SIST EN 480-11:2005

Admixtures for concrete, mortar and grout - Test methods - Part 11: Determination of air void characteristics in hardened concrete

This European Standard describes a test method for determination of the air- void structure in a hardened concrete sample which contains entrained air. The air-void structure is described by means of the following parameters, which are defined in clause 3.  i) Total air content, ii) Specific surface of air void system, iii) Spacing factor, iv) Air-void size distribution, v) Micro air content.

Zusatzmittel für Beton, Mörtel und Einpressmörtel -Prüfverfahren - Teil 11: Bestimmung von Luftporenkennwerten in Festbeton

Dieses Dokument beschreibt ein Prüfverfahren zur Bestimmung des Luftporengefüges in einer Festbetonprobe, die luftporenbildende Zusatzmittel enthält. Das Luftporengefüge wird durch die folgenden Kenngrößen beschrieben, die in Abschnitt 3 näher definiert sind:
i)   gesamter Luftporengehalt;
ii)   spezifische Oberfläche eingeführter Luftporen;
iii)   Abstandsfaktor;
iv)   Porengrößenverteilung;
v)   Gehalt an Mikroluftporen.
Das beschriebene Verfahren ist ausschließlich für Probekörper aus Beton geeignet, dessen ursprüngliches Mischungsverhältnis genauestens bekannt ist, wobei der Probekörper für dieses Mischungsverhältnis repräsentativ ist. Dies ist im Allgemeinen nur bei im Labor hergestelltem Beton der Fall.

Adjuvants pour bétons, mortiers et coulis - Méthodes d'essai -Partie 11: Détermination des caractéristiques des vides d'air dans le béton durci

La présente Norme européenne décrit une méthode d?essai permettant de déterminer la structure des vides
d?air dans un échantillon de béton durci contenant des adjuvants entraîneurs d?air. Cette structure est décrite
au moyen des parametres suivants, définis dans l?Article 3.
i) Teneur totale en air
ii) Surface spécifique des vides d?air
iii) Facteur d?espacement
iv) Distribution dimensionnelle des vides d?air
v) Teneur en microvides d?air
La méthode décrite ne s?applique qu?aux éprouvettes de béton durci dont on connaît avec précision la
composition, l?éprouvette étant représentative des proportions du mélange. En général, c?est uniquement le
cas du béton fabriqué en laboratoire.

Kemijski dodatki za beton, malto in injekcijsko maso – Preskusne metode – 11. del: Ugotavljanje značilnosti zračnih por v strjenem betonu

General Information

• Status: Published
• Publication Date: 30-Nov-2005
• ICS: 91.100.10 - Cement. Gypsum. Lime. Mortar
• ICS: 91.100.30 - Concrete and concrete products
• Technical Committee: BBB - Concrete, reinforced concrete and prestressed concrete
• Current Stage: 6060 - National Implementation/Publication (Adopted Project)
• Start Date: 01-Dec-2005
• Due Date: 01-Dec-2005
• Completion Date: 01-Dec-2005
• Directive: 89/106/EEC - Construction products
• Mandate: M/128 - Mandate to CEN/CENELEC concerning the execution of standardization work for harmonized standards on products for concrete, mortar and grout
• Ref Project: EN 480-11:2005 - Admixtures for concrete, mortar and grout - Test methods - Part 11: Determination of air void characteristics in hardened concrete

Relations

• Replaces: SIST EN 480-11:2002 - Admixtures for concrete, mortar and grout - Test methods - Part 11: Determination of air void characteristics in hardened concrete
• Effective Date: 01-Dec-2005

Standards Content (Sample)

SLOVENSKI STANDARD
SIST EN 480-11:2005
01-december-2005
1DGRPHãþD
SIST EN 480-11:2002
.HPLMVNLGRGDWNL]DEHWRQPDOWRLQLQMHNFLMVNRPDVR±3UHVNXVQHPHWRGH±
GHO8JRWDYOMDQMH]QDþLOQRVWL]UDþQLKSRUYVWUMHQHPEHWRQX
Admixtures for concrete, mortar and grout - Test methods - Part 11: Determination of air
void characteristics in hardened concrete
Zusatzmittel für Beton, Mörtel und Einpressmörtel -Prüfverfahren - Teil 11: Bestimmung
von Luftporenkennwerten in Festbeton
Adjuvants pour bétons, mortiers et coulis - Méthodes d'essai -Partie 11: Détermination
des caractéristiques des vides d'air dans le béton durci
Ta slovenski standard je istoveten z: EN 480-11:2005
ICS:
91.100.10 Cement. Mavec. Apno. Malta Cement. Gypsum. Lime.
Mortar
91.100.30 Beton in betonski izdelki Concrete and concrete
products
SIST EN 480-11:2005 en
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

