The effect of porosity on the strength of foamed concrete
E.P.Kearsley a,P.J.Wainwright b,*
a Department of Civil Engineering,University Pretoria,Pretoria0001,South Africa
b Department of Civil Engineering,University of Leeds,Leeds LS29JT,UK
Received14August2001;accepted20August2001
Abstract
A study has been undertaken to investigate the effects of replacing large volumes of cement on the properties of foamed concrete(up to 75%by weight)with both classified and unclassified fly ash.This is the third paper in a ries;it investigates the relationship between porosity and compressive strength and prents mathematical models that have been developed to describe this relationship.The compressive strength of the foamed concrete was shown to be a function of porosity and age,and a multiplicative model(such as the equation derived by Balshin)was found to best fit the results at all ages up to1year.In addition,it was concluded that the equation derived by Hoff could effectively be ud to predict the compressive strength of foamed concrete mixtures containing high percentages of ash.D
2002Elvier Science Ltd.All rights rerved.空气组成
Keywords:Foamed concrete;Porosity;Compressive strength;Fly ash
1.Introduction
This is the third paper in a ries reporting on the results of an investigation into the effects on the properties of foamed concrete of replacing large volumes of the cement with both a classified(pfa)and unclassified(pozz-fill)fly ash.The first paper[1]reported on the effects on the compressive strength,while the cond[2]on the relation-ship between porosity and permeability.This third paper investigates the relationship between porosity and compres-sive strength and prents mathematical models that have been developed to describe this relationship.The main aim of this part of this study was to investigate what effects the addition of the foam had on porosity and its relationship with strength.
The strength and porosity of foamed concretes with different casting densities were compared to tho of cement pastes with different water/cement ratios.Different percentages of both pfa and unclassified ash were ud to establish the effect of ash content on the strength–porosity relationship.2.Background
When concrete is fully compacted,the strength is taken to be inverly proportional to the water/cement ratio (Abrams rule)[3].In1896,Rene´Fe´ret formulated the following rule to relate the strength of concrete to the volumes of water,cement and air in the mixture(Eq.(1)): f c¼K
洋湖湿地c
cþwþa
2
ð1Þ
where:f c=concrete compressive strength(MPa);c,w, a=absolute volumetric proportions of cement,water and air;K=a constant.
The strength of concrete is influenced by the volume of all voids in the concrete(entrapped air,capillary pores,gel pores and entrained air)and a number of functions,includ-ing the following,have been propod to express this strength–porosity relationship[4,5](Eqs.(2)–(5)):
f c¼f c;0ð1ÀpÞnðBalshinÞð2Þf c¼f c;0eÀk;pðRyshkevitchÞð3Þf c¼k s ln
p0
p
ðSchillerÞð4Þ
*Corresponding author.Tel.:+44-113-233-2294;fax:+44-113-233-
2265.
E-mail address:p.j.wainwright@leeds.ac.uk(P.J.Wainwright).
Cement and Concrete Rearch32(2002)233–239
0008-8846/02/$–e front matter D2002Elvier Science Ltd.All rights rerved.
PII:S0008-8846(01)00665-
2
f c¼f c;0Àk H pðHaslmannÞð5Þwhere:f c=compressive strength of concrete with porosity p;
f c,0=compressive strength at zero porosity;p=porosity (volume of voids expresd as a fraction of the total concrete volume);n=a coefficient,which need not be constant; p0=porosity at zero strength;k r,k s,k H=empirical constants.
Ro¨ßler and Odler[4]determined the relationship between porosity and strength for a ries of cement pastes with different water/cement ratios after different periods of hydration.They concluded for porosities between5%and 28%that although all four of the strength–porosity equa-tions shown above could be ud,the relation between compressive strength and porosity can best be expresd in the form of a linear plot.Fagerlund[5]stated that it often ems as if one equation fits experimental data for porosities below a certain limiting porosity and another for porosities above this limit.At high porosities,it is normally necessary to u an equation,which indicates a critical porosity while the equations are too innsitive to change for u with low porosities.An equation that takes into consideration the effect of high as well as low porosity will include a critical porosity as well as a stress concentration factor.
