Assessment of Geopolymer Synthesis Parameters for Strength of Stabilized Fat Clay Using Statistical and Machine Learning Techniques

Abstract

Calcium-based chemical stabilizers are traditionally used for the stabilization of weak subgrade soils. However, these traditional stabilizers incur significant environmental costs which make them less desirable. As a result, alternative materials based on recycled waste and industrial byproducts are becoming popular. Geopolymers (GP) are a new addition to this list that are gaining traction because of their environmental benefits. GPs improve the soil by precipitation of a polymer gel as a result of mixing an alkaline activator (activator) with an aluminosilicate source (precursor). The effectiveness of GP and the improvement in engineering performance of GP-stabilized soils is contingent on sound GP synthesis parameters. This study investigates the effectiveness of GP-based treatments in improving weak soil and evaluates the significance of various parameters in contributing to the efficacy of GP treatment. As a result, a group of eight GP mixes was designed with a range of values for controlling parameters namely water/solid, activator/precursor, Si/Al and cation/Al ratios. A fat clay was treated by the application of these GP mixes at a dosage of 10% by dry weight. Improvements in mechanical strength were evaluated through unconfined compression strength testing. This was followed by statistical inference on laboratory strength data using analysis of variance (ANOVA) and post hoc tests. Ultimately, parameter importance was quantified by the random forest (RF) regression model. The results indicated that GP-based treatments enhanced the strength of untreated soil. Additionally, GP with higher aluminosilicate content and sufficient activator performed better. Overall, this study provides insight into the relative contribution of various GP synthesis parameters to the performance of GP-stabilized subgrade soils.

Keywords

geopolymer stabilization high plasticity clay recycled materials fly ash calcined clay alkali activators machine learning

Introduction

The socioeconomic growth of any country or region is dependent on the ease and speed with which goods and services can be moved ( 1 ). This underscores the significance of an optimally functioning transportation infrastructure for stakeholders at all levels. More often than not, the terrain itself poses a significant challenge to transportation assets. Given its scale, at least some part of the road infrastructure is bound to be constructed over ground characterized by poor conditions. Multiple studies have designated a subpar subgrade to be one of the most recurring causes of the performance-related problems in pavements ( 2 , 3 ). Repair, rehabilitation and reconstruction on account of damaged pavements because of poor ground conditions results in expenditure of millions of dollars in the United States alone ( 4 , 5 ). Therefore, a strong foundation system is crucial for the reliable serviceability of road networks.

In the context of subgrade soils, poor ground conditions can constitute a wide range of problems including shrink/swell potential, soft or weak and collapsible soils, sulfates and environmental conditions ( 6 , 7 ). Chemical stabilization, which involves the application of chemical stabilizers such as lime or cement to the soil, is a go-to method for arresting these issues as it is versatile and economical ( 8 – 10 ). However, these traditional stabilizers come with significant environmental costs in the form of emissions and natural resources. Cement production has been noted to contribute 7% to global greenhouse gas emissions ( 11 , 12 ). To offset these drawbacks, researchers have worked endlessly to come up with alternative materials that combine the economic and performance benefits of calcium-based stabilizers with environmental soundness. To this end, a wide range of materials such as cement kiln dust, silica fume, lime kiln dust, gypsum, blast furnace slag, recycled concrete aggregate fines, rubber waste, and biopolymers have been studied ( 3 , 4 , 9 , 13 – 20 ). These materials draw their environmental benefits from their being produced either as a byproduct or by the recycling of industrial waste.

Geopolymers (GP) are a relatively new addition to this family of materials that have recently risen in popularity being energy efficient with significantly lower environmental emissions ( 21 , 22 ). GPs are inorganic polymers formed as a result of mixing an aluminosilicate source (termed precursor) with an alkali activator (termed activator) ( 23 ). Calcined clay, metakaolin, fly ash, and ground granulated blast furnace slag are the most commonly predominantly used precursors, while sodium hydroxide (NaOH) and potassium hydroxide (KOH) are the most common activators. GP-based treatment of problematic soils has shown promising results in multiple studies whereby the application of GPs resulted in strength and stiffness improvements as well as a reduction in the swelling potential of soils ( 14 , 24 , 25 ). However, the effectiveness of GP treatment and performance is dependent on a range of complex factors such as the type of precursor and activator, GP dosage, activator concentration, curing temperature, activator-to-precursor ratio, water-to-solids ratio, and elemental ratios such as the Si/Al, and cation/Al ratio ( 26 – 29 ).

There is a consensus that higher curing temperatures, longer curing times, and higher GP dosages result in greater strength in the stabilized soil. As for the other factors, one study on the effect of the elemental ratios of Si/Al and cation/Al found that Si/Al ratio of 1.5:2 and cation/Al ratio of 1:1 resulted in the most densely packed GP microstructure leading to sound engineering performance. An increase in the Si/Al ratio led to degraded performance as a result of overly viscous GP. Moreover, potassium-based GPs generally resulted in a less porous structure and better engineering performance compared with sodium-based GPs ( 30 , 31 ). In contrast, other researchers found sodium-based GPs to have greater mechanical strength than potassium-based GPs ( 32 , 33 ). Different researchers investigated the effects of activator concentration, activator-to-precursor ratio, and standing time on GP performance. They noted an activator concentration of 8 to 14 M as being optimal for the dissolution of the precursor. In addition, an activator-to-precursor ratio of 0.46 and 72 h of standing time were reported to produce better performing GPs ( 34 , 35 ). Some other studies on GP dosage, the water content of the GP and the soil, and the activator-to-precursor ratio concluded that a GP dosage of 14% to 20% by dry weight of soil lead to a significant strength increase in the stabilized soil. Additionally, replacing a portion of the precursor with ground granulated blast furnace slag (GGBFS) was noted to help with early strength gain. Moreover, they recommended an activator-to-precursor ratio of 1 to be optimum ( 36 , 37 ). The controlling parameters found in literature may be subdivided into two broad categories, micro (Si/Al and cation/Al ratios, etc.) and macro (water/solids, activator/precursor ratios, etc.). Depending on the precursor and activator used, same macro parameters may yield GPs with significantly different micro parameters.

