Predicting the Permeability of Pervious Concrete From Non-Destructive Electrical Measurements
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Transcript of Predicting the Permeability of Pervious Concrete From Non-Destructive Electrical Measurements
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Predicting the Permeability of Pervious Concrete (Enhanced Porosity Concrete)
from Non-Destructive Electrical Measurements
N. Neithalath1, J. Weiss
2, and J. Olek
3
1
Clarkson University, Department of Civil and Environmental Engineering, Box. 5710,Potsdam, NY 13699; PH (315) 268-1261; FAX (315) 268-7985; e-mail:[email protected] Purdue University, School of Civil Engineering, 550 Stadium Mall Drive, West
Lafayette, IN 47907; PH (765) 494-2215; FAX (765) 496-1364; e-mail:
[email protected] Purdue University, School of Civil Engineering, 550 Stadium Mall Drive, West
Lafayette, IN 47907; PH (765) 494-5015; FAX (765) 496-1364; e-mail:
Abstract
The effectiveness of a pervious concrete pavement to transport water through it
depends on the intrinsic permeability of the system. However, this characteristic is
usually defined in terms of the porosity of the material. It has been observed that porosityalone is an inadequate indicator of the permeability of pervious concretes, since the
permeability depends on pore sizes, geometry and connectivity also. This paper presents
a unique non-destructive method to determine the permeability of pervious concrete fromelectrical conductivity measurements. Combining the normalized electrical conductivity
of pervious concrete determined using either alternating or direct currents with theporosity of the material, and applying it in a modified version of Kozeny-Carman
equation, a new parameter called hydraulic connectivity factor is introduced. This factor
can be thought of as a combination of parameters that describe the pore space volume andgeometry in such a way that the intrinsic permeability is related to porosity and hydraulic
connectivity factor. Using this factor, and the porosity, the hydraulic conductivity or
permeability of pervious concrete is determined. The hydraulic connectivity factor alsoprovides a means to classify pervious concretes based on their hydraulic characteristics.
The permeability values predicted using this method have a strong correlation with the
permeability measured using a falling head permeameter developed at Purdue University
for pervious concretes.
Introduction
Pervious concrete or Enhanced Porosity Concrete has a strictly gap graded coarse
aggregate phase and little or no fine aggregates so as to facilitate the formation of an
interconnected network of pores in the material. The material is designed with acementitious material content just enough to coat the coarse aggregate particles so that a
configuration that allows the passage of water at a much higher rate than conventional
concrete is produced. The major applications of pervious concrete include (i) surfaces forparking lots, to help in storm water conservation, (ii) pavements to reduce the tire-
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pavement interaction noise, and (iii) rigid drainage layers under exterior mall areas(Tennis et al. 2004, ACI Committee 522, 2005). However, the major thrust for using
pervious concrete stems from its capability to drain, and potentially de-pollute enormous
amounts of water in a short time, thus reducing the run off rates and protecting watersupplies. Pervious concrete, because of its unique pore configuration, allows the water to
percolate into the ground under the pavement or parking area. The EnvironmentalProtection Agency (EPA) has adopted a policy that recommends the use of perviouspavements as a part of Best Management Practice (BMP) as a means to mitigate the
problem of stormwater runoff.
The physical and mechanical properties of pervious concretes are reported
elsewhere (Onstenk et al. 1993, Yang and Jiang 2003, Neithalath 2004, Neithalath et al.2005, 2006, Tennis et al. 2004). The use of larger aggregate sizes up to 20 mm
maximum size has been recommended for pervious concrete since they result in large
sized pores in the material as well as reduced clogging (Nelson and Phillips 1994).Recently, ACI Committee 522 has suggested that the aggregate sizes for pervious
concrete should be between 9.5 mm and 19 mm, and that no fine aggregates should be
used. The water permeation capacity or the drainage properties are closely related to theaccessible porosity. For an accessible porosity of 20-29%, the coefficient of permeability
is about 0.01 m/s (Belgian Road Research Center Report BE 3415, 1994). It has also
been reported that the fine aggregate content determines the permeability. A drainage
rate of 100 to 750 l/min/m2
has been reported for several pervious concretes (Tennis et al.2004). Intrinsic permeability of 1 x 10-10 m2 to 5 x 10-10 m2 has been reported for
pervious concretes with porosity ranging from 17% to 28% (Neithalath et al. 2006).
