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Construction and Building Materials 73 (2014) 271–282
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Construction and Building Materials
journal homepage: www.elsevier .com/locate /conbui ldmat
A modified method for the design of pervious concrete mix
http://dx.doi.org/10.1016/j.conbuildmat.2014.09.0880950-0618/� 2014 Elsevier Ltd. All rights reserved.
⇑ Corresponding author.E-mail address: [email protected] (N. Sebaibi).
Dang Hanh Nguyen a,b, Nassim Sebaibi a,⇑, Mohamed Boutouil a, Lydia Leleyter b, Fabienne Baraud b
a Ecole Supérieure d’Ingénieurs des Travaux de la Construction de Caen (ESITC-Caen), 1, rue Pierre et Marie Curie, 14610 Épron, Franceb Normandie University, France, UCBN UR ABTE EA 4651, QALEA, F-14032 Caen, France
h i g h l i g h t s
� The new mix design method for pervious concrete is based on the excess paste theory.� The w/c, cement, aggregate content and the compaction energy were determined.� The permeability of concrete is always sufficient to drainer the rainwater.
a r t i c l e i n f o
Article history:Received 7 April 2014Received in revised form 22 September2014Accepted 25 September 2014
Keywords:Pervious concreteExcess pasteScaling factorBinder drainage test
a b s t r a c t
As a new material type for pavement, pervious concrete should be designed to maintain both porosityand the structural strength. The actual mix proportions for pervious concrete depend on the application,the mechanical properties required and the materials used. Actually, the mix proportions of pervious con-crete were determined for locally available materials based frequently on trial batching and experience.Another analytical method should be developed to facilitate the concrete producers. Based on theassumption that the cement paste only plays a role of coating, it does not fulfill the void among the grainsof gravel; this paper focuses on one modified method for the design of the pervious concrete. The volumecement paste is divided by the surface area of the aggregates to determine the thickness of the excesspaste. A scaling factor has been defined to evenly distribute the cement paste toward the size of gravel.Moreover, a binder drainage test is proposed to determine the critical w/c ratio towards to prevent theflow of cement paste to the lower layers of concrete under the action of vibration or compaction. Thepervious concrete has been formulated according to this method to validate it. The mechanical andhydraulic tests are performed to characterize the pervious concrete. The obtained pervious concretepresents a large sufficient permeability (1 mm s�1) for draining rainwater and good mechanicalresistance (Rc = 28.6 MPa) with regard to typical pervious concrete applications such as parking lots,walkways and low-traffic roadways. In addition, the mechanical strength of pervious concrete in thisresearch is found higher than that generally reported by other authors. The results indicate that the the-oretical mix design method is a successful theory for an optimizing composition of pervious concrete.
� 2014 Elsevier Ltd. All rights reserved.
1. Introduction adjusted. This brings the phenomenon of greenhouse and hot
With the population growth and the continual urbanization, ourcities are being covered with the impervious surface areas such asresidential and commercial buildings. Because of the lack of waterand air permeability of the common concrete pavement, the stormwater is not filtered underground, the runoff is rapidly increased.Therefore, the drainage system gets overloaded and flash floodingbecomes inevitably. In addition, with the impervious surface, it isdifficult for soil to exchange heat and moisture with air; therefore,the temperature and humidity of the Earth’s surface cannot be
land effects in city. At the same time, the plash on the road duringa rainy day reduces the safety of traffic of vehicle and footpassenger [1].
In civil engineering, the decrease of the ground water level cancause subsidence of soil of several meters, deconstruct buildings,structures and works.
Pervious concrete (PC) is a special type of concrete withcontinuous porosity ranged from 15% to 35% and the presence ofinterconnected large pores system allows the water flow easilythrough the pervious concrete [2–6]. In recent decades, the useof pervious concrete for the construction of secondary roads,parking lots, driveways, walkways and sidewalks is increasingcontinuously because of its various environmental benefits suchas [1–4]:
Nomenclature
a (%) percentage of aggregate larger than 80 lm in the aggre-gate mixture
b (%) absorption of aggregate (sand included)C (kg m�3) Ciment contentDi (m) average diameter of aggregate of the class iDp (mm) diameter characteristic of poresei (m) thickness of the layer of the excess paste covering grain imG (kg) weight of aggregate in on meter cubic of concretek (–) a scaling factormi (kg) mass of size Di aggregate grainNi (nbr) number of size Di aggregate grains of the class iN (nbr) number of particle aggregate in concretePt (%) total porosity of concretePp (%) porosity of cement pasteP0 (%) initial porosity of cement pasteQ (%) void content of dry compacted aggregateRc (MPa) compressive strength at 28 daysRt (MPa) tensile strength at 28 daysS (m2) total surface area of the grains aggregate in the mixtureS⁄ (m2) total surface area of the grains average of diameter
di + ei/2Si (m2) surface of grain size Di
Ssi (m2 kg�1) specific surface of aggregates of class i in themixture
Vfines (m3) volume of fines in concrete
VG (m3) solid volume of aggregateVG>80 (m3) volume of a greater than 80 lm aggregateVP (m3) volume of cement pasteVPC (m3) volume of compact pasteVPE (m3) volume of excess pasteVi (m3) volume of a size Di grainVv (%) volume of void in concreteVtotal (m3) total volume of concreteVW/G (m3) volume of the water retained by the aggregateW (kg m�3) quantity of water in concreteu ratio between total volume of void and total solid
volume of concretex ratio between aggregate volume and total solid volume
of concretea degree of hydration of cementa (1) degree of hydration of cement at infinite timeb (–) factor definiteqdry,compacted (kg m�3) dry, compacted bulk density of the
aggregateqspecify (kg m�3) specify bulk density of the aggregateqC (kg m�3) specify density of cementqW (kg m�3) specify density of waterc (–) compactness of aggregatew/c ratio of the weight of water to the weight of cement
272 D.H. Nguyen et al. / Construction and Building Materials 73 (2014) 271–282
1. The storm water can rapidly filtered into soil, and the ground-water resources can recharge.
2. The surface is air and water permeable and the soil below canbe kept wet. It improves the environment of road surface.
