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Figure 1

3D finite element meshes, dimensions of problem and axis location used in the analysis.
3D finite element meshes, dimensions of problem and axis location used in the analysis.

Figure 2

Underground location of tunnel relative to a single and group of piles.
Underground location of tunnel relative to a single and group of piles.

Figure 3

Piles cap dimension and Locations of piles in groups.
Piles cap dimension and Locations of piles in groups.

Figure 4

The zone of infuence in longitudenal direction.
The zone of infuence in longitudenal direction.

Figure 5

Zones of pile movement around a tunnel driven through soft clays and dense sands after the Heinenoord full-scale trial (Kaalberg et al. 1999).
Zones of pile movement around a tunnel driven through soft clays and dense sands after the Heinenoord full-scale trial (Kaalberg et al. 1999).

Figure 6

Distributions of normalized net pile head and soil surface settlement with tunnel advancement for single pile.
Distributions of normalized net pile head and soil surface settlement with tunnel advancement for single pile.

Figure 7

Displacement of soil at the end of excavation Y/D= +5. (Analysis I).
Displacement of soil at the end of excavation Y/D= +5. (Analysis I).

Figure 8

Distributions of normalized net pile head and soil surface settlement with tunnel advancement for group pile 3 x 3 (analysis IV and G).
Distributions of normalized net pile head and soil surface settlement with tunnel advancement for group pile 3 x 3 (analysis IV and G).

Figure 9

Soil displacement at the end of tunnel excavation Y/D= +5. (analysis VI).
Soil displacement at the end of tunnel excavation Y/D= +5. (analysis VI).

Figure 10

Variations of pile head settlement during tunnelling process for various E/D (analysis series I, II, III, IV, and V).
Variations of pile head settlement during tunnelling process for various E/D (analysis series I, II, III, IV, and V).

Figure 11

Variation of normalized net pile head settlement with E/D at the end of tunnel excavation (Y/D= +5).
Variation of normalized net pile head settlement with E/D at the end of tunnel excavation (Y/D= +5).

Figure 12

Variations of center pile head settlement at (3 x 3) piles group during tunnelling process for various E/D.
Variations of center pile head settlement at (3 x 3) piles group during tunnelling process for various E/D.

Figure 13

Distributions of normalized net pile head settlement with tunnel advancement for various C/D (single pile).
Distributions of normalized net pile head settlement with tunnel advancement for various C/D (single pile).

Figure 15

Distributions of normalized net pile head settlement with tunnel advancement for various C/D (group of piles). Analysis series (XV, XVI, XVII, and XVIII).
Distributions of normalized net pile head settlement with tunnel advancement for various C/D (group of piles). Analysis series (XV, XVI, XVII, and XVIII).

Figure 16

Distributions of net pile head settlement with tunnel advancement for two types of soils and a single pile analysis (C/D= 0.16, and E/D= 0).
Distributions of net pile head settlement with tunnel advancement for two types of soils and a single pile analysis (C/D= 0.16, and E/D= 0).

Figure 17

Virtual parallelogram represents the zone of significant influence during tunnel advancement.
Virtual parallelogram represents the zone of significant influence during tunnel advancement.

Figure 18

Comparison of the present numerical analysis with centrifuge test results.
Comparison of the present numerical analysis with centrifuge test results.

Details of centrifuge tests (prototype scale), Logagnathan et al. (2000).

Test No.Tunnel depth, H: m
1Pile length, Lp = 18 m Pile diameter, d= 0.8 m15
2EI= 1400 MN m2 Tunnel diameter, D= 6 m Stiff kaolin clay, ~75 kPa18
321

Analysis series for a single and group of piles with different offset ratio (E/D)

Single pilePile group (3×3)
Analysis seriesIIIIIIIVVVIVIIVIIIIXX
C/D0.160.160.160.160.160.160.160.160.160.16
E/D00.51.01.52.000.51.01.52.0

Soil parameters adopted in the numerical analysis (from Miro et al. 2012).

Soil Parameters HS model
Parametersvaluesunits
Friction angle, φ35
Dilatancy angle, Ψ5
Cohesion, c10[kN/m2]
Secant stiffness in the standard drained triaxial test, Eref50$E_{ref}^{50}$35000[kN/m2]
Tangent stiffness for primary oedometer loading, Erefoed$E_{ref}^{oed}$35000[kN/m2]
Unloading and reloading stiffness, Erefur$E_{ref}^{ur}$100000[kN/m2]
Reference pressure, pref100[kN/m2]
Power for stress-level dependency of stiffness, m0.7[-]
Failure ratio, Rf0.9[-]
Poisson’s ratio for unloading-reloading,Ѵur0.2[-]
Soil weight above phreatic level, γunsat17[kN/m3]
Soil weight below phreatic level, γsat20[kN/m3]
Strength reduction factor for interfaces in0.6[-]
PLAXIS, Rinter

Analysis series for a single and group of piles with different depth ratio (C/D).

Soil typeφ (degree)c (kN/m2)
1*3510
2370
*Soil 1 has the same parameters as the soil used in (Table 2)

Concrete parameters adopted in the numerical analysis.

ParametersValuesUnitsModel
PilePile capTunnel liningTBM shield
Diameter (D)1---mLinear
Thickness (t)-10.250.35melastic
Elasticity modulus (E)30×10630×10630×106210×106kN/m2kN/m3$\frac{{\text{kN}}/{{{\text{m}}^{\text{2}}}}\;}{{\text{kN}}/{{{\text{m}}^{\text{3}}}}\;}$
Unit weight (γ)25252538
Possion’s ratio (ѵ)0.20.20.20.3-
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Geosciences, other, Materials Sciences, Composites, Porous Materials, Physics, Mechanics and Fluid Dynamics