The experimental soil, a type of lean clay predominantly consisting of montmorillonite and other minerals, has its physical and chemical properties detailed in Table 1. For this study, the calcium-based stabilizer, denoted as B2, is a composite mixture of Portland cement (PC), lime (L), and fly ash (FA) with a mass ratio of 4:2:1(PC:L:FA), and the chemical compositions of these three components are illustrated in Table 2. The sodium carbonate ( Na 2 CO 3 ) and sodium silicate ( Na 2 SiO 3 · 9 H 2 O ) used in the experiments are all analytical pure chemical reagents produced by Shanghai Hushi Laboratory Equipment Co., Ltd (Shanghai, China).

The experimental procedures primarily consisted of compaction testing, specimen preparation and curing, and unconfined compression testing, conducted in accordance with the Chinese Standard JTG 3441-2024. Initially, the B2 stabilizer and dried soil were thoroughly mixed in a mass ratio of 4:2:1:100 (PC:L:FA:dry soil), yielding a base mixture. Then the maximum dry density and optimum moisture content of the base mixture were tested to be 1.79 g/cm³ and 15%, respectively, by the modified Proctor compaction test. Subsequently, 0.05% sodium carbonate and 0.05% sodium silicate (calculated relative to the dry soil weight and added in an aqueous solution manner) were then incorporated into part of the base mixture to form a testing mixture. The mixtures with and without the two sodium salts were then statically compacted into cylindrical specimens, each measuring 50 mm in height and 50 mm in diameter, at their optimum moisture content using a 30 kN hydraulic pressing machine. Then, the compacted specimens were transferred to a curing room maintained at a temperature of 20 °C ± 1 °C and a relative humidity of 95% ± 5%. After a 7-day curing period, unconfined compression tests were conducted using a 30 kN hydraulic pressing machine at a displacement rate of 1 mm/min.

After the compression tests, samples extracted from the tested specimens were subjected to SEM scanning. An FEI Quanta 650 FEG Environmental SEM (ESEM) was employed for the scanning process, operating within an acceleration voltage range of 200V to 30 kV and with a maximum beam current of 200 nA.

CP2K (Kühne et al., 2020) was employed to carry out the theoretical calculations in the framework of density functional theory (DFT). CP2K employed two representations of the electron density: localized Gaussian and plane wave basis sets. For the Gaussian-based (localized) expansion of the Kohn–Sham orbitals, we used a library of contracted molecularly optimized valence double-zeta plus polarization basis sets (VandeVondele and Hutter, 2007), and the complementary plane wave basis set had a cutoff of 400 Rydberg for the electron density. The generalized gradient corrected approximation of Perdew, Burke and Ernzerhof (PBE) (Blöchl, 1994) was adopted to relax the geometric structures. The energy and force convergence criteria of the self-consistent iteration were set to 10–5 eV and 0.03 eV Å-1. The ions are calculated in a 15 Å × 15 Å × 15 Å cell. Since montmorillonite has layered structure, no additional vacuum layer was set, which is consistent with previously reported montmorillonite calculations (Li et al., 2023; Peng et al., 2016). During calculation, all atoms remain relaxed.

The adsorption energies were used to assess the adsorption capacity of the montmorillonite models for molecules and ions. The adsorption energy is defined by Formula 3, where ΔE represents the adsorption energy, while E (surf), E (ion), and E (ion/surf) denote the total energies of the surface, the free ion, and the surface with the ion, respectively. The more negative the adsorption energy in value, the greater the exothermic heat released, and the more stable the system becomes. Δ E = E ion / surf   –   E surf   –   E ion (3)

Montmorillonite (PDF#13-0135), with the chemical formula CaAl₄Si₈O₂₄, belongs to the hexagonal crystal system. Figure 1 displays the top and side views of the montmorillonite model. The unit cell parameters are as follows: a = 5.169 Å, b = 5.169 Å, c = 15.02 Å, with angles α = 90.0°, β = 90.0°, and γ = 90.0°. In its structure, Ca²⁺ cations act as exchangeable ions located between the layers, while Al³⁺ cations reside in the bulk phase. The Si⁴⁺ cations are tetrahedrally coordinated within the SiO₄ units, and the O^2- anions are 2-coordinated in the OSi₂ environment and 3-coordinated in the OSiAl₂ environment.

The 7-day unconfined compressive strength of the base mixture was determined to be 1.182 MPa. After introducing 0.05% sodium carbonate and 0.05% sodium silicate, the 7-day unconfined compressive strength of the testing mixture escalated to 1.620 MPa, signifying a 34.5% enhancement in strength (Yin et al., 2025).

