Compression response of normal and high strength pervious concrete

Construction and Building Materials 109 (2016) 177–187

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Construction and Building Materials

journal homepage: www.elsevier .com/locate /conbui ldmat

Compression response of normal and high strength pervious concrete

http://dx.doi.org/10.1016/j.conbuildmat.2016.01.0510950-0618/� 2016 Elsevier Ltd. All rights reserved.

⇑ Corresponding author.E-mail addresses: [email protected] (R. Zhong), [email protected]

(K. Wille).

Rui Zhong, Kay Wille ⇑Department of Civil and Environmental Engineering, University of Connecticut, 261 Glenbrook Road, Unit 3037, Storrs, CT 06269-3037, United States

h i g h l i g h t s

� Investigation of compression response of pervious concrete.� Matrix mixture design up to 174 MPa.� Distinction between effective porosity and total porosity.� Evaluation of existing compressive strength predicting models.� Proposal of semi-empirical equation to predict compressive strength.

a r t i c l e i n f o

Article history:Received 8 January 2015Received in revised form 28 November 2015Accepted 28 January 2016Available online 8 February 2016

Keywords:Pervious concreteCompressive strengthEffective porosityTotal porosity

a b s t r a c t

The last century in the construction industry has shown an increasing interest in pervious concrete, anenvironmentally friendly material. Although emphasis has been placed on the relationship between com-pressive behavior of conventional pervious concrete and total porosity, not much research has been car-ried out to characterize the relationship between compressive behavior of pervious concrete with variedmatrix strengths, aggregate to binder ratios, and aggregate sizes. In this research 27 series of perviousconcrete were mixed and experimentally tested in compressive strength using matrix strengths rangingfrom 29 MPa to 174 MPa, aggregate to binder ratios from 2.5 to 3.5 and aggregate sizes from 1.2 mm to4.8 mm. A systematic analysis has been carried out to quantify the influence of matrix strength, amountof binder, and size of aggregates on the compressive strength of pervious concrete. Four existing com-pressive strength prediction equations are examined and their validity for the different series investi-gated. Based on the existing equations, an extended equation is proposed and its validity is verified bythe enhanced agreement between predicted and experimentally measured compressive strength. In thiscontext, the necessity to distinguish total porosity from effective porosity is highlighted and taken intoaccount.

� 2016 Elsevier Ltd. All rights reserved.

1. Introduction

Pervious concrete, also referred to as porous or permeable con-crete, is a class of concrete characterized by a relative high volumeof connected pores, typically in the range of 15–30% with poresizes ranging from 2 to 8 mm [1], and a water permeability ofabout 2–6 mm/s [2–3]. This is achieved by intentionally incorpo-rating continuous voids through gap grading the coarse aggregateand eliminating or minimizing the fine aggregate. The AmericanConcrete Institute (ACI) defines pervious concrete as ‘‘concretecontaining little, if any, fine aggregate that results in sufficientvoids to allow air and water to pass easily from the surface tounderlying layers” [4]. The ability to allow water penetrating

through its open pore structure makes it a very effective tool tocontrol storm water runoff. Although pervious concrete has beenused for over 30 years, the material is attracting renewed interestsdue to the Federal Water Pollution Control Act [5] and the Environ-mental Protection Agency (EPA) storm water regulations [6].Despite the various environmental benefits, the limited bondbetween the aggregates covered with cementitious matrix limitsthe raveling resistance of the material and thus its structural integ-rity. Therefore, conventional pervious concrete has typically beenapplied to sidewalks, parking lots and other light traffic areas.The bonding force between the aggregates is mainly influencedby the contact area (aggregate size) and the matrix tensile strength(directly correlated to the matrix compressive strength). The com-pressive strength of pervious concrete is a quick indicator reflect-ing the bond strengths between the gap-graded aggregates andthe effect of its porosity (aggregate to binder ratio).

