Effect of Lime and Phosphogypsum on the Geotechnical Properties of Dispersive Soil

Abstract

Dispersive soils are highly erodible and prone to segregation in water, posing significant risks to the soil and structural stability. Traditional stabilization methods using cement and lime are effective but raise sustainability concerns due to the high carbon emissions. This study explored the utilization of phosphogypsum (PG), a by-product of the fertilizer industry, as a sustainable alternative to improve dispersive soils. PG was evaluated both individually and in combination with lime, focusing on its effects on the plasticity, swell, consolidation, compaction, and unconfined compressive strength (UCS) characteristics. Soil samples were treated with varying proportions of lime (2–10%) and PG (2–10%). The results demonstrated that combining 4% lime with 8% PG significantly enhanced the properties of dispersive soil, reducing the swell pressure from 115 kN/m² to 72 kN/m² and the swell potential by 67%. The UCS increased by 320% after 7 days of curing, while the coefficient of consolidation improved 2.74 times and the compression index decreased by a factor of 8.55. Regression analysis was conducted and validated for UCS prediction. Utilizing PG not only improves the soil stability, but also offers a sustainable solution by recycling industrial waste and reducing the dependence on conventional materials. These findings underscore the potential of PG as an eco-friendly soil stabilizer for dispersive soils.

1. Introduction

The construction of structures such as embankments, channels, and canals on dispersive soils presents significant challenges in civil engineering. Dispersive soils are highly problematic due to their erodible nature and tendency to disperse in the presence of water. These soils are found in various regions globally, including India, Thailand, Latin America, South Africa, the United States, and Australia, and their presence poses considerable challenges for infrastructure stability [1]. Often referred to as sodic soils, dispersive soils are characterized by an abundance of exchangeable sodium ions within their structure. When immersed in water, the clay fraction of dispersive soil behaves like single-grained particles with minimal electrochemical attraction, preventing close association and resulting in dispersion [2]. The degree of dispersivity and its reduction through the application of additives can be assessed using methods such as the double hydrometer test, pinhole test, and crumb test [3,4].

The addition of lime and zeolite has been shown to significantly alter the dispersivity, compressibility, and swell characteristics of dispersive soils. Pozzolanic reactions between lime, zeolite, and soil play a crucial role in reducing these properties, leading to improved soil stability [5]. Studies have revealed that incorporating lime into a fly ash–soil mixture reduces the soil dispersivity, while fly ash alone induces minimal changes. Lime facilitates the flocculation of particles, while fly ash acts as a binding agent [6]. The use of class C fly ash enhances the strength of stabilized specimens over time due to pozzolanic reactions that occur during curing [7]. Similarly, the inclusion of a cement–lime mixture has been effective in decreasing the dispersivity [8].

In response to the growing need for sustainable engineering practices, phosphogypsum (PG), a by-product of the fertilizer industry, has emerged as a promising alternative for soil stabilization. By utilizing PG, an industrial waste product, this approach contributes to environmental sustainability by reducing the need for high-carbon-footprint materials such as cement and lime. The use of PG helps recycle waste, further promoting eco-friendly construction practices.

When combined with cement and fly ash, PG has been shown to improve the Atterberg limits, compaction characteristics, and unconfined compressive strength of expansive soils. Its addition reduces the plasticity index and enhances the soil strength due to accelerated pozzolanic reactions [9]. Moreover, the cementitious elements formed during these reactions facilitate bonding between the soil particles, restricting volume expansion and reducing the swell potential [10]. Although PG may contain trace amounts of heavy metals, its combination with stabilizers such as lime or cement immobilizes these contaminants. The stabilization process reduces the solubility and mobility of heavy metals by forming insoluble mineral phases, such as ettringite and calcium silicate hydrates (C-S-H), which effectively trap heavy metal ions, making it an environmentally safer option for construction applications [11].

