Assuming that the open pore-space is equally accessible to helium and to the saturating liquid used in the Archimedes method, the two methods measure the same porosity f[11]. HERON 54:227250, Rescic S, Fratini F, Tiano P (2010) On-site evaluation of the mechanical properties of Maastricht limestone and their relationship with the physical properties. known, we may state: The densities of the samples were measure with the help of Archimedes principle using water as immersion liquid. Abstract This paper discusses a method for measuring the porosities of core or outcrop samples using the attenuation of gamma rays. where \(v_{i} = V_{{\mathrm {s}}i}/V_{\mathrm {s}}\) is the solid volume fraction of the component i, and \(\rho _{i}\) its mineral density. Left we see that the porositydensity data for the entire set lie close to the ideal calcite line. 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. Wiley, New York, Lima FMS (2012) Using surface integrals for checking Archimedes law of buoyancy. PhD thesis, Gttingen, Hughes T, Lott GK, Poultney MJ, Cooper BJ (2013) Portland stone: a nomination for Global Heritage Stone Resource from the United Kingdom. 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. Similar results have been obtained by Becket al. We emphasize how the solid density depends on mineralogy and on closed porosity. If the drying is incomplete, the bulk density is overestimated while the porosity and the solid density are underestimated. The vacuum is maintained at least for 15-20 minutes. Currently, no standard method exists to estimate the open porosity (abusevely shorten to porosity) $\phi$ for acoustical materials. In most building limestones, the main carbonate mineral is calcite, although there is a small subgroup in which it is dolomite. Right shows the data of Cole and of Allison from Table2. Then the valve to the pump is shut and the vessel is opened to ambient air pressure for another 30-40 mins to ensure that water completely penetrates the test sample. Mater Struct 17:391394, Hall C, Hamilton A (2015) Porosity-density relations in stone and brick materials. 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. J Cult Herit 8:331338, Vanorio T, Mavko G (2011) Laboratory measurements of the acoustic and transport properties of carbonate rocks and their link with the amount of microcrystalline matrix. 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. [34], using helium pycnometry, reports solid densities for quarry and building specimens of 2680 and 2770kg/m3. \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. 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]. ISO 18754:2020 Both the chambers in the porosimeter have a volume of 150 cm3, and the sample has a bulk volume of 41.4 cm3. The mineral composition is complex, and tuffeau stones typically contain only about 50wt% calcite. Two different flow regimes were identified as a function of the particle The range of solid density is 25922759 kg/m3, clustered around a median value of 2703kg/m3, with five outliers, as shown in the box plot, Fig. 354 0 obj <>stream The Mettler Toledo XS 105 balance with density apparatus used for density and porosity measurements. Left Porosity f versus bulk density \(\rho _{\mathrm {b}}\) for 12 Leitha limestones[21] plus symbol and three Spanish limestones[20]. In a test in which the specimen is incompletely dried, a +1% relative error in the dry weight leads also to a 11% relative error in the porosity, and to a 2% relative error in the solid density. The composite mineral density is therefore expected to be in the range 27102715kg/m3. (1) When the test specimen is not completely dried \(w_{\mathrm {d}}\) is too high. This method is close to the one used for geomaterials called gas picnometer (which is detailed in various standards) . J Phys D 46:092003, Roels S, Carmeliet J, Hens H, Adan O, Brocken H, Cerny R, Pavlik Z, Hall C, Kumaran K, Pel L, Plagge R (2004) Interlaboratory comparison of hygric properties of porous building materials. The mass thus determined is the mass of the dry samples (m1). Density and Porosity Measurements of Solid Materials ISO 18754:2020 By adjusting the oilwater volume ratio from 1:1 to 4:1, the porosity of with \(C=\rho _{\mathrm {c}}\), the solid density of calcite, 2709kg/m3. There are now hundreds of publications containing porosity data, stretching back to the early method papers of Purdy and Moore[1], and of Washburn and his collaborators[24]. In this paper, we use the term limestone to include also chalks, marbles, and travertines. Simulations were conducted using the immersed boundary method for particle Reynolds numbers of 2070 with an Archimedes number of 23 600. 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. The solid squares mark outliers: 1 Portland Independent Whitbed, 2 Ham Hill Lower Bed, 3 Portland Bowers Base Bed, 4 Maastricht, 5 Green Purbeck Marble, 6 Totternhoe, 7, 8 Monte Acuto. WebArchimedes Principle itself isnt directly about volume, its about buoyancy. The porosity and the bulk density together x the solid density of the specimen, as only two of the three quantities are independent. WebPorosity is a complex measurement which is taken out after taking various samples from the scene. Figure 4. 