PCA R&D Serial No. 3003
Using Pore Parameters to Estimate Permeability or Conductivity of Concrete by M. R. Nokken and R. D. Hooton
©RILEM, Materials and Structures Journal 2008 All rights reserved
Materials and Structures DOI 10.1617/s11527-006-9212-y
O R I G I N A L A RT I C L E
Using pore parameters to estimate permeability or conductivity of concrete M. R. Nokken Æ R. D. Hooton
Received: 6 March 2006 / Accepted: 14 November 2006 RILEM 2006
Abstract This study investigated the relationships between pore parameters and transport properties. Fourteen concrete mixtures were investigated for water permeability, conductivity for the pore solutions and bulk concrete, as well as total porosity and critical pore diameter. The measured parameters allowed comparison to the Katz–Thompson relationship as well as Archie’s Law. Using a low-pressure device, measured permeability from 1 to 28 days was found to be approximately an order of magnitude higher than that calculated using the Katz–Thompson relationship for the six mixtures examined with this technique. Better agreement between measured and predicted permeability was found using apparatus capable of higher applied pressure. Comparing the data to other published data, the Katz–Thompson relationship seems to be a useful technique for the approximation of water permeability. The exponential relationship between porosity and normalized conductivity (the inverse of the Formation factor) forming the basis of Archie’s Law was found to hold within each specific concrete mixture. However, no overall
M. R. Nokken (&) Concordia University, Montreal, QC, Canada e-mail:
[email protected] R. D. Hooton University of Toronto, Toronto, ON, Canada
trend was apparent. The constants of the Archie’s Law vary over a wide range. Keywords Pore size Pore solution Conductivity Permeability Katz–Thompson Archie’s Law
1 Introduction There has been considerable interest in the relationship between porosity and transport in cement paste, mortar and concrete as many of the tests that directly measure transport properties require specialized equipment and long periods of time to complete (e.g. water permeability). To further compound this, the lack of a standard water permeability test creates difficulty in comparison of results between researchers. Some work has been done in this area [1], but to date no widely used standard test exists. There are two US Federal standards test methods, but one is not sensitive to good quality concrete [2] and the other is rarely used [3], even with improvements [4]. First discussed is the debate on the selection of a suitable pore parameter to correlate to permeability or other transport properties. Then, attempts to relate porosity to permeability including the Katz–Thompson relationship and Archie’s
Materials and Structures
law are examined. The Kozeny–Carman [5] relationship is not considered as the high specific surface area of cement pastes grossly overestimates permeability [6]. Attempts to relate pore parameters to other transport mechanisms (i.e. diffusion) exist, but will not be discussed in this paper.
1.1 Choice of pore parameter Numerous attempts have been made to correlate permeability to various parameters such as total or capillary porosity [7], surface area, volume of pores above some critical size [8, 9], and threshold pore size [8] or critical pore size [10]. The threshold and critical pore sizes are typically obtained from pore size distribution data as measured by mercury porosimetry. The threshold diameter is defined as the diameter where mercury begins to enter and percolate the pore system in appreciable quantity [11]. The critical diameter is obtained from maximum of the derivative of the pore distribution curve. Figure 1 shows the determination of these two pore diameters from a mercury intrusion curve. The critical and median pore diameters have similar values [12] and tend to be smaller than threshold diameter. Nyame and Illston [10] found the critical pore radius correlated very well to permeability regardless of the water to cement
1.2 Katz–Thompson relationship Katz and Thompson [17] used percolation theory to develop a relationship between air permeability and the critical pore diameter of sedimentary rock. They validated that the critical pore diameter represented a continuous path across the sample by measuring changes in electrical conductivity during mercury intrusion. Permeability is related to the square of the critical pore diameter and the ratio of bulk conductivity to pore solution conductivity by the following relationship [17] k¼
1 2 r d ; 226 c r0
ð1Þ
4E-05
0.16
Intruded Volume (cm3) .
0.14 0.12
3E-05
dV/dP curve Total porosity
3E-05
0.10 2E-05 0.08 Inflection point of curve gives critical radius
0.06
2E-05 1E-05
0.04 Threshold radius 0.02 0.00 0.001
0.01
0.1 Pore Radius (microns)
1
5E-06 0E+00 10
dV/dP
Fig. 1 Definition of pore parameters
ratio or degree of hydration of the sample. Marsh [13] found no unique relationship between the volume of pores greater than 50 nm radius or threshold radius. ‘‘A major influence was accredited to the presence or absence of a peak in the dv/d(log r) distribution at approximately 50 nm radius’’ [13, 14]. Li and Roy [15] found that the median pore radius correlated well with the water to solid ratio (volume basis), and reasonably well to permeability. Nyame and Illston [16] found a power law relationship (linear on log–log scale) between the product of porosity and hydraulic radius vs. permeability.