Although various studies have explored the stabilization of dispersive soils using materials such as class C fly ash, lime [12], cement, aluminum sulfate [13], sodium chloride [14], magnesium chloride [15], zeolites [2], polymers, and lignosulfonate [16], research on the use of phosphogypsum, either alone or in combination with lime, remains limited. Additionally, while phosphogypsum has been extensively studied for improving expansive clays [17], its application in stabilizing dispersive soils remains largely unexplored, presenting an opportunity to address the unique challenges posed by these soils. This gap underscores the need for further investigation into the potential of phosphogypsum and its mixtures for dispersive soil stabilization.

In the present study, efforts were directed toward improving the strength of dispersive soils through the addition of varying percentages of lime (2%, 4%, 6%, 8%, and 10%) and phosphogypsum (2%, 4%, 6%, 8%, and 10%) as well as by using a fixed optimum lime content (4%) with varying phosphogypsum percentages (2%, 4%, 6%, 8%, and 10%). The geotechnical properties evaluated included the Atterberg limits, differential free swell index, compaction characteristics, unconfined compressive strength, swell, and consolidation behavior. This investigation aims to provide valuable insights into the application of phosphogypsum and lime for enhancing the stability of dispersive soils while promoting sustainable practices in civil engineering applications.

2. Materials and Methods

2.1. Dispersive Soil

The dispersive soil used in this study was collected from Oragadam, Kanchipuram, Tamil Nadu, India. It was excavated at a depth of 2 to 3 m below ground level, a depth commonly associated with shallow foundations. Tests were conducted to determine the specific gravity, particle size distribution, liquid limit, plastic limit, and shrinkage limit of the soil. The degree of dispersivity of the soil was evaluated using physical and chemical methods, including the crumb test and double hydrometer test, as detailed in Section 3. The index properties of the soil, as determined through these tests, are summarized in

Table 1. Index properties of the soil.

S.no.	Properties	Values
1	Specific gravity	2.71
2	Gravel (%)	4
3	Sand (%)	20
4	Silt (%)	37
5	Clay (%)	39
6	Differential free swell index (%)	96
7	Liquid limit (%)	70
8	Plastic limit (%)	34
9	Plasticity index (Ip) (%)	36
10	Shrinkage limit (%)	13.6
11	Classification	CH
12	Maximum dry density (MDD) (kN/m3)	15
13	Optimum moisture content (OMC) (%)	17.15
14	Unconfined compressive strength at OMC (kN/m2)	107.33

. According to the Unified Soil Classification System, the soil is classified as clay of high plasticity (CH type).

2.2. Lime

The laboratory-grade lime (Ca(OH)₂), with the purity of the calcium oxide content exceeding 95%, was procured from the local market. Lime, a fine white powder with strong alkaline properties, was mixed with soil in proportions of 2%, 4%, 6%, 8%, and 10% to determine the optimal binding content. It is well-established that under specific curing conditions, soil achieves its maximum strength at the optimal lime content. Beyond this optimal content, further increments in lime do not result in a significant improvement in strength [18]. Based on the plasticity characteristics observed in this study, 4% lime was determined to be the optimal proportion. The soil–lime mixtures were cured for 0 and 7 days, after which the unconfined compressive strength (UCS) tests were conducted.

2.3. Phosphogypsum

The phosphogypsum (PG) used in this study was sourced from M/s Madras Fertilizer Limited, Manali, Chennai. Its major components are calcium oxide and sulfur trioxide. The percentage of phosphogypsum was varied in all test combinations at 2%, 4%, 6%, 8%, and 10%, with curing periods of 0 and 7 days. Phosphogypsum was incorporated at varying percentages for the determination of the index and engineering properties with and without curing.

3. Methods

Previous studies have extensively examined the mineralogical changes in dispersive soils treated with lime and phosphogypsum, and the formation of these phases is well-documented in the literature. For instance, Mashifana et al. [19] investigated the geotechnical and microstructural properties of lime-fly ash-phosphogypsum-stabilized soil, utilizing SEM and EDS to confirm the formation of C-S-H phases. Similarly, Oumnih et al. [20] conducted PXRD and SEM analyses on phosphogypsum-lime-stabilized bentonite and reported the transformation of montmorillonite into pozzolanic reaction products.

