phyygsical modeling for the evaluation of the seismic ... · • transversal seismic behavior and...

SERIES Workshop “Role of research infrastructures in seismic rehabilitation”Istanbul, 8 - 9 February 2012 SERIES Workshop

“Role of research infrastructures in seismic rehabilitation”Istanbul, 8 - 9 February 2012

Physical modeling for the evaluation of the y gseismic behavior of underground structures

TA- SERIES

G. Tsinidis, D. Pitilakis, E. Rovithis , E. Kirtas, A. Anastasiadis

TA SERIES

K. Pitilakis

Aristotle University, Thessaloniki Greece

In cooperatıon wıthp

Unıversıty of Cambrıdge UKIFSTTAR Nantes France

AUTH SDGEE

IFSTTAR Nantes France

SERIES Workshop “Role of research infrastructures in seismic rehabilitation”Istanbul, 8 - 9 February 2012

Underground structures

• Mountain tunnelsSubways

Underground structures

• Subways• Highway tunnels• Shallow and deep metro stationsp• Underground parking stations, commercial centers• Nuclear power plants ducts

• Their seismic design in seismically prone areas is of major importance• Safety - economy• Safety economy

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Observed damages in past earthquakesSeismic performance Seismic performance

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Observed damages in past earthquakes Observed damages in past earthquakes

Dakai subway, Kobe, 1995, Mw=6.9

• Collapse of the station• Designed with poor seismic design considerationsg p g

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Dakai subway, Kobe, 1995, Mw=6.9y, , ,

• The main cause of collapse is due to the shear and buckling failure of thecentre columns, which were designed and constructed with insufficienttransverse shear reinforcementt a sve se s ea e o ce e t

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Iida et al., 1996, Kawashima, 2000, Hashash et al., 2001


Dakai subway, Kobe, 1995, Mw=6.9y, , ,

1.72m 2.19m

Column 10Column 10

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Chi Chi earthquake (1999)

spalling

Chi Chi earthquake (1999)

cracks

cracks

spalling

(b) (c)lining cracks

cracks

kl h d ff b cracks

cracks

spalling

(d) (e)lining sheared off by

displaced fault(a)

cracks

localspalling

opening

(f) (g)

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(f) (g)Wang et al. (2001)


Kocaeli earthquake (1999)Kocaeli earthquake (1999)• Circular tunnel – failure during construction

ΗΕΒ

03 ‐ 0.4 m

Detail

0.3

AUTH SDGEE

Kontoe et al. (2008)


Seismic behavior

• Seismic behavior of underground structures is substantially different fromaboveground structures

• Imposed seismic ground deformations rather than inertial forces dominate• Imposed seismic ground deformations rather than inertial forces dominatethe structure’s seismic response

1x1 (m)

0m10m

8m 1x1 (m)

ρstr.=2.5t/m³E=29 GPa Mmax=683kNm αmax==0.37gαmax=0.62gMmax=444kNm

‐50m(a)

Vs=200m/secρ=2t/m³ξ=5%

8m

4m

1x1 (m)

ρstr.=2.5t/m³E=29 GPa

αmax=0.20g αmax=0.20g10m

Vs=200m/sec

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(b) ρ=2t/m³ξ=5%


Shaking• Shaking• Imposed seismic ground deformations and the relative stiffness or the

stiffness contrast between the structure and surrounding soil, control theoverall seismic behaviour of an underground structure

• Ground failure• The response is also controlled by the imposed permanent ground• The response is also controlled by the imposed permanent ground

deformations and displacements due to:• Liquefaction : Settlements, lateral spreading• Slope failure• Fault movements

• Crucial parameters controlling the soil – structure system behavior:

Soil to structure flexural stiffness (Flexibility ratio)• Soil to structure flexural stiffness (Flexibility ratio)

• Soil – tunnel interface conditions (rough or smooth interface)