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. The proportion of porosity could not be reliably quantified by metallography, and thus, porosity was measured by micro-CT and the Archimedes method, with a change in the processing parameters where at higher energy densities the porosity is lower than at lower energy densities as shown in Table 1. Porosity and the mechanism of absorption. Google Scholar, Washburn EW, Footitt FF (1921) Porosity: III. Zinc barium borotellurite glasses with the composition 10ZnO-30BaO-30B2O3-(30-x)TeO2 -CeF3 have been fabricated by using the melt-quenching technique This makes it necessary to control tile porosity during shaping. We aim to show that estimating the solid density from porosity and bulk-density data provides a simple quality check on the measured specimen porosity. The porosity of building stones is usually measured by the long-established Archimedes buoyancy methodsee[5, 6] for practical descriptions of such tests, and[7] for a recent discussion. In: Fort R, Alvarez de Buergo M, Gomez-Heras M, Vazquez-Calvo C (eds) Heritage, weathering and conservation. Not all published porositydensity data on limestones conform closely to the pattern of Fig. This method allows the simultaneous estimation of the high frequency limit of the dynamic tortuosity. In: Smith BJ, Gomez-Heras M, Viles HA, Cassar J (eds) Limestone in the built environment: present-day challenges for the preservation of the past. Cole[26] found at least 98wt% calcite in cores analysed by X-ray diffraction. Allowing for some uncertainty in the individual densities of opal-CT (\(\approx\)2000kg/m3), and clay (\(\approx\)2300kg/m3), we calculate a composite mineral density in the range 2570 30kg/m3, as found. porosity The schematic of the apparatus used to remove air from the sample pores and to soak distilled water into the sample pores is shown. 2 Archimedes' principle - Wikipedia WebPorosity (n in %) is defined as the ratio of accumulated (total) pore volume (VP in cm3) included in a rock specimen to the bulk volume VB of the specimen as follow: = n 100 VP / VB (2) Based on these equations, it is clear that the measurements of bulk volume and pore volume control mea- surement accuracy of density and porosity of rock The sample is weighed in air after being well soaked in water but dried quickly on the outside surfaces. We discuss here how measurement errors affect the calculated bulk density, solid density, and porosity. (1), (3), (5), and (7). Portland building stone is extracted at a number of quarries and mines on the Isle of Portland, Dorset, on the south coast of England. = = (, The solid density also provides a useful quality check when the porosity has been measured by a non-Archimedes method, such as mercury intrusion porosimetry or helium pyknometry. Other minerals which may be found in the composition (usually in small quantities) are quartz, occasionally feldspars, and the high-density iron minerals haematite, goethite and siderite. Google Scholar. Zeitschrift der Deutschen Gesellschaft fr Geowissenschaften 158:821868, Mosch S (2008) Optimierung der Exploration, Materialcharakterisierung von Naturwerkstein. WebArchimedes' principle shows the buoyant force and displacement of fluid. Further: Since \(\rho _{\mathrm {s}} > \rho _{\mathrm {w}}\), a positive relative error in the dry weight leads to a negative (and somewhat larger) relative error in the solid density. The Archimedes method is conceptually simple, but in practice prone to error. Geological Society, London, Engineering Geology Special Publications no 16, Appendix C, Mosch S, Siegesmund S (2007) Statistisches Verhalten petrophysikalischer und technischer Eigenschaften von Naturwerkstein. please solve this question Question 2.7 A core sample is placed inside a porosimeter. Figure 1: Force Balance on Submerged Core Figure6 shows that f\(\rho _{\mathrm {b}}\) data lie close to the ideal calcite line; there is a single marginal outlier, but this is a stone of unusually low porosity. The CMD may be known from previous work on the same or similar materials, or may be calculated from mineralogical data on the specimen, for example by quantitative X-ray diffraction analysis. Strictly, the quantity f is the open porosity, the pore-space accessible to the saturating liquid. Standard Test for Smoke Point for Kerosene and Aviation Turbine fuel, ASTM 13 Exp. The picnometer method is based on the injection of a gas under pressure in the volume enclosure. In a variant of the Archimedes method, used when the specimen is in the form of a regular cylinder or a rectangular block, the bulk volume \(V_{\mathrm {b}}\) is calculated directly from the specimen dimensions. The laboratory experiment was carried out using the direct measurement method which is also known as the gravimetric method and by buoyancy method which follows the Archimedes principle. %%EOF 2 The solid square marks one outlier: Bowers Hard Blue. Two examples of publications on Archimedes' principle applied to acoustical porous materials are listed below. The median solid density is 2705kg/m3, with an interquartile range of 7kg/m3. As shown in Fig. 3 ) is the fluid density. 