Effects of Muddy Water Infiltration on the Hydraulic Conductivity of Soils

Abstract

Despite the high sand content of Yellow River water in arid Northwest China, locals in the region opt to use muddy water to meet the demand for agricultural irrigation. Muddy water irrigation is a complex process and is still poorly understood. In this study, six sets of saturated soil column infiltration tests were designed, considering soil texture (silt loam, sandy loam, and sand) and muddy water sand content (3%, 6%, 9%, and 12%) as the influencing factors, with two sets of validation tests. Change in hydraulic conductivity (K_h), the average change rate of hydraulic conductivity (ΔK), and cumulative infiltration volume (I) were experimentally studied in the context of muddy water infiltration to respectively establish the separate functional models and developed to fit their relationship with time. The study results indicated that the hydraulic conductivity (K_h) decreased with increasing muddy water infiltration time. For silt loam and sandy loam, K_h stabilized at 0.0030 and 0.0109 cm/min, respectively, after 70 min of infiltration. In contrast, K_h in the saturated sandy soil column significantly declined throughout the muddy water infiltration, showing a 90.84% reduction after 90 min compared to the saturated hydraulic conductivity of the sandy soil. As the sand content of the muddy water increased from 3% to 12%, K_h decreased by 83.99%, 90.90%, 91.92%, and 92.21% for 3%, 6%, 9%, and 12% sand content, respectively, in the saturated sandy soil columns at the end of the infiltration period. The I values were 21.20, 9.29, 7.90, and 6.25 cm for 3%, 6%, 9%, and 12% sand content, respectively. The ΔK values were 0.0037, 0.0041, 0.0043, and 0.0044 cm/min² for the respective sand contents, at an infiltration time of 80 min. The validation test demonstrated that the segmented function model accurately emulated the changes in hydraulic conductivity of sandy soil textures throughout the infiltration period. Results from this study provide a significant basis for understanding the mechanisms to hinder muddy water infiltration and to efficiently utilize muddy water for irrigation.

1. Introduction

Scarce precipitation [1,2,3,4] and acute water scarcity for use in agricultural irrigation [5,6,7,8] in arid Northwest China have constrained local agricultural development. Concentrated rainfall distribution and severe soil erosion in the region [9,10,11,12] have contributed toward making the Yellow River, which flows through the region, the river with the highest sand content in the world [13,14,15,16]. To meet the demand for agricultural irrigation and to make full use of available water resources, some farmers in the region have actively implemented muddy water irrigation. An in-depth study of muddy water infiltration will be of great theoretical value and practical significance for alleviating water scarcity, expanding irrigation yield and improving irrigation quality in areas utilizing muddy water irrigation.

Sediment deposition results in the formation of a dense layer or a physical soil crust on top of a field. A dense soil layer can alter soil structure, enhance soil aeration and porosity, and impact infiltration [17,18,19,20]. Moreover, dense layers can mitigate evaporation from agricultural soil surfaces, thereby decreasing water loss, optimizing water use efficiency, and enhancing crop yields [21,22]. Studies have been carried out to investigate the mechanics of muddy water infiltration [23]. Liu et al. [24] investigated the effects of different initial water contents on cumulative infiltration and nitrogen transport under muddy water conditions; Zhong et al. [25] discovered that the sand content had a noteworthy impact on infiltration, where cumulative infiltration and wetting front transport distance decreased as sand content increased; Nasirian et al. [26] found that using muddy water for field irrigation can prevent deep infiltration.