Materials and Structures
where k = intrinsic permeability (m2), dc = critical pore diameter (m), r = bulk conductivity (S/ m), r0 = pore solution conductivity (S/m). The constant is the equation is not empirical, but based on theoretical considerations, assuming local cylindrical pore geometry consistent with mercury porosity interpretation. Studies have been performed on cementitious materials using water permeability (rather than air) to assess the validity of using the Katz– Thompson equation. Christensen et al. [18] found the relationship to hold, while El-Dieb and Hooton [19] and Tumidajski and Lin [20] disagreed. Halamickova et al. [21] found the relationship held for paste of 0.50 water to cement ratio, but not that of 0.40 when using a constant of 1/180 rather than 1/226, because it gave a better correlation between measured and calculated permeability. More detailed discussion of the published results will start with findings using cement pastes, then progress to mortar and concrete. El-Dieb and Hooton [19] reanalyzed published water permeability data and pore parameter data for cement pastes [22] and concretes [23]. The formation factor (r0/r) was not measured directly, but calculated from pore parameters by the equation proposed by Katz and Thompson [24] r de ¼ max gSðdemax Þ; r0 dc
ð2Þ
where r = conductivity of bulk specimen (S/m), r0 = conductivity of pore solution (S/m), demax = 0.34dc, dc = critical pore diameter (nm), g = total porosity (%), S(demax) = fractional volume of pores larger than demax. The measured permeabilities for the lower water to cement ratio pastes (0.25) were closer to that predicted by the relationship than the pastes cast at 0.36 w/c. The pastes were investigated at 7, 28, 91 and 182 days. The 7-day results of the 0.36 w/c pastes are similar to that calculated. The low (or negligible) measured permeability after 7 days may be an artefact of the equipment limitations. These authors consider that the low measured permeability of the lower water to cement ratio was coincidentally similar to that
predicted. The pressure used for measuring permeability after 7 days was 690 kPa (100 psi) [22]. Christensen et al. [18] measured conductivity and porosity directly, but used previously published permeability data from Nyame and Illston [16]. Relatively high pressures (7–14 MPa) were used to determine permeability. The predicted permeabilities are greater than those measured, but agree within 1.5 orders of magnitude. The total porosity was determined by water displacement, while mercury porosimetry was used to determine critical pore diameter. The paste samples ranged from 7 to 182 days in age at time of test. The results for the two studies on cement paste can be seen in Fig. 2. Halamickova et al. [21] measured permeability directly on both pastes and mortars of varying sand fractions, but used diffusion rather than conductivity in Eq. 1. Conductivity can be related to diffusivity through the Nernst–Einstein equation r0 D0 ¼ ; r D
ð3Þ
where D0 = diffusion of ion in solution (m2/s), and D = diffusion of ion in specimen (m2/s). These authors used 1/180 rather than 1/226 as the constant in Eq. 1. The permeability and critical pore diameter were not included in tabular form in the paper; these writers obtained the numerical values from Bentz [25]. The concrete tested by El-Dieb [19] was 8– 9 months old at the time of testing. It is interesting to observe in Fig. 3 that the concrete specimens with high water to cementing materials ratios lay above the equality line, while those with low water to cementing materials ratios lay at or below the line. But it also must be noted that the low water to cement ratio concrete had higher paste content, leading to higher measured permeability. Although there appears to be large scatter in the figure, the difference in measured and calculated permeability approaches that found by Christensen et al. [18]. In Tumidajski and Lin [20], where both the permeability and conductivities were measured directly on concrete, almost all the data plots are well below the line of equality. The conductivity
Materials and Structures Fig. 2 Katz–Thompson relationship for cement pastes
Calculated Permeability (m/s) .
1.E-06
El-Dieb and Hooton (1994) 0.25 w/c
1.E-08
El-Dieb and Hooton (1994) 0.36 w/c
1.E-10
Christensen et al. (1996)
1.E-12
1.E-14 1.E-14
1.E-12
1.E-10
1.E-08
1.E-06
Measured Permeability (m/s)
Fig. 3 Measured and calculated permeability (after [19])
1.E-11
Calcuated Permeability (m/s)
Note mixture designations (cement (kg/m3)/%SP/%SF/w/c)
250/0/0/0.90
350/0/0/0.64
1.E-12 250/3/0/0.64 500/0/0/0.45 350/1.8/0/0.46 250/3/20/0.65 350/4/10/0.32
500/3.7/5/0.32
1.E-13
500/2.5/20/0.28 500/2/15/0.32 500/1.8/10/0.32 500/2.2/0/0.32
1.E-14 1.E-14
1.E-13
1.E-12
1.E-11
Measured Permeability (m/s)
of the sample was determined by AC impedance and the conductivity of the expressed pore solution by resistivity probe as described in Tumidajski and Schumacher [26]. A modified Hoek– Franklin triaxial cell, described in Daw [27], was used to measure permeability. Many of the data have measured permeability two orders of magnitude greater than that calculated. The only mixture that comes close to the line of equality was 0.55 w/c with 65% replacement by fly ash. Note that the figures in the paper [20] do not agree with the tabular data. A check on the
calculations supports the values in the figures as being correct and Table 3 (in their paper) should have a corrected calculated permeability column heading as 10–12 m/s. Both the El-Dieb and Hooton and the Tumidajski and Lin studies were performed on concrete, yet there is a major discrepancy in the results as shown in Table 1. Note that the measured and calculated permeabilities are quite different. The calculated permeability of Tumidajski and Lin are on average an order of magnitude higher than those of El-Dieb and Hooton. This would seem
Table 1 Comparison between Katz and Thompson studies on concrete
El-Dieb and Hooton [4] Tumidajski and Lin [20]
w/c
Age at test
dc (lm)
r/r0
K measured (m/s)
K calculated (m/s)
0.64 0.65
8–9 months 28 days
0.04633 0.134
0.0042 0.0073
1.10e-13 2.08e-10
16.6e-13 5.7e-12
Materials and Structures 1.E-06
Calculated Permeability (m/s) .