Various researchers have used different controlling parameters and recommended a score of value ranges for these parameters for the synthesis of an optimal GP. This renders GP synthesis for industrial application too complex. For ease of reference, the salient features of various studies have been summarized in Table 1.

Table 1.

Summary of Various Studies on the Effects of Synthesis Parameters on GP Strength

	Materials			Parameters	Key Findings
Reference	Soil	Precursor	Activator	Parameters	Key Findings
Lizcano et al. 2012 ( 30 )	NA	Metakaolin—53% SiO₂, 43.8% Al₂O₃	KOH & NaOH with fumed silica	Cation/Al—1 Si/Al—1.25–2.5 H₂O/Al₂O₃—∼11 Curing at 80°C for 24 and 48 h	- Highest strength (∼30 MPa) for Si/Al ratio 1.5, 48 h curing and KOH specimens - KOH-based GP performed better than NaOH GP - 48 h cured specimens had better strength
Rahim et al. ( 32 )	NA	Class F fly ash—∼44.52% SiO₂, 22.5% Al₂O₃	KOH & NaOH with 8 M concentration	Si/Al—1.86 Curing at room temperature and 60°C for 1, 7, 14, and 28 days	- Highest strength (∼60 MPa) in NaOH-based GP after 14-day curing at 60°C - NaOH-based GP performed better than KOH GP - Better strength with longer curing and at higher temperature
Nmiri et al. 2016 ( 33 )	NA	Calcined kaolinite clay (Metakaolin)—53.2% SiO₂, 27.3% Al₂O₃	KOH & NaOH with 5,8,10,13,15, and 18 M concentration	Si/Al—1.65 A/P—0.83–1.17 Curing at room temperature for 28 days	- For NaOH max strength at 13 M concentration (∼35 MPa), with A/P 1.01 - For KOH max strength at 15 M concentration (∼33 MPa), with A/P 1.12 - At same concentration, NaOH GP has higher strength
Addis et al. 2023 ( 34 )	NA	Class F fly ash—51.7% SiO₂, 27.55% Al₂O₃	NaOH (10, 12, 14, and 16 M) with sodium silicate (ratio of NaOH/sodium silicate or N/NSi; 1.5, 2, 2.5, and 3)	A/P—0.44, 0.46, 0.48, 0.5 Standing time before start of curing—1.5, 24, 48, and 72 h Curing at 70°C for 24 h followed by 27-day at room temperature	- Parameter values for optimized strength (∼25 MPa); A/P 0.46, NaOH concentration 14 M, N/NSi 1.5, Standing time 72 h - Importance of synthesis parameters; Standing time > A/P > NaOH M > N/NSi ratio - Strength increased with increase in A/P until 0.46 after which it decreased
Samantasinghar and Singh 2018 ( 35 )	NA	Class F fly ash—57.4% SiO₂, 28.5% Al₂O₃ GGBFS—37.2% CaO, 31% SiO₂, 18% Al₂O₃	NaOH with 2, 4, 8, 12, and 16 M concentration	FA replacement with GGBFS—0%, 20%, 40%, 60%, 80%, and 100% A/P—0.25, 0.3, 0.35, 0.4, and 0.45 ml/g Curing at room temperature for 7, 28, and 90 days	- Highest aluminosilicate dissolution via leaching at 8 M NaOH concentration - Highest strength (∼23 MPa) for 8 M NaOH solution with 100% replacement of FA with GGBFS. Strength decreases with increase in NaOH concentration and increase in FA percentage. - Strength increased with increase in A/P until 0.35 ml/g after which it decreased
Yao et al. 2021 ( 36 )	Brown muddy clay (soft soil) with PI 28.5 and in-situ moisture content of 52%	Fly ash, slag, metakaolin, and lime	NaOH with sodium metasilicate	GP dosage—10%, 12%, and 14 % Soil moisture content—26%, 49%, and 52% Curing at room temperature and 75% humidity for 7, 28, and 90 days After curing, 24 h submersion in water before UCS test	- Increase in strength observed with increase in dosage (Max 7-day strength ∼0.8 MPa at 14% dosage) - Strength increased with longer curing with max 90-day strength ∼4.5 MPa for 14% GP dosage - Strength decreased with increase in moisture content of soil
Yaghoubi et al. 2018 ( 37 )	High plasticity silty clay with LL 50.4% PI 27	Fly ash—61.2% SiO₂, 28.6% Al₂O₃ GGBFS—42.7% CaO, 33.2% SiO₂, 13.5% Al₂O₃	NaOH (8 M) with sodium metasilicate in 30:70 ratio	FA+GGBFS content—10%, 20%, and 30% by wt of dry soil A/P—0.75, 1, and 1.25 Soil moisture content—0.75, 1, and 1.25 times LL Curing at 10, 25, and 40°C for 7 and 28 days	- UCS increased with higher FA+GGBFS content, longer curing and higher temperature - UCS increased with higher A/P until 1 after which it decreased - UCS increased with higher water content until 1 times LL after which it decreased

Note: A/P = Activator/Precursor; NaOH = sodium hydroxide; KOH = potassium hydroxide; GP = geopolymers; GGBFS = ground granulated blast furnace slag; UCS = unconfined compression strength; FA = fly ash; LL = liquid limit; PI = plasticity index; NA = not available.