13, 1942, pp. Right Solid density \(\rho _{\mathrm {s}}\) versus bulk density \(\rho _{\mathrm {b}}\) for the same 117 limestones. ) (7) These f\(\rho _{\mathrm {b}}\) data lie slightly but distinctly below the ideal calcite line. The open porosity of the membranes was determined by the Archimedes method. The porosity appears as a parameter in many technical calculations in building physics. Learn more about Institutional subscriptions, Purdy RC, Moore JK (1907) Pyro-chemical and physical properties of clays. 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. The total porosity \(f_{\mathrm {T}}\) is then calculated from Eq. = (, The determination of bulk density and porosity of monolithic materials using a water intrusion method known as the Archimedes method. Correspondence to Figure4 shows data on 23 British and Irish calcitic limestones from a reference source[22]. Photograph of apparatus used for determination of mass of immersed test piece and mass of soaked test piece. The stones included are: times symbol 61 British and Irish limestones from the BRE Stone List[13]; plus symbol 16 specimens of eight French and English limestones (Ancaster, Chauvigny, Clipsham, Massangis, Monks Park, Portland, and Richemont)[7]; white circle 20 specimens of Portland limestone[15]; white up-pointing triangle 11 specimens of Monte Acuto limestone[17]; diamond Savonnires limestone[18]; white down-pointing triangle Savonnires limestone[14]; white square Maastricht limestone[16]; filled circle four French limestones (Euville, Savonnires, Massangis, Coulmier-le-Sec)[19]; filled square two Spanish limestones (Fraga Campanil, Santa Pudia) [20]. w is the water permeability of the specimen and G its shear modulus, so that is generally a matter of seconds. ) (5) In measuring \(w_{\mathrm {sat}}\) liquid may be lost from the specimen by evaporation, or sometimes by drainage from low-suction cavities and cracks. - 213.202.212.252. (16) %PDF-1.5 % Because of its prominence and accessibility, Portland stone is often used in technical studies of stone behaviour and properties. Covalent Metrology Analytical Labs Published density/porosity data are not entirely consistent. The interquartile range (IQR), a measure of the spread in \(\rho _{\mathrm {s}}\), is 12kg/m3, about 0.4% of the median. Immersing They can however be detected by comparing the Archimedes bulk volume with that measured directly from the specimen dimensions. Degassing the test sample under reduced pressure. Vp and V can then be used to calculate the connected 1, with C=2709kg/m3. https://doi.org/10.1617/s11527-013-0231-1, http://projects.bre.co.uk/ConDiv/stonelist/stonelist.html. In construction materials the porosity is commonly measured by the Archimedes buoyancy method, from which the bulk density of the test specimen is also Stone is taken from three horizons at increasing depths, and designated as roach, whitbed and base bed respectively. English Stone Forum, Folkestone, pp 6678, Allison RJ (1987) Non-destructive determination of Youngs modulus and its relationship with compressive strength, porosity and density. The porosity f is then calculated from the formula \(f = 1 - \rho _{\mathrm {b}}/\rho _{\mathrm {s}}\) (Eq. WebOpen porosity characterization Pressure difference. The relative errors in the porosity and the solid density may sometimes be considerably larger than the relative errors in the measured weights. Eng Geol 176:6678, Smith MR (ed) (1999) Stone: building stone, rock fill and armour stone in construction. If its average density is less than that of the surrounding fluid, it will float. Provided that the bulk density has also been measured, then the solid density can be calculated from Eq. This difference sets an upper limit to the closed porosity \(f_{\mathrm {c}}\), which therefore appears to be negligible in Portland stone. = (, WebAn improved method based on Archimedes' Principle for measuring the porosity of scaffolds, using a density bottle, was developed. Powder Diffr 24:315326, Honeyborne DB (1982) The building limestones of France. Therefore the solid density \(\rho _{\mathrm {s}} = \rho _{\mathrm {b}} \rho _{\mathrm {CM}}/(f_{\mathrm {c}} \rho _{\mathrm {CM}} + \rho _{\mathrm {b}})\). Rates of infectious diseases will decrease. School of Engineering, University of Edinburgh, Edinburgh, EH9 3FB, UK, Department of Civil and Environmental Engineering, University of Strathclyde, Glasgow, G1 1XJ, UK, You can also search for this author in OPEN POROSITY CHARACTERIZATION - IDC-Online In addition this technique requires the skeleton of this material to be inert towards the fluid used for saturation. We have no quantitative mineralogical information on the Zeilerberg stone, but its petrographic description mentions the presence of quartz. ) (11) 5. For calcitic limestones as a group, the published data show that the porosity and bulk density generally lie close to Eq. Limestones are an important group of building materials used throughout the world as dimension stones in masonry construction. The associated relative error in the porosity \(e_{f}=-(1-f)e_{\rho _{\mathrm {b}}}/f\). where \(V_{\mathrm {s}}\), \(V_{\mathrm {b}}\) are the solid and bulk volumes of the specimen. Due to their buoyancy, air bubbles could affect the results. For Archimedes measurements, standard deviations are given in brackets next to the mean From our analysis, we suggest that it is valuable to apply two procedures to check porositydensity data obtained by the Archimedes method. = () (10) Archimedes porosity determination - SlideShare 2. 