Enhancing Frost Heave Resistance of Channel Sediment Hetao Irrigation District via Octadecyltrichlorosilane Modification and a Hydro-Thermo-Mechanical Coupled Model

Abstract

To address frost heave in winter-lined canals and sediment accumulation in the Hetao Irrigation District of Inner Mongolia Autonomous Region, while reducing long-term maintenance costs of canal linings and relocating sediment as solid waste, this study proposes the use of low-toxicity, environmentally friendly octadecyltrichlorosilane (OTS) to modify channel sediment. This approach aims to improve the frost heave resistance of canal sediment and investigate optimal modification conditions and their impact on frost heave phenomena, aligning with sustainable development goals of low energy consumption and economic efficiency. Water Droplet Penetration Time (WDPT) tests and unidirectional freezing experiments were conducted to analyze frost heave magnitude, temperature distribution, and moisture variation in modified sediment. A coupled thermal–hydraulic–mechanical (THM) model established using COMSOL Multiphysics 6.2 software was employed for numerical simulations. Experimental results demonstrate that the hydrophobicity of channel sediment increases with higher OTS concentrations. The optimal modification effect is achieved at 50 °C with a silane-to-sediment mass ratio of 0.001, aligning with the economic efficiency of sustainable development. The unidirectional freezing test results indicate that compared to the 0% modified sediment content, the 40% modified sediment proportion reduces frost heave magnitude by 71.3% and decreases water accumulation at the freezing front by 21.1%. The comparison between numerical simulation results and experimental data demonstrates that the model can accurately simulate the frost heave behavior of modified sediment, with the error margin maintained within 15%. In conclusion, OTS-modified channel sediment demonstrates significant advantages in enhancing frost heave resistance while aligning with the economic and environmental sustainability requirements. Furthermore, the coupled thermal–hydraulic–mechanical (THM) model provides a reliable tool to guide sustainable infrastructure development for hydraulic engineering in the cold and arid regions of Inner Mongolia, effectively reducing long-term maintenance energy consumption.

1. Introduction

The Hetao Region, located in the middle reaches of the Yellow River, boasts abundant water resources and modern water conservancy facilities that support extensive agricultural irrigation [1,2] and serves as a significant agricultural base in Inner Mongolia. The Hetao Irrigation District, located in a cold-arid region, is frequently subjected to extreme low temperatures. As a result, the lined canals experience frost heave in the foundation soil, often leading to channel uplift and cracking. Frost heave not only significantly compromises the structural stability of the lined canals but also markedly reduces their service life, thereby increasing maintenance costs [3,4].

In cold regions, frost heave and thaw settlement are common phenomena during soil freeze–thaw cycles. When soil is exposed to low-temperature conditions, the moisture within the soil freezes and expands, thereby forming frost heave [5]. Thaw settlement, on the other hand, occurs as temperatures rise and the ice within the soil begins to melt, leading to surface subsidence [6,7]. Inner Mongolia experiences significant diurnal temperature fluctuations, and hydraulic engineering structures are particularly susceptible to freeze–thaw cycle damage under extreme cold climate conditions. This damage can result in structural deformation, functional deterioration, and even severe structural failure. Moreover, the unique characteristics of frozen soil cause volume expansion during the freezing process, forming ice lenses that generate frost heaving forces [8]. If the development of frost heave in frozen soil is constrained by engineering structures, these accumulated frost heaving forces may exert uplifting damage to the overlying infrastructure.

In China, common domestic solutions to frost heave problems primarily involve physical and chemical improvement methods. Physical improvement techniques include the replacement method and thermal insulation layer installation. The replacement method involves substituting frost-susceptible soils with non-frost-susceptible materials such as gravel or crushed stone. This approach significantly reduces frost heave but incurs high costs and cannot fully prevent deep-seated frost heave [9]. It has been validated in the transition sections of road-bridge structures in the permafrost regions of the Qinghai-Tibet Railway. Thermal insulation layers, such as expanded polystyrene (EPS) boards [10], can reduce frost penetration depth. However, due to their low compressive strength, EPS boards may deform under long-term use, as observed in the channel renovation of the Nanchuan Irrigation District in Linxia City. Additionally, their non-biodegradable nature poses environmental pollution risks. Chemical stabilization methods include salt admixtures and polymer stabilizers. Salt admixtures mitigate frost heave by lowering the freezing point, but leaching of salts can contaminate groundwater, and their effectiveness diminishes after repeated freeze–thaw cycles, as observed in frost-susceptible soils in dry farmland of Nong’an County, Jilin Province [11]. Studies on polymer stabilizers for mitigating frost heave in red clay in Southwest China reveal that these agents reduce frost heave forces by binding soil particles [12]. While effective, their high cost and susceptibility to failure in low-temperature environments limit their application.

Compared to domestic approaches, international solutions for frost heave mitigation often incorporate thermodynamic control methods and electro-thermal technologies. Thermodynamic control methods, such as heat pipe technology, utilize the cyclic heat transfer of working fluids like ammonia or propane to extract geothermal energy [13]. This technique has been implemented in regions like Alaska but faces efficiency decline in extreme cold environments and high maintenance costs. Electro-thermal approaches involve embedding carbon fiber heating cables [14], which demonstrate short-term effectiveness but suffer from poor economic viability due to continuous power requirements. Additionally, microbial-induced calcification techniques reduce frost heave through calcium carbonate precipitation (ICP) that fills soil pores [15]. However, microbial activity is inhibited at low temperatures, and the slow lithification cycles hinder practical large-scale engineering applications.

In the Hetao Irrigation District, traditional soil replacement techniques commonly employ low frost-susceptible materials such as gravel and crushed stone, aiming to mitigate frost heave by substituting native soils [16]. However, these conventional methods often yield suboptimal results due to limitations imposed by the permeability and moisture content of the replacement materials. Traditional replacement methods only address shallow foundations, while the Hetao region experiences severe deep-seated frost heave. Replacement layers cannot fully prevent frost heave due to insufficient isolation [17]. The Hetao Irrigation District’s canals have high sediment content, and fine sand and clay deposited at the channel base may infiltrate the replacement layer, altering its gradation and reducing frost heave resistance [18]. Additionally, conventional replacement methods require significant water usage, which conflicts with the Hetao Irrigation District’s status as a priority area for Inner Mongolia’s “water-saving initiatives” under strained water resource allocation [19]. To address these challenges, this study innovatively explores a chemical modification approach, particularly focusing on enhancing the hydrophobicity of channel sediments to improve their frost heave resistance. Octadecyltrichlorosilane (OTS), with the chemical formula C₁₈H₃₇SiCl₃, is an organosilicon compound commonly used as a surface modifier, lubricant, and adhesive. It typically exists in liquid form and features a structure where a silicon atom is bonded to three chlorine atoms and an octadecyl group. As a superhydrophobic material, OTS has demonstrated promising applications in various fields, such as enhancing water repellency of fabrics [20] and modifying fibrous membranes [21]. This study innovatively applies OTS to chemically modify channel sediment, thereby enhancing its hydrophobicity. This hydrophobic property effectively reduces moisture content at the freezing front, thus suppressing frost heave in channel sediment. Furthermore, the research investigates the optimal modification parameters of OTS for channel sediment and evaluates the frost heave resistance of the modified sediment.

