design of segmental tunnel linings for serviceability...

Design of Segmental Tunnel Linings for Serviceability Limit State

Mehdi Bakhshi, PhD, PE ACI Committee 544 & AECOM, New York

[email protected]

April, 2015

AASHTO SCOBS T-20: Technical Committee for Tunnels

• Introduction on FRC Segments

• Summary of ACI Guideline for FRC Segments

• Design Example for Mid-Size Tunnels

• Design for Serviceability Limit States

• Current and Future Research Studies

• Conclusion

Outline

Introduction on FRC Segments

Precast Segmental Tunnel Lining

• Serves as both initial ground support and final lining in modern TBM tunnels

• Providing the required operational cross-section • Controlling groundwater inflow

Reference: AECOM tunnel design (2013) – North Shore Connector, Pittsburg, PA

• Used in more than 50 tunnel projects

• First FRC tunnel segments: Metrosud (1982)

FRC Precast Tunnel Segments

Reference: ACI 544.AR (2015)—Draft Emerging Technology Report on Design and Construction of Fiber-Reinforced Precast Concrete Tunnel Segments

• Tunnel functions: water/waste water, gas pipeline, power cable, subway, railway, and road tunnels

• Internal diameters: 7.2’-37.4’ (2.2-11.4 m)

• Min. & max thickness:

6” (15 cm) & 16” (40 cm)

• Steel fiber dosages:

40-100 pcy (25-60 kg/m3)

• Diameter-to-thickness:

12-30

General Information on FRC Segments Used in Tunnel Projects


• More ductility & robustness

• Crack width reduction

• High strength against unintentional impact loads

• Improved precast production efficiency

• Reduce spalling or bursting of concrete cover at vulnerable edges and corners

Advantages of FRC Segments

Reference: Maccaferri Asia (2013)—Segmental tunnel linings with fibre reinforced concrete, TUTG, Bangkok, 12 September 2013

Spalling/Bursting of Rebar-Reinforced-Concrete at Edges and Corners

Reference: SR99 Alaskan Way Viaduct

• Design by performance testing: before 1992 still being used occasionally in some projects • Design by pioneer tunneling guidelines: from 1992-2003

1. BV recommendation - German concrete association (1992) 2. Japan railway construction public corporation (1992) 3. Bekaert technical approach for tunnel linings by Moyson (1994)

• Design by recent FRC codes/guidelines: from 2003-present

1. RILEM TC 162-TDF (2003) 2. Concrete Society TR63 (2007) 3. Italian Standard CNR DT 204/2006 (2007) 4. Spanish Standard EHE-08 (2010) 5. fib Model Code (2010) 6. ACI 544.FR (2015)

Evolution of Design Procedures for FRC Segments

Design by Performance Testing

Full-scale bending test

Full-scale point load test

Misalignment

TBM

Cantilever load test

References: -Moccichino et al. (2010). Experimental Tests on Tunnel Precast Segmental Lining with Fiber Reinforced Concrete”, 2010 World Tunnel Congress, Vancouver, Canada.

-Poh et al. (2009). Structural Testing of Steel Fibre Reinforced Concrete (SFRC) Tunnel Lining Segments in Singapore. Proc. of the World Tunnelling Congress (WTC) 2009, Budapest, Hungary.

Design of FRC Segments By Pioneer Tunneling Guidelines (from 1992-2003)

BV recommendation - German concrete association (1992)

fbr = fL (EN 14651)

bbr = 0.45 feqm,Ι (fR1 from EN 14651)

mbr = 0.37 feqm,ΙΙ (fR4 from EN 14651)

Japan railway recommendation (1992)

-FRC constitutive models provided -Suitable for constructing axial force bending moment interaction diagrams - Load case of ground & groundwater discussed - Presentations of all load cases missing

Bekaert method by Moyson (1994)

Summary of ACI

Guideline for FRC

Segments

Covering Design for Strength or ULS

Governing Loads Cases

• Production and transient load cases:

Demolding, storage, transportation and handling

• Construction load cases :

TBM thrust, tail skin grouting, secondary (localized) grouting

• Final service load cases:

Ground and groundwater loads, longitudinal joint bursting, additional distortion, other loads


Segment Demolding

• Simulated by two cantilevers loaded under its self weight

(e.g. at 4 h)

Phase Maximum Developed Bending Moment Key Design Parameters

demolding wa2/2 sp* and f ’c at 4 h

* sp is the back calculated residual tensile strength for fiber reinforced concrete


Segment Storage

• Simulated by simply supported beams loaded under its self-weight and eccentricity loads (e.g. at 4 h)

• Segments comprising a ring piled up within one stock

Phase Maximum Developed Bending Moment Key Design Parameters

storage w(L2/8-S2/2)+F1e w(S2/2)+ F1e

sp* and f ’c at 4 h



Segment Transportation

• Simulated by simply supported beams loaded under its self-weight and eccentricity loads (at 28 d)

• Half of segments of each ring transported in one car

Phase Dynamic Shock Factor

Maximum Developed Bending Moment

Key Design Parameters

transportation 2.0 w(L2/8-S2/2)+ F2e w(S2/2)+ F2e

sp* and f ’c at 28 d



Segment Handling • Simulated by simply supported or cantilever beams

• handling from stack yard to trucks or rail cars carried out by slings, lifting devices or vacuum lifters.

