## 5 Conclusions  
The following conclusions can be drawn from this paper's analysis of the deformation-mechanical response during triaxial shear tests of granite residual soil and improved soil mixed with fly ash, as well as from the examination of variable head infiltration tests, microstructural observations and finite-element numerical simulations of granite residual soil backfilled slopes:  
1. Fly ash may be effectively added to granite residual soil to increase its shear strength. There may be an optimal amount of fly ash inclusion because the cohesiveness and internal friction angle of the soil body also first increase and then decrease. The granite residual soil boosted by fly ash had a cohesiveness of 38.51 kPa and an internal friction angle of 22.15\({}^{\circ}\) at a dose of 15% fly ash, which are greater than those of thevegetative soil by 213.6% and 14.12%, respectively. Fly ash primarily strengthens soil cohesiveness, which counteracts the increase in the angle of internal friction to increase the shear strength of granite residual soil. Upon fly ash addition, the permeability coefficient of the granite residual soil dramatically decreased; nevertheless, the permeability coefficients of the granite residual soil with varying quantities of fly ash did not significantly differ from one another. Fly ash effectively increases the durability of residual granite soils against erosion from rainfall. 2. Fly ash is used to improve the granite residual soil mechanism because the amount of granite residual soil particles between the gaps is too large, the interaction force between the particles is small and small particles in the fly ash used to fill the gaps can be uniformly distributed in the soil body between the gaps and generate flocculent or mesh structures in the crystalline material to enhance the interaction of the soil particles with the soil body to improve the shear strength of the soil body. The gelling material produced by the interaction of fly ash filling soil pores simultaneously reduces the permeability of the granite residual soil and the pore channels within the soil. Within a limited range, fly ash can be added to the soil to increase its strength; however, once the dose reaches its maximum, the fly ash fills the soil pores entirely. Further fly ash addition will not significantly improve the strength of the granite residual soil; rather, it will erode the skeleton of the soil and decrease its shear strength. 3. Under rainfall conditions, the displacement of granite residual soil slopes decreased after the incorporation of fly ash, and the displacement area changed from being concentrated in the fill area to a distribution that extended toward the excavated soil. Compared with those of vegetative soil slopes, plasticity cloud maps of improved soil slopes show a shift from a circular plastic zone running through the slope to the zone that extends toward the interior of the slope with values that are one order of magnitude lower. Under rainfall conditions, the safety factor of the fly ash-containing granite residual soil was much greater than that of regular backfill. This is due to the filling of the soil gaps with fly ash mixed into the granite residual soil. This filling considerably lowers the permeability coefficient and increases the shear strength of the granite residual soil, lowering the possibility that it will disintegrate in the event of rain. To fortify backfilled slopes, it is advised to add the necessary amount of fly ash when backfilling granite residual soil. Conceptualization, B.H. and Q.H. ; methodology, B.H. ; writing--original draft, B.H. ; resources, G.T. ; review and editing, G.T. ; funding acquisition, Y.L. ; visualization, Y.L. All authors have read and agreed to the published version of the manuscript. National Natural Science Foundation of China: 52078195; General Program of National Natural Science Foundation of China: U22A20232. Not applicable. Data Availability Statement: Data will be made available upon request.