Hydraulic conductivity is an important hydraulic property of soil that influences various hydrological processes including infiltration, water redistribution, solute transport, and evaporation [27,28,29,30]. Various factors can alter soil structure and influence soil hydraulic conductivity, including tillage, mechanical compaction, organic amendments, and freeze–thaw cycles [31,32,33,34]. Therefore, studying the changing patterns of soil hydraulic conductivity under variable conditions is necessary for understanding soil function. Several new concepts and techniques are being applied to the study of hydraulic conductivity [35,36]. Dong et al. [37] applied organic amendments to soil and found that the saturated hydraulic conductivity was significantly higher in soil treated with straw decomposer than without. Ming et al. [38] found that permafrost water film lowered the hydraulic conductivity by about 20%. Based on the theory of capillary flow, they proposed a new model to predict permafrost hydraulic conductivity that accounted for the flow of the water film. Sun et al. [39] investigated how soil crust changes soil hydraulic conductivity characteristics and found that the saturated hydraulic conductivity of cyanobacteria, cyanobacteria–moss mixture, and moss crusts was 77%, 69%, and 61% less, respectively, than that of bare soil. Further, the relationship between saturated hydraulic conductivity and biological fungal crust permeability in the air-dry state could be fitted well with a positive logarithmic linear model.

Many studies [23,24,25] have been conducted to investigate the infiltration patterns of soil under muddy water irrigation conditions, but few studies have explored the impact of muddy water infiltration on hydraulic conductivity. In sum, this study carried out one-dimensional saturated soil column infiltration tests indoors under muddy water conditions to explore the variation in soil hydraulic conductivity based on different soil textures and muddy water sand contents. The conclusions drawn from this study contribute significantly to the vigorous development of muddy water irrigation.

2. Materials and Methods

2.1. Test Materials

Samples of three different soils with varying textures were utilized in the study. These samples were taken from the topsoil layer (0–30 cm) of agricultural lands located in Xi’an Baqiao (34°18′42″ N, 109°9′1″ E), the northern outskirts of Xi’an in Shaanxi Province (34°24′21″ N, 108°58′25″ E), and Wuzhong in Ningxia Province (38°1′50″ N, 106°12′31″ E). After collection, the air-dried soil specimens were sieved through a mesh (2 mm). The particle size distribution of the soil was analyzed using a Mastersizer 2000 laser particle size analyzer (Malvern Instruments, Malvern, UK), capable of measuring particles ranging from 0.02 to 2000 mm (

Table 1. Properties of test materials.

Material	Particle Composition/%			Texture	Organic Matter/(g·kg−1)	Bulk Density (g·cm−3)
	<0.002 mm	0.002~<0.02 mm	0.02~2 mm
Soil	9.46	53.66	36.88	Silt loam	7.24	1.35
	4.87	21.21	73.92	Sandy loam	7.64	1.40
	1.04	6.50	92.46	Sand	11.86	1.76
Sediment in muddy water	4.22	42.14	53.64

).

The sediment employed for the infiltration test was sourced from the primary canal of the Jinghui irrigation area. This sediment was air-dried, sieved through a 1 mm mesh, and its particle composition was determined using a Mastersizer 2000 laser particle size analyzer (Table 1). Sediment physical and chemical properties were also tested and the results are shown in

Table 2. Physical and chemical properties of sediment.

Item	Sediment Characteristic
	Physical Properties			Chemical Properties
	Median Diameter/mm	Coefficient of Uniformity	Mean Diameter/mm	Na+/ (g·kg−1)	Ca2+/ (g·kg−1)	pH	Organic Matter /(g·kg−1)
Values	0.023	10.41	0.029	0.19	0.05	7.50	4.32

.

2.2. Test Setup and Methods

The necessary amount of sediment and deionized water was measured according to the sand content, then poured into a Markov bottle and stirred thoroughly to provide muddy water. The experiment was conducted in August 2023 at the State Key Laboratory of Eco-hydraulics in the Northwest Arid Region. The setup included a soil column made of plexiglass, with an inner diameter of 5 cm and a height of 13 cm, and a muddy water Markov bottle (Figure 1a). The soil column had a spacer at the bottom with openings for aeration, a pipe nozzle for water collection, and two piezometers to measure the head difference. Prior to testing, the soil layers were filled, reaching a height of 8 cm, with a filter paper at the bottom to prevent soil loss (Figure 1b). After saturating the soil for 12 h, infiltration testing was done.

