Increasing the Reliability of Formation Factor-Based Transport Property Prediction for High Performance Concrete Mixtures Through Innovative Matching Pore Solution Curing

Abstract

Recent specifications for concrete bulk resistivity tests (ASTM C 1876 and AASHTO TP 119) recommend a submerged standard (simulated) pore solution (SPS, solution conductivity = 78.74 mS/cm) for curing concrete specimens. The rationale for the bucket test is that immersing concrete specimens in a soak solution similar to their pore solution would eliminate the need to determine pore solution resistivity for calculating the formation factor (FF) of concrete mixtures. However, the thermodynamic modeling predictions of 91-day pore solution concentration (PSC) for eight high performance concrete (HPC) mixtures evaluated in the current study showed SPS to be a close representation only for reference ordinary Portland cement (OPC) and binary silica fume mixtures. In contrast, the average PSC of Class F and Class C fly ash mixtures was approximately 12% to 20% lower and 20% to 40% higher, respectively, than the SPS. Accordingly, an innovative matching pore solution (MPS) curing approach was developed in which mixtures are grouped based on the influence of supplementary cementitious materials (SCMs), that is, their type and replacement levels of the long-term PSC of concrete mixtures and, thereby, cured in a simulated solution matching the average PSC of a particular group. Based on experimental work in the current study, HPC mixtures under MPS demonstrated a lower coefficient of variation (COV) and more comparable (<10% difference) bulk resistivity (BR) and surface resistivity (SR) measurements compared with SPS. Moreover, the MPS improved the reliability in FF determination and FF-based transport property prediction for HPC mixtures, as verified by lower mean absolute error and improved R² between FF-predicted diffusion coefficients and experimental measurements.

Keywords

High Performance Concrete Resistivity Formation Factor Transport Properties Pore Solution Conductivity Pore Solution Curing Matching Pore Solution Curing

The high performance in high performance concrete (HPC) signifies an optimal durability performance of a mixture during the expected service life of the structure for its intended application under surrounding ambient exposure conditions ( 1 ). Texas Department of Transportation (DOT) uses Class S HPC mixtures comprising binary and ternary combinations of supplementary cementitious materials (SCMs) such as Class F fly ash (FFA), Class C fly ash (CFA) and silica fume (SF) for bridge deck construction in Texas ( 2 ).

Service life evaluation studies require determining the concrete mix’s transport properties, such as chloride diffusion (ASTM C 1556) or rate of absorption (ASTM C 1585), which primarily control ion/fluid ingress into concrete structures ( 3 , 4 ). However, these performance tests require laborious sample conditioning, are time-consuming and slow in implementation, and provide limited information on the measured properties in some cases, and, thus, are not ideal for implementation for quality control ( 5 , 6 ). However, the desire for rapid service life evaluation of concrete structures has led to the development of tests that rely on the electrical conduction of pore fluid to characterize the microstructure and transport properties of concrete mixtures ( 7 ).

Formation factor (FF) is a fundamental material property that describes the microstructure characteristics (permeable pore volume and pore connectivity) of concrete mixtures and is determined as the ratio of concrete resistivity to the resistivity of its pore solution ( 8 , 9 ). Since pore network characteristics of concrete control ion/moisture ingress and their movement through the bulk concrete, previous studies have shown concrete FF can be related to its transport properties, such as chloride ion diffusion ( 10 – 12 ), water sorptivity ( 13 , 14 ), and intrinsic permeability (15).

However, concrete resistivity measurements depend on three primary parameters: pore solution composition–ionic conductivity; pore structure characteristics–pore volume; and pore connectivity, and saturation state–moisture connectivity (16). Therefore, a key challenge in calculating FF is the reliable determination of pore solution composition (or conductivity, i.e., PSC) of concrete mixtures. PSC of concrete is determined either through extraction or modeling approaches. However, the extraction of pore solution from paste/mortar/concrete requires a complicated procedure, contingent on the applied pressure and is thus usually limited to early ages ( 17 , 18 ). As for modeling approaches, the online NIST model ( 19 ) is widely used to estimate the PSC of concrete mixtures based on bulk oxide compositions of concrete ingredients. However, several studies ( 18 , 20 ) have noted that while the NIST model provides a reasonable estimation of PSC for OPC mixtures, it significantly overestimates the PSC of fly ash mixtures, especially in cases of Class F FA ( 21 ). Of late, several researchers have successfully used the thermodynamic modeling approach to model hydration phase assemblage and predict the PSC of binary and ternary concrete mixtures ( 22 – 25 ). However, while the thermodynamic model can predict PSC with higher accuracy, it does not present a convenient approach for industry practitioners.

Additionally, the FF of concrete mixtures is typically determined based on resistivity measurements in the laboratory. Previous studies have shown that standard curing practices following ASTM C 511, such as moist curing and saturated lime water curing, influence resistivity measurements primarily through the leaching of ionic species (typically Na and K) from concrete mixtures ( 18 , 26 ).

Recently specifications for concrete BR tests (ASTM C 1876 and AASHTO TP 119) have recommended a submerged standard (simulated) pore solution (SPS) curing regimen (curing solution conductivity = 78.74 mS/cm) for sample curing ( 5 ). Accordingly, the “bucket test” (i.e., sample immersion in sealed buckets containing SPS curing solution) was proposed to resolve two primary issues of alkalis leaching and determination of the pore solution resistivity for calculating FF ( 18 ). In contrast, the applicability of a single standard ASTM C 1876 SPS solution to adequately represent the pore solution composition of concrete mixtures with different mix designs/proportions, SCM type/replacement levels, and ingredient variability is questionable. Furthermore, a previous study ( 18 ) noted that if concrete PSC does not match the bucket solution, it could result in significant overprediction or underprediction of FF; however, its effect on the reliability of FF determination and, consequently, its influence on transport properties prediction has not been investigated or quantified.

The rationale for the bucket test stems from immersing samples in curing solution with a similar composition of expected concrete pore solution would: (1) eliminate leaching and, thus, lower the variability in resistivity measurements; and (2) eliminate the need to determine pore solution resistivity based on the assumption that specimens’ pore solution eventually equilibrates with the bucket solution ( 18 ).Therefore, a mix-specific pore solution curing practice would eliminate/minimize leaching, ensure a good match between PSC and soak solution (bucket solution), and ensure high FF determination reliability. However, while PSC determination for individual mixtures is challenging, preparing individual solutions for curing each mix type is laborious, impractical, and unsuitable for field implementation.