178 R. Zhong, K. Wille / Construction and Building Materials 109 (2016) 177–187

Typical compressive strengths of conventional pervious con-crete with porosities between 15% and 30% range from 7 to25 MPa [3]. The variation of compressive strength with changesin porosity is shown in Fig. 1. Results with porosity lower than15% or higher than 30% [1] or specimens with special treatment[7] were not included here. Among researchers, consensus existsthat an increase of porosity will decrease the compressive strength.Furthermore, Fig. 1 demonstrates the influence of matrix strength,and thus bond strength between the aggregates, on the compres-sive strength of pervious concrete. Emphasis is placed on compar-ing the compressive strength of high strength pervious concrete(HSPC) using a cementitious matrix with strength of 174 MPa tothe compressive strength of conventional pervious concretes fromthe literature [1,8–13]. In most cases the matrix strength of con-ventional pervious concrete is not provided. However, based onthe provided range of water to cement ratio (0.27–0.38), theexpected matrices strengths potentially range between 40 and60 MPa based on Abram’s law [14].

HSPC has been developed by Wille and Zhong [15–16] throughthe application of mixture design principles of ultra-high perfor-mance concrete (UHPC) to the pervious concrete matrix.

Beside porosity and matrix strength, it is hypothesized that thecontact area between the aggregates affects the compressivestrength of pervious concrete. The contact area can be increasedby using smaller aggregates. It is worth noting that changingaggregate size and aggregate to binder ratio could have a signifi-cant effect on porosity. Therefore, it is necessary to isolate theparameters to draw suitable conclusions.

In this investigation, 27 series of various pervious concreteshave been designed, characterized in their compressive strengthand porosity, and analyzed to address the following currentdeficiencies:

– Most publications do not provide the matrix strength of the per-vious concrete mixes. This limits correlation between matrixstrength and pervious concrete strength.

– No test results for pervious concretes with matrix strength inexcess of 150 MPa have been reported.

Fig. 1. Influence of porosity and matrix strength on the compressive strength ofpervious concrete.

– Current equations to predict the compressive strength of pervi-ous concrete have not been verified for pervious concretes usinghigh and ultra-high strength matrices.

– The effect of aggregate size and aggregate to binder ratio hasnot been taken into account to predict the compressivestrength.

– The distinction between total and effective porosity and howeach affects the prediction of the compressive strength is oftenoverlooked.

2. Experimental study

2.1. Materials and mixture proportions of the matrix

In total 27 series of pervious concrete were investigated in their compressivestrength and porosity. The mixture designs include three different matrices, threedifferent sizes of quartz aggregates and three different aggregate to binder ratios.The three matrices are designated in accordance to their strength as normalstrength matrix (NSM), high strength matrix (HSM) and ultra-high strength matrix(UHSM). Their mixture proportions are presented in Table 1 together with theirspread values (see Fig. 2) and compressive strengths (see test set up in Fig. 3).

White cement was selected as a constituent for the design of ultra-high strengthmatrix due to its high amount of tricalcium silicate (C3S) and dicalcium silicate(C2S), as well as its low quantity of tricalcium aluminate (C3A). For simplicity, whitecement (Type I) was used for all matrices in this research meeting the ASTM C150specification for Portland cement. For the normal strength matrix a water to cementratio of 0.55 was employed leading to a spread value in accordance to ASTM C230/C230M of 220 mm (8.7 in) and a compressive strength of 29 MPa (4.2 ksi) after28 days obtained by using a 2-inch cube in accordance to ASTM C109/C109M-13.Reducing the water to cement ratio to 0.45 and adding a high range water reducer(HRWR) in the amount of 0.2% to the weight of the cement yielded comparableworkability (spread = 240 mm [9.4 in]) and an enhanced compressive strength of61 MPa (8.8 ksi). The mixture design of the ultra-high strength matrix (UHSM)was based on prior research on the material design of ultra-high performance con-crete [17–18]. The mix proportions of the UHSM, shown in Table 1, led to a com-pressive strength of 174 MPa (25.2 ksi). It is observed that for UHSM there is aloss of viscosity and workability during mixing and casting of pervious concrete.This result is because the low water to cement ratio of 0.22 accelerates the processof surface drying. Therefore, considering the large surface area of pervious concretethe workability of the UHSM was increased to a spread value of 340 mm (13.4 in) tocounteract the effect of viscosity loss.

