Introduction

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