After studying aerated concrete manufactured at factories in China,Baozhen and Erda[6]concluded that the com-pressive strength decreas as the porosity increas with the same relationship as indicated in the strength–porosity equation derived by Balshin(Eq.(2)).It was found that n varied from1to2.2in different ranges of porosity,indicat-ing that the strength of mixtures with low porosity was influenced more by small changes in porosity than the strength of mixtures with higher porosity.
Hengst and Tressler[7]concluded that the dominant parameter in controlling the strength of a foamed
Portland cement at a given bulk density is the flaw size,which correlates with the pore size.
Hoff[8]conducted rearch on the porosity–strength relationship of cellular concrete and concluded that there is a single strength–porosity relationship for given cement and this relationship can be expresd in terms of water/ cement ratio and density.Hoff[8]expresd the theoretical porosity of cellular concrete containing only water,cement and foam as the volume of voids as a fraction of the total volume.He ud an average value of0.2for the ratio of the water bound by hydration to cement(by weight)and derived the following equation:
n¼1Àd cð1þ0:20p cÞ
ð1þkÞp c g w
心情造句
ð6Þ
where:n=theoretical porosity;d c=concrete density; p c=specific gravity of the cement;g w=unit weight of water;k=water/cement ratio(by weight).
In the design of foamed concrete,the u of the space occupied by the evaporable water plus the air void space as the total void space in the concrete permits the determina-tion of a single strength–por
osity relationship for a given cement.The strength of cellular concrete in relation to any given cement can,according to Hoff,be expresd using the following equation:
s y
s0
¼
d c
1þk
b1þ0:2p
c
p c g w
b读书之人
ð7Þ
where:s y=compressive strength;s0=theoretical paste strength at zero porosity;k=water/cement ratio(by weight); p c=specific gravity of the cement;d c=concrete density;
g w=unit weight of water;b=empirical constant.
This equation does,however,only hold true for foamed concrete containing only air,water and cement.Adjustment will be required if additional components,such as fillers,are ud.Hoff evaluated bag-cured samples manufactured using different cements with water/cement ratios varying from 0.66to1.06and casting densities varying from320to1000 kg/m3.The analysis produced values of s0=245MPa and b=2.7with a correlation coefficient of.95for cement with a Blaine fineness of between4500and4650cm2/g.
3.Experimental procedure
3.1.Mix compositions
Foamed concrete is produced under controlled condi-tions from cement,filler,water and a liquid chemical that is diluted with water and aerated to form the foaming agent.The foaming agent ud was‘‘Foamtech,’’consist-ing of hydrolyzed proteins and manufactured in South Africa.The foaming agent was diluted with water in a ratio of1:40(by volume),and then aerated to a density of 70kg/m3.
The cement ud in this investigation was rapid hard-ening Portland cement(RHPC)from Pretoria Portland Cement(PPC),Hercules,Pretoria.Both the fly ashes ud were obtained from the Lethabo power station in South Africa.One was a graded ash(pfa),which was screened to remove some of the larger particles(thus reducing the particles larger than45m m in diameter to less than 12.5%),and the cond was an unclassified ash(pozz-fill). The chemical properties of all three binders are shown in Table1.
The compositions by mass of the different mixtures cast are shown in Table2;a total of27mixes were made as summarid below:
Cement pastes with water/cement ratios of0.3,0.4and
0.6;
Paste mixtures in which50%,66.7%and75%of the cement(by weight)was replaced with pfa and pozz-fill (ash/cement ratios of1,2and3).The water/binder ratio was kept constant at approximately0.3;and
E.P.Kearsley,P.J.Wainwright/Cement and Concrete Rearch32(2002)233–239 234
Foamed concrete mixtures of different casting den-sities(1000,1250and1500kg/m3)with differ-ent per
centages of ash replacement(50%,66.7% and75%).