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SIST EN 480-11:2005

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SIST EN 480-11:2005
EUROPEAN STANDARD
EN 480-11
NORME EUROPÉENNE
EUROPÄISCHE NORM
September 2005
ICS 91.100.30 Supersedes EN 480-11:1998
English Version
Admixtures for concrete, mortar and grout - Test methods - Part
11: Determination of air void characteristics in hardened
concrete
Adjuvants pour bétons, mortiers et coulis - Méthodes Zusatzmittel für Beton, Mörtel und Einpressmörtel -
d'essai -Partie 11: Détermination des caractéristiques des Prüfverfahren - Teil 11: Bestimmung von
vides d'air dans le béton durci Luftporenkennwerten in Festbeton
This European Standard was approved by CEN on 28 July 2005.
CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this European
Standard the status of a national standard without any alteration. Up-to-date lists and bibliographical references concerning such national
standards may be obtained on application to the Central Secretariat or to any CEN member.
This European Standard exists in three official versions (English, French, German). A version in any other language made by translation
under the responsibility of a CEN member into its own language and notified to the Central Secretariat has the same status as the official
versions.
CEN members are the national standards bodies of Austria, Belgium, Cyprus, Czech Republic, Denmark, Estonia, Finland, France,
Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Slovakia,
Slovenia, Spain, Sweden, Switzerland and United Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION
EUROPÄISCHES KOMITEE FÜR NORMUNG
Management Centre: rue de Stassart, 36  B-1050 Brussels
© 2005 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN 480-11:2005: E
worldwide for CEN national Members.

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SIST EN 480-11:2005
EN 480-11:2005 (E)
Contents
Page
Foreword .3
1 Scope .4
2 Normative references .4
3 Terms and definitions.4
4 Principle.5
5 Equipment .6
5.1 General .6
5.2 Specimen preparation .6
5.3 Microscopical analysis .6
6 Specimen production and preparation.7
6.1 Specimen production .7
6.2 Preparation of test surface.7
7 Microscopic procedure.8
7.1 Basic procedure.8
7.2 Values recorded .9
8 Calculations.10
8.1 Data obtained .10
8.2 Total traverse length.10
8.3 Total air content .10
8.4 Total number of chords measured .10
8.5 Specific surface of the air.11
8.6 Paste: air ratio .11
8.7 Spacing factor .11
8.8 Micro-air content.11

8.9 Air void distribution.11
9 Test report .13

Annex A (informative) Theoretical basis of calculation involved in Table 1 .15
Annex B (informative) Worked example of the calculation of air void distribution.18

2

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SIST EN 480-11:2005
EN 480-11:2005 (E)
Foreword
This European Standard (EN 480-11:2005) has been prepared by Technical Committee CEN/TC 104
“Concrete and related products”, the secretariat of which is held by DIN.
This European Standard shall be given the status of a national standard, either by publication of an identical
text or by endorsement, at the latest by March 2006, and conflicting national standards shall be withdrawn at
the latest by March 2006.
This document is part of the series EN 480 "Admixtures for concrete, mortar and grout – Test methods" which
comprises the following
Part 1 Reference concrete and reference mortar for testing
Part 2 Determination of setting time
Part 4 Determination of bleeding of concrete
Part 5 Determination of capillary absorption
Part 6 Infrared analysis
Part 8 Determination of the conventional dry material content
Part 10 Determination of water soluble chloride content
Part 11 Determination of air void characteristics in hardened concrete
Part 12 Determination of the alkali content of admixtures
Part 13 Reference masonry mortar for testing mortar admixtures
Part 14 Admixtures for concrete, mortar and grout - Test methods - Part 14: Measurement of corrosion
1)
susceptibility of reinforcing steel in concrete - Potentiostatic electro-chemical test method
This document is applicable together with the other standards of the EN 480 series.
This document supersedes EN 480-11:1998.
According to the CEN/CENELEC Internal Regulations, the national standards organizations of the following
countries are bound to implement this European Standard: Austria, Belgium, Cyprus, Czech Republic,
Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania,
Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Slovakia, Slovenia, Spain, Sweden, Switzerland
and United Kingdom.