Multiple researchers have studied various aspects of GP-stabilized high plasticity clays (CH) and found them to be significantly improved. One study evaluated the efficacy of construction and demolition waste (CDW) and GP-based treatment in improving CH soils and concluded that increasing the GP dosage resulted in a 7 to 8 times strength gain compared with untreated soil ( 38 ). Some researchers evaluated the efficacy of coal-fired fly ash and slag-based GPs for the stabilization of CH soils concluding that varying degrees of improvement in mechanical strength and durability may be achieved as a result of the treatment depending on the binder and activator concentration ( 39 , 40 ). However, a need was felt for a comprehensive study to evaluate the effect of micro-synthesis parameters as well as the type of precursor and activator on the stabilization of CH soils using GPs. This will help to identify which parameters most strongly affect performance, to rank them by importance, and to simplify the GP synthesis for use in real-world industry applications.

In response, a research study was conducted to evaluate the comparative effect various parameters have on the engineering performance of a GP-stabilized CH or high plasticity clayey soil. Multiple mixes were designed to cover a range of values for these parameters, and their performance was assessed for their mechanical strength after curing period. This was followed by a statistical and machine-learning (ML) based analysis and modeling to formulate an order of priority for the parameters.

Materials and Methods

Natural Soil

The soil was collected from a local pavement construction site located in Galveston, TX. Basic characterization was performed in accordance with the corresponding ASTM International and Texas Department of Transportation (DOT) standards, as listed in Table 2. This soil was noted to constitute 6.9% gravel, 8.3% sand, 52.8% silt, and 32% clay, as illustrated by grain size distribution curve in Figure 1a. Based on the liquid limit (70%) and plasticity index (44%), the soil was classified as fat clay with sand (CH) in accordance with the Unified Soil Classification System (USCS). The pH of soil was measured to be 7.8 in accordance with ASTM D4972. Figure 1b illustrates the moisture-dry density curve for the natural soil determined in accordance with ASTM D698 using standard energy. A maximum dry unit weight (MDUW) of 14.5 kN/m³ (92.4 pcf) was noted against an optimum moisture content (OMC) of 25.5 %.

Table 2.

Basic Characterization of the Natural Soil

Property	Unit	Standard	Value
Sand	%	ASTM D7928	8.3
Silt	%	ASTM D7928	52.8
Clay	%	ASTM D7928	32
Liquid limit	na	ASTM D4318	70
Plasticity index	na	ASTM D4318	44
USCS classification	na	ASTM D2487	CH (fat clay with sand)
Maximum dry unit weight	kN/m³ (pcf)	ASTM D698	14.5 (92.4)
Optimum moisture content	%	ASTM D698	25.5
Specific gravity, G_s	na	ASTM D854	2.75
Linear shrinkage strain	%	Tex-107-E	16.1
Free swell	%	ASTM D4546	10
Permeability, k	m/s	ASTM D2435	3.97 × 10⁻⁶

Note: Tex = Texas Department of Transportation Standard; USCS = Unified Soil Classification System; na = not applicable.

Figure 1.

Natural soil used for the study: (a) grain size distribution curve; and (b) moisture-density curve.

Precursors

Two types of precursors were used in this study. Class C fly ash (FA), in accordance with ASTM C618 specifications, sourced from a local commercial supplier operating in TX was used as the first precursor whereas the second precursor was a calcined kaolin clay (CC) sourced from a separate commercial supplier. The FA consisted of 53.24% aluminosilicates, 26.38% calcium oxide (CaO), 6.26% iron oxide, and 6.2% magnesium oxide (percent weight by weight). The CC was made up of 53.50% silicon dioxide, 42.50% aluminum oxide, and 1.9% of iron oxide (percent weight by weight). The chemical composition of both precursor materials is listed in Table 3.

Table 3.

Chemical Composition of Precursor Materials

Constituent	Unit	Class C fly ash	Calcined clay
Silicon dioxide (SiO₂)	%	36.45	53.50
Aluminum oxide (Al₂O₃)	%	16.97	42.50
Iron oxide (Fe₂O₃)	%	6.26	1.90
Calcium oxide (CaO)	%	26.38	0.20
Magnesium oxide (MgO)	%	6.20	0.10
Sodium oxide (Na₂O)	%	1.7	0.05

Alkali Activators

Reagent grade sodium hydroxide (NaOH) and potassium hydroxide (KOH) flakes were procured from a local commercial supplier. Activator solutions were prepared at a concentration of 8 m, as recommended in the literature, by mixing eight moles of NaOH and KOH in 1 L of deionized water separately. The solution was stirred for 24 h using a magnetic stirrer after the addition of activator flakes to ensure a homogeneous solution. A reagent grade sodium metasilicate (Na₂SiO₃) was obtained in the form of powder from a commercial supplier and was used in some of the mixes with the activator solution by prior mixing in deionized water for a target parameter value. Ample time was afforded to solutions for the dissipation of the heat of hydration and to equilibrate to room temperature before synthesis of GP.

