盾构管片结构设计算例(英文版)
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K
B1
B2
A1
A6
A2
A5
A3
A4
Figure 1 The cross section of the shield lining
Part Two: Computation by Force Method
(1) Load Conditions Judgment of Tunnel Type (by Terzaghi’s formula)
Angle of internal friction of soil: φ =30o
Cohesion of soil: c=0 kN/m2 Coefficient of reaction: k=50MN/m3 Coefficient of lateral earth pressure: λ =0.4 Surcharge: P0=39.7kN/m2 Soil condition: Sandy
The shield lining is fitted with 9 segmental pieces (one Key-type segment, two B-type segments and six other segments) as shown in Figure 1. Central angle of each segment piece is 40 degrees.
¾ Coefficients Calculation
n = n1 + n2 + n3 + n4 = 1 + 1 + 1 + 2 = 5
Note: if the joint just located at 180 degree of the half-ring lining, then its stiffness contribution to the whole structure should be considered as half of the total value.
KθP = 18070kN ⋅ m / rad (if inside part of lining is tensile)
KθN = 32100kN ⋅ m / rad (if outside part of lining is tensile)
EI = 3.0×104 ×103 × 6.4×10−3 = 192000kN ⋅ m2
(2) Computation of Member Forces
Figure 4 shows the simplified model of the segmental lining.
Figure 4 Simplified model diagram for calculation
¾ Calculation data
Ground Conditions
Overburden: H=12.3m Groundwater table: G.L.+0.6m =12.3+0.6=12.9m N Value: N=50 Unit weight of soil: γ =18kN/m3 Submerged unit weight of soil: γ ′ =8kN/m3
∑ δ 11
=
Rπ EI
+
n i =1
1 Kθ(i )
=
Rπ EI
+
2.5 KθP
+
2 KθN
=
4.55 × π 192000
p3+4 = p3 + p4 = 272.918 + 172.973 = 445.891kN / m
Where
Dc=Computational diameter= D0 − t = 9.5 − 0.4 = 9.1m
¾ Average self-weight
p5 = 1.2bγ ct = 1.2×1.2× 26× 0.4 = 14.976kN / m
= 2.29104×10-3m
pk = kδ ⋅ b = 50 × 103 × 2.29104 × 10−3 × 1.2 = 137.462kN / m
p6 = ph(1 − 2 cos2 ϕ )
π (
≤ϕ
≤
3π
)
4
4
Where
δ = Displacement of lining at tunnel spring η = Reduction factor of model rigidity = 0.8 E = Modulus of elasticity of segment = 3.0×104N/mm2 I = Moment of inertia of area of segment = 1/12×1.2×0.43 = 6.4×10-3m4 k = Coefficient of reaction = 50MN/m3 K = k ⋅ b = 50×1.2 = 60MN / m2 ϕ = the angle measured from the vertical direction around the tunnel
Figure 3 Load condition of the designed tunnel ¾ Vertical pressure at tunnel crown
Earth pressure:
pe1 = b(1.4P0 + 1.2γ ' H ) = 1.2× (1.4× 39.7 + 1.2×12.3) = 208.392kN / m
¾ Lateral resistance pressure
δ =（2 p1 − p3 − p3+4 + πp5 )Rc4 /[24(ηEI + 0.0454KRc4 )]
= (2×420.623-272.918-445.891+π×14.976) ×103×4.554/[24×(0.8 ×3.0×104×106×6.4×10-3+0.0454×60×106×4.554)]
Materials
¾ The grade of concrete: C30 Nominal strength: fck=20.1N/mm2 Allowable compressive strength: fc=14.3N/mm2 Allowable tensile strength: ft=1.43N/mm2 Elastic modules: E=3.0×104N/mm2
Water pressure
1.2
Computation of Loads
Computation element is a 1.2 meter (width of segment) part along the longitudinal direction, and Figure 3 shows the load condition to compute member forces of the segmental lining.
Type of segment: RC, Flat type Diameter of segmental lining: D0=9500mm Radius of centroid of segmental lining: Rc=4550mm Width of segment: b=1200mm Thickness of segment: t=400mm
Table 1 Load Types and Partial Factors
Load types Partial factors
Load types
Partial factors
Surcharge
1.4
Earth pressure
1.2
Dead load
1.2
Subgrade reaction
1.2
1.2
×1.2×10 ×
(12.9
+
0.4 2
)
=
188.64kN
/
m
p3 = qe1 + qw1 = 84.278 + 188.64 = 272.918kN / m
¾ Lateral pressure at tunnel bottom
p4 = 1.2b(λγ ' Dc + γ w Dc ) = 1.2×1.2× (0.4× 8× 9.1 + 10× 9.1) = 172.973kN / m
A Design of Shield Tunnel Lining
Part One: Design Data
(1) Function of Tunnel
The planned tunnel is to be used as a subway tunnel.
