Thermal Conductivity Characteristics and Prediction of Sodium Chloride-Containing Aeolian Sand Under Multi-Factor Influence

Abstract

Understanding the variation law and prediction method of thermal conductivity for NaCl-bearing aeolian sand is of great significance for the thermal parameter selection and temperature field analysis of engineering structures including subgrades, foundations and lined water conveyance canals in the saline soil region of southern Xinjiang. The thermal conductivity of NaCl-bearing aeolian sand under different dry densities, moisture contents and salt contents was measured via the transient plane source (TPS) method. The variation law and corresponding influence mechanism were analyzed, and a thermal conductivity prediction model was established. The experimental results indicate that the thermal conductivity of NaCl-bearing aeolian sand increases with increasing dry density and moisture content, showing strong linear correlations with both parameters. At a salt content of 2%, the maximum increase in thermal conductivity induced by increasing moisture content reached 29.3%, which was approximately 1.53 times the increase observed at a salt content of 8% (19.17%). In contrast, the influence of salt content on thermal conductivity exhibited a nonlinear trend. With increasing salt content, the thermal conductivity initially decreased and then increased, and the salt content corresponding to the minimum thermal conductivity shifted toward higher values with increasing moisture content. Specifically, this critical salt content gradually shifted from 2% to 6%. This law reveals that the increase in dry density and moisture content improves the thermal conductivity of the soil mainly by enhancing the solid and liquid heat transfer pathways, whereas the variation of salt content is controlled by the water–salt coupling effect. The model calculation results show that the established prediction model is in good agreement with the measured experimental data (R² = 0.9674), with favorable applicability and high prediction accuracy. It can provide a reliable reference for the thermal calculation of sandy foundations and related engineering materials in saline soil areas.

1. Introduction

The climate in the Southern Xinjiang region is extremely arid, characterized by scarce precipitation and intense evaporation [1]. Groundwater runoff is sluggish, and vertical evaporation dominates water–salt migration. Salts in the widely distributed aeolian sand foundation soils accumulate as capillary water rises, leading to the extensive development of saline soils in basins, alluvial–proluvial plains, and oasis margins. Such soils exhibit strong salt heave, collapsibility, and corrosiveness [2,3,4]. These foundations serve as the core engineering base for hydraulic structures such as lined canals and reservoir dams. Under the coupled effects of salt, water, and temperature, salt heave and frost heave in the foundation soil readily induce engineering distresses like the cracking of canal linings, posing a severe threat to the long-term safety and durability of infrastructure [5]. Studies indicate [6] that the essence of engineering distress in the cold-arid environment of Southern Xinjiang results from the coupling of water, salt, temperature, and stress fields within the foundation soil, along with the interaction between soil and structure. Temperature has been identified as the core driving factor, and thermal conductivity is a key parameter for establishing accurate temperature field models [7]. Therefore, systematic research on the thermal conductivity characteristics of saline aeolian sand in Southern Xinjiang is driven by clear engineering requirements and theoretical significance.

Significant progress has been made in the study of soil thermal conductivity. Existing findings generally indicate that moisture content, dry density, salt content, and temperature are the key factors governing variations in thermal conductivity [8,9,10]. Specifically, Abu-Hamdeh et al. [11] investigated soil thermal conductivity using a single-probe method and noted that increases in both moisture content and density significantly enhanced thermal conductivity, whereas salt and organic matter altered the magnitude of this change. Yan et al. [12] pointed out that an increase in moisture content shifted the soil heat transfer mechanism from particle contact conduction to liquid bridge conduction, thereby improving heat transfer efficiency. Subsequently, Lu et al. [13] further developed an improved thermal conductivity prediction model based on moisture content. Wu et al. [14] established a prediction formula for backfill soil thermal conductivity based on moisture content and dry unit weight. Nikoosokhan et al. [15] validated the close relationship between thermal conductivity, compaction degree, and moisture state from the perspectives of dry density, soil structure, and water conditions. These studies demonstrate that soil thermal conductivity is not governed by a single variable but results from the combined effect of multiple physical state parameters. Building on this, researchers have progressively focused on the role of salt and its regulatory mechanisms on pore fluid properties and heat transfer paths. Siddiqua et al. [16] found that changes in pore fluid chemistry significantly affect the thermal behavior of bentonite–sand mixtures, indicating that salt not only alters the thermal conductivity of the liquid phase but also influences inter-particle contact states and the electrical double-layer structure. Ju et al. [17] further proposed a modified thermal conductivity model for saline soils, asserting that existing conventional models struggle to accurately describe the thermal response of saline soils if salt effects are neglected. This suggests that salt is no longer merely an additional influencing factor but a non-negligible controlling condition in the prediction of thermal parameters for saline soils.

With the continued advancement of research on soil heat transfer mechanisms, the influence of mineral composition on soil thermal conductivity has received increasing attention. Different mineral constituents exhibit distinct solid-phase thermal properties. For instance, quartz generally has relatively high thermal conductivity, whereas feldspar, carbonate minerals, and clay minerals show different thermal characteristics. Therefore, even under comparable moisture content, dry density, and pore structure conditions, variations in mineral composition may still result in differences in soil thermal conductivity. Li et al. [18] reported that quartz content is a key parameter for predicting soil thermal conductivity and that directly using sand content as a substitute for quartz content may introduce considerable uncertainty into thermal conductivity estimates. Xu et al. [19]. further demonstrated that quartz, as a high-thermal-conductivity mineral, plays an important role in soil heat transfer, and neglecting its contribution may reduce the predictive accuracy of thermal conductivity models. These findings indicate that mineral composition, particularly the content of high-thermal-conductivity minerals such as quartz, is an important factor governing soil thermal conductivity, mainly by altering the intrinsic thermal conductivity of the solid phase and the heat transfer pathways within the soil skeleton.