Design of Mixes

Table 4 lists the mixes used for this study. Untreated soil (UT) was regarded as the control. A total of eight mixes were prepared with varying parameter values to be able to understand the effect of each on the engineering performance of GP-stabilized soil. As a general rule, mixes were designed so that optimum, low, and high values of various parameters, as reported in the literature, could be targeted in the whole group of mixes. The first letter in the mix designation refers to the activator and the second letter refers to the precursor, for example N-FA GP is synthesized using NaOH activator and FA precursor. For simplification and comparative evaluation of controlling parameter effects, the GP dosage for the stabilized soil mix was fixed at 10% by dry weight of soil. It is imperative to note that a dosage of 10% was selected, being the minimum observed in other studies where the effects of GP stabilization were prominent in comparison to the control ( 23 , 24 ). Moreover, the concentration of activator solution (NaOH and KOH) was fixed at 8 m (molal) as recommended in the literature. Additionally, Si/Al ratio value of 1.5 to 2, a cation/Al ratio value of 1, and a water/solid ratio value of 0.5 was targeted in accordance with the literature ( 24 , 30 , 35 – 37 , 41 ). It is pertinent to note here that although the water/solid ratio within the geopolymer varied between mixes, the ultimate moisture content in all the GP-stabilized soil mixes at the time of molding was the same (∼OMC or 25.5%). This was achieved by the addition of the required quantity of water directly to the soil after the addition of GP. For example, in N-FA, 20.5 g of water was added to 94 g of soil after pouring in 10.1 g of GP to bring the moisture content of the GP-soil mix to 25.5%. It is imperative to highlight here that aluminosilicate added to the soil was calculated as the sum of moles of Si and Al from the precursor, and Si from sodium metasilicate, normalized by the dry soil mass.

Table 4.

Different Geopolymer Mixes Used for the Study (N: NaOH, K: KOH, FA: Fly ash, CC: Calcined clay, N1 and K1: Cation/Al value ∼1 was targeted NSi: NaOH-Sodium metasilicate, KSi: KOH-Sodium metasilicate)

Parameter	N-FA	N-CC	K-FA	K-CC	N1-CC	K1-CC	NSi-CC	KSi-CC
Water/solids (wt/wt)	0.50	0.50	0.50	0.50	0.73	0.73	0.5	0.5
Activator/precursor (solution wt/solids wt)	0.51	0.51	0.60	0.60	1.28	1.51	0.51	0.60
Si/Al (mol/mol)	1.82	1.07	1.82	1.07	1.07	1.07	1.80	1.80
Cation/Al (mol/mol)	0.96	0.38	0.96	0.38	0.96	0.96	1.87	1.87
Added aluminosilicate (mmol/g of dry soil)	0.5	0.9	0.5	0.9	0.6	0.5	1.4	1.3

As highlighted earlier, depending on the precursor and activator used, same macro parameters may yield GP with significantly different micro parameters (mixes N-FA and N-CC below). These mixes were, therefore, designed to distinguish the effect of the type of precursor and activator, that ultimately affect micro parameters (mixes sodium hydroxide-fly ash or N-FA, sodium hydroxide-calcined clay or N-CC, potassium hydroxide-fly ash or K-FA, and potassium hydroxide-calcined clay or K-CC) and that of other parameters. While the target values for these parameters were aimed to be optimal, it may be noted that achieving the target value for one parameter may offset the value of another parameter, making it less than optimal. For example, an Si/Al ratio of 1.8 could not be achieved for CC-based mixes because of the chemical composition of the precursor unless sodium metasilicate was added. However, the addition of sodium metasilicate offsets the cation/Al ratio as a result of the provision of additional cations. Similarly, an offset to the activator/precursor and water/solids ratios had to be accepted to achieve a cation/Al ratio of 0.96 in N1-CC and K1-CC mixes. Therefore, N1-CC and K1-CC GP are CC-based mixes with a cation/Al ratio of ∼1. Similarly, NSi-CC and KSi-CC mixes include sodium metasilicate in the activator to achieve the Si/Al target value of 1.8. It is also highlighted here that since sodium metasilicate contributes both SiO₂ and metal cations to the GP, it was excluded from activator/precursor calculations. Overall, the mixes covered a range of high and low values for all the parameters studied for a sound statistical and ML analysis.

Specimen Preparation and Engineering Tests

Cylindrical specimens were prepared with a diameter of 33 mm and a height of 71 mm by static compaction in three layers to a target dry unit weight (14.5 kN/m³ or 92.4 pcf) at an optimum moisture content (25.50%). Untreated soil specimens were prepared by evenly mixing dry natural soil with the optimum moisture content (OMC) followed by static compaction. For GP-stabilized soil mixes, firstly, synthesis of the GP was carried out by mixing worked-out quantities of precursor, activator solution, and deionized water according to the target parameter values. Synthesized GP was then added into the dry natural soil followed by addition of required quantity of water to bring the moisture content of the soil up to the optimum. The mixture was then blended thoroughly to achieve a homogeneous soil matrix. Subsequently, the GP-stabilized soil mixes were molded into various specimens by static compaction in three layers. Triplicate specimens were prepared for all the mixes.

GP-treated specimens were demolded after compaction and allowed to cure for 7 days. Curing was carried out in hermetically sealed chambers at 23°C ± 2°C (73°F ± 4°F). In contrast, untreated soil (UT) specimens were subjected to engineering testing immediately after demolding. To undertake comparative evaluation of various mixes and to understand the effect of parameters on engineering performance, unconfined compression strength (UCS) tests were performed on all the specimens of untreated and GP-treated soil mixes. The test was performed in accordance with ASTM D2166 at a strain rate of 2%/min. Average peak normal stress from the stress-strain curves of the specimens was translated to UCS values.

Statistical Inference

ANOVA testing was carried out to infer the statistical significance of the difference in mean UCS values of various GP-stabilized soil mixes which was followed by Tukey post hoc testing with Bonferroni correction to pinpoint the differences. Statistical testing was performed using JASP which is an open-source program based on a free software environment for statistical computing called R. A 95% confidence level was used for all testing against an $α$ value of 0.05. After preparation of the data, descriptive statistics analysis was done to check for the existence of any outliers.

Figure 2 illustrates box plots of UCS values for various GP-stabilized soil mixes. It is worth noting that JASP allows for visual spotting of any outliers within boxplots by representing them as a solid dot outside the outlier range (represented as error bars).

Figure 2.

Boxplots of UCS values for various mixes, highlighting variability in the UCS of triplicates of each mix.

