Seismic Behvaior of Immersed Tunnels

LABORATORY OF BIOLOGICAL STRUCTURE MECHANICS

www.labsmech.polimi.it

Kiana Hashemi

Seismic Behavior of Immersed Tunnels with Specific Case of Port Island Immersed Tunnel in Japan

Monday 30th June 2014

2Table of Content

Immersed Tunnel

• Immersed Tunnels Construction Procedure

Seismic performance

• Behavior of Immersed Tunnels in Past Earthquakes• Seismic Performance of Immersed Tunnels• Deformation modes: Axial – Bending – Ovaling/Racking

Analysis

• Free Field Analysis• Soil-Structure Interaction Analysis against Longitudinal Deformation• Soil-Structure Interaction Analysis against Transversal Deformation• Pseudo-static/Dynamic Analysis

Results

• Soil-Structure Interaction Analysis against Longitudinal Deformation• Soil-Structure Interaction Analysis against Transversal Deformation

3Immersed Tunnels Construction Procedure

lowered with the help of special sinking rigs

prefabricated floatable segments constructed

in a dry dock

floated over a pre-excavated trench

Water is pumped into tanks in Immersed Tube and it is gradually sunk by adjusting buoyancy

tunnel consists of 6 pieces connected

through some flexible joints

4Immersion Flexible JointFl

exib

le J

oint

Gina gasket Hydrostatic compression

Omega seal Secondary line of defense

Tendon Tension

Shear key Shear

5Behavior of Immersed Tunnels in Past Earthquakes

Two immersed tunnels which are known to have been subjected to fairly strong seismic

the Bay Area Rapid Transit (BART) tunnel, California

Osaka South Port (OSP) immersed tunnel, Japan

- Total length of 5.8 km- Maximum Depth of 40 m - Built in the late 1960s- Subjected to 1989 Loma

Prieta Ms 7.1 earthquake- long-period acceleration

with PGA of order of 0.20-0.30 g

No damage, sustaining only a small relative

displacement between the end segments and the approach structures

- Total length of 1 km- Maximum Depth of 27 m - Almost completed when

it was hit by 1995 MJMA 7.2 Kobe earthquake

- experienced its design earthquake shaking with a recorded PGA of 0.27 g

Sustained no visible damages since neither

water leakage nor structural cracking were observed

6Seismic Performance of Immersed Tunnels

Surface Structures

Underground Structures

Seismic Performance

Designed according to inertial forces

caused by ground acceleration

Designed according to deformation imposed by surrounding soil

SOIL-STRUCTURE

INTERACTION

Gro

und

Res

pons

e to

Sh

akin

g

Ground Failure

Liquefaction

Slope Instability

Fault Displacement

Ground Shaking and Deformation

Axial extension and compression

Longitudinal bending

Ovaling for circular and racking for rectangular

tunnels

Adding an arrival time delay

Site response analysis

7Aseismic Analysis of Tunnels

Free-field Site Response Analysis

Obtaining free field deformation time histories

Subjecting the soil tunnel system to this motion

Seismic Analysis of

Tunnels

Soil-Structure Interaction

Pseudo-static Analysis

Dynamic Analysis

Sources of Ground motion incoherency

Wave passage

effect

Local site

effects

Random Geometric

Incoherence

Being neglected

𝑡𝑖=𝑥 𝑖/𝐶𝛼 = time lag = distance along the axis of the tunnel = is the apparent wave velocity = the shear wave velocity = the wave incidence angle from the vertical





1D wave propagation site response analysis

Equivalent frequency domain analysis

Nonlinear time domain analysis

Free field deformation to be used for SSI

Strain compatible shear wave velocity

To

find





1D wave propagation site response analysis

Equivalent frequency domain analysis

Nonlinear time domain analysis

Free field deformation to be used for SSI

Strain compatible shear wave velocity

To

find






Transversal Deformation

s

Finite Element method

Closed-form solution

Aga

inst

Pseudo - static Analysis

Dynamic Analysis

methods

SOIL STRUCTURE INTERACTION

Longitudinal Deformations



s



Aga

inst


Dynamic Analysis

methods


Assumptions:- soil system is modeled as an elastic

beam in elastic soil - Loading by sinusoidal wave of

wavelength of , displacement amplitude of , angle of incidence of

- Structure conforming in homogenous isotropic half-space medium

= modulus of elasticity = cross-sectional area = moment of inertia of the tunnel lining

if 𝑁𝑚𝑎𝑥=𝜋𝜆 𝐸 𝑙 𝐴𝑙𝐷0

if 𝑀𝑚𝑎𝑥=( 2𝜋𝜆 )2

𝐸𝑙 𝐼 𝑙𝐷0

Soil-structure interaction are modeled by springs in longitudinal and transverse directions as and

,

Shallow immersed tube tunnels → surface box foundation →→ elastodynamic solution by Gazetas (1991)