Markov bottles made of Plexiglas with an inner diameter of 6 cm are used to hold the muddy water. A magnetic stirrer ensures that the sand content is homogenized. The penetration test is initially carried out with fresh water to eliminate interfering factors, followed by muddy water, with the amount of penetrated water measured at regular intervals.

As muddy water infiltrates, fine particles from the sediment enter the saturated soil column, blocking the pore spaces responsible for hydraulic conduction in the soil. Meanwhile, most of the sediment deposits on the soil surface, forming a dense sedimentary layer (Figure 2). These sediment behaviors cause continuous changes in soil hydraulic conductivity, ultimately resulting in a multilayered structural system with significantly different properties along the direction of hydraulic conduction. However, throughout the entire process, the infiltration of muddy water in the saturated soil column still satisfies Darcy’s law [40], i.e., the flow rate is proportional to the hydraulic slope drop:

$$q ={\mathrm{K}}_{\mathrm{h}}iA$$

(1)

where q is the infiltration rate, cm³·min⁻¹; K_h is the hydraulic conductivity of soil, cm·min⁻¹; i is the hydraulic gradient; and A is the cross-sectional area of the soil sample, cm².

Since the K_h varies over time, the total outflow (Q(t)) per unit area after muddy water infiltration at time (T) is:

$$\mathrm{Q}(t)={\int }_0^{\mathrm{T}}{\mathrm{K}}_{\mathrm{h}}i\mathrm{dt}$$

(2)

where Q(t) is the total amount of outflow after moment T min, cm³.

In a small time period (Δt), this can be treated as a steady-flow problem. Therefore, the flow rate per unit area in this small time period (Δt) is [41]:

$$\frac{Q\left(t +\Delta t\right)-Q\left(t\right)}{\Delta t}=q$$

(3)

where Q(t + Δt) is the flow rate at time t, cm³; Q(t) is the flow rate before the time interval, cm³; Δt is the time interval, min; and the ratio of the two is the average flow rate during the time interval, which is approximated as the infiltration flow rate.

2.3. Experimental Design

To determine how muddy water infiltration varies in different soil textures, the test was divided into two parts: (1) Measurement of hydraulic conductivity (K_h) of saturated soil columns with different soil textures under muddy water conditions. The muddy water sand content was set at 6% (S = 6%), and there were three kinds of soil (silt loam, sandy loam, and sand, corresponding to the F1, F2, and T2 treatments, respectively). (2) Measurement of the K_h of saturated soil columns (sandy soil only) with different sand contents under muddy water conditions. Four levels of muddy water sand content were set up (S = 3%, 6%, 9%, and 12%, corresponding to T1, T2, T3, and T4 treatments, respectively), as were two groups of validation tests (S = 4% and 10%, corresponding to the T5 and T6 treatments), and each group was replicated three times. The specific scheme of the testing is shown in

Table 3. Experimental program.

Treatment	Soil Texture	Sand Content/%	Note
F1	Silt loam	6	Soil texture
F2	Sandy loam
T2	Sand
T1	Sandy soil	3	Sand content
T2		6
T3		9
T4		12
T5	Sandy soil	4	Verification tests
T6		10

.

2.4. Analysis of Data

Data processing was performed using Excel 2021 software (Microsoft, Redmond, WA, USA), while SPSS 26 (IBM, Armonk, NY, USA) was used for curve fitting and analyzing data, and Origin 2022 (OriginLab, Northampton, MA, USA) was used for plotting. Significance was tested using one-way ANOVA.

To assess the model’s accuracy, the alignment between the model’s calculated values and the experiment’s measured values was analyzed using the statistical coefficient of determination (R²), root mean square error (RMSE), and the absolute value of relative error (AE). The respective formulas for calculating these are:

$${\mathrm{R}}^2=\frac{{\sum }_{i=1}^n{{(M}_i-{\stackrel{-}{N}}_i)}^2}{{\sum }_{i=1}^n{{(N}_i-{\stackrel{-}{N}}_i)}^2}$$

(4)

$$\mathrm{RMSE}=\sqrt{\frac{1}{n}{\sum }_{i=1}^n{(N_i-M)}^2}$$

(5)

$$\mathrm{AE}=\frac{\left|M-N_i\right|}{N_i} \times 100\%$$

(6)

where n is the number of data points; N_i is the measured value; and M is the model-calculated value. Usually, as R² approaches 1 and both RMSE and AE approach 0, it signifies a closer resemblance between measured and calculated values.

