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Analytical solution for estimating groundwater inflow into lined tunnels considering waterproofing and drainage systems

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Abstract

When estimating groundwater inflow into lined tunnels in water-rich regions, waterproofing and drainage systems (WDS) are usually ignored or not fully considered in existing analytical solutions. In this study, a water drainage seepage model considering drainage pipes, waterproof membranes, and geotextiles was developed. An analytical solution was then derived to predict groundwater inflow into composite-lined tunnels. The proposed analytical solution can be reduced to Goodman’s solution for an unlined tunnel. When only the initial lining was considered, the difference between the proposed analytical solution and Wang’s solution (Tunn Undergr Sp Tech 23(5):552–560, 2008) was less than 0.5%. Subsequently, the proposed analytical solution was further verified using a numerical model and good agreement between both models was observed. Finally, the relationships between groundwater inflow and the parameters of composite linings were investigated. The results of this study suggest the following: (1) groundwater inflow significantly decreases with an increase in the distance between two circular drainage pipes; (2) the higher the rock permeability, the more significant the WDS effect on groundwater inflow; and (3) when the rock permeability exceeds 1 × 10−6 m/s, WDS effects should be considered in the design of WDS. The results of this study are helpful for the optimal design of WDS for tunnels, such as the estimation of the initial lining permeability and thickness, distance between circular drainage pipes, and geotextile hydraulic conductivity. Additionally, the application of the proposed solution could provide a basis for analyzing potential adverse environmental impacts caused by tunnel drainage.

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Abbreviations

r 0 :

Inner radius of the secondary lining (m)

r 1 :

Outer radius of the secondary lining (m)

r 2 :

The outer radius of the initial lining (m)

r 3 :

Radius of the affected zone by the drainage

h 2 :

Water head around the outside of the initial lining (m)

h c :

Water head at the geotextile (m)

H :

Water head outside of the affected drainage zone in the surrounding rock (m)

h m :

Water head in the middle of the two adjacent circular drainage pipes (m)

q :

Velocity of groundwater flowing into the circular drainage pipe from the geotextile

k 1 :

Permeability coefficients of the initial lining (m)

k r :

Permeability coefficients of surrounding rock (m/s)

L 1 :

Distance between the two adjacent circular frainage pipes (m)

k t :

Permeability coefficients of the geotextile (m/s)

t :

Geotextile thickness (m)

T :

Thickness of initial lining, r2-r1 (m)

D :

Diameter of the circular frainage pipe (m)

μ :

The drain coefficient

Q :

Groundwater inflow into the tunnel (m3/d m)

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Funding

This study was supported by the National Natural Science Foundation of China (Grant No. 41877246), Department of Transport of Yunnan Province (Grant No. [2019]36). The authors greatly appreciate the support provided.

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Authors and Affiliations

  1. College of Civil Engineering, Tongji University, 1239 Siping Road, Shanghai, 210098, China

    Jinghui Liu & Xiaojun Li

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  1. Jinghui Liu
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Correspondence to Xiaojun Li.

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Highlights

• An analytical solution for estimating groundwater inflow into lined tunnel considering waterproofing and drainage system (WDS) is proposed.

• The components of the waterproofing and drainage systems (waterproof membranes, geotextile, and blind pipes) could be consider.

• The proposed analytical solution is applied to analyze the WDS effect on the groundwater inflow into the tunnel.

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Liu, J., Li, X. Analytical solution for estimating groundwater inflow into lined tunnels considering waterproofing and drainage systems. Bull Eng Geol Environ 80, 6827–6839 (2021). https://doi.org/10.1007/s10064-021-02378-0

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