The main objective of this paper is to assess the physical features of the poresystem of pervious concrete as well as to assess its permeability. The electrical
conductivity of pervious concrete saturated with an electrolyte was measured and used todescribe the porosity and pore connectivity using a modified form of Archies equation
that considers two conducting phases. A falling head permeameter was used to quantify
the hydraulic conductivity. Results from the falling head permeameter were describedusing the Kozeny-Carman equation. This paper attempts to develop a relationship
between measured characteristics (i.e., pore volume and electrical conductivity) and the
pore structure (connectivity) for use in the prediction of hydraulic conductivity (i.e.,permeability) of pervious concrete. This paper draws upon the results from previous
work reported by the authors (Neithalath 2004, Neithalath et al. 2005, 2006, Marolf et al.
2004).
Experimental Program
This section describes the materials, mixtures, and test methods used in this study.Specifically, the determination of porosity by a water saturation method as well as image
analysis, electrical conductivity by impedance spectroscopy, and hydraulic conductivity
by a falling head permeameter are described.
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Pervious Concrete Mixtures. The mixture proportions used in this study are given in
Table 1. This is adopted from a larger study directed towards ascertaining the influenceof material structure of pervious concrete on hydraulic conductivity and acoustic
absorption (Neithalath 2004, Marolf et al. 2004). Single sized aggregates (limestone
aggregates with a specific gravity 2.72) - # 8 (2.36 - 4.75 mm), # 4 (4.75 9.5 mm), and
3/8" (9.5 12.5 mm), as well as the binary blends of these aggregate sizes (i.e., byreplacing 25, 50, and 75% by weight of the larger aggregates with smaller sized
aggregates) were used to proportion the mixtures. One series of mixtures had 2.5, 5, and
7.5% of # 4 aggregates replaced by river sand. The water-cement ratio (w/c) of all
mixtures was kept constant at 0.33. The mixtures were prepared using a 2 ft3
laboratorymixer, cast in 150 x 150 x 700 mm molds, and consolidated using external vibration.
Cylinders having a diameter of 95 mm were cored from the beam specimens after they
were cured for 28 days to study the hydraulic properties.
Table 1. Mixture proportions and porosity
Measurement of Porosity. Because of the presence of large interconnected pores in the
EPC system, two different procedures were adopted to determine the porosity. In the firstmethod, which is a volumetric method, the cylindrical specimens that are 95 mm in
diameter and 150 mm long were immersed in water for 24 hours. After this period, the
sample was removed from water and allowed to achieve a saturated surface dried (SSD)
condition. The sample was then enclosed in a latex membrane and the bottom of thecylinder was sealed to a stainless steel plate using silicone sealant. The combined mass
of the sample, latex membrane, and the steel plate (M1) was measured. Water was added
to the top of the sample until it was filled, which indicated that all the interconnectedpores were saturated. The mass of the system filled with water was then taken (M2). The
difference between the masses (M = (M2-M1)) was converted into a volume, andexpressed as a percentage of the total volume of the specimen to provide an indication of
the total porosity. Table 1 shows the porosities of various mixtures determined by the
procedure stated above. In addition to this procedure, porosity was also determined usingan image analysis procedure. In this procedure, the pervious concrete specimen was
Mixture ID % 3/8"aggregates
% # 4aggregates
% # 8aggregates
% Fineaggregate
(sand)
Water-Cement
ratio (w/c)
Porosity(volume
method)
Porosity
(imageanalysis
method)
100 - #8 0 0 100 0 0.33 0.207 0.214
75-#8 - 25-#4 0 25 75 0 0.33 0.208 0.305
50-#8 - 50-#4 0 50 50 0 0.33 0.247 0.260
25-#8 - 75-#4 0 75 25 0 0.33 0.225 0.276
100 - #4 0 100 0 0 0.33 0.206 0.203
75-#8 - 25-3/8 25 0 75 0 0.33 0.225 0.219
50-#8 - 50-3/8 50 0 50 0 0.33 0.190 0.151
25-#8 - 75-3/8 75 0 25 0 0.33 0.174 0.244
100 - 3/8 100 0 0 0 0.33 0.193 0.237
50-#4 - 50-3/8 50 50 0 0 0.33 0.264 0.303
97.5-#4 - 2.5 sand 0 97.5 0 2.5 0.33 0.187 0.189
95-#4 - 5sand 0 95 0 5 0.33 0.176 0.212
92.5-#4 - 7.5sand 0 92.5 0 7.5 0.33 0.160 0.231
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impregnated with a low viscosity epoxy, and sectioned at different depths. The surface ofeach section was scanned, and an image analysis procedure was employed to distinguish
between the connected and disconnected porosities (Marolf et al. 2004). The values of
porosities determined by this method are also given in Table 1. The differences inporosities between two methods exist because of the concepts of volumes and area
averaging used. However, the values from the volumetric method are used in furtheranalysis since it measures the volumes and not areas as in image analysis.
