Numerical Analysis In The Design Of Urban Tunnels
Torino, 19-24 June 2005Keynote LectureNumerical Analysis in the Design of Urban TunnelsMichael KavvadasAssoc. Professor of Civil EngineeringNATIONAL TECHNICAL UNIVERSITY OF ATHENSSCHOOL OF CIVIL ENGINEERING – GEOTECHNICAL DEPARTMENTNumerical Analysis in the Design of Urban TunnelsLecture Outline1. Characteristics of urban tunnels Need to control ground deformations Numerical analyses to predict ground deformations2. Tunnelling methods in urban areas (to control settlements) Emphasis on pre-convergence and face pre-treatment3. Methods of numerical analysis Continuum / discontinuum modelling Continuum 3-D modelling :Analysis of pre-convergence & face pre-treatment (for design)Estimation of ground parameters (E) by monitoring extrusion Continuum 2-D modelling :How to model the 3-D problem in 2-D (in a cross-section)
Main characteristics of urban (shallow) tunnelsMinimisation of ground surface displacementsModern multimulti storeybuildingNorth/South Line, AmsterdamHistoric buildingsStreet levelSoft clayFirst sand layerSoft siltTimber pilesSecond sand layerStiff clay6.5m diameter tunnelsMain characteristics of urban tunnelsMinimisation of ground surface displacementsSurface settlement trough above an advancing tunnelAdvanceTunnelSettlement depends on ground, depth, diameter and excavation method
Causes of ground surface displacements :1. Ahead of tunnel face : Axial face extrusion (radial pre-convergence)2. Behind tunnel face : radial convergenceTUNNELMinimisation of ground surface displacementsRelative contribution of pre-convergence and convergenceIn a properly supportednon-TBM tunnel, 70-80%of total surface settlementis due to deformationsahead of tunnel faceConvergencePre-convergenceSUPPORT IS INSTALLEDFaceextrusionIn TBM tunnels the fractionvaries significantly ( 70%)depending on the methodConclusion :In non-TBM tunnels,control of pre-convergence(face extrusion) is criticalin urban tunnelling
Control of pre-convergence is contrary to the basic NATM principleof mobilising rockmass strength by deformationThis NATM principle is mainly applicable in mountain tunnelsMountain tunnels : Stability is critical Deformation not critical(usually desirable)Urban tunnels : Deformation critical : tobe minimised Stability is ensured bycontrolling deformationCalculation of deformationsrequires numerical modelling(important in urban tunnels)Support loadUrban tunnelling methodsMinimisation of pre-convergence & convergenceTunnellingmethodMinimisation ofpre-convergenceMinimization ofconvergenceControl cutter-head overcutTBMAdequate face support :Pressure control (closed)Cutter-head openings (open)NATM(North of Alps)SATM(South of Alps)andtail-void groutingMultiple drifts(uR D)Face pre-treatmentEmphasis on pre-convergence, sinceit controls 70-80% of total settlementStiff supportEarly closure of ring
Urban tunnelling methods : TBM tunnellingControl of pre-convergence by face pressureand ground conditioning in closed-face machinesSlurry shieldpEPB shieldscrewconveyorp 0bentonite(pressure p)excavated soil(pressure p)Urban tunnelling methods : TBM tunnellingControl of pre-convergence by the sizeof cutter-head openings in open face machinesAthens Metro – 9.5m dia. open TBM
Urban tunnelling methods : TBM tunnellingInadequate control of pre-convergence by ground ravelingcaused by too large cutterhead openings in open TBMAthens Metro (1998)Urban tunnelling methods : NATM tunnelling (North of Alps)Control of pre-convergence by multi-drifting (uR D)Excavation with side-drifting and central pillarAthens Metro – Acropolis Station : excavation in“schist” (phyllite)
Urban tunnelling methods : NATM tunnelling (North of Alps) Control of pre-convergence by multi-drifting (uR D) Control of convergence by stiff support and early closure of ringUrban tunnelling methods : SATM tunnelling (South of Alps)Control of pre-convergence by face pre-treatment1. Face protection methods : Reduction of σ1 ahead of tunnel face1.1 Pipe-roofing (forepoling umbrella)Each forepole works independentlyalong its length (in bending)σ1σ1