(2) Design Conditions Dimensions of Segment
¾ How to check the safety of lining? Limit state method based on the national code GB50010-2002 is used to check the safety of lining.
(3) Geometric Design of Shield Lining
Water pressure:
pw1 = 1.2bγ w H w = 1.2×1.2×10×12.9 = 185.76kN / m
q1 = pe1 + pw1 = 208.392 + 185.76 = 394.152kN / m
q2 = 1.2b × 0.215Rγ = 1.2×1.2× 0.215× 4.75 ×18 = 26.471kN / m
KθP = 18070 kN ⋅ m / rad (if inside part of lining is tensile) KθN = 32100 kN ⋅ m / rad (if outside part of lining is tensile) Design Method
¾ How to compute member forces? Force method (Part Two) and Elastic equation method (Part Three) are used respectively to calculate member forces.
p1 = q1 + q2 = 394.152 + 26.471 = 420.623kN / m
¾ Vertical pressure at tunnel bottom
p2 = p1 + 1.2bπγ ct = 420.623 + 1.2×1.2π × 26× 0.4 = 467.671kN / m
Where γ c =Unit weight of RC segment=26kN/m2
¾ The type of steel bars: HRB335 Allowable strength: fy= fy’= 300N/mm2
¾ Bolt Yield strength: fBy=240N/mm2
Shear strength: τ B =150N/mm2
¾ Parameters for joint spring:
¾ Lateral pressure at tunnel crown Earth pressure:
qe1
=
λ(
pe1
+
1Βιβλιοθήκη Baidu2bγ
'
t) 2
=
0.4× (208.392
+
1.2 × 1.2 ×
8×
0.4 ) 2
=
84.278kN
/
m
Water pressure:
qw1
=
1.2bγ
w
(Hw
+
t 2
)
=
φπ
Figure 2 Judgment of tunnel type
B1
=
R0
cot(π 8
+
φ) 4
=
4.75× cot(π 8
+
30° ) 4
=
8.227m
h0
=
B1[1 − C /(B1γ tanφ
)][1 − exp(−
H B1
tanφ )]+
P0
exp(−
H B1
tanφ )
= 8.227[1 − 0][1 − exp(− 12.3 tan 31°)] + 39.7 × exp(− 12.3 tan 31°)
tan 31°
8.227
8.227
= 24.986m > H = 12.3m
So the designed tunnel is a shallow tunnel.
Load Types and Partial Factors
Table 1 shows the loads should be considered in the design and corresponding partial factors.
B1
B2
A1
A6
A2
A5
A3
A4
Figure 1 The cross section of the shield lining
Part Two: Computation by Force Method
(1) Load Conditions Judgment of Tunnel Type (by Terzaghi’s formula)
Angle of internal friction of soil: φ =30o
Cohesion of soil: c=0 kN/m2 Coefficient of reaction: k=50MN/m3 Coefficient of lateral earth pressure: λ =0.4 Surcharge: P0=39.7kN/m2 Soil condition: Sandy
The shield lining is fitted with 9 segmental pieces (one Key-type segment, two B-type segments and six other segments) as shown in Figure 1. Central angle of each segment piece is 40 degrees.
¾ Coefficients Calculation
n = n1 + n2 + n3 + n4 = 1 + 1 + 1 + 2 = 5
Note: if the joint just located at 180 degree of the half-ring lining, then its stiffness contribution to the whole structure should be considered as half of the total value.
KθP = 18070kN ⋅ m / rad (if inside part of lining is tensile)
KθN = 32100kN ⋅ m / rad (if outside part of lining is tensile)
EI = 3.0×104 ×103 × 6.4×10−3 = 192000kN ⋅ m2
(2) Computation of Member Forces
Figure 4 shows the simplified model of the segmental lining.