Building upon these findings, the present study evaluated the dispersive nature of the soil through preliminary assessments including the crumb test, double hydrometer test, and chemical identification methods. Lime and phosphogypsum were then incorporated separately and in combination, with their proportions systematically varied. The modified soil samples underwent a comprehensive set of laboratory tests to determine their index and engineering properties. These included the plasticity characteristics (ASTM D4318) [21], differential free swell index (IS 2720 part 40-1977) [22], compaction properties (ASTM D698) [23], unconfined compressive strength (ASTM D2166) [24], swell test (ASTM D4546) [25], and consolidation behavior (ASTM D2435) [26]. Through this integrated approach, the study aimed to correlate the mineralogical transformations with improvements in the geotechnical performance of the treated dispersive soils.

All experiments were conducted at the Soil Mechanics Laboratory, Anna University, Chennai, India, using specialized equipment for different test categories. Liquid limit tests were performed using a Casagrande liquid limit apparatus. Compaction properties were evaluated using a Standard Proctor compaction apparatus. The unconfined compressive strength (UCS) tests were conducted using a universal testing machine (UTM) with a proving ring of 5 kN capacity. The swell and consolidation behavior were analyzed using a swell testing apparatus and oedometer setup, respectively. All tests were performed under controlled environmental conditions following the respective ASTM and IS standards to ensure accuracy and reproducibility.

3.1. Crumb Test

The crumb test, as per ASTM D6572-21 [27], is a qualitative method designed to visually assess the dispersivity of clayey soils when exposed to water. In this study, a soil specimen with the initial dimensions of 2.9 cm × 1.5 cm was prepared and completely submerged in distilled water. Observations were made at intervals of 1, 2, 5, 10, and 30 min to monitor changes in the specimen’s dimensions, as depicted in Figure 1a–e. After 30 min of immersion, the width of the specimen increased by 200%, while the length increased by 48%. These significant dimensional changes are consistent with the dispersive characteristics of the soil, as evidenced by its tendency to break apart and disperse in water, resulting in increased cloudiness in the surrounding medium. Thus, the results confirm the soil’s susceptibility to dispersion.

However, the crumb test is a qualitative method that relies primarily on visual observations, which may limit its precision and reliability in assessing the soil dispersivity [28]. Therefore, the double hydrometer test and chemical analyses to determine the exchangeable sodium percentage (ESP) and sodium adsorption ratio (SAR) were conducted, as detailed in the forthcoming sections.

3.2. Double Hydrometer Test

The double hydrometer test is a widely accepted method for evaluating the dispersivity of soils. This procedure involves conducting two separate hydrometer analyses to determine the particle size distribution. As per ASTM D4221-18 [29], in the first analysis, the soil specimen is dispersed in distilled water with the aid of strong mechanical agitation and a chemical dispersant. In the second analysis, a separate soil specimen is tested in distilled water without the addition of a chemical dispersant.

The degree of dispersion is quantified as the ratio of the dry mass of soil particles smaller than 0.005 mm obtained without the dispersive agent to the dry mass of particles smaller than 0.005 mm obtained with the dispersive agent, expressed as a percentage. In this study, the dispersivity value exceeded 50%, which, according to Knodel [30], classifies the soil as dispersive in nature. The grain size distribution curve obtained from the double hydrometer test, with and without the dispersive agent, is presented in Figure 2.

3.3. Chemical Identification Test

The chemical analysis of the soil pore water extracts provides valuable insights into the dispersive behavior of soils, which is largely influenced by the presence of dissolved sodium ions in the pore water. In this study, the concentrations of sodium (Na), potassium (K), calcium (Ca), and magnesium (Mg) in the pore water extract were analyzed to evaluate the total dissolved cations. Calcium and magnesium were quantified using the EDTA titration method (ASTM E372-21) [31], while sodium and potassium were measured using a flame photometer (ASTM D1428-56 T) [32]. These measurements facilitated the calculation of key parameters indicative of soil dispersivity. The exchangeable sodium percentage (ESP) is a critical parameter for identifying sodic soils, which may exhibit a susceptibility to dispersion (ASTM D7503) [33]. In this study, the ESP value was determined as 15, indicating the soil’s susceptibility to dispersion. Additionally, the sodium adsorption ratio (SAR), which quantifies the relative concentration of sodium to calcium and magnesium in soil pore water, was calculated as 12.8. This SAR value falls within the moderate sodium hazard range (6–13), indicating a significant potential for soil dispersion and further supporting its classification as a dispersive soil [30].