2.2. Mixture proportion of pervious concretes

In addition to the variation in matrix strength (29 MPa, 61 MPa, 174 MPa), threesizes of aggregates (1.19 mm, 2.38 mm, 4.75 mm) and three aggregate to binder(A/B) weight ratios (2.5, 3.0, 3.5) were combined to design the 27 pervious concreteseries listed in Table 2.

2.3. Specimen preparation and curing

Prior to mixing, all aggregates were washed to remove adhered clay and impu-rities, dried and sieved to obtain single sized aggregates. First the matrix was mixedand then the aggregates were added. After mixing, the pervious concretes were castin three layers in cylindrical molds (76 mm [3 in] by 152 mm [6 in]) to full capacityusing slight vibration. Each layer was slightly compacted by a 2.4 kg (5.3 lb) ham-mer with three blows. During casting and compaction emphasis was placed on mit-igating discontinuity in material porosity over the specimen height. After casting,each specimen was covered with plastic sheets and stored at room temperaturefor 24 h. The next day the specimens were demolded and stored in a water tankat 20 �C for an additional 27 days. For each series, a total of five cylinders were cast,three for compressive strength testing and two for porosity testing.

2.4. Test methods

2.4.1. Compressive strengthThe compressive strength of pervious concrete was determined based on ASTM

C39. The load was applied under displacement control at a rate of 0.5 mm/min.Prior to testing, specimens were removed from the curing tank for test preparation.About 6 mm (1/4 in) was cut from each load surface of the cylinder. After being leftto dry in laboratory environment, the specimens were sulfur capped at both endsensuring smooth and parallel loading surfaces. The reported results reflect the aver-age compressive strengths of three specimens at an age of 28 days.

Table 1Mixture proportion for the matrices employed in this study.

Constituents Proportions by weight

UHSM HSM NSM

Cement 1 1 1Silica fume 0.25 0.00 0.00Silica powder 0.25 0.00 0.00Water 0.22 0.45 0.55High range water reducer 0.036 0.002 0.000

Spread in mm (in) 340 (13.4) 240 (9.4) 220 (8.7)Compressive strength f 0c0 in MPa (ksi)* 174 (25.2) 61 (8.8) 29 (4.2)

* 28 days, conventional curing under ambient temperature, average value out of3 specimens (2-in. cube).

(a) UHSM (b) HSM (c) NSM

Fig. 2. Spread of matrices.

(a) Load frame (b) Compressive strength test set up

Fig. 3. Compressive strength test equipment and sample set up.

R. Zhong, K. Wille / Construction and Building Materials 109 (2016) 177–187 179

2.4.2. Effective porosityThe pore system in pervious concrete comprises the spaces between the aggre-

gates and the pores in the matrix. The volumetric portion of the accessible pores isdefined as effective porosity here. In light of the high void volume, fraction standardtests, such as ASTM C173, are not directly applicable to measure the porosity of per-vious concrete. Therefore, the porosity was calculated using the weight differencebetween an oven dried sample and a water saturated sample. Eq. (1) was used todetermine the effective porosity:

/e ¼ 1� M1 þM2 �M3

qwVT

� �� 100% ð1Þ

where /e is the effective porosity of the sample, M1 is the mass of the oven driedsample, M2 is the mass of the container filled with water, M3 is the container withsaturated sample filled with water at the same level, qw is the density of water,and VT is the volume of the sample. The same level of water has been achieved byusing an automatic overflow system considering the water surface tension effect.Prior to testing, one inch was cut from both ends of the specimen, taking intoaccount the potential discontinuation of vertical porosity distributions in perviousconcrete [19].