Objective

The primary objective of the current research is to improve the reliability in the FF determination of concrete mixtures by introducing an innovative matching pore solution (MPS) curing approach for resistivity tests. Under the MPS curing regimen, mixtures are grouped based on the effects of SCM type/replacement levels on the long-term PSC of concrete mixtures and, thereby, cured in a simulated solution matching the average PSC of a particular group. Therefore, MPS curing is proposed as an improved mix-specific pore solution curing practice to increase the reliability in FF determination and, thereby, improve the FF-based transport property prediction for HPC mixtures. The specific objectives are:

Investigate the long-term PSC of eight binary and ternary HPC mixtures containing Class C FA, Class F FA, and SF using thermodynamic-based GEMS modeling.

Develop an MPS curing regimen for eight HPC mixtures evaluated in the current study based on the influence of SCM type on long-term PSC modification.

Measure the bulk resistivity (BR) and surface resistivity (SR) of HPC mixtures under both SPS and MPS curing regimens (7 to 180 days) to determine their apparent formation factor (AFF) and saturated FF.

Determine the effective diffusion coefficients (D_e) of HPC mixtures based on chloride ponding (ASTM C 1556) and chloride binding tests.

Predict the effective diffusion coefficients (D_e) of HPC mixtures based on the established FF-transport property relationship.

Compare experimentally versus predicted D_e for HPC mixtures and investigate the influence of SPS versus MPS curing regimens on the reliability of FF determination and FF-based transport property prediction for HPC mixtures.

Materials and Mix Designs

Materials

Type 1 ordinary portland cement (OPC, ASTM C 150), Class F and Class C fly ash (FA, ASTM C 618), and silica fume (SF, ASTM C 697) were used to prepare binary and ternary HPC mixtures evaluated in this study. Table 1 summarizes the bulk oxide composition of cementitious materials used in this project, measured using x-ray fluorescence (XRF). Table 1 also shows quantitative x-ray diffraction (QXRD) measurements for concrete ingredients. Using commercially available software (Diffrac EVA and TOPAS 5.0), the Rietveld refinement technique was employed to identify and quantify crystalline phases, while the amorphous content SCMs were determined using the partial or no known crystal structure (PONKCS) method ( 21 ). In addition, water-soluble alkali (ASTM C 114, modified) and available alkali (ASTM C 311) tests were performed on fly ashes (Table 1) to estimate their early and later-stage soluble alkali contribution to pore solution.

Table 1.

XRF, QXRD, and Soluble Alkali Tests for Ingredients

Test	Phase	Cement	Class C fly ash	Class F fly ash	Silica fume
XRF (%)	CaO	63.41	26.33	14.98	-
	SiO₂	20.43	37.51	55.26	97.9
	Al₂O₃	6.78	19.8	22.34	0.18
	Fe₂O₃	2.05	5.13	4.71	0.07
	SO₃	3.72	2.12	0.69	0.17
	MgO	1.13	5.45	2.8	0.21
	Na₂O	0.15	1.71	0.52	0.12
	K₂O	0.43	0.49	0.85	0.59
	Na₂O_eq (Bulk)	0.43	2.02	1.08	0.51
QXRD (%)	Bogue composition	C₃S 54.8	na	na	na
		C₂S 20.18
		C₃A 9.78
		C₄AF 4.51
	Crystalline/amorphous	na	59/41	26/74	3/97
	Theradnite (Na-SO₄)	0.23	1.98	0.37	na
	Arcanite+Syngenite (K-SO4)	0.64	0.60	0.69	na
Soluble alkali	Water soluble alkali (WSA) Na₂O_eq and (%Bulk)	0.30 (70%)	0.28 (14%)	0.07 (6%)	na
Soluble alkali	Available alkali (AA) Na₂O_eq and (%Bulk)	na	1.36 (67%)	0.42 (39%)	na

Note: XRF = x-ray fluorescence; QXRD = quantitative x-ray diffraction; na = not applicable.

Mix Designs

A total of eight binary and ternary HPC mixtures, including the control mix (100% OPC), were designed for this experimental program with a w/cm ratio of 0.42, coarse aggregate factor (CAF) of 0.67, and 520-580 lb/yd³ of cementitious material. HPC mixtures in the lab were designed following Texas DOT’s standard mix design practice for bridge deck concrete and matching with field practices in Texas. All HPC mixtures were prepared using siliceous river sand (sp. gr 2.61, absorption 0.44%) as fine aggregates and 1 in. (maximum aggregate size, MSA) siliceous river gravel (sp. gr 2.72, absorption 0.78%) as coarse aggerate, both conforming to ASTM C 33 gradation requirements. In addition, all HPC mixtures contained air-entraining admixtures (AEA, ASTM C 260), Type F high-range water reducer (HRWR, ASTM C 494), and fibers to meet target air content (4%–6%) and workability requirements (3–5 in.). Table 2 lists the HPC mixture proportions evaluated in this study and reports the results from fresh property tests: temperature (ASTM C 1064), slump (ASTM C 143), and air content by pressure method (ASTM C 231).

Table 2.

HPC Mix Proportions and Fresh Properties Testing (Slump and Air Content)

Mix designation	Control	6SF	25F	20F5SF	35F	35C	29C6SF	35C10SF
Total cementitious content (lb/yd³)	580	520	584	584	584	520	541	541
Cement, (lb/yd³)	580	489	438	438	380	338	352	298
Class F fly ash, (lb/yd³)	na	na	146	117	204	na	na	na
Class C fly ash, (lb/yd3)	na	na	na	na	na	182	157	189
Silica fume, (lb/yd³)	na	31	na	29	na	na	32	54
Coarse aggregate (1" MSA), (lb/yd³)	1,815	1,800	1,815	1,817	1,815	1,887	2032	2031
Fine aggregate, (lb/yd³)	1,236	1,296	1,236	1,230	1,275	1,192	1,056	1,043
Mixing water, (lb/yd³)	232	234	236	239	242	216	220	218
AEA, (fl. oz/100 lb cem)	0.5	0.5	0.5	0.5	0.5	0.5	0.5	0.5
Type F-HRWR, (fl. oz/100 lb cem)	7	7	7	7	7	7	7	7
Fibers (lb/yd³)	0.5	0.5	0.5	0.5	0.5	0.5	0.5	0.5
w/cm (design)	0.42	0.42	0.42	0.42	0.42	0.42	0.42	0.42
Fresh properties
Temperature, °F (ASTM C 1064)	70	68	68	68	70	70	68	70
Slump, in (ASTM C 143)	5.25	4.5	5	4.5	4.75	5.0	4.5	4
Air content (ASTM C 231)	6.2%	6.0%	5.3%	4.9%	5.0%	5.5%	5.5%	5.0%

Note: HPC = high performance concrete; Control = 100% OPC mix; AEA = air-entraining admixtures; na = not applicable.

