FC-CPU) condition. The triaxial stress disturbance process is divided into three stages: a primary static loading stage, a secondary fatigue cyclic loading stage with the same stress amplitude of 120 MPa, and a confining pressure unloading stage. The deformation, crack pattern and energy conversion were studied using the GCTS RTR 2000 rock mechanical system, post-test X-ray computed tomography (CT) scanning technique, and energy mechanism analysis. Results showthat the interbed orientation has an obvious effect on the deformation and crack pattern of marble. Four kinds of crack patterns are revealed from the CT images, and the crack morphology is the simplest for a sample with a 30° orientation. The interbed structure affects the damage accumulation at the fatigue cyclic stage that controls the final failure behavior. The dissipated energy used to drive the crack propagation is relatively large for marble samples undergoing the stress disturbance test compared to those under conventional triaxial tests. The energy dissipation result is in good agreement with the crack pattern, and it is found that the formation of a curved crack consumes much more energy than straight cracks. Through a series of triaxial compression tests under stress disturbance paths, the mechanism of the effect of interbed orientation on fracture behavior and energy evolution of marble are documented.

Archaeometric approach to identifying the provenance of white marbles from the shipwreck of Cala Cicala (Crotone, Calabria, Italy)

This paper presents the results of an archaeometric study performed on white marbles from the shipwreck of Cala Cicala (Crotone, Calabria, Italy). The stone materials, especially the white marbles, are an excellent tool for reconstructing the trade routes of the past and studying the relationships between ancient populations. The purposes of this study were to establish the provenance of the white marbles of the shipwreck of Cala Cicala (Crotone, Calabria, Southern Italy) and to use analysis of their composition to acquire more knowledge about trade routes in the Roman imperial age. The 35 samples of white marble were studied by X-ray diffraction (XRPD), optical microscopy (OM), and isotopic analysis (δ13C and δ18O). All of the archaeometric data collected indicate that the marble blocks in the cargos are from the Greek island of Thasos, in the northern Aegean Sea.

Measurement of Natural Radioactivity in Some Marble Samples by using (HPGe) Detector

Measurement of Natural Radioactivity in Some Marble Samples by using (HPGe) Detector

Anisotropic fatigue behaviour of interbeded marble subjected to uniaxial cyclic compressive loads

AbstractThe work aims to experimentally investigate the anisotropic fatigue characteristics of marble with different bedding orientations using uniaxial fatigue experiments and posttest computed tomography (CT) scanning. The impacts of interbed orientation on the strength, deformation, fatigue life, and stimulated fracture pattern were systematically analysed. Results show that the axial, lateral, and volumetric strain curves present a three‐stage deformation and are influenced by the interbed orientation. The volumetric strain is maximum and minimum for a marble sample with 30 and 90° orientation, respectively, which is closely related to the failure mode. The crack pattern in the CT images is related to the interbed orientation; the crack density and scale are the largest for a 90° orientation sample and are the smallest for a 30° orientation sample. Good correlation has been established between the fatigue lifetime and the interbed orientation. It is suggested that anisotropic cyclic behaviours of marble is structurally dependent.

Comparison of Post-Failure Strength of Micro-cracked Marble with Hoek-Brown Failure Criterion

Failure criteria of rock mass is the most important base for designing of surface and underground structures. However, behavior of jointed rock mass and its failure criteria are the controversial subjects of rock mechanics. Main reasons for this discussion are problems during or after the geotechnical application. However, some of the experimental and theoretical approaches are often preferred as they are practical, compatible with engineering considerations, and assist in decision-making process. On the other hand, the differentiation in the scale of the geosystem, which varies depending on the scale of geotechnical application, building process, and time, means that the failure conditions will also change. It is clear that the Mohr-Coulomb failure criterion, which is widely used in practice, cannot exactly represent discontinuous geo-environments (fractured rock) consisting of joint systems. Since the rock generally has a discontinuous character, it has been researched since the 1970s, and the Hoek-Brown failure criterion, put forth in the 1980s and modified many times until today, is widely accepted in application. Nevertheless, it is known that the empirical parameters used in this failure criteria proposed for different types of rocks are also open to discussion. In this paper, the results of the mechanical tests conducted on the previously-fissured model material, which is physically similar to rock mass are discussed. Marble samples whose grain boundaries were disturbed by cyclic thermal treatment were used as the model material. Post-failure curves of model material obtained from continuous failure state triaxial tests were compared with Hoek-Brown Failure Criteria. In conclusion, it was shown that the failure envelopes representing intergranular failure in the post-failure phase were similar and comparable to the Hoek-Brown Failure Criterion. However, it is found out that the post-failure strength in low confining stress may be lower than that of estimation by the Hoek-Brown criterion. Experimental studies have also shown that intergranular failure will develop among structural weaknesses in rock masses, and therefore the strength parameters commonly used in practice will depend on the size of geo-application.