3. Results and discussions

3.1. Effective porosity versus total porosity

The aforementioned method measures the volume of accessiblepores (Vap). The total volume V is the sum of total pore volume Vp,volume of the aggregate Vagg and volume of the matrix Vm. Here,effective porosity (/e) is defined as the ratio of Vap to the totalvolume V. The effective porosity /e is critical for the hydraulic con-ductivity of pervious concrete. Many researchers correlate effectiveporosity with compressive strength. However, it is the total poros-ity that influences the compressive strength. The total porosity (/t)is defined as the ratio of total pore volume Vp to the total volume V(Eq. (2)). The total porosity takes into account the volume of non-accessible pores (Vnap). The volume of non-accessible pores may befurther divided into non-connected pores left in the space betweenaggregates (Vncp) and the pores in the matrix (Vmp). Fig. 4 illustratesthe pore system in pervious concrete.

Table 2Mixture proportions of pervious concretes.

Serial No. Mixture No.a A/B Aggregate size (mm) Matrix strength (MPa)

P-UHSM UHSM-2.5-1.19 2.5 1.19 174UHSM-3.0-1.19 3.0 1.19 174UHSM-3.5-1.19 3.5 1.19 174UHSM-2.5-2.38 2.5 2.38 174UHSM-3.0-2.38 3.0 2.38 174UHSM-3.5-2.38 3.5 2.38 174UHSM-2.5-4.75 2.5 4.75 174UHSM-3.0-4.75 3.0 4.75 174UHSM-3.5-4.75 3.5 4.75 174

P-HSM HSM-2.5-1.19 2.5 1.19 61HSM-3.0-1.19 3.0 1.19 61HSM-3.5-1.19 3.5 1.19 61HSM-2.5-2.38 2.5 2.38 61HSM-3.0-2.38 3.0 2.38 61HSM-3.5-2.38 3.5 2.38 61HSM-2.5-4.75 2.5 4.75 61HSM-3.0-4.75 3.0 4.75 61HSM-3.5-4.75 3.5 4.75 61

P-NSM NSM-2.5-1.19 2.5 1.19 29NSM-3.0-1.19 3.0 1.19 29NSM-3.5-1.19 3.5 1.19 29NSM-2.5-2.38 2.5 2.38 29NSM-3.0-2.38 3.0 2.38 29NSM-3.5-2.38 3.5 2.38 29NSM-2.5-4.75 2.5 4.75 29NSM-3.0-4.75 3.0 4.75 29NSM-3.5-4.75 3.5 4.75 29

a Mixture identifications start with the type of matrix, followed by the aggregate to binder ratio (A/B) and the aggregate size d in millimeter.

Fig. 4. Pore system of pervious concrete.


Eq. (2) is defined as follows:

/t ¼ Vp=V ¼ 1� q=qt

q ¼ M=Vð2Þ

where Vp is the total volume of the pore system, V and q are thebulk volume and bulk density respectively and qt is the density ofthe void free pervious concrete which can be calculated by Eq. (3).

qt ¼magg þmm

Vagg þ Vm � DVm¼ M

Vagg þ Vm � DVm¼ ð1þ A=BÞ �mm

Vagg þ Vm � DVm

¼ ð1þ A=BÞ �mm

Vagg þ ð1� DVm=VmÞ � Vm

Vagg ¼ magg=qagg

Vm ¼ mm

qm¼ mw=qw þmc=qc þmSF=qSF þmGP=qGP

ð3Þ

where magg, mm, mw, mc, mSF and mGP are the weight of aggregate,matrix, water, cement, silica fume and glass powder respectively,Vagg and Vm are the dry volume of the aggregate and matrix, respec-tively, andDVm is the matrix volume reduction after hydration, qagg,qw, qc, qSF, qGP are the density of aggregate, water, cement, silicafume and glass powder, respectively. Research has shown that afterhydration matrix volume reduction is 25% of the volume of the non-evaporable water (Vnew). Neville [20] reported that the weight ofnon-evaporable water is about 23% of anhydrous cement based onthe assumption that cement is fully hydrated. This leads to Eq. (4)to calculate DVm:

DVm ¼ 25%� Vnew ¼ 25%� 23%�mc-hydrated=qw ð4Þwhere Vnew is the volume of non-evaporable water, mc-hydrated is themass of anhydrous cement which will be fully hydrated, qw is thedensity of water. Table 3 shows the calculated relative volumereduction after cement hydration.