Measurement of Bulk Resistance using Electrical Impedance Spectroscopy.Electrical Impedance Spectroscopy (EIS) measurements were conducted in this study
using a Solartron 1260 Impedance / Gain-Phase analyzer that was interfaced with apersonal computer for data acquisition. A typical Nyquist plot (plot of real versus
imaginary impedance) obtained from EIS measurements consists of two arcs the bulk
arc and the electrode arc. The two arcs meet at a point where the imaginary componentof the impedance is minimum, and the corresponding real impedance is the bulk
resistance (Rb) of the sample.
Figure 1 shows the specimen set up that was used for the experiments described inthis paper. The cylindrical specimen was enclosed in a latex membrane to contain the
electrolyte. The bottom of the specimen was sealed to a stainless steel plate using
silicone sealant. After the specimen was saturated with the electrolyte, another stainless
steel plate with a small acrylic dyke was placed at the top of the specimen, with a piece ofporous foam in between to ensure proper electrical contact. The entire set up was firmly
gripped with adjustable clamping mechanism.
Figure 1. Specimen set up for electrical impedance measurements
Specimen enclosed
in latex membrane
Stainless steel
late as bottom
Stainless steel plate top
electrode with dyke
C-clamp to hold the
specimen in place
Porous foam
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The stainless steel plates served as the electrodes and alligator plugs from theimpedance analyzer were attached to the electrodes. The impedance measurements were
made over the frequency range of 1 MHz to 10 Hz using a 250 mV AC signal.
Using the bulk resistance (Rb) obtained from the Nyquist plots, the effective
electrical conductivity (eff) of the sample was calculated as:
ARlb
eff = (1)
where l is the specimen length andA is the cross sectional area of the specimen.
The electrolytes used in this study were sodium chloride (NaCl) solutions of
varying concentrations (1%, 3%, and 10%). The conductivity of 1% NaCl solution was
1.56 S/m whereas the conductivities of 3% and 10% solutions were 4.40 S/m and 12.40S/m respectively.
Measurement of Hydraulic Conductivity. Since pervious concrete has a large
interconnected pore network, the conventional methods that are used to evaluate the
hydraulic conductivity of normal concrete are not directly applicable. To estimate the
hydraulic conductivity of pervious concrete, a falling head permeability cell has beendesigned, as shown in Figure 2.
Figure 2. Falling head permeability test set up
300mm
150mm
100mm
Top of the
sam le
Sample
Graduated cylinder
Drain pipe
O-Ring
Valve
95 mm
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The permeability cell consists of a 250 mm long acrylic tube with an innerdiameter of 92 mm. The top 150 mm of the tube was machined to an inner diameter of
95 mm so that the specimen can be seated on an O-ring at a distance of 100 mm from the
bottom. A 50 mm diameter valve connects the bottom part of the tube to a vertical pipethrough which water can drain out. The top of this pipe is positioned 10 mm above the
top of the specimen so that no unsaturated flow occurs during the test. A graduatedacrylic cylinder of 300 mm length was attached to the top of the specimen assembly andclamped tightly using a rubber sleeve. This was used to monitor the water level during
the test.
The specimen was enclosed in a latex membrane (as was done for the electrical
property measurements), and was inserted into the test set up. Water was added to thegraduated cylinder to fill the specimen cell and the draining pipe. The specimen was pre-
conditioned by allowing water to drain out through the pipe until the level in the
graduated cylinder was the same as the top of the drain pipe. This eliminated any airpockets in the specimen and ensured that the specimen was completely saturated. With
the valve closed, the graduated cylinder was filled with water. The valve was then
opened, and the time in seconds (t) required for water to fall from an initial head of 290mm (h1) to a final head of 70 mm (h2) measured. This procedure was repeated three
times, and the average value of t was used.