Rationale and Development of Matching Pore Solution (MPS) Curing Regimen

In the early stages of developing an MPS curing regimen, as a proof of concept, thermodynamic-based GEMS modeling was used to predict the Na and K ion concentration in the pore solution of HPC mixtures and thereby calculate the pore solution conductivity (PSC) following the approach outlined by Snyder et al. ( 27 ). However, while the thermodynamic model can accurately predict PSC, it does not present a convenient approach for industry practitioners. Therefore, to avoid this limitation in implementing MPS curing, the authors are currently developing simplified excel-based software to predict the long-term PSC of binary/ternary concrete mixtures. The model uses bulk oxide composition (XRF) of cementitious materials to predict PSC based on established equations that account for alkali dissolution and alkali binding, which is briefly mentioned in the Future Work section.

Thermodynamic Modeling for HPC mixtures

The current study used thermodynamic-based GEMS modeling (GEMS Selektor v 3.5 software) to predict the 91-day PSC of eight HPC mixtures based on their composition (Table 1) and mix proportions (Table 2) as inputs. A built-in thermodynamic database PSI-GEMS and cemdata18 were used to model cementitious systems’ equilibrium reactions and their hydrated products, following the approach outlined in previous studies ( 22 , 23 , 28 , 29 ). Based on an extensive literature review, typical 91-day degree of reaction (DOR) values for cement [ $α_{cem}$ ∼90%], SF for 5% to 15% replacement levels [ $α_{SF}$ ∼75%] Class F and C FA for 20% to 50% replacement levels [ $α_{FFA}$ ∼35% and $α_{CFA}$ ∼50%] ( 23 , 28 –33) were used to model ingredients’ reactivity with time. In cementitious materials, a fraction of total alkali is present in the form of crystalline alkali sulfate phases that are water-soluble and readily released into the pore solution on dissolution ( 34 , 35 ). Accordingly, water-soluble alkali (WSA) from ingredients measured following mod. ASTM C 114 procedure (Table 1) was modeled for rapid release into pore solution (i.e., instantaneous dissolution) in thermodynamic modeling. The remainder, that is, the bound alkali fraction incorporated in the cement clinker phases or the glass fraction of fly ashes, was modeled to be released into pore solution proportional to the ingredients’ DOR with time ( 23 ). The effect of alkali binding was modeled using distribution ratios developed by Hong and Glasser ( 36 ) through C-S-H model proposed by Kulik ( 37 ) as outlined by Lothenbach et al. ( 38 ).

Figure 1 shows the results from thermodynamic modeling for the 91-day PSC of HPC mixtures and compared with the conductivity of the ASTM C 1876 standard SPS curing solution.

Figure 1.

PSC of HPC mixtures versus ASTM C 1876 curing solution conductivity.

Pore Solution Conductivity (PSC) of HPC Mixtures

HPC mixtures were prepared using a Type I/II cement with a bulk alkali content (Na₂O_eq) of 0.43%. Accordingly, results from Figure 1 show the 91-day PSC of the CEM mix to be around 83.29 mS/cm as cement hydration releases a substantial amount of its bulk alkalis into pore solution on account of high WSA ∼69%) and a high degree of hydration (∼90%) at 91 days. However, cement replacement with 6% SF reduced the 91-day PSC of the 6SF mix by 6%, primarily attributed to cement dilution with some minimum reduction as a result of alkali binding by pozzolanic hydration product (C-S-H with low Ca/Si).

Class F FA used in this study contained a higher bulk alkali content (1.08% Na₂O_eq) than cement. While the soluble alkali contribution from F ash into pore solution is significantly low at early ages (6% WSA/TA), it increases through the release of bound alkalis from the amorphous phase over time, depending on DOR. However, alkali uptake through alkali binding by the pozzolanic C-S-H or C-S-A-H with low Ca/Si also increases as a function of DOR, which possibly explains 12% and 19% reductions in 91-day PSC for binary F ash mixtures 25F and 35F, respectively. However, for the ternary mix (i.e., 20F6SF), a high DOR of SF along with the increase of DOR of Class F FA given the nucleation effect offered by finer SF particles results in the formation of more pozzolanic C-S-H/C-S-A-H with low Ca/Si compared with 25F, which can uptake more alkali from pore solution. Accordingly, 20F5SF showed the highest 91-day PSC reduction (i.e., 20%) compared with the Control mix and binary F ash mixtures.

The Class C FA used in the current study contains high bulk alkali (i.e., 2.02% Na₂O_eq ), and compared with cement, the FA contained lower WSA (14% of TA) but a higher fraction of AA (∼67% ≈1.36 Na₂O_eq). Consequently, the soluble alkali contribution from Class C ash is expected to be higher than cement by 91 days. Although the DOR for Class C ash is higher than Class F, the pozzolanic hydration product (C-S-H) demonstrates a comparatively lower alkali binding potential given relatively higher Ca/Si as compared with Class F FA. As a result, the 35C mix showed a 40% PSC increase compared with the Control mix, even though Class C FA replaced the 35% cement. As SF addition enhances alkali uptake potential through the formation of low Ca/Si pozzolanic C-S-H, the ternary Class C ash and SF mixtures (i.e., 29C6SF and 35C10SF) show approx 19% and 31% increase in 91-day PSC, respectively, compared with the Control mix.

Development of the MPS Curing Regimen

Figure 1 and Table 3 show a comparative assessment of the PSC of HPC mixtures determined from thermodynamic modeling and ASTM C 1876 SPS curing solution. Results show the PSC values for Control and 6SF mixtures are close (i.e., within 1%–5%) to the SPS solution conductivity. However, while the PSCs of Class F FA mixtures (25F, 20F5SF and 35F) are 12% to 20% lower than the SPS solution, the PSCs of Class C FA mixtures (35C, 29C6SF and 35C10SF) are 20% to 40% higher than SPS solution conductivity. Therefore, results from Figure 1 and Table 3 clearly demonstrate that considering a single soak solution with conductivity = SPS conductivity is a good representation for Control and 6SF mixtures, but it creates a slight overestimation of soak solution PSC for F ashes mixtures and significant underestimation for C ash mixtures. A slight overestimation of soak solution PSC may not create any considerable error in resistivity measurement (discussed later) for F ash mixtures. However, significant underestimations for C ash mixtures may create a considerable error in resistivity measurement because of alkali leaching from the tested specimens.