3.4. Swell Test

The swell test was conducted using the oedometer consolidation test setup to evaluate the swelling characteristics of dispersive soil with various admixtures including lime and phosphogypsum. The swell potential and swell pressure values were determined using the expanding volume method for an initial surcharge pressure of 5 kPa, where compacted soil samples with admixtures were allowed to swell over a period of time. The soil samples were monitored for changes in height and volume, and once they reached a constant swell value, indicated by no further volume change, the swell potential and swell pressure were determined.

3.5. One Dimensional Consolidation Test

To understand the compressibility characteristics of dispersive soil stabilized with lime and phosphogypsum, one dimensional consolidation tests were carried out. The remolded soil samples were prepared in the mold near the liquid limit water content. The samples were then subjected to incremental loading in the following ranges: 0–50 kN/m², 50–100 kN/m², 100–200 kN/m², 200–400 kN/m², and 400–800 kN/m². The load was applied in each increment, and the corresponding settlement values were recorded at a specific time interval until consolidation was seized. From the e-log P curve and time–compression curve, the compression index (C_c) and coefficient of consolidation (C_v) values were respectively determined.

4. Results and Discussions

4.1. Effect of Lime on Plasticity and Shrinkage Characteristics

The plastic limit, liquid limit, and shrinkage limit of dispersive soil were evaluated at lime content levels of 2%, 4%, 6%, 8%, and 10%. Figure 3 illustrates the variations in plasticity and the shrinkage limit characteristics. The results revealed that the liquid limit and plasticity index decreased with increasing lime content, while the plastic limit increased correspondingly. This behavior can be attributed to the reduction in clay content and the corresponding increase in coarse particles with the addition of lime [34]. Specifically, at lime contents of 2% and 4%, the plasticity index decreased to 7.81% and 10.56%, respectively. The shrinkage limit increased with lime addition up to 4%, beyond which it remained constant. Based on these observations, the optimum lime content for the dispersive soil was determined to be 4%.

4.2. Effect of Phosphogypsum on the Plasticity and Shrinkage Characteristics

Dispersive soil was mixed with varying percentages of phosphogypsum (PG) at 2%, 4%, 6%, 8%, and 10%, and tests for the shrinkage limit, plastic limit, and liquid limit were conducted to evaluate the effects of PG addition. The results indicate that the plasticity index increased with the addition of 2% and 4% PG. However, beyond 4% PG, a significant decrease of 39% in the plasticity index was observed at 10% PG, as illustrated in Figure 4. Notably, both the plastic limit and shrinkage limit decreased with PG additions beyond 4%. In contrast to the lime-stabilized dispersive soil, the incorporation of PG at varying percentages did not result in any substantial changes in the plasticity characteristics or shrinkage limit of the dispersive soil.

4.3. Effect of Lime and Phosphogypsum on the Plasticity and Shrinkage Characteristics

Figure 5 illustrates the variation in the plasticity characteristics and shrinkage limit of dispersive soil treated with 4% lime and varying percentages of phosphogypsum (PG). The liquid limit exhibited a substantial decrease, reducing from 70% to 45.75% for the combination of dispersive soil with 4% lime and 10% PG, representing a 34.6% reduction. This reduction was attributed to the enhanced flocculation and agglomeration of clay particles resulting from the increased calcium ion concentration introduced by both the lime and PG. A comparable decrease in the liquid limit, from 63.76% to 50.96%, was reported by James and Pandian [9] for expansive soil treated with 0.25% PG and 3% lime.

