Modelling Leaching Using C-S-H Solid Solutions

Abstract

Leaching from cement can lead to a loss in performance and durability and can also have an environmental impact. Therefore, it is an important aspect to consider when new cements are being developed and where concrete is to be placed that could lead to the contamination of groundwater. Calibrated thermodynamic models can provide very useful predictions in a matter of seconds for any cement-based material. However, such models need to include accurate representations of the solid-solution nature of the C-S-H gels that are included for the incongruent dissolution of calcium and silica. This study presents the calibration of a thermodynamic model employing the pH-REdox-Equilibrium geochemical software 3.8.7, written in C (PHREEQC 3.8.7), to model the change in the pH and the leaching of calcium (Ca) and silica (Si) from cement against the Ca/Si ratio and over time. The predicted concentrations of Ca and Si and the pH in the leachate were calculated using three solid-solution C-S-H gel models that were taken from the cemdata18 database, namely, CSHQ, CSH3T, and tobermorite–jennite, which have not been analysed before and show good agreement. The calibrated model was used to predict leaching from a CEM II/A-L cement and a blended CEM I + fly-ash with a cement replacement level of 35%. The effect of a sulphate environment (Na₂SO₄) was also analysed.

1. Introduction

Leaching from cement-based materials is the gradual release of various chemical components, such as calcium (Ca) and silica (Si), into the surrounding environment and the breaking down of solid phases, such as calcium–silica–hydrate (C-S-H) and portlandite. It can affect performance and durability, as well as have a negative environmental impact, if these components enter groundwater or sensitive soils. An increase in calcium in groundwater can affect its alkalinity, with the resulting change in the pH affecting the drinking water quality and aquatic life. Any new cement or concrete should, therefore, consider leaching, especially if they are in environmentally sensitive areas. Not understanding leaching not only affects the durability and longevity of concrete structures but also poses potential environmental risks. Understanding cement leaching is a necessary consideration as new sustainable cement and concrete are developed, so their behaviour in this environment is crucial for determining their viability.

Leaching is affected by the environment and temperature and can take several weeks, months, or even years to observe. Therefore, calibrated prediction models that account for changing temperature and accurately represent the incongruent dissolution of calcium and silica within appropriate solid-solution models of C-S-H gels are vital to understand and mitigate the effects of cement leaching.

Haga et al. [1] and Hidalgo et al. [2] reported on the dissolution of cement into pore water and the measurement of the changing pH and ion concentrations. Cement paste dissolution models were developed by Atkinson et al. [3] and Berner [4] to model the long-term change in the composition of the leachate. Faucon et al. [5] concluded in their work that hardened cement paste was altered by ongoing leaching and dissolution, and changes in the solid hydrate phases occurred as a result. Others [6,7,8] summarised in their findings on the leaching of cement in deionised water that diffusion was the main transport mechanism of ions into the leachate. Haga et al. [1] found that research into the structural changes of hardened cement pastes due to dissolution had hardly been reported, and Liu et al. [9,10] reported on the dissolution kinetics of aluminosilicate precursors to provide a comparative framework for Si behaviour in leaching.

Hidalgo et al. [2] provided a summary of the influence of C-S-H and portlandite on the chemical properties of the liquid phase in a hydrating cement. The high initial pH (>13) created from the dissolution of sodium and potassium hydroxides from the cement was lowered to approximately 12.5 because of the dissolution of other constituent minerals, including portlandite and C-S-H. They reported that previous research [11,12] measured the ongoing decalcification of C-S-H pastes due to leaching until a constant value of the Ca/Si ratio was reached.

C-S-H is the main hydrate phase of Portland cement. The hyphens are used to symbolise the variable composition and poorly defined crystalline structure [13]. The C-S-H Ca/Si ratio and calcium concentration ultimately control the type of gel formed [2,14], which can change due to due to the addition of supplementary cementitious materials (SCMs) or leaching and chemical attack by external sulphates and/or carbonation [15]. There are many descriptions of C-S-H. Taylor [13] provided C-S-H (I) and C-S-H (II), which are similar to tobermorite and jennite, respectively [2]. C-S-H’s solubility can be modelled using solid-solution models [16,17,18] or, to a limited extent, using a surface complexation approach [15,19,20].