Table 3.

Pore Solution Conductivity (PSC) of Eight HPC Mixtures versus Composition and Conductivities of MPS and SPS Curing Solutions

#Mix	PSC (mS/cm)	Curing regimen	Specimen curing	Composition of curing solution
#Mix	PSC (mS/cm)	Curing regimen	Specimen curing	NaOH (g/L)	KOH (g/L)	Ca(OH)₂ (g/L)	Conductivity, mS/cm and (resistivity, Ohm-m)
Control	83.29	MPS curing	Group 1: No fly ash	4.8	12.32	2	80.64 (0.124)
6SF	77.98		Group 1: No fly ash	4.8	12.32	2	80.64 (0.124)
25F	73.00		Group 2: Class F fly ash mixtures	4.8	13.44	2	70.09 (0.143)
20F5SF	67.30
35F	69.97
35C	116.30		Group 3: Class C fly ash mixtures	14.8	10.08	2	108.00 (0.093)
29C6SF	108.80
35C10SF	98.90
All HPC mixtures		SPS curing	All HPC mixtures	7.6	10.64	2	78.74 (0.127)

Note: HPC = high performance concrete; MPS = matching pore solution; SPS = standard (simulated) pore solution.

Therefore, to avoid the errors/variability in resistivity measurements associated with a single SPS curing solution, the MPS curing regimen was developed in current research. Ideally, MPS curing demands mimicking the PSC of each mix, which is not practical. To make MPS curing effective and implementable, the eight HPC mixtures were divided into three groups: (1) Group 1, HPC mixtures with no fly ash, that is Control and 6SF (avg. PSC ∼±1%–5% of SPS); (2) Group 2, HPC mixtures containing Class F FA, that is, 25F, 20F5SF and 35F (avg. PSC < 12%–20% of SPS); and (3) Group 3, HPC mixtures containing Class C FA, that is, 35C, 29C6SF and 35C10SF (avg. PSC > 20%–40% of SPS). For each group, a representative curing/soak solution was designed with a PSC equal to the average PSC of all mixtures in that group. Next, the soak solution’s PSC, that is, ionic concentrations, Na (mol/L) and K(mol/L), were converted to respective NaOH and KOH dosages (g/L) based on their respective molar mass. Finally, each representative MPS solution was saturated with 2 g/L Ca(OH)₂ to mimic the concrete pore solution. The composition (dosage) and conductivity of MPS curing solutions for groups 1 to 3 and the SPS curing solution for all mixtures are presented in Table 3.

Test Methods

The test methods that were used to measure resistivity, chloride diffusion, and chloride binding are described below.

Resistivity and Formation Factor Evaluation

Resistivity Tests

For resistivity testing, three replicate 4 × 8 in. (4 ± 0.08 in. diameter and 8 ± 0.16 in. height) concrete cylinders were cast for each HPC mix design. Concrete cylinders were demolded at 24 ± 2 h and placed in sealed buckets containing soak solution with chemistry equal to SPS and MPS curing (prepared following Table 3) and a storage solution-to-sample ratio of 4:1 throughout the testing period. Resistivity measurements for all test samples were performed under standard room temperatures of 23°C ± 2°C and following ASTM C 1876/AASHTO TP 119 and AASHTO PP 84-18 specifications. At each testing age, samples were removed from the appropriate curing solution, wiped/blotted with a clean damp cloth to remove any solution, and measured for bulk and SR measurements within 5 min of being removed from the curing solution. The test cylinders’ temperatures were recorded at the time of testing to account for the temperature effects on resistivity measurements based on the Arrhenius correction function ( 39 ). Resistivity tests were performed on five replicate test cylinders for each HPC mix at 7, 14, 28, 56, 91, and 180 days for each curing regimen.

BR measurements (ASTM C 1876 /AASHTO TP 119) were performed using a resistivity meter (RCON) manufactured by Giatech Scientific at a frequency of ∼1 kHz at 23 ± 2°C. During the test, the end sponges of the device were saturated with conductive gel and placed between the specimens to ensure good electrical contact with the end electrodes. Based on the test cylinders’ dimensions (4 × 8 in.), a geometric correction factor (GCF) of 1.57 in. (3.98 cm) was used in BR determination ( 16 ). Surface resistivity (SR) measurements (AASHTO T 358) were performed using a commercially available four-point Wenner probe meter manufactured by Proceq. SR measurements were recorded in duplicate at 0°, 90°, 180°, and 270° along each cylinder’s circumference, and the average resistivity measurements are reported here. Based on the test cylinders’ dimensions (4 × 8 in.) and 1.5 in. (38 mm) probe spacing for the test device, the GCF of 1.92 was used in the SR determination ( 40 ).

Vacuum Saturation Conditioning

After resistivity testing at 91 days, three samples (4 × 8 in. concrete cylinders) of each HPC mix from the MPS and SPS curing regimen were cut using a wet saw to obtain 2-in. (50 mm) thick specimens from its midsection. First, the 4 × 2 in. specimens were towel-dried to saturated but surface dry (SSD) conditions and measured for BR. Next, the specimens were oven-dried at 105°C ± 2°C (212°F ± 3.6°F) to a constant mass (36–48 h), then placed in a desiccator connected to a vacuum pump, and the vacuum pressure was maintained for 3 h. Subsequently, an appropriate solution matching the curing regimen (i.e., SPS or MPS) was drawn into the chamber, and the vacuum pressure was maintained for an additional hour. Following the vacuum session, specimens were left submerged in the solution for the next 21h and recorded for saturated BR measurements $(ρ^{sat})$ under towel-dried SSD conditions. The samples’ degree of saturation and porosity were determined following ASTM C 642.

Apparent Formation Factor (AFF) and Saturated Formation Factor (FF)

Apparent formation factor (AFF) and saturated FF for eight HPC mixtures subjected to SPS and MPS curing regimens were determined following Equations 1 and 2, respectively.