The coefficient of permeability (K) was calculated according to Darcys law as:
=
1
2
2
1 logh
h
tA
lAK (1)
where A1 and A2 are the areas of the cross-section of the sample and the tube respectively
and l is the length of the specimen. For a given specimen geometry, and same initial and
final heads, the coefficient of permeability is given as:
t
AK= (2)
where A is a constant, which in this study was 0.084 m.
The measured values of hydraulic conductivity ranged from 0.001 to 0.005 m/s,with a standard deviation of 0.0003 to 0.0008 m/s (three repeated measurements).
Results and Discussions
The hydraulic conductivity (K) of a porous material is determined by the
arrangement of particles, pores, and their relative sizes. The intrinsic permeability (k) of
a porous medium can be thought of as a measure of the frictional resistance to a fluidflowing through it. Therefore, the intrinsic permeability depends on the porosity, pore-
size distribution, pore roughness, constrictions of the pore space, and the tortuosity and
connectivity of the internal pore channels (Garboczi 1990, deLima and Nivas 2000). Thehydraulic conductivity can be related to intrinsic permeability as:
gkK= (3)
where is the density of the fluid, g is the acceleration due to gravity, and is thedynamic viscosity of the fluid. For water flowing through the pore system, this equationcan be simplified as:
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710*kK= (in SI units) (4)
The intrinsic permeability (k) of porous media is typically described using theKozeny-Carman equation (Bear 1972, Chapuis and Aubertin 2003) as:
22
0
2
3
)1( ps
p
SF
k
= (5)
where p is the porosity, Fs is the generalized factor to account for different pore shapes, is the tortuosity, and S0 is the specific surface area of pores.
Relationship between Porosity, Pore Size, and Intrinsic Permeability. Several studies
have predicted the permeability (permeability in this paper refers to intrinsic
permeability) of porous media from the porosity. For example, it has been suggested thatDarcys law could be given a form similar to Archies law (deLima and Nivas 2000), to
relate the permeability and porosity of rock systems:1
1
bak = (6)
where k is the intrinsic permeability (units of m2
), is the porosity, and a1 and b1 areconstants.
Figures 3(a) and (b) depict the relationship between the aggregate sizes, pore sizes
(a), porosity (), and intrinsic permeability of pervious concretes. From Figure 3(a), itcould be observed that all the three specimens have similar values of porosity but thespecimen with 3/8 aggregate shows a remarkably higher permeability, possibly due to
its larger pore sizes. Figure 3(b) shows the permeability of pervious concrete mixtures
made from a blend of different sized aggregates.
Figure 3. Relationship between aggregate sizes, pore sizes, porosity, and intrinsic
permeability, (a) single sized aggregate mixtures, (b) blended aggregate mixtures
0
1
2
3
4
IntrinsicPermeability(m2)x10-10
# 8 # 4 3/8"
= 0.207a = 2.17mm
= 0.206a = 3.29mm
= 0.193a = 4.76mm
0
1
2
3
4
5
6
IntrinsicPermeability(m2)x10-10
25% #875% # 4
50% #850% # 4
50% #450% 3/8"
= 0.263a = 3.62 mm
= 0.225a = 2.83 mm
= 0.247a = 2.58 mm
(a) (b)
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It can be seen that the specimen that exhibits the highest permeability neither has
the highest porosity, nor the largest pore size. This proves that permeability is not a
function of the porosity and the pore sizes alone, rather the pore connectivity has to be
combined with easily measurable pore structure features like porosity and pore size togain a fundamental understanding of the permeability of the system. This aspect is
further emphasized in Figure 4, which shows the porosity-permeability relationship of thepervious concrete mixtures (without addition of sand) investigated in this study.
Figure 4. Porosity-Permeability relationship for pervious concrete mixtures
While permeability generally increases with an increase in porosity, there is nodefinitive relationship between these parameters. The reason for such poor correlation
can be explained by the fact that porosity is a volumetric property of the material,
whereas permeability is a parameter that defines the flow properties through the materialthat not only depends on the volume of the pores but also on the distribution of the pore
volume and its connectivity.
