warsaw course - 2011 - calculation of face stability for ... of face stability for epb machine model...

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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