Rock Mechanics and Rock Engineering

, Volume 47, Issue 3, pp 869–884 | Cite as

Modelling Discharge Rates and Ground Settlement Induced by Tunnel Excavation

  • G. Preisig
  • A. Dematteis
  • R. Torri
  • N. Monin
  • E. Milnes
  • P. Perrochet
Original Paper


Interception of aquifers by tunnel excavation results in water inflow and leads to drawdown of the water table which may induce ground settlement. In this work, analytical and numerical models are presented which specifically address these groundwater related processes in tunnel excavation. These developed models are compared and their performance as predictive tools is evaluated. Firstly, the water inflow in deep tunnels is treated. It is shown that introducing a reduction factor accounting for the effect of effective stress on hydrodynamic parameters avoids overestimation. This effect can be considered in numerical models using effective stress-dependent parameters. Then, quantification of ground settlement is addressed by a transient analytical solution. These solutions are then successfully applied to the data obtained during the excavation of the La Praz exploratory tunnel in the Western Alps (France), validating their usefulness as predictive tools.


Tunnel excavation Flow rate Ground settlement Effective stress Analytical and numerical modelling La Praz 

List of Symbols

a (m)

Lateral spacing of the aquifer

b (1/m)

Coefficient characterising the elastic resistance of fractures to compression

Cv (1/m)

Aquifer compressibility

d (m)

Distance between the tunnel and the surface via the aquifer

e (m)

Aquifer thickness

Es (Pa)

Aquifer elasticity

g (m/s2)

Gravitational acceleration

h (m)

Pressure head

h0 (m)

Pressure head prior to excavation

H (m)

Hydraulic head

H0 (m)

Hydraulic head prior to excavation

K (m/s)

Hydraulic conductivity

K0 (m/s)

Hydraulic conductivity at no stress

K (m/s)

Hydraulic conductivity tensor

L (m)

Tunnel/sector length

n (−)

Coefficient of asperities length statistical distribution

n (−)

Unit vector normal to the fracture plane

nxnynz (−)

Components of the unit normal vector

p (Pa)

Water pressure

Q (m3/s)

Volumetric discharge rate

Q0 (m3/s)

Volumetric inflow rate without considering effective stress

Qred (m3/s)

Volumetric inflow rate considering effective stress

r (m)

Radial coordinate

r0 (m)

Tunnel radius

s (m)

Water table drawdown

s0 (m)

Drawdown at the tunnel

Ss (1/m)

Specific storage coefficient

Ssm (1/m)

Rock matrix specific storage coefficient

Ssf (1/m)

Fracture specific storage coefficient

Ssf0 (1/m)

Fracture specific storage coefficient at no stress

t (s)


T (m2/s)


v (m/s)

Excavation speed

x (m)

Spatial coordinate

z (m)

Elevation head

Z (m)


α (−)

Reduction factor

αB (−)

Biot-Willis coefficient

\(\Updelta V_z\) (m)

Ground settlement

λ (−)

Ratio of horizontal to vertical stress

ν (−)

Poisson’s ratio

ρw (kg/m3)

Water density

ρr (kg/m3)

Rock mass density

ϕ0 (−)

Porosity at no stress

σ (Pa)


σh (Pa)

Horizontal stress

σv (Pa)

Vertical stress

σ′ (Pa)

Effective stress

σ0′ (Pa)

Fracture closure effective stress


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Copyright information

© Springer-Verlag Wien 2013

Authors and Affiliations

  • G. Preisig
    • 1
  • A. Dematteis
    • 2
  • R. Torri
    • 2
  • N. Monin
    • 3
  • E. Milnes
    • 1
  • P. Perrochet
    • 1
  1. 1.Centre for Hydrogeology and GeothermicsUniversity of NeuchatelNeuchâtelSwitzerland
  2. 2.SEA ConsultingTorinoItaly
  3. 3.Lyon Turin Ferroviaire (LTF)ChambéryFrance

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