As research deepens, the mechanisms governing the evolution of thermal parameters under temperature effects and during the freezing process have gradually become research foci [20,21]. Campbell et al. [22] noted that temperature variations affect soil thermal conductivity. Hiraiwa et al. [23] confirmed a significant response of soil thermal conductivity to temperature over a wider temperature range. Subsequently, Xu et al. [24], in a study of red clay, further discovered that thermal conductivity increases with rising temperature, and the role of latent heat transfer is more pronounced under moderate saturation conditions. In the context of frozen soil research, Wan et al. [25] focused on temperature’s effect on the thermal conductivity of lime-modified red clay, demonstrating that changes in unfrozen water content at low temperatures are the primary factor controlling thermal properties. Bi et al. [26] established a method for predicting frozen soil thermal conductivity based on the soil freezing characteristic curve, highlighting that the evolution of unfrozen water and phase change processes are critical links governing thermal behavior under low-temperature conditions. Thus, it is evident that temperature changes not only affect the thermal properties of individual soil phases but also further alter the heat transfer process through water migration, phase transformation, and changes in unfrozen water content.

However, under unsaturated or saline conditions, heat transfer is often accompanied by coupled processes such as latent heat exchange and pore liquid phase restructuring [27,28,29]. This renders the quantitative characterization of internal soil heat transfer mechanisms relatively difficult, and existing models are generally complex in form. Bayat et al. [30] utilized terrain attributes and soil physical parameters to construct a thermal conductivity prediction model based on artificial neural networks, validating the feasibility of machine learning methods in thermal parameter prediction. Wan et al. [25], based on the generalized thermal conductivity theory for geomaterials and considering the influence of particle shape, established a thermal conductivity prediction model for sodium sulfate saline soil, achieving a relative prediction error within 10%. Wu et al. [31], in a recent review, further summarized that research on soil thermal conductivity has progressively evolved from single-factor experimental analysis to a parallel paradigm involving multi-factor coupling, model refinement, and intelligent prediction.

Existing research has gradually advanced from single-factor analysis to stages involving multi-factor coupling and model prediction. However, systematic studies on the thermal conductivity characteristics of sodium chloride-bearing aeolian sand—a material widely distributed in the foundations of hydraulic structures in the Southern Xinjiang region—remain relatively scarce. The available findings are not yet sufficient to directly support regional engineering design. Accordingly, this study investigates typical sodium chloride-bearing aeolian sand from southern Xinjiang and conducts thermal conductivity tests on artificially remolded specimens under room-temperature conditions using the transient plane source method. Unlike previous studies on the thermal behavior of saline–alkali soils, which have mainly focused on fine-grained saline soils, bentonite–sand mixtures, or improved soils, and have commonly established empirical prediction relationships based on single or dual factors such as water content, density, or salt content, this study emphasizes the coupled effects of water content, dry density, and salt content in unsaturated saline aeolian sand. Specifically, the nonlinear response mechanism of thermal conductivity under the combined action of these three factors is elucidated from the perspectives of enhanced heat transfer through water bridges, improved interparticle contact efficiency induced by increased dry density, and pore filling by salt crystallization, which alters the heat conduction pathways within the porous medium. Furthermore, the regulating effects of individual variables and their coupling interactions on thermal conductivity are quantified through influencing-factor analysis, and a thermal conductivity prediction model applicable to saline aeolian sand in southern Xinjiang is developed by integrating multiple nonlinear regression and machine learning methods. These findings enrich the understanding of the thermal physical properties of saline aeolian sand in arid and cold regions, improve the regional applicability of temperature-field calculation and thermal-parameter prediction for saline soil foundations, and provide a theoretical basis for analyzing salt expansion and frost heave mechanisms and for the disaster prevention and mitigation design of hydraulic structures in saline soil areas of southern Xinjiang. They may also serve as a reference for subsequent studies on thermal conductivity under subzero temperature conditions.

2. Experimental

2.1. Test Materials

The soil samples were collected from aeolian sand of the Taklimakan Desert near the airport in Aral City, Xinjiang Uygur Autonomous Region, at a depth of 1 m below the ground surface. The samples were air-dried, crushed, and sieved prior to use. Basic physical and chemical property tests were conducted in accordance with the Standard for Geotechnical Testing Method (GB/T 50123-2019) [32]. The particle size distribution is presented in

Table 1. Basic physical parameters of soil samples.

Soil Type	Different Particle Size Gradation/(%)
	>1 mm	0.5~1 mm	0.25~0.5 mm	0.075~0.25 mm	<0.075 mm
Aeolian Sand	0	0.07	0.12	86.63	13.18

, and the compaction curve is shown in Figure 1. The granulometric composition of the soil sample was dominated by particles ranging from 0.075 mm to 0.25 mm, accounting for 86.63% of the total. The soil sample contained soluble salts. The ion contents in the soil sample were determined with reference to *Soil Testing—Part 16: Method for Determination of Total Water-Soluble Salt* [33], and the results are listed in

Table 2. The content of salt ions in soil samples.

