English Stone Forum, Folkestone, pp 6678, Allison RJ (1987) Non-destructive determination of Youngs modulus and its relationship with compressive strength, porosity and density. ) (20), Do not sell or share my personal information. J Am Ceram Soc 5:4856, Ross KD, Butlin RN (1989) Durability tests for building stone, Building Research Establishment report 141. a fluid). The spread of the data is shown in Fig. The solid density may also provide a useful test of data quality in measurements of porosity using other methods, such as helium pycnometry and mercury intrusion porosimetry. The reflected waves are approximated by the waves reflected at the first air-porous interface. 3). WebArchimedes Principle itself isnt directly about volume, its about buoyancy. It is a rather neat result that three such weight measurements can yield so much information about the solid material lattice density, the average density of the sample material, and the percentage of the porosity volume. For example, in the case of incomplete saturation in a specimen with a solid density of 2500kg/m3 and porosity 0.2, a 1% relative error in the saturated weight \(w_{\mathrm {sat}}\) leads to a 11% relative error in the porosity. Careful experimental technique is required to minimize such amplification in errors. Figure 1. From our analysis, we suggest that it is valuable to apply two procedures to check porositydensity data obtained by the Archimedes method. Standard Test for Smoke Point for Kerosene and Aviation Turbine fuel, ASTM 13 Exp. Slider with three articles shown per slide. The magnitudes of the two relative errors are usually similar. The median value is 2705kg/m3, the interquartile range 7kg/m3. The signal-to-noise ratio for the measurement of the dynamic bulk modulus is the main source of uncertainties when using these estimations given that one asymptote is visible in the frequency range of the measurement. They can however be detected by comparing the Archimedes bulk volume with that measured directly from the specimen dimensions. At first, raw materials including titanium WebWe study the effects of fluidparticle and particleparticle interactions in a three-dimensional monodispersed reactor with unstable fluidization. Trans Am Ceram Soc 9:204318, Washburn EW (1921) Porosity: I. In construction materials the porosity is commonly measured by the Archimedes buoyancy method, from which the bulk density of the test specimen is also obtained. Degassing the test sample under reduced pressure. These conclusions are supported here by our analysis of data on calcitic limestones, but the recommendations stand with equal force for all porous construction materials tested by the Archimedes method. Porosity (%) = [1 ( f / s )] 100, (2) in which, f is the apparent density of nanocomposite foams obtained using Archimedes method and s is the theoretical density of the samples. Left Porosity f vs bulk density \(\rho _{\mathrm {b}}\) for 117 calcitic limestones. Matrix Transformations on Paranormed Sequence Spaces Related To De La Valle- 3 capitulo-iii-matriz-asociada-sem-14-t-l-d, Methods to determine pressure drop in an evaporator or a condenser, Navier stokes equation in coordinates binormal, tangent and normal, the Archimedes porosity determination, one measures or is given the following quantities: Correspondence to Limestones are an important group of building materials used throughout the world as dimension stones in masonry construction. Immersing the test piece in water and determining the mass of the soaked test piece. volume48,pages 12651271 (2015)Cite this article. SECTOR 81 DLF ULTIMA "" 8287494393""8287494393 || DLF ULTIMA , THE ULTIMATE L Matrix Transformations on Some Difference Sequence Spaces, Dual Spaces of Generalized Cesaro Sequence Space and Related Matrix Mapping, International Refereed Journal of Engineering and Science (IRJES), One particle to_onepartlce_scattering_sqrd, Hawkinrad a source_notes iii _withtypocorrected_sqrd, Homogeneous Components of a CDH Fuzzy Space. In: Fort R, Alvarez de Buergo M, Gomez-Heras M, Vazquez-Calvo C (eds) Heritage, weathering and conservation. What is surprising about the result reported in[7] is how little variation there is in the measured solid density in a large set of commercial limestones. We note that Mosch and Siegesmund[23] (see alsoMosch[24]) have carried out statistical analyses of the technical properties of large number of building stones, including more than 200 limestones. WebSpecifically, for the sample in Figure 6A, a relative density of 98.9% was measured by image analysis (97.5% by the Archimedes method) with an average defect size of 143 m 2. Tuffeau is the name used to describe certain high-porosity siliceous limestones of northern France. Sci. Simulations were conducted using the immersed boundary method for particle Reynolds numbers of 2070 with an Archimedes number of 23 600. (13) may be used as a check on volume measured by calipers or by fluid displacement. These may be severe in specimens with coarse porosity which lose liquid by drainage. PhD thesis, University of Southampton, Palmer TJ (2005) Limestone petrography and durability in English Jurassic freestones. In other words, the method gives information on surface parameters. = ( Compressive strength of each sample was measured according to JIS H 7902 standard (200809) using a universal testing machine ZWICK (Z250) (ZWICK, The porosity observed at the fracture surface consistently demonstrated higher porosity than that suggested by Archimedes density. The porosity values obtained from both methods were compared against the mechanical results. Although there are numerous petrographic descriptions of materials from different quarries and different geological horizons (see for example Cole[26] and Palmer[27]), quantitative mineralogical analysis is sparse. volume49,pages 39693979 (2016)Cite this article. By adjusting the oilwater volume ratio from 1:1 to 4:1, the porosity of 74(3), 2003, pp. In: Jones ME, Preston RMF (eds) Deformation of sediments and sedimentary rocks. Our analysis of published data on calcitic limestones shows that the solid density is generally close to the ideal crystallographic density of calcite. = () (10) k The change of density caused by the addition of the wetting agent to the water is negligible. In addition this technique requires the skeleton of this material to be inert towards the fluid used for saturation. - 213.32.24.66. They are removed for the desiccator and weighed immediately. Not all published porositydensity data on limestones conform closely to the pattern of Fig. We thank Maurice Rogers for drawing our attention to the data contained in the BRE stone list, and for useful discussions on British sandstones; Tim Yates (BRE) for providing new data on Ancaster limestone and information on test procedures; and Vicky Pugsley and Isobel Griffin for unpublished data. J Geol 62:102107, Article The densities of the samples were measure with the help of Archimedes principle using water as immersion liquid. 2424-2433, This allows the solid density (the composite mineral density) to be estimated and compared with the solid density calculated from the bulk density and porosity. = (, Outlier 2 is Ham Hill Lower Bed limestone. Small deviations can often be traced to variations in mineral composition. Published density/porosity data are not entirely consistent. Palgrave, Basingstoke, Hall C, Hoff WD (2012) Water transport in brick, stone and concrete, 2nd edn. 3) is plotted against \(\rho _{\mathrm {b}}\). N 2 permeation measurement through the membrane was conducted using home-made equipment. ) (18) Determination of porosity By Helium porosimeter, Jessore University of Science & Technology, Petroleum lab experiment 03 - cloud pour point, Introduction to transport phenomena bodh raj, NFC Institute of Engineerng and Fertilliser Research aisalabad Pakistan, South-Eastern Finland