Steel sets embeddedin shotcreteSteel setsForepolesFiber-glass nailsShotcreteapplicationFace pre-treatment : Forepoling umbrella1. Face protection methods : Reduction ofσ1 ahead of tunnel faceFace protection using forepoling umbrella : How it worksσ1σ1σ3Excavation reduces σ3 to zerocausing face instability.Forepoling :The presence of a stiff beamreduces the major (vertical)stress (σ1) on the faceopen facegeostaticΔσ1
Urban tunnelling methods : SATM tunnelling (South of Alps)Control of pre-convergence by face pre-treatment1. Face protection methods : Reduction of σ1 ahead of tunnel face1.2 Improved arch above tunnel crestGrouted umbrella arch methodGrouted umbrella archarchσ1Control of pre-convergence by face pre-treatment1. Face protection methods : Reduction of σ1 ahead of tunnel face1.2 Improved arch above tunnel crestΦ 1.2m pipesAthens Metro : Monastiraki Station (18m wide span)micro-tunnel pipe arch (bicycle chain)
1. Face protection methods : Reduction of σ1 ahead of tunnel face1.3 Vertical nails (or piles) from ground surfaceATHENSMETROTension elements reduceσ1σ1Urban tunnelling methods : SATM tunnelling (South of Alps)Control of pre-convergence by face pre-treatment2. Face reinforcement methods : Increase ofσ3 ahead of tunnel faceFace reinforcement with fibre-glass nails
2. Face reinforcement methods : Increase ofσ3 ahead of tunnel faceFace reinforcement withfibre-glass nailsFG-nailsLateral confinement (σ3) :σ3σ3 n FyP A ( FS F ) AFactor of safety before nailing :FSo Ns σ32(1 λ ) N s2 poσ cmσ1 (1-λ) popo geostatic stressFactor of safety with FG-nails :FS FSo 1 σ3 2 φ tan 45 (1 λ ) po 2 Urban tunnelling methods : SATM tunnelling (South of Alps)Control of pre-convergence by face pre-treatment3. Face improvement methods : Increase of cohesion ahead of tunnel faceFace groutingFace improvementusing groutingGrouting : increases cohesion (Δc)Factor of safety before grouting :FSo Ns Factor of safety after grouting :FS FSo 2 poσ cm2(1 λ ) N sσ1 (1-λ) po2 Δc φ tan 45 (1 λ ) po 2
Control of pre-convergence by face pre-treatment3. Face improvement methods : Increase of cohesion ahead of tunnel faceFace improvement using groutingAthens MetroAthens Metro : Ground improvement ahead of TBM (via a pilot tunnel)using fiber-glass anchors and TAM groutingNumerical Analysis in the Design of Urban TunnelsLecture Outline1. Characteristics of urban tunnels2. Tunnelling methods in urban areas (to control settlements)3. Methods of numerical analysis Continuum vs. discontinuum modelling Continuum 3-D modelling :Analysis of pre-convergence & face pre-treatment (for design)Prediction of ground parameters (E) by monitoring extrusion Continuum 2-D modelling :How to model the 3-D problem in 2-D (in a cross-section)
Urban tunnel design using numerical analysisTunnel excavation and support is traditionally an empirical artNumerical analyses are useful in the following cases : Calculation of ground surface settlements Design of face pre-treatment in difficult ground conditions(selection among alternative methods) Sensitivity analyses :¾ Effect of locally inferior ground on the support system¾ Comparison of alternative support methods Selection of most appropriate corrective action in case of contingency Assessment of ground properties ahead of the excavation face usingmonitoring data (mainly face extrusion) “Legal” support of design decisions(decisions based on “engineering judgment” rarely stand in courts)Design using numerical analysis: Continuum / Discontinuum modelsInfluence of rockmass discontinuitiesContinuum modelsIntact rock strengthcontrols responseDiscrete modelsStructural featurescontrol responseContinuum modelsRockmass strengthcontrols response