Fig. 4 Measured and calculated permeability for all mixtures
Ref [18]
1.E-08
1.E-10
Ref. [19] 0.25 w/c
1.E-12
Ref [19] 0.36 w/c
1.E-14 1.E-14
reasonable given the difference in concrete maturity in the two studies. However, the measured permeability is approximately three orders of magnitude greater for the Tumidajski and Lin study. Although the data of El-Dieb are for mature concrete, it seems unlikely that such a marked decrease in the measured permeability would occur with additional hydration. It seems plausible that the measured permeability data of Tumidajski and Lin are too high and that the calculated values may be closer to reality. No details of the pressure used are given in the paper [16]. The results for all the studies related to the Katz–Thompson prediction are shown in Fig. 4. Given the high variability known to occur in water permeability measurements, the Katz–Thompson relationship seems to give a reasonable estimate of permeability using data obtained from mercury porosimetry and direct or indirect conductivity measurements, when disregarding the data of Tumidajski and Lin and the 0.36 w/cm pastes of El-Dieb and Hooton. Deviations from the relationship seem to be due to differences in the permeability measurement technique. The problematic matter in using The Katz– Thompson relationship is the determination of the formation factor. Obtaining pore solutions from mature pastes require specialized equipment [28] and yields small volumes of solution for analysis. Equation 1 can be used as mentioned previously or estimates can be made from material composition (i.e., sodium equivalent, Na2Oe, content of cement and supplementary materials gives an approximation of hydroxyl concentration) or water to cement ratio. Alternatively, relative
1.E-12 1.E-10 1.E-08 Measured Permeability (m/s)
1.E-06
conductivity of cement pastes without the addition of silica fume can be estimated from capillary porosity using Eq. 4 [29]. Capillary pores are the remnants of originally water filled space at the time of mixing ranging in size from 10 to 1,000 nm r ¼ 0:0004 þ 0:03p2 þ H ðp 0:17Þ 1:7ðp 0:17Þ2 ; r0 ð4Þ where r = conductivity of bulk specimen (S/m), r0 = conductivity of pore solution (S/m), H = Heaviside function (H(x) = 1 when x > 0 and 0 otherwise), p = capillary porosity. The relative conductivity can be thought of as a measure of tortuosity and connectivity of the pore structure [6, 30] r ¼ bVs ; r0
ð5Þ
where b = a microstructural parameter related to the tortuosity and connectivity of the capillary porosity, Vs = volume fraction of capillary porosity (equivalent to p). This equation can also be written as r ¼ Cr0 ;
ð6Þ
where G = the microstructure dependent part. 1.3 Archie’s Law An older relationship developed for rock formations, correlates the formation factor to porosity, and was proposed by Archie [31]
Materials and Structures
r ¼ ar0 pm :
ð7Þ
Constants, a and m, in the above equation were determined by Wong et al. [32] as a equal to approximately one and m lying between one and two. In geomaterials, a is associated with degree of saturation and m with tortuosity. Taking a = 1, Eq. 7 can be rewritten as r ¼ r0 ppm1 :
ð8Þ
The similarities to Eq. 5 are apparent, where pm–1 is equivalent to b. Here the relative conductivity is based only on total porosity, rather than size distribution. Archie’s Law cannot be used to predict relative conductivity from a single sample, but rather requires a series of similar samples of varying porosity [6]. A hydrating cement paste of a particular water to cement ratio provides a logical method to interpret the exponent for that particular system. Tumidajski et al. [33] investigated the validity of Archie’s Law using cement paste and mortar systems. The constants of Eq. 7 were determined to be near that of Wong et al. with a = 1.89 and 1.02, and m = 2.55 and 2.14 for paste and mortar, respectively. These authors reanalysed data by Christensen et al. [34] and Taffinder and Batchelor [35] to find a much more varied range for the constants with a = 0.14 and m = 4.8 for the former, and a = 7.71 and m = 3.32 for the later.