,

= shear modulus at , = Poisson’s ratio of the soil ,

and = the soil parameters B and L = the width and length of the tunnel

The closed-form solution is just the quasi-static

analysis because inertia effects in

soil-structure interaction are

neglected



Finite Element Model:- Tunnel segments as beam

elements- Connection to soil through springs

and dashpots- Immersion joint as two set of node-

frames connected to each other

with SDOF nonlinear springs • Longitudinal direction: Gina gasket

• Transverse direction: “gap” elements which would only transmit shear after the shear key allowance closes


s



Aga

inst


Dynamic Analysis

methods



14Results of Aseismic Analysis of Tunnels

longitudinal deformation

of immersed tunnels Depends on

- the total number of joints → decreasing number

of joints → increasing the segment length →

increasing the deformation

- properties of Gina gaskets → increasing

thickness of the Gina gasket → allowing greater

initial hydrostatic compressive deformation →

wider deformation margins


s



Aga

inst


Dynamic Analysis

methods



OUTPUT


Structural internal forces or material

strains in the lining

Soil Structure Interaction Analysis

against TRANSVERSE deformations

Free field response Racking deformation

INPUT


s



Aga

inst


Dynamic Analysis

methods




Calculation of the maximum

free-field ground shear

strain 𝜸𝒎𝒂𝒙=𝝉𝒎𝒂𝒙 /𝑮𝒎

Determination of the

differential free-field relative

displacements ∆ 𝑭𝒓𝒆𝒆−𝑭𝒊𝒆𝒍𝒅=𝑯×𝜸𝒎𝒂𝒙

Calculating the racking

stiffness () of the structure

𝑲 𝒔

Obtaining the flexibility ratio ( 𝑭=

𝑮𝒎

𝑲 𝒔× 𝑩𝑯


s



Aga

inst


Dynamic Analysis

methods



Determining the racking ratio, R 𝑹=

𝟐𝑭𝟏+𝑭

Calculating the racking

deformation of the structure

∆𝒃𝒐𝒙=𝑹×∆𝑭𝒓𝒆𝒆− 𝑭𝒊𝒆𝒍𝒅Calculation of the internal forces as well as material

strains by imposing

WANG Method (1993)



s



Aga

inst


Dynamic Analysis

methods



Numerical analysis by applying the free-field racking

displacement at the boundaries of the model changing linearly through the height of the box

structure

Two-dimensional analysis for selection of model

parameters

One-dimensional site response analysis to compute the free

field racking deformation, and strain compatible shear wave

velocity

𝑑𝑖𝑚=𝑥𝐻 ∆𝐹𝑟𝑒𝑒−𝐹𝑖𝑒𝑙𝑑

𝑅=∆𝑏𝑜𝑥

∆𝐹𝑟𝑒𝑒−𝐹𝑖𝑒𝑙𝑑

HASHASH Method (2010)



s



Aga

inst


Dynamic Analysis

methods



Numerical analysis by applying the displacement time history at

the base of the model and achieving the displacement

time histories at four monitored points (A, B, C, and D)

Two-dimensional analysis for selection of model

parameters: soil properties from site response analysis

and structural properties

One-dimensional site response analysis to compute the

acceleration and displacement time histories for the layer

corresponding to bottom of 2-D model

HASHASH Method (2010)

20Results of Aseismic Analysis of Tunnels


s



Aga

inst


Dynamic Analysis

methods



• → racking stiffness of box structure racking stiffness of surrounding soil → the soil is usually soft and the racking deformations are relatively large.

• → racking stiffness of box structure racking stiffness of surrounding soil → the soil is stiff and racking deformations are small

• Soft soil profile ( → dynamic and pseudo-static analysis results appear to be quite similar and they are slightly above the relationship proposed by Wang

• Moderately stiff soil () → analyses by dynamic interaction give the racking deformation larger than that computed from the pseudo-static analyses. The racking ratios computed from pseudo-static and dynamic soil-structure interaction analyses plot above the Wang relationship

• Stiff soil () → dynamic analyses results in term of racking ratio are slightly lower than that of pseudo-static analyses and both are less than those for Wang

21Conclusion

• In design of immersed tunnels, the seismic loading which is characterized in terms of

deformations imposed by the soil on the structure and the interaction between them should be

considered in addition to static forces.

• The magnitude of deformation developing in the segment joints as the result of the combined

longitudinal and lateral vibrations is the critical case of loading for the seismic safety of an

immersed tunnel.

• Even in very large magnitude earthquakes with high level of Peak Ground Acceleration, the net

tension and excessive compression between the segments can be avoided by a suitable design of

join gaskets and relatively small segments length.

• The analyses also highlight the importance of dynamic analyses to verify and supplement the

results of pseudo-static soil-structure interaction analyses. However, in the case of structure

surrounding by soft soil, application of just pseudo-static analyses is enough since it provides

quite similar result as the dynamic analyses and dynamic analyses is much more

computationally demanding.

22

Grazie Mille

Documents

Seismic Behvaior of Immersed Tunnels