To validate the frost heave resistance of modified sediments, this study establishes a hydro–thermal–mechanical (HTM) coupled model using COMSOL Multiphysics 6.2 software to numerically simulate the frost heave process. The model incorporates the heat transfer equation with phase change latent heat, combined with the Van Genuchten water retention model and the Gardner permeability model, to describe the coupled transport processes of soil moisture and heat.

The application of environmentally friendly OTS to modify channel sediment can effectively alleviate frost heave in lined channels and address sediment accumulation issues. This approach significantly reduces long-term maintenance costs for lined channels and minimizes the relocation of sediment as solid waste, aligning with the principles of sustainable development through low energy consumption, economic viability, and environmental compatibility.

2. Material and Methods

2.1. Material Preparation

2.1.1. Material Physical Properties

(1) The channel sediment samples were collected from the Hetao Irrigation District in Bayannur City. According to the GB/T 50123-2019 Standard for Geotechnical Testing Methods [22], their particle size distribution ranges are shown in Figure 1.

(2) The limit moisture content test (Atterberg limits) determines the liquid and plastic limits of soil, which are used to classify soil types, calculate natural consistency, and derive the plasticity index. According to the GB/T 50123-2019 Standard for Geotechnical Testing Methods [22], cone penetration depth and moisture content data were obtained using a combined liquid–plastic limit apparatus, as shown in

Table 1. Cone penetration and moisture content data.

Number	Moisture Content/%	Cone Penetration Depth/mm
A	16.4	2.5
B	19.8	9
C	22.3	17.5

.

The relationship curve between moisture content (as the x-axis) and cone penetration depth (as the y-axis) for points A, B, and C was plotted on a double logarithmic coordinate system (Figure 2). The results showed that the liquid limit of the channel sediment was 19.63%, and the plastic limit was 16.44%. Using Equation (1), the plasticity index of the channel sediment was calculated to be 3.19, which is less than 5. Therefore, the channel sediment is classified as non-plastic soil.

$$I_p=w_L-w_p$$

(1)

where $I_p$: plasticity index; $w_L$: liquid limit water content; $w_p$: plastic limit water content.

(3) OTS was purchased from Runyou Chemical (Shenzhen, China) Co., Ltd., with a purity of 95%, containing 5–10% branched isomers.

2.1.2. Preparation of Modified Channel Sediment

To ensure sufficient reaction between OTS and channel sediment and to investigate the optimal modification parameters of OTS, the channel sediment was first air-dried at room temperature. Subsequently, OTS solutions were prepared based on different mass concentrations of silane to channel sediment. After thorough mixing of OTS and channel sediment using a micropipette, the containers were sealed and placed in a drying oven at a preset temperature for 24 h of reaction time [23]. The experimental group configurations are as follows:

Experimental Parameter Design

• Temperature Gradient

30 °C, 40 °C, 50 °C, 60 °C (four temperature levels)

2.

Silane-to-Channel Sediment Mass Ratio

Low-concentration Zone: 0.0002%, 0.0004%, 0.0006%, 0.0008%, 0.001% (with a stepwise increment of 0.0002% per level)

High-concentration Zone: 0.002%, 0.003%, 0.004%, 0.005% (with a stepwise increment of 0.001% per level)

Total Concentration Gradient: Each temperature group comprises 9 mass ratios (5 in the low-concentration zone and 4 in the high-concentration zone).

3.

Experimental Group Designation

Experimental Groups S1–S36: Arranged in ascending order of temperature (30 °C → 60 °C) and concentration (low → high).

(The specific groups are listed in

Table 2. Design parameters of experimental groups.

Temperature (°C)	Mass Ratio of Silane to Sediment (%)	Experimental Group Number
30	Low-concentration Zone: 0.0002%, 0.0004%, 0.0006%, 0.0008%, 0.001%	S1–S5
30	High-concentration Zone: 0.002%, 0.003%, 0.004%, 0.005%	S6–S9
40	Low-concentration Zone: 0.0002%, 0.0004%, 0.0006%, 0.0008%, 0.001%	S10–S14
40	High-concentration Zone: 0.002%, 0.003%, 0.004%, 0.005%	S15–S18
50	Low-concentration Zone: 0.0002%, 0.0004%, 0.0006%, 0.0008%, 0.001%	S19–S23
50	High-concentration Zone: 0.002%, 0.003%, 0.004%, 0.005%	S24–S27
60	Low-concentration Zone: 0.0002%, 0.0004%, 0.0006%, 0.0008%, 0.001%	S28–S32
60	High-concentration Zone: 0.002%, 0.003%, 0.004%, 0.005%	S33–S36

)

2.1.3. Basic Physical Properties of Modified Channel Sediment

The channel sediment under optimal modification conditions was mixed with unmodified channel sediment at 0%, 10%, 20%, 30%, and 40% mixing proportions. Subsequently, samples were prepared under a moisture content of 18% [24,25], and their thermal conductivity and specific heat capacity were measured. The thermal diffusivity was calculated accordingly, with specific values detailed in

Table 3. Thermophysical properties for modified sediment with varying contents.

	0% Modified Sediment Mixing Proportion	10% Modified Sediment Mixing Proportion	20% Modified Sediment Mixing Proportion	30% Modified Sediment Mixing Proportion	40% Modified Sediment Mixing Proportion
specific heat capacity KJ/(kg·K) $\mathrm{c}$	0.86	0.83	0.81	0.78	0.76
thermal conductivity W/(m·K) $\lambda$	1.48	1.45	1.42	1.39	1.36
Density (kg/m3) $\rho$	2006	2006	2006	2006	2006
Thermal Diffusivity (W·m2)/KJ $\alpha$	8.58 × 10−5	8.71 × 10−5	8.74 × 10−5	8.88 × 10−5	8.92 × 10−5

.

(1) The specific heat capacity was calculated via the calorimetric method [26]. First, the sample was heated to a known high temperature. Then, the hot sample was immersed into a known mass of low-temperature water with a known initial temperature, and the equilibrium temperature of the mixture was recorded. Finally, the specific heat capacity of the sample was determined using Equation (1)

$$m_x\cdot c_x\cdot \left(T_1-T_2\right)=m_w\cdot c_w\cdot \left(T_2-T_0\right)$$

(2)

where $c_x$: specific heat capacity of the sample; $c_w$: specific heat capacity of water; $m_x$: mass of the sample; $m_w$: mass of water; $T_0$: initial water temperature; $T_1$: preset temperature; $T_2$: Equilibrium temperature.