3. Results

3.1. Effect of Soil Texture on Hydraulic Conductivity

Under the muddy water conditions, the hydraulic conductivity of the saturated soil columns changed over time, as shown in Figure 3, and the saturated hydraulic conductivities (K_S) of the three soil types (silt loam, sandy loam, and sand) started at 0.0034, 0.0124, and 0.3823 cm·min⁻¹, respectively. As can be seen in Figure 3, the K_h of the three soils gradually decreased as infiltration proceeded. The K_h of sandy soil had the largest rate of change, with a highly significant decrease (p < 0.01) after 20 min of infiltration. This value was 81.45% lower than that of sand K_S. By this 20 min mark, the silt contained in the muddy water had formed an obvious silt layer on the sandy soil surface, extending the infiltration pathways and retaining some of the silt in the soil column. This silt layer reduced the sandy soil pore space and thus reduced the infiltration capacity. After 20 min, the hydraulic conductivity decreased at a slower rate, reaching 0.0382 cm·min⁻¹ after 90 min. Therefore, the hydraulic conductivity was reduced by 90.84% overall compared with sand K_S.

The K_h of silt loam and sandy loam also decreased at a decelerating pace, but the overall change was gentle. In the first 5 min, the conductivities were reduced by 4.03% and 2.94%, respectively; then, after the first 20 min, they were reduced by 5.88% and 6.45%, respectively, compared with the initial K_S. Both reduction rates were significantly smaller than that of the sandy soil; after 70 min, the K_h of the silt loam and sandy loam no longer changed, and they remained at 0.0030 and 0.0109 cm·min⁻¹, respectively. After 90 min, the silt loam and sandy loam hydraulic conductivities had decreased 11.76% and 12.10% from their respective initial K_S. The results in

Table 4. One-way ANOVA results.

Soil Texture		Average Values/ (cm·min−1)	Coefficients of Variation/%	p-Values of Sources of Variation	Least Significant Difference Values/ (cm·min−1)	Significant Difference
Sandy soil	0 min	0.3823	0.07	0.00 *	0.00100	*
	20 min	0.0709	0.42			*
	30 min	0.0382	1.05			*
Silt loam	0 min	0.0034	1.62	0.00 *	0.00018	*
	20 min	0.0032	0.95			*
	30 min	0.0030	1.17			*
Sandy loam	0 min	0.0124	1.62	0.00 *	0.00003	*
	20 min	0.0116	0.95			*
	30 min	0.0109	1.17			*

Note: The significance of the p-value was tested at the 0.05 level of significance. Multiple comparisons were conducted using the Tukey test, with ‘*’ indicating significance tested at the 0.05 level.

show that the infiltration of turbid water has a significant impact on the permeability of the three soil types at 0 min, 20 min, and 90 min (α = 0.05). Additionally, significant variations are observed across different time points within each soil type (α = 0.05).