Before ANOVA testing, assumptions of variance homogeneity and normality were verified using Levene’s test and Q-Q plots of residuals. The null hypothesis of Levene’s test assumes that variances within groups are homogeneous. The test returned a p-value of 0.013 for UCS values which was rectified by means of natural log transformation. After log transformation the test returned a p-value of 0.3 confirming homogeneity of variances. Resultantly, log-transformed UCS values were used for ANOVA and post hoc testing. Figure 3 illustrates Q-Q plot of residuals confirming normal distribution of log-transformed UCS values.

Figure 3.

Q-Q plot for log-transformed UCS values for various mixes.

The effect of activator and precursor types on UCS was evaluated using factorial ANOVA. The statistical analysis evaluated the main effects of precursor type (FA and CC), activator type (NaOH and KOH), and their interaction effects on log-transformed UCS. Subsequently, a linear regression model was also fitted for statistical inference on the coefficients. This was carried out using R-Studio, which is also based on R.

Parameter Importance Using Machine Learning (ML)

An RF regression model ML technique was used to analyze the effect of various parameters on GP-stabilized soil engineering performance. RF regression uses predictions from multiple decision trees to predict continuous outcomes by leveraging randomness. RF regression modeling was also carried out on R-Studio, an open-source platform. UCS values were designated as the dependent variable, whereas precursor type, activator type, aluminosilicate (Al-Si) content, W/S, activator/precursor, Si/Al, and cation/Al ratios were used as features. Modeling was carried out with the “rminer” library of R-Studio using the K-fold method by undertaking fivefold cross-validation, whereby data is split randomly into five folds, and each fold is used for model testing once. To ensure repeatability, the set-seed feature was enabled. Comprehensive regression metrics including mean absolute error (MAE), root mean squared error (RMSE), R², and mean absolute percentage error (MAPE) were also calculated to indicate model performance. Ten independent model runs were carried out and performance metrics were averaged across the runs. After model training, feature importance was also obtained using the simple perturbation-based global sensitivity (simpg) method in “rminer” which estimates importance by assessing how changes in a feature affect model output. A higher sensitivity value points to a feature being more important.

Results and Discussions

Unconfined Compression Strength (UCS) and ANOVA Testing

Figure 4 depicts the results of UCS tests conducted on various GP-stabilized soil mixes. Table 5 lists the results of ANOVA tests on log-transformed UCS values and Table 6 catalogs the p-values for post hoc tests using Bonferroni correction.

Figure 4.

UCS values for various GP-stabilized soil mixes (N: NaOH, K: KOH, FA: Fly ash, CC: Calcined clay, N1 and K1: Cation/Al value ∼1 was targeted NSi: NaOH-Sodium metasilicate, KSi: KOH-Sodium metasilicate).

Table 5.

ANOVA Testing Results for Log-Transformed UCS

Case	Sum of squares	df	Mean square	F statistic	p-value	Remarks
Model	8.48	8	1.06	72.53	4.1 × 10⁻¹²	Significant
Residuals	0.26	18	0.015	na	na	na

Note: UCS = unconfined compression strength; ANOVA = analysis of variance; na = not applicable.

Table 6.

p-values for Post Hoc Testing on Log-Transformed UCS values (N: NaOH, K: KOH, FA: Fly ash, CC: Calcined clay, N1 and K1: Cation/Al value ∼1 was targeted NSi: NaOH-Sodium metasilicate, KSi: KOH-Sodium metasilicate, D: Different or statistically significant, S: Similar or statistically insignificant, Significance criteria: p < $α$ (0.05) deemed significant or different)

Mix Type	UT	N-FA	K-FA	N-CC	K-CC	N1-CC	K1-CC	NSi-CC	KSi-CC
UT	na	1.3 × 10^–8 (D)	1.2 × 10^–6 (D)	1.1 × 10^–8 (D)	1.3 × 10^–8 (D)	3.3 × 10^–9 (D)	5.0 × 10^–8 (D)	1.1 × 10^–12 (D)	1.1 × 10^–11 (D)
N-FA	1.3 × 10⁻⁸ (D)	na	1 (S)	0.08 (S)	0.11 (S)	0.01 (D)	0.49 (S)	1.2 × 10^–8 (D)	6.8 × 10^–7 (D)
K-FA	1.2 × 10⁻⁶ (D)	1 (S)	na	0.08 (S)	0.12 (S)	0.01 (D)	0.51 (S)	1.2 × 10^–8 (D)	7.1 × 10^–7 (D)
N-CC	1.1 × 10⁻⁸ (D)	0.08 (S)	0.08 (S)	na	1 (S)	1 (S)	1 (S)	1.6 × 10^–6 (D)	0.0003 (D)
K-CC	1.3 × 10⁻⁸ (D)	0.11 (S)	0.12 (S)	1 (S)	na	1 (S)	1 (S)	1.1 × 10^–6 (D)	0.00016 (D)
N1-CC	3.3 × 10⁻⁹ (D)	0.01 (D)	0.01 (D)	1 (S)	1 (S)	na	0.52 (S)	7.0 × 10^–6 (D)	0.002 (D)
K1-CC	5.0 × 10⁻⁸ (D)	0.49 (S)	0.51 (S)	1 (S)	1 (S)	0.52 (S)	na	2.4 × 10^–7 (D)	3 × 10^–5 (D)
NSi-CC	1.1 × 10⁻¹² (D)	1.2 × 10⁻⁸ (D)	1.2 × 10⁻⁸ (D)	1.6 × 10⁻⁶ (D)	1.1 × 10⁻⁶ (D)	7.0 × 10⁻⁶ (D)	2.4 × 10⁻⁷ (D)	na	0.18 (S)
KSi-CC	1.1 × 10⁻¹¹ (D)	6.8 × 10⁻⁷ (D)	7.1 × 10⁻⁷ (D)	0.0003 (D)	0.00016 (D)	0.002 (D)	3 × 10⁻⁵ (D)	0.18 (S)	na

Note: UCS = unconfined compression strength; K-CC = potassium hydroxide-calcined clay; K-FA = potassium hydroxide-fly ash; K1-CC = potassium hydroxide_1-calcined clay; KSi-CC = potassium hydroxide-sodium metasilicate-calcined clay; N-CC = sodium hydroxide-calcined clay; N-FA = sodium hydroxide-fly ash; N1-CC = sodium hydroxide_1-calcined clay; NSi-CC = sodium hydroxide_sodium metasilicate-calcined clay; UT = untreated soil; na = not applicable.