Soil Type	Contents of Various Ions/(mg/L)						Total Salt Content/(%)	Types of Saline Soil
	Cl−	SO42−	K+	Ca2+	Na+	Mg2+
Aeolian Sand	76.7	17.89	33.47	24.65	111.52	7.93	0.21	Non-Saline Soil

. The contents of Cl⁻, SO₄²⁻, K⁺, Ca²⁺, Na⁺, and Mg²⁺ in the soil, as well as the total soluble salt content of 0.21%, were obtained. According to the classification criteria for salt content in the Safety Standard for Geotechnical Engineering Investigation (GB/T 50585-2019) [34], the total salt content was less than 0.3%, and the soil can therefore be classified as non-saline soil.

To investigate the influence of natural salt content on thermal conductivity, specimens of unwashed aeolian sand, plain soil (washed five times with distilled water), and aeolian sand containing 0.21% sodium chloride (prepared by salt addition after washing) were fabricated at the same moisture content and dry density based on the total salt content of the selected soil sample. Thermal conductivity was measured at room temperature, and the results are presented in

Table 3. Effect of desalination treatment on the thermal conductivity of aeolian sand.

	Natural Aeolian Sand	Desalted Aeolian Sand	Desalted Aeolian Sand Prepared with 0.21% Sodium Chloride
Thermal Conductivity (W/(m·k))	1.047	1.04	1.015

. The difference between the minimum and maximum values is 3.15%, indicating a relatively minor influence. Nevertheless, to eliminate potential errors, a desalination pretreatment was applied to the natural aeolian sand according to a standardized washing procedure. The soil sample was washed five times with distilled water at a soil-to-water ratio of 1:5 per wash, involving thorough stirring followed by the decantation of the supernatant. After the fifth wash, the soluble salt content of the treated soil was measured as 0.023%. This desalinated soil was subsequently used to prepare artificially salinized samples. To achieve a homogeneous distribution of sodium chloride (NaCl), which is critical for reproducibility, the “wet soil plus dry salt” method was employed. Specifically, the moisture content of the desalinated soil was first raised to 11% by spraying and homogenizing a calculated amount of distilled water. Anhydrous NaCl was then incorporated into the moist soil according to the desired target salt content. The mixture was immediately and thoroughly stirred to promote initial salt dispersion, after which it was sealed with plastic film and allowed to stand for one day. During this 24-h period, the soil–salt mixture was remixed repeatedly to enhance uniform salt distribution. After the standing period, the artificially salinized soil was air-dried, crushed, and stored in sealed containers for later use.

X-ray diffraction (XRD) patterns are shown in Figure 2. The mineral composition of the desalinated aeolian sand was dominated by quartz, plagioclase, and K-feldspar, with contents of 33.6%, 33.4%, and 17.9%, respectively. These three minerals accounted for 84.9% of the total mineral fraction, indicating that the sample was primarily composed of quartz–feldspar detrital minerals. The contents of carbonate minerals were relatively low, with calcite and dolomite accounting for 7.5% and 1.2%, respectively. In addition, minor amounts of mica, amphibole, and clay minerals were present, with contents of 2.1%, 1.5%, and 2.7%, respectively. Regarding the clay mineral assemblage, illite and chlorite were the dominant clay minerals, with relative contents of 64.6% and 27.5%, respectively, whereas kaolinite and smectite occurred in relatively low proportions, accounting for 4.2% and 3.7%, respectively. Overall, the desalinated aeolian sand was mainly characterized by quartz and feldspar minerals, together with a low clay mineral content. This mineralogical feature suggests that the solid skeleton of the sample was predominantly granular and exhibited relatively low clay activity.

SEM images of desalinated aeolian sand and salt-bearing aeolian sand under dry conditions are shown in Figure 3. SEM observations were conducted to further characterize the microstructural features of aeolian sand with different salt contents under dry conditions. For the desalinated aeolian sand with 0% salt content, the SEM images obtained at magnifications of 150× and 350× showed that the particles were mainly irregular blocky and sub-angular to sub-rounded in shape. The particle surfaces were relatively rough, with local pits, grooves, and fracture planes. Under the dry and loose condition, the particles were mainly arranged through point-to-point or point-to-surface contacts.

For the aeolian sand with 8% salt content, the SEM images obtained at magnifications of 200× and 2000× showed that the overall particle morphology remained irregular and sub-angular. Distinct salt crystallization could be observed on particle surfaces and within local interparticle spaces, particularly at the higher magnification of 2000×. The salt crystals mainly occurred as fine and granular, flaky, or clustered deposits attached to the particle surfaces, and some crystals accumulated near particle edges and contact zones. Compared with the aeolian sand with 0% salt content, the surface of the 8% salt-content sample was partially covered by salt precipitates, which may fill micro-pores and form local cementation or bridging structures between adjacent particles. These salt crystal bridges can increase the effective contact area and provide additional solid-phase heat transfer pathways.