In contrast, the plastic limit increased from 34% to a peak of 45.05% at 4% lime and 4% PG, followed by a slight decline with further PG additions. Similarly, the shrinkage limit surged significantly from 13.6% to a maximum of 22.05% at 4% lime and 4% PG. These results demonstrate that the combined application of lime and phosphogypsum led to notable improvements in the plasticity characteristics and shrinkage limit of dispersive soil, surpassing the performance of soil treated with either lime or PG alone.

4.4. Effect of Lime, Phosphogypsum, and Combination of Phosphogypsum and Lime on Differential Free Swell Index (DFSI) Values

The DFSI of dispersive soil initially decreased with increasing lime content up to 2%, after which it began to rise again. This trend, shown in Figure 6, suggests that lime addition may initially reduce the swelling, but beyond a certain point, an increase in swelling can be observed. Soundara et al. [35] also observed a similar pattern, where lime addition resulted in a reduction in dispersion up to an optimum concentration of 5% due to flocculation and ion exchange reactions. However, at higher concentrations, such as 9%, there was minimal further reduction due to the saturation level of lime, with excess lime primarily contributing to the formation of cementitious compounds, which are time-dependent and do not immediately affect the swelling.

The DFSI was calculated for dispersive soil mixed with varying percentages of phosphogypsum (PG) at 2%, 4%, 6%, 8%, and 10%. A reduction in DFSI was observed from 2% to 8% PG, indicating a decrease in soil swelling with the addition of phosphogypsum. However, beyond 8% PG, a noticeable increase in DFSI was recorded. Phosphogypsum, which contains sulfates, can influence the swelling behavior by promoting the formation of expansive minerals such as ettringite, leading to an increase in swelling beyond a certain threshold.

There was a significant reduction in DFSI with the addition of PG between 2% to 8% and when added with 4% lime, beyond which the DFSI increased. It implies that the reduction in the swelling value was effective in the up to 8% PG in dispersive soil + 4% lime mix. This aligns with the findings of Shivanshki et al. [36], which suggest that while lime stabilization generally reduces swelling, the introduction of sulfates can cause an increase in swelling due to the formation of expansive minerals.

The DFSI values for 4% lime + phosphogypsum and phosphogypsum alone were similar due to the opposing effects of lime stabilization and sulfate-induced swelling from the phosphogypsum. While lime initially reduced the swelling through cation exchange and pozzolanic reactions, the sulfates in phosphogypsum promoted the formation of expansive minerals like ettringite, especially beyond an 8% PG content. This balance between stabilization and expansion resulted in comparable DFSI values.

4.5. Effect of Lime, Phosphogypsum, and Combination of Phosphogypsum and Lime on the Compaction Characteristics

From the compaction curve, the maximum dry density (γd max) and optimum moisture content (OMC) values for dispersive soil were determined, with variations shown in Figure 7 and Figure 8, respectively. The compaction curve for dispersive soil for varying percentages of phosphogypsum with 4% lime is presented in Figure 9. The results indicate that the γd max decreased while the OMC increased with increasing lime content. This behavior is consistent with the findings by Chandra and James [37], who explained that the decrease in the maximum dry density was due to the flocculation of fine soil particles, leading to the formation of a more open and less compact soil structure. The increase in optimum moisture content, on the other hand, was attributed to the additional water required for the hydration process of lime. Furthermore, Herin and Mitchell [38] noted that while lime addition generally increases the OMC, the optimal lime content for stabilization is typically around 4% by weight of soil, as higher amounts produce diminishing returns in moisture requirement and stabilization efficiency.

While the MDD of dispersive soil decreased slightly from 15 kN/m³ at 0% PG to 14 kN/m³ at 10% PG, the optimum moisture content (OMC) increased from 17.15% to 29.2%, corresponding to dispersive soil + 10% PG. This trend was also observed with the addition of lime. The addition of chemical admixtures like PG to soil led to the formation of a flocculated structure, resulting in a higher water retention capacity, thereby decreasing the MDD and increasing the OMC. The behavior observed in this study is consistent with the findings of Outbakat et al. [39] and Maaitah and Banat [17], who found that phosphogypsum promoted the flocculation of soil particles by releasing calcium ions, which led to enhanced aggregation and changes in the soil’s physical properties including reduced MDD and increased OMC.