Table 3Relative volume reduction.

Matrix A/B DVm=Vm (%) DVm=ðVagg þ VmÞ (%)2.5 2.53

NSM 3.0 6.62 2.243.5 2.01

2.5 2.69HSM 3.0 7.20 2.38

3.5 2.13

2.5 1.51UHSM 3.0 4.74 1.32

3.5 1.18

Table 4Porosity and compressive strength of pervious concrete mixtures.

Mix /e (%) /t (%) fc0* (MPa) /t-adj** (%) fc0-adj* (MPa)

UHSM-2.5-1.19 9.51 19.84 65.8 27 47.8UHSM-3.0-1.19 15.72 24.65 52.9 27 47.0UHSM-3.5-1.19 20.56 29.18 42.3 27 47.8UHSM-2.5-2.38 11.62 20.93 47.5 27 31.9UHSM-3.0-2.38 19.60 27.08 31.7 27 31.9UHSM-3.5-2.38 25.58 31.04 21.5 27 31.9UHSM-2.5-4.75 13.95 22.46 34.9 27 23.1UHSM-3.0-4.75 23.60 26.97 23.4 27 23.3UHSM-3.5-4.75 26.70 30.22 14.6 27 22.9HSM-2.5-1.19 16.28 23.81 23.4 27 18.4HSM-2.0-1.19 24.16 29.62 14.4 27 18.5HSM-3.5-1.19 28.37 32.03 10.6 27 18.6HSM-2.5-2.38 17.05 23.46 22.9 27 17.3HSM-2.0-2.38 24.56 29.74 12.9 27 17.2HSM-3.5-2.38 29.41 32.75 8.6 27 17.6HSM-2.5-4.75 20.40 25.88 18.1 27 16.4HSM-2.0-4.75 25.82 30.25 11.3 27 16.4HSM-3.5-4.75 29.57 31.63 9.1 27 16.5NSM-2.5-1.19 13.63 17.02 23.2 27 12.5NSM-3.0-1.19 23.88 27.06 12.4 27 12.5NSM-3.5-1.19 29.11 30.94 8.4 27 12.6NSM-2.5-2.38 18.75 22.10 17.6 27 12.4NSM-3.0-2.38 24.90 27.85 11.5 27 12.4NSM-3.5-2.38 29.59 31.59 7.5 27 12.4NSM-2.5-4.75 20.49 23.35 16.0 27 12.1NSM-3.0-4.75 25.89 28.59 10.5 27 12.2NSM-3.5-4.75 28.27 30.18 8.8 27 12.2

* f 0c and f 0c�adj are measured and adjusted strength.** /t-adj is the reference total porosity (average value) used to calculate adjusted

strength.


The low w/c ratio of UHSM does not provide sufficient water forfull cement hydration, which is considered to be at w/c = 0.36 [20].Therefore for P-UHSM, cement is separated into two parts: ahydrated part (amount equivalent to w/c = 0.36) and an un-hydrated part (Fig. 5). The potential volume change through thepozzolanic reaction of silica fume has not been considered here.

Based on Eqs. (2)–(4), the total porosity can be calculated.Table 4 summarizes the effective porosity, total porosity and themeasured compressive strength. Additionally, Table 4 lists theadjusted compressive strengths related to the reference totalporosity of 27%. The compressive strengths and adjusted compres-sive strengths will be used in Section 3.2 and the followingsections.

Finally, the measured effective porosity /e is plotted against thecalculated total porosity /t in Fig. 6. Their relationship over all theseries can be expressed by Eq. (5)

/t ¼ 0:67/e þ 12 ð5ÞA similar relationship is reported by Lian and Zhuge [13]

(Fig. 6).

