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Seismic Design and Risk

Assessment of Underground Long

Structures

Kyriazis Pitilakis

Sotiris Argyroudis and Grigoris Tsinidis

MONICO Workshop – 18 March 2011, Athens

Aristotle University

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MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities

March 18, 2011 - Athens, Greece

AUTH SDGEE2

Underground structures - tunnels

• Mountain tunnels in rock conditions

• Subways

• Highway, railway, water and sewage tunnels in alluvial soils

• Metro stations

• Underground parking stations, commercial centers etc

• Their seismic design and risk assessment in seismically prone

areas is of major importance

• Public Safety - Economy



AUTH SDGEE3

Introduction

• Conceptual, geometrical, and operational features of

underground long structures, make their seismic behavior very

distinct from aboveground structures

• Imposed seismic ground deformations rather than inertial forces

dominate the structure’s seismic response

• Relative lack of well-documented case histories, lack of well

validated methodologies and lack of specific guidelines and

seismic code regulations for seismic design



AUTH SDGEE4

Introduction



AUTH SDGEE5

Summary

• To provide a short but comprehensive review of the analysis and

design methods of long underground structures

• To highlight and discuss some open issues mentioned before

• To provide a short review and ongoing research activities of

underground structures vulnerability and risk assessment under

seismic loading

• Example:

• an immersed tunnel that is planned to be constructed also in

Thessaloniki, is utilized as a typical example



AUTH SDGEE6

Contents

• Typology – construction methods – case studies

• Observed damages and behavior in past earthquakes

• Design principles in practice

• Determination of input motion

• Transversal seismic analysis

• Longitudinal seismic analysis

• Ground failure

• Importance of seismic design compared to static

• Real time risk assessment and Early Warning Systems

• Vulnerability of underground structures under seismic loading

• Conclusions



AUTH SDGEE7

Typology

Construction methods



AUTH SDGEE8

Typology

cut and cover (rectangular) bored tunnel (circular)

Power et al.,1996

cut and cover (vertical tubes)

cut and cover

(center columns or wall)



AUTH SDGEE9

Immersed tunnel Aktio-Preveza, Greece



AUTH SDGEE10

Bosporous-Marmara railway crossing, Turkey



AUTH SDGEE11

Athens Metro, Sepolia Station, Greece

Station Entrance



AUTH SDGEE12

Construction methods

• Bored linear underground structures (e.g. tunnels) – Usually

circular cross sections

• Cut and cover type structures (e.g. tunnels or subway stations,

parking and metro stations) - Rectangular cross sections

• Immersed structures (e.g. immersed tunnels) – Segmented

constructions connected through special joints

Before Initial Contact

roof

IPEGina gasket steel strip

gasket supporting plate

boltsroof

boltsgrout fill

steel stripOmega seal

bolts

After installation of Omega



AUTH SDGEE13

Example : Immersed highway tunnel

• 2.9 km cut and cover segmented tunnels

• 1.2 km immersed tunnel (8 segments, 155m each)

• 1.2 km conjunction ramps to the local road system

Section A-A :

immersed tunnel (2x3 lanes)

Section C-C :

cut and cover tunnel (1 lane)Section B-B :

cut and cover tunnel (2x3 lanes)

Section E-E :

cut and cover tunnel

(2x2 lanes)

Section D-D :

cut and cover tunnel

(3 lanes)

open entry rampfrom Kountouriotou Str.

entry tunnel branch

from Kountouriotou Str. open exit ramp

from Politechniou Str.

exit tunnel branchtowards Politechniou Str.

legends

immersed tunnel

cut and cover tunnels

open entry / exit ramps

service buildings

number of traffic lanes3

C

CE

E

Thermaikos Gulf

A

A

33

B

B

2

1

2

2

33

1

2

3

open exit ramp

towards M. Alexandrou Ave.

eastern cut and cover tunnel

immersed tunnel

service building C

open entry ramp

from Kaftantzoglou Str.

entry tunnel branch

from Kaftantzoglou Str.

open entry ramp

from M. Alexandrou Ave.

service building B

western

cut and cover

tunnel

open entry/exit ramp

at the new western

entrance of Thessaloniki

service building A

ΔΙΑΤΗ

ΡΗΤΕ

Ο

ΚΤΙΣΜ

Α ΟΣΕ



AUTH SDGEE14

Cross section 35.1

8.8

1.11.30.6 1.45

1.3

1.1

17

7.5

P1 P2

Τ1Τ2

P3

Τ4Τ3

P4 P5 P6

17

SM-SC

Loose silty clayey sand

CL

Stiff sandy silty clay

SM-SC

Dense silty clayey sand

CL

Very stiff sandy clay

Section A-A

A-A

A-A

CL

Stiff sandy silty clay

CL

Very stiff sandy clay

Section B-B

B-B

B-B

GM

Well graded gravels -

sand mixtures

water - Thermaikos bay

0.00 m

-10.50 m

-14.50 m

-22.50 m

-30.50 m

-66.50 m

-110.50 m

Vs =130m/s, γ=18.6kN/m³

Vs =270m/s, γ=21.0kN/m³

Vs =380m/s, γ=21.5kN/m³

Vs =500m/s, γ=22.0kN/m³

Vs =700m/s, γ=22.0kN/m³

Compacted gravel material

Vs =380m/s, γ=21.5kN/m³tunnel cross section

Example : Immersed highway tunnel



AUTH SDGEE15

Observed damages and

behavior in past earthquakes



AUTH SDGEE16

Heavy

to moderate damages

when:

• Depth < 50m

• Soft soils

• PGA surf > 0.15g

• M > 6

• R < 50 km

Sarma et al, 1991

Seismic performance of tunnels



AUTH SDGEE17

Seismic performance of tunnels: Overview 1/2

• Underground structures seem less vulnerable than above ground

structures

• Deep or underground structures in rock seem to be safer

• Lined and grouted tunnels are safer than unlined tunnels in rock

• Damage from shaking can be reduced by stabilizing the ground

around a tunnel

• Structure vulnerability is better correlated with ground velocity

than peak ground acceleration

• Spatial variability of ground motion, together with the magnitude

Mw and epicentre distance R, are the main controlling parameters

for the seismic design and vulnerability assessment

Hashash et al., 2001



AUTH SDGEE18

Seismic performance of tunnels : Overview 2/2

• Duration of earthquake is of utmost importance because it may

cause fatigue failure and therefore, large deformations

• High frequency motions, expected mainly at small distances from

the causative fault, may explain the local spalling of rock or

concrete along planes of weakness

• Ground motion may be amplified if wavelengths are between one

and four times the tunnel diameter

• Damages manifested with slope instability near tunnel portals may

be significant

• Typical case of good performance: BART tunnel in San Francisco CA

design and constructed in ’60. (Loma Prieta earthquake, 1989,

Mw=6.9)



AUTH SDGEE19

Observed damages in past earthquakes

• Collapse of the station

• Designed with poor seismic design considerations

Dakai subway, Kobe, 1995, Mw=6.9

Large space underground structures present certain particularities

compared to classical circular lined or unlined bored tunnels



AUTH SDGEE20

• The main cause of collapse is due to the shear and buckling failure

of the centre columns, which were designed and constructed with

insufficient transverse shear reinforcement

Iida et al., 1996, Kawashima, 1999, Hashash et al., 2001




AUTH SDGEE21




AUTH SDGEE22




AUTH SDGEE23

Seismic behavior



AUTH SDGEE24

Seismic behavior



AUTH SDGEE25

• In general the inertial forces (accelerations) are lower for

underground structures

Mmax=683kNm

0.20g

0.37g

0.20g

0.62gMmax=444kNm



AUTH SDGEE26

• PGA is not the best parameter to evaluate the seismic performance of an

underground structure. The response and the seismic vulnerability of an

underground structure is controlled by the imposed seismic ground

deformations and not by the inertial forces



AUTH SDGEE27

Deformation modes of

tunnels due to ground

shaking (travelling

seismic waves)

Seismic response – ground shaking

Owen & Scholl, 1981



AUTH SDGEE28

Seismic behavior

• Shaking

• The imposed seismic ground deformations and the relative stiffness

or the stiffness contrast between the structure and surrounding soil,

control the overall seismic behaviour of an underground structure

• Ground failure

• The response is also controlled by the imposed permanent ground

deformations and displacements

• Large permanent deformations due to:

• Liquefaction : Settlements, lateral spreading

• Slope failure

• Fault movements



AUTH SDGEE29

Design principles



AUTH SDGEE30

Design principles

Static analysis

Seismic analysis

1. Seismicity –

Earthquake design

criteria

MDE

Final analysis output and Design

Seismic hazard

(PSHA or DSHA)

2. Ground response

characteristics

Ground

shaking

3. Structure

seismic response analysis

and design

Transversal seismic

analysis

Longitudinal seismic

analysis

Ground

failure

ODE



AUTH SDGEE31

Design principles

• Design loading criteria

• Operational Design Earthquake (ODE) (10% in 50 years): The

structure remain in elastic range

• Maximum Design Earthquake (MDE) (5% in 50 years):

Prevention collapse, inelastic deformation acceptable, plastic

hinges occur, design to provide sufficient ductility to crucial

components of the structure (e.g. joints)



AUTH SDGEE32

• Total seismic and static loads

MDE U = D + L + E1 + E2 + EQ

ODE U =1.05D + 1.3L + (1.05-1.30)E1 + E2 + 1.3EQ

D : Dead loads

L : Live loads

E1 : Vertical loads (soils, water)

E2 : Horizontal loads (soils, water)

EQ : Seismic loads

max U for (max E2, min E1)• If the flexural strength of the structure lining, using elastic

analysis, is found not to be exceeded, no more check needed

• If it is exceeded, sufficient ductility (if it is possible) must be

provided



AUTH SDGEE33

Input motion



AUTH SDGEE34

Design input motion

Seismic code regulations

• Practically inexistent

• Seismic regulations normally refer to aboveground structures

and usually to different return periods

Site specific seismic hazard analysis

• Mandatory



AUTH SDGEE35

Required design input motion parameters

• Determination of seismic input for outcrop (Seismic Hazard)

• Site effects in free-field conditions (1D,2D,3D)

• PHGA, PVGA, PGV, PGD, PSA, PSV, Sd, strains (γ), and stresses (σ) at

the ground surface and at different depths

• Asynchronous motion characteristics (apparent velocity...),

differential displacements

• Induced phenomena and ground failure (liquefaction and liquefaction

induced phenomena, uplift, settlements, lateral spreading...), fault

displacement, landslide displacements



AUTH SDGEE36

SW

Lateral

propagation

SH

1D

Design input motion considering complex 2D effects



AUTH SDGEE37

Bedrock motion > Deconvolution design principles

Usually ground motion deconvolution method is applied to estimate,

from a known surface ground motion, the bedrock motion and finally the

FREE FIELD ground response at the level of each tunnel segment



AUTH SDGEE38

22.7 22.75 22.8 22.85 22.9 22.95 23 23.05 23.1 23.15 23.2

40.4

40.45

40.5

40.55

40.6

40.65

40.7

40.75

40.8

100

120

140

160

180

200

220

240

260

280

300

320

340

360

380

400

0.15g

0.20g

0.24g

0.28g

Τm=475

Site specific seismic

hazard assessment

Thessaloniki T= 475

years

0.1

0.15

0.2

0.25

0.3

0.35

PHGA (g)