(2) The thermal conductivity was calculated via the heating probe method [27,28]. First, the sample was uniformly filled into a container to avoid air voids. Then, a heating probe was inserted into the sample, powered on to apply heat, and the heating rate was recorded. Finally, the thermal conductivity of the sample was calculated using Equation (2).

$$\lambda ={\displaystyle \frac{P}{4\pi r}}\cdot {\displaystyle \frac{1}{\Delta T/t}}$$

(3)

where $\mathit{P}$: heating power; $r$: probe radius; $\Delta T$: temperature rise; t: heating time; $\lambda$: thermal conductivity of the sample.

(3) The thermal diffusivity $\alpha$ [29] was calculated using the thermal diffusivity calculation Formula (3).

$$\alpha ={\displaystyle \frac{\lambda }{\rho \cdot c}}$$

(4)

$\rho$: Density of samples prepared under a moisture content of 18% with modified channel sediment at different mixing proportions. Since the density of modified channel sediment is nearly identical to that of unmodified channel sediment, this parameter ($\rho$) is excluded from further analysis; $c$ specific heat capacity and $\lambda$ thermal conductivity of modified channel sediment at different mixing proportions, with values detailed in Table 3.

2.2. Experimental Methods

2.2.1. Water Drop Penetration Time Test (WDPT)

The hydrophobic stability or durability of modified channel sediment was evaluated using the Water Drop Penetration Time Test (WDPT) [30]. The WDPT measures the penetration time of an 80 μL water drop into the channel sediment. According to the rating scale system, the water repellency of channel sediment is classified into multiple grades, ranging from wettable (Grade 0, penetration time < 5 s) to extreme water repellency (Grade 10, penetration time > 5 h). For water drops remaining on the surface of channel sediment for 5 h or longer, the test is terminated to prevent evaporation effects from influencing the results.

2.2.2. Unidirectional Freezing Test [31]

In this experimental process, a thin layer of Vaseline was first applied to the inner walls of the sample box to prevent adhesion between the sample and the box walls. A filter paper was placed at the bottom, and another filter paper was placed on the top surface to ensure tight contact between the sample and the top plate. Subsequently, a 700 g soil–sand mixture was prepared according to the mixing proportions of modified channel sediment (0%, 10%, 20%, 30%, and 40%). An appropriate amount of water was added, and the mixture was thoroughly stirred. The mixture was then poured into a sample cylinder with an inner diameter of 100 mm and a height of 100 mm. Using a compaction hammer to apply pressure, the soil sample was consolidated to the target moisture content of 18%.

After the soil sample preparation was completed, the corresponding pipelines and connectors were connected, and the sample cylinder was placed into a constant-temperature chamber. Temperature sensors were installed on both sides of the sample cylinder and connected to a multi-channel temperature-deformation data logger to enable real-time monitoring of temperature changes. Meanwhile, the inlet and outlet pipelines of the sample cylinder were connected to a circulating water bath, and an insulation board was wrapped around the exterior of the sample cylinder to ensure the stability of the experimental environment. Additionally, the displacement-deformation sensor was calibrated to facilitate subsequent data acquisition.

At the beginning of the experiment, the temperature of the constant-temperature chamber was set to 5 °C, and the top cooling bath was adjusted to −15 °C according to experimental requirements. This condition was maintained for 6 h to ensure the sample reached thermal equilibrium. After the initial temperature stabilized at 5 °C, the top cooling bath temperature was rapidly lowered to −15 °C and held for 0.5 h to induce rapid freezing of the sample. Throughout the entire experiment, temperature and deformation data were recorded hourly to provide foundational information for subsequent analysis.

After the freezing test was completed, all valves and power sources were shut off, and the data were exported. The pipelines and electrical wires were disassembled, and the soil sample cylinder was removed. Subsequently, the fixing device of the sample cylinder was dismantled, and the soil sample was cut into layers at 1 cm intervals. The layers were separately placed into 10 aluminum sample boxes and weighed to obtain their initial masses. Finally, the samples were dried in a 105 °C oven for 48 h until reaching a constant weight, cooled, and reweighed to determine the dry soil mass. The moisture content distribution across different soil layers was then measured. The entire experimental process was successfully completed.

2.3. Model Development

To numerically simulate the frost heave process, this study established a thermal–hydro–mechanical coupled model using COMSOL Multiphysics software. The governing equation for the temperature field was derived based on Fourier’s law of heat conduction, incorporating the latent heat of phase change. The moisture field governing equation was formulated using a modified Richards equation that included a water-ice phase change term. The stress field governing equation was developed by accounting for volumetric expansion effects during phase change. Fundamental assumptions were defined, calibrated parameters were applied, and boundary conditions were set to construct a two-dimensional axisymmetric cylindrical model. After validating grid independence to ensure accuracy, simulations of frost heave behavior in modified sediment were conducted. The simulated frost heave displacement, temperature distribution, and moisture content were compared with experimental data to validate the model.

3. Results

3.1. Optimal Parameters for OTS-Modified Channel Sediment

Figure 3 is the hydrophobic classification chart based on the Water Drop Penetration Time Test (WDPT).

Figure 3 clearly demonstrates that, within the low-concentration range (0.0002%, 0.0004%, 0.0006%, 0.0008%, and 0.001%), the hydrophobicity of the channel sediment increases progressively with rising silane concentration across all temperature groups, peaking at 0.001%. In the high-concentration range (0.002%, 0.003%, and 0.004%), further increases in silane concentration do not result in significant changes in hydrophobicity for any temperature group. Notably, in the 30 °C, 40 °C, and 60 °C test groups, a final enhancement in hydrophobicity occurred when the mass ratio of silane to channel sediment was elevated from 0.004% to 0.005%, achieving the maximum rating value. In the experimental group at 50 °C, the maximum hydrophobicity was achieved when the silane-to-sediment mass percentage was 0.001%. Further increases in OTS concentration did not significantly enhance hydrophobicity, indicating a boundary effect in the modification efficiency of OTS on channel sediment [32]. This occurs because higher OTS concentrations facilitate the formation of a denser polysiloxane network structure, thereby improving hydrophobic performance [33]. However, as the silane concentration continues to rise, a compact hydrophobic layer has already formed on the sediment surface, leaving insufficient space for further polysiloxane network development. Consequently, the modification effect becomes limited [34].

Furthermore, as the temperature increased gradually from 30 °C, the modification effect of OTS on channel sediment progressively improved, reaching its maximum at 50 °C. However, further temperature elevation significantly reduced the modification efficiency. This is primarily because higher temperatures promoted more complete hydrolysis of OTS, leading to the formation of a denser polysiloxane network and a more compact hydrophobic layer. Nevertheless, excessively high temperatures may damage the polysiloxane network structure, causing the hydrophobic layer to degrade under thermal stress [35]. Notably, in the 30 °C, 40 °C, and 60 °C test groups, the hydrophobicity of the channel sediment underwent the final enhancement when the mass ratio of silane to sediment increased from 0.004% to 0.005%. This is because lower- or higher-temperature groups failed to form a dense hydrophobic layer on the sediment surface at lower silane concentrations due to the aforementioned reasons. However, with further silane concentration elevation, the hydrophobic layer on the sediment surface achieved its maximum development [36]. Therefore, 50 °C is considered the optimal temperature for OTS modification of channel sediment.