More details relating to the materials ud and casting procedure can be found in the previous publications[1,9].3.1.1.Compressive strength
The compressive strength of foamed concrete was deter-mined from100-mm cubes,which were cast in steel moulds,demoulded after24±2h,wrapped in polythene and kept in a constant temperature room at22±2°C up to the day of testing.The compressive strengths recorded are the average of three cubes.The cement paste cubes were
Table1
Binder properties
Oxides RHPC from
PPC Hercules(%)
世界十大灾难Procesd fly ash(pfa)from
Lethabo(%)
新年布置图片
Pozz-fill from
Lethabo(%)
CaO61.7 4.7 5.0 SiO221.253.954.8 Al2O3 4.633.531.7 Fe2O3 1.8 3.7 3.8 Na2O0.10.70.8 K2O0.70.70.8 MgO 4.3 1.3 1.11 SO3 2.00.10.3 CO2 2.6
Free CaO 1.2
Loss on ignition0.80.8 Blaine surface area(m2/kg)431350280 Particles>45m m(%)839 Calculated surface area(m2/kg)408540 Table2
Mix proportions and hardened concrete properties
Mix number Type
of ash
Target density
多打折(kg/m3)a/c w/c w/binder
Compressive strength
(365days)(MPa)
Measured porosity
(365days)(%)
Dry density
(kg/m3)
Saturated density
(kg/m3)
1none full00.300.3085.428.21958.32057.5
2none full00.400.4078.931.01817.31968.5
3none full00.600.6046.737.21450.31753.0
4pfa full10.600.3080.329.81751.01920.0
5pfa full20.860.2981.527.01715.51889.5
6pfa full3 1.170.2958.130.61570.81819.0
7pfa150010.600.3039.543.31287.31530.5
8pfa150020.860.2935.643.61273.31509.5
9pfa15003 1.170.2936.143.11274.31531.5
10pfa125010.600.3019.848.41055.81304.5
11pfa125020.860.2918.452.51023.51254.0
12pfa12503 1.170.2919.149.51040.81318.5
13pfa100010.600.309.259.3833.01079.0
14pfa100020.860.298.662.6820.81064.5
15pfa10003 1.170.297.161.9810.01111.0
16poz full10.600.3093.431.71695.51871.5
17poz full20.860.2978.731.61561.01800.0
18poz full3 1.170.2963.133.21524.51789.0
19poz150010.600.3037.043.01341.51545.5
20poz150020.860.2941.341.11327.01537.5
21poz15003 1.170.2938.838.21308.51560.5
22poz125010.600.3019.850.01058.01303.0
23poz125020.860.2919.851.11055.01281.0
24poz12503 1.170.2917.648.31014.01280.5
25poz100010.600.297.058.7823.51097.5
26poz100020.860.297.560.6849.51088.0
27poz10003 1.170.29 5.862.6772.51023.5红糖姜水怎么煮
E.P.Kearsley,P.J.Wainwright/Cement and Concrete Rearch32(2002)233–239235
crushed on a standard cube press,but as the foamed concrete strengths were relatively low,the cubes were crushed on a more nsitive machine with a50-MPa capacity and recorded to the nearest0.1MPa.Cubes were crushed after7,28,56,84,168,270and365days.
3.1.2.Porosity
The porosity of the foamed concrete was determined using the Vacuum Saturation Apparatus as developed by Cabrera and Lynsdale[10]at the University of Leeds[11]. Porosity measurements were conducted on slices of68-mm diameter cores that were drilled out of the centre of a100-mm cube.The slices were dried at100±5°C until constant weight had been achieved and were then placed in a desiccator under vacuum for at least3h,where after the desiccator was filled with de-aired,distilled water.The porosity was calculated using the following formula[10] (Eq.(8)):
P¼ðW satÀW dryÞ
ðW satÀW watÞ
Â100ð8Þ
where:P=vacuum saturation porosity(%);W sat=weight in air of saturated sample;W wat=weight in water of saturated sample;W dry=weight of oven-dried sample.
4.Results
Details of mix proportions and lected hardened con-crete results are shown in Table2.The porosity of the foamed concrete is the sum of the air voids and the voids in the paste.The relationship between dry density and porosity is shown in Fig.1from which it can be en that porosity is largely dependent on dry density and not on ash type or ash content.The porosities vary between29%(for cement paste with a water/cement ratio of0.3)and67%(for foamed concrete with a casting density of1000kg/m3and a pfa/ cement ratio of3).The lowest porosity,at29%,was measured for the cement paste with a water/cement ratio of0.3containing no ash.The cement paste with a water/ cement ratio of0.6had a porosity of40%,which is virtually the same as the porosity of the foamed concrete mixtures with a casting density of1500kg/m3and an ash/cement ratio of3.