3. The pervious concrete pavement can absorb the noise of vehi-cles, which creates quiet and comfortable environment.
4. The pervious concrete pavement materials have holes that cancumulate heat. The pavement can adjust the temperature andhumidity of the Earth’s surface and eliminates the phenomenonof hot island in cities.
Since its various environmental benefits, pervious concrete isone of the most important emerging technologies for sustainablefacilities and infrastructure. Therefore, pervious concrete is recog-nized as the best solution for storm water management and one ofthe key elements of sustainable development by US EnvironmentalProtection Agency [2,3].
The mix design of pervious concrete is different from the con-ventional one. The materials mix design of PC is composed of Port-land cement, uniform coarse aggregate (allowing relatively littleparticle packing), approximately 7% fine aggregate by weight oftotal aggregate and water. The addition of a small amount fineaggregate as sand provided additional compressive strength, betterdurability and high resistance to freeze/thaw cycles. Generally,pervious concrete mix consists of 270–415 kg m�3 of cement,1190–1480 kg m�3 of aggregate and water to cement ratio rangedfrom 0.27 to 0.40. The typical 28-day compressive strength rangesfrom 3.5 to 28.0 MPa and permeability coefficient varies from 0.2to 5.4 mm s�1 [2,3]. Additionally, the characteristic pore sizesrange from 2 to 8 mm depending on the type of aggregates andthe method of compaction [2,7].
Many previous studies have reported the proprieties of perviousconcrete in varying the water-to-cement ratio, aggregate-to-cement ratio, aggregate sizes, binder material type or effects of com-paction energy [1–8]. However, the number of publications on themethod for the design of pervious concrete mix is very limited.
There can be mentioned here the American concrete institutemethod [2], Zouaghi’s method [8] and Zheng’s method [9]. More-over, these design methods are not complete; they present manydisadvantages, as shown in Table 1. For example, they do not indi-cate how to determine the w/c ratio or they do not take into accountthe effect of compaction on the properties of concrete, etc.Therefore, there are no recognizing methods to establish the mixdesign of pervious concrete at the present time, the pervious con-crete mixture proportions are always selected from experimentalstudies [3].
2. Principal of the proposed mix proportioning method
In this paper, a modified method is proposed for mix design ofPC. This method is based on the quantification of the layer ofcement paste coating the gravel and on the assumption that thecementious paste act only as a coating; it does not fulfill the voidamong the grains of gravel. This method of mixture proportioningis divided into three steps: the determination of aggregate volume,cement paste volume and water–cement ratio.
2.1. Determination of aggregate volume
Aggregate occupies most of the pervious concrete’s volume andis the principal load-bearing component. In this section, fourhypotheses were adopted for the determination of aggregatevolume.
Hypothesis #1. To facilitate the calculation, the aggregate isassumed of spherical shape. Only a perfect sphere can be charac-terized by a single value of size which is the diameter. The purposeof this equivalent sphere hypothesis is to describe an object inthree dimensions by a single value.
Fig. 1 shows the components of ordinary concrete in whichaggregates are spaced by the cement paste. Assuming that, theaggregates are compacted at maximum to have the solid volume
Table 1Synthesis of mix design methods from literature.
Method ACI [2] Method Zouaghi [8] Method Zheng et al. [9]
Input – Physical properties of aggregates– Dry-rodded volume of coarse aggregate in
a unit volume of concrete– Porosity selected that fulfills the required
function of the application desired
– Physical properties of aggregates– Porosity selected that fulfills the
required function of the applica-tion desired
– Physical properties of aggregates– Compressive strength and permeability to water neces-
sary that fulfills the required function of the applicationdesired
Output – Cement paste content– Aggregate content– Fines content
– Cement content– Water content– Coarse aggregate content
– Cement content. Water content– Coarse aggregate content
Advantage – Simple – Very simple – Simple
Disadvantage – Database of dry-rodded volume of coarseaggregate in a unit volume of concrete islimited
– No indicator on w/c ratio– The weight per cubic of components is not
accordance with experimental workspublished
– Non-take account the effect of compaction– A correction step through experimentation
is necessary to adjust the composition
– Relationship between w/c and C isapplied for locally gravel
– Coarse aggregate content deter-mined is not realistic
– Non-take account the effect ofcompaction
– A correction step through experi-mentation is necessary to adjustthe composition
– Relationships among parameters are applied for locallygravel
– Relations are derived from data obtained on the perviousconcretes very low resistance
– Need both of permeability and compressive strength asinput data
– Coarse aggregate content determined is not realistic– Non-take account the effect of compaction– A correction step through experimentation is necessary
to adjust the composition
Compaction
VPE
VPC
VG
Fig. 1. Model of a concrete structure.
D.H. Nguyen et al. / Construction and Building Materials 73 (2014) 271–282 273
of aggregate (VG), the excess paste (VPE) which covers aggregatesand the compact paste (VPC) which fill the voids of the skeleton thatcan be extracted separately.
Hypothesis #2. The thickness of the excess paste layer isnegligible when compared to the size of the coarse aggregate.Thus, the presence of this excess paste layer does not influence thevoid volume among the grains of aggregate (intergranular air void).This void will be filled with the compact paste (Fig. 2). Thus, thevolume of compact paste VPC is considered equally to the volume ofspace between dry and compacted grains aggregate VV.
Considering a dry, compacted volume of aggregate Vtotal, thevolume of compact paste VPC can be calculated as:
VPC ¼ VV ¼ Vtotal � VG ð1Þ
VPC ¼VG
c� VG ¼ VG
1� cc
ð2Þ
Aggregates
Void
Excess paste
Compact paste
Thicknessof excesspaste
Adding paste
Fig. 2. Illustration of the theory of excess paste.
