# Theoretical Approach to Predicting the Diffusion Radius of Fracture Grouting in Soil-Rock Mixtures
## 1 Introduction
Reference [12] studied fracture and fracture-permeation grouting in weathered granite soils in the Korean Peninsula. Theoretical equations were derived by studying the fracture pressure, fracture length, and thickness, and the effect of grouting pressure on the slurry percolation phenomenon was investigated. Reference [13] studied the diffusion characteristics of grout in soft clay and structured soil through experiments and numerical models. The numerical simulation of slurry diffusion in a single sand layer has been studied [14; 15; 16]. To improve the stability of the tunnel surrounding the rock, references [17; 18] studied the diffusion radius of slurry in gravel and the compressive strength of the soil-rock mixtures under the influence of multiple factors through laboratory experiments. Reference [19] focused on verifying the radial Bingham flow of cementitious grout using a fracture model constructed from acrylic glass. A grout penetrability method based on explicit grout forehead pressure (EGFP) algorithm for joints and cracks in a rock mass was developed in [20]. The diffusion characteristics of slurry in fractured rock have also been well studied [21; 22]. Reference [23] proposed that the flow pattern properties of cement grouts with different water-cement ratios could remain unchanged with time. The characteristics of cement grouting were studied [24; 25]. Reference [26] presented a study on the use of chemical additives to optimize the performance of cement slurry, which significantly improves the quality of grouting. On the properties of cement materials, particular attention was given to the rheological characteristics, namely, the composite transportability while maintaining the specified strength characteristics [27]. To increase the strength characteristics of the created composite, fullerene-astarlene was used as a nanomodified additive [28]. Reference [29] investigated the cement-and-gravel mixture's transportability (rheological characteristics). Activation treatment of composite components or adding some activating additive is one way to improve the quality of the cement-and-gravel mixture [30]. References [27; 29; 30] showed that using finely dispersed fractions in backfill improves the rheological properties of the cement-and-gravel composite and increases its transportation range and permeability. Reference [31] used \"shallow anchor grouting + deep anchor cable grouting\" in combination with a fracture grouting mechanism to reinforce the roadway. Reference [32] proposed a simulation method for the grouting process based on the 3D fracture network model, considering the flow-solid coupling effect. Reference [33] established an analytical model of grouting diffusion for a single rough fracture under constant pressure control based on Bingham fluid's intentional equation. Some scholars have studied soil-rock mixtures' strength parameters and cracking damage characteristics [34; 35]. The shear modulus of the soil-rock mixtures gradually increased with the increase in rock regardless of temperature, and the increment rate of the shear modulus increased rapidly [36]. Reference [37] presented a random generation method of periodic mesostructures of soil-rock mixtures based on the random polygon. An automatic generation method of PFC, similar to a 2D numerical model of soil-rock mixture microstructure, based on digital image processing and experimental simulation were carried out with Matlab [38]. In terms of soil mechanical properties, changes in the degree of saturation can significantly affect the peak strength [39; 40], elastic moduli [41], and Poisson ratio of soil. In summary, most of the injected media involved in the existing research on the mechanism of fracture grouting are crushed stone, gravel, clay, or rock with a single and isotropic material composition. However, in practice, the injected media conditions may be a mixture of various materials, and research on the diffusion mechanism of fracture grouting based on composite geological conditions is limited.