AFF (SPS / MPS) = \frac{ρ_{SPS / MPS}^{app}}{ρ_{SPS / MPS at (t = 91 d)}^{ps}}

(1)

FF (SPS / MPS) = \frac{ρ_{SPS / MPS}^{sat}}{ρ_{SPS / MPS at (t = 91 d)}^{ps}}

(2)

where $ρ_{SPS / MPS}^{app}$ and $ρ_{SPS / MPS}^{sat}$ represent the 91-day apparent BR of HPC mixtures from SPS and MPS curing regimen and their saturated BR measurements following the vacuum saturation conditioning. For 91-day AFF or FF, resistivity measurements were normalized with their 91-day SPS or MPS bucket conductivity measurements containing those mixtures.

Determination of Effective Diffusion Coefficients (D_e) for HPC Mixtures

The effective diffusion coefficient of concrete mixtures describes the transport of free chlorides in the concrete pore solution that is primarily responsible for corrosion initiation in concrete structures. The effective chloride diffusion ( $D_{e}$ ) for HPC mixtures was determined based on two different approaches: (1) experimental determination based on ASTM C 1556 ponding tests and chloride binding experiments; and (2) predicted based on 91-day FF and AFF of HPC mixtures. The approach is outlined below.

Experimental Determination of Diffusion Coffecients for HPC mixtures

Bulk (Apparent) Chloride Diffusion Coefficient ( $D_{a}$ )

For chloride ponding tests, three replicate 4 × 8 in. (4 ± 0.08 in. diameter and 8 ± 0.16 in. height) concrete cylinders were cast for each HPC mix design and cured in ASTM C 511 fog room for 56 days. Next, 3-in. thick specimens were cut from the midsection and coated with Sikadur 32 Hi-Mod epoxy on the bottom and sides to ensure a unidirectional ingress of chloride ions from the top surface. Subsequently, specimens were immersed with the top face exposed to 2M NaCl solution (16.2% NaCl,wt%) for 56 days instead of the 35-day exposure period recommended in the specification ( 41 ). At the end of the exposure period, specimens were removed, washed with tap water to rinse salt deposits, and dried for one day at 23°C ± 2°C and 50 ± 3% RH. Next, samples were sliced into eight layers at specific depths, ground to powder (<850 microns), dissolved in a nitric acid solution, and an auto-titration device was used to determine each layer’s total (acid-soluble) chloride content. Finally, the mixtures’ apparent chloride diffusion coefficient (D_a) was determined based on Crank’s solution to Fick’s 2^nd law of diffusion fit to depth-wise acid-soluble chloride content, following ASTM C 1556.

Chloride Binding Capacity of HPC Mixtures

The chloride binding capacity of HPC mixtures was evaluated following the procedures outlined in a previous study ( 42 ).Three replicate 2 × 4 in. paste samples for each HPC mix design were prepared following ASTM C 1738 and in sealed containers containing saturated limewater (ASTM C 511) for 56 days. Next, the paste samples were crushed and sieved (finer than <2.36 mm) and dried for 72 h in a sealed desiccator maintained at 11% RH using a laboratory-grade lithium chloride (LiCl), and the humidity levels were continuously monitored. After conditioning, 25 g of powdered samples of each HPC mix were immersed in sealed containers containing 100 ml of lime-saturated NaCl solution of five different chloride concentrations—0.1, 0.4, 0.8, 1.0, 2.0, and 3.0 mol/L—for 56 days. At the end of the ponding period, the solution’s residual chloride concentration of equilibrated solutions was determined using a commercially available auto-titrator. The change in chloride concentration of the exposure solution before and after ponding was used to calculate the bound chloride content ( $C_{b})$ . Finally, for each HPC mix, the bound chloride ( $C_{b})$ and free chloride content $(C_{f})$ at equilibrium were plotted for different concentrations, and the resulting curves were fitted using a Freundlich isotherm to determine binding coefficients ( $α & β)$ . Previous studies ( 10 , 43 ) have shown Freundlich isotherms to be a better descriptor of the binding phenomenon for free chloride concentrations of 0.05 M or higher in pore solution.

Effective Diffusion Coefficients of HPC Mixtures ( $D_{e}$ )

In the current research, the effective chloride diffusion coefficient ( $D_{e})$ for HPC mixtures was determined by analyzing the ASTM C 1556 acid-soluble chloride profile with the inclusion of chloride binding ( 44 ). A finite-difference modeling approach with a time step of 864 sec (∼0.01 day) and 0.5 mm depth step was used to calculate chloride profiles and compare them against the total (the acid-soluble) chloride content for the same exposure period. Finally, the GRG algorithm by Microsoft excel solver was used to minimize the error function and determine the $D_{e}$ for HPC mixtures.

Prediction of D_e-based on AFF and FF of HPC mixtures

D_e for HPC mixtures are predicted using the 91-day AFF and FF from SPS and MPS curing regimen following Equation 3, proposed in previous studies ( 5 , 10 , 45 )

D_{e} = \frac{D_{e}}{1 + (\frac{1}{ϕ}) (\frac{d C_{b}}{d C_{f}})} = \frac{(D_{o} / FF)}{(1 + \frac{1}{ϕ} \cdot α β C_{f}^{β - 1})}

(3)

where

$D_{o} = 1.9 \cdot 10^{- 9} \frac{m^{2}}{s} at 25$ °C represents the self-diffusion coefficient of chloride ions in water,

$ϕ is$ the volume of permeable pore space in concrete (ASTM C 642), and

$C_{f}$ demotes the concentration of free chloride in concrete pore solution, assumed to be in equilibrium with exposure solution from ponding tests (2.8M NaCl).

Following ASTM C 642 boiling tests, the porosity of HPC mixtures was determined to be 12% ± 1.6%, while after vacuum saturation, the porosity of HPC mixtures was determined to be 16% ± 2.1%. Although Equation 3 was proposed for FF, the rationale for using AFF to predict D_e is based on the consideration that air voids in concrete are typically isolated and are seldom saturated in practice and, thus, have a negligible effect on transport properties. Unlike FF, the AFF of concrete describes pore structure characteristics of concrete mixtures, excluding air voids. In addition, concrete specimens in ASTM C 1556 ponding tests are submerged in 2.8M NaCl solution; thus, air voids typically remain unsaturated under these conditions ( 46 , 47 ).

Results and Discussion

Note: For consistency, the ASTM C 1786 SPS and MPS curing solution or soak solution will be referred to as SPS and MPS, respectively. Test parameters for HPC mixtures (e.g., BR, AFF, etc.) will be identified following the applicable curing regimen as BR-SPS, AFF-MPS, and so forth.

