MR23

Department of Structural and Geotechnical Engineering

Giovanni BarlaGiovanni Barla

Tunnelling under Tunnelling under Squeezing ConditionsSqueezing Conditions

(Part 2)(Part 2)

Lecture OutlineLecture Outline Design Analyses Case Study Conclusions

Design AnalysesDesign Analyses

METHODS FOR DESIGN ANALYSIS OF METHODS FOR DESIGN ANALYSIS OF TUNNELS IN SQUEEZING CONDITIONSTUNNELS IN SQUEEZING CONDITIONS

SHOULD CONSIDERSHOULD CONSIDERTHE THREETHE THREE--DIMENSIONAL STATE OF DIMENSIONAL STATE OF STRESS NEAR THE TUNNEL FACESTRESS NEAR THE TUNNEL FACE

THE ONSET OF YIELDING WITHIN THE ONSET OF YIELDING WITHIN THE ROCK MASS, AS DETERMINED BY THE ROCK MASS, AS DETERMINED BY THE SHEAR STRENGTH PARAMETERS THE SHEAR STRENGTH PARAMETERS RELATIVE TO THE INDUCED STRESSRELATIVE TO THE INDUCED STRESS

THE TIME DEPENDENT BEHAVIOURTHE TIME DEPENDENT BEHAVIOUR

The use of numerical analyses is advisable when The use of numerical analyses is advisable when the rock mass strength/in situ stress ratio is below the rock mass strength/in situ stress ratio is below 0.3 and it is highly recommended if this ratio falls 0.3 and it is highly recommended if this ratio falls below about 0.15, when the stability of the tunnel below about 0.15, when the stability of the tunnel face may become a critical issueface may become a critical issue

0.1 0.2 0.3 0.4 0.5 0.60123456789

101112131415

Strain greater than 10 %Extreme Squeezing

Strain between 5 and 10 %Very severe Squeezing

Strain between 2.5 and 5 %Severe Squeezing

Strain less than 1 %No Squeezing

Strain between 1 and 2.5 %Minor Squeezing

Rock Mass Strength/In situ stress ( cm /po)

Tunnel

Wall

Dis

pla

cem

ent/

Radiu

s (

ur/

a)

t

s

INITIAL STATEOF STRESS

v

h

t

s

2D 3D

v

h

t

s

2D 3D

v

h

v

h

t

s

2D 3D

A

A

EXCAVATIONDIRECTION

C1 m

S

5 m 1 m

Longitudinal Section Longitudinal Section Transversal Section ATransversal Section A-- AA

Problematiche aperte esempi3D Analyses advisable3D Analyses advisable

Methods for Design AnalysisMethods for Design Analysis

Introduzione


-15

-10

-5

0

5

10

15

0 5 10 15 20 25

[MPa]

t [M

Pa

]

Sidewall

Crown/Invert

Flac

Flac3D

Flac3D

Flac

4m S

C

4 m 1.5 m

1.5 m

I 1.5 m

arrival of the face

arrival of the face

s [MPa]

STRESS PATH AT POINTSTRESS PATH AT POINT C (crown), I ( C (crown), I (invertinvert), S (), S (sidewallsidewall))

ILEILE

INFLUENCE OF 3D CONDITIONSINFLUENCE OF 3D CONDITIONS

3D Analyses advisable3D Analyses advisable

Introduzione



0

5

10

15

0 5 10 15 20 25 s [MPa]

t [M

Pa

]

Face of the excavation

F Excavation

STRESS PATH AT POINT FSTRESS PATH AT POINT F(FACE OF THE EXCAVATION)(FACE OF THE EXCAVATION)