Design input motion

Metro

Immersed

roadway



AUTH SDGEE39

0 5 10 15 20 25 30

Settlements (cm) due to liquefaction

0

0.05

0.1

0.15

0.2

0.25

Thessaloniki, Tm = 500 years

500 years PGV

Design input motion (PGV m/s) and liquefaction settlements



AUTH SDGEE40

Design input motion in the longitudinal analysis

• Spatial variability of ground motion

• Time lag (Phase difference)

• Incoherency of the ground motion

Wavefront

1 2 3 1 2 3

epicenter

heterogeneity

1 2 3

epicenter

A

faultB

1 2 3

1 2 3: Underground structure



AUTH SDGEE41

Transversal seismic analysis



AUTH SDGEE42

Methods

• Equivalent static analysis

• Analytical close-form solutions

• Statically imposed seismic ground deformations

• Full dynamic time-history analysis

“Open” issues

• Estimation of seismic earth pressures

• Estimation of seismic shear stresses along the perimeter

• Impedance functions

• Modeling features



AUTH SDGEE43

• Seismic forces are acting as equivalent static inertial forces:

• Equivalent static forces: Calculated for an average acceleration

estimated along the structure’s depth. Applied either directly on the

structure or through springs

• Dynamic earth pressures: Limit - state Mononobe - Okabe approach

and seismic code regulations for non-deformable walls

• Hydrodynamic pressures: Westergaard theory

• Seismic shear stresses: Applied through the shear springs

Equivalent static analysis

H

λογH 0.5 aγH

1.5 aγH

H

i

β

δ

h

EAE



AUTH SDGEE44

• Equivalent static forces (case A)


(a)

(d)

(c) (b) (e)

(b)

(a)(c)(b) (e)(f)g2+q

structure's

weight +

inertia forces

soils weight + inertia forces

(a) geostatic pressures, (b) hydro-dynamic pressures, (c) hydrostatic pressures, (d) seismic shear stresses,

(e) seismic earth pressures, (f) dead (g2) and live loads (q)



AUTH SDGEE45

• Equivalent static forces (only dynamic part) (case B)


δx

structure's

weight +

inertia forces

soils weight + inertia forces

seismic shearstresses

springs-impedance

functionsKx,Ky

seismic shearstresses

bedrock

dynamic pressures

ground differential displacement

between surface and bedrock

hydro-dynamic pressures

hydro-dynamic pressures

dynamic pressures



AUTH SDGEE46


Open issues

• Impedance functions for underground structures ?

• Modeling of kinematic and inertial aspects of Soil-Structure

Interaction

• Seismic earth pressures considering structure’s flexibility

• Ground acceleration ?

• Seismic shear stresses in the perimeter ?

• Importance and effect of relative soil-structure flexibility ?



AUTH SDGEE47

Example : Immersed roadway tunnel

• Model- loads (dynamic part)

a: Equivalent static inertial forces, b: Seismic earth pressure, c: Hydrodynamic pressures

Kwx

Kwz

Ksx

x

z F1=32.95kN/m

F2=5.90kN/m

1.5 aγΗ=76.44 kN/m

0.5aγΗ=

32.34 kN/m

(b)

(a)

(a)

Kzx

Kwz

Ksx

x

z

15.20 kN/m

26.95 kN/m

15.20 kN/m

26.95 kN/mKzx

(c) (c)

2B=34m

h=

7.5

m

D=

11

m



AUTH SDGEE48

Impedance functions – Kw,x Few are specifically for tunnels

Kwx

Kwz

Ksx Ksz

x

z



AUTH SDGEE49

Impedance functions – Ks,x – Kb,z Few are specifically for tunnels

Kwx

Kwz

Ksx Ksz

x

z



AUTH SDGEE50

Impedance functions – Ks,z – Kw,z Few are specifically for tunnels

Kwx

Kwz

Ksx Ksz

x

z



AUTH SDGEE51

Analytical close-form solutions

Two categories:

• Solutions ignoring SSI effects

• Solutions taking into account SSI effects

Main assumptions:

• The soil behaves as elastic infinite homogeneous isotropic medium

• Elastic behavior for the structure

• Structure is modeled an elastic beam on elastic foundation in the

longitudinal direction

• Structure considered under plane strain conditions in the

transversal direction

• Full slip or no slip conditions may be considered for the soil-

structure interface



AUTH SDGEE52

Analytical close-form solutions with no SSI

• Νο SSI effects

• Circular cross section

Wang, 1993, Hashash et al., 2001

maxγΔd

d 2

max m

Δdγ v

d2 1

structure free fieldγ γ



AUTH SDGEE53


• SSI effects are not taken into account

• Rectangular cross section

Hashash et al., 2001




AUTH SDGEE54

• SSI effects are taken into account in a simplified way


• Solutions for full slip

Analytical close-form solutions considering SSI

1 max

Δd 1K Fγ

d 3

mmax 1 max

m

E1T K Rγ

6 1 ν

2mmax 1 max

m

E1M K R γ

6 1 ν

m1

m

12 1-νK =

2F+5-6ν

όπου:

Wang, 1993

Moment:

Axial force:

2m l

l m m

E 1-ν RC

E t 1 ν 1- 2ν

2 3m l

l m

E 1-ν RF

6E I 1 ν

Compressibility

ratio

Flexibility

ratio



AUTH SDGEE55



• Solutions for no slip


όπου:

mmax 2 max 2 max

m

ET =±K τ r=±K Rγ

2(1+ν )