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Flexibility ratio • Penzien, 2000• Deformations of rectangular cavity

ff s ffτ G γ=

c ffγ βγ= ff

( )c ff sβ γ γ 4 1 v= = −

G

• Stiffness of outside soil, inside soil and lining• Compatibility of deformations

ssoil si

Gk τ H= =

( )il ilk k 3 4v= −( )soilo soil sk k 3 4v

( )stru is s ffΔd Δd 4 1 v γ H+ = −

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Wang 1993• Wang, 1993• Concentrated load P - Fixity of the invert slab• S1: force required to cause unit racking to structure – estimate from simple

i l istatic analysis

G d f

Rectangular

Ground surface

sm

Δ τγ

Η G= =

gsoil element

ms

τ τG

ΔγΗ

= =

Rigid Base Soil column

Under simple shear

1s

1 1 s

ΗSΔ P τW τ τγ

ΔΗ ΗS ΗS γ WH

= = = → = =

m

1

G WF

ΗS=

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Important “open” issuesImportant open issues

• Input motion intensity and characteristics and modeling issuesTransversal seismic behavior and analysis• Transversal seismic behavior and analysis

• Estimation of seismic earth pressures• Estimation of seismic shear stresses along the perimeterg p• Deformation pattern• Estimation of impedance functions• Modeling features (i.e. equivalent static loads, boundaries etc.)

• Longitudinal seismic behavior and analysis• Estimation of the asynchronous seismic motion• Estimation of the asynchronous seismic motion• Estimation of impedance functions• Deformation patterns and modelling

• Several other issues coming from the design and construction point of view• Joints performance, design and construction, in case of segmented

underground structures (e g immersed tunnels)

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underground structures (e.g. immersed tunnels)


Important “open” issues – example Important open issues example • Input motion? Shear stresses• Equivalent static forces?• Impedance functions?

h

ground differential displacementbetween surface and bedrock

δxsoils weight + inertia forces

seismic shearstresses

dynamicpressures

dynamicpressures δx

structure'sweight +

pressures pressures

weight +inertia forces

i i dsprings‐impedancefunctionsKx,Ky

seismic shearstresses

bedrock

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bedrock


Physical modeling of seismic behavior of underground structures

Short literature review

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Physical modeling of seismic behavior of underground Physical modeling of seismic behavior of underground structures

• Few well-documented case histories, lack of comprehensive methodologiesspecific guidelines and seismic code regulations for the seismic design ofunderground structures with the exception maybe of gas and oil pipelines

• Physical modeling and numerical analysis are used to better understand thephysical problem and in particular the soil structure interaction phenomenonphysical problem and in particular the soil-structure interaction phenomenon

• Physical modeling provide quality data under perfectly controlled conditionsfor the validation of the numerical procedures and codes

Indicative examples (a list of references is presented at the end)• Indicative examples (a list of references is presented at the end)

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Case 1• Researchers: Bilotta et al., 2009, Lanzano et al., 2010 (ReLUIS project)• Type of structure: Circular tunnels• Type of experiments: dynamic centrifuge tests performed on aluminum

tunnel models embedded in dry sand under 80g, to study the affection ofburial depth on the seismic behavior and mainly to produce data for thevalidation of the design methods (uncoupled and coupled methods)

• Tests conducted at the Centrifuge facility of the Schofield Center in alaminar boxlaminar box

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Case 1• Round Robin numerical Test on Tunnels under seismic loading (TC104,

TC203 and TC204)• Blind prediction numerical testBlind prediction numerical test• AUTH participation

500mm

Displacement constrains

Acc 11Acc 15

Acc 8 Acc 9

LVDT045 LVDT059

124mm124mm110mm500mm

110mm

m0mm

23.2m1g

constrains

Acc 16

SW SE

NW NEAcc 7

Acc 14Acc 6Acc 12

Acc 3Tunneld=75mm

290m

m

mm

144m

m

130

57.5

7.5

40.0 m

a(t)

Scale Factor N=80

Acc 13Acc 1

Acc 4SW SE

Acc 5

Acc 10

Dry FractionE sand

125m57

45

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Shake direction

Accelerometer ‐ sensingdirection towards left LVDT Strain gauge Reference accelerometer

recording input signal


Case 2Case 2• Researchers: Cilingir & Madabhushi (2010a, 2010b, 2011)• Type of structure: Square, Circular tunnels• Type of experiments: dynamic centrifuge tests performed on aluminum

tunnel models embedded in dry sand under 50g, to study the affection ofthe input motion characteristics and of the burial depth of the tunnels onp pthe seismic behavior

• Tests conducted at the Centrifuge facility of the Schofield Center at theUniversity of Cambridge UK using a Rigid box with a windowUniversity of Cambridge UK using a Rigid box with a window