University of Applied Sciences, Transport phenomena (Continuity Equation). Here the spread about the ideal calcite line is large, with an interquartile range of 218kg/m3. To obtain \(w_{\mathrm {d}}\), the specimen must be completely dried without thermal alteration of the material composition or structure. Panneton & Gros [PG05] weigh a porous sample before and after removing part of the air contained within the pores by means of an air pump. The value of \(\rho _{\mathrm {s}}\), although much lower than that of calcite, is consistent with the reported XRD mineral composition (wt% calcite 48; quartz 23; opal-CT 13; orthoclase 2; glauconite/smectite clay 14). Learn more about Institutional subscriptions, Purdy RC, Moore JK (1907) Pyro-chemical and physical properties of clays. In most cases, the solid density \(\rho _{\mathrm {s}}\) is not reported, but we have calculated it from the published bulk-density and porosity data. Both the solid density and the real density are the same as the calcite mineral density, so there is no indication of any closed porosity in these calcitic limestones. [FBLD+03] have developed a method to estimate the surface porosity of a material sample from the measurement, at ultrasound frequencies, of the reflection coefficients for two oblique incidences. These f\(\rho _{\mathrm {b}}\) data lie slightly but distinctly below the ideal calcite line. Right Porosity f versus bulk density \(\rho _{\mathrm {b}}\): data of Cole[26] for Swanworth (plus symbol), Perryfield WB (blue circle) and Perryfield BB (times symbol) Portland stones, and of Allison[28] (blue square) for Purbeck stone. Powder Diffr 24:315326, Honeyborne DB (1982) The building limestones of France. The outlier 1 is from the Leitha Zeilerberg quarry (mean of 7 specimens). For a regular, non-porous solid specimen of uniform density, the hydrostatics of the Archimedes weight is simple (for example [22]) but for the rarer case of an irregular specimen of arbitrary shape, Gausss divergence theorem can be used to relate the hydrostatic pressure acting on the immersed surface of the specimen to its volume [23, 24]. WebArchimedes' principle (also spelled Archimedes's principle) states that the upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially, is equal to the weight of the fluid that the body displaces. This causes the bulk volume \(V_{\mathrm {b}}\) to be underestimated, and as a result \(\rho _{\mathrm {b}}\) is overestimated, and f underestimated, while the value of \(\rho _{\mathrm {s}}\) is correct. In order to ensure that all the air trapped in pores has been removed from the test sample, the vessel is isolated from the vacuum pump by closing the valve. Instrum. WebIn construction materials the porosity is commonly measured by the Archimedes buoyancy method, from which the bulk density of the test specimen is also obtained. Vp and V can then be used to calculate the connected \end{aligned}$$, $$\begin{aligned} V_{\mathrm {s}}=(w_{\mathrm {d}}-w_{\mathrm {A}})/\rho _{\mathrm {w}}, \end{aligned}$$, $$\begin{aligned} V_{\mathrm {b}}=(w_{\mathrm {sat}}-w_{\mathrm {A}})/\rho _{\mathrm {w}}, \end{aligned}$$, \(f_{\mathrm {T}}= 1-\rho _{\mathrm {b}}/\rho _{\mathrm {r}}\), \(\rho _{\mathrm {b}}= w_{\mathrm {d}}/V_{\mathrm {b}}\), \(f = 1 - (w_{\mathrm {d}}-w_{\mathrm {A}})/(\rho _{\mathrm {w}} V_{\mathrm {b}})\), \(\rho _{\mathrm {s}} = w_{\mathrm {d}}/V_{\mathrm {s}}\), \(f = 1 - \rho _{\mathrm {b}}/\rho _{\mathrm {s}}\), $$\begin{aligned} \rho _{\mathrm {CM}}= \sum v_{i} \rho _{i}, \end{aligned}$$, \(v_{i} = V_{{\mathrm {s}}i}/V_{\mathrm {s}}\), \(f_{\mathrm {c}} = f_{\mathrm {T}} - f = \rho _{\mathrm {b}}(1/\rho _{\mathrm {s}}-1/\rho _{\mathrm {CM}})\), \(\rho _{\mathrm {s}} = \rho _{\mathrm {b}} \rho _{\mathrm {CM}}/(f_{\mathrm {c}} \rho _{\mathrm {CM}} + \rho _{\mathrm {b}})\), $$\begin{aligned} \rho _{\mathrm {b}} = C(1-f), \end{aligned}$$, \(\rho _{\mathrm {s}}=\rho _{\mathrm {c}}\), \(\rho _{\mathrm {s}}=\rho _{\mathrm {b}}/(1-f)\), \(e_{w_\mathrm {d}} = (w_{\mathrm {d}}^{\prime} - w_{\mathrm {d}})/ w_{\mathrm {d}}\), \(e_{\rho _{\mathrm {b}}} = e_{w_{\mathrm {d}}}\), \(e_{f}= - e_{w_{\mathrm {d}}} (\rho _{\mathrm {s}}/\rho _{\mathrm {w}})(1-f)/f\), \(e_{\rho _{\mathrm {s}}} = [(1-f)e_{\rho _{\mathrm {b}}} + fe_{f}]/[1-f(e_{f}+1)] =[-(\rho _{\mathrm {s}}-\rho _{\mathrm {w}})e_{w_{\mathrm {d}}}]/[\rho _{\mathrm {w}}+\rho _{\mathrm {s}}e_{w_{\mathrm {d}}}]\), \(\rho _{\mathrm {s}} > \rho _{\mathrm {w}}\), \(e_{w_\mathrm {sat}} = (w_{\mathrm {sat}}^{\prime} - w_{\mathrm {sat}})/ w_{\mathrm {sat}}\), \(e_{f}= (1-f)(\rho _{\mathrm {s}}/\rho _{\mathrm {w}})e_{w_{\mathrm {sat}}}/f\), \(e_{\rho _{\mathrm {s}}} =\rho _{\mathrm {s}}e_{w_{\mathrm {sat}}}/(\rho _{\mathrm {w}}-\rho _{\mathrm {s}}e_{w_{\mathrm {sat}}})\), \(\rho _{\mathrm {s}}e_{w_{\mathrm {sat}}}\), \(e_{\rho _{\mathrm {b}}} = -e_{w_{\mathrm {sat}}}/[e_{w_{\mathrm {sat}}}+\rho _{\mathrm {w}}/[(1-f)\rho _{\mathrm {s}}+f\rho _{\mathrm {w}}]]\), \(e_{f}=-(1-f)e_{\rho _{\mathrm {b}}}/f\), https://doi.org/10.1617/s11527-015-0767-3, Relationships Between Petrophysical and Mechanical Properties of Certain Calcarenites Used in Building, High temperature effects on the properties of limestones: post-fire diagnostics and materials durability, Influence of Weathering on Pore Size Distribution of Soft Rocks, Evaluating Size Effects for a Porous, Weak, Homogeneous Limestone, Building geopolymers for CuHe part I: thermal properties of raw materials as precursors for geopolymers, An investigation on sample size in Leeb hardness test and prediction of some index properties of magmatic rocks, An experimental investigation into the salt-weathering susceptibility of building limestones, Features of Determining Ceramic Material Porous Structure Parameters, Salt weathering in granitoids: an overview on the controlling factors, http://creativecommons.org/licenses/by/4.0/. Mater Struct 48:12651271, European Standard EN 1936: 2006 Natural stone test methodsdetermination of real density and apparent density, and of total and open porosity, European Standard EN 7724: 1998 Methods of test for masonry unitspart 4: determination of real and bulk density and of total and open porosity for natural stone masonry units, ASTM C97 (2009) Standard test methods for absorption and bulk specific gravity of dimension stone, Hall C, Hoff WD (2012) Water transport in brick, stone and concrete, 2nd edn. 2023 Springer Nature Switzerland AG. Wiley, New York, Lima FMS (2012) Using surface integrals for checking Archimedes law of buoyancy. This technique was introduced by Leo Beranek in 1942 [Ber42] and was later improved by Champoux, Stinson and Daigle [CSD91]. Left we see that the porositydensity data for the entire set lie close to the ideal calcite line. We are grateful to the following for information and advice: Wim Dubelaar, Rob van Hees, Rudolf Holzer, David Jefferson, Roman Koch, Tim Palmer, Maurice Rogers, and Tiziana Vanorio. indicates the apparent submerged mass. It is unusual however for laboratories using the procedures of EN 1936 to report both open and total porosity. The requirement that the liquid is in hydrostatic equilibrium throughout the pore space is important, but for most materials of interest pressure diffusion in a laboratory size specimen is rapid. In publications providing porosity data, the bulk density is sometimes also reported. If the drying is incomplete, the bulk density is overestimated while the porosity and the solid density are underestimated. Taylor & Francis, London, pp 914, Van Hees RPJ, Nijland TG (2009) Assessment of the state of conservation of a Middle Neolithic flint mine in Maastricht limestone. Is this porosity total or effective? 