Design using numerical analysis: Discontinuum modelsApplicable : mainly in rock where structural features control response1. Analysis of wedge stability (at roof and sidewalls) :Typical numerical analysis using computer programs : UNWEDGE (for tunnels) SWEDGE (for slopes)Design using numerical analysis: Discontinuum models2. Analysis of tunnel excavation and support using discontinuum models :Discrete Element Method: Calculation schemee.g. programs UDEC (2-D) , 3-DEC (3-D)2-D analysis oftunnel facestability:UDEC ResultsKamata & Mashimo(2003)Kawamoto & Aydan, (1999)
Design using numerical analysis: Continuum models3-D models : Check face stability / design face pre-treatmentModelling stages are direct :1. Geostatic (initial conditions)2. Installation of face support3. Advancement of the excavation (one step)4. Installation of side support5. REPEAT steps 3–4 until new face support6. Install face support .However : Input preparation and outputpresentation is often complicated Analysis is time consuming Improved accuracy may beincompatible with the level ofknowledge of ground conditionsDesign using numerical analysis: Continuum models / 3-DzUse of 3-D FE/FD models for face pre-treatment : Modelling face treatment Constitutive model (E-sensitive analyses) Knowledge of input ground parameters (E)
Use of numerical analyses in assessing ground parametersGround parameters for tunnelling can be obtained by : Boreholes & lab tests : not very relevant Field tests (inside the tunnel) : expensive, slow and not very relevant Exploitation of excavation data (monitoring)Wall convergence (not sensitive)Face extrusion (very useful)Use of numerical analyses in assessing ground parametersMeasurement of face extrusion by sliding micrometers ahead of the tunnel faceLunardi & Bindi (2004)
Use of numerical analyses in assessing ground parameters3-D numerical analyses (using FLAC-3D) were performed to assess the magnitudeof face extrusion in terms of critical ground parameters (modulus E)1.81.6Purely elastic response for Ms 4uy,max maximum extrusion(at tunnel face)1.4uy,max / D (%)L 1m , t 10cmL 1m , t 20cmL 1m , t 30cm1.2Spyropoulos, 2005unlined tunnel1.0u y ,max0.8D0.6 0.0004 M s 2.25Ms 0.40.2E1000 γ H 0.90 D 0.100.00.000.200.400.600.800.90Ms E / 1000γH1.001.201.400.10DMaximum extrusion uy,max (at tunnel face) as a function of the controlling groundparameter Ms. Extrusion is not influenced by the installation of shotcrete lining(thickness t) behind the face (distance L) correlation uy,max & Ms is useful EUse of numerical analyses in assessing ground parameters2.2Purely elastic response for Ms 42.0crown settlement / D (%)1.8L 1m , t 10cmL 1m , t 20cmL 1m , t 30cmuz,max crown settlement(at tunnel face)1.61.4Spyropoulos, 20051.2unlined tunneluz ,max 0.001 M s 1.80D1.00.80.6unlined tunnelMs 0.4E1000 γ H 0.90 D 0.100.20.00.00.20.40.6Ms E / 1000γH0.80.90D1.01.21.40.10Crown settlement uz,max (at tunnel face) as a function of the controlling groundparameter Ms. Crown settlement is strongly influenced by the installation of shotcretelining (thickness t) behind the face (distance L).Crown settlement cannot be used to assess the value of Ms ahead of the tunnel face
Use of numerical analyses in assessing ground parameters1.00.9uy,max maximum extrusion (at tunnel face)0.8uy extrusion at distance (x) from tunnel faceuy / uy,max0.7Spyropoulos, 20050.6uy0.50.4u y ,max0.3 (1 e)x 2x RR0.20.10.00.000.250.500.751.00x/ R1.251.501.752.00Extrusion uy as a function of the distance from tunnel face. Since the value of uy,maxis related to Ms correlation uy & Ms (for any x/R) is useful EReduction of face extrusion (uy,max) by using FG-nails1.6Spyropoulos, 2005uy,max / D (%)1.41.2n number of FG-nailsF mean axial force in FG-nailsA tunnel section areaγ H vertical overburdenwithout FG-nailsunsupported or supported with shotcrete1.00.8fG 1000fG 40000.6fG 8000f G 0.4nFAγ HMs E1000 γ H 0.90 D 0.100.81.00.20.00.00.20.40.6MsFace extrusion can be reduced up 30 - 50% by installing FG-nails1.2