Eq. (2) allows determining the volume of compact paste fromthe volume of gravel in the concrete matrix, which can also bewritten as:
VPC ¼ Vtotal � VG ¼mG
qdry;compacted� mG
qspecifyð3Þ
VPC ¼VG � qspecify
qdry;compacted� VG ¼ VG
qspecify
qdry;compacted� 1
!ð4Þ
On the other hand, it is noted that the sum of volumes ofcement paste VP, of granular solid VG, of the water retained bythe aggregate VW/G and of the voids VV form a unit volume ofpervious concrete:
VP þ VG þ VW=G þ VV ¼ 1 ð5Þ
where VP ¼ VPE þ VPC ð6Þ
Then VPE þ VPC þ VG þ VW=G þ VV ¼ 1 ð7Þ
For a given particle size, the volume of aggregates larger than80 lm VG>80 is related to the total volume of the aggregate VG bythe factor ‘‘a’’:
VG>80 ¼ VG � a ð8Þ
with a 6 1.VG>80 is the volume of aggregates larger than 80 lm, which is
surrounded by the suspension consisting of cement paste and finesmaller than 80 lm. In fact, the aggregate can be decomposed intotwo parts depending on the size of the particles. The first part com-poses the fines, smaller than 80 lm, and they are in the same ordersize of the solid components in the cement paste (cement and fil-ler). The second part is thus formed by aggregates larger than80 lm, denoted as G > 80. This threshold value (80 lm) allows con-sidering that smaller particles cover the larger particles. In the cal-culation of the thickness of the paste in excess, it is assumed thatthe paste consists only of particles of size smaller than 80 lm.
Thus the total volume of aggregates VG is written:
VG ¼ Vfines þ VG>80 ð9Þ
Similarly, the volume of water absorbed VW/G is proportional tothe total aggregate through an absorption coefficient of aggregate‘‘b’’, and it is determined using Eq. (10):
e1
e2
e3
D1
D2
D3
Fig. 4. Thickness of excess paste proportional to the diameter.
274 D.H. Nguyen et al. / Construction and Building Materials 73 (2014) 271–282
VW=G ¼ VG � b ¼ VG>80
a� b ¼ b
a� VG>80 ð10Þ
From Eqs. (2), (7), (8) and (10), the volume of excess paste VPE
can be obtained from Eq. (11):
VPE ¼ 1� VV � VG>80baþ 1
ac
� �ð11Þ
For a grain of aggregate size Di coated by a layer thickness ei
(Fig. 3), the volume of excess paste is:
VPEi ¼p6
Di þ 2eið Þ3 � p6
Dið Þ3 ð12Þ
For all grain of aggregate:
VPE ¼Xn
i¼1
p6
Di þ 2eið Þ3 � p6
Dið Þ3h i
Ni ð13Þ
Hypothesis # 3. The thickness of the excess paste is not the samefor different aggregates sizes, but it is proportional to the size ofthe aggregate (see Fig. 4). A scaling factor can be defined betweenthe diameter of raw aggregate diameters and that of the aggregatecovered. Indeed, the coarse aggregates have overall surface areasmaller than the small aggregates; therefore, for the same volumeof excess paste, the thickness of paste is more important when theparticle of aggregate is large.
In that case, for a class i of aggregates size Di, the thickness ofthe excess paste ei:
D1 þ 2e1
D1¼ D2 þ 2e2
D2¼ � � � ¼ Di þ 2ei
Di¼ � � � ¼ Dn þ 2en
Dn¼ k ð14Þ
From Eqs. (13) and (14), the coefficient k can be deduced by Eq.(15):
k ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þ 6VPE
pPn
i¼1Ni � D3i
3
s¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þ VPE
VG>80
3
sð15Þ
From Eqs. (15) and (11), the volume of aggregates larger than80 lm VG>80 can be deduced as Eq. (16):
VG>80 ¼1� VV
k3 � 1þ 1acþ b
a
ð16Þ
From Eqs. (8) and (16), the total volume of the aggregate VG canbe calculated as Eq. (17):
VG ¼1� VV
a k3 � 1� �
þ 1c þ b
ð17Þ
Eq. (17) is for calculating the amount of aggregate in presence ofcompact paste in the matrix of concrete.
Hypothesis #4. For pervious concrete, a composition is ideal when(Fig. 5):
Di
Di + 2ei
ei
Fig. 3. Thickness of excess paste.
– the aggregates are just covered with the excess paste to have asufficient strength,
– the space between the aggregates is kept empty so that watercan pass through the matrix.
A composition is defined as ‘‘good’’ when the aggregates arecoated with a layer of thickness ei from the excess paste, and thevolume of a compact paste is zero:VPC ¼ 0 ð18Þ
From Eqs. (6), (18), and (7) can be rewritten:VPE þ VG þ VW=G þ VV ¼ 1 ð19Þ
From Eqs. (10) and (19), the volume of excess paste VPE can bededuced as Eqs. (20) and (21):
VPE ¼ 1� VV � VG � VG � b ð20Þ
VPE ¼ 1� VV � VG � ð1þ bÞ ¼ 1� VV � VG>80 �1aþ b
a
� �ð21Þ
According to Eq. (15), the parameter k can be written as follow:
k3 ¼ 1þ VPE
VG>80ð22Þ
Therefore:
VPE ¼ ðk3 � 1ÞVG>80 ¼ ðk3 � 1Þ � VG � a ð23Þ
From Eqs. (21) and (23), the amount of aggregate can be deter-mined as following equations:
ðk3 � 1ÞVG>80 ¼ 1� VV � VG>801aþ b
a
� �ð24Þ
1� VV ¼ k3 � 1þ 1aþ b
a
� �� VG>80 ð25Þ
VG>80 ¼1� VV
k3 � 1þ 1a þ b
a
ð26Þ
VG ¼1� VV
a� ðk3 � 1Þ þ 1þ bð27Þ
Eq. (27) is used to calculate the amount of aggregate on theassumption that the compact paste volume is zero.
Excess paste
Aggregate
Void
Fig. 5. Model of the matrix of pervious concrete.
D.H. Nguyen et al. / Construction and Building Materials 73 (2014) 271–282 275
Concerning the quantity of sand, the effect of using sand in per-vious concrete mixes was investigated by many studies [3,10,11]and all of these studies showed that the replacement of 7% byweight of the coarse aggregate with sand brought significantincreases to strength and the best performance to the freeze thawcycles. It is the reason why the percentage of sand is fixed at 7% byweight of the coarse aggregate in this method.
2.2. Determination of cement paste volume
Cement paste coats the aggregate particles, providinglubrication for workability, and hardened contact area for loadtransfer. As more cement paste is incorporated, the mixturebecomes more workable, although reducing porosity. In thismethod of mixture proportioning, to obtain the content of cementpaste, it is necessary to determine the total surface area ofaggregate and the paste layer thickness.