2.2. Experimental Program

Under a constant temperature of 25 °C, remolded specimens of sodium chloride-bearing aeolian sand with varying moisture content W, dry density ρ_d, and salt content C were prepared using the controlled variable method. Systematic measurements of thermal conductivity were carried out based on the transient plane source method to elucidate the variation patterns of thermal conductivity of sodium chloride-bearing aeolian sand under the combined influence of these three factors.

2.2.1. Specimen Preparation

Moisture content, denoted by W, was controlled at five levels: 9%, 11%, 13%, 15%, and 17%. Dry density, denoted by ρ_d, was selected with reference to the compaction curve at values of 1.44 g/cm³, 1.46 g/cm³, 1.48 g/cm³, 1.50 g/cm³, and 1.52 g/cm³. In the Southern Xinjiang region, the salt content of saline soils typically ranges from 2.0% to 5.0% and above. Previous investigations by our research group along the S207 highway in Southern Xinjiang indicate an average total salt content of approximately 8%. Considering the engineering geological characteristics of the area, salt content, denoted by C, was controlled at five levels: 0%, 2.0%, 4.0%, 6.0%, and 8.0% (sodium chloride by mass of dry soil).

Specimens were prepared using standard cutting rings with a volume of 60 cm³, and the specimen volume was controlled to be consistent with the ring volume. Purified water was added to the air-dried sodium chloride-bearing aeolian sand to achieve the target moisture content. After thorough mixing, the material was sealed and allowed to stand for 18 h. Specimens were then compacted to the required dry density using a static compaction apparatus, whereby all the soil was pressed into the cutting ring, yielding specimens with different moisture contents, salt contents, and dry densities. To prevent changes in moisture content due to ambient conditions, only one specimen was prepared at a time and measured immediately after preparation. Three replicate specimens were fabricated for each set of controlled conditions to minimize potential errors. The ambient temperature during the tests was maintained at 25 °C.

2.2.2. Thermal Conductivity Measurement

A Hot Disk Thermal Constants Analyzer (model TPS 2200, Kegonas Instrument Trading (Shanghai) Company Limited, Shanghai, China) was employed for the measurements. The instrument operates on the transient plane source method and uses a type 5501 probe with a measurement range of 0–100 W/(m·K). The instrumental accuracy is better than 5%. Parallel tests were conducted on the same specimen under identical conditions, and the maximum deviation of the average value among replicates was required to be less than 3%. As illustrated in Figure 4, the specimen was placed on the test platform, and the probe was positioned between the specimen and a smooth-surfaced insulating foam block. A 500-g weight was placed on top of the upper foam layer to expel air and ensure good contact. To avoid measurement errors, the assembly was allowed to equilibrate for 5 min to equalize the temperatures of the probe and the specimen. Subsequently, the instrument parameters were set, and the thermal conductivity was measured.

3. Results

3.1. Influence of Dry Density on Thermal Conductivity of Sodium Chloride-Bearing Aeolian Sand

Figure 5 illustrates the variation of thermal conductivity with increasing dry density. Under conditions of constant moisture content and salt content, the thermal conductivity of sodium chloride-bearing aeolian sand exhibited an overall upward trend as dry density increased, indicating a positive correlation between the two parameters. For instance, at a moisture content of 13% and a salt content of 0%, the thermal conductivity increased from 1.117 W/(m·K) to 1.297 W/(m·K) with rising dry density, representing an increase of 0.180 W/(m·K) and a relative increment of 16.11%.

Nevertheless, the curves corresponding to different salt contents present staggered upward trends in each subplot. This phenomenon stems from the combined action of two intrinsic mechanisms. An increase in dry density exerts an approximately linear promoting effect on thermal conductivity by enlarging intergranular contact areas and increasing particle coordination numbers. In comparison, salt content imposes distinctly nonlinear impacts on thermal conductivity. The superposition of these two factors ultimately forms the unique staggered variation pattern of thermal conductivity with rising dry density displayed in the subplots.

3.2. Influence of Moisture Content on Thermal Conductivity of Sodium Chloride-Bearing Aeolian Sand

Figure 6 presents the evolution characteristics of thermal conductivity with increasing moisture content. As can be observed from the figure, the thermal conductivity λ of all specimens increased with rising moisture content W, exhibiting a significant positive correlation between the two variables. For the condition with ρ_d = 1.52 g/cm³ and C = 4%, the thermal conductivity increased from 1.109 W/(m·K) to 1.399 W/(m·K), representing an increment of 0.290 W/(m·K) and a relative increase of 26.15%.

3.3. Influence of Salt Content on Thermal Conductivity of Sodium Chloride-Bearing Aeolian Sand

Figure 7 illustrates the variation of thermal conductivity with increasing salt content. As can be seen from the figure, the thermal conductivity of sodium chloride-bearing aeolian sand exhibited a pronounced nonlinear correlation with salt content. Moreover, the influence of salt content on thermal conductivity was modulated by the moisture content, and the overall trend is characterized by an initial decrease followed by a subsequent increase as salt content rises. The threshold salt content corresponding to the inflection point of this trend gradually shifted to higher values with increasing moisture content. Specifically, the data characteristics are as follows: an inflection point at 2% salt content corresponded to a moisture content of 9%; an inflection point at 4% salt content corresponded to moisture contents of 11–13%; and an inflection point at 6% salt content corresponded to moisture contents of 15–17%.