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Case 3• Researchers: Shibayama et al., 2010• Type of structure: Urban mountain type tunnels• Type of experiments: pseudo-static centrifuge tests performed on

aluminum tunnel models embedded in dry sand, to study the effect ofburial depth and the connection of the invert slab with the tunnel lining

Welded model

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Non-welded model


Case 4• Researchers: Chou et al., 2010, Kutter et al., 2008, Travasarou & Chacko,

2008, Travasarou, 2010T f t t : i d t l t fit h k f th i ti g BART• Type of structure: immersed tunnel, retrofit check of the existing BARTsystem

• Type of experiments: 2 dynamic centrifuge tests performed on PVC tunnelmodels, under 40g, to evaluate the potentially uplift of the BART tubecaused by liquefaction (UC Davis USA)

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Case 5• Researchers: Chen et al., 2010• Type of structure: Rectangular utility tunnel• Type of experiments: 46 shaking table tests performed on RC models (one

jointless and one with 2 construction joints) embedded in unsaturatedsand to study the effect of the non-uniform ground motion along thealignment of a utility tunnel

• Sensors to measure slippage at the interface, displacement and rotationat the jointsat the joints

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Main remarksMain remarks

• For horizontal shaking appearance of vertical acceleration components(i.e. Yukio et al., 2001)

• Physical modeling can help to understand the uplift behavior of immersedtunnels during liquefaction, validate the efficiency of the countermeasuretunnels during liquefaction, validate the efficiency of the countermeasureretrofit techniques and validate the numerical models (i.e. Adalier et al.,2003, Chou et al., 2010 etc.)

• Kinematic loads (ground strains) are more important than inertial forces• Kinematic loads (ground strains) are more important than inertial forces(i.e. Iwaga et al., 2006)

• Internal forces, in case of flexible embedded structures; Three distinctivet b d l t i t t f ll i b t d t tstages are observed namely a transient stage following by steady state

circles and finally a post-earthquake residual stage, (i.e. Bilotta et al, 2010,Lanzano, 2009, Cilingir & Madabhushi, 2010a, 2010b, 2011)

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• Shear stresses around the perimeter of an underground structure: It isvery difficult to be measured accurately. Their values depend on severaly y pfactors (intensity of the input motion, rugosity of the soil lining interface,measuring equipment etc) (Tohda et al, 2010).

• Flexible tunnels (square or circular) tend to deform inward (i e Cilingir &• Flexible tunnels (square or circular) tend to deform inward (i.e. Cilingir &Madabhushi, 2010a, 2010b, 2011). Except for racking or ovalingdeformations

• Non-uniform earthquake excitations produce higher intensities comparedto uniform ones (i.e. Chen et al., 2010)

• Non-uniform earthquake excitations can lead to important differentialq pdisplacements and rotation of the joints in case of segmented structures(i.e. Chen et al., 2010)

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• Questions on crucial “open” issues are not fully answered, namely:

• Input motion (characteristics, asynchronous motion)?• Seismic earth pressures on the side walls?

Seismic shear stresses around the embedded structure perimeter?• Seismic shear stresses around the embedded structure perimeter?• Deformation patterns• Impedance functions for underground structures?p g• Effect of backfill material on the seismic behavior of underground

structures?J i t f d i t d ig ?• Joints performance and appropriate design?

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AUTH ongoing research projects on the seismic behavior of rectangular embedded structureswith reference to physical modelling in the

framework of SERIES

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Introduction Introduction • Further experimental and numerical study deemed to be necessary,

especially in case of rectangular embedded structures, to answer the “open”d h dquestions and improve the seismic design

• Two relevant research projects are running within the Transnational Accesstask of SERIES, titled:

• “Investigation of the seismic behavior of shallow rectangularunderground structures in soft soils using centrifuge experiments”

• “Investigation of several aspects affecting the seismic behavior ofshallow rectangular underground structures in soft soils”

• The first program is running at the centrifuge facility of IFSTTAR in Nantes,France, whereas the second program is running at the centrifuge facility ofthe Schofield Center at the University of Cambridge, UK

• Centrifuge testing of rectangular embedded structures in dry or saturated

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g g g ysands submitted to simple sine waves or real recordings


• Main objectives:

• Study the influence of the relative flexibility ratios on the driftdisplacement

• Study the seismic earth pressures distribution along the side-walls

• Study the seismic shear stresses distribution and magnitude along they g gperimeter of underground structures

• Estimate proper impedance functions for underground structures toEstimate proper impedance functions for underground structures tomodel kinematic and inertial soil structure interaction effects

• Study the effect of backfill material (e.g. gravel), on the seismicStudy the effect of backfill material (e.g. gravel), on the seismicbehavior of an underground structure

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“Investigation of the seismic behavior of shallow rectangular underground structures in

soft soils using centrifuge experiments”

Centrifuge facility of IFSTTAR, Nantes, France

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General descriptionGeneral description• Centrifuge tests on rectangular tunnel models, embedded in saturated or dry

sand under a centrifugal acceleration of 40g will be carried out at thet if f ilit f IFSTTAR i N t Fcentrifuge facility of IFSTTAR in Nantes, France

54mm or 47mm 400mm360mm

326mm

Section A‐A ‐ Soil instrumentation

Model

mm Α Α

Model

m10

0mm

180mm

15mm

50mm

10mm180mm

340m

Dry FontainebleauSand (Dr=70%)

320m

m


360m

m

30mm

130m

m

Scale Factor N=40Shake direction

800mm

1Accelerometer ‐ sensingdirection towards left

Pore pressuresensor

Reference accelerometerrecording input signal

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• Objectives:j• Seismic earth pressures distribution along the side-walls• Seismic shear stresses distribution along the perimeter• Impedance functionsImpedance functions

• Reduction factor N=40• 2 models: flexible model rigid model (2017 A aluminium alloy)• 2 models: flexible model, rigid model (2017 A aluminium alloy)• 2 levels of rugosity (smooth interface: , rough interface: )• Dry / saturated Fontainebleau sand NE34 (Dr=70%)

Real recordings of increasing amplitude (+ sine wavelets)

aluminiumδ δ= δ φ=

• Real recordings of increasing amplitude (+ sine wavelets)• 7 tests + 1 free field test

Model 1 Model 2

m 1 5m

47mmModel 1

m

Model 2

54mm

mm

5

m

6mm 1.5mm

1.5mm50mm

50mm 6m

5mm

m

5mm

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6mm

6mm


• Estimation of the flexibility ratio for the proposed model sections Estimation of the flexibility ratio for the proposed model sections • Takatori, 1995 (scaled to 0.05g (EQ1), 0.10g (EQ2), 0.15g (EQ3), 0.20g (EQ4),

0.30g (EQ5))

Ri id t lFlexible tunnel

12

14

16 Rigid tunnel

1

1.2

8

10

12

bility ratio

0.6

0.8

bility ratio

4

6

flexib

Saturated sandDry sand 0.2

0.4flexib

0

2

Initial EQ1 EQ2 EQ3 EQ4 EQ5

0

Initial EQ1 EQ2 EQ3 EQ4 EQ5

2mG HW

F ψ12 EI

⎛ ⎞= ⎜ ⎟

⎝ ⎠

6mm 1.5mm

mm

47mm

0mm

54mm

6mm

5

5mm

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R12 EI⎜ ⎟⎝ ⎠

6mm

6

1.5mm50 50 5mm

6mm


• Large ESB box is utilized to minimize the boundary effects

• ESB dimensions: 800x350x410 (mm)

54mm or 47mm

Model

340m

m Α Α

Dry Fontainebleau mm

ySand (Dr=70%)

320m

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• Special connection of the tunnel models ends to the laminar box to avoid any limitation of the models deformation that can affect the plane strain behavior

• 10mm thick Teflon plate + waterproof knob + aluminium plate glued on the knob

54mm or 47mm

Model

m Α Α

340m

m


320m

m

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Model configuration instrumentation scheme • Model configuration – instrumentation scheme

360mm

Section A‐A ‐ Soil instrumentation

Model

m

400mm360mm

326mm180mm

mm

10mm180mm

mm

0mm

100m

m15mm

50m


360m

30mm

130

Shake direction800mm

1

Scale Factor N=40

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Accelerometer ‐ sensingdirection towards left

Pore pressuresensor

Reference accelerometerrecording input signal


Check of the plane strain conditions with diagonal extensonmeters at three • Check of the plane strain conditions with diagonal extensonmeters at three sections of the model (2 ends, middle)

Strain ga gegauge

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• System of extensometers to measure the lateral displacement profile of the walls of the culvert due to the soil pressure

• At each level of the cross section a 2 tooth fork equipped with strain gaugeswill give the lateral displacement of the culvert wall at this level

Distance of walls to be measuredDistance of walls to be measured

2 independant extensometers

1 mm max.