3, the data plot close to the ideal calcite line, with a small interquartile range. ) (12) Geophysics 76:E105E115, Derluyn H (2012) Salt transport and crystallization in porous limestone: neutron-X-ray imaging and poromechanical modeling. A serious practical problem in implementing the Archimedes method is that reference materials of certified porosity are not available. Even allowing for some variability in the materials tested, it appears that the solid density of Maastricht stone is not known to better than about 3%. The Archimedes density method and the fracture surface method result in different porosity values but appear to be correlated quite closely for this AM material, w is the water permeability of the specimen and G its shear modulus, so that is generally a matter of seconds. hWmo6+aW ; %#$l)lHq qw|yQHJ() . WebAn improved method based on Archimedes' Principle for measuring the porosity of scaffolds, using a density bottle, was developed. A quantitative mineral composition, for example by quantitative Rietveld XRD, is an invaluable item of support information. = Drying the test sample in an oven. Mater Struct 17:391394, Hall C, Hamilton A (2015) Porosity-density relations in stone and brick materials. 2. Soaking of the test samples: The test sample is placed in the glass vessel which is evacuated to a pressure of less than 2500 Pa (Figure 2). Porosity vs. Permeability Is There a Difference? Water as an absorption liquid. The solid line is the ideal calcite line. = ( 3) (6) ) [15] report from XRF analysis that the Portland whitbed stone from Bowers Quarry has a calcite content of 9798wt%, with 12wt% silica, and is almost free of clay and iron minerals. All the additional data come from published research studies in which the materials and test methods are clearly described[7, 1420]. However, the relative errors in the porosity and solid density are more complicated in form. a fluid). We have looked in detail at porositydensity data from the sources that we list in Table2. In (5), ( ) (19) Any closed porosity is included in the solid matrix and contributes to the solid density. Two different flow regimes were identified as a function of the particle However, it is an open question whether this assumption is precisely true. Subbing (10) into (11): 7 has C=2708kg/m3, indistinguishable from the calcite line. The corresponding solid densities (see Table 2) are not consistent with the high calcite mineral composition. 2. Right, where the solid density of each specimen, \(\rho _{\mathrm {s}}=\rho _{\mathrm {b}}/(1-f)\) (Eq. ISO 1183 has essentially the same method. Most inorganic construction materials, including the main building stones, are porous. While Fig. Both the chambers in the porosimeter have a volume of 150 cm3, and the sample has a bulk volume of 41.4 cm3. Provided by the Springer Nature SharedIt content-sharing initiative, Over 10 million scientific documents at your fingertips, Not logged in 2 The porosity of freshly pressed ceramic bodies governs green tile behavior during the process (drying, glazing, and firing) and largely determine the properties of the final product. Figure 3. Determination of the apparent mass of the soaked test sample in air: The test sample is removed from the liquid and immediately wiped with a tissue to remove the droplets and the surface film of the liquid while avoiding drawing liquid from the pores by performing the wiping operation very quickly. Weight of saturated sample submerged in water, W, Accurate in better quality rocks if effective, In poorer quality rocks, difficult to completely, Saturating fluid may react with minerals in, Very accurate for both high-quality (high, Used to test compatibility of injection fluids, Used to estimate probability of formation. The sample is weighed in air after being well soaked in water but dried quickly on the outside surfaces. For tuffeau quarry specimens from Marigny-Brizay, Robert[35] found the Archimedes porosity f=0.460, and the solid density \(\rho _{\mathrm {s}}= 2550\) kg/m3 (mean values, n=15). This value should be checked for consistency with the composite mineral density. For the Spanish stones, the calcite