Figure 2 shows the SEM images of soil samples before and after the addition of Na₂CO₃ and Na₂SiO₃. In the SEM images of the B2 stabilizer-soil mixture, prominent pores can be observed, along with only a small amount of fibrous or reticular cementitious substances and acicular crystals on the particle surfaces (Cao et al., 2022; Wu et al., 2018). After adding Na₂CO₃ and Na₂SiO₃, the pores are filled with fibrous or reticular cementitious substances and acicular crystals, and similar deposits are observed coating the particle surfaces. This suggests that the addition of Na₂CO₃ and Na₂SiO₃ promotes the formation of cementitious and crystalline substances which are deduced to be C-S-H and calcium carbonate according to chemical reaction Equations 1, 2. These newly formed substances effectively modify the surface characteristics of the soil particles, fill interparticle voids, and enhance interparticle bonding. As a result, the strength of the stabilizer-soil mixtures increase from 1.182 MPa to 1.620 MPa, which aligns well with findings reported in previous studies (Abdullah et al., 2021; Chung et al., 2021; Dengliang and Aimin, 1988; Murmu et al., 2020; Phummiphan et al., 2016; Rivera et al., 2020; Teerawattanasuk and Voottipruex, 2019; Yin et al., 2025).

However, the existing techniques are difficult to characterize the microscopic processes and mechanisms of nucleation and crystallization of Na₂CO₃ and Na₂SiO₃ in the pores and on the surface of montmorillonite. Therefore, subsequently, the DFT method was adopted to study their nucleation and crystallization mechanisms as well as physicochemical properties.

Montmorillonite contains both exchangeable layers and surfaces. Accordingly, the adsorption behaviors of Ca²⁺, Na⁺, CO₃ ^2-, and SiO₃ ^2- in these two distinct scenarios were investigated.

Figure 11 shows the differential charge density plots of Ca²⁺, Na⁺, CO₃ ^2- and SiO₃ ^2- on the on the montmorillonite surface.

It can be observed that there are significant changes in charge densities near the Ca²⁺ atoms and the surface O atoms of montmorillonite. Ca²⁺ atoms tend to lose electrons, characterized by a decrease in electron-cloud density (blue regions) around them. In contrast, the electron - cloud density around the surface O atoms that bond with Ca²⁺ increases (yellow regions). This indicates that during the adsorption of Ca²⁺, electrons are transferred from Ca²⁺ atoms to the surface atoms, forming ionic or polar covalent bonds. Such charge transfer enhances the interaction between Ca²⁺ and the montmorillonite surface. During the adsorption of Na⁺, the charge transfer is less intense compared to that of Ca²⁺. Therefore, in the figure, charge accumulation is only shown between the Na-O bonds.

When CO₃ ^2- is adsorbed on the surface, there are notable changes in charge densities in the bonding regions between CO₃ ^2- and the Ca²⁺ and Si atoms on the montmorillonite surface. There is an overlap and redistribution of electron clouds between the O atoms in CO₃ ^2- and the Ca²⁺ and Si atoms. The increase in electron-cloud density around the O atoms indicates the inflow of electrons, leading to the formation of chemical bonds.

When SiO₃ ^2- is adsorbed on the surface, significant changes in electron-cloud densities occur at the bonding sites between the O atoms of SiO₃ ^2- and the Ca²⁺ and Si atoms on the montmorillonite surface. The electron-cloud enrichment around the O atoms (yellow regions) indicates that electrons are transferred from the surface atoms to the O atoms, forming stable chemical bonds.

Table 3 shows the charge transfer between Ca²⁺, Na⁺, CO₃ ^2- and SiO₃ ^2- with the montmorillonite surface. Ca²⁺ and Na⁺ exhibit significantly stronger charge transfer with surface atoms than with interlayer Ca. Notably, the charge transfer between Na⁺ and interlayer Ca²⁺ is extremely weak, with a magnitude of only 0.03|e|. The charge transfer trends highlight that Ca²⁺ and Na⁺ primarily interact with montmorillonite surfaces through cationic charge donation, with Ca²⁺ exhibiting stronger binding due to higher charge transfer. In contrast, both CO₃ ^2- and SiO₃ ^2- demonstrate substantial charge transfer with both surface and interlayer Ca²⁺ atoms. CO₃ ^2- and SiO₃ ^2- form stable associations with both surface and interlayer Ca²⁺ via electron acceptance, consistent with the structural insights from differential charge density plots.

The alkaline treatment process of montmorillonite has also been examined as shown in Figures 12, 13. The OH group adsorbs onto the Ca²⁺ atom in the layer, forming a Ca-O bond with a bond length of 194 pm. Additionally, the OH group forms a hydrogen bond with the surface, with a bond length of 251 pm, indicating the formation of a moderately strong hydrogen bond. The adsorption energy of the OH group is −6.5 eV, which is close to the −6.8 eV of CO₃ ^2-, but weaker than the −8.7 eV of SiO₃ ^2-.

Upon comparing the adsorption behaviors of hydroxide ions, carbonate ions, and silicate ions on the montmorillonite surface, it is observed that hydroxide ions primarily adsorb by forming hydrogen bonds with the surface, while carbonate and silicate ions adsorb via oxygen-silicon bonds. Since the bond energy and stability of hydrogen bonds are weaker than those of oxygen-silicon bonds, this is one of the reasons why the strength of lime-treated soils is often lower than that of soils stabilized with lime combined with sodium silicate or sodium carbonate.