2 Materials, casting and experimental methods Fourteen concrete mixtures form the basis of the new test results in this paper. Program parameters investigated were water to cementing materials ratio and the inclusion of supplementary cementing materials. Portland cement mixtures with water to cementing materials ratios investigated ranged from 0.30 to 0.90 (to minimise segregation, ground quartz powder was added to the 0.70 and 0.90 mixtures). The large range was used to determine the variation in magnitude of transport properties observed in concrete used for all types of construction from high performance to residential applications. Supplementary cementing materials, silica fume, fly ash and ground granulated blast furnace slag, were used at typical replacement levels (7, 20 and 35%, respectively). The mixture proportions are given in Table 2. Cementing materials consisted of low-alkali ASTM Type I Portland cement (PC) with Bogue composition of 57.4% C3S, 15.6% C2S, 8.5% C3A, 7.9% C4AF and the same cement blended with approximately 7% silica fume (SF); a CSA Class CI fly ash (FA) with 17.5% CaO; and a ground granulated blast furnace slag (SG). The fine aggregate, a local glacial sand, had a density of 2,700 kg/m3, an absorption of 0.8%, and a fineness modulus of 2.56. A crushed 10 mm limestone with a density of 2,670 kg/m3 and absorption of 1.76% was used as the coarse aggregate. Concrete
Table 2 Concrete mixture proportions (kg/m3) Mixture
Water
Cement
Slag
Fly ash
Silica fume
Powdered quartz
Fine aggregate
Coarse aggregate
0.30 0.31 0.35 0.35 0.40 0.40 0.40 0.40 0.40 0.40 0.55 0.69 0.70 0.90
150 130 150 150 135 150 170 150 150 150 150 200 150 150
500 305 429 321 338 375 425 244 300 375 273 290 214 167
– 115 – 107 – – – 131 – – – – – –
– – – – – – – – 75 – – – – –
– * – * – – – – – * – – – –
– – – – – – – – – – – – 115 162
679 872 739 730 859 787 692 782 767 784 872 1,205 1,200 1,200
1,100 1,042 1,100 1,100 1,100 1,100 1,100 1,025 1,025 1,100 1,100 684 700 700
PC HPC PC HPC PC (135) PC PC (170) 35% SG 20% FA 7% SF PC PC PC PC
*CSA Type 10SF Blended cement with ~7% silica fume
Materials and Structures
mixtures included an ASTM Type A waterreducer and a naphthalene sulfonate-based superplasticizer were used to obtain workable mixtures. A 20-l pan mixer was used to mix successive batches of a particular concrete mixture to yield sufficient quantity of concrete (and mortar) for all tests performed. Dry materials first added to the mixer and were mixed for 1 min with the water slowly added over the subsequent minute. The resulting concrete was mixed for three minutes prior to measuring slump, entrained air and yield. Concrete was cast into 100 mm by 200 mm cylinders within 15 min of mixing. Mortar recovered from fresh concrete passing a 5 mm sieve, similar to the procedure in ASTM C403, was used for mercury intrusion porosimetry. The mortar was cast into 30 mm by 45 mm cylinders. Similar cement paste mixtures were mixed in a Waring blender. Paste samples were cast in 30 mm by 45 mm molds, sealed and then rotated to prevent segregation and bleeding. Concrete, mortar and paste cylinders were removed from the molds 18– 24 h after casting and stored in lime-saturated water until testing. The concrete mixtures were tested at 1, 2, 3, 7, 14, 21 and 28 days of age for permeability, conductivity of concrete and pore solution, and porosity and critical pore sizes. Permeability was further tested at 28 days in a more sensitive, highpressure device. For early age permeability testing, the specimens were removed from cylindrical moulds and cut to 50 mm thickness between 18 and 21 h after casting. The top and bottom few centimetres of the cylinders were discarded. Two specimens from each of six concrete mixtures were vacuum-saturated with distilled water for at least 3 h prior to placing in the testing apparatus. The equipment used was similar to that described by Hearn and Mills [36] but with minor improvements. The confining pressure was provided by a room-temperature-vulcanized (RTV) rubber ring encased in a metal ring on the outer circumferential surface that was compressed by a screw jack acting on the top and bottom stainless steel plates. Stainless steel cylinders having pistons fitted with linear voltage displacement transducers were used to measure the movement of the inflow and outflow
pistons to micrometer accuracy (for conversion to volume flow). Significant improvements were made to the existing equipment for the measurement of permeability at early ages. The inflow and outflow cylinders were changed to stainless steel with approximately 19 mm (3/4 inch) internal diameter. The inflow piston was also changed to stainless steel and the ratio of length to diameter was increased to prevent rotation of the piston within the cylinder. Teflon gaskets were added to the bottom of the pistons to ensure smooth operation. In addition, the confining pressure was approximately determined by tightening the screw jack with a torque wrench. (The torque used enabled use of a maximum 830 kPa (120 psi) pressure differential.) The actual differential pressure used was approximately 0.4 MPa. Transparent, thick-walled plastic tubing (~2 mm internal diameter) capable of withstanding 9 MPa (1,300 psi) pressure used for inflow and outflow allowed for the detection of air bubbles (the previous tubing was made from a different material, but still transparent). After approximately 28 days, one specimen from each concrete mixture, which was removed from the low-permeability cell, was retested in a high-pressure permeability cell. The apparatus the same as that described by El-Dieb and Hooton [4]. The permeability cell is a Hassler type triaxial cell originally developed to test permeability of rock. The cell is able to withstand the high confining pressures (up to 24.5 MPa) necessary for measuring flow in materials with permeability as low as 10–16 m/s. Confining water pressure was applied to a 10 mm thick neoprene sleeve using a Haskel pump to amplify pressure from laboratory compressed air supply. The confining pressure on the neoprene sleeve prevented flow around the circumference of the sample. The applied pressure gradient was applied through use of a lever arm arrangement with hanging weights providing force to a stainless steel piston. The driving pressure (pressure gradient) used in this study ranged from 5.5 to 7 MPa (800–1,000 psi). The confining pressure was at least twice the driving pressure, in the range of 13–17 MPa. Driving and confining pressures were measured with pressure gauges for visual confirmation and by pressure transducers
Materials and Structures