2.2.1. Determination of total surface area of aggregateThe specific surface area of an aggregate corresponds to the
total surface of the grains obtained by assimilating them to thespheres of average diameter Di and an absolute density qspecific.
Consider the class i whose average size is Di. The surface of eachgrain is:
Si ¼ pD2i ð28Þ
The volume of each grain is:
Vi ¼pD3
i
6ð29Þ
The mass of each particle is:
mi ¼ qspecify � Vi ð30Þ
The amount of aggregate in pervious concrete being mG, thenumber of particle aggregates in concrete is:
N ¼ mG
mið31Þ
Total surface area of aggregate in concrete:
S ¼ N � Si ¼mG
mi� pD2
i ¼mG
qspecifypd3
i6
� pD2i ¼
6mG
Di � qspecifyð32Þ
Sphere ofdiameter Di
eiei Di
Sphere ofdiameter Di+ei
Sphere ofdiameter Di+2ei
Excess paste
Aggregate
Fig. 6. Scheme of grain aggregate covered by cement paste.
2.2.2. Determination of cementitious paste volumeThe volume of cement paste in concrete can be calculated by:
VP ¼CqCþ W
qWð33Þ
where qC and qW are respectively the density of cement and ofwater.
For an aggregate with diameter Di, the cementitious paste issupposed to distribute regularly and will act only as the excesspaste. The thickness of the excess paste is ei. The thickness ei canbe calculated by Eq. (34):
ei ¼VP
Sð34Þ
From Eq. (14), it can be written as:
k ¼ Di þ 2ei
Dið35Þ
When the value of k is obtained, the thickness corresponding ofexcess paste ei can be determined for each aggregate size Di:
ei ¼Diðk� 1Þ
2ð36Þ
According to Eqs. (32), (34) and (36), the volume of the pastecan be deduced as follow:
VP ¼3mGðk� 1Þ
qspecifyð37Þ
To be more precise, the thickness of the cement paste can berecalculated by converting the following scheme (Fig. 6). In thiscase, the thickness of the cement pastes:
ei ¼VP
S�ð38Þ
VP ¼ S� � ei ¼ SDi þ ei
Di
� �2
� ei ð39Þ
VP ¼3mG � ðk� 1Þ
qspecify
Di þ ei
Di
� �2
ð40Þ
Vp ¼3ð1� VV Þ � ðk� 1Þa� ðk3 � 1Þ þ 1þ b
� Di þ ei
Di
� �2
ð41Þ
Then, the volume of paste is rewritten as:
Vp ¼ b� ð1� VV Þ ð42Þ
With:
b ¼ 3ðk� 1Þa� ðk3 � 1Þ þ 1þ b
� Di þ ei
Di
� �2
¼ 3ðk� 1Þa� ðk3 � 1Þ þ 1þ b
� kþ 12
� �2
ð43Þ
2.2.3. Determination of excess paste layer thickness ‘‘ei’’The thickness of the layer of cement paste ei may be determined
by dividing the paste volume by the total area of gravel (Eq. (34)).Furthermore, the thickness ei can be determined according to theexpression of Weymouth which is usually applied for a hydraulicconcrete [12]:
ei ¼12
1þ Q x
1þ Q
� �1=3
� 1
" #Di ð44Þ
Q: void content of dry compacted aggregate; Q can be calculated byfollow:
Q ¼ 1�qdry;compacted
qspecifyð45Þ
Qx ¼1þ u
x� 1 ð46Þ
u: total void volume/total solid volume,x: aggregate volume/total solid volume,
Table 2Coefficient k calculated according to Deo et al. for concrete mix design [16].
Coefficient k Mix No1 Mix No2 Mix No3
According to Eq. (39) 1.1173 1.1175 1.1177According to Eq. (54) 1.11876 1.128 1.1185
276 D.H. Nguyen et al. / Construction and Building Materials 73 (2014) 271–282
u ¼ VV
Vsolidð47Þ
x ¼ VG
Vsolid total¼ VG
VG þ VE þ VC¼ VG
VG þ VPð48Þ
From Eq. (44), it can be written as:
Di þ 2ei
Di¼ 1þ Q x
1þ Q
� �1=3
ð49Þ
k ¼ 1þ Q x
1þ Q
� �1=3
ð50Þ
The value k varies among authors. According to [13–16], the coeffi-cient ‘‘k’’ varies from 1.064 to 1.233. See for example in Table 2.
The determination of k plays an important role on the amountof cement in concrete while the cement is the most expensiveconcrete constituent. In addition, the pervious concrete is oftenused for low-load applications which do not need much resistance.So it is better to reduce as much as possible the amount of cementin the mix. Also, from the optimization study of the mix of perviousconcrete achieved in the laboratory, it is noticed that a low value ofk near to 1.116 still carries a good pervious concrete. This valuesimile to the value founded by Deo and Neithalath [16]. Thus, apreliminary study is recommended for k = 1.116.
and the ratioei
Di¼ 0:058 ð51Þ
2.3. Aggregate and cementitious paste amount correction
In the calculation above, the void volume VV is equal to the vol-ume of empty space among the aggregates. Therefore, the porosityof the cement paste is not included in the calculation of voidvolume.
For the total porosity accessible to water assessed byhydrostatic weighing (according to the AFPC-AFREM procedure[17]), this total porosity, denoted as Pt, is the inter-granularporosity + porosity of aggregate + porosity of the cementpaste + porosity of the transition zone. To simplify the calculation,it can be assumed that the total porosity accessible to water is the sumof the inter-granular porosity and the porosity of the cement paste.