Holes in the fork for fixingOn the culvert bottom slab Piled extensometer systems

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On the culvert bottom slab Piled extensometer systems


Preliminary test (December 2011)

• Flexible model in dry sand excited with a real record from the Northridge

Preliminary test (December 2011)

earthquake• 3 “earthquakes” of increasing amplitude were fired

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Preliminary numerical analysis Preliminary numerical analysis • Preliminary numerical analysis can be used to optimize the experimental set

up giving a general idea of the expected performanceN i l i l ti f th fl ibl t l d l i d d i d l l• Numerical simulation of the flexible tunnel model in dry sand in model scaleusing the ABAQUS

Tunnel: Linear elastic

3

E 70GPa

γ 27.17 kN m

=

=


Interface:Coulomb friction μ=0.4

Hard contact(no separation is allowed)360mm (no separation is allowed)

PIN CONSTRAIN

Soil: Mohr Co lomb

40g

3

sm

γ 16.3kN m

V 234m s

=≈

Soil: Mohr Coulomb

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800mma(t)

gο οφ=32 ,ψ 4

c 0.001MPa

D 5%

===


• Dynamic Step• Dynamic Step• Horizontal acceleration – EQ2 (t=0.43s)

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• Dynamic Stepy p• Residual pressures after strong excitations • Larger pressures at joints (corners)

60

70

40

50

σ (kPa)

20

30

8 4

mσ 45kPa*≈

8

8.2

8.4

mσ 7.5kPa*≈

7 4

7.6

7.8

σ (kPa)

AUTH SDGEE7

7.2

7.4*Mean values during the test


Dynamic Step• Dynamic Step• Shear stresses at maximum racking distortion

Maximum value

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Dynamic Step• Dynamic Step• Shear stresses at maximum racking distortion vs. Mohr Coulomb limit stress

Shear stress along the tunnel perimeter (time step @ max. racking distortion)

0 0.04475 0.0895 0.13425 0.179A B C D A

D C

10‐505

D C

‐25‐20‐15‐10

S12 (kPa) A

x=0

B

‐45‐40‐35‐30

Shear strainMohr‐Coulomb limit stress

Maximum value

45 Mohr‐Coulomb limit stress

{ }max stat .,yy dyn.,yySlabs : σ σ σ tanφ= + ×

AUTH SDGEE

{ }{ }max stat .,xx dyn.,xx

ο

Side walls , σ σ σ tanφ

φ=32

= + ×


“Investigation of several aspects affecting the i i b h i f h ll t g l seismic behavior of shallow rectangular underground structures in soft soils”

Centrifuge facility of Schofield Center, University of Cambridge, UK y g ,

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General description General description • Centrifuge tests on square tunnels embedded in dry Hostun S32 sand, under

centrifugal acceleration of 50g, performed at the centrifuge facility of the S h fi ld C t f th U i it f C b idSchofield Center of the University of Cambridge

100mm

mm

Tunnel

Plate t=10mm

220m Α

Tunnel

Sand

Α

60mm

m

673mm

427m

m

370m

m

100m

m

Tunnel

m

286.5mm 100mm 286.5mmm

60mm

100m

m

Tunnel

Sand ‐ Dr=90%

210m

673mm

Sand ‐ Dr=50%

370m

m

427m

10m

m

Sand ‐ Dr=50%

40mm

286.5mm 100mm 286.5mm

Sand Dr=90%

AUTH SDGEE

673mm


170

673mm


• Objectives:• Influence of the relative flexibility ratios on the drift displacements• Effect of the flexibility ratio on the seismic earth pressures and the

seismic shear stresses distribution along the perimeter• Effect of the backfill material, on the seismic behavior of an

underground structureg

• Reduction factor N=50

• The tests are performing in the large ESB box (673x427x253 (mm))