3.2. Effect of matrix type on compressive strength and porosity ofpervious concrete

Fig. 7 shows the influence of total porosity and matrix type onthe compressive strength of the investigated pervious concretes.As expected a decrease in total porosity and an increase in thematrix strength, increases the compressive strength of perviousconcrete. It is worth noting that the relationship between porosityand concrete strength is well represented by a linear correlation forP-NSM and P-HSM (expressed by R2). Further improvement, espe-cially for P-UHSM, might potentially be achieved by considering

Fig. 5. Volume reduction of m

the effect of contact area varied through different sizes of aggre-gates. In order to isolate the effect of total porosity on the compres-sive strength the linear equations for P-HSM and P-NSM (Fig. 7)and for P-UHSM (Fig. 8) will be used to adjust the compressivestrength to a reference total porosity of 27%. This value representsthe average total porosity over all the series.

The effect of matrix strength on compressive strength is illus-trated in Fig. 9 for all the series with A/B = 2.5. Once the total poros-ity is set to the reference porosity of 27%, the linear increase of theadjusted compressive strength with the increase of matrix strengthbecomes apparent (Fig. 9a). The same trend is observed for all ser-ies with A/B = 3.0 (Fig. 10a) and A/B = 3.5 (Fig. 11a).

The increase of the compressive strength with the increase ofmatrix strength is attributed to the better bond strength betweenmatrix and aggregate. Enhanced particle packing and improved

atrix hydration product.

Fig. 6. Effective porosity versus total porosity.

Fig. 7. Influence of /t and matrix strength on compressive strength of perviousconcrete.

Fig. 8. Enhanced correlation between total porosity and strength of P-UHSM.


fine particle distribution densifies the ITZ for P-UHSM incomparison to P-HSM and P-NSM. Consequently, better bondstrength and ultimately higher compressive strength is achieved.Matrix-aggregate bond improvement for pervious concrete bythe addition of silica fume was also reported by Chen et al. [21].It is notable that for the different matrices at the same A/B ratios,different strengths were observed. This implies that aggregate sizeinfluences the strength of pervious concrete in addition to totalporosity and matrix strength.

3.3. Effect of aggregate size on compressive strength

The effect of different aggregate sizes in the mixture design ofpervious on the compressive strength and total porosity ofpervious concrete is plotted in Figs. 12–14 for P-UHSM, P-HSMand P-NSM series, respectively. The general trend shows thedecrease in compressive strength with the increase of aggregatesize. Yang and Jiang [7], Bhutta et al. [22] and Huang et al. [23]reported a similar trend. From Figs. 12b, 13b and 14b it is observedthat the influence of aggregate size on the total porosity ismarginal. Due to gap grading of pervious concrete a largeraggregate size increases the pore size. Assuming unchanged totalporosity, an increase in pore size will lead to a decrease in thenumber of pores per unit volume. This results in a reduced contactarea between the aggregates covered by the cementitious matrix. Itis hypothesized that the reduction in contact area per unit volumereduces the compressive strength of pervious concrete.

Once the total porosity is set to the reference porosity of 27%, itbecomes apparent that a linear relationship exists between theadjusted compressive strength and aggregate size. It is observedthat the influence of aggregate size on compressive strengthincreases with matrix strength. The absolute value of the averageslope of the linear regression relationship between aggregate sizeand pervious concrete strength increases from 0.09 for P-NSM to0.56 and 6.4 for P-HSM and P-UHSM, respectively.

Furthermore, the adjusted compressive strengths also indicatethat the influence of the A/B ratio on the compressive strength ismarginal. This can be seen by the almost overlapping linear regres-sion relationships for different A/B ratios. It is worth noting thatchanging the A/B ratio is only one influential parameter to controlthe porosity, and thus the compressive strength. The results sug-gest that the A/B ratio does not affect the compressive strengthbeyond the effect of porosity (Figs. 12–14).

Additionally, visual inspection of the failed specimens confirmsthat the failure of pervious concrete is initiated by microcrackdevelopment between aggregate and matrix followed by microc-rack coalescence (see Fig. 15).