Figure 4 Simplified model diagram for calculation
¾ Calculation data
Ground Conditions
Overburden: H=12.3m Groundwater table: G.L.+0.6m =12.3+0.6=12.9m N Value: N=50 Unit weight of soil: γ =18kN/m3 Submerged unit weight of soil: γ ′ =8kN/m3
∑ δ 11
=
Rπ EI
+
n i =1
1 Kθ(i )
=
Rπ EI
+
2.5 KθP
+
2 KθN
=
4.55 × π 192000
p3+4 = p3 + p4 = 272.918 + 172.973 = 445.891kN / m
Where
Dc=Computational diameter= D0 − t = 9.5 − 0.4 = 9.1m
¾ Average self-weight
p5 = 1.2bγ ct = 1.2×1.2× 26× 0.4 = 14.976kN / m
= 2.29104×10-3m
pk = kδ ⋅ b = 50 × 103 × 2.29104 × 10−3 × 1.2 = 137.462kN / m
p6 = ph(1 − 2 cos2 ϕ )
π (
≤ϕ
≤
3π
)
4
4
Where
δ = Displacement of lining at tunnel spring η = Reduction factor of model rigidity = 0.8 E = Modulus of elasticity of segment = 3.0×104N/mm2 I = Moment of inertia of area of segment = 1/12×1.2×0.43 = 6.4×10-3m4 k = Coefficient of reaction = 50MN/m3 K = k ⋅ b = 50×1.2 = 60MN / m2 ϕ = the angle measured from the vertical direction around the tunnel
Figure 3 Load condition of the designed tunnel ¾ Vertical pressure at tunnel crown
Earth pressure:
pe1 = b(1.4P0 + 1.2γ ' H ) = 1.2× (1.4× 39.7 + 1.2×12.3) = 208.392kN / m
¾ Lateral resistance pressure
δ =（2 p1 − p3 − p3+4 + πp5 )Rc4 /[24(ηEI + 0.0454KRc4 )]
= (2×420.623-272.918-445.891+π×14.976) ×103×4.554/[24×(0.8 ×3.0×104×106×6.4×10-3+0.0454×60×106×4.554)]
Materials
¾ The grade of concrete: C30 Nominal strength: fck=20.1N/mm2 Allowable compressive strength: fc=14.3N/mm2 Allowable tensile strength: ft=1.43N/mm2 Elastic modules: E=3.0×104N/mm2
Water pressure
1.2
Computation of Loads
Computation element is a 1.2 meter (width of segment) part along the longitudinal direction, and Figure 3 shows the load condition to compute member forces of the segmental lining.
Type of segment: RC, Flat type Diameter of segmental lining: D0=9500mm Radius of centroid of segmental lining: Rc=4550mm Width of segment: b=1200mm Thickness of segment: t=400mm
Table 1 Load Types and Partial Factors
Load types Partial factors
Load types
Partial factors
Surcharge
1.4
Earth pressure
1.2
Dead load
1.2
Subgrade reaction
1.2
1.2
×1.2×10 ×
(12.9
+
0.4 2
)
=
188.64kN
/
m
p3 = qe1 + qw1 = 84.278 + 188.64 = 272.918kN / m
¾ Lateral pressure at tunnel bottom
p4 = 1.2b(λγ ' Dc + γ w Dc ) = 1.2×1.2× (0.4× 8× 9.1 + 10× 9.1) = 172.973kN / m
A Design of Shield Tunnel Lining
Part One: Design Data
(1) Function of Tunnel
The planned tunnel is to be used as a subway tunnel.
(2) Design Conditions Dimensions of Segment
¾ How to check the safety of lining? Limit state method based on the national code GB50010-2002 is used to check the safety of lining.
(3) Geometric Design of Shield Lining
Water pressure:
pw1 = 1.2bγ w H w = 1.2×1.2×10×12.9 = 185.76kN / m
q1 = pe1 + pw1 = 208.392 + 185.76 = 394.152kN / m
q2 = 1.2b × 0.215Rγ = 1.2×1.2× 0.215× 4.75 ×18 = 26.471kN / m
KθP = 18070 kN ⋅ m / rad (if inside part of lining is tensile) KθN = 32100 kN ⋅ m / rad (if outside part of lining is tensile) Design Method
¾ How to compute member forces? Force method (Part Two) and Elastic equation method (Part Three) are used respectively to calculate member forces.
p1 = q1 + q2 = 394.152 + 26.471 = 420.623kN / m
¾ Vertical pressure at tunnel bottom
p2 = p1 + 1.2bπγ ct = 420.623 + 1.2×1.2π × 26× 0.4 = 467.671kN / m
Where γ c =Unit weight of RC segment=26kN/m2
¾ The type of steel bars: HRB335 Allowable strength: fy= fy’= 300N/mm2
¾ Bolt Yield strength: fBy=240N/mm2
Shear strength: τ B =150N/mm2
¾ Parameters for joint spring:
¾ Lateral pressure at tunnel crown Earth pressure:
qe1
=
λ(
pe1
+
1Βιβλιοθήκη Baidu2bγ
'
t) 2
=
0.4× (208.392
+
1.2 × 1.2 ×
8×
0.4 ) 2
=
84.278kN
/
m
Water pressure:
qw1
=
1.2bγ
w
(Hw
+
t 2
)
=
φπ
Figure 2 Judgment of tunnel type
B1
=
R0
cot(π 8
+
φ) 4
=
4.75× cot(π 8
+
30° ) 4
=
8.227m
h0
=
B1[1 − C /(B1γ tanφ
)][1 − exp(−
H B1
tanφ )]+
P0
exp(−
H B1
tanφ )
= 8.227[1 − 0][1 − exp(− 12.3 tan 31°)] + 39.7 × exp(− 12.3 tan 31°)
tan 31°
8.227
8.227
= 24.986m > H = 12.3m
So the designed tunnel is a shallow tunnel.
Load Types and Partial Factors
Table 1 shows the loads should be considered in the design and corresponding partial factors.