EPB Face Pressure Lab

What is modelled

An earth pressure balance machine keeps the excavated soil in a pressurised chamber behind the cutterhead. A screw conveyor removes the soil at exactly the rate it arrives, and the chamber pressure must lie between the active earth pressure, below which the face fails, and the passive pressure, above which the ground heaves. If the pressure is below the at-rest value the ground relaxes and a settlement trough forms over the tunnel.

Equations

• Effective stress σ'v = σv − u, with u = γw (z − zw) below the water table.
• Active σa = Ka σ'v − 2c √Ka + u, at rest K0 σ'v + u, passive Kp σ'v + 2c √Kp + u, with Ka = tan2(45° − φ/2) and K0 = 1 − sinφ.
• Chamber dp/dt = (Kb/Vc)(Qin − Qout) with a proportional screw controller.
• Peck trough S(x) = Smax exp(−x2/2i2), Smax = Vs / (i √(2π)), i = K z0.

Checks run in the page

• The active limit found by turning the Mohr circle against the Coulomb line.
• The trough area equals the lost volume and its inflection point is at x = i.
• The integrated chamber pressure settles where the closed form says.
• Stresses summed in thin layers match the closed-form profile with the water table.

Honest simplifications

The soil is one uniform drained layer with a straight pressure line, the face is treated as a plane, the chamber is one compressible volume, and the link between pressure deficit and volume loss is an illustrative empirical rule and not a prediction for a real site. Real design uses site investigation and monitoring.

• Press Pressure too low and watch the volume loss and the trough deepen.
• Press Screw runs 15 % fast: a weak controller lets the chamber pressure sag below the set point.
• Press Shallow cover, risk of blow-out and compare the pressure window with the deep tunnel.