Others have employed discrete solid phases (DSPs) to model C-S-H, which provide reasonable comparisons with measured data of changing pH values and Ca and Si concentrations for molar Ca/Si ratios ranging from 2.7 to 0. Deriving DSPs for any ideal or non-ideal solid solution has been proposed by Walker et al. [18] and Kulik et al. [21]. This was further developed by Holmes et al. [22,23], who derived DSPs for the three end-member CSH3T and four end-member CSHQ gel solubility models within the Cemdata18 database [15]. These have been successfully used within PHREEQC 3.8.7 [24] to model various plain and blended cements as well as the effect of harsh environments, including carbonation, sulphate, and sea water. The geochemical software HYDCEM [25,26,27,28,29], developed for users to set up and model their own cement blends, also uses DSPs to model various cement systems.

PHREEQC has been used by many authors over the years to model leaching from cementitious as well as waste materials, which is summarised in

Table 1. Previous studies using PHREEQC for modelling cementitious material leaching.

Author	Summary of Contributions
Halim et al. [30]	A leaching model was developed using PHREEQC to simulate the leaching of Pb, Cd, As, and Cr from cementitious wastes in the presence of simple and complex leachates. The model provided good agreement with the measured data and demonstrated its appropriateness for longer-term predictions.
Walker et al. [31]	Here, leaching was modelled by controlling the dissolution of the alkalis (K2O and Na2O), portlandite, C-S-H, and ettringite. The C-S-H was modelled using a non-ideal solid-solution aqueous solution (SSAS) between it (CaH2SiO4) and portlandite.
Tiruta-Barna [32]	In this work, PHREEQC was employed to account for the leachate as a complex reactive/transport system. The focus of the study was the dynamic leaching of monolithic porous materials, with the leachate acting as a complex reactor where chemical and inter-phase mass transfer and convection processes take place. The model was validated using analytical solutions of the system from equations with good comparisons.
Martens et al. [33]	The researchers used PHREEQC to model the leaching of Ca, Mg, Al, and Pb from carbonated and uncarbonated cement–waste samples. The predicted and measured experimental results gave good comparisons.
Hareeparsad et al. [34]	This work focused on the reactivity of coal fly ash in aqueous solutions, developed a PHREEQC model to determine the quantities of different solid phases comprising the coal fly ash. The numerical predictions, again, gave good comparisons with the experimental data and confirmed the feasibility of the approach.
Cornelis et al. [35]	The antimonate (Sb(OH)6−) leaching in hydrated cement pastes was modelled using adsorption isotherms with cement minerals. PHREEQC was used to model the pH and carbonation-dependent leaching of matrix elements (i.e., Ca, Al, Si, Fe, S, and C) using total elemental concentrations and the carbonate concentration.
Solpuker et al. [36]	The leaching potential of pervious concrete and its capacity for immobilizing common urban run-offs, including Cu, Pb, and Zn, were investigated. PHREEQC equilibrium modelling showed that mixing interstitial alkaline matrix waters with capillary pore water could re-produce the observed water chemistry.
Han et al. [37]	This work presented a long-term study of fly ash-blended concrete in a low- and intermediate-level radioactive waste (LILW) repository. The modelling was undertaken using PHREEQC thermodynamic equilibrium calculations combined with the CEMDATA18 database.
Vega-Garcia et al. [38]	Simulations of the leaching of selected metals under plaster and mortar over a 18-month period in accordance with the Construction Products Regulation (CPR) [39] were produced. The PHREEQC-Matlab coupled model used the Lawrence Livermore National Laboratory (LLNL) thermodynamic database to reproduce the experimental results with a high degree of accuracy.

.

This paper compared measured data from 777 C-S-H gel equilibrated solutions for pH, Ca (mmol/L), and Si (mmol/L) to develop a calibrated model using a CEM I cement and the PHREEQC geochemical software to simulate leaching from the cement using solid-solution gel models from the cemdata18 database, namely, CSHQ, CSH3T, and tobermorite–jennite, which have not been reported previously in the literature for this application. Analysis was undertaken using the previously developed DSPs for these gel models as well as the SOLID_SOLUTION data block in PHREEQC. The calibrated model was then further developed to model the dissolution of a CEM II/A-L and a blended CEM I + fly-ash with cement replacement levels of 20 and 35%. The effect of a sulphate environment (Na₂SO₄) on leaching was also predicted for all three cement types.