The untreated soil mix (UT) was noted to be very weak in mechanical strength with a UCS value of only 34.5 pounds per square inch (psi) (238 kPa). In contrast, the UCS for all the GP-stabilized soil mixes was noted to be significantly higher, indicating that GP treatment is associated with better engineering performance. Depending on the values of various synthesis parameters, the GP-stabilized soil mixes exhibited mechanical strengths ranging between 80 psi (550 kPa) and 280 psi (1930 kPa). The range of UCS values observed are consistent with literature where multiple researchers noted the strength of GP-stabilized clayey soils to be between 58 psi (400 kPa) and 290 psi (2000 kPa) for 8% to 10% binder/GP dosage ( 24 , 38 – 40 ). The difference in mean UCS values for various mixes was also confirmed to be statistically significant by the ANOVA test. The test returned an F-statistic value of ∼72.53 against a p-value significantly lower that the $α$ value of 0.05, thereby rejecting the null hypothesis.

Careful examination of UCS values indicated that the NaOH-based GP mixes generally performed relatively better than the corresponding KOH-based GP mixes. The mixes of sodium hydroxide-fly ash (N-FA), sodium hydroxide-calcined clay (N-CC), sodium hydroxide_1-calcined clay (N1-CC), and sodium hydroxide_sodium metasilicate-calcined clay (NSi-CC) have relatively high UCS values compared with the mixes of potassium hydroxide-fly ash (K-FA), potassium hydroxide-calcined clay (K-CC), potassium hydroxide_1-calcined clay (K1-CC), and potassium hydroxide-sodium metasilicate-calcined clay (KSi-CC), respectively. However, examination of p-values from post hoc testing pointed out that the difference in mean UCS values for most of these mixes was statistically insignificant. This is consistent with literature, whereby given the effects of metal cation on the reaction kinetics of polymerization, studies have concluded that NaOH performs better as an activator ( 32 , 33 ). It is pertinent to note here that values of GP synthesis parameters for respective N-based and K-based mixes are almost identical. Post hoc testing, however, flagged the differences in UCS values of respective N-based and K-based mixes, that is, N-FA versus K-FA, N-CC versus K-CC, N1-CC versus K1-CC, and NSi-CC versus KSi-CC to be statistically insignificant.

Another trend observed was that CC-based mixes generally exhibit higher mechanical strength as compared with FA-based mixes. This is evident from the comparison of UCS values for N-FA (84.1 psi or 580 kPa) against those of N-CC (115.6 psi or 797 kPa) and UCS values of K-FA (83.6 or 576 kPa) against those of K-CC (113.1 or 780 kPa). This may be a result of the higher aluminosilicate content of the CC (∼96%) precursor compared with FA (∼53%).

UCS values for N-CC (115.6 psi or 797 kPa) and N1-CC (126.6 psi or 873 kPa) as well as K-CC (113.1 psi or 780 kPa) and K1-CC (102.9 psi or 709 kPa) indicate that increasing the cation/Al ratio (from 0.38 to 0.96) with reduced aluminosilicate content (from ∼0.9 mmol/g to 0.5 mmol/g of dry soil) does not affect mechanical strength significantly (post hoc p = 1). The iteration of N1-CC and K1-CC mixes to NSi-CC and KSi-CC mixes enhanced the Si/Al and cation/Al values from 1.07 to 1.8 and 0.96 to 1.87, respectively. Moreover, the added aluminosilicate content also increased by 0.8 mmol/g. This enhancement translates to statistically significant improvement in mechanical strengths as confirmed by post hoc testing. It is pertinent to note here that the Si/Al values for NSi-CC, KSi-CC, N-FA, and K-FA are identical. However, mechanical strength varies greatly, indicating that higher overall aluminosilicate content (0.5 mmol/g of dry soil in FA-based GP and ∼1.3 mmol/g in Si-CC based GP) positively affects engineering performance positively in the presence of sufficient alkali cations. Ultimately, this demonstrated that an increase in the aluminosilicate content and the Si/Al ratio has to be accompanied by an increase in the cation/Al ratio (for optimal aluminosilicate dissolution) for the higher strength gain. This is consistent with the literature whereby an increase in the Si/Al and cation/Al ratios results in an increase in GP strength ( 35 ). Table 7 lists the results of factorial ANOVA to assess the main and interaction effects of activator and precursor types on the UCS.

Table 7.

ANOVA for Main and Interaction Effects of Activator and Precursor Types

Term	Sum of squares	Df	Mean square	F statistic	p-value	Remarks
Precursor Type	0.2648	1	0.27	11.15	0.0033	Significant
Activator Type	0.0174	1	0.017	0.724	0.41	Insignificant
Interaction	0.006	1	0.006	0.25	0.62	Insignificant
Residuals	0.48	20	0.024	na	na	na

Note: ANOVA = analysis of variance; na = not applicable.

The results of the ANOVA revealed that the precursor type has a statistically significant main effect (p-value 0.003) on UCS, indicating that the UCS differs significantly between the FA and CC mixes. However, the main effect of activator type and the interaction effect of the two variables were noted to be insignificant (p-values 0.41 and 0.62, respectively). Table 8 lists the coefficients and related statistics for a linear model where log-transformed UCS was regressed on activator and precursor types as well as their interaction.