3.4. Effect of aggregate to binder ratio (A/B) on compressive strength

Figs. 16–18 show the effect of aggregate to binder ratio (A/B) onthe compressive strength and total porosity for mixtures with theaggregate size of 1.19 mm, 2.38 mm and 4.75 mm, respectively.The trend for the unadjusted values shows an increase in porositywith increase of A/B ratio. This is attributed to the fact that lessmatrix is available to fill the pores between aggregates leading toa higher total porosity. Increased porosity results in decreasedcompressive strength. A similar observation is reported by Parkand Tia [24]. The negligible direct influence of A/B ratio on thestrength of pervious concrete becomes apparent when adjustedstrength is plotted against A/B ratio (Figs. 16–18) resulting innearly horizontal trend lines. This confirms that the influence ofA/B ratio on the strength of pervious concrete is solely throughits effect on total porosity in the range investigated here.

Fig. 9. Effect of matrix strength on pervious concrete properties (A/B = 2.5).




3.5. Compressive strength prediction model

Since porosity is one of the most important and easily obtainedmicrostructure features, extensive research has been conducted toinvestigate its effect on mechanical properties. Three models

proposed for different porous materials are presented in Table 5(model 1–3).

Despite progress made in the development of compressivestrength prediction models, few of them are proposed exclusivelyfor pervious concrete (Table 5, model 4–6) [1,13,28]. According

Fig. 12. Effect of aggregate size on pervious concrete properties (P-UHPM).

Fig. 13. Effect of aggregate size on pervious concrete properties (P-HSM).

Fig. 14. Effect of aggregate size on pervious concrete properties (P-NSM).


to the limited literature available, most of the models are devel-oped using effective porosity for normal strength pervious con-crete with compressive strength below 25 MPa. Due to the use of

high and ultra-high strength matrix and the necessity to distin-guish between effective and total porosity, their validity isexamined here.

Fig. 15. Failed specimen.

Fig. 16. Effect of A/B on pervious con

Fig. 17. Effect of A/B on pervious con


The linear model (model 3) is exemplified to show the correla-tion of measured strength to predicted strength using effective andtotal porosity (Fig. 19).

Less scattered data along the fitting line and improved R2 byusing total porosity confirms the necessity to distinguish totalporosity from effective porosity in predicting the compressivestrength. The performances of the aforementioned models arecompared and summarized in Table 6.

The linear model (model 3) outperforms the power (model 1),exponential (model 2) and mixed model (model 6), which is con-firmed by the strong linear relation between strength and porosityin Fig. 7. The linear relationship between matrix strength (r0) andcompressive strength defined in the existing models is stronglyexpressed and confirmed in Figs. 9–11. However, none of the mod-elsmentioned above take into consideration the effects of aggregatesize, which increases with matrix strength. Therefore, an equationemploying total porosity is proposed (Eq. (6)) which is applicabletomatrix strengths ranging from 29 to 174 MPa and able to accountfor the impact of aggregate size. Since the A/B ratio affects thestrength only through change in total porosity, this parameter isnot explicitly incorporated into the proposed equation.

r ¼ r0ð1�m/Þ dd0

� �n

ð6Þ

crete properties (d = 1.19 mm).

crete properties (d = 2.38 mm).

Fig. 18. Effect of A/B on pervious concrete properties (d = 4.75 mm).

Table 5Summary of compressive strength prediction models.

No. Equation Originally for Author Year

1 r = r0(1 � /)n* Metal Balshin [25] 19492 r = r0 exp (�n/)* Ceramic Ryshkevitch [26] 19533 r = r0(1 � n/)* Glass Hasselmann [27] 19644 r = r0 exp [�(m � nn)/]* Pervious concrete Chindaprasirt [28] 20095

r ¼ a0 þ a1lnðdMFS ÞlnðdnÞ

� �þ a2

/ASp

� ��1þ a3 lnðC3DÞ**

Pervious concrete Deo et al. [1] 2010

6 r ¼ r0

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffið1� /Þme�n/

qPervious concrete Lian [13] 2011

* m and n are empirical constants, r0 is the matrix strength, n is the fineness modulus of aggregate.** dMFS is the mean free spacing of pores which is defined as the average value of uninterrupted surface-to-surface distances between all the neighboring pores, /A area

fraction of pores from 2D images, Sp is specific area of pores, C3D is three dimensional pore distribution density, dn is the number averaged pore size and can be calculated

from dn ¼P

NidiPNi

, in which Ni is the number of pores with an average diameter of di.

