Using the Solid Density to Assess Data Quality
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Materials and Structures DOI 10.1617/s11527-015-0767-3 ORIGINAL ARTICLE Porosities of building limestones: using the solid density to assess data quality Christopher Hall . Andrea Hamilton Received: 15 June 2015 / Accepted: 16 December 2015 Ó The Author(s) 2016. This article is published with open access at Springerlink.com Abstract A good knowledge of the volume-fraction the solid density should always be calculated for this porosity is essential in any technical work on porous purpose when the Archimedes method is used. This materials. In construction materials the porosity is check can be useful also when porosities are measured commonly measured by the Archimedes buoyancy by helium pycnometry or by mercury intrusion method, from which the bulk density of the test porosimetry. specimen is also obtained. The porosity and the bulk density together fix the solid density of the specimen, Keywords Porosity Á Density Á Archimedes method Á as only two of the three quantities are independent. Limestone Á Calcite The solid density, although rarely discussed, is determined by the mineralogy of the specimen, and therefore can provide a valuable check on the accuracy 1 Introduction of porosity and bulk density measurements. Our analysis of published data on calcitic limestones Most inorganic construction materials, including the shows that the solid density is generally close to the main building stones, are porous. In research on ideal crystallographic density of calcite. Small devi- mechanics, transport, and durability in these materials, ations can often be traced to variations in mineral the porosity is often used as an explanatory (indepen- composition. However some published porosity–den- dent) variable, and so it is measured and reported as a sity data are inconsistent with the known mineralogy. material property. The porosity appears as a parameter Deviations which cannot be ascribed to composition in many technical calculations in building physics. may be assumed to arise from measurement errors. We There are now hundreds of publications containing show the value of using the solid density as a quality porosity data, stretching back to the early method check on the measured porosity. We recommend that papers of Purdy and Moore [1], and of Washburn and his collaborators [2–4]. The data on construction materials form a subset of the larger resource that & C. Hall ( ) includes related work in geology, petrophysics, and School of Engineering, University of Edinburgh, Edinburgh EH9 3FB, UK industrial ceramics. e-mail: [email protected] Unfortunately, reported porosity data are not always of high quality. Porosity values are sometimes incon- A. Hamilton sistent with the stated bulk densities and the known Department of Civil and Environmental Engineering, University of Strathclyde, Glasgow G1 1XJ, UK mineral compositions, and are therefore probably e-mail: [email protected] inaccurate. In this paper, we examine some published Materials and Structures data on the porosities of limestones, a group of building Vs ¼ðwd À wAÞ=qw; ð4Þ materials where the material composition is often known, or can be assumed to lie within narrow limits. and We aim to show that estimating the solid density from Vb ¼ðwsat À wAÞ=q ; ð5Þ porosity and bulk-density data provides a simple w quality check on the measured specimen porosity. where Vs, Vb are the solid and bulk volumes of the specimen. Of the quantitities qs, qb and f, any two are independent (knowing two, the third is fixed). In 2 Measuring the porosity publications providing porosity data, the bulk density is sometimes also reported. Surprisingly, the solid 2.1 The Archimedes method density is rarely given. Even if given, it is rarely the subject of much comment. The porosity of building stones is usually measured by The Archimedes method is conceptually simple, the long-established Archimedes buoyancy method— but in practice prone to error. In measuring wA and see [5, 6] for practical descriptions of such tests, wsat, it requires care to achieve complete saturation of and [7] for a recent discussion. Test procedures can be the specimen using vacuum apparatus. To obtain wd, found in EN 1936 [8], which is the basis of many the specimen must be completely dried without European national standards. Similar methods are thermal alteration of the material composition or described in EN 772 [9]. No equivalent American structure. In measuring wsat liquid may be lost from the standard method exists for porosity in natural stone. In specimen by evaporation, or sometimes by drainage ASTM C97 [10] the bulk density is determined by a from low-suction cavities and cracks. buoyancy method, but the porosity is not calculated. Equations 1–3 show how these three sources of In the Archimedes method three quantities are mea- measurement error affect the estimates of f, qb, and