• 2 tunnel models (BS5251-H24 Aluminum alloy):• 2 tunnel models (BS5251-H24 Aluminum alloy):• flexible model: 100 x 100 x 220 (mm), thickness 0.5mm• rigid model: 100 x 100 x 220 (mm), thickness: 2mm

• Teflon plates, 110 x 110 x 10 (mm) in dimensions, bonded with each otherwith a large screw, were used to avoid the entrance of sand in the tunnel

d l d h

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model during the test


• A two layered soil deposit will be used to study the effect of the commonlyused backfill material on the seismic behavior

• Sine wavelets of increasing amplitude

• 3 tests• 3 tests

• Records in terms of:• Accelerations in several points in the soil and on the model using• Accelerations in several points in the soil and on the model, using

accelerometers• Earth pressures at two locations on the one side wall of the structure,

i th llusing earth pressure cells• Settlement of the soil surface at two locations, using LVDTs• Movement of the tunnel (i.e. rocking), using potensiometers• Strains on the model (axial and bending) using full bridge strain gauges

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• Instrumentation scheme Accelerometer sensingAccelerometer sensing

LVDT1

LVDT2 145mm190mm

POT1 POT2

400mmAccelerometer ‐ sensingdirection towards left

Strain gauges

Accelerometer ‐ sensingdirection towards left

Strain gaugesm

Tunnel

Acc10Acc3

Acc6

Acc7

0mm

45mm

Strain gauges(Bending moment)

M

POV

Strain gauges(Bending moment)

M

POV

370m

m

427m

m Acc5

Acc2Acc4Acc9

m40mm100 POV

Accelerometer ‐ sensingdi ti

POV

Acc1Acc8

Acc17Air hammer17

0mm

50mm

Acc11Strain gauge

direction up

673mm

Acc16Acc15

(Axial force)

N

LVDT

MM

N

PC2

SG3SG4

SG8

Acc13

Acc14

Pressure sensors

AUTH SDGEEM

MNN

N PC1

PC2

SG1

SG2SG5

SG6

SG7Acc12


• 2 flights per test• 1 flight: main test using CDAQS (sampling rate: 4kHz)• 2 flight: Air hammer testing using Dasylab (sampling rate: 50kHz) to

estimate the Vs profile

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• Model configuration for the first test (performed on 26-27/1/2012)100mm

mm

Tunnel

Plate t=10mm

220

Sand

Α

673mm

m

60mm

00mm

Tunnel

427m

m

370m

m

1010

mm

286.5mm 100mm 286.5mm21

673mm

Sand ‐ Dr=50%

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1st test • Relatively rigid model (t=2mm)

1 test

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• Tunnel model embedded in soil

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• Final model

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• Four sine wavelets of increasing amplitude and same frequency were fired in • Four sine wavelets of increasing amplitude and same frequency were fired in a row, having maximum amplitudes: 0.2g, 0.26g, 0.32g, 0.38g respectively

• Unfortunately the strain gauges did not record something measurable• Unfortunately, the strain gauges did not record something measurablebecause the model was rather rigid and the strains quite small to bemeasured

• Indicative results • Acceleration at base of the model – EQ1

Input motion ‐ EQ1 (prototype scale) ‐ filtered 0.1‐10Hz

0 15

0.2

0.25Input motion ‐ EQ1 Fourier

0 8

1

0

0.05

0.1

0.15

A(g)

0 4

0.6

0.8

A(g)

0 2

‐0.15

‐0.1

‐0.05 0 10 20 30 40 50

A

max: 0.197gmin: ‐0.22g 0

0.2

0.4

AUTH SDGEE

‐0.25

‐0.2t(s)

min: 0.22g0 2 4 6 8 10f(Hz)


Settlement of the soil surface dynamic part• Settlement of the soil surface – dynamic part• Smaller settlements above the tunnel – rigid structure• ε = 2% !!