Through the Water Drop Penetration Time Test (WDPT), it was confirmed that the optimal modification efficiency of OTS on channel sediment occurred at 50 °C with a silane-to-sediment mass percentage of 0.001%, demonstrating strong cost-effectiveness. Therefore, in subsequent unidirectional freezing tests, the selected modification parameters were a temperature of 50 °C and a silane-to-sediment mass percentage of 0.001%.

3.2. Various Frost Heave Parameters in the Unidirectional Freezing Test

3.2.1. Temperature Profiles Across Depths

Under water-supply conditions, the moisture content of the soil–sand mixture was controlled at 18%, with the cold-end boundary temperature maintained at −15 °C and the hot-end boundary temperature at 5 °C. Unidirectional freezing tests were conducted on soil–sand mixtures with modified sediment mixing proportions of 0%, 10%, 20%, 30%, and 40%, resulting in the following temperature–time variation characteristic curves for different modified sediment proportions (Figure 4).

According to Table 3, as the mixing proportion of modified sediment increased, both the thermal conductivity and specific heat capacity of the soil–sand mixture exhibited a decreasing trend. Therefore, the thermal diffusivity was introduced to characterize the diffusion capability of the temperature field within the soil-sand mixture.

Through the calculation of thermal diffusivity, it was observed that the thermal diffusivity of the soil–sand mixture gradually increases as the mixing proportion of modified sediment rises. By analyzing the cooling times for the five different modified sediment proportions shown in Figure 4, the cooling time for the 0% modified sediment case was approximately 42.2 h, 10% at 38.1 h, 20% at 33.2 h, 30% at 29.5 h, and 40% at 24.2 h. As thermal diffusivity increases, the required freezing time decreases progressively [37], indicating that the modified sediment stabilizes more rapidly. This reduces the duration of moisture migration and ultimately lowers the total amount of migrated water, thereby suppressing ice crystal growth [38,39].

Analysis of the temperature gradient in the soil–sand mixture from Figure 4 revealed that the temperature gradient decreases progressively as the proportion of modified sediment increases. This is attributed to the increased thermal diffusivity of the mixture caused by higher modified sediment content, which enables faster heat transfer and results in a more uniform temperature distribution within the soil–sand mixture. Consequently, the reduced temperature gradient effectively suppresses moisture migration toward the freezing front [40,41], thereby mitigating frost heave damage.

The approximate position of the 0 °C isotherm at temperature stabilization can be calculated from Figure 4. Under the 0% modified sediment condition, the 0 °C isotherm stabilized at 2.9 cm along the soil column height; for 10% modified sediment, it stabilized at 3.1 cm; for 20% modified sediment, at 3.3 cm; for 30% modified sediment, at 3.5 cm; and for 40% modified sediment, at 3.7 cm. It was observed that as thermal diffusivity increased, the freezing front moved farther away from the warm-end boundary, thereby reducing frost heave [42,43].

3.2.2. Moisture Content at Different Depths

Under water-supply conditions, the moisture content of the soil–sand mixture was controlled at 18%, with the cold-end boundary temperature maintained at −15 °C and the hot-end boundary temperature at 5 °C. Unidirectional freezing tests were conducted on soil-sand mixtures with modified sediment mixing proportions of 0%, 10%, 20%, 30%, and 40%, resulting in the following five moisture characteristic variation plots (Figure 5).

Observation of Figure 5 reveals two moisture content peaks near the cold-end boundary and the freezing front. The peak near the cold-end boundary forms because, under water-supply conditions, the water supply head impedes moisture migration and air release, leading to localized moisture accumulation. The second peak arises from the formation of the freezing front, where a significant portion of the moisture converts to ice. It is evident that the positions of these moisture content peaks align closely with the 0 °C isotherm.

As shown in Figure 5, with increasing modified sediment mixing proportion, the overall moisture content of the soil–sand mixture gradually decreased, particularly at the freezing front. Moisture content measurements revealed that the peak near the freezing front reached 35.5% for the 0% modified sediment group; 33.5% for 10%; 31.5% for 20%; 29.5% for 30%; and 28% for 40%. This is attributed to the hydrophobic film formed by OTS modification on the sediment particles, which reduced water absorption capacity and thus lowered the overall moisture content of the soil column. The reduced moisture content directly weakened the driving force for moisture migration toward the freezing front during freezing [44,45], resulting in lower moisture content peaks at the freezing front.

3.2.3. Variation in Frost Heave Amount

Under water-supply conditions, the moisture content of the soil–sand mixture was controlled at 18%, with the cold-end boundary temperature maintained at −15 °C and the hot-end boundary temperature at 5 °C. Unidirectional freezing tests were conducted on soil–sand mixtures with modified sediment mixing proportions of 0%, 10%, 20%, 30%, and 40%, resulting in the following frost heave amount variation plots (Figure 6).

As shown in Figure 5, the development stages of frost heave amount in soil–sand mixtures can be divided into three stages: the declining compaction stage, the rapid freezing stage, and the stable growth stage [46,47].

As the modified sediment mixing proportion increased, the frost heave rate during the rapid freezing stage gradually decreased, and the final frost heave amount showed a significant reduction. The frost heave reached 7.02 mm at 72 h for the 0% modified sediment group, whereas the 40% modified sediment group exhibited only 2.01 mm. This is attributed to two factors: First, the increased modified sediment proportion enhanced the thermal diffusivity, which reduced the temperature gradient and weakened the driving force for moisture migration, thereby slowing the freezing front advancement and decreasing the frost heave rate during the rapid freezing stage [48]. Second, the increased modified sediment content formed a hydrophobic layer on the sediment surface through OTS modification, lowering the moisture content of the soil–sand mixture [49]. The reduced moisture content limited the available water at the freezing front, restricting water supply and slowing ice crystal growth, which ultimately led to a substantial reduction in the final frost heave amount [50,51].

4. Discussion

4.1. A COMSOL Multiphysics-Based Coupled Hydrological–Thermal–Mechanical Model

For the mathematical model of soil column frost heave, the following assumptions are made:

• Isotropic continuous medium assumption;
• Liquid-phase water migration is considered, neglecting vapor diffusion;
• Linear relationship between thermal parameters and moisture content/ice saturation;
• Neglecting temperature-dependent effects on thermal conductivity.

4.1.1. Governing Equation for the Temperature Field

The governing equation for permafrost temperature is derived from Fourier’s law of heat conduction, with phase change latent heat as the primary heat source:

$$\rho C(\Theta ){\displaystyle \frac{\partial T}{\partial t}}= \lambda (\Theta ){\nabla }^{2}T+L·{\rho }_i{\displaystyle \frac{\partial {\Theta }_i}{\partial t}}$$

(5)

$\rho$: soil density; C: specific heat capacity; T: temperature; t: time; $\lambda$: thermal conductivity; L: latent heat of phase change (typically 334.56 kJ/kg) [52,53]; ${\rho }_i$: the ice density

Solid-to-Liquid Ratio [54]:

$$B_I={\displaystyle \frac{{\Theta }_i}{{\Theta }_u}}=\left\{\begin{array}{c}{1.1({\displaystyle \frac{T}{T_f}})}^B-1 T<T_f\\ 0 T\ge T_f\end{array}\right.$$

(6)

$T_f$: the freezing temperature of the soil; $B$: a constant that varies depending on soil type [54].

