KENYA STANDARD                     KS 2177:  2017 
                
   
Kenya Standard         KS 2769 -11: 2018 
 
 
 
 
 
 
  
 
 
 
 
 
 
 
 
Admixtures for concrete, mortar and grout 
Test methods  
 
Part 11: Determination of air void 
characteristics in hardened concrete  
  
 
 
 
 
 
 
 
 
©KEBS 2018                         First  Edition 2018 
 
 
 
 
 
 KS 2177: 2017                                                                                                            
 
ii                     © KEBS 2017 — All rights reserved   
 
 
 
TECHNICAL COMMITEE REPRESENTATION  
 
The following organizations were represented on the Technical Committee:  
 
1. Architectural Association of  Kenya  
2. Bamburi Cement  
3. CHRYSO Eastern Africa Limited  
4. Concrete Products (K)Ltd  
5. Consumer Information Network  
6. Howards  Humpreys East Africa LTD  
7. Institute of quantity surveyors of Kenya  
8. Kenya Industrial Research and Development Institute (KIRDI  
9. Kenya Institute of Highways and Building Technology (KIHBT)  
10. Ministry of Transport, Infrastructure, Housing and Urban Development.  
11. National Environment Management Authority  
12. National Housing Corporation  
13. Technical University of Kenya  
14. University of Nairobi  
15. Kenya Bureau of Standards — Secretariat  
 
 
 
 
 
 
 
 
 
 
 
REVISION OF KENYA STANDARDS  
  
In order to keep abreast of progress in industry, Ke nya Standards shall be regularly reviewed. Suggestions 
for improvements to published standards, addressed to the Managing Director, Kenya Bureau of Standards, 
are welcome.  
 
 
 
 
 
 
 
 
 
 
© Kenya Bureau of Standards, 20 17 
  
Copyright. Users are reminded that by virtue of Section 25 of the Copyright Act, Cap. 12 of 2001  of the Laws of Kenya, copyright 
subsists in all Kenya Standards and except as provided under Section 26 of this Act, no Kenya Standard produced by Kenya Bure au of 
Standards may be reproduced, stor ed in a retrieval system in any form or transmitted by any means without prior permission in writing 
from the Managing Director . 
 
 
 
 
 
 
 KENYA STANDARD                                  KS 2177 : 2017 
                
 © KEBS 2017 — All rights reserved            iii  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Admixtures for concrete, mortar and grout 
Test methods  
Part 11: Determination of air void 
char acteristics in hardened concrete  
  
 
 
 
 
 
KENYA BUREAU OF STANDARDS (KEBS)  
 
Head Office:  P.O. Box 54974, Nairobi -00200, Tel.: (+ 254 020 ) 605490, 602350, Fax: (+254 020 ) 604031  
E-Mail: info@kebs.org,  Web:http://www.kebs.org   
 
Coast Region     Lake Region          Rift Valley Region  
P.O. Box 99376, Mombasa -80100   P.O. Box 2949, Kisumu -40100        P.O. Box 2138, Nakuru -20100  
Tel.: (+254  041) 229563, 230939/40  Tel.: (+254 057) 23549, 22396        Tel.: (+254 051) 210553, 210555  
Fax: (+254  041) 229448    Fax: (+25 4 057) 21814         
 
 
 
 KS 2177: 2017                                                                                                            
 
iv                     © KEBS 2017 — All rights reserved  Foreword  
 
This Kenya Standard was revised  by the Concrete Technical Committee, under the guidance of the 
standards Projects Committee, and it is in accordance with the procedures of the  Kenya  Bureau  of 
Standards .  
This Kenya Standar d is part of the series KS 2769  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 blee ding 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 vo id characteristics in hardened concrete  
 
— Part 12: Determination of the alkali content of admixtures  
 
— Part 13: Reference masonry mortar for testing mortar admixtures  
 
— Part 14: Determination of the effect on corrosion susceptibility of reinforcing stee l by potentiostatic  
electro -chemical test  
 
— Part 15: Reference concrete and method for testing viscosity modifying admixtures  
 
This standard is applicable together with the standards of the series KS 2770 Admixtures for concrete, 
mortar  and grout.  
 
. 
 