Effective Electrical Conductivity as a Descriptor of the Pore System. The complexdistributions of pore and solid phases in a saturated porous material with different volume
fractions of constituents and electrical conductivities differing by orders of magnitude
have been approximated by simpler models (Christensen et al. 1990, Glover et al. 2000,Bussian 1983). One such model is the parallel model where the effective electrical
conductivity (eff) is given by the arithmetic mean of the conductivities of the saturated
pore phase (p) and the solid phase (s), and their respective volume fractions (p and s),as expressed by the following equation.
ssppeff += (7)
The first element represents the conductivity associated with the free electrolytein the larger pores of pervious concrete while the other represents the conductivity
associated with the matrix that binds the aggregates. The necessity of considering
pervious concrete as a two-phase conducting medium with the matrix phase also
0.16 0.18 0.20 0.22 0.24 0.26 0.28
Porosity (p)
0
1
2
3
4
5
Intrinsic
permeabilityx10-10
(m
2)
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conducting has been elaborated elsewhere (Neithalath et al. 2006). The drawback of
Equation 7 is that this representation does not take into account the connectivity of the
pore and the solid networks. To counter this, the parallel model has been modified by
including a connectivity factor () (Garboczi 1990). The modified parallel model thenbecomes:
ssspppeff += (8)
where p and s are termed the connectivity factors, representing the connectivities of thepore and the solid phases respectively.
Considering that the solid phase network has a connectivity of 1.0 (it can be
proved that this is the case), Equation 8 reduces to:
sspppeff += (9)
A term, modified normalized conductivity )(p
sseff
, which is equal to the
product of the porosity and the pore connectivity factor is defined (hereinafter expressed
as norm*
), which can be thought of as a true measure of the pore structure of the material.From Equation 9, the product of porosity () and pore phase connectivity (p) is
given by:
*)(
norm
p
sseff
pp == (10)
The effective conductivity (eff) can be easily deduced using Equation 1 in whichthe bulk resistance is equal to the real impedance when the imaginary impedance is a
minimum, as shown with arrows for different single sized aggregate pervious concrete
mixtures in a Nyquist plot (Figure 5).
Figure 5. Nyquist plot for pervious concrete mixtures saturated with 3% NaCl
solution (the arrows indicate the corresponding bulk resistances)
100 200 300 400 500 600 700
Real impedance (Z')
0
-100
-200
-300
-400
-500
-600
-700
Imaginaryimpedance(Z")
100% 3/8"
100% #4
100% #8
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The porosity can be measured using the procedure described in the section onexperimental program. The conductivity of the solution filling the pores is also known.
The only unknown in Equation 10 to determine norm* is the conductivity of the solid
phase (s). In this study, the solid phase conductivity has been determined by using amodified form of Archies law which accounts for two-phase conducting media. The
specimen was saturated with electrolytes of three different conductivities, resulting inthree variants for the modified Archies law, which can then be solved for the unknowns,
one of which is s. More details about this procedure can be found in (Neithalath et al.2006).
Relating Pore Structure Features and Permeability through Electrical Properties.
The relationship between porosity and permeability is given by the Kozeny-Carman
relation (Equation 5). It can be shown that the pore tortuosity () in that equation isequivalent to the inverse of pore connectivity ( = 1/p).
Equation 12 equates pp to*
norm . Therefore, the term
2
pin Kozeny-
Carman equation is equivalent to, and can be replaced by 2* ][ norm . Using this approach,
Kozeny-Carman equation can be rewritten as:
[ ]( )
=
2
2*
2
0 1
1
p
p
norm
s SFk
(11)
This illustrates that the intrinsic permeability (k) is equal to the product of a
constant that describes the shape and specific surface area of pores, the square ofmodified normalized electrical conductivity, and a function that accounts for the pore
volume fraction. The expression [ ]2*2
0
1norm
s SF
is defined as hydraulic connectivity factor
(H). The Kozeny-Carman equation can then be simplified as:
( )
=
21 p
p
Hk
(12)
The intrinsic permeability therefore is represented as a function of porosity (p),and the hydraulic connectivity factor (H). The hydraulic connectivity factor (H) can bethought of as a combination of parameters that describe the pore space volume and
geometry in such a way that the intrinsic permeability is related to porosity and hydraulic
connectivity factor. The relationship between k and H is shown in Figure 6.