2

m m m

22

m m m m m

1F 1- 2ν - 1- 2ν C - 1- 2ν 2

2K 15

F 3 - 2ν 1- 2ν C C - 8ν 6ν 6 - 8ν2

Hoeg, 1968

Axial force:

2m l

l m m

E 1-ν RC

E t 1 ν 1- 2ν

2 3m l

l m

E 1-ν RF

6E I 1 ν

Compressibility

ratio

Flexibility

ratio



AUTH SDGEE56


Racking coefficient 1

structure

structure structure

free-fieldfree-field free-field

ΔΔ γHR= = = β( vs)

ΔΔ γ

HPenzien (2000)

“Racking” Approach (Penzien)



AUTH SDGEE57


• Estimation of free field deformations (through 1D analysis)

• Estimation of “flexibility ratio” F = soils stiffness/ structure stiffness

ΙR

ΙS

ΙW

Δstructure=R x Δfree field

W

H

E

2 2

m

w R

G H W HWF= +

24 EI EI

“Racking” Approach (Wang, Penzien)



AUTH SDGEE58

F 0 Rigid structureNo racking deformation will be

displayed

F<1.0Structure is stiffer than the

surrounding soil

Structural deformation smaller

than free-field deformation

level

F=1.0Structure and soil have

the same stiffness

Structure will follow the free-

field deformation

F>1.0 Soil stiffer than the structure

Structure racking deformations

amplified compared to the free-

field deformations

“Racking” Approach (Wang, Penzien)



AUTH SDGEE59

• Estimation of Δstructure through the racking evaluation

• “Static” analysis of the structure with the imposed Δstructure

F flexibility ratio

R=Δ

stru

ctu

re/Δ

free f

ield

Wang,1993

Circular Tunnels

Rectangular

Tunnels

“Racking” Approach (Wang)



AUTH SDGEE60

• Pseudo-Static numerical analysis

• Free-field ground deformations applied at the mesh soil boundaries

• Soil-structure interaction is explicitly taking into account

• 2D FE models utilizing 2D plain strain elements or springs for the

soil and beam elements for the structure

Imposed seismic ground deformations

Open issues

• Appropriate side-boundaries distances to the structure’s cross

section?

• Spring values in case of using this model



AUTH SDGEE61

• Case A : SSI modeling using soil springs

seismic shear

stresses

seismic shear

stresses

δ'x

Free Field

ux (m)

t (sec)

Free Field

ux (m)

t (sec)

t1

δx(t1)=

ux surface (t1)-

ux bedrock(t1) =max

δ'x

δx (t1)

springs-impedance

functions

Kx,Ky

bedrock

Max free-field ground

differential displacement

δ'x



AUTH SDGEE62

• Case B : Soil and SSI modeling through 2D plain strain elements -

the ground seismic displacements are imposed at the soil

boundaries

free field ground differential displacement

between surface and bedrock

Plain Strain

Finite Elements



AUTH SDGEESeismic design of large, long underground structures: Metro and parking stations, highway tunnels 63


Model boundary

Initial

soil

layers

Δu=0.012m

d = 5.0m

z = -20.0m

Inclined bed

• Seismic ground deformations for the initial soil layers



AUTH SDGEE64


2D model

(ADINA FE code)

Full dynamic analysis



AUTH SDGEE65


water - Thermaikos bay

-10.50 m

-14.50 m

-22.50 m

-30.50 m

-66.50 m

-110.50 m

Vs =130m/s, γ=18.6kN/m³

Vs =270m/s, γ=21.0kN/m³

Vs =380m/s, γ=21.5kN/m³

Vs =500m/s, γ=22.0kN/m³

Vs =700m/s, γ=22.0kN/m³

Compacted gravel materialVs =380m/s, γ=21.5kN/m³tunnel cross section

Thessaloniki 1978

Surface

-6

-4

-2

0

2

4

6

A (

m/s

ec2)

Free Field (0.50g)Near the structure (0.39g)

z=-14.50m

-6

-4

-2

0

2

4

A (

m/s

ec2)


z=-22.50m

-4

-3

-2

-1

0

1

2

3

A (

m/s

ec2)

Free Field (0.28g)

Near the structure (0.27g)

z=-30.50m

-3

-2

-1

0

1

2

3

A (

m/s

ec2)


Input motion - Bedrock (0.24g)

-2

-1

0

1

2

A (

m/s

ec2

)Full dynamic analysis



AUTH SDGEE66

Discussion

• Differential slab displacements (drift)

• Seismic earth pressures

• Seismic shear stress developed around the structure

• Bending moments, axial and shear forces on critical cross sections

• Accuracy of the impedance factors



AUTH SDGEE67

a) Differential slab displacements (drift)

F-R analytical

solution

and

full dynamic analysis

are well compared


Differential slab displacements (Thessaloniki 78)

-0.008

-0.004

0

0.004

0.008

d (

m)

Differential slab displacements (Kozani95)

-0.008

-0.004

0

0.004

0.008

d (

m)

Closed-form solution (Wang)

Full dynamic time-history analysis



AUTH SDGEE68

• Due to the tunnel’s complex behaviour during ground shaking, the earth

pressures developed along the side-walls, vary between passive and active

limit state, reaching values between the two limit state earth pressures


b) Seismic earth pressures

σyy Earth Pressure on tunnel wall

-7.5

-6.5

-5.5

-4.5

-3.5

-2.5

-1.5

-0.5

0 50 100 150 200 250 300 350

σyy(kPa)

z(m

)

Seismic pressure THESS

Seismic pressure KOZ

Rigid Wall E.A.K. 2003

Average (time history)

M.O.- uniformly distributed

M.O. triangularly distributed

M.O. passive



AUTH SDGEE69

c) Seismic shear stresses

Example : Metro tunnel in Thessaloniki

1D site response analysis

MethodShear stress YZ (KN/m²)