1) This part is under preparation
3

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SIST EN 480-11:2005
EN 480-11:2005 (E)
1 Scope
This document describes a test method for determination of the air-void structure in a hardened concrete sample
which contains entrained air. The air-void structure is described by means of the following parameters, which are
defined in Clause 3.
i) Total air content
ii) Specific surface of air void system
iii) Spacing factor
iv) Air-void size distribution
v) Micro air content
The method as described is only suitable for use on hardened concrete specimens where the original mix
proportions of the concrete are accurately known and the specimen is representative of these mix proportions.
This will generally be the case only where the concrete concerned is produced in a laboratory.
2 Normative references
The following referenced documents are indispensable for the application of this document. For dated
references, only the edition cited applies. For undated references, the latest edition of the referenced
document (including any amendments) applies.
EN 480-1, Admixtures for concrete, mortar and grout – Test methods – Part 1: Reference concrete and
reference mortar for testing;
EN 934-2, Admixtures for concrete, mortar and grout – Part 2: Concrete admixtures –Definitions, requirements,
conformity, marking and labelling
ISO 1920-3, Testing of concrete - Part 3: Making and curing test specimens
3 Terms and definitions
For the purposes of this European Standard, the following terms and definitions apply.
3.1
air void
space enclosed by the cement paste that was filled with air or other gas prior to the setting of the paste. This
does not refer to voids of submicroscopic dimensions, such as the porosity inherent in a hydrated cement
paste. For the purposes of this test method, all voids within the cement paste are considered that are visible at
the test magnification with an intercepted chord length of up to 4 mm, other than obvious cracks
3.2
total air content A
proportion of the total volume of the concrete that is air voids; expressed as a percentage by volume
3.3
paste content P
proportion of the total volume of the concrete that is hardened cement paste, expressed as a percentage by
volume. This is the sum of the proportional volumes of cement, mixing water and any admixtures present. For
the purposes of this test method it is calculated from the batch weights of the test concrete.
4

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SIST EN 480-11:2005
EN 480-11:2005 (E)
3.4
specific surface of air void system α
-
calculated parameter representing the total surface area of the air voids divided by their volume; units are mm
1
. The calculation method used is based on the average chord length and is valid for any system of spherical
voids
3.5
spacing factor
calculated parameter related to the maximum distance of any point in the cement paste from the periphery of
an air void, measured through the cement paste; units are mm. The calculation of this parameter assumes
that all air voids present are of uniform size and are evenly distributed through the cement paste such that the
model system has the same total volume and surface area as the real system
NOTE This model is an approximation; the value obtained is probably larger than the actual value.
3.6
air-void distribution
set of calculated values of the number and/or volume of air voids of various diameters within the hardened
cement paste
NOTE The model used for this calculation assumes that only voids having diameters of certain discrete values are
present. This model will therefore lie between the real case and the single diameter model that is used in the calculation of
the spacing factor. A graphical representation of the distribution can be obtained by plotting the volume of air attributable
to each size of void, either as a volume percentage of the cement paste or as a proportion of the total air content.
3.7
micro air content A
300
calculated parameter representing the air content attributed to air voids of 0,3 mm (300 µm) diameter or less.
The value for this parameter is obtained during the calculation of the air void distribution
3.8
traverse line
One of a series of lines across the polished specimen face traced by the relative motion of the microscope and
specimen during the test
3.9
length of traverse T
tot
total distance traversed across the surface of the specimens during the test measurement. It is made up of two
parts, the total traverse across the surface on solid phases, T , and across air voids, T , in each case the units
s a
are mm
3.10
chord length l
distance along the traverse line across an air void, units are µm
3.11
chord length classification
chord lengths across individual air voids are classified into classes based on the length of the chord. The total
number of chords in any particular class, i, is designated by C. in8.9 and Table 1 contain details of the boundary
i
values for the classes
4 Principle
Hardened samples of air-entrained concrete are sectioned perpendicular to the original free upper surface to
produce specimens for analysis. These specimens are then ground and polished to produce a smooth flat
surface finish suitable for microscopic investigation.
5