3.4. Significance Analysis of Influencing Factors

3.4.1. Experimental Method

To quantitatively analyze the degree of influence exerted by dry density, moisture content, and salt content on the thermal conductivity of aeolian sand, an orthogonal experimental design with three factors and five levels was employed. Let A, B, and C denote dry density, moisture content, and salt content, respectively, with thermal conductivity serving as the evaluation index. The levels of each factor are presented in

Table 4. Factors and levels of the orthogonal experiment.

Level	A: Dry Density (g/cm3)	B: Water Content (%)	C: Salt Content (%)
1	1.44	9	0
2	1.46	11	2
3	1.48	13	4
4	1.5	15	6
5	1.52	17	8

.

3.4.2. Range Analysis

An L₂₅(5³) orthogonal array was adopted, and 25 combinations were selected from the 125 sets of experimental data on the thermal conductivity of sodium chloride-bearing aeolian sand for range analysis, as shown in

Table 5. Orthogonal experimental design and corresponding thermal conductivity.

Test Number	A	B	C	Dry Density (g/cm3)	Water Content (%)	Salt Content (%)	Thermal Conductivity (W/(m·K))
1	1	1	1	1.44	9	0	1.063
2	1	2	2	1.44	11	2	1.129
3	1	3	3	1.44	13	4	1.127
4	1	4	4	1.44	15	6	1.204
5	1	5	5	1.44	17	8	1.287
6	2	1	2	1.46	9	2	1.034
7	2	2	3	1.46	11	4	1.071
8	2	3	4	1.46	13	6	1.167
9	2	4	5	1.46	15	8	1.32
10	2	5	1	1.46	17	0	1.369
11	3	1	3	1.48	9	4	1.064
12	3	2	4	1.48	11	6	1.161
13	3	3	5	1.48	13	8	1.2146
14	3	4	1	1.48	15	0	1.343
15	3	5	2	1.48	17	2	1.328
16	4	1	4	1.5	9	6	1.096
17	4	2	5	1.5	11	8	1.178
18	4	3	1	1.5	13	0	1.294
19	4	4	2	1.5	15	2	1.309
20	4	5	3	1.5	17	4	1.33
21	5	1	5	1.52	9	8	1.158
22	5	2	1	1.52	11	0	1.253
23	5	3	2	1.52	13	2	1.247
24	5	4	3	1.52	15	4	1.3
25	5	5	4	1.52	17	6	1.357

.

The results of the range analysis for each factor are presented in

Table 6. Results of range analysis.

Factor	Level 1	Level 2	Level 3	Level 4	Level 5	Range R
A (Dry density) (Ki)	5.81	5.961	6.1106	6.207	6.315	—
A (Dry density) (ki)	1.162	1.1922	1.2221	1.2414	1.263	0.101
B (Water content) (Ki)	5.415	5.792	6.0496	6.476	6.671	—
B (Water content) (ki)	1.083	1.1584	1.2099	1.2952	1.3342	0.2512
C (Salt content) (Ki)	6.322	6.047	5.892	5.985	6.1576	—
C (Salt content) (ki)	1.2644	1.2094	1.1784	1.197	1.2315	0.086

Note: K_i denotes the sum of thermal conductivity values at the *i*-th level of a given factor; k_i denotes the corresponding mean value; and R denotes the range.

. A larger range value indicates a more significant influence of the corresponding factor on the evaluation index. The results show that the ranges for dry density, moisture content, and salt content are 0.1010, 0.2512, and 0.0860, respectively. Accordingly, the order of influence of the three factors on thermal conductivity, from primary to secondary, is as follows: moisture content > dry density > salt content. Among these, moisture content exhibited the largest range, indicating that it is the dominant factor governing the variation in thermal conductivity; dry density ranked second; and salt content exerted the relatively smallest influence. From the average values at each factor level, it can be observed that thermal conductivity generally increases with rising moisture content and dry density, whereas it exhibits a pattern of initial decrease followed by a subsequent increase with increasing salt content. This finding is consistent with the experimental results.

3.5. Predictive Model for Thermal Conductivity of Sodium Chloride-Bearing Aeolian Sand

Based on the aforementioned experimental results, the thermal conductivity of sodium chloride-bearing aeolian sand is jointly governed by three factors: dry density, moisture content, and salt content. Among these, the influences of dry density and moisture content on thermal conductivity generally manifest as a positive enhancement, whereas the effect of salt content exhibits pronounced nonlinear characteristics. To quantitatively characterize the combined influence of these three factors on thermal conductivity and to establish an empirical expression suitable for engineering calculations, multivariate nonlinear regression analysis was performed on the 125 sets of experimental data.

Regarding the selection of the model form, considering that thermal conductivity generally exhibits a monotonically increasing trend with variations in dry density and moisture content, linear terms were adopted to represent the contributions of these two factors. In contrast, the influence of salt content on thermal conductivity displayed a phased fluctuation pattern characterized by an initial decrease followed by a subsequent increase. A purely linear or quadratic function is insufficient to adequately capture such localized undulations. Consequently, a cosine function term was introduced to describe the fluctuating characteristics under the influence of salt content. Accordingly, the fundamental form of the empirical model for the thermal conductivity of sodium chloride-bearing aeolian sand was established as follows:

$$\lambda =\mathit{aG}+\mathit{bW}+\mathit{ccos}(\mathit{dC}+e)+f$$

(1)

where λ is the thermal conductivity of sodium chloride-bearing aeolian sand, W/(m·K); G is the dry density of sodium chloride-bearing aeolian sand, g/cm³; W is the moisture content of sodium chloride-bearing aeolian sand, %; C is the sodium chloride salt content, %; and *a*, *b*, *c*, *d*, *e*, *f* are model parameters. Definitions and units of variables and model parameters are listed in

Table 7. Definitions and units of variables and model parameters.