 KENYA STANDARD                                  KS 2177 : 2017 
                
 © KEBS 2017 — All rights reserved         
   5 KENYA  STANDARD                       KS 2769 -11: 2018  
 
Admixtures for concrete, mortar and grout - Test methods - Part  
11: Determination of air void characteristics in hardened  Concrete  
 
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. 0 
 
i) T o t a l  a i r  c o n t e n t  
 
ii) Specific surface of air void system  
 
iii)  S p a c i n g  f a c t o r 
 
i v ) A i r-v o i d  s i z e  d i s t r i b u t i o n  
 
v) M i c r o  a i r  c o n t e n t  
 
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 
propor tions. 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.  
 
KS 2769 , Admixtures for concrete, mortar and grout — Test methods — Part 1: Reference concrete and 
reference mortar for testing;  
 
KS 2 770, 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 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 poros ity 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 KS 2177: 2017                                                                                                    
        
 
6                     © KEBS 2017 — All rights 
reserved  proportion of the total volume of the concrete that is hardened cement paste, expressed as a percentage by 
volume. This is t he 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.  
 
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, ei ther 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 paramete r 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 distan ce 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 s, and across air voids, T a, in each case the 
units are mm  
 
3.10.   
chord length l  
distance along the  traverse line across an air void, units are pm  
 
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 i. in 8.9 and Table 1 contain details of the 
boundary 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 gro und and polished to produce a smooth 
flat surface finish suitable for microscopic investigation.  
 KENYA STANDARD                                  KS 2177 : 2017 
                
 © KEBS 2017 — All rights reserved         
   7 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 describ ed 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 indiv idual 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 sur face, 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 l ead 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 di ameter of the smallest visible voids. These 
may lead to counting variations and different values for calculated parameters.  KS 2177: 2017                                                                                                    
        
 
8                     © KEBS 2017 — All rights 
reserved  6. Specimen production and preparation  
 
6.1.  Specimen production  
 
Two samples, of minimum dimension 150 mm, shall be cast from the concret e under investigation. For testing 
admixtures in accordance with  KS 2769 -2 the concrete shall conform with KS 2770 -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 surfa ce 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 e nsure 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 exa mination 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. Car e 
should be taken at all stages of the grinding and lapping processes to ensure that voids do not become 
clogged with grinding residues.  
 KENYA STANDARD                                  KS 2177 : 2017 
                
 © KEBS 2017 — All rights reserved         
   9 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 ca n 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 measuremen t 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 fill ed 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 difficu lt 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 m ade 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 ma de 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 dama ged 
areas exist on the surface.  KS 2177: 2017                                                                                                    
        
 
10                     © KEBS 2017 — All rights 
reserved  
 
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 magnifica tion 
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 separa te measures of the total distances traversed across;  
 
a) the solid portions of the specimen surface, T s; 
 
b) any voids intercepted, Ta; 
 
 
The sum of these two values gives the total traverse distance, T tot; 
 
If the pore size distribution and/or the content of mi cro 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 pm;  
 
d) total number of cho rds 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 pm. The only exceptions to this being obvious cracks.  
 
If, in sp ite 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 ning the relevant chord length is shown in Figure 3.1) 
 
 
 
                                                      
1 Automatic imaging systems will not be able t o make this correction and this may lead to errors in the final 
analysis.  KENYA STANDARD                                  KS 2177 : 2017 
                
 © KEBS 2017 — All rights reserved         
   11 
 
Key 
1 Traverse line  
2 Zero chord length ( I) 
Figure 3 — Estimation of chord length, I 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.  
Ttot =Ts + T a in mm  
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.  
 
expressed as % by volume  
 
8.4. Total number of chords measured  
 
This is calculated a s the sum N of the number of chords in each of the size classes.  
 N=∑C i 
 
 
 
 
 
 
 
 
 
 
 KS 2177: 2017                                                                                                    
        
 
12                     © KEBS 2017 — All rights 
reserved   
 
8.5. Specific surface of the air  
 
 (4) 
 
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 a ir content A, calculated from equation (2).  
 
 
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.  
 
 
 
8.8.  Micro -air content   
 
 
The micro -air content A300 is taken directly from Table 1 as the calculated value in column 10 for class 
18 expressed as % by volume.  
 
8.9. Air void distribution  
  
8.9.1.  Basis of calculation  
The air void distribution is calculated from the dis tribution 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 tot, and the chord length distribution. A 
worked example is given in Annex B.  
 