This study adopts the Van Genuchten (VG) soil water retention model (1980) and the Gardner hydraulic conductivity model (1958) [55] and defines the relative saturation $\mathrm{S}$ of frozen soil as

$$S={\displaystyle \frac{{\Theta }_u-{\Theta }_r}{{\Theta }_s-{\Theta }_r}}$$

(7)

Simplify Equation (7) into the following form:

$${\Theta }_u=S({\Theta }_s-{\Theta }_r)+{\Theta }_r$$

(8)

${\Theta }_u$: volumetric unfrozen water content; ${\Theta }_i$: ice content; ${\Theta }_r$: residual water content; ${\Theta }_s$: saturated water content. The relative saturation $S$ is selected as the substitution variable for ${\Theta }_i$ in the calculations.

Simplify Equation (6) into the following form:

$${\Theta }_i=B_I·{\Theta }_u$$

(9)

Substitute Equations (8) and (9) into Equation ${\displaystyle \frac{\partial {\Theta }_i}{\partial \mathrm{t}}}$ to obtain:

$${\displaystyle \frac{\partial {\Theta }_i}{\partial t}}={\displaystyle \frac{\partial B_I·{\Theta }_u}{\partial t}}={\displaystyle \frac{\partial B_I·\left(S\right({\Theta }_s-{\Theta }_r)+{\Theta }_r)}{\partial t}}=({\Theta }_s-{\Theta }_r)·({\displaystyle \frac{\partial B_I}{\partial t}}·S+B_I·{\displaystyle \frac{\partial S}{\partial t}})$$

(10)

Substitute Equation (10) into Equation (5) to obtain:

$$\rho C\left(\Theta \right){\displaystyle \frac{\partial T}{\partial t}}+\nabla ·(- \lambda (\Theta )\nabla ·T)=L·{\rho }_i·({\Theta }_s-{\Theta }_r)·({\displaystyle \frac{\partial B_I}{\partial T}}·{\displaystyle \frac{\partial T}{\partial t}}·S+B_I·{\displaystyle \frac{\partial S}{\partial t}})$$

(11)

Rearrange Equation (11) to obtain the following form:

$$\left(\rho C\right(\Theta )-L·{\rho }_i·({\Theta }_s-{\Theta }_r)·{\displaystyle \frac{\partial B_I}{\partial T}}·S){\displaystyle \frac{\partial T}{\partial t}}+\nabla ·(- \lambda (\Theta )\nabla ·T)=L·{\rho }_i·({\Theta }_s-{\Theta }_r)·B_I·{\displaystyle \frac{\partial S}{\partial t}}$$

(12)

In COMSOL, the temperature field is modeled using the Coefficient Form PDE, as follows:

$$e_a{\displaystyle \frac{{\partial }^{2}T}{\partial t^2}}+d_a{\displaystyle \frac{\partial T}{\partial t}}+\nabla ·(-c\nabla ·T-\alpha T+\gamma )+\beta ·\nabla T+aT=f$$

(13)

where $\nabla =[{\displaystyle \frac{\partial t}{\partial x}},{\displaystyle \frac{\partial t}{\partial y}}]$

By comparing Equation (12) with Equation (13), the following can be obtained

$$\left\{\begin{array}{c}{d}_a=\rho C\left(\Theta \right)-L·{\rho }_i·({\Theta }_s-{\Theta }_r)·{\displaystyle \frac{\partial B_I}{\partial T}}·S\\ c=\lambda \left(\Theta \right)\\ f=L·{\rho }_i·({\Theta }_s-{\Theta }_r)·B_I·{\displaystyle \frac{\partial S}{\partial t}}\end{array}\right.$$

4.1.2. Governing Equation for the Water Content Field

Assuming that the moisture migration mechanism in frozen soil follows similar principles as in thawed soil, the Richards equation for moisture movement in frozen soil is derived by incorporating the water–ice phase change term into the governing equation for unsaturated soil moisture movement.

$${\displaystyle \frac{\partial {\Theta }_u}{\partial t}}+{\displaystyle \frac{{\rho }_i}{{\rho }_w}}{\displaystyle \frac{\partial {\Theta }_i}{\partial t}}=\nabla \left[D\right({\Theta }_u)\nabla {\Theta }_u+k({\Theta }_u\left)\right]$$

(14)

where ${\Theta }_u$: volumetric unfrozen water content; k: hydraulic conductivity of the soil.

The hydraulic diffusivity of unfrozen water in frozen soil is calculated as follows:

$$D\left({\Theta }_u\right)={\displaystyle \frac{k{(\Theta }_u)}{c{(\Theta }_u)}}·I$$

(15)

$k{(\Theta }_u)$: hydraulic conductivity of the soil (m/s); $c{(\Theta }_u)$: specific water capacity (1/m); $I$: impedance factor [56], which describes the resistance of ice to moisture migration in frozen soil. Its calculation formula is:

$$I={10}^{-10{\Theta }_u}$$

(16)

k(${\Theta }_u$) is calculated using the following equation:

$$k\left({\Theta }_u\right)=k_s·S^l(1-(1-S^{1/m}{)}^m{)}^2$$

(17)

c(${\Theta }_u$) is calculated using the following equation:

$${c(\Theta }_u)=a_{0}m/(1-m\left)S^{1/m}\right(1-S^{1/m}{)}^m$$

(18)

Substitute Equations (17) and (18) into Equation (15) to obtain:

$$D({\Theta }_u)={\displaystyle \frac{k{(\Theta }_u)}{c{(\Theta }_u)}}·I={\displaystyle \frac{k_s·S^l(1-(1-S^{1/m}{)}^m{)}^2}{a_{0}m/(1-m)S^{1/m}(1-S^{1/m}{)}^m}}·I=D(S)$$

(19)

Therefore, simplifying component $\nabla \left[D\right({\Theta }_u)\nabla {\Theta }_u]$ in Equation (14) yields the following result:

$$\nabla \left[D\right({\Theta }_u)\nabla {\Theta }_u]=\nabla \left[D\right(S)\nabla {\Theta }_u]={\displaystyle \frac{\partial }{\partial y}}\left[D\right(S\left){\displaystyle \frac{\partial {(\Theta }_u)}{\partial y}}\right]={\displaystyle \frac{\partial }{\partial y}}\left[D\right(S\left){\displaystyle \frac{\partial \left(\right({\Theta }_s-{\Theta }_r)\mathrm{S}+{\Theta }_r)}{\partial y}}\right]=({\Theta }_s-{\Theta }_r){\displaystyle \frac{\partial }{\partial y}}\left[D\right(S\left){\displaystyle \frac{\partial \left(S\right)}{\partial y}}\right]=({\Theta }_s-{\Theta }_r)\nabla \left[D\right(S)\nabla S]$$