Symbol	Definition	Unit
λ	Thermal conductivity of NaCl-bearing aeolian sand	W/(m·K)
G	Dry density of the specimen	g/cm3
W	Moisture content of the specimen	%
C	NaCl content of the specimen	%
a, b, c, d, e, f	Empirical fitting coefficients obtained by multivariate nonlinear regression	—

.

Multivariate nonlinear regression analysis of the experimental data yielded the following model parameters: *a* = 1.2308, *b* = 0.0323, *c* = −0.0605, *d* = 2.7288, *e* = 1.8921, and *f* = −0.9971, with a correlation coefficient R² = 0.9674. The prediction accuracy of the model was further evaluated using RMSE, MAE, and MAPE. The calculated RMSE, MAE, and MAPE values were 0.01867, 0.01514, and 1.2545%, respectively, indicating that the proposed model provides high prediction accuracy and good agreement with the experimental measurements. Consequently, Equation (1) becomes:

$$\lambda =1.2308G+0.0323W-0.0605\mathit{cos}(2.7288C+1.8921)-0.9971$$

(2)

Equation (2) thus constitutes the computational model for the thermal conductivity of aeolian sand under the influence of sodium chloride. From the structural perspective of the model, parameters *a* and *b* are both positive, indicating that within the experimental range, increases in dry density and moisture content both contribute to an enhancement of thermal conductivity, which is consistent with the experimental trends described previously. In contrast, the salt content term adopts a cosine function form, signifying that its influence on thermal conductivity is not a simple monotonic variation but rather manifests as a certain phased fluctuation. This behavior aligns with the combined regulatory mechanisms of salt within the pores, including dissolution, ionic interactions, crystallization precipitation, and their effects on partsicle contact states. Therefore, the model not only captures the overall response trend of thermal conductivity to the primary influencing factors but also adequately describes the localized nonlinear characteristics induced by variations in salt content.

Figure 8 presents the fitting relationship curve between the experimentally measured values of the thermal conductivity λ of sodium chloride-bearing aeolian sand and the model-predicted values. All data points are closely distributed on both sides of the identity line *y* = *x*, with no significant dispersion. This result fully validates the rationality and applicability of the established computational model, which can be employed for the quantitative characterization of the thermal conductivity of aeolian sand under the influence of sodium chloride.

To further evaluate the predictive performance of the proposed model, previously published soil thermal conductivity prediction models were compared with the present model, as summarized in

Table 8. Comparison of selected thermal conductivity models.

Paper Title	Soil Type	Model Form	Main Input Variables	Reported R2
Thermal Conductivity Characteristics and Prediction Model of Silty Clay Based on Actively Heated Fiber-Optic FBG Method	Silty clay	λ = λdry + λr (λsat − λdry)	Particle composition, dry density, water content, organic matter content, salt content	0.866
Prediction of the Thermal Conductivity of Freezing Soils Using the Soil Freezing Characteristic Curve	Freezing soils	λ = λsθsλwθwλiθiλaθa	Soil freezing characteristic curve, unfrozen water content, ice content, porosity, quartz content	0.961
Present study	NaCl-bearing aeolian sand	λ = 1.2308G + 0.0323W − 0.0605cos (2.7288C + 1.8921) − 0.9971	Dry density, water content, NaCl content	0.9674

. Hu et al. [10]. modified the Johansen model by incorporating particle composition, dry density, water content, organic matter content, and salt content, obtaining an R² value of 0.866. Bi et al. [26]. established a thermal conductivity prediction model for freezing soils based on the soil freezing characteristic curve and the geometric mean model, with a reported R² value of 0.961. In comparison, the prediction model developed in this study for NaCl-bearing aeolian sand uses dry density, water content, and NaCl content as the main input variables and achieves an R² value of 0.9674, which is higher than those of several existing empirical or semi-empirical models. This result indicates that the proposed model has good predictive accuracy in describing the thermal conductivity variation of NaCl-bearing aeolian sand under the coupled effects of dry density, water content, and salt content.

4. Discussion

To systematically elucidate the multi-factor response mechanism governing the thermal conductivity of sodium chloride-bearing aeolian sand, this section sequentially discusses the individual effects and intrinsic coupling mechanisms of dry density, moisture content, and salt content on thermal conductivity from three perspectives: the optimization of solid-phase heat conduction pathways, the construction of liquid-phase heat conduction channels, and the dissolution–crystallization phase transition of salt.