The MDD decreased from 15 kN/m³ for soil + 4% lime to 13 kN/m³ for soil + 4% lime + 10% PG, with only a marginal reduction observed between 4% and 10% PG. Conversely, the OMC increased from 17.15% to 29.79% for soil + 4% lime + 10% PG, with minimal variation beyond 4% PG (Figure 9). This improvement can be attributed to the synergistic effects of lime-induced pozzolanic reactions and the formation of cementitious compounds like ettringite from sulfate–calcium interactions, which enhance the soil’s strength by creating a denser and more stable matrix. These findings align with James and Pandian [40], who observed similar strength improvements in lime-stabilized soils with the addition of phosphogypsum.

4.6. Unconfined Compressive Strength

The lime and phosphogypsum percentages were varied individually at 2%, 4%, 6%, 8%, and 10%, and combinations of varying phosphogypsum percentages with a fixed 4% lime content were tested. These tests aimed to evaluate the individual and combined effects of lime and phosphogypsum on the unconfined compressive strength (UCS) of dispersive soil. The UCS was assessed at 0- and 7-day curing periods to evaluate the initial strength development of the treated soil. The long-term effects were not investigated in this study due to the focus on early-stage strength gain, which is critical for understanding the initial stabilization mechanisms. Additionally, the long-term strength evolution is influenced by prolonged pozzolanic reactions and environmental factors, requiring extended monitoring beyond the feasibility of this study.

4.6.1. Lime Admixed Dispersive Soil

UCS tests were conducted with increasing lime contents of 2%, 4%, 6%, 8%, and 10% (Figure 10). The peak failure strength of dispersive soil rose with lime addition, reaching a maximum of 129.57 kN/m² at 4% lime compared with 107.33 kN/m² for the untreated soil, after which the strength stabilized. Bell [41] explained that the strength did not increase linearly with the lime content, as excessive lime can reduce the strength due to lime’s lack of inherent friction or cohesion. With 7 days of curing, the dispersive soil-lime mix demonstrated a significant enhancement in strength, with the UCS for 4% lime increasing to 353.12 kN/m², 229% higher than the untreated soil and 172.5% higher than the 0-day cured soil with 4% lime. This behavior aligns with Mitchell and Hooper [42], who noted that the strength gain in lime-treated soils was time-dependent.

4.6.2. Phosphogypsum Admixed Dispersive Soil

The unconfined compressive strength (UCS) values for dispersive soil with varying percentages of phosphogypsum (PG) are presented in Figure 11. At 0 days of curing, the UCS value increased from 107.33 kN/m² to a maximum of 149.66 kN/m² for dispersive soil with 8% PG, showing a 39% increase compared with the untreated soil. However, beyond an 8% PG content, the UCS value began to decrease. A similar trend was observed after 7 days of curing, where the UCS value for soil with 8% PG increased by 74%, but further additions of PG led to a reduction in strength. This behavior was attributed to the sulfate content in phosphogypsum, which reacts with soil particles to form cementitious compounds such as calcium silicate hydrate, calcium aluminate hydrate, and ettringite, creating a spatial network structure and enhancing the strength. When the phosphogypsum content exceeded 8%, the mixture became acidic, leading to the dissolution of ettringite and weakening of the cementitious structure, resulting in a decrease in UCS. These findings align with Zhang et al. [43], who reported that the strength of phosphogypsum-stabilized soil initially increased but decreased when the phosphogypsum content exceeded a critical level.

4.6.3. Lime and Phosphogypsum Admixed Dispersive Soil

The UCS value for soil + 4% lime + 8% phosphogypsum yielded a higher strength for the 0- and 7-day curing periods, with values of 157.46 kN/m² and 450.69 kN/m², respectively, as illustrated in Figure 12. The corresponding improvement was 47% and 320% over the untreated soil. Among all combinations of dispersive soil with chemical admixtures, 4% lime + 8% PG exhibited a higher UCS strength compared with soil + 4% lime (improvement of 21% for 0 days curing and 229% for 7 days curing) and soil + 8% PG (improvement of 39% for 0 days curing and 74% for 7 days curing).