(20)

Substitute Equation (8) into ${\displaystyle \frac{\partial {\Theta }_u}{\partial t}}$ to obtain:

$${\displaystyle \frac{\partial {\Theta }_u}{\partial t}}={\displaystyle \frac{\partial \left(\right({\Theta }_s-{\Theta }_r)S+{\Theta }_r)}{\partial t}}=({\Theta }_s-{\Theta }_r){\displaystyle \frac{\partial S}{\partial t}}$$

(21)

simplifying component $\nabla \left[k\right({\Theta }_u\left)\right]$ in Equation (14) yields the following result:

$$\nabla \left[k\right({\Theta }_u\left)\right]={\displaystyle \frac{\partial {\left(k\right(\Theta }_u\left)\right)}{\partial y}}={\displaystyle \frac{\partial (k·(({\Theta }_s-{\Theta }_r)S+{\Theta }_r\left)\right)}{\partial y}}=({\Theta }_s-{\Theta }_r){\displaystyle \frac{\partial \left(k\right(S\left)\right)}{\partial y}}=({\Theta }_s-{\Theta }_r)\nabla \left[k\right(S\left)\right]$$

(22)

Substitute Equations (20)–(22), and (10) into Equation (14) to obtain:

$${\displaystyle \frac{\partial S}{\partial t}}+{\displaystyle \frac{{\rho }_I}{{\rho }_w}}·({\displaystyle \frac{\partial B_I}{\partial t}}·S+B_I·{\displaystyle \frac{\partial S}{\partial t}})=\nabla \left[D\right(S)\nabla S+k(S\left)\right]$$

(23)

Rearrange Equation (23) into the following form:

$$\left((1+{\displaystyle \frac{{\rho }_i}{{\rho }_w}}{B}_I)\right){\displaystyle \frac{\partial S}{\partial t}}+\nabla [-D(S)\nabla S-k(S\left)\right]+{\displaystyle \frac{{\rho }_i}{{\rho }_w}}·{\displaystyle \frac{\partial B_I}{\partial t}}·S=0$$

(24)

In COMSOL, the moisture field is modeled using the Coefficient Form PDE as follows

$$e_a{\displaystyle \frac{{\partial }^{2}S}{\partial t^2}}+d_a{\displaystyle \frac{\partial S}{\partial t}}+\nabla ·(-c\nabla ·S-\alpha S+\gamma )+\beta ·\nabla S+aS=f$$

(25)

By comparing Equation (24) with Equation (25), the following can be obtained

$$\left\{\begin{array}{c}{d}_a=1+{\displaystyle \frac{{\rho }_i}{{\rho }_w}}{B}_I\\ c=D\left(S\right)\\ \gamma =-k\left(S\right)\\ a={\displaystyle \frac{{\rho }_i}{{\rho }_w}}·{\displaystyle \frac{\partial B_I}{\partial t}}\end{array}\right.$$

4.1.3. Governing Equation for the Stress Field

Due to the predominance of vertical uplift and cracking in practical engineering channel frost heave damage, and the fact that vertical strain significantly exceeds horizontal strain, simplifying the model to consider only vertical strain maintains accuracy while reducing computational complexity. Therefore, only the vertical strain tensor of the soil column is considered [57,58]. The volumetric expansion ratio during water-to-ice phase change per unit volume is $({\displaystyle \frac{{\rho }_w}{{\rho }_i}}-1)$. The difference between current and initial saturation $(S-S_0)$ reflects the proportion of unfrozen water converted to ice. Combining the phase change-induced volumetric expansion with the effective saturation change and multiplying by the saturated water content ${\Theta }_s$, the total strain is derived. Therefore, the vertical strain tensor of the soil column is expressed as:

$$\epsilon =({\displaystyle \frac{{\rho }_w}{{\rho }_i}}-1)·{\Theta }_s·(S-S_0)$$

(26)

4.2. Determination of Coupling Parameters Between Equations

4.2.1. Thermophysical Properties

(1)

Thermal Conductivity

The thermal conductivity of frozen and unfrozen soils is primarily governed by water content and ice content, respectively. For unfrozen soils, thermal conductivity decreases with decreasing water content, whereas for frozen soils, it decreases with decreasing ice content [59,60]; the effect of temperature on thermal conductivity is relatively weak and can be neglected in calculations. To comprehensively characterize the variation of thermal conductivity, the expression adopted in this study is as follows:

$$\lambda ={\lambda }_s^{1-{\theta }_s}{\lambda }_w^{{\theta }_u}{\lambda }_i^{{\theta }_i}$$

(27)

${\lambda }_s$: thermal conductivity of soil–sand mixtures, W/(m·°C); ${\lambda }_w$: thermal conductivity of water, W/(m·°C); ${\lambda }_i$: thermal conductivity of ice, W/(m·°C); ${\Theta }_u$: volumetric unfrozen water content; ${\Theta }_i$: ice content; ${\Theta }_s$: saturated water content.

(2)

Volumetric Heat Capacity

By applying the mass-weighted average approach to frozen and unfrozen soil–sand mixtures [61,62], the volumetric heat capacity is formulated as a twice continuously differentiable function:

$$\left\{\begin{array}{l}C={\rho }_d{C}_s+{\rho }_w{\theta }_u{C}_w+{\rho }_i{\theta }_i{C}_i\\ C_s=C_{sf}+\left(C_{su}-C_{sf}\right)H\left(T\right)\end{array}\right.$$

(28)

$C$: volumetric heat capacity; $C_s$: specific heat capacity of modified soil skeleton, kJ/(kg·°C); $C_{sf}$: specific heat capacity of frozen soil–sand mixture, kJ/(kg·°C); $C_{su}$: specific heat capacity of unfrozen soil–sand mixture, kJ/(kg·°C); ${\rho }_d$: dry density of soil, kg/m³; ${\rho }_w$: density of water, (1000 kg/m³); ${\rho }_i$:density of ice, (900 kg/m³); $C_w$: specific heat capacity of water, kJ/(kg·°C); $C_i$: specific heat capacity of ice, kJ/(kg·°C). $H\left(T\right)$ is the unit step function, acting as a switching function to describe the abrupt change in specific heat capacity during phase transitions (e.g., solid–liquid phase transition). During the frozen soil phase $\left(T<T_f\right), H\left(T\right)=0, C_s=C_{sf}$; during the unfrozen soil phase $\left(T\ge T_f\right), H\left(T\right)=1, C_s=C_{su}$; $T_f$: soil freezing temperature; ${\Theta }_u$: volumetric unfrozen water content; ${\Theta }_i$: ice content.

(3)

Soil Freezing Temperature

The fundamental formula for soil freezing temperature $T_f$ must integrate the following three categories of factors [63,64]:

• Water Content $\mathrm{w}$: Higher water content strengthens capillary action and adsorption, resulting in a lower freezing temperature.
• Salinity $\mathrm{S}$: Salt reduces the freezing temperature, with a critical concentration threshold.
• Porosity $\mathrm{n}$: Smaller pore radii enhance the surface curvature effect of ice crystals, leading to a lower freezing temperature.