4.1.Effect of porosity on compressive strength
The relationship between measured porosity and the compressive strength(after1year)of foamed concrete is shown in Fig.2.From this graph,it can be en that the relationship is not significantly influenced by the u of pfa or pozz-fill.Mixtures with an ash/cement ratio of2em to yield marginally higher strengths for a given porosity and mixtures with no ash or an ash/cement ratio of3em to yield marginally lower strengths for a given porosity.The differences are,however,only small and it can be concluded that for the results available,the volume of ash ud does not significantly influence the porosity–strength relation-ship of foamed concrete.
Ro¨ßler and Odler[4]ud four expressions that had been derived by other workers to express the relationship between porosity and compressive strength of porous solids. They determined the optimum values of the constant terms and sought the equation that best expresd the existing relationship between strength and total porosity for their t of Portland cement pastes.
The same procedure was ud to determine whether the equations could be ud to express the relation between porosity and strength of the author’s
foamed
Fig.1.Porosity as a function of dry density.
E.P.Kearsley,P.J.Wainwright/Cement and Concrete Rearch32(2002)233–239
236
concrete mixtures with high ash contents.The results in Table3indicate that for the1-year results,any one of the four equations can be fitted,resulting in a relatively strong relationship between the compressive strength and the porosity of the foamed concrete.While Ro¨ßler and Odler [4]concluded that the linear relation(Haslmann)fits their results best,the author’s results are best fitted to an exponential function(Ryshkevitch).The solid line in Fig.2 fits the exponential function(f c=981eÀ7.43p)as shown in Table3.The porosities of the cement pastes analyd by Ro¨ßler and Odler were below0.3(30%),while the porosities of the authors’foamed concrete samples were as high as0.66(66%).From Fig.2,it can be en that a linear function would fit the foamed concrete mixtures with lower porosities(say below0.4)and the results do therefore em to concur with the conclusions drawn by Ro¨ßler and Odler.
The multiplicative model(Balshin),fitted as shown in Table3,has a power of3.6,which is much higher than the values of up to 2.2calculated for aerated concrete by Baozhen and Erda[6].The fact that the authors’investiga-tion contains data with a larger spectrum of porosities as well as higher strengths could explain this difference.For the foamed concrete mixtures ud in this investigation,the strength–porosity equation fitted using an exponential func-tion best explains this relationship with a high correlation coefficient of.967.
All the authors’foamed concrete strengths and porosities ud to fit the functions were,however,measured1year after casting.The compressive strength of the mixtures incread significantly between28and365days,while bad on literature reviewed[12,13],it was assumed that the change in porosity during this period would be negli-gible.The equations as fitted can therefore only be valid for the1-year results and another factor will have to be added to the equation,taking time since casting into account.When the equations shown in Table3are fitted for strengths at different ages,the equation derived by Balshin gives the best result for the combination of all ages.The effect of age can be taken into account by taking the equation as derived by Balshin(Eq.(2))and expanding it to u a variable strength at zero porosity(changing s0to a function of time instead of using the fixed value of321that was derived for the1-year strengths).Fitting a multiplicative model through linear regression results in the following:
f c¼39:6ðlnðtÞÞ1:174ð1ÀpÞ3:6ð9Þwhere:f c=compressive strength of foamed concrete(MPa); t=time since casting(days);p=mature porosity(measured after365days).
The R2statistic indicates that this model,as fitted, explains89.6%of the variability in compressive strength.
A correlation coefficient of.946indicates a relatively
strong
Fig.2.Effect of porosity on compressive strength at1year.
Table3
Equations for the strength–porosity relationship of foamed concrete
Authors’foamed concrete
Equation Equation fitted by Ro¨ßler and Odler Equation fitted R2Correlation coefficient Balshin s c=540(1Àp)14.47f c=321(1Àp)3.6.926.962
Ryshkevitch s c=636eÀ17.04p f c=981eÀ7.43p.936.967
Schiller s c=81.5Ln(0.31/p)f c=109.5Ln(0.66/p).89.943
Haslmann s c=158À601p f c=147À226p.848.921
E.P.Kearsley,P.J.Wainwright/Cement and Concrete Rearch32(2002)233–239237
