## 1 Introduction  
For deep-buried mountain tunnels in rich water areas, if design or construction is improper, groundwater will continue to pour into a tunnel throughout its construction and operation period, destroying the surface environment and affecting the durability and stability of the tunnel structure [1, 2, 3, 4, 5].Considering factors such as structural safety and ecological environment, tunnels in high water level areas mostly adopt the waterproofing and drainage design criteria of \"mainly blockage, limited discharge\" [6, 7, 8]. Presently, the prediction of tunnel water inflow and the calculation of structural external water pressure are very important for the design of waterproofing and drainage of deep-buried mountain tunnels in high water level areas. The permeability coefficient is an important factor that affects prediction accuracy. Surrounding rock is often heterogeneous due to the coupling of ground stress and excavation disturbances; therefore, studying the influence of surrounding rock heterogeneity on tunnel water inrush has important theoretical significance and engineering application value.  
The literature [9, 10, 11, 12, 13, 14, 15, 16] regards the permeability coefficient of surrounding rock as a fixed value, and has deduced the calculation formula of tunnel water inflow, analyzed the water blocking mechanism of a grouting circle, and provided a theoretical basis for the design of the grouting circle. In the research on the influence of the heterogeneity of surrounding rock on water inrush in a tunnel, Reference [17] considered the water gushing condition of a tunnel when complex hydrogeology is involved. The authors of [18]calculated the influence of changes in hydraulic conductivity on the calculation of inrush water. Reference [19] derived a calculation formula of water inflow for underwater tunnels based on the constructed water inflow calculation model. The authors of [20] analyzed the damage of surrounding rock induced by engineering disturbances and their influence on the permeability of rock mass. Assuming that the permeability coefficient of a damage zone is a fixed value, the influence of the change in the surrounding rock structure on tunnel water inrush and external water pressure were studied using a theoretical analysis method.  
In summary, scholars have conducted extensive research on the prediction of water inflow and external water pressure, but the prediction methods are all based on the premise of homogeneous or layered homogeneity of the surrounding rock. In actual engineering, the permeability coefficient of surrounding rock is often affected by excavation disturbance and ground stress, and presents heterogeneity, it also changes gradually with spatial position coordinates. Based on this, this paper considers the spatial dispersion of the permeability coefficient of surrounding rock with the influence of depth and excavation disturbance, and constructs a one-dimensional seepage calculation model in the vertical section. The calculation formula for the water inflow and the structural head was derived and carried out for degradation verification, in order to make meaningful attempts to supplement the prediction and calculation methods of the water inflow and the external water pressure of the structure.