2. Materials and Methods

Walker et al. [18] reported that there are over 45 published C-S-H gel solubility models with Ca/Si ratios (mol/mol) of greater than 0.8. These, however, do not include those C-S-H solid solutions developed for the cemdata18 [15] database, namely, tobermorite–jennite, CSH3T, and CSHQ. These C-S-H solid solutions were employed here to predict the expected changes in pH, Ca, and Si against changing Ca/Si ratios using the PHREEQC geochemical code. The measured data from 777 C-S-H gel equilibrated solutions for pH, Ca (mmol/L), and Si (mmol/L), taken from Walker et al. [18], are shown in Figure 1. Using the selection criteria used by Walker et al. [18], namely, a curing temperature range of 17–30 °C and a curing time of ≥1 week, the final Ca/Si ratio of the C-S-H was measured, calculated, or calculable, the liquid phase was fully characterised, and the data were real. The solubility data in Figure 2 were used to compare the predicted pH, Ca, and Si against the C-S-H Ca/Si ratio. These data were deemed to be representative of C-S-H gel near equilibrium near room temperature (17–30 °C), with a curing time of one week or more.

The PHREEQC [24] analysis was undertaken using the chemical and physical properties of a commercially available CEM I cement, as described in Table 1. The chemical compositions of the materials were determined by X-ray fluorescence (XRF). The phase composition was calculated using normalisation.

Thermodynamic Modelling

Thermodynamic calculations were carried out using the PHREEQC geochemical software along with the cemdata18 thermodynamic database to simulate leaching and provide predictions of the Ca, Si, and pH in the leachate at 25 °C. The CSHQ, CSH3T, and tobermorite–jennite C-S-H solution models were analysed using their derived DSPs [22,23] and the SOLID_SOLUTIONS data block in PHREEQC.

The thermodynamic model was based on the image shown in Figure 3, where 100 g of cement was placed in 1000 mL of pure water (Solution 1) with a water/solid (w/s) ratio of 10. Every fourteen days, Solution 1 was replaced with 1000 mL of pure water (Solution 0) until all the C-S-H and portlandite was dissolved. Separate PHREEQC models, depending on the C-S-H solid solution employed, provided simulations of the changing pH, calcium (mmol/L), and silica (mmol/L) in the replaced leachate (Solution 1) as well as the Ca/Si ratio of the C-S-H solid phase. The analysis included 266 changes, which was equivalent to 10 years.

The PHREEQC inputs for Solution 0 and Solution 1 are shown and described in

Table 2. Composition of CEM I cement.

Oxide (g/100 g)		Phase (g/100 g)
SiO2	19.52	C3S	54.53
Al2O3	4.41	C2S	15.51
Fe2O3	2.63	C3A	7.33
CaO	60.57	C4AF	8.10
MgO	2.84	Lime	1.01
K2O	0.90	Calcite	3.45
Na2O	0.31	Gypsum	2.46
SO3	2.00	Periclase	0.61
CaO (free)	1.00	K2SO4	1.52
CO2	1.50	Na2SO4	0.32
Periclase	0.60	K2O	0.09
LOI	3.20	Na2O	0.17
Blaine fineness (m2/kg)	395	MgO	2.87
		SO3	2.02

. The CEM I data input for the model within the EQUILIBRIUM_PHASES data block is shown in

Table 3. PHREEQC input for solution data.