connected to a datalogger. Inflow and outflow were measured with linear voltage displacement transducers with micrometer resolution also connected to the datalogger. The outflow piston is 12.7 mm diameter allowing accurate measurements of small volumes of flow. Transparent tubing capable of withstanding 9 MPa (1,300 psi) pressure was used throughout to allow for the detection of air bubbles. Conductivity was measured using equipment normally employed in ASTM C1202 [37]. The particular device used allows the operator to select the voltage applied across the specimen as well as the test time. The samples were 50 mm slices of 100 mm diameter cylinders. Two specimens from each concrete mixture were removed from the lime-saturated water bath and were vacuum saturated under tap water for 3 h. The specimens were wiped saturated surface dry and then wrapped with vinyl electricians’ tape. The same two samples were tested at all ages. The samples were kept in the apparatus for the first 3– 7 days and then returned to lime water between subsequent weekly measurements. A sodium hydroxide solution (0.3 M) was used in both chambers of the ASTM C1202 [37] apparatus. The solution was selected to approximate pore solution as well as to minimize leaching. The use of sodium chloride would have changed conductivity over time due penetration combined with the difference in conductivity of chloride and hydroxyl ions. The current measured after passing 30 volts through the sample for 15 min was used to calculate conductivity. Fifteen minutes was seen as compromise between obtaining a stable reading and the commencement of heating effects. The term bulk conductivity is used to clarify that the current flows through the composite sample (the hydrated solid material and the pore solution). Mortar specimens for mercury intrusion porosimetry were crushed using a mortar and pestle. Particles passing the 2.5 mm sieve and retained on the 1.25 mm sieve were kept for analysis. Particles were immediately immersed in propanol for a minimum of 24 h. Solvent replacement was followed by drying in a 50C vacuum oven for a minimum of 24 h. A Quantachrome Autoscan 60 capable of maximum pressure of 415 MPa was
used for mercury intrusion. The contact angle was assumed to be 140. Pore solution analysis of cement paste used an expression device similar to that of Barneyback and Diamond [28]. The 50 mm diameter by 100 mm paste cylinders were removed from their moulds and crushed with a mortar and pestle into pieces a couple centimetres in size. The chamber of the pore squeezing device was filled with as many pieces as would fit, then capped with a Teflon disk to prevent leakage. Since the strength of the pastes varied with time and mixture design, no consistent pressure sequence was used for all samples. For samples at early age and high water to cement ratio, little pressure was required to extract several millilitres of pore solution. At later ages, the pressure reached the limitations of the apparatus with little to no pore solution extracted. Hydroxyl ion concentrations were determined by automatic potentiometric titration against sulphuric acid with volumes of pore solution ranging from 0.25 to 1.0 ml. If a sufficient volume of pore solution remained after hydroxyl determination, at least 0.2 ml was required to determine concentrations of sodium and potassium by flame photometer.
3 Results 3.1 Low-pressure water permeability Water permeability measurements are known to be difficult to obtain and often results have high variability. This problem is compounded at early ages due to rapid rates of hydration and due to small differences in kinetics of reaction between samples. In this project, duplicate samples yielded permeability differences as much as an order of magnitude for a particular age. Due to the hydration of early age concrete during the test, steady state flow through the samples was unobtainable. Although not theoretically valid due to lack of steady-state flow, permeability was calculated using Darcy’s law, Eq. 4.1, using the water inflow rate; results are shown in Table 3 K¼
QLqg ADP
ð9Þ
Materials and Structures Table 3 Low-pressure water permeability (10–12 m/s) Mixture
0.31 0.40 0.40 0.40 0.40 0.69
HPC Steam PC (150) 35% SG 20% FA 7% SF PC
Age at test (Days) 1
2
3
7
14
21
28
13.4 37.7 – 66* 20* 300
4.5 4.6 15 28 9.0 155
1.5 2.2 8.0 9.0 5.6 105
0.6 0.7 0.9 14 2.1 47
0.6 0.6 2.0 13 1.0 24
0.9 0.5 2.0 19 0.6 17
0.4 0.3 2.0 12 0.4 13
*Low 1-day strength due to set retardation resulting from water reducer
where K = permeability coefficient (m/s), Q = rate of flow (m3/s), L = thickness of specimen (m), q = unit density of water (assumed to be 1,000 kg/m3), g = acceleration due to gravity (9.8 N/kg), A = area of specimen (m2), DP = applied pressure (Pa). Since the inflow pistons have finite length of travel, the pressure began to drop when the pistons reached the bottom of the cylinders. The rate of flow was calculated from the slope of the inflow LVDT (converted to volume) vs. time when over which the pressure was constant. In cases where the permeability was not calculated at the times listed in the table, the permeability was estimated from adjacent determinations. Due to the experimental conditions—a driving pressure of 0.4 MPa (60 psi), combined with the sensitivity of the LVDTs—the apparatus reached its limitations as testing progressed. The low flow rates observed at later ages brought about increased scatter of the piston displacement vs. time data used to calculate permeability. Small changes in slope at low flow rates yield significant changes in permeability (as much as an order of magnitude). It is this authors’ opinion that with this particular experimental set-up and test conditions, the limitation of the equipment is approximately 10–12 m/s. Data in Table 3 below this value should be interpreted with caution. The results presented are from single experiments. The results of the high-pressure permeability tests performed at 28 days are presented in Table 4. It was expected that there would be some variation between measured permeability at 28 days in the low-pressure device and those of
the high-pressure method. Specimens were removed from the low-pressure device for testing in the high-pressure apparatus at approximately 28 days. As it took approximately a week to obtain a reasonable amount of data in the highpressure apparatus (i.e. to 35 days of age), it would be expected that somewhat lower permeabilities would be obtained since the samples were undoubtedly further hydrated during measurement. It can be seen that results from the high-pressure device give notably lower values of permeability, up to 3 orders of magnitude lower than the low-pressure values. It was noted previously that the low-permeability device has an approximate lower permeability limit of 10–12 m/ s, so many of the 28 day values in Table 3 are likely unreliable. This observation is further validated by the relatively similar values of permeability obtained in both devices for the 0.69 PC concrete (13 and 5.5 · 10–12 m/s). Due to high conductivity at early ages, the current measured after passing 30 volts through the sample for 15 min was used to calculate conductivity at a given time of hydration Conductivity ¼
I L ; VA
ð10Þ
where I = current measure at 15 min (amps), L = thickness of specimen (cm), V = applied voltage (30 volts), A = cross-sectional area of specimen (cm2). The calculated conductivity shown in Table 5 is the average of two samples. Conductivity decreases with time for a particular concrete mixture. The influence of water to cementing materials ratio, supplementary materials and
Materials and Structures
It was expected that increasing unit water content of the mixture at the same water to cementing materials ratio would increase conductivity due to an increased paste volume; this effect was not observed. But as the paste volume increases, the aggregate volume decreases, giving a lower total surface area of aggregate for the formation of interfacial transition zones, creating a competing effect, possibly acting to lower conductivity with increased water content.