3.2. Effect of Muddy Water Sand Content on Hydraulic Conductivity

Changes in the hydraulic conductivity of the saturated sandy soil columns with different sand contents (S) in muddy water are shown in Figure 4. From Figure 4, it is evident that the hydraulic conductivity of each treatment gradually decreased as infiltration continued, and that the hydraulic conductivity (at the identical infiltration duration) decreased as the S increased. In the first 20 min of infiltration, the hydraulic conductivity values shrank rapidly, and the hydraulic conductivity values of each treatment, in order of increasing level of sand content, were 0.1976, 0.0705, 0.0580, and 0.0152 cm·min⁻¹ at 20 min, which were 48.31%, 81.56%, 84.83%, and 87.84% less than the initial K_S of the sandy soil, respectively. This difference indicates that when the muddy water sand content was 3%, the dense layer was slow to form during infiltration, but when the sand content was 6% or greater, the dense layer formed more rapidly on the surface of the soil, thus having a substantial impact on hindering the infiltration of water. Throughout the infiltration duration, the rate of decrease of hydraulic conductivity slowed, and the hydraulic conductivity values of each treatment, in order of increasing level of sand content, were 0.0612, 0.0348, 0.0309, and 0.0298 cm·min⁻¹ at 90 min, which were 83.99%, 90.90%, 91.92%, and 92.21% less than the initial K_S of the sandy soil, respectively. In sum, the values of different treatments began to converge after 90 min of infiltration.

3.3. Simulation Analysis and Verification

Because the change in hydraulic conductivity values varied greatly before and after 20 min of infiltration, a segmented function was employed to accurately model the relationship between hydraulic conductivity change and infiltration duration. The segmentation function used was as follows:

$$K_h=\left\{\begin{array}{ll}a{t}^b,& t\le 20 \mathrm{m}\mathrm{i}\mathrm{n}\\ c\mathrm{l}\mathrm{n}\left(t\right)+d,& t>20 \mathrm{m}\mathrm{i}\mathrm{n}\end{array}\right.$$

(7)

where K_h is the hydraulic conductivity, cm·min⁻¹; a and b are the fitting coefficients and fitting indices before 20 min, respectively; and c and d are the fitting coefficients and fitting intercepts after 20 min, respectively.

The results of fitting the hydraulic conductivity values over the infiltration duration are shown in

Table 5. Fitting parameters of hydraulic conductivity and infiltration duration for each treatment.

Treatment	Sand Content/%	a	b	R2	RMSE	c	d	R2	RMSE
T1	3	0.4005	−0.1965	0.9150	0.7764	−0.0848	0.4430	0.9856	0.0300
T2	6	0.3951	−0.6102	0.9800	0.2129	−0.0214	0.1302	0.9794	0.0016
T3	9	0.3716	−0.7390	0.9445	0.1472	−0.0193	0.1176	0.9910	0.0006
T4	12	0.3705	−0.8182	0.9577	0.1256	−0.0090	0.0677	0.9042	0.0001

Note: The fitting process for a and b used the portion of Equation (7) where t ≤ 20 min, while c and d used the portion of Equation (7) where t > 20 min.

. Here, R² was above 0.90, and the RMSE value was below 0.8 cm·min⁻¹, which indicates that the fitting effect was good and that the segmented function model performed well in simulating the change in hydraulic conductivity values in accordance with infiltration duration.

Throughout Table 5, the fitting parameters change very obviously with the sand content. In a certain range, the fitting parameters a, b, and d gradually decreased as sand content gradually increased, while the fitting coefficient c gradually increased after 20 min. Specifically, the sand content S increased from 3 to 12%, and the fitting coefficient decreased from 0.4005 to 0.3705 before 30 min, the fitting index decreased from −0.1965 to −0.6480 before 20 min, the fitting intercept decreased from 0.4430 to 0.0677 after 20 min, and the fitting coefficient increased from −0.0848 to −0.0090 after 20 min. The b and c fitting result values were less than 0, and the absolute values were recorded for the convenience of research. Analysis revealed that the relationships between a and |b| and sand content S conformed to the exponential and linear functions, respectively, while the fittings of |c| and d to the exponential relationship conformed to the power function relationship. As follows, the functional relationship was derived according to the process of variation of each fitted parameter with sand content S (

Table 6. Relationship of each fitting parameters as a function of sand content.

Fitting Parameter	Fitting Function	R2	RMSE
a	$a=0.4136{\mathrm{e}}^{-0.0100S}$	0.8832	0.0054
b	$\left|b\right|=0.0665S+0.0925$	0.8661	0.1012
c	$\left|c\right|=0.4138S^{-1.5110}$	0.9802	0.0056
d	$d=1.6604S^{-1.2830}$	0.9749	0.0320

).