Fig. 19. Effect of /e and /t on strength prediction of linear model.

Table 6Coefficient of determination R2 for different models.

Linear Power Exponential Mixed Proposed

/e 0.87 0.16 0.18 0.24 0.88/t 0.97 0.40 0.38 0.45 0.99

Table 7Performance comparison of linear model and proposed equation.

Mix r = r0(1 �m/t) r ¼ r0ð1�m/tÞ dd0

� ��n

R2 m R2 m n

P-UHSM 0.33 �3.0 0.82 �2.7 �0.50P-HSM 0.97 �2.6 0.99 �2.6 �0.13P-NSM 0.82 �2.1 0.82 �2.1 0.00


where d0 is 1.19 mm, which is the smallest aggregate size used inthis study, and m, n are empirical constants. Its usefulness is vali-dated by the higher coefficient of determination R2 of 0.82, 0.99

and 0.82 (Table 7) for P-NSM, P-HSM and P-UHSM, respectively,in comparison to the linear model without considering the effectof aggregate size. It is worth pointing out that the value of ndecreases as the matrix strength increases. This trend is in agree-ment with the experimental result that the influence of aggregatesize on the strength of pervious concrete is greater for higherstrength matrices.

The measured and predicted compressive strength using theproposed equation is plotted in Fig. 20.

Fig. 20. Measured compressive strength versus predicted compressive strength.


4. Conclusions

Based on the experimental tests and the parameters investi-gated in this study, the following conclusions can be drawn:

1. It is necessary to distinguish total porosity from effective poros-ity for predicting the compressive strength of pervious concrete.The measured effective porosity, useful for predicting thehydraulic conductivity, is smaller than total porosity.

2. Porosity is a necessary, but insufficient parameter, for predict-ing the compressive strength of pervious concrete with matrixstrengths ranging from 29 MPa to 174 MPa. Matrix strength,aggregate size, and aggregate to binder ratio significantly affectstrength.

3. An increase in matrix strength linearly increases the compres-sive strength of pervious concrete within the range investigatedhere.

4. A decrease in aggregate size increases the strength of perviousconcrete. This is attributed to the increased total bond areabetween neighboring aggregates. The influence becomes morepronounced with an increase of matrix strength.

5. The aggregate to binder ratio affects the strength of perviousconcrete only through altering the total porosity. The resultssuggest no further influence on strength.

6. Based on the analyzed correlation of matrix strength, porosity,aggregate size, and aggregate to binder ratio, a semi-empiricalmodel is proposed predicting the compressive strength of per-vious concrete using matrix strengths from 29 MPa to174 MPa, total porosities from 17% to 32%, aggregate sizes from1.17 mm to 4.75 mm, and aggregate to binder ratios from 2.5 to3.5. Emphasis has been placed on providing a suitable equationfor practical use with reasonable accuracy, incorporating read-ily accessible parameter such as porosity, aggregate size andmatrix strength.

It is notable that pore size and its distribution influence the fail-ure of pervious concrete. In this research this is indirectlyaccounted for through the variation of aggregate size and aggre-gate to binder ratio. Research is carried out to provide furtherand more detailed information on the influence of pore size andpore size distribution on the strength of pervious concrete.

Acknowledgements

This research has been supported by a fellowship from the StateScholarship Fund of China, the China Scholarship Council (CSC),and the University of Connecticut. The authors express their greatgratitude for the support. Additionally, the authors would also liketo acknowledge the support from the following companies: ElkemMaterials and Lehigh Cement Company.

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Compression response of normal and high strength pervious concrete