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 (Kh), 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 (Kh) decreased with increasing muddy water infiltration time. For silt loam and sandy loam, Kh stabilized at 0.0030 and 0.0109 cm/min, respectively, after 70 min of infiltration. In contrast, Kh 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%, Kh 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.