Max Effective

1D FF Analysis (mean value) 95.0 66.5

1D FF Analysis (Kozani 95) 68.0 47.6

Dynamic Analysis (Kozani 95) 65.0-70.0 48.0

• 1D ground response analysis provides reasonable estimation of the

horizontal shear stresses



AUTH SDGEE70


• Comparison with soil shear strength (Mohr Coulomb)

• Solid connection between structure and soil, usually adopted in dynamic

analysis, does not always occur. Interface behavior maybe quite complex

• Side walls:

Effective shear stress at side walls

-7.5

-5

-2.5

0

-50 -25 0 25 50 75 100 125 150 175 200

σyz(kPa)

z(m

)

Thessaloniki time-history

Kozani time-history

Mohr-Coulomb limit stress



AUTH SDGEE71


• Roof slab:

Effective shear stress σyz at roof slab

-150

-100

-50

0

50

100

0 8.5 17 25.5 34

L (m)σyz (

kPa)

Thessaloniki time-history- Roof slab

Kozani time-history- Roof slab

Mohr Coulomb limit stress-Roof slab



AUTH SDGEE72


• Inverted slab:

Effective shear stress σyz at inverted slab

-50

0

50

100

150

200

250

0 8.5 17 25.5 34

L (m)

σyz (

kPa)

Thessaloniki time-history- Inverted slab

Kozani time-history- Inverted slab

Mohr Coulomb limit stress- Inverted slab



AUTH SDGEE73


• Side walls: Effective shear stresses applying different methods

Effective seismic shear stress σyz at the side walls (Kozani95)

-7.5

-5

-2.5

0

-60 -40 -20 0 20 40 60 80 100 120

σyz(kPa)

z(m

)

Dynamic analysis

Imposed seismic

ground deformations

Wang (mean value)

Wang (Initial soil

properties)

Wang (Gravel material

properties)



AUTH SDGEE74


• Roof slab: Effective shear stresses applying different methods

Effective seismic shear stress σyz at the roof slab (Kozani95)

-140

-120

-100

-80

-60

-40

-20

0

20

40

60

80

100

120

0 8.5 17 25.5 34

L (m)

σyz (

kPa)

Dynamic analysis


Wang (mean value)

Wang (Initial soil properties)

Wang (Gravel material properties)

..



AUTH SDGEE75


• Inverted Slab: Effective shear stresses applying different methods

Effective seismic shear stress σyz at the inverted slab

(Kozani95)

-100

-80

-60

-40

-20

0

20

40

60

80

100

120

0 8.5 17 25.5 34

L (m)

σyz (

kPa)

Dynamic analysis


Wang (mean value)

Wang (Initial soil properties)

Wang (Gravel material properties)

.



AUTH SDGEE76

d) Section internal forces

• “Effective” values

Bending moment time - history (Thessaloniki78)

-2000

-1600

-1200

-800

-400

0

400

800

1200

1600

Bendin

g m

om

ent

(kN

m)

P4 left bending moment time history

Effective value (1123.8kNm)



AUTH SDGEE77


P1 P2

Τ1 Τ2

P3

Τ4Τ3

P4 P5 P6

Axial force results

-1250

-1000

-750

-500

-250

0

250

500

750

1000

P1 l

eft

P1 c

ente

r

P1 r

ight

P2 l

eft

P2 c

ente

r

P2 r

ight

P3 l

eft

P3 c

ente

r

P3 r

ight

P4 l

eft

P4 c

ente

r

P4 r

ight

P5 l

eft

P5 c

ente

r

P5 r

ight

P6 l

eft

P6 c

ente

r

P6 r

ight

T1 u

p

T1 d

ow

n

T2 u

p

T2 d

ow

n

T3 u

p

T3 d

ow

n

T4 u

p

T4 d

ow

n

Axia

l fo

rce (

kN

)

Imposed seismic ground deformationsDynamic analysis Equivalent static analysis

• Equivalent static - Imposed seismic ground displacements – Full

dynamic analysis



AUTH SDGEE78



dynamic analysisP1 P2

Τ1 Τ2

P3

Τ4Τ3

P4 P5 P6

Shear force results

-1000

-800

-600

-400

-200

0

200

400

600

800

P1 l

eft

P1 c

ente

r

P1 r

ight

P2 l

eft

P2 c

ente

r

P2 r

ight

P3 l

eft

P3 c

ente

r

P3 r

ight

P4 l

eft

P4 c

ente

r

P4 r

ight

P5 l

eft

P5 c

ente

r

P5 r

ight

P6 l

eft

P6 c

ente

r

P6 r

ight

T1 u

p

T1 d

ow

n

T2 u

p

T2 d

ow

n

T3 u

p

T3 d

ow

n

T4 u

p

T4 d

ow

n

Shear

forc

e (

kN

)




AUTH SDGEE79


P1 P2

Τ1 Τ2

P3

Τ4Τ3

P4 P5 P6


dynamic analysis

Bending moment results

-1750

-1500

-1250

-1000

-750

-500

-250

0

250

500

750

1000

1250

1500

P1 l

eft

P1 c

ente

r

P1 r

ight

P2 l

eft

P2 c

ente

r

P2 r

ight

P3 l

eft

P3 c

ente

r

P3 r

ight

P4 l

eft

P4 c

ente

r

P4 r

ight

P5 l

eft

P5 c

ente

r

P5 r

ight

P6 l

eft

P6 c

ente

r

P6 r

ight

T1 u

p

T1 d

ow

n

T2 u

p

T2 d

ow

n

T3 u

p

T3 d

ow

n

T4 u

p

T4 d

ow

n

Bendin

g m

om

ent

(kN

m)