PHREEQC Input		Description
Solution	0	Defines the aqueous concentration, the amount of water, and the temperature and pressure for Solution 0 [24]
-Temp	25	Sets temperature to 25 °C
pH	7 charge	Sets initial pH to 7 and allow charge balance
-Water	1	Sets water to 1 kg
-Units	mmol/kgw	Sets units for initial Ca and Si in solution
Ca	1.00 × 10−12	Adds initial Ca to aid calculations
Si	1.00 × 10−12	Adds Si to aid calculations
Save Solution	0	Saves solution
END
Solution	1	Defines the aqueous concentration, the amount of water, and the temperature and pressure for Solution 1 [24]
-Temp	25	Sets temperature to 25 °C
pH	7 charge	Sets initial pH to 7 and allow charge balance
-Water	1	Sets water to 1 kg
-Units	mmol/kgw	Sets units for initial Ca and Si in solution
Ca	1.00 × 10−12	Adds initial Ca to aid calculations
Si	1.00 × 10−12	Adds initial Si to aid calculations

.

The thermodynamic end-members of the three C-S-H gel solid solutions, taken from cemdata18, are summarised in

Table 4. PHREEQC input for the cement data and phases in EQUILIBRIUM_PHASES.

PHREEQC Input			Description
EQUILIBRIUM_PHASES 1			Defines a set of minerals that react with a solution [24]
C3S	0	0.23880	Phase names, saturation indexes, and molar concentrations for the cement phases and solid hydrates that may form. Molar concentrations for the cement are the masses (g; Table 1) divided by their molar masses (g/mol).
C2S	0	0.0900
C3A	0	0.0271
C4AF	0	0.0167
Lim	0	0.0181
Cal	0	0.0345
Gp	0	0.0143
Periclase	0	0.0151
K2SO4	0	0.0087
Na2SO4	0	0.0023
K2O	0	0.001
Na2O	0	0.0028
MgO	0	0.0713
SO3	0	0.0253
Portlandite	0	0
Syngenite	0	0
Brc	0	0
Hydrotalcite	0	0
Ettringite	0	0
Fe-ettringite	0	0
Monocarbonate	0	0
Femonocarbonate	0	0
Hemicarbonate	0	0
Fe-hemicarbonate	0	0
monosulphate14	0	0
Fe-monosulphate	0	0
C3AH6	0	0
C3FH6	0	0
Amor-Sl	0	0

. The PHREEQC input data for the SOLID_SOLUTIONS data block are shown in

Table 5. Solid-solution end-members (taken from [15]).

Solid Solution	End-Member		log_k
CSHQ	CSHQ-TobH	(CaO)0.67(SiO2)1(H2O)1.5 + 1.33H+ = 0.67Ca2+ + 2.17H2O + SiO2(aq)	8.286
	CSHQ-TobD	((CaO)1.25(SiO2)1(H2O)2.75)0.67 + 1.67H+ = 0.83Ca2+ + 2.67H2O + 0.67SiO2(aq)	13.655
	CSHQ-JenH	(CaO)1.33(SiO2)1(H2O)2.17 + 2.67H+ = 1.33Ca2+ + 3.5H2O + SiO2(aq)	22.179
	CSHQ-JenD	(CaO)1.5(SiO2)0.67(H2O)2.5 + 3H+ = 1.5Ca+2 + 4H2O + 0.67SiO2	28.730
CSH3T	CSH3T-T2C	((CaO)0.75(SiO2)0.5(H2O)1.25)2 + 3H+ = 1.5Ca2+ + 4H2O + SiO2(aq)	25.271
	CSH3T-TobH	(CaO)1(SiO2)1.5(H2O)2.5 + 2H+ = Ca2+ + 3.5H2O + 1.5SiO2(aq)	12.529
	CSH3T-T5C	((CaO)1(SiO2)1(H2O)2)1.25 + 2.5H+ = 1.25Ca2+ + 3.75H2O + 1.25SiO2(aq)	18.137
Tobermorite– jennite	Tob-II	(SiO2)1(CaO)0.83(H2O)1.33 + 1.67H+ = 0.83Ca+2 + 2.17H2O + SiO2	11.144
	Jennite	(SiO2)1(CaO)1.67(H2O)2.1 + 3.33H+ = 1.67Ca+2 + 3.77H2O + SiO2	29.311

. The TRANSPORT data block in PHREEQC (

Table 6. PHREEQC input for the solid-solution calculations.

