## 7 Conclusions  
Through systematic laboratory experiments, this study investigated the effects of fine particle ratio, grouting pressure, and water-cement ratio on three key performance parameters of self-drilling anchors in sandy pebble strata: peak pull-out force, ultimate displacement, and anchor diameter. Furthermore, employing PFC-based discrete element numerical simulations of the self-drilling anchor grouting process, we examined how grouting pressure, drilling speed, and slurry viscosity influence the slurry diffusion radius. The main findings of this investigation are summarized as follows:  
1. The orthogonal test results revealed the following order of influencing factors on peak pull-out force: fine particle ratio > water-cement ratio > grouting pressure. A similar dominance pattern was observed for ultimate displacement and anchorage body diameter: fine particle ratio > grouting pressure > water-cement ratio. Through optimization of water-cement ratio and grouting pressure according to particle size gradation in sandy pebble strata, the stability of self-drilling anchor bolts can be substantially improved. 2. The peak pull-out force exhibits three distinct characteristic relationships with the investigated parameters: it decreases monotonically with increasing fine particle content; it demonstrates a convex relationship with grouting pressure, initially decreasing before reaching a minimum value and subsequently increasing; and it follows a threshold-dependent behavior with respect to water-cement ratio, showing an increasing trend below a critical ratio but decreasing progressively when this threshold is exceeded. 3. The slurry diffusion radius of self-drilling bolts exhibits distinct relationships with three key parameters: it increases proportionally with grouting pressure while decreasing with both drilling speed and slurry viscosity. Among these factors, sensitivity analysis reveals slurry viscosity as the most influential parameter, followed by grouting pressure, with drilling speed demonstrating the least impact. Based on these observed relationships, we establish that the diffusion radius follows a power-law function of grouting pressure, drilling speed, and slurry viscosity, from which we derive the following empirical formula. 4. The overall diffusion form of the slurry is large in the upper part and gradually decreases along the drilling direction, but the slurry is mainly concentrated in the outlet area. The slurry diffusion radius will increase with the increase of grouting pressure, but the rate of increase will gradually decrease. When the drilling speed is 0.5 m/min, the slurry diffusion radius is the smallest, which is 32.7 cm. When the drilling speed decreases to 0.3 m/min, the slurry diffusion radius increases to 52.6 cm, an increase of 60.9%. When the drilling speed decreases from 0.3 m/min to 0.1 m/min, the slurry diffusion radius increases to 95.9 cm, an increase of 82.3%. When the slurry viscosity increases from 83.3 mPa-s to 833.3 mPa-s, the slurry diffusion radius decreases by 72%. This study investigates the grouting diffusion characteristics and anchoring performance of self-drilling anchors in sandy cobble strata through laboratory pull-out tests and the development of a grouting model. While the experimental procedures and modeling approach were designed to closely simulate actual construction processes of self-drilling anchors, certain idealized assumptions were necessarily incorporated, which may introduce some discrepancies compared to real-world field conditions. Prior to this investigation, field tests were conducted to examine the anchoring performance of self-drilling anchors in sandy cobble strata. Future research will comprehensively account for natural environmental factors affecting slurry diffusion and anchoring behavior, with particular emphasis on the unique characteristics of self-drilling anchors and their practical engineering applications. Conceptualization, X.G. and C.W. ; methodology, X.G. and C.W. ; software, M.Z. ; validation, X.G., M.Z. and C.W.