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SIST EN 480-11:2005
EN 480-11:2005 (E)
The air void structure is examined by scanning along a series of traverse lines running parallel to the original free
upper surface. The number of air voids intersected by the traverse lines are recorded, as are the individual chord
lengths of the traverse across the air voids.
A mathematical analysis of the recorded data then allows a description of the air void system in terms of the
required parameters.
Other methods of air void analysis such as the point count method may be used provided that they can be
shown to give essentially the same results for the air void parameters required as the method described herein.
In the case of dispute the method described in this document shall be used.
5 Equipment
5.1 General
The following list of equipment has been found suitable for this test. Other apparatus may be used if it can be
shown to produce satisfactory results. Not all the equipment may be required for individual test measurements.
5.2 Specimen preparation
a) Diamond saw;
b) Grinding machine. One or more instruments able to provide a finished surface of the required quality.
These include instruments with a cast iron disc, usually with a minimum diameter of 400 mm, used in
conjunction with silicon carbide powder of various grain sizes (typically 120, 60, 30, 16 and 12 µm) or
instruments with special grinding discs of the varying grain sizes;
c) Refrigerator and oven;
d) Various chemicals for treatment of the polished surface, including; glycerol, stamp ink (matt or dull black,
not water soluble), zinc paste and gypsum powder (grain size ≤ 3 µm).
5.3 Microscopical analysis
a) A motorised or hand operated cross traverse table. This consists of a platform, on which the specimen
rests, which is mounted on lead screws by means of which it can be moved smoothly in two
perpendicular directions. One lead screw is required for movement in a direction perpendicular to and two
lead screws for movement parallel to the original upper surface. The lead screws should be capable of
providing a measure of the total distance travelled to an accuracy of 1 %;
b) Lighting equipment;
c) A means of recording the traverse distances and the total number of air voids traversed, divided into
classes based on the individual chord lengths;
d) Stereoscopic microscope, magnification (100 ±10) x. The instrument used must be capable of providing
the necessary resolution to classify the chords measured into classes as detailed in section 7.2. Other
forms of imaging may be used, such as a television camera mounted on the microscope with linked
monitor. In these cases the image used for measurements shall be selected so as to produce results for
voids counted which are consistent with those produced using direct visual examination through a
microscope.
NOTE Use of imaging systems of other magnification may lead to differences in the diameter of the smallest visible
voids. These may lead to counting variations and different values for calculated parameters.
6

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SIST EN 480-11:2005
EN 480-11:2005 (E)
6 Specimen production and preparation
6.1 Specimen production
Two samples, of minimum dimension 150 mm, shall be cast from the concrete under investigation. For testing
admixtures in accordance with EN 934-2 the concrete shall conform with EN 480-1. Suitable sample
geometries include 150 mm cubes or 150 mm diameter cylinders. Manufacture and curing of the samples
shall conform with ISO 1920-3.
After the concrete has been cured for a minimum of 7 days, a specimen approximately 100 mm wide by
150 mm high by 20 mm thick shall be cut from the approximate centre of each sample, such that the four cut
surfaces are perpendicular to the sample face that was uppermost during manufacture, see Figure 1. One of
the largest faces of each specimen is used, after preparation, for microscopic examination.

Key
1 Upper face during manufacture (original free upper surface)
Figure 1 — Production of 150 mm x 100 m x 40 mm specimen from 150 mm sample
(approximate dimensions)
6.2 Preparation of test surface
The intended test surfaces, one for each specimen, shall be wet ground until they are flat.
After wet grinding, a finely lapped finish to the test surface shall be produced. When this is complete the test
surface shall be cleaned to remove any residues.
NOTE The time required for wet grinding depends on the equipment used and will take approximately 5 min.
During this procedure, care should be taken to ensure that the test surface and the opposite face of the
specimen are as plane parallel as possible.
The exact procedure used will depend on the equipment available. The purpose of the lapping procedure is to
produce a surface suitable for microscopic examination of the air void structure within the concrete. A suitable
surface should have a matt sheen when dry and have no noticeable relief between the paste and aggregate
surface. The edges of voids should be sharp, and should not be broken or rounded. Care should be taken at
all stages of the grinding and lapping processes to ensure that voids do not become clogged with grinding
residues.
7

