Concrete 2003 Brisbane July 2003 Design Of Pre-cast Buried Structures For Internal Impact Loading
Jan 06, 2016
Concrete 2003Brisbane July 2003
Design Of Pre-cast Buried Structures For
Internal Impact Loading
Introduction• Finite element analysis of a pre-cast arch cut and
cover rail tunnel• Reasons for the study
o Increased collision design loadso Increasing use of arch cut and cover tunnelso Comparatively thin section thicknesso Lack of guidance in codes
• Analyses Comparedo Simple analysis with equivalent static loadso Nin-linear analysis with equivalent static loadso Non-linear “push-over” analysis
Rail Collision Design Loads• Current Austroads Bridge Design Code – 1992
Longitudinal:2000 kN
Transverse:
1000 kN• Draft Australian Standard Bridge Design Code -
2000
Longitudinal:3000 kN
Transverse:
2000 kN
• Loads applied simultaneously at a height of 2 metres above rail level – Ultimate Limit State Load
Analysis Procedure• 2D plane strain finite element analysis• The fill was modelled as a mohr-coulomb elasto-
plastic material• Non-cohesive fill between pile caps• Arch modelled using beam elements including
moment-curvature behaviour• Friction elements allowed slip between the arch
and the soil• Varying fill properties• Material and geometric non-linearity included• Effects of fill stiffness and strength and concrete
section strength and ductility assessed
Arch Cross Section
Detail of Finite Element Model
Analysis runs considered
1. Simplified model: All materials linear elastic; no friction elements
2. Non-linear soil, linear elastic beam elements
3. Moment-curvature behaviour of beams added
4. Friction elements added
5. Non-linear geometry added
6. Model 5 with varying soil and concrete section parameters
Parameters for run series 6
Run No.
Fill Concrete
Elastic Modulus,
MPa
Poisson’s Ratio
Strength
Tensile Reinf.
Density %
Ultimate Curvature,
m-1
6A 10 0.3 40 0.76 0.30
6B 30 0.3 40 0.76 0.30
6C 60 0.3 40 0.76 0.30
6D 30 0.3 40 1.72 0.087
Moment Curvature Diagram
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
Curvature m-1
0
100
200
300
400
Ben
ding
Mom
ent,
kN
m
Series 1 2A 3A 3B
Moment-curvature diagrams
Bending Moments; Linear elastic concrete
-100 0 100 200 300 400 500 600 700
Bending Moment; kNm
0
1
2
3
4
5
6
7
Pos
ition
abo
ve b
ase,
m
Run 1 Run 2
Runs 1-2, Bending Moments
Shear Forces; Linear elastic concrete
-600 -500 -400 -300 -200 -100 0 100 200 300 400 500
Shear Force; kN
0
1
2
3
4
5
6
7
Pos
ition
abo
ve b
ase,
m
Run 1 Run 2
Runs 1-2, Shear Forces
Bending Moments; Non-linear concrete
0 0.2 0.4 0.6 0.8 1 1.2
Load Factor
0
50
100
150
200
250
Ben
ding
Mom
ent,
kNm
Run 3Run 4Run 5
Bending Moment v Load Factor
Shear Forces; Non-linear concrete
0 0.2 0.4 0.6 0.8 1 1.2
Load Factor
0
50
100
150
200
250
300
350
She
ar F
orce
, kN
Run 3Run 4Run 5
Shear Force v Load Factor
Deflections; Non-linear concrete
0 0.2 0.4 0.6 0.8 1 1.2
Load Factor
-0.01
0
0.01
0.02
0.03
0.04
X D
efle
ctio
n, m
Run 2Run 3Run 4Run 5
Deflection v Load Factor
Beam curvature; Non-linear concrete
0 0.2 0.4 0.6 0.8 1 1.2
Load Factor
0
0.05
0.1
0.15
Cur
vatu
re, m
-1
Run 2Run 3Run 4Run 5
Curvature v Load Factor
Summary, Runs 2-5
2 3 4 5
Run No
Mo
men
t, S
hea
r; k
N,m
0
0.05
0.1
0.15
Def
lect
ion,
rot
atio
n, m
, m
-1
Bending Moment Shear Force X Deflection Curvature
Push over analysis animation
Push over analysis animation
Bending moments; push over analysis
0 20 40 60 80 100 120
Deflection, mm
0
100
200
300
400
500
Ben
ding
Mom
ent,
kNm
Run 6ARun 6BRun 6CRun 6D
Bending Moment, Runs 6A-6D
Shear Forces; push over analysis
0 20 40 60 80 100 120
Deflection, mm
0
100
200
300
400
500
She
ar F
orce
, kN
Run 6ARun 6BRun 6C
Run 6D
Shear Force, Runs 6A-6D
Curvature; push over analysis
0 20 40 60 80 100 120
Deflection, mm
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Cur
vatu
re, m
-1
Run 6ARun 6BRun 6CRun 6D
Curvature, Runs 6A-6D
Applied Force; push over analysis
0 20 40 60 80 100 120
Defection, mm
0
500
1000
1500
2000
App
lied
For
ce, k
N
Run 6AData 6BData 6CData 6D
Applied Force
Summary, Runs 6
6A 6B 6C 6D
Run No
0
500
1000
1500
2000
Ap
pli
ed F
orc
e; k
N
0
10
20
30
40
50
60
70
Def
lect
ion,
mm
Appiled Force at 100 mm deflection Deflection at 1000 kN applied load
Summary, Runs 6
6A 6B 6C 6D
Run No
0
0.05
0.1
0.15
0.2
0.25
0.3
Cu
rvat
ure
, m
-1
0%
100%
200%
300%
400%
500%
600%
DF
acto
r, %
Curvature at 1000 kN applied load Ductility Factor
Conclusions• Linear elastic analysis overestimates the bending
moments and shear forces in the structure • A typical arch section had adequate ductility for
rail impact loading, When the moment-curvature behaviour of the arch section was included in the analysis
• Slip at the soil/concrete interface, and geometric non-linearity effects have a significant effect on the arch forces and deflections
• Increasing the amount of tensile reinforcement reduced the ductility of the section, and is not recommended.
• The provision of confinement reinforcement had only limited effect on the section ductility.
Conclusions
• The fill stiffness is important. With low stiffness (10 MPa) fill, the ductility of the section used in this paper was only just adequate.
• Three dimensional distribution of the impact pressures through the fill, and the dynamic stiffness of the fill provide an additional level of safety.
• Provide an alternative load path to maintain the stability of the structure, in the event of the failure of one precast panel.
Recommendations• 2D finite element analysis of the impact load.• Distribute the load across one precast panel• Include the fill and foundations within the zone of
influence of the structure• Allow for slip between the structure and the soil• Allow for both material and geometric non-
linearity• Model moment-curvature behaviour of the
reinforced concrete • Include the required stiffness of the fill material in
the project specification.• Provide an alternative load path to maintain the
stability of the structure, in the event of the failure of one precast panel