Reduction of crest settlement (uz at x 0) by using FG-nails0.90.8without FG-nailsunsupported0.7u z (x 0) / D (%)n number of FG-nailsF mean axial force in FG-nailsA tunnel section areaSpyropoulos, 20050.6γ H vertical overburdenwithout FG-nailssupported with shotcrete0.5f G nFAγ HfG 40000.40.3fG 80000.2Ms E1000 γ H 0.90 D 0.100.81.00.10.00.00.20.40.61.2MsCrest settlement is only slightly reduced by installing FG-nails(and any reduction is masked by the shotcrete liner)Reduction of face extrusion (uy,max) by using forepoles3.0Spyropoulos, 20052.5without forepolesfF1 1uy,max / D (%)2.0Purely elastic response for Ms 4fF1 51.5fF1 I / S (cm3),I moment of inertia of a forepole tubeS axial distance between forepolesL length of forepole overlapD tunnel diameterfF1 10Ms fF1 251.0fF1 50E1000 γ H 0.90 D 0.10fF1 100L / D 0.400.50.00.00.10.20.30.40.50.6Practical forepoling applications correspond to fF1 20Ms0.7
Reduction of crest settlement (uz at x 0) by using forepoles1.0fF1 I / S (cm3),I moment of inertia of a forepole tubeS axial distance between forepolesL length of forepole overlapD tunnel diameterunsupportedwithout forepolesonly shotcrete0.8uz(x 0) / D (%)fF1 1fF1 50.6Purely elastic response for Ms 4fF1 10fF1 25fF1 500.4Ms E1000 γ H 0.90 D 0.10fF1 1000.2L / D 0.40Spyropoulos, 20050.00.00.10.20.30.40.5Practical forepoling applications correspond to0.6MsfF1 20Design using numerical analysis: Continuum models3-D models : Most suitable for face pre-convergence / face pre-treatment2-D models : Analysis of tunnel cross-section (from 3-D to 2-D)3-D model using FLACDisadvantage : sophisticated2-D model using PHASE2Disadvantage : cannot model face0.7
Design using numerical analysis: Continuum models / 2-D0 λ 1λ 1The analysis is performedby gradually reducing theinternal pressure “p”λ 0Zone 1unsupportedZone 2po geostatic stress (isotropic)supported(ΙΙΙ)p tunnel “internal pressure”(Ι)(ΙΙ)λ deconfinement ratioλ 1 p p po (1 λ )poNeed to know λ λ(x)λ 1λ 00 λ 1(ΙΙΙ)(ΙΙ)(Ι)Design using numerical analysis: Continuum models / 2-DUse of deconfinement ratio (λ)Deconfinement usinginternal pressure reduction :p (1 λ ) popo geostatic stress (isotropic)Example :λ 0.70 p 30% poλDeconfinement usingsection modulus reduction : (1 2ν ) (1 λ ) E Eo() ν λ12 Eo ground E-modulusExample :λ 0.70 E 10% EoAdvantage : Good in anisotropic fields
Use of deconfinement ratio (λ)and equivalent “reduced modulus” 00.500.400.300.200.10λ 1 - p/poν 0.250.5710.4380.3330.2500.1820.1250.0770.036Values of Ε/Εο forν 0.300.5330.4000.3000.2220.1600.1090.0670.031ν 0.350.4800.3500.2570.1870.1330.0900.0540.025E (1 2 ν ) (1 λ ) (1 2ν ) λEoDetermination of the deconfinement ratio (λ) along the tunnel axisuR(p)Tunnel wall displacement (uR)varies along the tunnel axis3-D model2-D modelCalculation method :3-D model : uR uR(x)2-D model : uR uR (p)or uR uR (λ)Thus :λ λ(x)Standard diagrams are availableuR(x)x
Determination of the deconfinement ratio (λ) along the tunnel axisFLAC-3D : Spyropoulos, 2005-40u R / u R,max (crest settlement)-0.1-0.2-0.3-0.4-0.5-3-2-10123x/R 4Purely elastic response for Ms 4 k 1 K 1 u2 R 1 λ 1 (k 1)N s u R FLAC3DChern, 2000uR x 1 exp 2.2 M s0.37 u R R Unlu, 2003-0.6-0.7 x Rλ f ; Ms Panet, 1995Ms -0.8-0.9TUNNEL 1.2E1000 γ H 0.90 D 0.10curves plotted for Ms 0.20-1Excavation with side-driftingand central pillar40 mm surface settlementAthens Metro : Acropolis Stationexcavation in“schist” (phyllite)
Numerical Analysis in the Design of Urban TunnelsConclusions1. Ground deformations are critical2. Estimates of ground deformations require 3-D numericalanalyses ( ground model ground properties)3. Relevant ground properties (mainly E) can be obtained bymeasurement of face extrusion & numerical back-analyses(or use of the normalised graphs)4. For many tunnel designers, 3-D analyses may seem toosophisticated : Methods exist to analyse the problem in 2-D using the“deconfinement method (λ)” Normalised graphs are available to estimate (λ) intunnels without / with face pre-treatmentThank you .Athens Metro (Jan. 2003)Collapse of a tunnel under construction (NATM)
UDEC Results Kamata & Mashimo (2003) Design using numerical analysis: Continuum models 3-D models : Check face stability / design face pre-treatment Modelling stages are direct : 1. Geostatic (initial condit
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