qs. suredonasinglespecimen:wd, the weight of the dry (1) When the test specimen is not completely dried wd specimen; wsat, the weight in air of the specimen fully is too high. It then follows that qb is overestimated, saturated with a liquid (usually water); and wA, the while both f and qs are underestimated, as shown weight of the saturated specimen suspended and fully schematically in Fig. 1. (2) As discussed in [7], failing immersed in the saturating liquid. The last of these, to saturate the specimen completely leaves the value wA, is known as the Archimedes weight. From these of qb unchanged, but leads to underestimates of both f three quantities, the bulk density qb, the solid density and qs. (3) Any loss of water from the surface of the qs, and the volume-fraction porosity f of the specimen saturated specimen before it is weighed in air means can be calculated from the following equations: that wsat is too low. This causes the bulk volume Vb to w q be underestimated, and as a result qb is overestimated, q ¼ d w ; b ð1Þ and f underestimated, while the value of qs is correct. wsat À wA None of these three measurement errors causes the wdqw solid density to be overestimated. qs ¼ ; ð2Þ wd À wA A serious practical problem in implementing the Archimedes method is that reference materials of wsat À wd qb f ¼ ¼ 1 À : ð3Þ certified porosity are not available. This makes traceable w À w q sat A s calibration difficult. The published literature also shows Here qw is the density of the saturating liquid at the a wide variation in the estimates of uncertainty used by temperature of the measurement. Strictly, the quantity different authors in reporting porosity and density. f is the open porosity, the pore-space accessible to the saturating liquid. Any closed pores are treated as part 2.1.1 Effects of measurement errors on porosity of the solid material, and the solid density qs is and density estimates accordingly the density of the impermeable matrix, including any closed pores. We have indicated qualitatively how the calculated Equations 2 and 3 follow from the Archimedes values of the bulk density, solid density and porosity buoyancy relations are affected by the various measurement errors. In the Materials and Structures closed porosity (although the evidence for this is not Complete drying clear). The total porosity fT is then calculated from Eq. 3: fT ¼ 1 À qb=qr. It is unusual however for laboratories using the procedures of EN 1936 to report f Incomplete both open and total porosity. When both are deter- s ρ drying mined, the difference f À f is used as a measure of f , Complete T c drying the volume-fraction closed porosity, although as the small difference of two experimental quantities it may Solid density be of low accuracy. Detecting and measuring closed porosity in stones and other porous inorganic materials Volume fraction porosity is a difficult matter, for which there are no satisfactory Incomplete general methods. drying 2.3 Variants and alternatives Bulk density ρ (kg/m3) Bulk density ρ (kg/m3) b b In a variant of the Archimedes method, used when the Fig. 1 A schematic to show the effect of incomplete drying on the estimates of bulk density, porosity, and solid density. Lines specimen is in the form of a regular cylinder or a are calculated from Eqs. 1–3. If the drying is incomplete, the rectangular block, the bulk volume Vb is calculated bulk density is overestimated while the porosity and the solid directly from the specimen dimensions. The bulk density are underestimated density is then calculated from the formula qb ¼ wd=Vb, and the porosity from the formula f ¼ 1À Appendix we give the exact relations between the ðwd À wAÞ=ðqwVbÞ. The saturated weight wsat is not relative errors in the dry weight or in the saturated required, although the specimen must be fully satu- weight and the associated relative errors in the rated in order to measure the Archimedes weight wA. calculated quantities. The relative errors in the poros- This variant eliminates errors arising from problems in ity and the solid density may sometimes be consider- weighing the saturated specimen in air. These may be ably larger than the relative errors in the measured severe in specimens with coarse porosity which lose weights. For example, in the case of incomplete liquid by drainage. saturation in a specimen with a solid density of An alternative to the standard Archimedes method 2500 kg/m3 and porosity 0.2, a -1 % relative error in is to obtain the open porosity f by helium pycnome- the saturated weight wsat leads to a -11 % relative try [11], a technique often used in petrophysics but error in the porosity. In a test in which the specimen is rarely for building materials. The solid volume Vs of incompletely dried, a ?1 % relative error in the dry the specimen is measured directly by expanding a weight leads also to a -11 % relative error in the known volume of helium gas into the open pores.