This improvement can be attributed to the synergistic effects of lime-induced pozzolanic reactions and the formation of cementitious compounds like ettringite from sulfate–calcium interactions, which enhance the soil’s strength by creating a denser and more stable matrix. These findings align with James and Pandian [41], who observed similar strength improvements in lime-stabilized soils with the addition of phosphogypsum.

4.6.4. Multilinear Regression Method

A multilinear regression equation was developed to establish the relationship between the dependent variable, unconfined compressive strength (UCS), and the independent variables, namely the lime content (L), phosphogypsum content (PG), maximum dry density (MDD), optimum moisture content (OMC), liquid limit (LL), plastic limit (PL), plasticity index (PI), shrinkage limit (SL), and differential free swell index (DFSI). The results of the regression analysis are presented in

Table 2. Predictive models for UCS with the performance indices.

Model	Equation	R2	Standard Error
I	$\begin{array}{ll}UCS=-591.868& +0.568L+9.456PG+75.109MDD\\ & -10.957OMC+398.566LL-408.411PL\\ & -407.763PI-7.795SL+7.382DFSI\end{array}$	0.96	5.76
II	$\begin{array}{ll}UCS=1206.309& -0.329L-2.173PG-58.109MDD\\ & -3.55OMC-47.647LL+46.861PL\\ & +46.478PI-1.684DFSI\end{array}$	0.73	14.32
III	$\begin{array}{ll}UCS=574.29& +0.977L+3.448PG-10.38OMC+217.31LL\\ & -224.627PL-224.029PI-5.54SL\\ & +3.617DFSI\end{array}$	0.93	7.52

. The regression estimate describes the mathematical relationship between each independent variable and the dependent variable. Three different sets of variable combinations were generated based on the coefficient of correlation. The first set included all of the independent variables. In the second set, the shrinkage limit (SL) was excluded due to its high p-value. The third set excluded the maximum dry density (MDD). It was observed that all variables in Model I were statistically significant, with p-values less than 0.05.

The coefficient of determination (R-squared) represents the proportion of variance in the response variable that can be explained by the predictor variables. An R-squared value of 0.96 indicates that 96% of the variance in UCS can be predicted by the lime content, phosphogypsum content, liquid limit, plastic limit, plasticity index, shrinkage limit, maximum dry density, optimum moisture content, and differential free swell index. The final regression equation is as follows:

$$\begin{array}{ll}UCS=-591.868& +0.568L+9.456PG+75.109MDD-10.957OMC\\ & +398.566LL-408.411PL-407.763PI-7.795SL\\ & +7.382DFSI\end{array}$$

To validate this equation, data from [9,40] were used. The study focused on the effects of lime and phosphogypsum on expansive soil. The UCS value predicted using the regression equation was 250 kN/m², while the measured settlement from the monitoring readings was 300 kN/m². This indicates that the regression equation can predict settlement in similar soil conditions with an acceptable level of variation. The regression model was developed based on the available dataset, which primarily represents the dispersive soil. While the model’s applicability to diverse soil types has not been extensively validated, its robustness can be assessed by incorporating additional datasets in future studies.

4.7. Swelling Characteristics of the Lime and Phosphogypsum Admixed Dispersive Soil

The swell characteristics of dispersive soil were evaluated for the optimum percentages of admixtures such as soil with 4% lime, soil with 8% phosphogypsum, and soil with 4% lime + 8% phosphogypsum (Figure 13 and Figure 14).