PHREEQC Input			Description
SOLID_SOLUTIONS 1
CSHQ_model			Name of solid solution
-comp	CSHQ-TobH	0	Name of end-members (from cemdata18 database [15]; Table 4) and initial concentration (moles)
-comp	CSHQ-TobD	0
-comp	CSHQ-JenH	0
-comp	CSHQ-JenD	0

) was used to replace Solution 1 with Solution 0 (Figure 3) at regular, defined intervals.

The modelling approach assumed that equilibrium simulations between the evolving solid-phase assemblage and its pore solution accurately represented the near-equilibrium conditions presumed to dominate the system during leaching. This was predicated on the knowledge that dissolution and precipitation reactions occurring during leaching are generally rapid in relation to the underlying transport. A second assumption was that the discretisation of the solid-solution reactions, as described in our previous work [22,23], accurately represented the dissolution of these solids whilst increasing the speed of computation significantly.

3. Results

Using the input data above to analyse the cement described in Table 1, Figure 4 shows a comparison of the changes in Ca, Si, and pH during leaching against the C-S-H Ca/Si ratio using (1) the CSHQ gel model employing the DSP [22,23] and (2) the solid-solution option in PHREEQC. As may be seen, both approaches gave similar predictions, with the DSP showing kinks across the compositional range. This was a result of the non-ideal nature of the CSHQ DSP gel model, where imperfect mixing and incomplete solubility led to the ‘jagged’ output shown. While both provided clear predictions, the SOLID_SOLUTIONS data block was employed here throughout.

The results from the predicted leaching of the cement described in Table 1, undergoing the water changes shown in Figure 3, are shown in Figure 5 for the three C-S-H solid-solution gel models in Table 4. As may be seen, all three models provided reasonable predictions of the selected C-S-H gel solubility data for the Ca/Si ratios from 2.7 to 0.5 shown. While all three C-S-H gel models provided good comparisons with the measured data from the literature, CSH3T performed slightly better. In terms of pH, for example, the tobermorite–jennite model underestimated at Ca/Si ratios greater than 1.0. It also appeared to overestimate the Ca and Si concentrations at higher Ca/Si ratios.

4. Discussion

The leaching of cement is a long-term process by which material is removed according to its relative solubility. At a practical level, this can be simulated in several ways, such as the ‘bucket brigade’ calculations used here, in which a quantity of the pore solution is removed at each reaction (or time) step and replaced with fresh water, and re-equilibration of the system is carried out to perform the next discrete leaching step. There are other approaches, including coupled chemical-transport methods, in which a hypothetical column (or a single cell) has its contents moved into an adjacent cell at each reaction step, and the system is re-equilibrated. This approach has the advantage of spatial as well as temporal simulations and is, therefore, capable of representing dispersion effects and more complex phenomena.

The method described here has the advantage of simplicity and rapid run-times and has proved robust and reliable. Irrespective of the conceptual model underlying a leaching calculation, the predictions are very similar, showing the cement pore solution is buffered by one dominant hydrate—the most soluble salt in the assemblage—until exhausted.

Subsequently, the hydrate assemblage re-equilibrates with the pore solution, establishing a new solution chemistry, governed by the hydrates in the solid. This state continues (theoretically, at least) until all the solid is removed from the system.

For the cement example shown in this paper, the portlandite was completely depleted after 280 days or 20 cycles. C-S-H was still present but will be depleted by approximately 5000 days (~360 cycles). The depletion of ettringite after c. 2000 days (~142 cycles) will cause a further reduction in Ca in the solution. It should be noted, however, that secondary phases, such as zeolites or amorphous silica, may precipitate under certain conditions that can modify silica availability in ways that may not be fully accounted for in equilibrium-based models. These uncertainties suggest that while thermodynamic models provide valuable insights, experimental measurement and validation remain crucial for refining predictions.

The model was used to provide predictions for the dissolution of a CEM II/A-L and a blended CEM I + fly-ash cement, as described in

Table 7. PHREEQC input for the replacement of Solution 1 with Solution 0 every 14 days.

PHREEQC Input		Description
Transport
-cells	1	Number of cells in 1D column (default = 1)
-shifts	266	Number of changes
-time_step	1,209,600	Interval between changes/shifts (seconds)
-punch_cells	1	‘Punch’/write output to file (default = 1)
-punch_frequency	1	How often data are output (default = 1)

,

Table 8. Composition of CEM II/A-L cement.