content is known by analysis to be 97wt%. This technique was introduced by Leo Beranek in 1942 [Ber42] and was later improved by Champoux, Fluid saturation For brick and stone materials c = 4104 Accessed 16 Dec 2013, Ross KD, Butlin RN (1989) Durability tests for building stone, Building Research Establishment Report 141, BRE, Watford, UK, Hurst VJ, Storch SP (1981) Regional variation in the cell dimensions of metamorphic quartz. The results show that hydrophilicity and surface energy were improved. PubMedGoogle Scholar. (3) Any loss of water from the surface of the saturated specimen before it is weighed in air means that \(w_{\mathrm {sat}}\) is too low. In Fig. The mass thus determined is the mass of the immersed test piece (m2). 2 shows that a large number of the calcitic limestones used in construction have solid densities close to that of pure calcite, there are of course exceptions. Calculation of the solid material density, the bulk apparent sample density, and the percentage of porosity. [36] on tuffeau specimens of similar composition from Saint-Cyr-en-Bourg. 13, 1942, pp. Course Hero is not sponsored or endorsed by any college or university. However a relative error in the saturated weight \(e_{w_\mathrm {sat}} = (w_{\mathrm {sat}}^{\prime} - w_{\mathrm {sat}})/ w_{\mathrm {sat}}\) produces errors in the calculated porosity and the calculated solid density. Christopher Hall. Umnova et al. 2023 Springer Nature Switzerland AG. Determination of the apparent mass of the immersed test sample: The test sample is suspended in the distilled water and weighed while completely immersed in liquid (Figure 3). This makes it necessary to control tile porosity during shaping. [21] report porosity data on 12 limestones from the Leitha formation in Austria using this method. 2 with a dataset in which the solid density is obtained directly on crushed material, so perhaps reducing the possibility of including any closed porosity in \(\rho _{\mathrm {s}}\). 13. Optical methods have also been developed to estimate the open porosity of porous media. ( The vacuum is maintained at least for 15-20 minutes. Archimedes principle for submerged core: As shown in Fig. Strengths Unmatched volumetric measurement accuracy Excellent reproducibility and reliability Flexible analytical modes for wide array of sample types Zinc barium borotellurite glasses with the composition 10ZnO-30BaO-30B2O3-(30-x)TeO2 -CeF3 have been fabricated by using the melt-quenching technique The points plotted for Leitha stones are the means of measurements on several specimens from each source (89 in total), and for the Spanish stones the means of nine specimens of each type. An alternative method has been proposed by Leclaire and colleagues [LUKM03]. (15) Am. b. Gravimetric (Archimedes) Wsat - Wdryfluid 2. In this study titanium nanocomposite foams with different porosity percentages were produced using TiH2, as foaming agent, by powder metallurgy technique. If the relative error \(e_{w_\mathrm {d}} = (w_{\mathrm {d}}^{\prime} - w_{\mathrm {d}})/ w_{\mathrm {d}}\), where \(w_{\mathrm {d}}^{\prime}\) denotes the erroneous dry weight and \(w_{\mathrm {d}}\) the true value, then it follows directly from Eq. hb```f``e`a`fd@ A+s,2~ hjJ&|n&n~BDn~Z6]7Lc``h`` C#@Li1@,vD? ?b|Bb ku#zn5PH3}MXU4f -X e *?g Outliers (white circle) are: 1 Purbeck, U Jurassic[28], 2 Coombefield WB[30], 3 Swanworth Purbeck[26], 4 Bowers Base Bed[13], 5 Independent WB[13]. The test pieces are then placed in the desiccator until they have cooled to room temperature. = Immersion liquid: Distilled water is used as the immersion liquid. The gamma-ray transmission and Archimedes method are useful methodology to determine the porosity property of material but gamma-ray is advantage methodology Right Solid density \(\rho _{\mathrm {s}}\) versus bulk density \(\rho _{\mathrm {b}}\) for the same 117 limestones. Geological Society, London, Engineering Geology Special Publications no 