Surface settlement (dynamic part)2 Surface settlement (dynamic part)

1

0

1

2

0 1 2 3 4t(s))

190mm400mm

LVDT2LVDT1

‐3

‐2

‐1 0 1 2 3 4t(s)

ment (mm)

Tunnel

‐6

‐5

‐4

settle

LVDT‐2

‐8

‐7 LVDT‐1

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• Pressure at the side wall – invert slab joint – EQ4 • Pressure at the side wall invert slab joint EQ4

Earth Pressure (Joint) ‐ Dynamic part40 Earth Pressure (Joint) ‐ Dynamic part40

20

30 PC1

20

30 PC1

10 t(s)

(kPa) 10 t(s)

(kPa)

‐10

0

0 0.2 0.4 0.6 0.8 1

Pressure

‐10

0

0 0.2 0.4 0.6 0.8 1

Pressure

‐20‐20

‐40

‐30Test Mononobe Okabe (dynamic part)

{φ=32ο δ=0ο k =0 462g K =0 74 γ=14kN/m3}‐40

‐30Test Mononobe Okabe (dynamic part)

{φ=32ο δ=0ο k =0 462g K =0 74 γ=14kN/m3}

AUTH SDGEE

{φ=32 , δ=0 , kh=0.462g, KAE=0.74,γ=14kN/m }{φ=32 , δ=0 , kh=0.462g, KAE=0.74,γ=14kN/m }


Preliminary numerical analysis Preliminary numerical analysis • Numerical simulation in model scale using the ABAQUS, 2009)

E 70GPa=


Interface:Perfect bonding

3

E 70GPa

γ 27.0kN m=

Perfect bonding370mm

PIN CONSTRAIN

3

sm

γ 15.4kN m

V 220m s

=≈

Soil: Linear elastic

673mm

a(t)

D 5%=

50g

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• Dynamic step• Dynamic step• Soil shear stresses around the tunnel for different tunnel section thickness

Maximum valueMaximum valueMaximum value

τ=128 kPa

Maximum value

τ=128 kPa

t=1mm

Maximum value

τ=80.5 kPa

t=2mm

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Some important issuescontrolling the tests controlling the tests

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Estimation of soil properties• Elastic mechanical properties (E,v) - Gmax profile estimation (G(z))

Estimation of soil properties

• Gmax compatible to the actual test intensities and deformations (i.e. Brennanet al., 2005) – CPT tests before and after each flight or bender elements

• Empirical expressions (i.e. Hardin and Drnevich,1972) may overestimateGmax (i.e. Brennan et al., 2005)

G G‐γ RC or TS testsG‐γ in the centrifugeGmax

G

Estimated by empirical

f l tiGmax,cen

Geff

Geff,cen

Gformulations

Geff,cen

zGeff

AUTH SDGEEγ (%)γeff


Flexibility ratio • Penzien, 2000• Deformations of rectangular cavity

ff s ffτ G γ=

c ffγ βγ= ff

( )c ff sβ γ γ 4 1 v= = −

G

• Stiffness of outside soil, inside soil and lining• Compatibility of deformations

ssoil si

Gk τ H= =

( )il ilk k 3 4v= −( )soilo soil sk k 3 4v

( )stru is s ffΔd Δd 4 1 v γ H+ = −

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• Depended on the actual soil shear modulus (degraded during the shaking)

• An overestimation of the shear modulus can lead to an overestimation of theflexibility ratio

• Assumptions for the calculation of the flexibility ratio?

• Example: Wang, 1993, Hashash et al., 2001 etc.: static analysis for theExample: Wang, 1993, Hashash et al., 2001 etc.: static analysis for thedetermination of the flexibility ratio assuming fix invert slab. Is the invertslab fixed during the shaking? Deformation modes? Rocking of the tunnel?

mG WF

S H=

1S H

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Estimation according Wang 1993• Estimation according Wang, 1993• Concentrated load P - Fixity of the invert slab• S1: force required to cause unit racking to structure – estimate from simple

i l istatic analysis

G d f

Rectangular

Ground surface

sm

Δ τγ

Η G= =

gsoil element

ms

τ τG

ΔγΗ

= =

Rigid Base Soil column

Under simple shear

1s

1 1 s

ΗSΔ P τW τ τγ

ΔΗ ΗS ΗS γ WH

= = = → = =

m

1

G WF

ΗS=

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Th k Thank you

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Cili i U M d bh hi SPG (2010b) Eff f d h i i f i l l C

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Università di Napoli Federico II


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underground reinforced concrete duct-type structures in nuclear power stations – Part 2.Experimental aspects of laminar shear sand box excitation tests with embedded RC models.

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phyygsical modeling for the evaluation of the seismic ... · • transversal seismic behavior and...

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