## 1 Introduction  
The construction of roads, railways, and municipalities has led to the presence of many exposed slopes. This caused the destruction of ecological diversity, which needs to be restored. The ecological restoration of slopes refers to the process of planting plants to restore the vegetation on those exposed slopes after the treatment of slope reinforcement [1, 2]. The most effective method of ecological rock slope restoration is soil spraying technology. However, determining which soil spraying technology is the most effective for the ecological restoration of rock slopes has been a difficult problem in slope restoration [3, 4, 5]. In areas where rainfall is concentrated and intense, the soil mass sprayed onto the slope is often eroded by rain because of its low slip resistance, leading to a poor ecological restoration effect [6, 7, 8]. To address this problem, many scholars have improved the slip resistance of soil by addingfunctional materials. We propose that the permeability and shear strength are important indexes for characterizing the slip resistance of borrowed soil [9; 10; 11; 12; 13]. Research on soil improvement materials has mainly focused on inorganic and organic materials. Common inorganic materials are lime, fly ash, cement, and slag silicate [14; 15; 16; 17]. These materials improve the soil's slip resistance by absorbing the water in the soil to form cementitious substances. Thus, the slip resistance of the soil is improved. However, the added inorganic materials affect the growth of plants, which is not conducive to ecological restoration [18; 19]. In reference to the organic materials, scholars have used modified carboxymethyl cellulose (M-CMC) for the stability treatment of silt. When the content of M-CMC was within the range of 0-1.3%, the shear strength of silt increased as the content increased, but its permeability decreased [20]. Scholars used xanthan gum biopolymers to treat soil samples, and found that the strength of the soil samples increased, as did their permeability [21]. Scholars have used the chemical stabilizer RBI-81 to strengthen clay and sand soil, thereby effectively improving the mechanical strength of the soil [22]. Other scholars have treated soil samples with polyacrylamide (PAM) polymers, and found that the dry density, plasticity index, unconfined compressive strength, and disintegration resistance of the soil samples were improved [23; 24; 25]. Scholars have also used vinyl acetate polymer to treat soil samples, and found that it enhanced the water-retaining properties, anti-erosion resistance, strength, and durability of soil, and also had a promoting effect on vegetation growth [26]. Moreover, a styrene-acrylic emulsion was used in physical engineering, and the results indicated that the polymer was beneficial in improving the water-damage resistance so that plants could grow for a long time [27]. In addition, polymeric materials form thin films in soil. Some scholars have studied the influence of those films on the soil structure. They found that the thin films increased the elastic stiffness of the material, and they established descriptive formulas [28; 29; 30; 31]. However, these studies were mainly based on experience and lack evidence of the quantitative characterization of the soil mass improvement. Thus, it has remained difficult to conduct quantitative analyses on the improvement effects of restoration efforts in practical engineering applications. In light of the above deficiencies, we used an aqua-dispersing nano-binder (ADNB) to modify the slip resistance of clay in our laboratory research. Through the research results, quantitative characterization models were established. The improvement mechanism was revealed, and accordingly, the optimal addition amount interval was determined. We then verified the modified models' rationality and reliability via an engineering application to solve the problem of determining the addition amount through repeated tests due to the lack of a quantitative characterization model in soil improvement.