Table 4 28-day high-pressure permeability test results Mixture
High pressure permeability (10–15 m/s)
0.30 0.31 0.35 0.35 0.40 0.40 0.40 0.40 0.40 0.40 0.55 0.69 0.70 0.90
8.4 2.9 52 7.0 11 59 50 8.6 9.4 13 80 5,500 394 3,790
PC HPC Steam PC HPC PC (135) PC (150) PC (170) 35% SG 20% FA 7% SF PC PC PC PC
3.2 Mercury intrusion porosity The total porosity correlates to the maximum volume of mercury intruded and the critical diameter is determined from the maximum of the differential volume pressure curve, the results are shown in Tables 6, 7. In the case of the 0.69 PC concrete mixture, there was no readily apparent critical diameter, so the values given are estimates. Total porosity determined by mercury intrusion is seen as more indicative of the porosity available for transport, i.e., pores in the capillary size range than larger values of combined capillary and gel (including interlayer) porosity obtained gravimetrically using water displacement. As expected, porosity decreases with continued hydration as was also observed by others [8, 22]. In some instances, porosity increases are ob-
water content can be seen in the results. The 0.30 w/c Portland cement mixture initially had a lower conductivity than all other mixtures, but over time, the mixtures with supplementary cementing materials developed lower conductivity. This shows that it is not only the water to cement ratio that controls transport. The silica fume mixtures obtained particularly low values of conductivity at 28 days. The earlier results for these two SF mixtures do not agree with Christensen et al.’s [38] observation of little increase in bulk resistance of silica fume concrete for first 100 h. The variation in water content does not consistently influence the conductivity results. Table 5 Conductivity of concrete specimens (uS/cm) Mixture
0.30 0.31 0.35 0.35 0.40 0.40 0.40 0.40 0.40 0.40 0.55 0.69 0.70 0.90
PC HPC Steam PC HPC PC (135) PC (150) PC (170) 35% SG 20% FA 7% SF PC PC PC PC
Age at test (Days) 1
2
3
7
14
21
28
364 640 449 765 549 459 547 712* 820* 600* 476 881 538 626
286 524 353 462 407 379 423 574 479 338 406 699 447 579
265 419 319 378 353 345 379 478 421 321 357 602 406 506
213 148 291 159 271 295 317 211 272 131 329 501 340 422
183 40 228 46 233 218 249 110 201 70 263 335 275 289
152 25 183 31 211 190 200 82 154 37 210 297 223 246
141 19 172 25 185 161 236 53 120 29 189 267 203 214
*Low 1-day strengths were also noted due to set retardation resulting from water reducer
Materials and Structures Table 6 Total porosity (%) of mortar by MIP Mixture
0.30 0.31 0.35 0.35 0.40 0.40 0.40 0.40 0.40 0.40 0.55 0.69 0.70 0.90
PC HPC Steam PC HPC PC (135) PC (150) PC (170) 35% SG 20% FA 7% SF PC PC PC PC
Age at test (Days) 1
2
3
7
14
21
28
28 dry
14.5 13.0 12.8 16.6 12.3 15.0 13.8 14.7* 13.5* 14.0* 13.6 13.7 14.2 14.9
12.9 12.4 12.0 14.9 10.4 13.0 12.0 13.8 11.3 12.5 12.7 12.0 12.6 12.6
10.0 10.5 11.2 12.8 9.8 11.8 11.0 12.6 10.9 12.1 10.7 13.6 11.6 12.1
9.4 8.5 9.1 9.7 7.4 10.7 10.2 11.9 9.3 8.4 11.2 11.2 11.8 12.3
8.2 7.5 8.9 9.4 7.9 10.4 8.3 8.3 7.3 8.5 10.7 13.4 12.3 12.2
7.5 7.0 8.9 9.3 8.6 10.6 9.6 8.0 7.6 7.9 8.2 10.6 11.4 12.1
8.5 7.2 8.6 8.5 6.0 9.8 9.3 7.1 6.8 7.5 8.8 7.3 11.1 11.9
12.1 7.5 9.9 10.1 7.3 10.3 8.3 8.0 7.6 7.9 9.9 11.9 11.8 –
*Low 1-day strengths were also noted due to set retardation resulting from water reducer
served between two successive ages. As with the other destructive tests performed in this work, variations between samples are expected. (Only the permeability and conductivity tests were performed on the same specimens over time.) In most instances, an additional portion of the same crushed sample was tested, yielding similar results. As mentioned in the procedures section, the paste specimens were axially rotated until set to prevent bleeding. The specimens were removed from the moulds at 1 day and immersed in saturated lime solution. As a comparison, one
specimen for each sample was kept in a sealed condition in the mould for 28 days. In this case, additional water was not available from the environment for further hydration. In all but one case, the porosity was higher for the sealed specimen. As seen in Table 7, the variation in unit water content of concrete did not consistently influence the mortar porosity or critical diameter results. The critical pore radius decreased with hydration for all mixtures investigated. Again, variations in critical pore radius occurred at later ages.