ELPLAELPLA

INFLUENCE OF 3D CONDITIONSINFLUENCE OF 3D CONDITIONS

Yield Surface

Introduzione



Maximum displacement = 44 mm

ufut

Introduzione



Onset of yielding around the tunnel

SIMPLIFIED METHODS OF ANALYSIS AND DESIGN OF TUNNELS IN

SQUEEZING CONDITIONS

THE ONSET OF YIELDING WITHIN THE ONSET OF YIELDING WITHIN THE ROCK MASS, AS DETERMINED BY THE ROCK MASS, AS DETERMINED BY THE SHEAR STRENGTH PARAMETERS THE SHEAR STRENGTH PARAMETERS RELATIVE TO THE INDUCED STRESSRELATIVE TO THE INDUCED STRESS

CONSIDERCONSIDER

ElastoElasto--plastic closed form solutions for rock plastic closed form solutions for rock mass response to excavation of a circular mass response to excavation of a circular tunnel can be usedtunnel can be used

If the rock mass is assumed to behave as an If the rock mass is assumed to behave as an elastoelasto--plastic plastic isotropic medium, the following models can be adopted:isotropic medium, the following models can be adopted:

Elastic perfectly plastic (a)Elastic perfectly plastic (a) ElastoElasto--plastic with strain softening behaviour (b)plastic with strain softening behaviour (b) ElastoElasto--plastic, with brittle behaviour (c)plastic, with brittle behaviour (c)

1-3

a a a

1-3 1-3(a)(a) (b)(b) (c)(c)

((e.g.Browne.g.Brown et al.,1983;et al.,1983;.Carranza.Carranza--TorresTorres and and FairhurstFairhurst,1999),1999)

570

251.

0

cmpl

p.

R

R

=

2

0020

=

0

cmr

p.

Ru

BASED UPON THE ABOVE SOLUTIONS DIMENSIONLESS PLOTS CAN BE BASED UPON THE ABOVE SOLUTIONS DIMENSIONLESS PLOTS CAN BE DERIVED FROM THE RESULTS OF PARAMETRIC STUDIES WHERE THE DERIVED FROM THE RESULTS OF PARAMETRIC STUDIES WHERE THE INFLUENCE OF THE VARIATION IN THE INPUT PARAMETERS ARE STUDIED INFLUENCE OF THE VARIATION IN THE INPUT PARAMETERS ARE STUDIED BY THE MONTE CARLO ANALYSIS, UNDER THE ASSUMPTION OF ELASTIC BY THE MONTE CARLO ANALYSIS, UNDER THE ASSUMPTION OF ELASTIC PERFECTLY PLASTIC BEHAVIOUR OF THE ROCK MASS, WITH ZERO PERFECTLY PLASTIC BEHAVIOUR OF THE ROCK MASS, WITH ZERO VOLUMETRIC CHANGE (HOEK,1998,1999)VOLUMETRIC CHANGE (HOEK,1998,1999)

Rock mass Rock mass strengthstrength/in /in situsitu stressstress Rock mass Rock mass strengthstrength/in /in situsitu stressstress

Tunn

el

Tun n

el d

efor

ma t

ion

def o

rma t

ion /

tunn

el

/tu n

nel r

adiu

sra

d ius

Pla s

tic z

o ne

Pla s

tic z

o ne

rad i

usra

d ius

/tu n

nel

/tu n

nel r

adiu

sra

d ius

IntroduzioneIl Passato ed il Presente Passato e Presente

Time DependentTime Dependent

Rock Mass Behaviour

Time IndependentTime Independent

ElasticElastic

PlasticPlasticPlastic

Strain

Str

ess

Strain

Str

ess

33

Delayed ElasticDelayed Delayed Elastic

Time DependentTime Dependent

Strain

Str

ess

StrainS

tres

s

2211

33

to

t >to

22

Time Time -- dependent behaviourdependent behaviour


1 1 -- Strain Strain -- hardeninghardening2 2 -- Perfectly plasticPerfectly plastic3 3 -- Strain softeningStrain softening

Time Time -- dependent postdependent postpeak behaviourpeak behaviour Time Time -- dependent peakdependent peakand ultimate strengthand ultimate strength