Resistivity Measurements and Formation Factor

Five replicate test samples of each HPC mix design from the MPS and SPS curing regimen were tested for BR and SR measurements at 7, 28, 56, 91, and 180 days. However, only selective results pertinent to the discussion are presented in relevant sections for brevity.

Figure 2 shows the BR and SR (avg and covar) of HPC mixtures at 91 days from MPS and SPS curing. Concrete resistivity measurements depend on PSC and microstructure parameters (pore volume and connectivity) and thus in a simulated pore solution curing regimen, are influenced by the concentration/conductivity of curing solution ( 16 , 48 ). As such, the BR-SPS and BR-MPS for HPC mixtures cannot be directly compared. For example, the BR-SPS measurements are around 1.4 to 1.5 times higher than BR-MPS for all Class C FA mixtures (Figure 2). Interestingly, the MPS conductivity for C ash mixtures is 1.37 times higher than SPS conductivity (i.e., 108 S/m versus 78.74 S/m). Therefore, the higher the difference between MPS and SPS conductivity, the higher the difference in BR values.

Figure 2.

91-day average (and COV) BR and SR of HPC mixtures in MPS and SPS curing.

However, analysis of the coefficient of variation (COV) in resistivity measurements from Figure 2 shows BR-MPS demonstrated a generally lower COV (i.e., 3.5%) compared with BR-SPS (i.e., 4.8%) at 91 days. Nonetheless, while the COV in resistivity measurements decreased with the curing age for both curing regimens, SR measurements generally demonstrated higher COV than BR. Overall, the COV in resistivity measurements was observed to decrease as SR-SPS (∼6.0%) > BR-SPS (∼4.8%) ≥ SR-MPS(∼4.6%) > BR-MPS (∼3.5%).

SR/BR Ratio of HPC Mixtures

Concrete resistivity is an intrinsic parameter; therefore, BR and SR tests after applicable geometric correction factors should yield a similar value for a given HPC mix. In the current study, the average SR/BR ratio for HPC mixtures was determined from 7 to 180 days for both MPS and SPS, and the average SR/BR ratios of HPC mixtures are plotted in Figure 3 as a function of test age.

Figure 3.

SR/BR ratio of HPC mixtures: MPS versus SPS curing regimen.

Results from Figure 3 show that the MPS curing regimen resulted in more comparable (i.e., ≤10% difference) BR and SR measurements for HPC mixtures at all ages, with SR/BR ratios ranging from 0.91 at 28 days and gradually increasing up to 0.96 at 180 days. In contrast, the SR/BR- SPS ranged between 0.86 and 0.92, with a ratio decreasing from 0.92 to 0.86 from 7 to 28 days and subsequently increasing to 0.92 at 180 days. Specifically, Class C ash mixtures in SPS curing demonstrated a high variability between SR and BR between 7 and 28 days, attributed to a 20% to 40% difference between PSC of C ash mixtures and SPS (PSC > SPS). The high PSC of C ash mixtures compared with surrounding SPS possibly creates a pore solution concentration gradient between the bulk interior versus outer surface of the specimen, which explains a higher variability between SR and BR, also noted in a previous study ( 27 ). However, the gradual increase in SR/BR ratio from 28 to 180 days indicates a possible reduction in alkali leaching given microstructure densification by SCMs pozzolanic reactions or homogeneity achieved between bulk and surface PSC after sufficient leaching.

Curing Solution Conductivity

The conductivities of SPS and MPS curing solutions were measured at 91 days of sample curing and compared with reference solutions at the start of the test. The results plotted in Figure 4 show the conductivity of reference SPS and MPS solutions as shown in Table 3 (solid markers), and the min-max from 91-day MPS and SPS conductivity for C and F ash mixtures are shown as deviations from reference markers. In addition, the PSC of Class C and F FA mixtures (from GEMS modeling) are shown for reference.

Figure 4.

PSC versus curing solution conductivity measurements.

As shown in Figure 4, the 91-day MPS conductivity for F and C ash mixtures ranged between 70 and 64 mS/cm and 107 to 111 mS/cm (resp.), that is, 7% and 4% variation compared with reference solutions. MPS closely mimics the average PSC for C and F ash mixtures, and consequently, it eliminates alkali leaching, as evidenced by the low variation between 91-day and reference conductivity values. On the other hand, 91-day SPS conductivity containing F ash mixtures demonstrated marginally higher variation (i.e., 8% to 10% lower versus reference), which could be attributed to alkali precipitation on the surface of specimens and general variability in conductivity measurements.

However, 91-day SPS conductivity for C ash mixtures ranged between 77 and 94 mS/cm, demonstrating a significant (15% to 20%) increase compared with reference SPS. As the average PSC of C ash mixtures (∼20% to 30%) is higher than SPS solution, which results in possible alkali leaching from test specimens into SPS solution and, thus, increasing the SPS conductivity. In addition, a possible alkali leaching in C ash test specimens also explains previous observations of high COV and a high SR/BR ratio variability for these mixtures in SPS, attributed to a significant difference between average PSC and SPS solutions

Saturated Resistivity and Formation Factors

The 91-day saturated BR ( $ρ_{sat})$ , FF, and AFF of HPC mixtures are reported in Table 4. Compared with (apparent) BR, saturated BR measurements demonstrated higher COV (7% to 8%), possibly because of the effects of the vacuum conditioning procedure and subsequent saturation of air voids with a curing solution. The COV reported for AFF and FF of HPC mixtures from the MPS and SPS curing regimen reflects the difference in AFF and FF (Equations 1 and 2) for two cases: 1) $ρ^{ps}$ = equal resistivity of reference MPS/SPS solution from Table 3; and 2) $ρ^{ps} is$ equal to 91-day conductivity (1/resistivity) measurements of MPS or SPS. Typically, the FF for concrete mixtures following the bucket test is calculated by normalizing concrete resistivity with the resistivity of bucket solution, often assumed to be equal to the reference value. However, these assumptions are not valid, especially in cases where SPS is significantly lower than the PSC of concrete mixtures. For example, results from Table 4 show that in cases such as C ash mixtures in SPS curing, an incorrect consideration of SPS conductivity (i.e., 78.74 mS/cm, reference versus 94 mS/cm, @ 91d) would result in a 22% error in FF determination for those mixtures.

Table 4.

Resistivity and FF at 91 days and Diffusion Tests.