Furthermore, the hydrophilicity of OH-absorbed montmorillonite was calculated, revealing that its H₂O adsorption energy is −1.3 eV. This value is weaker than the −2.6 eV of molecular adsorption (Figure 7b) and the −3.1 eV of dissociative adsorption (Figure 7c), indicating that after the absorption of OH, the water affinity of montmorillonite decreases.

The formation of a moderately strong hydrogen bond and the reduction in water affinity help explain why lime treatment can enhance the strength and water stability of soils.

The structures of CO₂ on the Ca-montmorillonite and CaCO₃-montmorillonite surface are shown in Figure 14. The adsorption energy of CO₂ on the Ca-montmorillonite surface is calculated to be −0.2 eV. When CaCO₃ forms on the montmorillonite surface, the adsorption energy of CO₂ increases to −0.5 eV. These theoretical calculations suggest that the adsorption of CO₂ by Ca-montmorillonite is thermodynamically favorable and is further enhanced by the nucleation of surface CaCO₃. This is consistent with the findings of Song et al. (2024), who reported that increased carbonate content promotes CO₂ storage.

In addition, Liu et al. (2025) reported that increased water content promotes CO₂ adsorption. Under CO₂-rich water conditions in deep underground environments, carbonate minerals can dissolve and recrystallize (Song et al., 2024), potentially affecting the stability of stabilized montmorillonite. This study focuses on improving the stability of stabilized montmorillonite near the Earth’s surface, where both pressure and temperature are relatively low. Although the adsorption energy for CO₂ increases after nucleation, in practical engineering applications, the stabilizer-soil mixture is typically compacted at optimum water content, and the reaction products fill the pore spaces, increasing hydrophobicity. This significantly reduces water permeability of the stabilized soils, making it difficult to establish a CO₂-rich water environment, thereby minimizing the risk of compromising stability and integrity.

The schematic diagram illustrating the mechanisms of nucleation, stabilization, and hydrophilicity is shown in Figure 15. When CO₃ ^2- or SiO₃ ^2- ions are present in the Ca-montmorillonite system, they preferentially nucleate and form precipitates on the surface of montmorillonite rather than adsorb onto the interlayer calcium ions. This is because, compared to adsorption on interlayer calcium ions (Figures 3c,d), the adsorption energy is lower when the calcium ions are adsorbed and nucleation occurs on the montmorillonite surface (Figures 5c,d). The lower the adsorption energy, the more stable the system becomes. Therefore, it can be speculated that, when free calcium ions, CO₃ ^2- ions, and SiO₃ ^2- ions coexist in the calcium-based stabilized soil system, these ions tend to form a spatial network structure of calcium carbonate and calcium silicate on the montmorillonite surface and within the pores through the sharing of calcium ions. This process enhances the overall integrity of montmorillonite, thereby improving its shear strength. This hypothesis aligns with the results observed in the SEM images (Figure 2).

Before stabilization, except for physical absorption (Figure 7a), the adsorption energies of water molecules in the interlayers of montmorillonite are relatively negative, and they are prone to adsorb through molecular absroption (Figure 7b) and dissociative adsorption (Figure 7c). This explains the strong hydrophilicity of montmorillonite, volume expansion after water absorption, and reduced macroscopic engineering properties. After stabilization, Na⁺ has almost minor effect on the hydrophilicity of montmorillonite, while Ca²⁺, CO₃ ^2- or SiO₃ ^2- significantly reduce its hydrophilicity. This can explain that calcium-based stabilizer alone, or in combination with Na₂CO₃ and Na₂SiO₃ can ruduce the affinity of montmorillonite for water.

By comparing the water adsorption energy of Ca-montmorillonite (Figure 5a) and Na-montmorillonite (Figure 5b), the calcium ions released by calcium-based stabilizer will exchange with Na⁺ and other ions through ion exchange, thus reducing the thickness of the water film. However, by comparing the reduction in water adsorption energy between montmorillonite adsorbed with calcium ions (Figure 9a) and montmorillonite adsorbed with calcium carbonate (Figure 9c) and calcium silicate (Figure 9d), it is evident that the improvement in water stability due to ion exchange is weaker than the improvement by the formation of precipitates.

The results above demonstrate that DFT calculations can effectively and quantitatively elucidate the interaction mechanisms between stabilizers and montmorillonite from the perspective of adsorption energy and electron transfer. This method can transform the selection of stabilizer components from a trial-and-error approach into a more targeted process based on the understanding of the interactions between clay minerals and candidates, reducing time-consuming, labor-intensive macro-mechanical tests and saving experimental costs. The DFT method is expected to not only enhance material screening for soil stabilization but also have broader applications in areas such as carbon sequestration, landfills, and beyond.