Table 7 Critical pore radii of mortar (um) by MIP Mixture
0.30 0.31 0.35 0.35 0.40 0.40 0.40 0.40 0.40 0.40 0.55 0.69 0.70 0.90
PC HPC Steam PC HPC PC (135) PC (150) PC (170) 35% SG 20% FA 7% SF PC PC PC PC
Age at test (Days) 1
2
3
7
14
21
28
28 dry
0.022 0.039 0.105 0.092 0.028 0.100 0.030 0.145* 0.131* 0.039* 0.043 0.054 0.175 0.190
0.018 0.018 0.037 0.025 0.020 0.041 0.021 0.039 0.036 0.025 0.040 0.037 0.070 0.168
0.014 0.017 0.033 0.019 0.022 0.031 0.019 0.026 0.028 0.015 0.035 0.028 0.052 0.137
0.016 0.012 0.030 0.011 0.017 0.031 0.021 0.022 0.023 0.015 0.030 0.034 0.043 0.128
0.015 0.009 0.024 0.013 0.019 0.024 0.013 0.014 0.018 0.019 0.026 0.030 0.038 0.077
0.015 0.009 0.028 0.011 0.021 0.032 0.014 0.016 0.013 0.015 0.023 0.023 0.034 0.057
0.019 0.007 0.024 0.009 0.011 0.031 0.011 0.020 0.015 0.013 0.028 0.018 0.034 0.075
0.025 0.009 0.021 0.020 0.011 0.038 0.013 0.020 0.015 0.014 0.029 0.023 0.036 –
*Low 1-day strengths were also noted due to set retardation resulting from water reducer
Materials and Structures
Asymptotic values were achieved for total porosity and critical diameter after 7 days except for mixtures at high water to cementing materials ratio. For the sealed samples measured at 28 days, the critical diameter was not significantly larger than the immersed sample at the same age. At 28 days, no consistent trend in critical pore radius is observed with water to cementing materials ratio.
after which it decreases. These observations are consistent with Diamond [40] and Christensen et al. [38]. Slag and fly ash do not seem to affect the pore solution conductivity, other than by dilution in an amount approximately equal to volume replacement of cement.
3.3 Pore solution analysis
4.1 Conductivity coupled with pore parameters to predict permeability
4 Discussion
As the volume of pore solution was insufficient to measure conductivity directly, the method of Snyder et al. [39] was used to determine the conductivity of the pore solution from the concentrations of hydroxyl, potassium and sodium ions. The results are presented in Table 8. The lower water to cementing materials ratios mixtures did not yield necessary quantities of pore solution for analysis of hydroxyls and alkalis at later ages. Where concentrations of all ions were not available, no conductivity was estimated. (It would have been possible to roughly estimate conductivity based on charge balance of OH– with the sum of Na+ and K+, but it was since the Na+/K+ ratio was not constant with either time or mixture, it was decided not to approximate the conductivity.) For the pastes containing Portland cement only, the calculated conductivity increases with time. For those pastes containing silica fume (0.31 HPC, 0.35 HPC, and 0.40 7% SF), conductivity reached a maximum after approximately 3 days,
Figure 5 gives the measured and predicted permeability for ages up to 28 days, where pore solution conductivities were available. In all cases, the predicted permeability is lower than that measured. In general, the values are approximately an order of magnitude different, but more than two orders of magnitude in the case of the 0.31 HPC mixture at later ages. The opinion of the authors is that with the low-pressure device, permeability values below 1 · 10–12 m/s are suspect; and the greatest deviations occur for sample data below this value. The permeability determined in the low-pressure device at 28 days is greater than that observed in the high-pressure device for the same specimens a few days later. It has been shown elsewhere that pressure gradient affects permeability results [1]. Figure 6 shows the measured 28-day highpressure permeability and that predicted from the Katz–Thomson relationship (Eq. 1). (The mixtures not represented here had insufficient
Table 8 Calculated pore solution conductivity (mS/cm) Mixture
0.30 0.31 0.35 0.35 0.40 0.40 0.40 0.40 0.55 0.69 0.90
PC HPC Steam PC HPC PC 35% SG 20% FA 7% SF PC PC (0.70) PC
Age at test (Days) 1
2
3
7
14
21
28
137 150 96 66 67 57 60 69 49 38 29
139 153 101 76 76 66 74 66 52 42 32
143 – 121 78 80 64 74 71 54 43 34
– 131 112 76 83 63 92 60 63 47 35
– 98 – 51 94 88 – 54 63 48 35
– 81 – 47 102 84 – 45 66 51 37
– 64 – 54 – 91 112 49 63 50 37
Materials and Structures
1.E-09 Calculated Permeability (m/s) .