AUTH SDGEE80

Longitudinal seismic analysis



AUTH SDGEE81

Longitudinal seismic analysis

• Full dynamic time history analysis utilizing continuum FE models

• Dynamic Beam on Winkler foundation type models

• Analytical closed form solutions

Open issues

• Asynchronous seismic ground motion

• Joints seismic performance and modeling, in case of segmented

underground structures (e.g. immersed tunnels)

• Impedance functions (springs and dashpots frequency depended)



AUTH SDGEE82

• Seismic shaking varies in space in terms of wave amplitude, frequency

characteristics, time of arrival and duration

• Simplest modeling is with a phase difference approach

• Apparent velocity : Vapp (Cs) = 700 -1500 m/sec

• For tunnels min L = 100 m - 150 m (Kawashima et al.,1996)

• Time lag due to apparent velocity:

Asynchronous motion – Apparent velocity

θ tunnel

propagation direction

shear wave

iapp i+1 i

app

V LV t -t =

Vsinψ

ad

t

ad

t

ad

t

ad

t

t i t i+1 t i+2

Li LiLi

S1 S2 S3 S4



AUTH SDGEE83

• Joints of segmented tunnels, consist of special joints (e.g. Gina) and

shear keys

• Joints (Gina-Omega Seal)

Joints seismic design and modeling

0 20 40 60 80 100 120

Compression (mm)

2500

0

250

500

750

1000

1250

1500

1750

2000

2250

Forc

e(kN

/m)

10

0

1

2

3

4

5

6

7

8

9

Conta

ct p

ress

ure

(N

/mm

²)

Force of endless seal Local contact pressure

Daewoo,2004

Material law for GINA gasket

Treleborg



AUTH SDGEE84

Fy, Fz

δy, δz

< 5cm

• Shear keys

shear key

shear key



AUTH SDGEE85

• Joints final design

roof

inverted slab

Shear Key

Detail A

Omega seal

Gina Gasket

TendonDetail A



AUTH SDGEE86


• Analytical solution based on Newmark’s 1965 work

• SSI effects are not taken into account

St. John & Zahrah, 1987

Tunnel under simple

harmonic wave excitation




AUTH SDGEE87


• Tunnel under simple harmonic wave excitation

2

3c cc c

E I 2π 2πxM cos φE I Asin

ρ L L / cosφ

3

4c c

M 2π 2πxV cos φE I Acos

x L L / cosφ

c c

2π 2πxQ sinφcosφE A Acos

L L / cosφ


Moment:

Shear force:

Axial force:



AUTH SDGEE88


• Elastic beam theory


όπου:


2

3

c c4

4c c

h

2πcos φ

2πxLM E I Asin

L / cosφE I 2π1 cos φ

K L

3

4

c c4

4c c

h

2πcos φ

2πxLV E I Acos

L / cosφE I 2π1 cos φ

K L

c c2

2c c

a

2πsinφcosφ

2πxLQ E A Acos

L / cosφE A 2π1 cos φ

K L

Moment:

Shear force:

Axial force:



AUTH SDGEE89

• How can we calculate the soil stiffness ?

• Still, an open issue

• St. John & Zahrah, proposed:


όπου:


h a

ym

16πG 1 vP dK K

u 3 4v L



AUTH SDGEE90

• Closed form solution

• Free field ground deformations (γstructure = γfree-field )

Longitudinal seismic analysis – Analytical solutions

3s s

axial u axial e2

s s

v αε = ×sinφ×cosφ+r× ×cos φ Δ ε l

C CPower et al.,1996


Max joint deformation as function of Cs

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

500 750 1000 1250 1500 1750 2000 2250 2500Cs (m/sec)

Δu (

m)

Thessaloniki 78

Kozani 95



AUTH SDGEE91

3s s

axial 2

s s

u axial e

v αε = ×sinφ×cosφ+r× ×cos φ

C C

ε l Power et al.,1996


Max joint deformation as function of φ

0.000

0.005

0.010

0.015

0.020

0.025

0 10 20 30 40 50 60 70 80 90φ (deg)

Δu (

m)

Thessaloniki 78

Kozani 95



AUTH SDGEE92

• Tunnel is modelled as a linear equivalent elastic beam on dynamic Winkler

foundation modelled with springs and dashpots

Beam on Dynamic Winkler Foundation Model

• Crucial issues for modelling:

• The joints’ behaviour (between segments) is

difficult to be modelled, as their stiffness is

varying with seismic excitation

• Asynchronous motion

• Soil springs and dashpots (frequency depended)



AUTH SDGEE93

• Sensibility analysis: effect of phase difference, joints stiffness and

variability of soil properties along the tunnel axis


time lagjoint

material law soil properties

Model A no linear Uniform soil - no damping

Model B yes linear Uniform soil - no damping

Model C yes linear Uniform soil - damping

Model D yes linear Variable soil - damping

Model E yes bi-linear Uniform soil - damping

Model F yes bi-linear Variable soil - damping



AUTH SDGEE94


• Joint axial deformations

Joint 5 axial deformation (Winkler models)

-0.225

-0.2

-0.175

-0.15

-0.125

-0.1

-0.075

-0.05

-0.025

0

0.025

δx(m

)

Model BModel CModel DModel EModel F

Hydrostatic pressure Seismic excitation

t = 0

sec

+ (tension)

- (compresion)

Joint Failure



AUTH SDGEE95


• Joint axial deformations

Thessaloniki 78

m

o

d

e

l

Joint 1 Joint 5 Joint 9

maxΔx

(m)

minΔx

(m)

maxΔx

(m)

minΔx

(m)

maxΔx

(m)

minΔx

(m)