The hydraulic connectivity factor H offers a means of classifying EPC based ontheir hydraulic characteristics. The mixtures with similar H values exhibit similarpermeability (k). The mixture with a low H value (i.e., 100% # 8 aggregates) has a smallaggregate size. Therefore, the inter-particle pore sizes are also small and as a result its
ability to sustain water flow is lower. Similarly, the mixture with 50% # 8 and 50% 3/8"
aggregates also has a low H value since the smaller aggregates fill in between the largerparticles, resulting in a reduced porosity and a reduced flow capacity. The mixtures with
the highest H values either have a large porosity and pore size as with mixtures having
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100% 3/8" aggregates or has a blend of aggregate sizes that helps to create a verycontinuous pore structure, as in mixtures with 75% #4 and 25% #8 aggregates.
Figure 6. Relationship between the hydraulic connectivity factor and intrinsic
permeability
The electrical conductivity is related to the intrinsic permeability of pervious
concrete in the following paragraphs. Equation 11 showed that the intrinsic permeabilitycould be related to the square of the modified normalized conductivity. This is similar to
the findings of Wong et al. (1984). It should however be noted that some authors (Martys
and Garboczi 1992) have expressed the intrinsic permeability as:
2'
cplk = (13)
where is a factor that accounts for the tortuosity (or connectivity) of the pores (similarto p),and lc is a characteristic length.
Equation 13 can be rewritten using normalized conductivity, to yield Equation 14.
[ ] 2'
*
c
p
norm lk
= (14)
From this equation, it can be seen that permeability could be considered as being directlyproportional to the modified normalized conductivity.
The modified normalized electrical conductivity, as well as its square are plotted
against the intrinsic permeability in Figures 7(a) and (b) respectively. The plots showthat there is no significant statistical difference between the two (R2 values of 0.93 and
0.92, respectively), but as Equation 11 can be easily derived from the Kozeny-Carman
equation, it is recommended that the permeability of pervious concrete should be taken asbeing related to the square of the electrical conductivity.
0 2 4 6 8 10 12 14
Hydraulic connectivity factor (H) x 10-10
0
1
2
3
4
5
Intrinsicpermeabilityx10-10(m
2)
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Figure 7: Relationship between intrinsic permeability and (a) modified normalized
conductivity, (b) square of modified normalized conductivity
Conclusions
This paper has outlined a methodology to non-destructively assess the hydraulic
properties of pervious concrete using electrical property measurements. The porosity andpore size of pervious concrete mixtures made using single sized aggregates and blends of
these aggregates were measured using volumetric method and image analysis procedure.
The hydraulic conductivity was measured using a falling head permeameter specificallydesigned and fabricated for this purpose. It was observed that the porosity and pore sizes
did not bear any direct relation to permeability.
Electrical impedance spectroscopy was used to determine the effectiveconductivity of pervious concrete samples saturated with sodium chloride solutions of
varying concentrations. Using a modified version of parallel law of mixtures, a term
called modified normalized conductivity was defined, which related to the pore structure
features of the material.Using the Kozeny-Carman equation, a hydraulic connectivity factor was defined,
which can be thought of as a combination of parameters that describe the pore space
volume and geometry in such a way that the intrinsic permeability is related to porosity
and hydraulic connectivity factor. The hydraulic connectivity factor H
offers a means of
classifying EPC based on their hydraulic characteristics. The mixtures with similarhydraulic connectivity values exhibit similar permeability.
Acknowledgements
The authors gratefully acknowledge the support received from the Institute for
Safe, Quiet, and Durable Highways (SQDH) and the Center for Advanced Cement Based
0.00 0.01 0.02 0.03 0.04
Modified normalized conductivity
0
1
2
3
4
5
Intrinsicpermeabilityx10-10(m2)
R2=0.93
0 0.0004 0.0008 0.0012 0.0016
Square of modified normalized conductivity
0
1
2
3
4
5
Intrinsicpermeability
x10-10
(m
2)
R2=0.92
(a) (b)
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Materials (ACBM). This work was conducted in the Charles Pankow Concrete MaterialsLaboratory of Purdue University; as such the authors gratefully acknowledge the support
that has made this laboratory possible.
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