CEM II/A-L Oxide (g/100 g)		Phase (g/100 g)
SiO2	17.50	C3S	47.86
Al2O3	4.60	C2S	15.17
Fe2O3	2.60	C3A	7.96
CaO	62.00	C4AF	8.09
MgO	2.30	Lime	1.66
K2O	0.50	Calcite	14.57
Na2O	0.26	Gypsum	4.21
SO3	2.45	Periclase	0.61
CaO (free)	1.62	K2SO4	0.85
CO2	6.27	Na2SO4	0.27
Periclase	1.00	K2O	0.05
LOI	7.22	Na2O	0.15
Blaine fineness (m2/kg)	474	MgO	2.35
		SO3	0.11

, and

Table 9. Composition of fly ash (pulverised fuel ash).

Oxide (g/100 g)		Phase (g/100 g)
SiO2	53.70	Quartz	1.29
Al2O3	16.81	Calcite	1.11
Fe2O3	13.46	Hematite	4.65
CaO	7.41	Mullite	7.95
MgO	2.08	Magnetite	3.37
K2O	2.03	Amorphous	81.65
SO3	1.11
P2O5	0.41
TiO2	1.82
MnO	0.13
LOI	2.55
Blaine fineness (m2/kg)	450

, taken from [40,41], respectively. The fly ash was blended with the CEM I with a cement replacement level of 35%.

The SOLID_SOLUTIONS data block for the CEM II/A-L cement was identical to that shown in Table 5, whereas for the CEM I + 35% fly-ash model, the input shown in

Table 10. PHREEQC input for the C-A-S-H solid-solution calculations.

PHREEQC Input			Description
SOLID_SOLUTIONS 1
CASH_model			Name of solid solution
-comp	INFCA	0	Name of end-members (from cemdata18 database [15]) and initial concentration (moles)
-comp	TobH-CNASHss	0
-comp	5CA	0
-comp	T5C-CNASHss	0
-comp	T2C-CNASHss	0

was employed to account for the C-A-S-H gel model. The predicted changes in the Ca, Si, and Al concentrations and pH over time are shown in Figure 6. While there were minimal differences between the predictions for the CEM I and CEM II/A-L cements, the blended cement was somewhat different. This was due to the sequential leaching and eventual depletion of the hydrate minerals from the blended cements.

The change in the hydrate phases over time with ongoing exposure to 25 g/L of Na₂SO₄ is shown in Figure 7. The depletion of C-S-H and portlandite was much faster with the precipitation of thaumasite and higher volumes of ettringite than would be expected in pure water. These predictions are similar to the work of [42,43] and in terms of thaumasite precipitation, the lowering of the pH, and the expansion due to sulphate exposure, respectively. Previous work [44,45] has shown that the maximum rate of thaumasite formation is between 5 and 10 °C, but is stable above this range.

5. Conclusions

Cement leaching is an important process to consider, as it can adversely affect performance and durability and the environment within which it is placed. The ongoing development of new sustainable cementitious materials means leaching will need to be considered to minimise the environmental impact and ensure the longevity of the concrete. While the monitoring of natural leaching is very time-consuming (taking several years, typically), this work showed that thermodynamic predictive models employing three C-S-H gel solid-solution models (CSHQ, CSH3T, and tobermorite–jennite), which have not been used before, can simulate the incongruent dissolution of calcium and silica from this phase within seconds. These models can provide rapid, robust, and reliable predictions (within 10% of measured data overall) of the C-S-H internal Ca/Si ratio and the leachate’s pH and calcium and silica concentrations. They can also provide predictions of how the hydrate phases will break down over time.

Having access to these C-S-H gel models provides users with the opportunity to simulate leaching and predict the changes in the chemical composition under a range of conditions. However, predicting the changing silica concentration remains a challenge due to uncertainties around the possibility of amorphous silica-rich gels forming. Experimental validation will remain essential to refine model parameters and improve the predictions shown here, as C-S-H structures have complex and non-ideal dissolution behaviours.