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). [LUKM03] Leclaire P., Umnova O., Horoshenkov K., Maillet L., Porosity measurement by comparison of air volumes, Rev. 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. 3, and this should be compatible with the known mineral composition. 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. 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. The test sample is then weighed immediately (Figure 4). The reflected waves are approximated by the waves reflected at the first air-porous interface. Portland stone is a high-calcite limestone which has been used in the construction of public buildings in Britain for many centuries[25]. To estimate the porosity of acoustical facings which have a usual thickness of 1 mm or less and can have a porosity lower than 1% a particular method has been developped by Jaouen & Bcot [JB11]. 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. Gotechnique 27:435438, Ingham JP (2005) Predicting the frost resistance of building stone. [FBLD+03] Fellah Z. E., Berger S., Lauriks W., Depollier C., Aristgui C., Chapelon J. Y., Measuring the porosity and the tortuosity of porous materials via reflected waves at oblique incidence, J. Acoust Soc Am. Archimedes porosity determination. WebAn improved method based on Archimedes' Principle for measuring the porosity of scaffolds, using a density bottle, was developed. 7 has C=2708kg/m3, indistinguishable from the calcite line. The balance is a Mettler Toledo XS105. Hall, C., Hamilton, A. Porosities of building limestones: using the solid density to assess data quality. Any closed porosity is included in the solid matrix and contributes to the solid density. ) (13) Ceramic Material Porous Structure Prepared Using WebThe porosity of freshly pressed ceramic bodies conditions green tile behaviour during the process (drying, glazing, and firing) and largely determines the properties of the final product. = Umnova et al. WebWe study the effects of fluidparticle and particleparticle interactions in a three-dimensional monodispersed reactor with unstable fluidization. The sample sections were polished (using the Tegramin-30 automatic polishing machine, Struers Inc., Cleveland, OH, USA), working down to A manometer monitoring the pressure checks that the pressure does not rise due to further air coming out of the test sample. ) (12) Instead of measuring the pressure increase, one has to equal the volume of the chamber containing the porous sample with the volume of a reference chamber by means of syringes. 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. HMSO, London, Fronteau G, Schneider-Thomachot C, Chopin E, Barbin V, Mouze D, Pascal A (2010) Black-crust growth and interaction with underlying limestone microfacies. Methods WebThe bulk volume Vis measured using either vernier callipers and assuming that the sample is perfectly cylindrical,or by Archimedes Method (discussed later), or by fluid displacement using the saturatedsample. ) (2) Thus, \(e_{f}= (1-f)(\rho _{\mathrm {s}}/\rho _{\mathrm {w}})e_{w_{\mathrm {sat}}}/f\). Indeed, The surface porosity of a material sample can differ from the volumic porosity due to the foaming process or due to the cutting of the sample itself. Subbing (6) and (13) into (14): The observed solid density is accounted for by 2.5wt% goethite, and 5wt% quartz. In the event that the \(\rho _{\mathrm {s}}\) and \(\rho _{\mathrm {CM}}\) differ significantly, then errors of type (1) and (2) in the Archimedes tests may be suspected. Since \(\rho _{\mathrm {w}}\) is generally much greater than \(\rho _{\mathrm {s}}e_{w_{\mathrm {sat}}}\), a negative relative error in the saturated weight leads to a negative, and numerically larger, relative error in the solid density. mol), Which of the following is unlikely to occur with a rise in global temperatures? A specimen of solid volume \(V_{\mathrm {s}}\) consists of i mineral components, each of volume \(V_{{\mathrm {s}}i}\), so that. This technique was introduced by Leo Beranek in 1942 [Ber42] and was later improved by Champoux, Stinson and Daigle [CSD91]. The porosity data are reported to only two significant figures, so the uncertainty in the calculated solid density \(\rho _{\mathrm {s}}\) is greater than for limestones from other sources. 2. 2 Porosities of building limestones: using the solid density to assess data quality, $$\begin{aligned} \rho _{\mathrm {b}}=\frac{w_{\mathrm {d}} \rho _{\mathrm {w}}}{w_{\mathrm {sat}} - w_{\mathrm {A}}}, \end{aligned}$$, $$\begin{aligned} \rho _{\mathrm {s}}=\frac{w_{\mathrm {d}} \rho _{\mathrm {w}}}{w_{\mathrm {d}}-w_{\mathrm {A}}}, \end{aligned}$$, $$\begin{aligned} f=\frac{w_{\mathrm {sat}}-w_{\mathrm {d}}}{w_{\mathrm {sat}}-w_{\mathrm {A}}}=1-\frac{\rho _{\mathrm {b}}}{\rho _{\mathrm {s}}}.
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