Increases in dry density significantly enhance soil thermal conductivity through the dual strengthening effects on solid-phase heat conduction pathways. On the one hand, at the microstructural scale, elevated dry density promotes tighter arrangements of soil particles, accompanied by remarkable increases in the effective contact area and coordination number between particles, which establishes a more continuous and efficient conduction network for heat flux transfer within the solid skeleton. Experimental investigations by Yun and Santamarina have verified that the quality of inter-particle contacts and the number of contacts per unit volume jointly dominate heat conduction behavior in dry soils [35]. The continuous rise in soil coordination number with increasing dry density is not merely a direct geometric consequence of reduced porosity; more importantly, it implies that individual particles form more heat-conducting pathways with adjacent particles, enabling heat to bypass originally isolated gas-filled pores and transfer efficiently along continuous solid-phase routes. Meanwhile, enlarged contact areas effectively reduce inter-particle thermal contact resistance, further optimizing the transfer efficiency of solid-phase heat conduction pathways [36]. Fei et al. pointed out that the weighted coordination number, which comprehensively considers particle connectivity and contact area, can more accurately characterize the evolution law of effective thermal conductivity in dry granular materials, revealing the intrinsic regulatory mechanism of dry density on solid-phase heat conduction from the perspective of microstructural parameters [37]. On the other hand, at the macrostructural scale, increased dry density directly reduces porosity. Given that the thermal conductivity of air is only approximately 0.026 W m⁻¹ K⁻¹ under ambient temperature and pressure, far lower than that of soil mineral solid phases (e.g., approximately 7.7 W m⁻¹ K⁻¹ for quartz), the reduction in porosity decreases the volumetric proportion of low-conductivity air medium within soils and weakens the adverse impact of the gas phase on overall heat transfer. Existing studies have demonstrated a strong linear negative correlation between the thermal conductivity of mineral soils and air-filled porosity, whereby the decrease in air-filled porosity directly corresponds to a linear increase in thermal conductivity [38]. Collectively, the significant improvement in soil thermal conductivity induced by increased dry density is ultimately achieved via two synergistic physical mechanisms: the enhanced inter-particle contact heat transfer efficiency of solid particles and the reduced volumetric fraction of the low-conductivity air phase.

Under constant salt content and dry density, the effect of moisture content variation on thermal conductivity can be explained by two competing physical mechanisms, i.e., liquid-phase thermal enhancement and solid-phase attenuation. As moisture content increases, the volumetric fraction of gas phase in soil pores gradually decreases, accompanied by a corresponding rise in liquid-phase proportion, and air is continuously displaced by water and saline solution. At 20 °C, the thermal conductivity of pure water is 0.600 W/(m·K), and the thermal conductivity of sodium chloride solution with a concentration of 0–20% ranges from 0.578 to 0.599 W/(m·K). Both values are far higher than the thermal conductivity of air at ambient temperature, which is 0.026 W/(m·K) [39,40,41]. Pore water inside soil predominantly exists as free water, which easily forms continuous water films and liquid heat conduction channels among soil particles. Therefore, the substitution of gas phase by liquid phase effectively optimizes the inter-particle thermal contact state at the microscopic scale, and liquid bridges form between particles with the growth of moisture content. This conclusion agrees well with the experimental results reported by Deng et al. [42], who verified that soil thermal conductivity increases with rising moisture content under identical salt content and temperature conditions. Water films not only fill the pore space originally occupied by air but also construct liquid heat conduction bridges between adjacent particles. The thermal conduction capacity of these bridges is nearly two orders of magnitude higher than that of air. The inefficient heat transfer relying on point contact is converted into high-efficiency heat transport through continuous liquid medium, thereby remarkably improving the overall thermal conductivity of soil.

On the other hand, elevated moisture content facilitates salt dissolution under high salinity conditions and reduces the content of solid salt crystals, which weakens the heat transfer contribution of solid phase to a certain degree. For example, for aeolian sand with a dry density of 1.52 g/cm³, the thermal conductivity increases by 19.17% at the salt content of 8%, while the growth rate reaches 29.3% at the salt content of 2%, 1.53 times higher than the former. Experimental results indicate that the liquid-phase enhancement effect remains dominant despite the relatively lower growth magnitude of thermal conductivity under high salt content. Accordingly, the thermal conductivity of sodium chloride-containing aeolian sand generally increases with the rise of moisture content.

Experimental results revealed that the thermal conductivity of sodium chloride-containing aeolian sand does not present a monotonic increasing or decreasing trend with the variation of salt content. Instead, it exhibits staged characteristics of initial decline, subsequent slow variation, and final recovery or stabilization under different moisture content conditions. Essentially, this complex heat conduction behavior is governed by the changing occurrence state of salt within soil and its dynamic regulation effect on the microscopic heat transfer network.

In the low salt content range where salt content is below the critical threshold corresponding to each moisture content, salt mainly exists in the form of ions in pore solution. For instance, sodium chloride can be completely dissolved to form an electrolytic solution in specimens with a moisture content of 9% when the salt content is lower than 2%. At 20 °C, the thermal conductivity of pure water is 0.600 W/(m·K), which is higher than that of sodium chloride solution with a concentration ranging from 0% to 20% (0.578–0.599 W/(m·K)) [41]. The conversion of pure water into saline solution reduces the thermal conductivity of pore fluid. Meanwhile, salt dissolution decreases the proportion of solid phase. Combinedly, these two factors lead to the reduction of soil thermal conductivity. Lei et al. [43] systematically investigated the thermal conductivity of fine-grained saline soils and pointed out that the correlation between thermal conductivity and salt content is regulated by moisture content. At the low salt stage, added salt first alters the thermophysical properties of pore solution and further affects thermal conductivity.