Mathematical Formulation:

$$T_f=T_0-\Delta T_{\mathit{capillary}}\left(w,n\right)-\Delta T_{\mathit{salt}}\left(S,w\right)-\Delta T_{\mathit{pore}}\left(n\right)$$

(29)

where:

$T_0$: Pure water freezing temperature (0 °C);

$\Delta T_{\mathit{capillary}}$: Freezing temperature depression due to capillary effect;

$\Delta T_{salt}$: Freezing temperature depression induced by salinity;

$\Delta T_{pore}$: Freezing temperature depression caused by porosity.

$\Delta T_{\mathit{capillary}}$ is the capillary effect term:

The capillary effect is related to water content $w$ and porosity $n$, and the formula is as follows:

$$\Delta T_{\mathrm{capillary}}={\displaystyle \frac{2\gamma }{r{\rho }_{w}L}}\cdot f\left(w,n\right)$$

(30)

$\gamma$: surface tension of water (0.072 N/m); $r$: average pore radius, related to porosity $n$ as $r$ = k$n^{-1}$, with k = 0.45 specific to the Hetao Irrigation District in Inner Mongolia; ${\rho }_w$: density of water, (1000 kg/m³); $L$: Latent heat of phase change, (334 kJ/kg).

$f\left(w,n\right)$: Correction function for water content and porosity, defined based on the error deviation between simulated and experimental values as:

$$f\left(w,n\right)=w\cdot \left(1-n\right)$$

(31)

$\Delta T_{salt}$ is the salinity project

The freezing point depression induced by salinity is described by the following equation:

$$\Delta T_{salt}=K_f\cdot C_{eff}$$

(32)

$K_f$: the cryoscopic constant of the solution, taken as 1.86; $C_{eff}$: the effective salt concentration (considering only the effect of salt crystallization, $C_{eff}$ is simplified to the salinity S).

$\Delta T_{pore}$ is the porosity term

The effect of porosity on freezing temperature is primarily manifested through the ice crystal surface curvature effect:

$$\Delta T_{\mathrm{p}\mathrm{o}\mathrm{r}\mathrm{e}}=\alpha \cdot \left({\displaystyle \frac{1}{r}}\right)\cdot n$$

(33)

$\alpha$: the curvature effect coefficient, calibrated through experiments as $\alpha =0.015 °\mathrm{C}$;

$r$: average pore radius, negatively correlated with porosity $n$, defined as $r=k\left(1-n\right)$. For the Hetao Irrigation District in Inner Mongolia, $k$ = 1.2.

4.2.2. Hydraulic Characteristic Parameters

(1)

Hydraulic Conductivity

Hydraulic conductivity is one of the key indicators characterizing water migration capacity, and its magnitude is jointly influenced by the water content, ice content, temperature variations, and pore size within the soil matrix. The expression for calculating hydraulic conductivity is:

$$k\left({\Theta }_u\right)=k_s·S^l(1-(1-S^{1/m}{)}^m{)}^2$$

(34)

$k_s$: the permeability of the saturated soil, l: a parameter of the hydraulic conductivity function; S: the effective saturation.

(2)

Specific Water Capacity

Specific water capacity is a parameter quantifying the soil’s ability to retain water. Its value is influenced by soil texture, water content, temperature, and soil density, among other factors. In this study, the widely used van Genuchten (VG) model is adopted, with the mathematical formulation:

$${c(\Theta }_u)=a_{0}m/(1-m\left)S^{1/m}\right(1-S^{1/m}{)}^m$$

(35)

In Equations (34) and (35), $a_0$, $m$: empirical parameters determined by soil properties, S: the effective saturation.

(3)

Moisture Diffusion Coefficient

Considering the impact of ice on water flow in frozen soils, a new physical parameter—the ice impedance factor I—is introduced to reduce both the hydraulic conductivity and the moisture diffusion coefficient. The adjusted expressions are:

$$D\left(S\right)={\displaystyle \frac{k{(\Theta }_u)}{c{(\Theta }_u)}}·I$$

(36)

4.3. Model Setup

4.3.1. Geometric Model

The geometric model is a cylinder with a height of 10 cm and a diameter of 10 cm, matching the dimensions of the specimen used in the unidirectional freezing test. For numerical simulation, the model is simplified to a 2D planar model with a length and width of 10 cm each, assuming axisymmetric geometry.

4.3.2. Thermal Boundary Conditions

In COMSOL’s Temperature Field module, the cold-end boundary temperature of −15 °C and the hot-end boundary temperature of 5 °C are specified as Dirichlet boundary conditions.

4.3.3. Moisture Field Boundary Conditions

To account for vertical groundwater recharge, a constant flux boundary condition is applied at the model base, representing the moisture influx per unit area per unit time. The recharge rate q is determined using an empirical formula and is set accordingly [65].

q =1.2 × 10⁻⁶ m/s

Both the top surface and side walls are set to zero-flux boundary conditions to simulate a closed environment with no moisture exchange.

4.3.4. Stress Field Boundary Conditions

The top boundary of the cylindrical model is treated as a free surface, the bottom boundary as a fixed constraint, and the left/right boundaries are constrained to zero lateral displacement.

4.4. Mesh Independence Study

In this study, the freezing process of a soil–sand mixture was simulated using the PDE Module in COMSOL Multiphysics to couple thermal, hydraulic, and mechanical responses. This approach enabled the derivation of temperature and moisture variations at different depths, as well as the overall frost heave. To ensure computational accuracy, a mesh independence study was conducted. A cylindrical model with a height of 10 cm and diameter of 10 cm was constructed using thermal–hydraulic parameters corresponding to a 40% modified sediment content scenario. The cold and hot end boundary temperatures were set to −15 °C and 5 °C, respectively, with a simulation time step of 100 h. Calculations were performed for varying mesh densities to validate mesh independence.

Figure 7 presents the numerical results of frost heave displacement at the final simulation time under different mesh sizes. It can be observed that when the mesh size increases from 25 to 225, the calculated frost heave shows an increasing trend. However, beyond 225 mesh elements (up to 1000), the frost heave displacement remains nearly constant, varying within ±0.1 mm. Based on this convergence analysis, the model with a mesh size of 400 was ultimately selected to balance computational accuracy and efficiency.

4.5. Experimental Data Validation

Numerical simulations were conducted using a modified channel sediment mixing ratio of 40%, with a cold-end temperature of −15 °C, a hot-end temperature of 5 °C, and an initial water content of 18%. The subgrade soil parameters, thermal parameters, and hydraulic parameters were determined based on

Table 4. Soil hydrothermal parameters for 40% modified sediment content.