For one cement paste, depending on the w/c ratio, the porosityof cement paste can be calculated according to some followingequations [18]:
Total porosity of the cement paste:
Pp ¼ Po � 0:53� a� ð1� PoÞ ð52Þ
Initial porosity of the cement paste Po:
Po ¼Vw
Vw þ Vc¼ w=qw
w=qw þ c=qc¼ w=c
w=c þ 0:32ð53Þ
Degree of hydration of cement a:According to Powers and Brownyard [18], the theoretical
predictable hydration is determined on data of the consumptionof water in the hydration reactions:
If w=c < 0:42 : að1Þ ¼ w=c0:42
ð54Þ
If w=c > 0:42 : að1Þ ¼ 1 ð55Þ
According to Mills [19], the degree of hydration can becalculated from a phenomenological model also based on the w/cratio:
að1Þ ¼ 1:031�w=c0:194þw=c
ð56Þ
According to Waller, one phenomenological model based onexperimental results and a compilation of measurements foundin the literature has been developed [20]:
að1Þ ¼ 1� exp �3:4wc
� �ð57Þ
The void volume of the concrete according to the total porosityof the cement paste:
VV ¼ Pt � Vp � Pp ð58Þ
With Eqs. (43) and (58), the void volume can be written asfollow:
VV ¼ Pt � Vp � Pp ¼ Pt � ð1� VV Þ � b� Pp ð59Þ
Then, the void volume can be deduced as:
VV ¼b� Pp � Pt
b� Pp � 1ð60Þ
and the total porosity is calculated as:
Pt ¼ b� Pp � ð1� VV Þ þ VV ð61Þ
2.4. Determination of w/c ratio by using the binder drainage test
The correct amount of water will maximize the strength with-out compromising the permeability characteristics of the perviousconcrete. Generally a w/c ratio ranging from 0.27 to 0.40 is used forpervious concrete mix design [2,3]. The relation between strengthand w/c ratio is not clear for pervious concrete, because unlike con-ventional concrete, the total paste content is less than the voidscontent between the aggregates. Therefore, making the pastestronger may not always lead to increased overall strength. Watercontent should be tightly controlled. The correct water content hasbeen described as giving the mixture a sheen, without being sosoupy that it flows off the aggregate. From this concept, the binderdrainage test is proposed to determine an appropriate w/c ratiothat will yield a high permeability of pervious concrete,maintaining a good gravel coating to ensure mechanical strength.
To determine the state of drainage of the cement paste with w/c,the ratio between the aggregate volume and the cement pastevolume (VG/VP) is kept constant. For this, it is important to chooseinitially mG/C and w/c in order to have sufficient volume of thecement paste to coat the grains aggregate. Generally, the perviousconcrete has mG/C P 4, therefore, the ratio mG/C = 4 is taken. Ini-tially, the ratio w/c = 0.32 is chosen. This is a typical value of w/cratio of pervious concrete. Indeed, the choice of w/c initial is justto calculate the ratio VG/VP and keep it constant with another w/cratio.
Starting from the choice w/c = 0.32 and mG/C = 4, it can bededuced VG/VP = 2.29 by subtracting the absolute density of cementand aggregate. Table 3 shows the amounts of different materialsfor different w/c ratio for the binder drainage test. The mass ofaggregate in saturated surface dry state for the test is 2500 g.
Protocol of binder drainage test:Test protocol binder drainage is performed according the
following steps, in case w/c = 0.36 (written in bold) from Table 3for example (Figs. 7 and 8):
Table 3Quantities of material using for binder drainage test.
mG (g) w/c C (g) W (g) Total mass VP (L) VG (L) VP/VG VG/VP
2500 0.28 666.7 186.7 3353.4 0.40 0.91 0.44 2.292500 0.30 645.2 193.5 3338.7 0.40 0.91 0.44 2.292500 0.32 625.0 200.0 3325.0 0.40 0.91 0.44 2.292500 0.34 606.0 206.0 3312.0 0.40 0.91 0.44 2.292500 0.36 588.1 211.7 3299.8 0.40 0.91 0.44 2.292500 0.38 571.3 217.1 3288.4 0.40 0.91 0.44 2.292500 0.40 555.4 222.1 3277.5 0.40 0.91 0.44 2.29
Preparation of concrete Vibration of concrete in the sieve
Fig. 7. Binder drainage test.
w/c = 0.36: No cement paste on the sieve
w/c = 0.38: Presence of the cement paste at the bottom of
screen
w/c = 0.40: Presence of large cement paste on the sieve
Fig. 8. Observation of the presence of the cement paste at the bottom of the sieveafter vibration.
Table 4Example of calculation of the specific surface area via the surface area factor [22].
Sieve size(mm)
Cumulative passpercentage (%)
Factor specificsurface
Specific surface area(m2/kg)
(a) (b) (c) (d) = (b) ⁄ (c)
20 0.41 014 0.41 012.5 100 0.41 0.419.5 91.9 0.41 0.376794.75 0.65 0.41 0.0026652.36 0.44 0.82 0.0036081.18 0.43 1.64 0.0070520.425 6.14 00.15 12.29 00.075 32.77 0Sum = 0.80011
D.H. Nguyen et al. / Construction and Building Materials 73 (2014) 271–282 277
� Weigh 2500 g aggregate which the absorption coefficient, thedust content are known.� Weigh 588.15 g of cement and 211.73 g of water.� Mix with a small mixer for 5 min.� Discharge the fresh concrete to a metal sieve. The holes diame-
ter depends on the size of aggregates. Indeed, the choice ofholes diameter is to simulate the pore size of concrete. The poresize of the pervious concrete depending on the size of aggre-gates, as shown in equation [21]: Dp = 1.44 + 0.36 � Di. Forexample, with the average size of 5.125 mm, a sieve with holessize of 3 mm can be used.� Vibrate the metal sieve for 15 s with a vibrating table. The
choice of the vibration time depends on the execution methodused in situ or in the precast plant and is normally longer thanthe time spent on field or in the factory.� Keep an eye on the bottom of the sieve. If a lot of cement paste
sticks to the bottom (the cement paste too liquid), w/c is notappropriate.� Collect the concrete on top layer of fresh concrete in sieve, mea-
suring the weight denoted M1. The top layer of concrete is cho-sen because it shows the amount of cement paste can coat theaggregate under in the compaction effort.� Rinse with water to remove all the fresh concrete cement paste
to avoid lost of grain gravel.� Dry the gravel for 24 h at 105 �C and weigh the mass M2.� By subtracting the content dust, the mass of cement paste coats
the gravel is M3 = M1 � (1 + b/100) �M2.� Calculate the volume of cement paste VP from the mass of
cement paste M3 and the ratio w/c used in the test.� Determinate the thickness of the cement paste e = VP/S. S is the
total surface area of aggregate. S can be determined using thefactor specific surface area of aggregate (Table 4) [22] or canbe calculated assuming the aggregate in spherical form withsize Di.� Calculate the volume content of cement paste from the volume
of aggregate.