When thermal conductivity approaches the inflection point under a certain moisture content, salt begins to transform from a dissolved state to a crystalline state [44]. Taking specimens with a moisture content of 11–13% and salt content around 4% as examples, the salt concentration in pore solution reached the solubility critical point, and sodium chloride microcrystals started to precipitate at particle contact positions or pore throats. The newly generated salt microcrystals partially filled tiny pores and enhanced the mechanical and thermal contact areas between particles, which preliminarily offset the adverse effect caused by the declined thermal performance of pore solution. The slowing changing rate of thermal conductivity at this stage marked the transition of heat conduction mechanism from solution-dominated pattern to solid-participated pattern.

When salt content exceeds the inflection point and enters the high salt stage, salt crystallization is remarkably intensified and gradually forms locally continuous structures. For samples with moisture content of 15–17% and salt content higher than 6%, abundant salt crystals built salt bridges among soil particles and formed additional solid heat conduction pathways. Although high-concentration pore solution still possesses low thermal conductivity, the crystalline network constructed by sodium chloride single crystals with a thermal conductivity of approximately 6.182 W/(m·K) at 20 °C [45] greatly optimizes the overall heat transfer framework. Accordingly, thermal conductivity slowly rises or tends to be stable with the continuous increase of salt content.

The influence mechanism of moisture content on transition threshold is closely associated with the dissolution-crystallization balance of salt. Under high moisture content conditions such as 15–17%, pore water produced a prominent dilution effect on salt, and salt tended to remain dissolved. Thus, a higher salt content of up to 6% is required to reach supersaturation and trigger large-scale crystallization. By contrast, limited pore water volume under low moisture content (e.g., 9%) made salt easily reach solubility limit at a relatively low salt content of 2%, resulting in advanced crystallization phase transition. This phenomenon explains why the transition threshold shifts to a higher salt content level as moisture content increases.

In summary, the evolution of thermal conductivity in sodium chloride-bearing aeolian sand is essentially a dynamic reflection of the trade-off and mutual adaptation among the solid–liquid–gas three-phase heat conduction pathways. An increase in dry density enhances intergranular thermal contact at the solid skeleton level, serving as the fundamental mechanism for improved thermal conductivity. Elevated moisture content induces a dominant thermal enhancement effect by constructing liquid-phase heat conduction bridges. Variations in salt content exert nonlinear influences by regulating the thermophysical properties of pore solution and the structure of salt crystal networks. These three factors do not act in isolation but rather exhibit a coupled effect by modifying the volume fraction and contact morphology of each phase: moisture content modulates the threshold of salt dissolution–crystallization equilibrium, dry density affects the efficiency of salt crystal network formation, and salt content counteracts the thermal performance of the liquid phase—collectively governing the macroscopic thermal conductivity behavior of the soil.

5. Conclusions

This study investigated the variation patterns of the thermal conductivity of sodium chloride-bearing aeolian sand under different dry densities and moisture contents based on the transient plane source method. The following conclusions are drawn:

(1) The thermal conductivity of sodium chloride-bearing aeolian sand increases with rising dry density and moisture content. The enhancement is attributed to an increase in both solid-phase and liquid-phase heat transfer pathways, and the relationship exhibits a favorable linear trend.

(2) The thermal conductivity varies nonlinearly with salt content, exhibiting a pattern of an initial decrease followed by a subsequent increase. The threshold salt content shifts to higher values as moisture content increases: a threshold of 2% salt content corresponds to 9% moisture content; a threshold of 4% salt content corresponds to moisture contents of 11–13%; and a threshold of 6% salt content corresponds to moisture contents of 15–17%. This behavior originates from the fact that salt dissolution reduces the thermal conductivity of the pore solution, whereas subsequent salt crystallization forms thermal bridges that provide a compensating effect on heat transfer.

(3) A theoretical prediction model for the thermal conductivity of sodium chloride-bearing aeolian sand was established. Comparative analysis with measured data validated the good applicability and predictive accuracy of the model. The model provides a quantitative description of the variation of aeolian sand thermal conductivity under multi-factor coupling effects and can serve as a parametric basis for further analysis of the mechanisms of heat conduction in soils subjected to salt influence. Moreover, the model can offer a reference for the determination of thermal parameters and for thermal calculations of replacement materials in the design of roadbeds, foundations, lined canals, and sandy bases of hydraulic structures in saline soil regions, thereby improving the efficiency of thermal conductivity estimation and reducing the workload of repeated testing.

The findings of this study have practical significance for thermal parameter selection and temperature-field analysis of saline aeolian sand foundations in southern Xinjiang. The proposed model can provide parameter support for the thermal design of roadbeds, foundations, lined canals, and hydraulic structures, and it may contribute to the assessment of potential salt expansion risks. However, this study was conducted on remolded specimens under room-temperature laboratory conditions without fully considering the effects of in situ soil structure, seasonal temperature variations, freeze–thaw cycles, and field-scale water–salt migration. Future studies should therefore focus on field-scale validation of the proposed model and further investigate the temperature-dependent thermal conductivity of sodium chloride-bearing aeolian sand, particularly under subzero and freeze–thaw conditions.