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SIST EN 480-11:2005
EN 480-11:2005 (E)
After the fine lapping is complete, the test surfaces should be cleaned to remove any residues. Suitable
methods are to use water and compressed air or a suitable fine brush. Care should be taken during the
cleaning process to ensure that the edges of the voids are not damaged. This may be of particular importance
if ultrasonic cleansing is used.
Reproducible results can be expected only with careful and appropriate fine lapping and cleaning of the test
surfaces.
The specimen surface can be treated to produce a better contrast between the air-voids and the cement paste,
should this be required by the intended measurement procedure. It is likely that this will be necessary if
automatic procedures are to be used. This can be done by first applying ink to the surface of the specimen
from a stamp pad or roller. Care should be taken to prevent the ink from sinking into the air-voids. The
specimen is then placed in an oven at 50 °C for 4 h. It is then covered with zinc paste and refrigerated before
any excess zinc paste is removed. Finally, the surface is covered with fine gypsum powder which is pressed
into the zinc paste filled air-voids. The excess gypsum powder is then removed with a scraper.
7 Microscopic procedure
7.1 Basic procedure
The specimens are placed on the cross-traverse table so that the traverse lines which are to be followed run
parallel to the original free upper surface of the specimen.
A minimum traverse distance of 1200 mm is required for each specimen, giving a minimum total of 2400 mm
per test. A number of traverses across the specimen face are made to give the required total distance. As it is
often difficult to ensure a perfect surface finish to the very edge of a specimen, care shall be taken to ensure
that any damaged area is not included in the traverse length. The traverse lines shall be laid out as follows,
see also Figure 2.
a) Four traverse lines are made in the upper region of the surface, across its width. The uppermost line
should be approximately 6 mm from the upper edge of the specimen and subsequent lines should be
spaced by approximately 6 mm from each other;
b) A further four traverse lines are made in the lower region of the surface. The lowest line should be
approximately 6 mm from the lower edge of the specimen and subsequent lines should be spaced by
approximately 6 mm from each other;
c) Further traverse lines are laid out in the central region of the surface, spaced by approximately 6 mm from
each other, so as to produce the total traverse distance required. A minimum of four traverse lines will be
required in this area, more may be needed to provide the required minimum traverse lengths if damaged
areas exist on the surface.
8

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SIST EN 480-11:2005
EN 480-11:2005 (E)

Key
1 Traverse lines at 6 mm separation
Figure 2 — Distribution of traverse lines on the test surface
7.2 Values recorded
The surface shall be viewed through the microscope at a magnification of (100 ±10) x. The magnification shall
not be changed during the period of measurement. The sample is viewed along the lines of traverse described
in 7.1. During the traverse, the two lead screws for movement parallel to the original free upper surface shall
be used to provide separate measures of the total distances traversed across;
a) the solid portions of the specimen surface, T ;
s
b) any voids intercepted, T ;
a
The sum of these two values gives the total traverse distance, T ;
tot
If the pore size distribution and/or the content of micro pores has to be determined then, in addition, a
separate tally of the number of chords produced by the intersection of the traverse lines with air voids shall be
kept as follows:
c) estimated length of each chord to the nearest 5 µm;
d) total number of chords in each class, using the class limits given in Table 1 and further explained in 8.9.
This procedure provides a subdivision of all chords occurring into 28 classes of different lengths. This
classification can then be used to calculate a corresponding air void distribution. In the counting procedure,
include all chords which are across visible voids in the hardened cement paste with a chord length on the
traverse line of between 0 and 4000 µm. The only exceptions to this being obvious cracks.
If, in spite of careful grinding, the edges of voids are broken and such a breakage lies on a traverse then the
completed circular section shall be used as the basis for determining the chord length. The method of determi-
2)
ning the relevant chord length is shown in Figure 3.