A 0.058 -0.056 0.011 -0.01 0.059 -0.062

B 0.07 -0.061 0.045 -0.048 0.06 -0.058

C 0.07 -0.061 0.044 -0.046 0.06 -0.058

D 0.07 -0.057 0.099 -0.088 0.088 -0.049

E 0.07 -0.052 0.043 -0.039 0.059 -0.06

F 0.07 -0.052 0.099 -0.071 0.078 -0.05

analytical solution

(φ=0o, Cs=1000 m/sec)

0.0095 m

Joint 1

Joint 9

Joint 5



AUTH SDGEE96

Ground failure



AUTH SDGEE97

• Ground failure Large permanent deformations due to:

• Liquefaction

• Slope instability

• Fault displacements

• Liquefaction: pore water pressure build-up due to seismic excitation

reduction of effective stresses in saturated loose cohesionless silty sandy

soils deformations due to lateral spreading or settlements - uplift

• Liquefaction uplift mechanism: Study of retrofitting the BART system

Ground failure – Liquefaction

Kutter et al.,2008



AUTH SDGEE98

• Centrifuge experiments and numerical analyses (FLAC, UBCSAND and

OpenSees (Elgamal et al.))

• Uplift mechanism related primarily to movement of soil under the tunnel

during an earthquake

Kutter et al.,2008

FLAC (Version 5.00)

LEGEND

17-Oct-07 5:59 step 879504

Flow Time 4.0000E+01Dynamic Time 4.0000E+01

-6.500E+01 <x< 6.500E+01 -1.300E+02 <y< -2.000E+01

User-defined Groups

MPSA_ClayOFill

SurmudFCourseSFill

Grid plot

0 2E 1

Displacement vectors

scaled to max = 3.000E+00

max vector = 2.885E+00

0 1E 1

-1.200

-1.000

-0.800

-0.600

-0.400

(*10 2̂)

-5.000 -3.000 -1.000 1.000 3.000 5.000(*10 1̂)

JOB TITLE :

fugro fugro

0

10

20

30

0 20 40 60 80 100 120 Ανύ

ψω

ση

Σή

ρα

γγα

ς (

cm

)

Πείραμα

FLAC

OpenSees

Tunnel

uplift

(cm

)

Travasarou & Chacko, 2008

Experiment

FLAC

OpenSees



AUTH SDGEE99

• Differential shear displacements at joints (e.g. due to liquefaction lateral

spreading) are anticipated with the use of shear keys

• Liquefied soil soil-spring stiffness is usually reduced to 10% of their

initial values

• Two shear-slip scenarios are examined:

• (a) Uniform displacement (horizontal and vertical) imposed upon the tunnel

segment, while the segments next to it remain in their place

• (b) Differential displacement imposed upon the tunnel segment, due to

possible movement of the opposite segment




AUTH SDGEE100

• Horizontal shear key - b x d x l=1900x600x700 (mm)

• Vertical shear key - b x d x l=600x1650x700 (mm)

• Model adopted:

tunnel segment

shear key

restrains ux=uy=uz=0

displacement time history




AUTH SDGEE101

Concrete shear strength

1500 kN (without

considering the shear key

reinforcement and the

participation of the

tendons at the joint)

Horizontal lateral spreading displacement

Case (a) Case (b)

d (m) Vsd (kN) d (m) Vsd (kN)

0.10 3630 0.10 19200 15600

0.05 1815 0.05 9600 7800

0.01 363 0.01 1920 1560

Vertical displacement (settlements)

Case (a) Case (b)

d (m) Vsd (kN) d (m) Vsd (kN)

0.10 38150 0.10 51330 13160

0.05 19075 0.05 25665 6580

0.01 3815 0.01 5133 1316


Concrete shear

strength 2600 kN

Extreme scenario



AUTH SDGEE102

Importance of the seismic loads

compared to the static ones



AUTH SDGEE103

• Static loads:

• Dead loads of the structure (g1+g2)

• Live loads of the structure (q)

• Hydrostatic pressures and uplift force at the structure (E1)

• Geostatic pressures at the structure (E2)

g1

Kwx

Kwz

KsxKsz

g1+g2

g1+g2+E1

g1

E1 E1

E1

E2 E2

g1+g2+q



AUTH SDGEE104

Real Time

Early Warning



AUTH SDGEE105

Different components and time scales in seismic risk



AUTH SDGEE106

Basic concepts and measurements of earthquake early

warning systems



AUTH SDGEE107

Time depended risk assessment

Hazard

Exposure/value

Vulnerability

Risk

Non-Poissonian recurrence

* * *

Population & economic growth

=

?

Foreshock

Aftershock

Retrofitting

Time

Evacuation

Time

Time

Time



AUTH SDGEE108

Vulnerability assessment



AUTH SDGEE109

Vulnerability assessment



AUTH SDGEE110

Fragility Curves

• Empirical / statistical

• Analytical / numerical

• Expert judgment

• Hybrid

• Provide the probability for the element at risk to be in or exceed a certain

damage state under a seismic event of given intensity

• Illustration of the relationship between seismic excitation and damage

1.0

0.0

0.0

Damage

Probability

Seismic

Motion

Complete Damages

NOT FUNCTIONAL

Minor damage

FUNCTIONALITY

ai

Pf

Pc



AUTH SDGEE111

Empirical fragility curves for tunnels (ALA, 2001)

• Fragility curves for tunnels with poor to average construction quality in soil

or cut and cover conditions, subject to ground shaking



AUTH SDGEE112

General flowchart of the procedure for deriving

numerical fragility curves for tunnels in alluvial deposits

Tunnel typology

Basic models

Soil type

Typical soil profiles (P)

Seismic input motion

Accelerograms (A), intensity levels (S)