Fig. 5 Measured and calculated permeability at early ages—low pressure device
0.31 HPC
1.E-10 0.40 PC (150) 1.E-11 0.40 35% SG
1.E-12 line of equality 1.E-13
0.40 20% FA
1.E-14 0.40 7% SF 1.E-15 1.E-15
1.E-14
1.E-13
1.E-12
1.E-11
1.E-10
1.E-09 0.69 PC
Measured Permeability (m/s)
pore solution at 28 days for the direct determination of conductivity.) To obtain the predicted permeability, the bulk conductivity was measured on concrete, the pore solution conductivity on paste, and the critical pore radius on mortar extracted from the concrete. It can be seen that the predicted permeability is well within an order of magnitude of that measured. The agreement between the measured and predicted permeabilities is similar to that reported by Christensen et al. [18]. The 0.69 PC concrete lies furthest from the line, with approximately an order of magnitude discrepancy. The critical pore radius of this mortar seems low compared to other values, particularly when compared to the 0.70 PC mixture. The low critical pore radius would lead to a low predicted permeability. 4.2 Archie’s Law validity in concrete Figure 7 shows the normalized conductivity vs. total porosity. This relationship is the same as that used in Archie’s Law. Rearranging Eq. 7,
0.31 HPC
1.E-11 Calculated Permeability (m/s) .
Fig. 6 Measured and calculated 28-day permeability—high pressure device
the relationship between porosity and normalized conductivity should be of a simple power law form with constants a and m. Table 9 gives the fitted constants and correlation coefficient for Archie’s Law using measured paste porosity. The overall data plotted in Fig. 7 give a as 41.71 and m as 4.22. Wong et al. [32] predicted the values of constants a as approximately 1 and m between 1 and 2. Recall that these authors’ work was on rock. Other researchers’ results in cementitious systems give a in the range of 0.14–7.71 and m from 2.14 to 4.8. The constant a varies over orders of magnitude. The constant m is always greater than 1 and often greater than 2, but has a much smaller range. To be fair, recall that the porosity was measured from mortar, pore solution conductivity was determine from paste, while the bulk conductivity was from concrete. The overall fitted constants for using the paste porosity (results not provided here) give a as 0.08 and m as 2.42. This numerical value for the constant m is closer to that given by previous researchers.
0.35 HPC 0.40 PC (135)
1.E-12
0.40 PC (150) 0.40 PC (170)
1.E-13
0.40 35% SG line of equality
0.40 7% SF
1.E-14
0.55 PC 1.E-15 1.E-15
0.69 PC 1.E-14
1.E-13
1.E-12
Measured Permeability (m/s)
1.E-11
0.70 PC 0.90 PC
Materials and Structures Fig. 7 Total porosity in mortar vs. normalized conductivity
0.025
0.30 PC
Normalized Conductivity .
0.31 HPC 0.020
0.35 PC
4.22
y = 41.71x R2 = 0.72
0.35 HPC 0.40 PC (150)
0.015
0.40 35% SG 0.40 20% FA
0.010
0.40 7% SF 0.55 PC
0.005
0.69 PC 0.000 0.00
0.70 PC 0.05
0.10
0.15
0.20
0.90 PC
Total Porosity
Table 9 Archie’s Law constants and correlation coefficients Mixture
a
m
R2
0.30 0.31 0.35 0.35 0.40 0.40 0.40 0.40 0.55 0.69 0.70 0.90
0.036 25 0.052 25 4.6 35 57 7.3 0.92 4.3 102 210
1.34 4.23 1.25 4.25 3.38 4.16 4.16 3.49 2.31 2.88 4.52 4.73
0.79 0.97 0.74 0.94 0.83 0.99 1.00 0.92 0.88 0.27 0.65 0.50
PC HPC Steam PC HPC PC (150) 35% SG 20% FA 7% SF PC PC PC PC
It can be seen that good relationships exist between porosity and normalized conductivity within a single mixture. There is no unifying relationship between all mixtures, but rather unique relationships exist for each mixture, agreeing with Garboczi [3]. It was also found that there was no unique relationship when combining pore parameters; such as the product of the porosity and the critical pore radius.
5 Conclusions The validity of the Katz–Thompson relationship for predicting permeability based on normalized conductivity and pore parameters, has been the source of debate. Although developed for use in rocks, the technique could be a useful predictive tool for other porous materials. Water permeability is a difficult test to perform as well as a
time and equipment intensive procedure with duplicate specimens exhibiting high variability. The idea that alternate, simple tests could predict permeability is a powerful notion. The Katz–Thompson relationship to calculate permeability from pore parameters and normalized conductivity agreed reasonably well to the measured permeability. Given the high coefficients of variation in measured permeability testing, combined with the necessary specialized equipment and long testing time, the Katz– Thompson method to obtain estimates of permeability seems useful. The correlation to the Katz– Thompson relationship depends highly on the capabilities and limitations of the permeability method used. Previously published results that give poor correlation to the Katz–Thompson relationship are considered to be deficient in regards to the measured permeability results. Measured permeability is dependent on the pressure used as well as the sensitivity of the flow measurement. Permeability tests were performed on replicate concrete and paste specimens from an early age using both the low and high-pressure apparati. The permeability determined using the low-pressure device was higher than that observed at high-pressure by approximately an order of magnitude. The difference in measured permeability was not directly proportional to the applied pressure difference. In addition to measured water permeability difficulties, the precision of the normalized conductivity and critical pore radius values creates variability of the predicted permeability results but not to as large as an extent.
Materials and Structures
Archie’s law relating normalized conductivity to porosity does not represent a unique relationship for concrete. However, within a single mixture the correlation coefficient is high. There was found to be a large range in the fitted constants a and m. The fitted constants for any particular mixture do not agree with the published values for rock.
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