In conclusion, with the drainage test, the w/c can be determinedto prevent the flow of cement paste. In addition, it can be used todetermine the amount of cement paste needed to coat the gravel,consequently the content of the cement paste in pervious concrete.
3. Procedures of the proposed mix proportioning method
Proportioning procedure of the proposed method is asfollowing:
1. Required data on coarse aggregate: Gradation, drycompacted bulk density, specify bulk density, absorption,compactness by shake-table compactness testing of LCPC
Table 5Physical and chemical properties of cement CEM I 52.5 R.
Chemical analysis (%) Physical properties
CaO 63.4 Specify gravity (kg m�3) 3140SiO2 19.2 Specific surface Blaine (cm2 g�1) 4900Al2O3 4.5 Compressive strength (MPa)Fe2O3 3.9 2 days 39MgO 1.1 7 days 53SO3 3.5 28 days 64K2O 0.90 Initial setting time (min) 170N2O 0.07Loss on ignition 2.6
Phase composition C3S C2S C3A C4AF68% 9% 6% 13%
1 2 3 4 5 6 7 80
102030405060708090
100
Perc
ent p
assi
ng (%
)
Grain size (mm)
Aggregate 4/6.3 mm
Sand 0/4 mm
Fig. 9. Sieve analyses of aggregate.
278 D.H. Nguyen et al. / Construction and Building Materials 73 (2014) 271–282
[23] in which a pressure of 10 kPa was applied, percentage offines.
2. Select continuous porosity Vv from the application desired ofpervious concrete.
3. Calculate the volume of aggregate according to Eq. (27) withthe value k = 1.116.
4. Calculate the mass of sand and mass of coarse aggregate inassuming the percentage of sand is about 7% of the massof coarse aggregate.
5. Compare the volume of coarse aggregate calculated with thecompactness of coarse aggregate determined by shake-table.If this volume is greater than the compactness, it wouldeither increase the amount of sand or increase the compac-tion pressure (above 10 kPa) during implementation. On theother hand, if the volume is smaller than the compactness, itshould be compacted concrete with a compaction pressureof less than 10 kPa during the placement.
6. Determine the w/c ideal with the binder drainage test. Thistest can be started with w/c = 0.32.
7. Calculate the degree of hydration of cement according to Eq.(54), Eq. (56) or Eq. (57) and the porosity of cement pasteaccording to Eq. (52),
8. Calculate the parameter b according to Eq. (43),9. Calculate the total porosity of concrete Pt according to Eq.
(62),10. Calculate the volume of cement paste and the mass of
cement and water according to Eq. (42),11. Mix and determine the unit weight, total porosity,
continuous porosity, strength and permeability for the levelcompaction determined in step 5,
12. Adjust batch weight or adjust the compaction level.
4. Experimental validation of proposed mix proportioningmethod
4.1. Mix design
In this section, the excess paste theory and binder drainage testwill be used to design one composition of a pervious concrete thatwill provide optimum performance.
4.1.1. k ValueThe value k = 1.116 is used to validate this approach.
4.1.2. Target void volume of concreteFor sufficient permeability, the continuous porosity of pervious
concrete should be higher than 15%. In this work, a continuousporosity of 17.0% is initially chosen.
4.1.3. Materials usedThe cement used in this study is an Ordinary Porland Cement
(OPC) CEM I 52.5 R. The chemical and physical properties of thiscement are summarized in Table 5. This cement contains smallquantities of C3A that reduces its water demand and increasesthe compressive strength at 7 days approximately 80–90% at28 days [4,24,25].
The alluvial quartz sand with a grain size 0/4 mm was used. Thissand presents a specific gravity of 2620 kg m�3, an absorption coef-ficient of 0.50% and a fineness modulus of 2.81. To ensure theinfiltration capacity of pervious concrete, the selection ofmonogranular aggregate (single-sized aggregates) is critical toachieve the interconnection of the porous system [1–4]. Themonogranular angular aggregate fraction 4/6.3 mm was employedwith a specified gravity of 2740 kg m�3, water absorption of 0.48%.The flakiness index of the aggregate 4/6.3 mm is 20.1. The com-pactness of the aggregate obtained by the shake-table compactness
testing under a pressure of 10 kPa is 0.5627. The size distributionof the aggregate 4/6.3 mm and sand 0/4 mm is given in Fig. 9.
4.1.4. Design calculationAccording to previous works, the percentage of sand is 7% by
weight of coarse aggregate allows the balance of the mechanicalstrength and permeability, and give a better resistance againstfreeze/thaw [3,10,12]. In this mix design method, the amount ofsand is 7 wt% of coarse aggregate is always set. From this amount,the average aggregate diameter is 4.79 mm can be easy calculated.
Then, according to Eq. (27), the amount of aggregate required iscalculated: Vg = 0.5920 m3 and the volume of coarse aggregate andsand is respectively 0.5530 m3 and 0.039 m3. Comparing withcompact gravel after compaction under 10 kPa, the volume ofcoarse aggregate is smaller than the compactness of coarseaggregate obtained by shake-table compactness testing. Therefore,the pervious concrete is needed to be compacted with a pressureless than 10 kPa. A pressure of 7.5 kPa was adopted for theplacement of concrete.
With the void volume is equal to 0.17, the parameter b can becalculated using Eq. (43), b = 0.279293.
Then, from Eq. (42), the amount of paste is Vp = 0.231.For a pervious concrete without admixtures, w/c ratio is
recommended from 0.34 to 0.40. The w/c ratio is determined bythe binder drainage test presented above (Figs. 7 and 8). The ratiow/c = 0.30, 0.32, 0.36, 0.38, 0.40 were tested and it is remarkablethat from a w/c ratio equal to 0.38, the paste cement is liquidand it starts to drain down under the effect of vibration (Fig. 8).So the w/c = 0.37 is taken.
To calculate the degree of hydration of cement, since the con-crete will be characterized at 28 day of maturation, the calculationof the degree of hydration of cement according to the formula
0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.600.5
0.6
0.7
0.8
0.9
1.0D
egre
e of
hyd
ratio
n of
cem
ent
w/c ratio
Power [18] Mills [19]
Waller [20]
Fig. 10. Theoretical calculation of the degree of hydration of cement.