8.9.2.  Calculation of chord frequency  
8.9.3.   
The chords measured are divided between a num ber of classes in Table 1, based on length, recorded to the 
nearest 5 pm. 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  
um 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 tot 
and placing the results in column 4.  
 KENYA STANDARD                                  KS 2177 : 2017 
                
 © KEBS 2017 — All rights reserved            
13 8.9.4.  Calcul ation 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;  
 
 
 
where  
t: ma, and e min are the maximum and minimum chord lengths within the class.  
 
The factor of 5 in the numerator of the equation is present due to the rounding of all chords to the 
nearest 5 pm. The equation itself is based on a statistical evaluation of the void population.  
 
8.9.5.   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 value for the current class and placed in column 7. For example, the column 7 value for 
class 10 is derived by subtracting the column 6 value for class 11 from the column 6  value for class 10.  
 
NOTE It is possible, in some cases, for values in column 7, and therefore in those columns subsequently calculated from it, to be 
negative. This is due to the division of chords into classes and the class boundaries used; it can be a voided if the class boundaries are 
adjusted appropriately. This will not materially affect the final derived air volume distribution. For calculation purposes the negative value 
should be retained and not ignored.  
 
8.9.6.  Calculation of air content  
 
The total vol ume of air attributed to each class of voids is calculated by multiplying column 7 by column 8, 
which contains the volume of one void of the class diameter, to give the air content as a fraction and then 
multiplying by 100 % to express this as a percentage.  The result is placed in column 9. The cumulative air 
content, the running total of column 9, is then placed in column 10.  
 
NOTE The final total in class 28, Column 10 is nominally the total air content. This should be similar to that calculated in 8.3 b ut may 
vary slightly due to the different calculation procedures used . 
 
8.9.7.  Presentation of results  
The air void distribution can be plotted against nominal air void diameter using values for the upper 
diameter of each class from column 2 and the value in column  10. This can be plotted either as a 
cumulative percentage as obtained in column 10 or as a cumulative fraction of the total air content by 
dividing each value in column 10 by the total calculated air content as represented by the value in column 
10 for cl ass 28.  
 
8.9.8.  Column Contents  
The various columns on Table 1 can be briefly described as follows:  KS 2177: 2017                                                                                                            
 
14                     © KEBS 2017 — All rights 
reserved  Column 1: The class designation number  
 
Column 2: The upper and lower boundaries  of chord length for each class  in µm.  
 
Column 3: The number of chords observed fo r each class.  
 
Column 4: The number of chords per mm of traverse line.  
 
Column 5: The fraction of possible voids that will have been actually counted. This factor has units of 
mm2.  
 
Column 6: The total number of voids per mm3 of concrete containing a chor d of the particular class 
size.  
 
Column 7: The total number of voids of diameter equal to the upper limit of the class per mm3 of 
concrete.  
 
Column 8: The volume attributed to each void of a class in mm3. 
 
Column 9: The total volume attributed to all voi ds within a class expressed as a percentage of the volume 
of concrete.  
Column 10: A cumulative total air content for air voids up to the current class expressed as a percentage 
of the volume of concrete.  
 
9.  Test report  
The test report shall include the foll owing information  
 Full details of the mix design of the concrete tested together with details of the density and 
measured air content of the fresh concrete.  
 
 Details of the calculation of the paste content of the concrete.  
 
 Calculated values for the total air content, specific surface of air void system and 
spacing factor. If required  
 
 Micro air content  
 
 Plot of the air void distribution.  KENYA STANDARD                                  KS 2177 : 2017 
                
 © KEBS 2017 — All rights reserved            15 Table 1 - Determination of air void distribution  
Total traverse length. T tot 
Column  1 2 3 4 5 6 7 8 9 10 
Subject  Class Class width  Recorded num ber Chord  Fraction  Possible  Voids  Void Air Cumulative  
   of chords in  
class  Frequency  Encountered  Total  in class  Volume  Content  Air Content  
Source   The values shown in  as Column 3  The values shown in  Column 4  Column 6 minus  The values shown in  Column 7 mul tiplied  Cumulative  
  Columns 1, 2, 5 and 8  measured  divided by  Columns 1, 2, 5 and 8  divided  next va lue Columns 1, 2, 5 and   by Column 8  Total of  
  do not change from test  Ci, Ttot do not change from  by l in 8 do not change f rom multiplied by 100  Column 9  
  to test1)   test to test1) Column 5  Column 6  test to test1)   
Units   µm  mm-1  mm2 mm-3 mm -3 mm3 %' % 
 1 
2 
3 
4 
5 0 to 10    0.0001178    5.24x10'    
 15 to 20    0.0002749    4,19x104   
 25 to 30    0.0004320    1.41x103   
 35 to 40    0.0005890    3.35x103   
 45 to 50    0.0007461    6.54x103   
  