Numerical Analysis of Fracture Behaviour on Marble Samples Containing Two Flaws

Uniaxial compression tests were conducted on marble specimens containing two flaws. There are coplanar flaws and noncoplanar flaws. The inclination angle and spacing of flaws were considered of the coplanar flaws model, and the step angle and spacing of flaws were considered of the noncoplanar flaws model. Strength failure and crack coalescence behaviour were analysed in the paper. The crack evolution process containing microcrack initiation, coalescence, and failure is focused on the rock bridge coalescence and the extent of the pre‐existing flaws. There are four forms of rock bridge coalescence: tensile crack coalescence, shear crack coalescence, mixed tensile and shear crack coalescence, and no coalescence. Also, there are four forms of the rock failure mode: tensile failure, shear failure, mixed tensile and shear failure, and split fracture. The outer end of the critical stress values were used to compare with the crack initiation strengths, and the crack initiation strengths were slightly larger than the critical stress. In addition, energy dissipation laws were analysed during the model fracturing process. The crack evolution mechanisms around the pre‐existing flaw in the model were revealed by the distribution of microcrack and energy dissipation.

Provenance analysis of marble ecclesiastical elements from the extra-mural Byzantine Church of Udhruh (South Jordan)

The aim of this research is to assign the provenance of marble samples uncovered from the extra-mural Byzantine Church of Udhruh (Augustopolis), south Jordan. The church is a three-nave basilica that most probably was built in the fifth century CE. In later expansion phases, it was remodeled by the addition of two side chapels and several rooms. The research investigated the physical, mineralogical, and isotopic properties of twenty-four marble samples of different functions using naked eyes, lenses, and multiple analytical techniques including optical microscopy, mass spectrometry, and X-ray diffraction. The results showed that the architectural elements were made of the gray calcitic Proconnesus-1 marble (Marmara, Turkey); while the four fonts or basins were carved out of the beige dolomitic Thasos-3 marble (Thasos Island, Cape Vathy, Greece); and the small squared column of unknown function was carved out of the fine-grained white calcitic Penteli marble (Mount Pentelikon, Attica, Greece). The results indicate that the most popular supply of the ecclesial marble to the south (and north) Jordan during the Byzantine period was the gray Proconnesus-1. The use of white Penteli and Thasos-3 marbles were limited to ritual elements.

Influence of Dolomite and Granite Waste Content on The Properties of Artificial Marble

The main objective of this work is to characterize and investigate the effect of mineral dolomite and granite waste content on the physical and mechanical properties of artificial marble. Five different samples of artificial marble were prepared with different proportions of fillers. In this study, granite waste is used a filler by substitute the dolomite content from 10 wt% to 40 wt%. Test specimens were evaluated for water absorption analysis, flexural, compression and Barcol hardness properties. It is found that the optimum 10 wt% of granite waste in the composition has increase the flexural and compression strength and reduces the water absorption rate, while the substitution of granite waste does not change significantly the Barcol hardness properties.

A Modified Cubic Law for Rough‐Walled Marble Fracture by Embedding Peak Density

The property of water flow through a single rock fracture is the base of describing the seepage characteristics of jointed rock mass. Five artificial tensile fractures of coarse‐grained cylinder marble samples were made at about the midpoint of the long axis by using a self‐made splitting mold. The upper and lower surfaces of the tensile fractures were scanned by a 3D laser scanner (OKIO) to obtain their 3D coordinates. Then, the Geomagic Studio Software and rock surface topography scan test software were used to obtain peak density values of each single fracture surface. To study the seepage characteristics of open fracture, 4 rectangular plastic spacers with the size of about 3 mm × 2 mm × 0.2 mm were put into the fracture when water flowed through the single rough fracture tests were conducted under different normal stresses using the self‐developed radial flow system. According to the testing data, the relationships between the seepage characteristics of single rough rock fracture and the peak density of fracture surface were studied. It is discovered that the 3D fracture morphology had great influences on the seepage characteristics of the single rock fracture. A modified cubic law was put forward to present the relationship between the seepage characteristics of a rough rock fracture and peak density of two fracture surfaces. Comparison between the modified cubic law and the experimental data showed a relatively good agreement.