0,28 0,30 0,32 0,34 0,36 0,38 0,40 0,420
5
10
15
20
25
w/c ratio
Past
e co
nten
t, pe
rcen
t by
volu
me
(%)
0,10
0,12
0,14
0,16
0,18
0,20
0,22 T
hick
ness
of e
xces
s pas
te (m
m)
Fig. 11. Variation of paste content (black line) and thickness of excess paste (redline) in function of w/c. (For interpretation of the references to color in this figurelegend, the reader is referred to the web version of this article.)
D.H. Nguyen et al. / Construction and Building Materials 73 (2014) 271–282 279
Power (Eq. (54)) seems inappropriate because it often gives ahigher degree of hydration compared to the two remaining equa-tions (Eqs. (56) and (57)) (Fig. 10). By cons, in literature the formulaof Waller (Eq. (57)) is often used to estimate the degree of hydra-tion. This is why this equation is used to calculate the degree ofhydration of cement. With the w/c = 0.37, the degree of hydrationa = 0.71.
From the values of w/c and the degree of hydration obtained,the porosity of the cement paste Pp is calculated according toEqs. (52) and (53), Pp = 0.36.
In addition, by the binder drainage test, the amount of cementpaste that coats the grains of coarse aggregate and does not flowunder the effect of vibration is shown in Fig. 11 as a function ofw/c ratio. It is noticed that this amount varies linearly with thew/c ratio. A high regression determination coefficient shows a goodcorrelation between the cement paste amount and the w/c ratio.Although the volume of cement paste obtained in Fig. 11 is quitelow compared to the value recommended which range from 15%to 25% [2,3], it also gives us an idea of the difference in the amountof paste by changing the w/c ratio. The detailed composition of themixes of the pervious concrete is summarized in Table 6. The the-oretical designed unit weight of pervious concrete composed is2080 kg m�3.
Table 6Mix of pervious concrete obtained.
Vv Cement (kg m�3) Water (kg m�3) Gravel (kg m�3
0.17 335 124 1515
4.2. Preparation of sample and testing methods
The compaction method for manufacturing pervious concrete isone of the most influential factors in the sample preparation. Thetime necessary to mix pervious concrete is 7 min to get a homoge-neous mixture. The cubic samples 15 � 15 � 15 cm were pressedunder a pressure of 7.5 kPa. The workability of mixture was mea-sured with the concrete slump test.
Immediately after casting, all mixtures were kept in their moldsduring the first 24 h in a chamber at 20 ± 2 �C and 95% relativehumidity. After demolding specimens were moist-cured in a watertank at a constant temperature of 20 �C for 28 days before mechan-ical, physical and hydraulic test.
– Compressive test: the compressive strength is measured on cubic15 � 15 � 15 cm specimens in accordance with the EuropeanStandard EN 12390 [26]. These tests were performed using aconstant rate loading of 0.06 MP s�1.
– Splitting test: The tensile strength is deducted after the splittingtest on cubic specimens 15 � 15 � 15 cm according to NF EN1338 [27].
– Porosity and density: the total porosity and the dry bulk densityof the concrete are determined by the method of hydrostaticweighing. The measurements are performed according to therecommendations of the AFGC [17]. The porosity is also deter-mined by an image processing according to the protocol definedby Sebaibi et al. [28]. The continuous porosity and the unitweight in air are performed according to the procedure of Mata[29].
– Water permeability test: the water permeability of a material isdefined as its ability to pass through the water under the effectof a pressure gradient. It is expressed by Darcy’s relationship isvalid in laminar flow regime [30]. This test determines the per-meability coefficient as a constant load and variable load. Theconstant head permeability is measured with levels of255 mm and the falling head permeability is evaluated withan initial water level h1 = 255 mm and final heighth2 = 75 mm. The device for measuring permeability of perviousconcrete is shown in Fig. 12.
– Freeze–thaw resistance: profile cycle freeze/thaw to determinethe sustainability freeze/thaw is defined in standard NF EN1338 [27]. However, a sample of pervious concrete is consid-ered at the off state due to freeze/thaw when the mass loss isabout 15% [11].
– Abrasion and skip strength: the abrasion and skip strength(Pendulum skip Resistance Tester) are performed according tostandard NF EN 1338 [27]. The abrasion resistance is measuredby the wearing machine and the resistance to skip wasperformed using the pendulum friction.
More details of these experimental tests can be found in [4,31].
4.3. Test results and discussions
4.3.1. Fresh concrete propertiesFresh pervious concrete is characterized by having a very low
slump, even zero slumps (Fig. 13). Fresh concretes are very stiffsince they contain less water and cement paste. This characteristicconforms to common experience with this type of concrete.
) Sand (kg m�3) W/C G/C S/G VP
106 0.37 4.52 0.07 0.231
100
100
100
Valve tokeep theconstantwater level
Graduated transparentpipe with an insidediameter of 99.4 mm
Inlet valve
Outletvalve
Drain pipe
Perviousconcretepaverenclosed inmold
55
Fig. 12. Device for measuring the permeability coefficient of pervious concrete.
Fig. 13. Consistency of fresh concrete.
Table 7Characteristics of pervious concrete.
Characteristic Value
Cube compressive strength of 15 � 15 � 15 cm (MPa) 28.6 (1.7)Splitting tensile strength of cube 15 � 15 � 15 cm (MPa) 4.0 (0.5)Unit weight of fresh concrete (kg m�3) 2034
(59)Unit weight in air (kg m�3) 2025
(15)Dry bulk density (kg m�3) 1979 (3)Water accessible porosity (%) 26.5 (0.2)Continuous porosity (%) 17.2 (0.2)Porosity by image processing (%) 19.2 (2.0)Permeability test according to variable load (mm/s) 1.1 (0.1)Permeability by constant load test (mm s�1) 0.8 (0.1)Hydration at 28 days as measured by loss on ignition (%) 71.9 (0.8)Abrasion resistance according to the standard NF EN 1338 (mm) 28.9 (0.7)The angle of friction – slip resistance (�) 89 (0.9)Number of cycles of freeze/thaw cycles experienced by the
concrete88 (5)
(): standard deviation.