55 to 60    0.0009032    1.13x104   
 65 to 80    0.0022780    2.68x104   
 85 to 100    0.0029060    5.24x104   
 105 to 120    0.0035340    9.05x103   
 125 to 140    0.0041630    1.44x103   
 11 145 to 160    0.0047910    2.14x103--   
 12 165 to 180    0.0054190    3.05x103   
 13 185 to 200    0.0060476    4.19x103   
 14 205 to 220    0.0066760    5.58x103   
 15 225 to 240    0.0073040    7.24x103   
 16 245 to 260    0.0079330    9.20x10    
 17 265 to 280    0.0085610    1.15x103   
 18 285 to 300    0.0091890    1.41x103   
 19 305 to 350    0.0257200    2.24x103   
 20 355 to 400    0.0296500    3.35x103   
 21 405 to 450    0,0335800    4.77x10    
 22 455 to 500    0,0375000    6.54x103   
 23 505 to  1000    0.5910000    5.24x101   
 24 1005 to 1500    0.9837000    1.77   
 25 1505 to 2000    1.3760000    4.19   
 26 2005 to 2500    1.7690000    8.18   
 27 2505 to 3000    2.1620000    1.41x10-1   
 28 3005 to 4000    5.5020000    3.35x10-1   
1) The columns of 
values  1. 2, 5 and 8 do not change from test to test.  KS 2177: 2017                                                                                                            
 
16                     © KEBS 2017 — All rights 
reserved  Annex A  
(informative)  
 
Theoretical basis of calculation involved in Table I  
 
A.1 Introduction  
 
The purpose of the calculation carried out in Table 1 is to derive the distribution of air void diameters  from the 
measured distribution of chords. Once an air void diameter distribution is known then the volume of air 
entrained can be calculated.  
 
During the linear traverse only those air voids intercepted by the traverse line will be counted in the chord 
distribution; a large number will not be intercepted and are therefore not included in the chord distribution. The 
calculations in Table 1 provide a means of estimating the total number of voids from those intercepted by 
means of a statistical analysis.  
 
A.2 Assumptions  
 
The basic assumption is that no air void is intercepted more than once during the linear traverse. This 
means that each chord recorded represents a separate air void.  
 
A second assumption, made to ensure an easier calculation procedure, is th at the real air void distribution 
can be represented by a calculated distribution containing air voids of only those diameters listed as the 
maximum value in each class width (column 2 of Table 1). No extension of this to a true, continuous 
distribution of  air void diameters is given here.  
 
Step 1: Classification of chord lengths and calculation of chord frequency  
 
As the linear traverse is performed, as well as producing a total for the traverse length across air voids, T a, the 
individual chords are classi fied to the nearest 5 pm and recorded in the various classes. The classes are 
specified in Column 2 of the Table and the number of chords in each class is recorded in Column 3. This 
classification procedure is the final measurement procedure. The remainder  of the table is concerned with 
calculation.  
 
The first calculation step is to calculate the number of chords in each class detected per mm of total traverse 
length, T 10. This is placed in Column 4. The purpose of this is to provide measurements per unit l ength to 
allow future calculations to be made to produce a percentage value for the air content.  
 
