## 1 Introduction  
Over the last two decades, the swift advancement of urbanization in China has propelled the rapid growth of the regional economy while concurrently giving rise to severe urban environmental pollution. As a typical inorganic pollutant, heavy metal pollution has a varied geographical distribution in China due to factors such as the level of economic development, industrialization, and distribution of mineral resources. As shown in Figure 1, compared with the eastern and western regions, the central region of China has a larger number of metal mines and coal mines, and the level of industrialization is more developed, so soil heavy metal pollution is more prominent and the rate of soil heavy metal pollution accounts for about 34.23% of the total pollution rate [1]. In 2014, the Ministry of Environmental Protection and the Ministry of Land and Resources released the National Soil Pollution Survey Communique that explicitly stated that the Yangtze River Delta, Pearl River Delta, and Northeast China's mature industrial bases had, due to inadequate control measures and unregulated discharges, substantially surpassed the permissible levels for inorganic pollutants, notably heavy metals [2]. Currently, heavy metals have emerged as the primary contaminants influencing soil environmental quality in China. Residual heavy metals generated from industrial and domestic activities integrate with the soil matrix through processes such as self-diffusion, precipitation, and adsorption, culminating in soil corrosion, structural degradation, and alterations in physical and mechanical properties. These transformations exert an adverse influence on the quality of regional engineering construction [3]. To enhance the guidance of engineering practices, it is imperative to investigate the characteristics of soil contaminated with heavy metals. The exploration of contaminated soil commenced with the inaugural International Contaminated Soil Conference held in the Netherlands in 1985. Subsequently, numerous institutions embarked on research endeavors concerning contaminated soil. In contrast, the investigation of contaminated soil in China commenced at a later date, only gaining momentum in the 1980s when Tongji University initiated comprehensive research on the migration patterns of pollutants in soil [4]. At present, there are many branches of research on contaminated soil, and scholars at home and abroad have drawn a large number of conclusions. [PERSON] et al. [5] found that the introduction of tin tailings results in a decrease in the liquid limit of the soil matrix, with the plasticity index exhibiting an incremental trend corresponding to the quantity of tin tailings incorporated. Concurrently, tin tailings exert an influence on the permeability and undrained strength characteristics of the soil mass. [PERSON] et al. [6] found that the introduction of heavy metal ions led to a reduction in the clay particle content within contaminated loess. [PERSON] et al. [7] found that the introduction of Zn\({}^{2+}\) into soil resulted in an increase in both soil particle size and the pore size between soil particles. [PERSON] et al. [8] studied the permeability of expanded soil after Cu\({}^{2+}\) immersion and found that the permeability coefficient of contaminated soil showed a trend of first decreasing and then increasing with the increase in Cu\({}^{2+}\) ion concentration. [PERSON] et al. [9] found that the increase in heavy metal ion concentration increased the permeability coefficient of contaminated soil while reducing its unconfined compressive strength. [PERSON] et al. [10] showed that the increase in heavy metal pollution concentration in test soil led to the decrease in unconfined compressive strength, the decrease in clay content, and the increase in soluble salt content. [PERSON] et al. [11] found that the compressibility of heavy metal-contaminated expansive soil increased with the increase in heavy metal ion concentration through consolidation testing under cyclic loading. [PERSON] et al.