Case StudyCase Study

Introduzione

0 2 4 6 8 10 km

Landslide

NS

D = 14 m

Step for facereinforcement

Case study Case study

Case studyCase study

SRTASoft Rock Triaxial Apparatus

SRTASoft Rock Triaxial Apparatus

HPTAHigh Pressure Triaxial Apparatus

HPTAHigh Pressure Triaxial Apparatus


Load Cell

LDT

ProximityTransducers

LVDT


Internal Pressure max 64 MPa

Specimen diameter 50, 70, 100 mm and height up to 200 mm

Maximum vertical load 200 kN


Axi

alR

adia

l


f

f

f

f

0.001

0.01

0.1

1

10

100

0.1 1 10 100 1000Tempo [min x 100]

Vel

. def

orm

azio

ne v

ertic

ale

[%/m

in /

1000

]

q/q = 0.55

q/q = 0.78

q/q = 0.87

q/q = 1.00CreepCreep TestsTests in in

undrained undrained conditionsconditionson on clayclay--shalesshales forfor the the

studystudy of time of time dependentdependent responseresponse of of

tunnel facetunnel face

(q/qf = mobilised strength)

Time

Ver

tica

l st

rain

rat

eCase studyCase study

ELASTOELASTO--VISCOPLASTIC MODELVISCOPLASTIC MODEL((LemaitreLemaitre and and ChambonChambon, 1996), 1996)

TheThe viscoplastic strains depend on the viscoplastic strains depend on the deviatoric deviatoric stress state stress state only and do not induce only and do not induce volumetric strainsvolumetric strains

ElasticitElasticitElasticityF0

PlasticityF=0

PlasticityF=

2233

11


Problematiche aperte esempi

Time (year)

Time (hour)Ax

ial S

trai

n (%

)

Test Model Test Model


axisaxis--symmetricsymmetric conditionsconditions circularcircular cross cross sectionsection initialinitial state of stress state of stress constantconstant and and isotropicisotropic coupledcoupled analysisanalysis in undrained in undrained conditionsconditions two two casescases consideredconsidered::-- Osteria Access Osteria Access AditAdit ((depthdepth = 148 m)= 148 m)

MohrMohr--CoulombCoulomb elastoelasto--plasticplastic perfectlyperfectly plastic modelplastic model-- Raticosa Tunnel (Raticosa Tunnel (depthdepth = 50 m) = 50 m)

ElastoElasto viscovisco--plasticplastic modelmodel


0

20

40

60

80

100

120

140

45 50 55 60 65 70 75 Face advance [m]

Long

itudi

nal d

ispl

acem

ent [

mm

] 04/07/98

05/07/98

07/07/98

08/07/98

Mohr-computedvalues

0 5 10 15 20 25 30

Sliding micrometer installation (zero): 03/07/98

Mohr-Coulomb computed values

OsteriaOsteria Access Access AditAdit


0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

Face advance [m]

Long

itudi

nal d

ispl

acem

ent [

mm

] 04/07/98 05/07/98 06/07/98 15/07/98

Serie1Serie4Serie6Serie8

Sliding micrometer installation (zero): 28/06/98

Lemaitre computed values

Visco-plastic

Raticosa TunnelRaticosa Tunnel


ConclusionsConclusions

Introduzione

We have discussed some of the current issues in We have discussed some of the current issues in the analysis and design methods for tunnels in the analysis and design methods for tunnels in squeezing rock conditions. Performance interactive squeezing rock conditions. Performance interactive monitoring of tunnel response associated with monitoring of tunnel response associated with numerical numerical modellingmodelling is shown to be an essential is shown to be an essential tool for successful design and constructiontool for successful design and construction

A case study of a tunnel excavated along the A case study of a tunnel excavated along the Apennines in clayApennines in clay--shalesshales has been used to illustrate has been used to illustrate how to deal with full face excavation. It is how to deal with full face excavation. It is important to be able to decide the constitutive important to be able to decide the constitutive model to adopt for the ground, being it timemodel to adopt for the ground, being it time--independent or timeindependent or time--dependentdependent

MR23

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