2) Automatic imaging systems will not be able to make this correction and this may lead to errors in the final analysis.
9

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SIST EN 480-11:2005
EN 480-11:2005 (E)

Key
1 Traverse line
2 Zero chord length (l)
Figure 3 — Estimation of chord length, l for broken void edges during microscopic examination
8 Calculations
8.1 Data obtained
The following data will be available from values obtained during the test procedure. For the purposes of the
calculation, the totals for both specimens for the same test concrete shall be added together.
I) Paste content by volume calculated from the mix proportions, P
II) Total length of traverse across solid phases, T
s
III) Total length of traverse across air voids, T
a
IV) The number of individual chords across air voids in the various size classes, C
i
8.2 Total traverse length
This is calculated as the sum of the traverse lengths across the solid phases and the voids.
= +   i n mm (1)
T tot T s T a
The total traverse length shall be at least 2400 mm.
8.3 Total air content
This is calculated as the proportion of the total traverse length that was made across voids.
⋅ 100
T a
A =  expressed as % by volume (2)
T tot
8.4 Total number of chords measured
This is calculated as the sum N of the number of chords in each of the size classes.
N = ∑ (3)
Ci
10

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SIST EN 480-11:2005
EN 480-11:2005 (E)
8.5 Specific surface of the air
4 ⋅ N
-1
α =  i n (4)
mm
T
a
8.6 Paste: air ratio
This is calculated as the ratio R of the volume paste content P, determined from the mix proportions, and the
total air content A, calculated from equation (2).
P
R = (5)
A
8.7 Spacing factor
The equation used for this calculation is dependant on the value of R calculated from equation (5).
If R > 4,342 then equation (6) shall be used, if R ≤ 4,342 then equation (7) shall be used.
1/3
3 [ 1,4 ( 1 + R ) - 1 ]
L =  i n mm (6)
α
or
P ⋅
T
tot
L =  i n mm (7)
400 ⋅ N
8.8 Micro-air content
The micro-air content A is taken directly from Table 1 as the calculated value in column 10 for class 18
300
expressed as % by volume.
8.9 Air void distribution
8.9.1 Basis of calculation
The air void distribution is calculated from the distribution of chord lengths measured during the traverse
procedure. The calculated distribution is based on a model which assumes only a nominal set of air void
diameters are present. The nominal diameters are those corresponding to the maximum chord length in each of
the classes.
The required data for this calculation are the total length of traverse, T , and the chord length distribution. A
tot
worked example is given in Annex B.
8.9.2 Calculation of chord frequency
The chords measured are divided between a number of classes in Table 1, based on length, recorded to the
nearest 5 µm. The class designation numbers and boundaries are given in columns 1 and 2. By comparison
with the class boundaries, each chord is placed in a class, for example a chord of length 150 µm is placed in
class 11. The total number of chords in each class is entered in column 3. The number of chords per
millimetre of the traverse line is then calculated by dividing the values in column 3 by T and placing the
tot
results in column 4.
11

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SIST EN 480-11:2005
EN 480-11:2005 (E)
8.9.3 Calculation of void frequency
Not every void within the cement paste will have been intersected during the traverse, as the traverse lines do
not cover the whole volume of the concrete sample. It is therefore necessary to calculate the number of voids
per cubic millimetre of concrete so as to be able to determine the air void distribution. It is possible to calculate
the fraction of the total number of voids that might contain a chord of a particular length that have been
intersected.
The value for this fraction for each class of chord lengths is shown in column 5. Dividing column 4 by column 5
therefore gives the total number of voids within a cubic millimetre of concrete that could contain chords of the
particular class. This value is entered into column 6.
NOTE The values in column 5 are constant for all cases and are derived from the equation;
π ⋅ ( 5 + - ) ⋅ ( + )
l l l l
max min max min
2
Fraction of air voids encountered = ( )
mm
6
4 ⋅ 10
where
l and l are the maximum and minimum chord lengths within the class.
max min
The factor of 5 in the numerator of the equation is present due to the rounding of all chords to the nearest
5 µm. The equation itself is based on a statistical evaluation of the void population.
8.9.4 Calculation of void distribution
A chord of any particular length can be found in any void of diameter greater than the chord length. Therefore
the value in column 6 for any class includes all voids of diameter greater than the upper limit of that class as
well as voids of diameter within that class. To provide a measure of the number of voids of diameter equal to
that of the upper boundary of a class the value in column 6 for the next highest class is subtracted from the
val
...