Developing a laboratory facility to assess friction coefficients of standing samples

The numerical representation of the dynamic response of art works is the most reliable instrument to predict their seismic safety. Their adoption, however, require the knowledge of the effective mechanical properties of the artifacts and their restraint conditions. Namely, the amount of friction arising between standing art works and their supports largely affects the quality of their collapse and, therefore, the choice of the model to adopt in the analysis. In this work a facility for assessing the dynamic contact behaviour of marble sample standing on different supports has been investigated. The facility consists of a dynamic test to perform through the bidirectional shaking table at the Disaster Resilience Simulation Laboratory at the Politecnico di Torino. The friction coefficient has been found from the dynamic test by comparing the acceleration registered at the load cell, which is related to the reaction of the sample, and one measured at the shaking table surface. The obtained values of friction coefficient have been related to the velocity of the adopted input. A preliminary test on a single concrete sample has been performed to check the proposed procedure, by considering three different loading conditions: one of them is the acceleration history of a real ground motion, while the other two have a constant amplitude and a constant frequency, respectively.

Calculation of Radiogenic Heat Productions from Marble and Glazed Tiles Used as Covering Building Materials in Turkey

Covering or decorative building materials derived from rock and soil include primordial radionuclides such as 238 U and 232 Th series, and potassium radioisotope ( 40 K) varying from one country to another and from one location to another in the same country. The kinetic energy of radiation emitted from these radionuclides in the covering building materials like other building materials are sources of radiogenic heat. Marble tiles are commonly used as wall and floor covering, facing materials for buildings, kitchen counter- top, vanity tops and inner and outer decorative materials because of their appearance, attractive colours, polished surface and durability against external conditions and high resistance to wear. In this study, radiogenic heat productions of marble and glazed tiles samples are calculated based on the elemental concentrations of uranium (in terms of mg/kg), thorium (in terms of mg/kg) and potassium (in terms of %) in the samples collected from various provinces in Turkey. The radiogenic heat productions from the marble tile samples varied from 0.05 to 2.17 µW/m 3 with an average of 0.26 µW/m 3 . The average the radiogenic heat production of the marble tile samples is approximately four times lower than the average continental crust of 0.9 µW/m 3 .

Crystallographic and Seismic Anisotropies of Calcite at Different Depths: A Study Using Quantitative Texture Analysis by Neutron Diffraction

Eight samples of limestones and marbles were studied by neutron diffraction to collect quantitative texture (i.e., crystallographic preferred orientations or CPO) of calcite deforming at different depths in the crust. We studied the different Texture patterns developed in shear zones at different depth and their influence on seismic anisotropies. Samples were collected in the French and Italian Alps, Apennines, and Paleozoic Sardinian basement. They are characterized by isotropic to highly anisotropic (e.g., mylonite shear zone) fabrics. Mylonite limestones occur as shear zone horizons within the Cenozoic Southern Domain in Alpine thrust-and-fold belts (Italy), the Briançonnais domain of the Western Alps (Italy-France border), the Sardinian Paleozoic back-thrusts, or in the Austroalpine intermediate units. The analyzed marbles were collected in the Carrara Marble, in the Austroalpine Units in the Central (Mortirolo) and Western Alps (Valpelline). The temperature and depth of development of fabrics vary from <100 ∘ C, to 800 ∘ C and depth from <10 km to about 30 km, corresponding from upper to lower crust conditions. Quantitative Texture Analysis shows different types of patterns for calcite: random to strongly textured. Textured types may be further separated in orthorhombic and monoclinic (Types A and B), based on the angle defined with the mesoscopic fabrics. Seismic anisotropies were calculated by homogenizing the single-crystal elastic tensor, using the Orientation Distribution Function calculated by Quantitative Texture Analysis. The resulting P- and S-wave anisotropies show a wide variability due to the textural types, temperature and pressure conditions, and dip of the shear planes.

Statistical volume element averaging scheme for fracture of quasi-brittle materials

To capture the randomness and inhomogeneity of rock at microscale, a statistical volume element (SVE) averaging approach is proposed. The microcrack statistics of a real-world Yuen-Long marble sample is used to realize 2D microcracked domains. The size effect, i.e. the decrease of the mean and variation of homogenized strength field by increasing SVE size, is analyzed. Increasing the crack density is shown to have a similar effect. While smaller SVEs maintain a greater level of inhomogeneity and are preferred for fracture analysis, it is shown that low density of microcracks pose a lower limit on the SVE size. Beside the actual power-law distribution of microcrack length, by varying the Weibull model shape parameter m other domains are created with different microcrack distribution shapes. Macroscopic fracture simulations, by the asynchronous Spacetime Discontinuous Galerkin (aSDG) method, study the effect of m for a uniaxial tensile problem. By increasing m from 0.5 to 4, the length distribution of microcracks become more uniform; this corresponds to a more uniform and stronger mesoscopic strength field, which results to about 3 and 6 times increase to macroscopic tensile strength and toughness, respectively. However, the more uniform length distribution of microcracks is shown to reduce rock brittleness.