Table 8.

Results of Linear Regression Model for Log-Transformed UCS on Activator and Precursor Type

Term	Estimate	Standard error	T statistic	p-value	Remarks
Intercept	2.13	0.05	41.19	<2 × 10⁻¹⁶	Significant
Precursor Type–FA	−0.21	0.10	−2.008	0.05	Marginally Significant
Activator Type- NaOH	0.07	0.07	0.987	0.335	Insignificant
Interaction-FAxNaOH	−0.07	0.15	−0.5	0.622	Insignificant

Note: Model Summary–Residual standard error 0.16 on df 20; R² of 0.38; F statistic 4.04; p-value 0.021; UCS = unconfined compression strength; FA = fly ash; NaOH = sodium hydroxide.

The linear regression model regarded CC-KOH as the reference case. Values of coefficients from the model indicated that switching from CC to FA results in lower UCS (effect estimate −0.21) and a p-value pf 0.05 suggested it to be marginally significant. The model indicated that change from KOH to NaOH led to higher UCS (effect estimate 0.07) whereas the interaction term indicated that NaOH in FA-based mixes results in lower UCS (effect estimate −0.07). However, both the activator and interaction effects were flagged as statistically insignificant. The results of the linear regression model were consistent with ANOVA. However, the model explained only 38% of the variance in the log-transformed UCS values, indicating moderate explanatory power and a need for the inclusion of other predictors or nonlinear modeling techniques to better capture the behavior.

Random Forest Regression Model

Figure 5 presents the predictive performance plot for the RF regression ML model for UCS values as the dependent variable. An MAE value of 17.8 is observed for the model with an MAPE value of 12.4 %. A coefficient of determination or R² value of 0.84 was noted. These metrics indicate a robust performing predictive model indicating a good fit.

Figure 5.

Predictive performance of RF regression model.

Figure 6 presents the plot for feature importance for the global sensitivity values. Feature importance yields valuable insights into the relative contributions of each feature (parameters) in the prediction of UCS values or engineering performance. Sensitivity values of 0.368, 0.09, and 0.026 were noted for macro parameters of precursor type, activator type and activator/precursor ratio respectively. The W/S ratio had a minimal effect and an importance value of only 0.004 was recorded. On the other hand, values of 0.215, 0.185, and 0.111 were observed for microparameters of Al-Si content, cation/Al and Si/Al ratios respectively. As a result, the analysis categorized the precursor type, Al-Si content, cation/Al ratio, and Si/Al ratio to be the most important parameters contributing to the mechanical strength in that order. The contribution from Si/Al is relatively small, indicating that the chemical and physical properties of GP ingredients and their reaction dynamics affect performance more. This is consistent with engineering and statistical analysis in previous sections where sodium hydroxide-fly ash (N-FA) and potassium hydroxide-fly ash (K-FA) mixes had significantly different UCS values than sodium hydroxide-sodium metasilicate-calcined clay (NSi-CC) and potassium hydroxide-sodium metasilicate-calcined clay (KSi-CC) mixes, despite a similar Si/Al ratio (∼1.8). The activator type, A/P ratio, and W/S ratio had minimal effect. Moreover, this is consistent with the statistical analysis, where precursor type had a statistically significant effect, with the effects of interaction and activator type being insignificant. It is pertinent to note here that the minimal effect of the W/S ratio may be attributed to only minimal change in the parameter value across these mixes (0.5 to 0.7).

Figure 6.

Normalized MDI values of GP synthesis parameters.

It was hypothesized that the strength gain was directly proportional to the amount of aluminosilicates added within the soil, provided sufficient activator was available for dissolution and polymerization reactions. Within this model, the type of precursor is directly related to the aluminosilicate content being added to the natural soil (aluminosilicate content of ∼53% for FA against ∼96% for CC). However, the ultimate aluminosilicate content being added into the stabilized soil mix is dependent on other synthesis parameters as well. It can be seen that an increase in cation/Al and W/S ratios affects the quantity of aluminosilicate content. For example, in N1-CC mix, an increase in W/S (0.73) and cation/Al ratio (0.96) resulted in a decrease of added Al-Si content (0.5 mmol/g) as compared with N-CC (W/S 0.5, Cation/Al 0.38 and Al-Si content 0.9 mmol/g). N-CC has higher Al-Si content (0.9 mmol/g) compared with N1-CC (0.6 mmol/g); however, the strengths of both mixes are somewhat similar (115.6 psi and 126.6 psi respectively). On the other hand, NSi-CC has the highest Al-Si content (1.4 mmol/g) with higher cation/Al ratio of 1.87 and exhibits the highest strength, which was flagged as significant in comparison to both other mixes in statistical analysis. This may be attributed to the presence of insufficient activator in N-CC despite higher Al-Si content and lower Al-Si content in N1-CC despite higher cation/Al. The presence of ample alkali cations is imperative for dissolution of the aluminosilicate source leading up to the polymerization process. Therefore, the model was deemed to be capturing the underlying behavior accurately and the established parameter importance order was considered sound.

A potential implication of this direct proportionality between Al-Si content and mechanical strength could be that FA-based GP may necessitate a higher dosage to achieve a similar performance as that of a lower dosage CC-based GP because of the difference in their aluminosilicate content. Moreover, the need to balance the aluminosilicate and activator content of GP also suggests that optimization is necessary for the best engineering performance of a GP-stabilized soil system. Both these aspects ultimately affect the economics of the project and would therefore necessitate due attention.