		Control	6SF	25F	20F5SF	35F	35C	29C6SF	35C10SF	Avg. COV (%)
BR (91d) kOhm-cm	MPS	16.6	28	28.2	42.7	37.8	18.1	29.5	31.6	3.5%
BR (91d) kOhm-cm	SPS	15.8	26.7	26.0	39.3	32.0	28.0	43.0	50.0	4.8%
Saturated BR (91d) kOhm-cm	MPS	8.1	16.5	19.0	30.8	26.2	11.9	19.9	21.6	7.0%
Saturated BR (91d) kOhm-cm	SPS	8.7	15.6	14.2	24.3	18.6	16.3	27.4	30.7	8.2%
AFF (91d)	MPS	1,341	2,262	1,974	2,989	2,646	1,955	3,186	3,413	~7%
AFF (91d)	SPS	1,296	2,189	2,132	3,223	2,624	2,626	4,033	4,690	10%–20%
FF (91d)	MPS	651	1,334	1,329	2,157	1,835	1,284	2,146	2,330	10%
FF (91d)	SPS	713	1,275	1,162	1992	1,523	1,533	2,567	2,877	15%–22%
Apparent diffusion coffecient	D_a (x10^-12 m²/s)	9.9	5.4	4.4	2.9	3.6	4.0	3.2	2.7	15.4%
Chloride binding (Freundlich isotherm)	α (mg/g)	10.51	9.82	11.67	10.83	12.21	10.82	10.21	9.92	8%
Chloride binding (Freundlich isotherm)	β	0.39	0.35	0.38	0.32	0.38	0.30	0.32	0.35	8%
Effective diffusion coffecient	D_e (x10^-12 m²/s)	4.3	2.5	1.5	1.0	1.2	1.8	1.3	1.0	17.6%

Note: FF = (saturated) formation factor; AFF = apparent formation factor; BR = bulk resistivity; MPS = matching pore solution; SPS = standard (simulated) pore solution; COV = coefficient of variation; Control = 100% OPC mix.

Measured versus Predicted Diffusion Coefficients

The results from the ASTM C 1556 test for apparent chloride diffusion coefficient (D_a), chloride binding isotherms, and experimental determination of effective chloride diffusion coefficients ( $D_{e}$ ) for HPC mixtures are presented in Table 4. The experimentally determined D_e for HPC mixtures are compared with D_e predictions based on 91-day AFF and FF from SPS and MPS curing, and the results are shown in Figure 5.

Figure 5.

Measured versus predicted effective diffusion coefficients of HPC mixtures.

For all HPC Mixtures, the FF-based D_e predictions (i.e., D_e[FF-MPS] and D_e[FF-SPS]) demonstrate a higher correlation coefficient (R²) with experimentally determined D_e as compared with AFF-based D_e predictions (i.e., D_e[AFF-MPS] and D_e[AFF-SPS]). Overall the correlation coefficient (R²) decreases as D_e(FF-MPS) > D_e(FF-SPS) > D_e(AFF-MPS) > D_e(AFF-SPS). However, FF appears to significantly overestimate D_e compared with AFF, as FF-D_e predictions demonstrate a mean absolute error (MAE) of ∼83% with experimental values as opposed to 35% MAE for AFF-D_e. Overall, the MAE decreases as ∼93% D_e(FF-SPS) >∼78% D_e(FF-MPS) > 42% D_e(AFF-SPS) > 24% D_e(AFF-MPS). Figure 5 visually represents the above discussion, wherein, the experimentally determined D_e for HPC mixes are plotted against FF- and AFF-predicted diffusion coefficients, along with a 1:1 slope line (measured value = predicted value) for reference. The FF-predicted D_e demonstrates the larger deviation (i.e., significantly higher or significant overprediction) from the 1:1 slope line (versus AFF-D_e), confirming that despite a higher R² with experimental measurements, they are less suited to predict D_e. Therefore, results clearly demonstrate that the AFF of HPC mixtures with the inclusion of chloride binding is a better predictor of D_e than FF.

Furthermore, between SPS and MPS, the AFF-MPS-based D_e predictions demonstrate a higher R² and lower MAE with experimental D_e, compared with AFF-SPS-based D_e predictions. The improvement in D_e predictions for AFF-MPS compared with AFF-SPS is primarily attributed to a more robust determination of AFF (i.e., pore network characteristics) for HPC mixtures in MPS compared with SPS. As the MPS more closely represents the PSC of HPC mixtures, it eliminates any alkali leaching effects on resistivity measurements and, thus, results in a more reliable determination of AFF compared with SPS. Therefore, improved reliability in FF determination in MPS curing improved the FF-based transport property prediction for HPC mixtures.

Conclusions

The primary objective of the current research was to improve the reliability in FF determination of HPC mixtures through an innovative MPS curing approach for resistivity tests. Under the MPS curing regimen, mixtures are grouped based on the effects of SCM type/replacement levels on the long-term PSC of concrete mixtures. Accordingly, the studied HPC mixtures containing Class C (35% to 45%) and F FA (20% to 25%), and SF (6% to 10%) were divided into three groups (Group 1, Control and SF mixtures; Group 2, F ash mixtures ± SF; and group 3, C ash mixtures ± SF) and cured in a simulated solution that most closely represent the average PSC mixtures in the group. MPS curing was proposed as an improved mix-specific pore solution curing practice to increase the reliability of FF determination and thereby improve the FF-based transport property prediction for HPC mixtures.

The significant findings from the current study are summarized below.

SCMs such as Class C and F FA and SF significantly modify the long-term PSC of HPC mixtures through their soluble alkali contribution and alkali binding by pozzolanic hydration product (C-S-H with low Ca/Si ratio).

a. 91-day PSC of HPC mixtures from GEMS modeling shows SPS to be a good representation only for Control and 6SF mixtures (avg. PSC∼1% to 5% SPS). However, average PSC for F and C ash mixtures is 12% to 20% lower and 20% to 40% higher than SPS.

Curing F ash mixtures in an SPS soak solution of higher conductivity did not create any considerable error in resistivity measurements. However, curing C ash mixtures in SPS solution with an average 20% to 40% lower conductivity (versus average PSC) resulted in a considerable error in resistivity measurement, possibly because of alkali leaching from the tested specimens.

a. SPS curing, especially for C ash mixtures, demonstrated: 1) high COV in SR and BR measurements at all ages; 2) high SR to BR variability, especially at early ages; 3) a 15% to 20% increase in 91-day SPS conductivity versus initial soak solution conductivity as a reference; and 4) 20% to 22% average error in AFF and FF determination.