Substituting the function model of the fitted parameters obtained from Table 4 into Equation (6), the model of hydraulic conductivity versus infiltration duration t and sand content S under different conditions of muddy water sand content was obtained as follows:

$$K_h=\left\{\begin{array}{ll}0.4136{\mathrm{e}}^{-0.0100S}{t}^{-0.0665S-0.0925},& t\le 20 \mathrm{m}\mathrm{i}\mathrm{n}\\ -0.4138S^{-1.5110}\mathrm{l}\mathrm{n}\left(t\right)+1.6604S^{-1.2830},& t>20 \mathrm{m}\mathrm{i}\mathrm{n}\end{array}\right.$$

(8)

The reliability of Equation (8) was verified by tests T5 and T6. The measured values of the tests and the calculated values of the model were compared and analyzed, and the results are shown in Figure 5. In Figure 5, the maximum AE between the model (Equation (8)) and the measured values were 12.54% and 9.50% (less than 15%), and the RMSEs were 0.0015 and 0.0008 cm·min⁻¹ (T5 and T6), with a small overall error (less than 0.0020 cm·min⁻¹). This indicates that the developed model effectively described the relationship of hydraulic conductivity K_h with infiltration duration t and with sand content S.

3.4. Effect of Muddy Water Sand Content on the Average Rate of Change of Hydraulic Conductivity

To explore the hydraulic conductivity dynamics more effectively, the average rate of change of hydraulic conductivity (ΔK) was investigated. The ΔK was defined as follows:

$$\Delta K=\frac{K_S-K_h}{t}$$

(9)

where ΔK is the average rate of change of hydraulic conductivity, cm·min⁻²; and K_h is the value of hydraulic conductivity at the moment t. The greater the magnitude of ΔK, the more pronounced the change of hydraulic conductivity K_h.

Figure 6 shows the trend of the ΔK in accordance with infiltration duration. The ΔK gradually decreased as infiltration duration increased. In contrast, the ΔK increased as sand content increased, relative to the same infiltration duration. After 10 min of infiltration, the ΔK of each treatment (T1, T2, T3, and T4) were 0.0119, 0.0285, 0.0304, and 0.0314 cm·min⁻², respectively. After 80 min of infiltration, the ΔK of each treatment basically stabilized, and the ΔK were 0.0037, 0.0041, 0.0043, and 0.0044 cm·min⁻², respectively. At this time, the values of the ΔK were very similar across all treatments.

After analysis, the average rate of change of hydraulic conductivity at different sand contents showed a highly significant power function relationship with infiltration duration. The power function used was as follows:

$$\Delta K =p{t}^q$$

(10)

where p and q are the fitting coefficient and fitting exponent of ΔK, respectively. The data shown in Figure 6 were fitted to Equation (10), and Table 5 shows the results of the specific fitting parameters of Equation (10). As can be observed from

Table 7. Fitting parameters of change in average rate of change of hydraulic conductivity (ΔK) and infiltration duration (t) for each treatment.

Treatment	Sand Content/%	p	q	R2	RMSE
T1	3	0.0348	−0.4740	0.9763	0.0007
T2	6	0.1968	−0.8610	0.9842	0.0027
T3	9	0.2200	−0.8820	0.9315	0.0079
T4	12	0.2272	−0.8840	0.9495	0.0075

, the R² exceeded 0.9, and the RMSE was under 0.0080 cm·min⁻², both of which are good fitting results and indicate that the correlation with the power function model (Equation (10)) was significant.

In addition, the fitting coefficient of the average rate of change of hydraulic conductivity p gradually increased as sand content increased, and the sand content increased from 3% to 12%, while p increased from 0.0348 to 0.2272. At the same time, the fitting exponent q showed the opposite rule of change, with q decreasing from −0.4740 to −0.8840. The power function is known to be affected more by p than by q in the early stage, but when the infiltration duration t is large enough, the power function value is influenced increasingly by q. When the soil column water conductivity capacity was at its maximum, the saturated soil column surface did not have a dense layer. Therefore, when the muddy water first entered the soil column, the muddy water infiltration water flux peaked, and the sediment rapidly formed a dense layer on the surface of the soil column. The greater the sand content, the faster this process became and the larger the average change in hydraulic conductivity was, thus corresponding to the larger p-value. The thickness of the dense layer increased as muddy water infiltration continued, and the values of the average rate of change of hydraulic conductivity converged under different treatments as the values of hydraulic conductivity decreased and also converged.