Step 2: Calculation of total possible number of chord intercepts  
 
As mentioned above, not all voids will be intersected during the linear traverse. To allow a  calculation of 
the total air content, the fraction of the possible total that have actually been registered must be found. This 
is possible through the following:  
 
Consider one air void, sufficiently large so as to contain chords between x and x' in lengt h. A diagram 
representing this void is shown in Figure A.1.  KENYA STANDARD                                  KS 2177 : 2017 
                
 © KEBS 2017 — All rights reserved            
17 
 (A.2) 
 
16 
 
  
Side view  Cross section  
(along traverse line)  (across traverse line)  
 
Figure A.1 — Void geometry  
If this was the only void in a mm3 of concrete, symmetrically placed around the traverse line , then the probability of this 
void being penetrated by the traverse line to produce a chord within the limits given can be calculated by the cross 
sectional area of the void which would produce such a chord divided by the total cross sectional area of the  volume 
of concrete considered. The cross sectional area of concrete is 1 mm2 (106 pm2). The relevant cross sectional area of 
the void can be easily calculated through classical geometry and can be seen to be:  
 
 (A.1) 
  
 
This can be simplified to:  
 
 
 
 
and then expanded to:  
 
 
   
  (A.3) 
This would be exactly correct if the exact chord lengths were used in the classification. However, the chord lengths 
are recorded to the nearest 5 µm. If x and x' are the real limits of the chords then the class limit  boundaries, listed in 
Table 1, column 2, y and y' are given by:  
 
x+ 2.5  and y_ = x_ - 2.5 (A.4) 
 
Substituting into the previous equation gives:  
4  [ ( y ' + 2 . 5 ) + ( y -2 . 5 ) ] ' [ ( y ' + 2 . 5 ) -(y-2 . 5 ) ]  (A.5) 
 
simplifying:  KS 2177: 2017                                                                                                            
 
18                     © KEBS 2017 — All rights 
reserved  CD ENG 24 -11:2005 (E)  
 (A.6)  
The probability of intersecting this void , in a total cross section area of 106 pm2, is therefore:  
 
 
 
This value is constant for each class of chords and can be calculated. The calculated values are given in 
Column 5 of the Table 1. If this is the probability of intersecting one void, it can be used to calculated the total 
number of voids existing as the number actually penetrated per mm of traverse line (which is the length of line 
contained in the 1 mm3 discussed above) is known from Column 4 of the Table 1. The total number of voids 
existing, which contain potential chords in the group considered, is the number actually recorded divided 
by the probability of intersecting any single void, i. e. Column 4 divided by Column 5 on the Table 1. The 
resulting value is entered in Column 6. Because of th e boundaries set in the above discussion, these 
values are the number of chords in each class per mm3 of concrete.  
 
Step 3: Calculation of total number of voids  
Column 6 contains the possible total number of chord intercepts, by class, whether or not actua lly penetrated 
during the linear traverse. This is not the same as the total number of voids. Each void can contain chords in a 
number of chord classes and will therefore have been counted in the above calculation the same number of 
times as the number of chord classes that it contains. Put another way, a chord in class n can be found in 
voids of diameter n and above.  
 
 
Consider the total number of chords in class 12, this is made up of chords in voids of diameter from the 
maximum in class 12 up to class 28 . If v n, is taken as the number of voids of diameter n, and c n as the 
number of chords in class n, then:  
 
C12 = V 12 + V 13 + V 14 + ••• + V 28 
 
Similarly:  
C13 = V 13 + V 14 + ••• + V 28 
 
Therefore:  
V12 = C 12-C13 
 
This allows the total number of voids of a partic ular diameter to be calculated from the total number of chords. 
This is carried out in Column 7 of the Table 1.  
 
Step 4: Calculation of air content  
 
The final step is to calculate the total air content. Column 8 gives the volume of a void of diameter equal  to the 
maximum limit of each class. This, multiplied by the number of voids of that diameter gives the total air volume 
per mm3 of concrete as a fraction, multiplying by 100 gives the value as a percentage, which is placed in 
Column 9. A cumulative air co ntent is then calculated in Column 10.  
 KENYA STANDARD                                  KS 2177 : 2017 
                
 © KEBS 2017 — All rights reserved            
19 Annex B  
(informative)  
Worked example of the calculation of air void distribution  
 
Calculation of air void distribution is described in 8.9 and Table B.1 shows the details of the calculation 
procedure used. The exam ple only covers the determination of the air void distribution and the micro air content, it 
does not include the calculation of total air content, specific surface or spacing factor.  
Example data for calculation;  
 
a) Total traverse length = 2400 mm  
 
b) Chord le ngth dist ribution, as recorded in Column 3 of Table B.1.  KS 2177: 2017  
            