16, Appendix C, Mosch S, Siegesmund S (2007) Statistisches Verhalten petrophysikalischer und technischer Eigenschaften von Naturwerkstein. Immersing under the creative commons license Attribution 3.0 Unported (CC BY 3.0). = (, Anyone you share the following link with will be able to read this content: Sorry, a shareable link is not currently available for this article. We have indicated qualitatively how the calculated values of the bulk density, solid density and porosity are affected by the various measurement errors. Determination of the mass of the dry test samples: The test samples are kept in an oven at 110C over night to ensure that test samples are completely dry. The significance of the solid density can be overlooked but it is informative both as a material property and as a method of identifying errors in data. Taylor and Francis, London/New York, Robie RA, Bethke PM, Beardsley KM (1967) Selected X-ray crystallographic data, molar volumes, and densities of minerals and related substances. The open porosity of a specimen of stone or brick material is often measured using a gravimetric method based on Archimedes principle. All measurements are made on the dry specimen, and liquid saturation is not needed (although it may be used to obtain the specimen bulk volume \(V_{\mathrm {b}}\)). Of the quantitities \(\rho _{\mathrm {s}}\), \(\rho _{\mathrm {b}}\) and f, any two are independent (knowing two, the third is fixed). 1. It follows from Eq. WebTwo methods are described and are designated as Methods A and B, as follows: Method A: Determination of bulk density, apparent solid density and apparent porosity by liquid displacement (Archimedes' method). First, in all cases, the solid density \(\rho _{\mathrm {s}}\) should be calculated from the experimental data using Eq. For calcitic limestones as a group, the published data show that the porosity and bulk density generally lie close to Eq. The median of \(\rho _{\mathrm {s}}\) is 2709kg/m3, the same as the mineral density of calcite. HERON 48:221229, Cnudde V, Dierick M, Vlassenbroeck J, Masschaele B, Lehmann E, Jacobs P, Van Hoorebeke L (2007) Determination of the impregnation depth of siloxanes and ethylsilicates in porous material by neutron radiography. 7 with the constant C close to the crystallographic density of calcite. 2 Archimedes porosity determination In the Archimedes porosity determination, one measures or is given the following quantities: (14) Barium phosphates are used in a variety of technological applications due to their several exclusive properties such as high thermal expansion coefficient, low viscosity, ultraviolet (UV) transmission, electrical conductivity, high solubility for rare earth ions and non-toxicity [35]. To these 61 limestones, we have now added data from other sources to make a larger porositydensity dataset of 117 calcitic limestones. (14) Episodes 36:221226, Cole DI (1971) Ultrasonic velocity measurements on limestones from the Portland group: correlation with porosity and other lithological factors. However a relative error in the saturated weight \(e_{w_{\mathrm {sat}}}\) produces a relative error in the bulk density \(e_{\rho _{\mathrm {b}}} = -e_{w_{\mathrm {sat}}}/[e_{w_{\mathrm {sat}}}+\rho _{\mathrm {w}}/[(1-f)\rho _{\mathrm {s}}+f\rho _{\mathrm {w}}]]\). a.country's economy generally grows if it can rely on cheap energy resources.b.Low energy costs often result in a rise in inflation.c.High oil prices usually lead to. ( The solid line is the ideal calcite line. 3. (3 Figure 4. The investigated method is based on the assumption that when a Incomplete drying Here there is an error in the measured dry weight \(w_{\mathrm {d}}\). Constr Build Mater 41:868878, Bednarik M, Moshammer B, Heinrich M, Holzer R, Laho M, Rabeder J, Uhlir C, Unterwurzacher M (2014) Engineering geological properties of Leitha Limestone from historical quarries in Burgenland and Styria, Austria. ) (11) 607624, . Here, indicates mass.