3.5. Effect of Muddy Water Sand Content on Cumulative Infiltration

Cumulative infiltration (I) is defined as the total amount of water that has infiltrated into the soil per unit area of the surface at a given time after infiltration begins. The I volume of each treatment varied with time, as shown in Figure 7. At the onset of infiltration, the K_h was large, and so the I increased rapidly. This was especially true in the T1 treatment where the muddy water had low sand content, and the resulting dense layer had a weak influence on the K_h. During continued infiltration, sediment from the muddy water continuously accumulated onto the soil column’s surface, gradually thickening the dense layer. This layer subsequently acted as a barrier to water, leading to a reduction in infiltration rate. The I decreased as muddy water sand content increased. When the infiltration duration reached 90 min, the I of the T1, T4, T5, and T6 treatments were 21.20, 9.29, 7.90, and 6.25 cm, respectively, the latter of which were 56.18%, 62.74%, and 70.52% less than that of the T1 treatment, respectively. This indicates that the presence of a dense layer enhances the infiltration reduction effect and thereby greatly reduces the cumulative infiltration volume under different treatments of muddy water sand content, thus effectively preventing water infiltration to a certain extent. The greater the S of muddy water, the more obvious the seepage reduction effect and the smaller the cumulative infiltration amount.

Cumulative infiltration (I) and infiltration duration (t) were compared between different treatments, and a power function was found to describe the relationship [42]:

$$I=\alpha t^{\beta }$$

(11)

where α and β are the cumulative infiltration fit coefficient and cumulative infiltration fit index, respectively.

Table 8. Fitting parameters of cumulative infiltration and infiltration duration for each treatment.

Treatment	Sand Content/%	α	β	R2	RMSE
T1	3	0.8810	0.7394	0.9859	0.9884
T2	6	0.6432	0.6230	0.9521	0.4972
T3	9	0.6327	0.5564	0.9893	0.0758
T4	12	0.5441	0.5426	0.9881	0.0723

shows the fitting results of the power function relationship between I and t for different treatments. The R² exceeds 0.9, and the RMSE is below 1, which indicates that the fitting results are good and that the power function accurately captures the relationship between I and t. As the sand content increased from 3% to 12%, the fitting coefficient of cumulative infiltration α in the power function model decreased from 0.8810 to 0.5441, and the fitting exponent of cumulative infiltration β decreased from 0.7394 to 0.5426, respectively.

4. Discussion

This paper investigated the effect of muddy water sand content on hydraulic conductivity and the variation in cumulative infiltration volume under different sand contents by running an infiltration test of saturated soil columns under muddy water conditions. The K_h of soil is affected by pore morphology, soil structure, and other factors [42,43,44,45]. Unlike unsaturated flow, which is affected by capillarity and adsorption [46,47], soil hydraulic conductivity tends to be a constant value under saturation. In this study, as slurry water continued to infiltrate, a dense layer formed at the top boundary of the soil column, leading to a decrease in K_h from 0.3823 to 0.0382 cm/min (S = 6%) after 90 min. Soil crusts usually create a dense surface structure, reducing surface-layer porosity and consequently affecting hydraulic conductivity [48]. When crusts form on the soil surface, hydraulic conductivity changes [39,49]. Wang et al. [50] found that the saturated hydraulic conductivity of soil covered with biocrusts was reduced by 66% compared to bare soil.