Implementation of the MPS curing regimen demonstrated the following improvements in the resistivity measurements and, thereby, in the AFF and FF determination of HPC mixtures:

a. 1) low COV in SR and BR measurements at all ages; 2) comparable SR and BR measurements (i.e., SR/BR ratios ∼0.91 to 0.96); 3) minimal (4% to 7%) variability between 91-day MPS conductivity versus initial soak solution conductivity as a reference; and 4) 7% to 10% average error in AFF/FF determination.

b. Therefore, both bulk and SR tests with MPC curing provide accurate, reliable, and repeatable resistivity measurements for concrete mixtures compared with SPS curing.

c. As the difference between 91-day MPS PSC and PSC of the initial soak solution is less because of the elimination of leaching, initial bucket solution resistivity can be used for AFF and FF determination.

The transport of free chloride ions in concrete pore solution through the pore network (i.e., effective diffusion coefficient, D_e) is responsible for corrosion initiation in structures.

a. Experimental determination of D_e requires ASTM C 1556 ponding test, which is time-consuming (91 days), requires laborious sample preparation and conditioning, demonstrates a high COV (∼15.4%), and is limited to the salt concentration of the ponding solution.

b. In contrast, chloride binding experiments are relatively easy to perform and cover a wide range of ponding solutions or, more recently, can be predicted ( 10 , 49 ). However, this study did not investigate the validity of the proposed prediction models.

c. D_e predictions based on 91-day FF and AFF show that although FF-D_e demonstrates higher R² with experimentally determined D_e, it significantly overestimates D_e compared with AFF. Overall, based on MAE, the AFF of HPC mixtures with the inclusion of chloride binding is a better predictor of D_e than FF for both MPS and SPS curing.

d. Between SPS and MPS, the AFF-MPS-based D_e predictions demonstrate a higher R² and lower MAE with experimentally determined D_e, compared with AFF-SPS-based D_e predictions.

Overall, results from the current study show:

a. MPS more closely represents the PSC of HPC mixtures; it minimizes the effects of alkali leaching on resistivity measurements and, thus, results in a more reliable determination of AFF compared with SPS.

b. The robust determination of AFF (i.e., pore network characteristics) of HPC mixtures in MPS significantly improves the reliability/accuracy of AFF-based D_e predictions.

Future Work

As a part of an ongoing research project at Texas A&M Transportation Institute (TTI), the development of the following is in progress:

A simplified excel-based tool (TTI model-2) to predict the PSC of binary and ternary concrete mixtures containing SCMs (fly ash and SF) at long-term hydration ages has been developed. The TTI model-2 predictions of PSC demonstrate a favorable validation based on GEMS modeling and extraction measurements (results to be published soon). Currently, the model is in the testing stages. As an application for the MPS curing regimen, TTI model-2 will be used in the future to estimate the PSC of binary and ternary cement-SCM mixtures instead of the GEMS model.

An excel-based tool (Texas DOT tool) for durability-based performance evaluation of cast-in-place HPC bridge deck concrete mixtures is currently under development. The Texas DOT tool is envisioned to assist the adoption of MPS curing in practice to facilitate: (a) resistivity/FF-based performance classification for QA/QC; and (b) Texas DOT contractors and industry practitioners in selecting the most appropriate mix design for construction based on anticipated durability performance. The Texas DOT tool is expected to facilitate the adoption in practice in the following ways:

a. estimate the composition and dosage (NaOH, KOH, and Ca[OH]₂) of the most appropriate MPS curing solution for curing based on user inputs of ingredients composition and mix designs;

b. compute FF, provide pertinent FF-based performance classification and thereby, predict transport properties (apparent and effective diffusion coefficients) based on user inputs of 28-day BR measurements (MPS curing + AASHTO TP 119 accelerated curing); and

c. evaluate anticipated service life performance (i.e., time to rebar corrosion and probability of failure) based on user inputs of ambient conditions (location and month of construction in Texas), construction (rebar type and depth), and chloride exposure (surface and critical concentrations).

Footnotes

Author Contributions

The authors confirm their contribution to the paper as follows: study conception and design: A. Mukhopadhyay; P. Saraswatula; data collection: P. Saraswatula; analysis and interpretation of results: P. Saraswatula; A. Mukhopadhyay; draft manuscript preparation: P. Saraswatula. All authors reviewed the results and approved the final version of the manuscript

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The authors acknowledge and thank the sponsors of this research: the Texas Department of Transportation (TxDOT), Texas A&M Transportation Institute (TTI), and Texas A&M University.

ORCID iDs

Pravin Saraswatula

Anol Mukhopadhyay

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Increasing the Reliability of Formation Factor-Based Transport Property Prediction for High Performance Concrete Mixtures Through Innovative Matching Pore Solution Curing

Abstract

Keywords

Objective

Materials and Mix Designs

Materials

Mix Designs

Rationale and Development of Matching Pore Solution (MPS) Curing Regimen

Thermodynamic Modeling for HPC mixtures

Pore Solution Conductivity (PSC) of HPC Mixtures

Development of the MPS Curing Regimen

Test Methods

Resistivity and Formation Factor Evaluation

Resistivity Tests

Vacuum Saturation Conditioning

Apparent Formation Factor (AFF) and Saturated Formation Factor (FF)

Determination of Effective Diffusion Coefficients (De) for HPC Mixtures

Experimental Determination of Diffusion Coffecients for HPC mixtures

Bulk (Apparent) Chloride Diffusion Coefficient ( D a )

Chloride Binding Capacity of HPC Mixtures

Effective Diffusion Coefficients of HPC Mixtures ( D e )

Prediction of De-based on AFF and FF of HPC mixtures

Results and Discussion

Resistivity Measurements and Formation Factor

SR/BR Ratio of HPC Mixtures

Curing Solution Conductivity

Saturated Resistivity and Formation Factors

Measured versus Predicted Diffusion Coefficients

Conclusions

Future Work

Footnotes

Author Contributions

Declaration of Conflicting Interests

Funding

ORCID iDs

References

Determination of Effective Diffusion Coefficients (D_e) for HPC Mixtures

Bulk (Apparent) Chloride Diffusion Coefficient ( $D_{a}$ )

Effective Diffusion Coefficients of HPC Mixtures ( $D_{e}$ )

Prediction of D_e-based on AFF and FF of HPC mixtures