                              © KEBS 2017 — All rights 
reserved  20 Table B.1 – Determination of air void distribution  
Total traverse length T tot  2400 mm        
Column  1 2 3 4 5 6 7 8 9 10 
Subject  Clas
s Class width  Recorded number  
of chords in class  Chord  
Frequ ency  Fraction  
Encountered  Possible  
Total  Voids  
in class  Void  
Volume  Air  
Content  Cumulative  
Air Content  
Source   1) as  
measured  
C. Column 3  
divided by  
Trot ) Column 4  
divided  
by Column 5  Column 6 minus  
next value in  
Column 6  1) Column 7 multip lied by  
Column 8 multiplied by  
100 Cumulative  
Total of  
Column 9  
Units   pm  mm' mm2 mm-3  mm-3 
mm mm3 % % 
 1.  0 to 10  65 0.02708  0.0001178  229.90945  140.483  5.24x10-7 0.007  0.01 
 2.  15 to 20  50 0.02458  0.0002749  89.42646  9.372  4.19x10-6 0.004  0.01 
 3.  25 to 30  83 0.03458  0.0004320  80.05401  6.483  1.41x10-5 0.009  0.02 
 4.  35 to 40  104 0.04333  0.0005890  73.57102  24.427  3.35x10-5 0.082  0.10 
 5.  45 to 50  88 0.03667  0.0007461  49.14444  13.161  6.54x10-5 0.086  0.19 
 6.  55 to 60  78 0.03250  0.0009032  35.98317  11.108  1.13x10-4 0.126  0.31 
 7.  65 to 80  136 0.05667  0.0022780  24.87562  13.405  2.68x10-4 0.359  0.67 
 8.  85 to 100  80 0.03333  0.0029060  11.47052  3.925  5.24x10-4 0.206  0.88 
 9.  105 to 120  64 0.02667  0.0035340  7.54575  2.341  9.05x10-4 0.212  1.09 
 10.  125 to 140  52 0.02167  0.0041630  5.20458  2.682  1.44x10-3 0.386  1.48 
 11.  145 to 160  29 0.01208  0.0047910  2.52209  0.600  2.14x10-3 0.128  1.61 
 12.  165 to 180  25 0.01042  0.0054190  1.92225  0.613  3.05x10-3 0.187  1.79 
 13.  185 to 200  19 0.00792  0.0060476  1.30906  0.623  4.19x10-3 0.261  2.05 
 14.  205 to 220  11 0.00458  0.0066760  0.68654  0.230  5.58x10-3 0.128  2.18 
 15.  225 to 240  8 0.00333  0.0023040  0.45637  0.036  7.24x10-3 0.026  2.21 
 16.  245 to 260  8 0.00333  0.0079330  0.42019  0.079  9.20x10-3 0.073  2.28 
 17.  265 to 280  7 0.00292  0.0085610  0.34069  0.114  1.15x10-2 0.131  2.41 
 18.  285 to 300  5 0.00208  0.0091890  0.22672  0.032  1.41x10-2 0.046  2.462) 
 19.  305 to 350  12 0.00500  0.0257200  0.19440  0.054  2.24x10-2 0.121  2.58 
 20.  355 to 400  10 0.00417  0.0296500  0.14053  0.016  3.35x10-2 0.055  2.63 
 21.  405 to 450  10 0.00417  0.0335800  0.12408  0.035  4.77x10-2 0.168  2.80 
 22.  485 to 500  8 0.00333  0.0375000  0.08889  0.072  6.54x10-2 0.471  3.27 
 23.  505 to 1000  24 0.01000  0..5910000  0.01692  0.014  5.24x10-1 0.753  4.03 
 24.  1005 to 1500  6 0.00250  0.9837000  0.00254  0.0010  1.77 0.182  4.21 
 25.  1505 to 2000  5 0.00208  1.3760000  0.00151  0.0008  4.19 0.338  4.55 
 26.  2005 to 2500  3 0.00125  1.7690000  0.00071  0.0005  8.18 0.420  4.97 
 27.  2505 to 3000  1 0.00042  2.1620000  0.00019  0.0002  1.41x10+1 0.272  5.24 
 28.  3005 to 4000  0 0.0000  5.5020000  0.00000  0.000  3.35x1 0+1 0.000  5.24 
1) The columns of values 1,2,5,and 8 do not change from test to test  
 
 2)  The boxed value in column 10 is the  value for A 300