As the sand content in the muddy water increased, the K_h of the sandy soil decreased to 0.1976, 0.0705, 0.0580, and 0.0152 cm/min at 20 min (with sand contents of 3%, 6%, 9%, and 12%, respectively). Generally, soil crusting induced by rainfall reduces hydraulic conductivity. Zambon et al. [51] found that soil crusts formed under high rainfall intensities (>56.7 mm·h⁻¹) exhibit lower hydraulic conductivity compared to those formed under low rainfall intensities (<56.7 mm·h⁻¹), influenced by factors such as crust thickness and porosity. These findings parallel the effects observed with varying sand content in muddy water on hydraulic conductivity.

There were variations in hydraulic conductivity changes during muddy water infiltration across different soil textures. In sandy soil, K_h decreased by 90.84% compared to K_S after 90 min of infiltration, whereas in sandy loam and silt loam, the decrease was only 11.76% and 12.10%, respectively. Research indicates that crusts exert different impacts on various soil textures [52]. Qiu et al. [52] observed that biological crusts had a more significant effect on soil hydraulic conductivity in sandy soils compared to loamy soils. In sandy soils covered by cyanobacteria, cyanobacteria–moss mixtures, and moss crusts, K_S decreased notably, whereas in loamy soils, the reductions were 49.0%, 68.7%, and 36.0%, respectively.

In the case of muddy water infiltration, as S increases, the K_h of sandy soil continuously decreases. At 90 min, the I values were 21.20, 9.29, 7.90, and 6.25 cm for sand contents of 3%, 6%, 9%, and 12%, respectively. The infiltration rate decreased with the duration of infiltration, a trend akin to the infiltration of muddy water under unsaturated conditions [25]. Liu et al. [24] demonstrated that the power function model effectively simulates the infiltration process of unsaturated muddy water. Similarly, in this study, the power function model proves highly suitable for simulating the infiltration process of saturated sandy soil columns under muddy water conditions.

This study is based on results from indoor saturated soil column infiltration tests with muddy water, which have inherent limitations compared to field conditions. Moreover, natural water infiltration processes involve more intricate unsaturated soil dynamics, necessitating further validation of the applicability of the findings from this study to such conditions.

5. Conclusions

In this study, saturated soil column muddy water infiltration tests were conducted to investigate the effects of soil texture (silt loam, sandy loam, and sandy soil) and muddy water sand content on soil hydraulic conductivity characteristics, and the following key conclusions were drawn:

(1) After 70 min of muddy water infiltration, the hydraulic conductivity (K_h) values of the silt loam and sandy loam decreased to 0.0030 and 0.0109 cm·min⁻¹, respectively, and then stabilized. In contrast, the K_h of the sandy soil continued to decrease over time, albeit at a slowing rate.

(2) The K_h of the saturated sandy soil columns with different muddy water sand contents decreased as infiltration duration increased. At the same infiltration durations, K_h decreased with increasing muddy water sand content (S). In the first 20 min of infiltration, the K_h of each treatment decreased rapidly, and then the rate of change of K_h was reduced after 20 min. At 90 min of infiltration duration, the K_h values of each treatment began to converge.

(3) Segmented functions of power and logarithmic functions were used to fit the process of sand hydraulic conductivity values with infiltration duration for the first 20 min and for 20–90 min, respectively. Validation of the segmented function model used treatments with muddy water sand contents of 5% and 10%, respectively. The validation results demonstrate that the model has high reliability and accuracy.

(4) In the case of sand, the average rate of change of hydraulic conductivity (ΔK) of each treatment gradually decreased as infiltration duration increased, and the higher the S of muddy water, the higher the ΔK at a particular infiltration duration. The rates of change of hydraulic conductivity converged after 80 min. The ΔK showed a highly significant power function relationship at different sand contents and infiltration durations.

(5) The cumulative infiltration of the saturated sandy soil column increases over time, though the rate of increase diminishes. Cumulative infiltration and infiltration duration had a power function relationship. As the S increased, both the fitting coefficient of cumulative infiltration α and the fitting exponent of cumulative infiltration β of the power function model decreased. This study contributes to the development and application of muddy water irrigation theory.