280 D.H. Nguyen et al. / Construction and Building Materials 73 (2014) 271–282
The fresh unit weight test was performed on the pervious con-crete immediately after mixing and the actual density of the mix-ture was determined, equal 2034 kg m�3, which is in a tolerance ofplus or minus 80 kg m�3 of the designed unit weight [3].
4.3.2. Hardened concrete propertiesThe mechanical, the physical and the hydraulic properties of
pervious concrete hardened are presented in Table 7.Compressive strength:The compressive strength of the cubic samples 15 � 15 � 15 cm
of pervious concrete is 28.6 MPa so that the compressive strengthon cylindrical specimens is approximately 24.3 MPa (coefficient0.85), which is within pervious concrete compressive strengthvalues reported in literature, from 3.5 to 28 MPa [3]. Also, the com-pressive strength of pervious concrete designed by our method isclose the compressive strength required for most conventionalapplications, typically 24.1–27.6 MPa [32]. Hence, the pervious
concrete can be used not only for parking lots, low-traffic pave-ments, pedestrian walkways but also for structure as for construct-ing walls for buildings.
Tensile strength:The splitting tensile strength was 4.0 MPa, corresponding to
14.0% of the compressive strength. Similar to the compressivestrength, it can be observed that the tensile strength of perviousconcrete is in the range published (0.85–4.3 MPa) [11,33] and isin the upper part of this range. The relationship between compres-sive strength and tensile strength of concrete is accorded with therelationship found by Crouch et al. [34]:
Rt ¼ 0:4378� ðRcÞ0:6667 ð62Þ
Porosity and density:The continuous porosity is 17.2% against the desired value ini-
tially 17.0%. The difference between two values is very small(1.2%). This result indicates that the proposed method allows for-mulating a concrete meeting the specifications set initial. The totalporosity accessible to water is 26.5% so the desired value is initially25.5%. The difference between two values is 3.9%. Indeed, in thecalculation of the porosity of the cement paste, it is assumed thatthe cement is fully hydrated while the concrete is characterizedafter 28 days of storage. Consequently, a small difference betweenthe measured porosity and the targeted porosity shows the preci-sion of this design method.
The porosity of the pervious concrete specimens determinedusing the image analysis procedure are 19.2% (Fig. 14). It can beobserved that the continuous porosity and the porosity by imageprocessing are fairly different. In fact, as the pores are of varyingsizes, and the image processing is likely to join together two verysmall bright features into one big feature and identify it as a largepore, the average porosity thus obtained was not thought to be anadequate indicator of the representative porosity in the specimen.
The unit weight in air and the dry bulk density of pervious con-crete were 2024 and 1979 kg m�3 respectively. There is significantdifference between dry bulk density and the unit weight in air. Thelower value of dry bulk density can be explained by the totalevaporation of the evaporable water (adsorbed on the walls ofthe large pores and absorbed into the capillary pores of the cementpaste), and the partial removal of chemically bound water of thecement hydrates.
Water permeability:The permeability of pervious concrete is 1.1 mm s�1 by variable
head test and 0.8 mm s�1 by constant head test. The smallpermeability coefficients are consistent with the small continuous
(b)(a)
2 cm
Fig. 14. Scanned image (a) and image threshold established.
D.H. Nguyen et al. / Construction and Building Materials 73 (2014) 271–282 281
porosity and the high compressive strength in comparing with theprevious works [2–4,31,33–35]. Indeed, the variation of thepermeability of pervious concrete is inversely proportional tothe compressive strength and proportional to the porosity. Adifference in the permeability coefficient obtained by two methods(at variable load and constant) was observed, in accordance withthe previous work [4].
Freeze/thaw resistance:In agreement with Table 7, pervious concrete present weak
durability to freeze/thaw attacks compared to the ordinary con-crete. The mass loss of concrete after 25 cycles of freeze/thaw is0.3% and concrete is the off state after 88 cycles. Specimens sub-jected to freeze/thaw cycles are kept saturated whilst in reality,the pervious concrete are rarely seen in saturation capacity ofdrainage. Indeed, in a sufficiently saturated specimen, perviousconcrete degradation is mainly due to the hydraulic pressure. Anincrease of 9% in volume from the transformation of the water intoice [36] leads to a great force on the walls of the pores.
Abrasion strength:According to Table 7, the length of abrasion of pervious concrete
is 28.9 mm. Others authors show similar results with lengths vary-ing from 29.2 mm to 34.7 mm [1]. Indeed, because of the specifictexture of pervious concrete, the cement paste and the aggregatesare easily loosened from the surface of concrete and the length ofabrasion of pervious concrete is greater than that required(20.0 mm) for traditional concrete paving block [27].
Skip strength:There are few studies on the slip resistance of pervious con-
crete. It can be seen that the concrete studied has a very good skidresistance. The slip resistance value in the wet state (averaged overthe total surface of 5 measurements) is 89. This value is greaterthan 40, critical value to ensure adequate resistance to slipperinessfor city traffic at 50 km/h. In addition, slip resistance value of theorder of 90 indicate that there is no risk of slip in wet weather [37].
5. Conclusion
In this paper, the theory of the excess paste was used to deter-mine the thickness of the paste coating each aggregate with a givendiameter of constituting granular skeleton, then generalized todetermine total amount of paste to the coating property of thegravel grains avoiding clog the inter-granular pores between thegrains of the granular skeleton. One scaling factor ‘‘k’’ which canbe similar for different size of concrete aggregates is introduced.The concrete mix design for draining characteristics thus passesfirst by determining the amount sufficient of gravel and an ade-quate amount of cement paste assuming that the amount of thecompact paste is zero. Then, with a volume of cement paste
determined, it is necessary to determine the w/c ratio for cementpaste not too liquid to avoid the flow of the cement paste due tovibration or compaction. The binder drainage test proposedprotocol is simple and gives very good results.
The mix design method presented in this paper is interesting asit is based on study mixed: theoretical–experimental. The superi-ority of our methods compared to older methods is:
– It applies to any type and size of gravel.– It shows the method of determining the ratio w/c.– It takes into account for the effect of compaction.
The properties of concrete made from this method are very con-sistent with data in literature. In addition, this is a concrete with agood strength. The small gap between the targeted porosity andthe porosity obtained confirms the accuracy of this method.
The proposed methodology, interesting to compose a perviousconcrete, must be confirmed with other experimental field studiedand different types of materials.
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