1D equivalent linear analysis of the soil profiles - input motions

models (PxAxS)

Quasi static response of the soil-tunnel

models

Soil deformations and soil stiffness parameters

Damage index (DI), damage states (ds),

thresholds values of DI for each ds

Evolution of damage with earthquake parameter (EP), median threshold

value of EP for each ds

Fragility curves for each tunnel and soil type

Uncertainties

(seismic demand, tunnel capacity, definition of DI and ds)

Argyroudis & Pitilakis 2011 (submitted)



AUTH SDGEE113

Deformed Mesh

Extreme total displacement 43.07*10-3

m

(displacements scaled up 100.00 times)

Bending momentExtreme bending moment -84.28 kNm/m

Mmax=-84.3 kNm/m

Axial forcesExtreme axial force -692.68 kN/m

Nmax=-692.7 kN/m

b)

Tunnel response analysis

• A plane strain ground model and the tunnel cross sections are simulated

using the Plaxis finite element code (Plaxis, 2002)

• Shear deformations that are calculated by 1D linear equivalent soil

response analysis, for the different levels of peak ground acceleration are

imposed on the boundaries of the plain strain model

• Stresses and deformations of tunnel lining can be assessed due to the shear

distortion of the surrounding ground



AUTH SDGEE114

Comparison Analytical vs Empirical (minor damage)

Circular (bored) tunnel - Minor damage

0.0

0.3

0.5

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

PGA (g)

Pro

ba

bilit

y o

f d

am

ag

e 0

soil D

soil C

soil B

Empirial - ALA 2001

(good quality construction)



AUTH SDGEE115

Comparison Analytical vs Empirical (moderate damage)

Circular (bored) tunnel - Moderate damage

0.00

0.25

0.50

0.75

1.00

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

PGA (g)

Pro

ba

bilit

y o

f d

am

ag

e

soil D

soil Csoil B

Empirial - ALA 2001

(good quality construction)



AUTH SDGEE116

Conclusions



AUTH SDGEE117

• Input motions and seismic design loads must be estimated

through a detailed seismic hazard analysis, considering the

specific site effects due to local soil and site conditions

• There is no doubt that the most accurate method for seismic

design of extended underground structures is the full dynamic

time-history analysis, utilizing 2D or 3D FE, FD, BE models, and

adequate soil and structural models with appropriate

constitutive relationships. This approach can successfully model

the complex soil-structure interaction effects

• Underground structures should be designed for imposed seismic

ground deformations rather than inertial forces



AUTH SDGEE118

• Analytical methods utilizing the racking coefficient method (i.e.

Wang, 1993), seems to give rather acceptable results, in case of

shallow underground structures (tunnels). Further improvement

and extension is deemed necessary

• Quasi-static imposed seismic ground deformation methods

combined with numerical modelling, provide an interesting

approach. Soil-structure interaction can be directly taken into

account.



AUTH SDGEE119

• Equivalent static analysis is proved to be conservative for

shallow tunnels, while for subway stations and deep large

underground structures is clearly un-conservative

• In general it is unable to describe correctly all seismic

phenomena and the actual seismic response of the deep and

large spaced structures

• Issues, such as the estimation of appropriate impedance

functions for underground structures to model soils behaviour

and SSI effects, the modelling of equivalent static seismic

inertial forces, the estimation of seismic earth pressures, the

seismic shear stress developed during the shaking along the

perimeter of the structure, are still open, and more research is

deemed necessary



AUTH SDGEE120

• Longitudinal seismic analysis of long segmented structures is

equally important with the transversal analysis. Asynchronous

ground motion must be absolutely considered in the analysis

procedure. Simple phase difference introducing a simple time

lag may not be always accurate enough. The apparent velocity

should be accurately estimated based on accurate geological and

geotechnical data. A conservative value of Capp = 800m/s could

be used. Special seismic design provisions must be taken for

joints and shear keys, as these elements are the most vulnerable

parts of an underground structure



AUTH SDGEE121

• Ground permanent displacements due to liquefaction, slope

instability or fault rupture must be seriously taken into

consideration, as they can affect seriously the overall design and

safety of the structure

• Static loads and especially uplifting from buoyancy, are

controlling in general the overall design of an underground

structure

• Seismic loads are becoming very important when uplift buoyancy

loads are minimized, for PGA >0.2g (outcrop conditions) and

medium stiffness soils which amplifies considerably the ground

motion



AUTH SDGEE122

• A research program is undergo in Aristotle University aiming to

provide specific answers to several of the subjects discussed,

namely:

- Seismic earth pressures for rigid and flexible structures

- Shear stresses development and distribution

- Impedance functions (frequency depended springs and

dashpots)

- Importance and quantification of structure’s flexibility

and to propose a solid methodology for the seismic analysis and

design of tunnels and large space underground structures

• Centrifuge test experiments in LCPC-Nantes and the University of

Cambridge will provide the necessary experimental validation and

breakthrough to better understand the physical problems and

validate the numerical modelling (SERIES project)



AUTH SDGEE123

Moreover Aristotle University is participating in ongoing major EU

research projects aiming to contribute significantly to:

• the development of improved methods for the risk assessment

at system’s level considering intra and inter-dependencies in

the system’s vulnerability and risk assessment considering

buildings, facilities, lifelines and infrastructures, including

tunnels as parts of a global system

(SYNER-G http://www.syner-g.eu) Coordinator

• the real time seismic risk assessment of structures (buildings,

tunnels etc) with emphasis to the development of time

depended fragility (vulnerability) of elements at risk and

advanced, more efficient, early warning technology

(REAKT)



AUTH SDGEE124

Thank you

seismic design and risk assessment of underground …. pitilakis - seismic design... · assessment...

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