Calculation of Face Stability for EPB
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CALCULATION OF FACE STABILITY FOR EPB MACHINEMODEL OF ANAGNOSTOU & KOVARI (1996)
Design Abacus
Prof. Eng. Daniele PEILA
Course in Tunnelling and Tunnel Boring Machine
Kurs w zakresie drążenia tuneli oraz maszyny drążącej
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HORN’S MODEL (1961)
Calculation model
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Calculation model
Drained conditions:
● Soil permeability > 10-7 ÷ 10-6 m/s
● Excavation advancing ratio ≤ 0.1 ÷ 1 m/h
Strenght parameters to use: DRAINED for sands and gravels. For the clay only
in machine stop conditions.
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Calculation model
The pressure must be applied in terms of EFFECTIVE stresses.
Contact “grain-grain” of the soil
The water pressures into the bulk chamber affect the presence of the seepage
forces .
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Calculation model
1. The submerged weight G’
2. The vertical force V’
3. The seepage forces Fx e Fz
4. The pressure applied on the tunnel face S’
5. The ortoghonal force on the inclined surface N’
6. The orizontal forcesortoghonal to the lateralsurface
7. The shear forces thatdevelopes at the interfaces
Acting forces on the soil wedge:
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Calculation model
Boundary conditions for the seepage forces:
● constant permeability
● pressure inside the tunnel hf ≤ h0
● constant underground water height
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Calculation model
Calculation procedure for the stability analysis of the tunnel face:
1. Numerical modelling of the flow field
2. Calculation of the forces acting on the soil wedge with the sliding geometry
assumption
3. Calculation of the force that must be applied on the tunnel face
Choice of the critical sliding surface by the iteration of steps 2 and 3.
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Dh
cFh'γFcFD'γF's 3210
∆−∆+−=
The pressure that must be applied is affected by different parameters:
s’= f(D, H, hf, h0, c, j, g’, gd)
By a dimensional analysis has been obtained the following formulation:
Calculation of the effective pressure thet must be applied on the tunnel face
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Effective pressure calculation that must be applied at the tunnel face
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Effective pressure calculation that must be applied at the tunnel face
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Effective pressure calculation that must be applied at the tunnel face
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Effective pressure calculation that must be applied at the tunnel face
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Great Belt Project (Denmark):
Data:
D = 7 m
H = 30 m
h0 ≈ 47 m
ϕ = 32,5°
γ’ = 13 kN/m3
Example of calculation
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Example of calculation
F0 = 0.2F0 = 0.2
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Example of calculation
F1 = 2F1 = 2
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Example of calculation
F2 = 0.43F2 = 0.43
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Example of calculation
F3 = 0.108F3 = 0.108
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Example of calculation
Obtained values using the abacus:
● F0 = 0,2
● F1 = 2
● F2 = 0,43
● F3 = 0,108
Obtaining:
s’= 18 –2c+5,6(h 0 – h f) – 0,016c(h 0 – h f)
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Example of calculation
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Observations on the obtained results and on the applic ative aspects
Important observations:
● Static equivalence of different technological solutions.
● Importance of the water pressure into the bulk chamber (calculation of the
pressure in the soli pores without tunnel face pressure).
● Problems due to high effective pressures into the bulk chamber.
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Possible problems with high effective pressure into the bulk
chamber.
Observations on the obtained results and on the applic ative aspects