Conclusions

A research study was conducted to investigate relative importance of various geopolymer (GP) synthesis micro and macro parameters by using statistical and machine learning (ML) techniques. A group of eight GP mixes with varying synthesis parameter values was designed and used to stabilize a fat clay. Engineering performance of GP-stabilized soil mixes was evaluated for mechanical strength through UCS testing. This was followed by statistical inference using ANOVA and post hoc tests, and ultimately RF regression modeling analysis. The key findings of the study are summarized as follows:

Problematic subgrade soils such as fat clay can be effectively stabilized by application of a suitable GP treatment to the untreated soil (UT). Performance enhancement in GP-treated soil mixes was observed to be statistically significant with an ANOVA F-statistic value of 72.53 and a p-value of 4.1 × 10⁻¹². The extent to which engineering performance is enhanced depends on the synthesis criteria of GP.

The type of activator somewhat influences the engineering performance of GP-stabilized mixes with superior performance observed in NaOH-based or N mixes. This difference in engineering performance is ∼1% for FA-based GP mixes and 2%, 19%, and 22% for calcined clay (CC), 1-CC, and sodium silicate-CC (Si-CC) based mixes, respectively. Statistical and machine learning random forest (RF) models, however, deemed the effect of activator type to be insignificant (ANOVA p-value 0.41) and minimal (RF sensitivity value 0.09).

Generally, calcined clay (CC) based mixes (sodium hydroxide-CC or N-CC and potassium hydroxide-CC or K-CC) exhibited over 25% higher mechanical strength than the respective fly ash–based FA mixes (N-FA and K-FA), which may be a result of the higher aluminosilicate (Al-Si) content of CC (96%) than that of FA (53%). The effect of precursor type was noted to be significant in statistical analysis (ANOVA p-value 0.003), and the RF model also determined it to be the most important feature (sensitivity value 0.368).

The order of parameter importance established by the RF model was precursor type > Al-Si content > cation/Al > Si/Al > activator type > activator/precursor (A/P) > water/solid (W/S). Activator type and the A/P and W/S ratios were noted to have minimal effect on UCS with sensitivity values of 0.09, 0.026 and 0.004 respectively. Minimal effect of W/S ratio may be attributed to the negligible change in parameter value across all mixes.

Higher Al-Si content (dependent on precursor type and other synthesis parameters) is associated with better engineering performance, provided sufficient activator is present for optimum aluminosilicate dissolution as highlighted by RF sensitivity values of 0.215 and 0.185 for Al-Si content and cation/Al features, respectively. This is evident in significantly higher UCS (post hoc, p < 0.05) observed in sodium hydroxide_sodium metasilicate-calcined clay (NSi-CC, UCS 279.8 psi or 1929 kPa) and potassium hydroxide_sodium metasilicate-calcined clay (KSi-CC, UCS 212.8 psi or 1,467 kPa) mixes corresponding to the highest Al-Si content of ∼1.3 mmol/g and cation/Al value of 1.87 as compared with other mixes. FA (N-FA and K-FA)and 1-CC (N1-CC and K1-CC) mixes have lower Al-Si content (∼0.5 mmol/g), whereas N-CC and K-CC mixes had lower cation/Al ratio (0.38).

Despite similar Si/Al values of 1.8, NSi-CC and KSi-CC mixes with UCS 279.8 psi or 1929 kPa and 212.8 psi or 1,467 kPa respectively rendered significantly better engineering performance compared with N-FA and K-FA mixes with UCS 84.1 psi or 580 kPa and 83.6 psi or 576 kPa, respectively, suggesting lower contribution by feature as highlighted by RF sensitivity value of 0.111.

A precursor with a higher aluminosilicate content may economize the GP dosage required for target mechanical strength if GP synthesis is properly optimized.

Overall, this study showcases the efficacy of GP-based treatments for high plasticity subgrade soils. Additionally, it provides insights into the effects of GP synthesis parameters on the UCS of GP-treated high plasticity clays. This will help facilitate the field application of innovative and environmentally friendly solutions in the development of transportation infrastructure. Field implementation of such innovative materials may potentially reduce the economic as well as environmental costs of transportation infrastructure without compromising performance. However, industry adoption is recommended after undertaking large-scale laboratory testing, followed by field-scale testing to crystallize material and mix specifications by regulating agencies.

It is pertinent to note here that this study is limited to evaluating the effect of select synthesis parameters such as Si/Al, cation/Al, activator/precursor ratios, and aluminosilicate content while keeping other significant parameters such as curing conditions, dosage, activator molarity, and so forth constant. Moreover, this is also limited in scope to high plasticity clay (CH) stabilized by fly ash and calcined clay-based GPs. Therefore, future studies may also be carried out to incorporate the effect of other parameters, soil types, and precursors.

Footnotes

Author Contributions

The authors confirm contribution to the paper as follows: study conception and design: Anand J. Puppala, Vinay Lakshminarayanan Krishnan; data collection: Muddassir Sanei, Vinay Lakshminarayanan Krishnan; analysis and interpretation of results: Muddassir Sanei, Vinay Lakshminarayanan Krishnan; draft manuscript preparation: Muddassir Sanei, Vinay Lakshminarayanan Krishnan, Anand J. Puppala. All authors reviewed the results and approved the final version of the manuscript.

Declaration of Conflicting Interests

The authors declared the following potential conflicts of interest with respect to the research, authorship, and/or publication of this article: Anand J. Puppala is a member of the Transportation Research Record’s Editorial Board. All other authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The authors would like to acknowledge the support of National Science Foundation Award # 2414953. The authors would also like to appreciate the support of the NSF Industry-University Cooperative Research Center (I/UCRC) program-funded Center for Integration of Composites into Infrastructure (CICI) site at Texas A&M University, College Station, Award #2017796 (Phase III).

ORCID iDs

Muddassir Sanei

Vinay Krishnan

Anand J. Puppala

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