The swell potential and swell pressure of the untreated soil were 6.6% and 115 kN/m², respectively. With the addition of 4% lime, 8% phosphogypsum, and their combination (4% lime + 8% phosphogypsum), the swell potential decreased to 2.33%, 4.73%, and 2.2%, showing reductions of 65%, 20%, and 67%, respectively. Similarly, the swell pressure was reduced to 74 kN/m², 95 kN/m², and 72 kN/m², reflecting reductions of 35%, 17%, and 37%, respectively. The combination of lime and phosphogypsum demonstrated superior performance in reducing the swell potential and swell pressure compared with their individual effects. The synergistic interaction between lime and phosphogypsum contributed to this improvement. Lime facilitates pozzolanic reactions, generating calcium silicate hydrates and calcium aluminate hydrates that bind soil particles, while phosphogypsum introduces sulfate ions, promoting the formation of cementitious compounds like ettringite. Microstructural analysis by James and Pandian [9] revealed the formation of a dense, compact mass in the stabilized soil, indicating enhanced stability and reduced swelling potential in a soil with both lime and phosphogypsum.

4.8. Consolidation Characteristics of the Lime and Phosphogypsum Admixed Dispersive Soil

Consolidation tests were conducted on four sets of samples: dispersive soil alone, dispersive soil with 4% lime, dispersive soil with 8% phosphogypsum, and dispersive soil with 4% lime and 8% phosphogypsum. All samples were prepared at their respective liquid limit water contents. The coefficient of consolidation (Cv) was determined from the time–compression curve for the pressure increment of 100–200 kN/m², shown in Figure 15, and the compression index (Cc) values were calculated from the e-log P curves (Figure 16).

The C_v values for dispersive soil with 4% lime, 8% phosphogypsum, and the combination of 4% lime and 8% phosphogypsum were 4.35 × 10⁻⁴ cm²/s, 2.02 × 10⁻⁴ cm²/s, and 3.21 × 10⁻⁴ cm²/s, respectively, compared with 1.17 × 10⁻⁴ cm²/s for the dispersive soil alone, indicating a significant increase in the rate of consolidation with the addition of lime and phosphogypsum. The corresponding Cc values were 0.419 for dispersive soil alone, 0.099 for soil with lime, 0.39 for soil with phosphogypsum, and 0.049 for the combination, showing a reduction of 76%, 6.9%, and 88% in compressibility for the stabilized soils compared with the dispersive soil alone.

5. Conclusions

This study evaluated the potential of phosphogypsum as a sustainable material for stabilizing dispersive soils. The results demonstrated that a combination of 8% phosphogypsum and 4% lime, over a 7-day curing period, enhanced the treated soil’s strength by 320%, identifying it as the optimal dosage for strength improvement. This remarkable improvement was a result of the combined action of pozzolanic reactions initiated by lime and the development of cementitious compounds like ettringite, which arise from interactions between sulfates and calcium. These mechanisms work together to form a more compact and stable soil structure.

In terms of the strength, swell pressure, and swell potential, the phosphogypsum-lime combination outperformed both lime alone and phosphogypsum alone. Specifically, the addition of 4% lime and 8% phosphogypsum reduced the swell pressure of the soil from 115 kN/m² to 72 kN/m² and the swell potential from 6.6% to 2.2%. For the same mix, the compression index decreased by 88%, and the coefficient of consolidation improved by 2.74 times. Although the maximum dry density (MDD) decreased and the optimum moisture content (OMC) increased across all variations of lime, phosphogypsum, and their combinations, the plasticity characteristics consistently improved for the lime-phosphogypsum mixtures. The differential free swell index (DFSI) reduced up to a threshold value for all admixtures but increased beyond that due to the formation of expansive minerals such as ettringite. A multilinear regression analysis was carried out to develop a co-relation between the dependent and independent variables. It was observed that the lime content, phosphogypsum content, maximum dry density, optimum moisture content, plasticity index, shrinkage limit, and differential free swell were significant factors to predict the UCS value of soil. A regression equation was proposed to determine the UCS value of soil admixed with lime and phosphogypsum, which was validated with the observations from [9,37].

The findings indicate that phosphogypsum, when used in combination with lime, is a superior additive for improving the strength and reducing swelling in dispersive soils. While the study highlights phosphogypsums’ potential as a soil stabilizer, further investigations focusing on the long-term durability of treated soils under varying environmental conditions, such as wet–dry and freeze–thaw cycles can be carried out to validate its applicability in field-scale implementations.