Parameter Classification	Parameter	Magnitude	Parameter Classification	Parameter	Magnitude	Parameter Classification	Parameter	Magnitude
Modified Channel Sediment	density of water (kg/m3)${\rho }_w$	1000	Thermophysical Properties	latent heat of phase change (KJ/kg) L	334.56	Hydraulic Characteristic Parameters	saturated water content (%) ${\Theta }_s$	0.32
	density of ice (kg/m3) ${\rho }_i$	918		specific heat capacity of unfrozen soil-sand mixture KJ/(kg·K) $C_{su}$	0.76		residual water content (%) ${\Theta }_r$	0.076
	dry density of soil (kg/m3) $\rho$	1700		specific heat capacity of frozen soil-sand mixture KJ/(kg·K) $C_{sf}$	0.735		the permeability of the saturated soil (m/s) $k_s$	9.54 × 10−7
	Initial Water Content (%)	18		specific heat capacity of water KJ/(kg·K) $C_w$	4.2		Specific Water Capacity Parameter α0	1.8
	Initial Temperature (°C)	−15		specific heat capacity of ice KJ/(kg·K) $C_i$	2.1		Specific Water Capacity Parameter m	0.6
	Soil Porosity n	0.7		thermal conductivity of soil-sand mixtures W/(m·K) ${\lambda }_s$	1.36		a constant that varies with soil type and salt content B	0.56
	Salinity S	0.02		thermal conductivity of water W/(m·K) ${\lambda }_w$	0.63		a parameter of the hydraulic conductivity function l	0.41
				thermal conductivity of ice W/(m·K) ${\lambda }_i$	2.31

and the formulas presented in this paper. The simulated frost heave magnitude, temperature profiles at various depths, and moisture content profiles were validated against experimental data. To ensure consistency with actual field conditions, the model was configured with a soil sample height of 10 cm and a time step of 72 h. The following three comparative numerical plots (Figure 8) were obtained.

By comparing the experimental and simulated values of frost heave magnitude, temperature profiles at various depths, and moisture content profiles, it was found that the overall error was controlled within 15%, and the overall trends were in good agreement with the actual conditions. Therefore, the model can be used to characterize the frost heave behavior of modified channel sediment.

4.6. Experimental Results

To investigate the effect of modified sediment mixing ratio on frost heave, the base parameters of the modified channel subgrade soil were kept constant. Thermal–hydraulic parameters for modified sediment contents of 0%, 10%, 20%, and 30% were measured, as detailed in

Table 5. Hydrothermal parameters for varying modified sediment contents.

	0% Modified Sediment Mixing Ratio	10% Modified Sediment Mixing Ratio	20% Modified Sediment Mixing Ratio	30% Modified Sediment Mixing Ratio
specific heat capacity of unfrozen soil–sand mixture KJ/(kg·K) $C_{su}$	0.86	0.83	0.81	0.78
specific heat capacity of frozen soil–sand mixture KJ/(kg·K) $C_{sf}$	0.835	0.805	0.785	0.755
thermal conductivity of soil–sand mixtures W/(m·K) ${\lambda }_s$	1.48	1.45	1.42	1.39
saturated water content (%) ${\Theta }_s$	0.4	0.38	0.36	0.34
residual water content (%) ${\Theta }_r$	0.08	0.079	0.078	0.077
the permeability of the saturated soil (m/s) $k_s$	2.02 × 10−6	1.58 × 10−6	1.32 × 10−6	1.05 × 10−6
a constant that varies with soil type and salt content B	0.64	0.62	0.6	0.58
a parameter of the hydraulic conductivity function l	0.45	0.44	0.43	0.42

. Comparison of Table 4 and Table 5 reveals that as the modified silt content increases, both the thermodynamic parameters and hydraulic characteristic parameters of the soil–sand mixtures decrease. Boundary conditions were consistent, with the initial water content remaining at 18%. The cold and hot end boundary temperatures were set to −15 °C and 5 °C, respectively. The model was configured with a soil sample height of 10 cm and a time step of 72 h. The calculated frost heave magnitudes under different modified sediment mixing ratios were obtained using a coupled thermal–hydraulic–mechanical model, as shown in Figure 9.

Numerical simulations do not account for the decline consolidation phase; therefore, the frost heave magnitude change is herein categorized into two phases: the rapid freezing phase and the stable growth phase.

As shown in Figure 9, with increasing modified sediment mixing ratio, the freezing rate of the soil-sediment mixture during the rapid freezing phase significantly decreases, and the final frost heave magnitude is substantially reduced. The final frost heave magnitudes under mixing ratios of 0%, 10%, 20%, 30%, and 40% are 6.65 mm, 5.42 mm, 4.23 mm, 3.06 mm, and 1.9 mm, respectively. This demonstrates that the OTS-modified channel sediment exhibits significantly enhanced frost heave resistance, effectively mitigating the frost heave phenomenon. By comparing Figure 6 and Figure 9, it can be observed that at the end of the rapid freezing phase (0–36 h), the frost heave displacements for the experimental group under modified silt content conditions of 0%, 10%, 20%, 30%, and 40% were 5 mm, 4.19 mm, 3.45 mm, 2.7 mm, and 1.95 mm, respectively. For the simulation group under the same conditions, the displacements were 4.7 mm, 3.96 mm, 3.23 mm, 2.53 mm, and 1.83 mm, with discrepancies between experimental and simulated data remaining within 15%. During the steady growth phase (36–72 h), the final frost heave displacements for the experimental group were 7.02 mm, 5.71 mm, 4.48 mm, 3.24 mm, and 2.01 mm, while the simulation group yielded 6.65 mm, 5.42 mm, 4.23 mm, 3.06 mm, and 1.9 mm, respectively. The discrepancies in this phase also remained within 15%. Therefore, the hydro-thermal–mechanical coupled model employed in this study effectively captures the frost heave behavior of modified silt.

5. Conclusions

This study demonstrates that octadecyltrichlorosilane modification significantly enhances the frost heave resistance of channel sediment in the Hetao Irrigation District by optimizing hydrophobicity through a 0.001% silane-to-sediment mass ratio at 50 °C. Unidirectional freezing experiments further reveal that a 40% modified sediment proportion reduces frost heave magnitude by 71.3% and suppresses water accumulation at the freezing front, validating OTS’s efficacy in mitigating soil expansion during freeze–thaw cycles. Complementing these findings, a coupled thermal–hydraulic–mechanical model developed in COMSOL Multiphysics accurately simulates frost heave behavior with an error margin of ≤15%, offering a reliable predictive tool for cold-arid regions. Furthermore, OTS-modified sediment presents a sustainable, cost-effective solution for frost heave mitigation in the Hetao Irrigation District. By reducing long-term maintenance costs, minimizing waste from sediment relocation, and employing an eco-friendly process, it outperforms traditional methods like soil replacement or insulation layers. Its hydrophobic properties align with sustainability goals by conserving water and reducing environmental pollution compared to conventional materials. However, the study’s lab-scale, unidirectional freezing experiments may not fully reflect real-world complexities such as variable temperature gradients, heterogeneous soil structures, or prolonged freeze–thaw cycles. The THM model also assumes isotropic soil behavior and overlooks OTS degradation over time. Therefore, future research should validate field performance and aspsess long-term durability under repeated freeze–thaw cycles to ensure practical reliability.