Phase Dynamic Shock Factor Maximum Developed Bending Moment Key Design Parameters

Handling 2.0 w(L2/8-S2/2)+w(L/2+S)f (slings) wa2/2 (others)

sp* and f ’c at 28 d



TBM Thrust Jack Forces

Analysis and design methods:

• Simplified equations

• Analytical methods

• Finite Element Analyses (2D/3D)

• Non-linear Fracture Mechanics

Design checks:

• Bursting tensile stresses

• Spalling tensile stresses

• Compressive stresses


Simplified Equations for TBM Thrust Action

)2(5.0;125.0:318 ancburstanc

puburst ehdh

hPTACI

)2(4.0;2

125.0: ancburst

anc

anc

puburst ehdeh

hPTDAUB

h-2e

hanc

ACI 318 DAUB

j

dcco

j

pu

jcA

Aff

A

PACI 85.0:318 ,s

Bursting Design:

Compression Design:

Analytical Method for TBM Thrust Action

• Bursting stresses (scx) vary from face toward inside segment

• Determined as a fraction of fully spread compressive stress (scm = F/ab).

Iyengar (1962) Diagram for Bursting Design

Finite Element (FE) Simulations for TBM Thrust Action

Compressive Stresses Transverse Bursting and Spalling Stresses


Tail Skin Grouting Pressure

sg = 225 kPa

sg = 264.5 kPa

sg = 245 kPa

114 kN.m

Bending Moments 1573 kN

Axial Forces

• Simulated in 2D by a solid ring

• Grout pressure at crown is slightly higher than groundwater pressure

• Invert grout pressure is calculated from equilibrium b/w grout pressure, self-weight and shear stresses of semi-liquid grout

• Radial pressure is applied with a linear distribution


Secondary Grouting Pressure

• To fill a local gap between lining and excavation profile after primary grouting

• Simulated in 2D by a solid ring • Interaction with ground is modeled

by radial springs

• Grout pressure applied with a triangular distribution

36O

max sg = 225 kPa distributed

triangularly over a 36o

1734 kN

Axial Forces

-159 kN.m

Bending Moments

Reference: International Tunneling Association (ITA) Working Group 2 (2000). Guidelines for the Design of Shield Tunnel Lining”, Tunneling and Underground Space Technology, 15 (3): 303–331.

Ground and Groundwater Loads (Elastic Equation Method)

Recommended by International Tunnel Association (ITA) and Japan Society of Civil Engineers (JSCE)

Recommended by JSCE, AASHTO and Austrian Society for Concrete and Construction Technology (ÖVBB)

• Model: Segmented Double Ring Beam-Spring • Ground Interaction: Radial, Tangential and longitudinal Springs • Segment and Ring Joints Simulated by Springs

Interaction spring stiffness calculated by US Army Corps of Engineers (USACE) method

156 kN.m -1,666 kN

Axial Forces

Bending Moments

Ground and Groundwater Loads (Beam-Spring Method Simulation)

Ground and Groundwater Loads ( 2D FEM Simulations)

• 2D Continuum Analyses with FEM Usually Sufficient for Tunnels without Sudden Changes in Cross Section or Concentrated Load Intensities

Recommended by ÖVBB & AFTES for Tunnels in Soft Ground

Advantages:

• Considering Ground Behavior After Failure

• Redistribution of Loads Resulting from Lining Deformation

• Considering Excavation Stages

• Validity for Non-Uniform and Anisotropic Initial Stresses

Ground and Groundwater Loads (Discrete Element Method Simulations)

• 2D Discontinuum Analyses

• Intact Rock & Joint Set Properties Used for Modeling

• Bending Moment Distribution is Different than in Soft Ground

Recommended for Tunnels in Fractured Rock

0 2 4 6 8m

Reference: Bakhshi & Nasri (2013). Practical Aspects of Segmental Tunnel Lining Design. Proceedings of the World Tunnel Congress (WTC) 2013. Geneva, Switzerland.

Design checks:

• Bursting tensile stresses

• Compressive stresses

• Analytical methods

Longitudinal Joint Bursting Forces

Analysis and design methods:

• Simplified equations

• Finite Element Analyses (2D/3D)

Tensile Stress

Compressive Stresses

DAUB (2013)

Reference: Bakhshi & Nasri (2014). Guidelines and Methods on Segmental Tunnel Lining Analysis and Design – Review and Best Practice Recommendation. World Tunnel Congress 2014. Iguassu Falls, Brazil.

Other Loading Cases • Earthquake

• Fire

• Explosion

• Breakouts

• Excessive Longitudinal Bending Moments

• Additional Distortion

Seismic Analysis

• Seismic Analysis: Ovaling, Axial and Curvature Deformations Analysis

• Fire Loading Simulated by Temperature Gradient b/w Intrados and Extrados of Lining

• Explosion Simulated by Increasing Radial Pressure at Service Condition (e.g. 1 bar or 14.5 psi)

Breakouts & Additional Distortion Loading Cases Simulated by 3D FEM

• Simulation of Tunnel in Areas of Intersection between Crosscuts and Main Tunnel

• Simulation of External Loads due to Nearby Existing Structures (other Tunnels/Bridge Piles) Tensile

Stress in Invert of Existing Tunnel

Induced Bending Moment due to Opening

Reference:

Design Example for Mid-Size

Tunnels (ULS)

Geometry and Strength Parameters

• Di = 5.5 m (18 ft)

• b = 1.5 m (5 ft)

• h = 0.3 m (12 in)

• Lcurved = 3.4 m (11.2 ft)

• f’c @ 4h: 15 MPa (2,200 psi)

• f’c @ 28d: 45 MPa (6,500 psi)

• f1 = 3.8 MPa (540 psi)

• f’D150 @ 4h: 2.5 MPa (360 psi)

• f’D150 @ 28d: 4 MPa (580 psi)

• THTBM = 20,000 kN on 16 jack pairs

• Jack Shoes Contact Area: 0.2 x 0.87m

• Ring composed of 5+1 segments

• The tunnel is excavated in fractured rock

Reference: Bakhshi & Nasri (2015)—New ACI report on design of fiber reinforced concrete tunnel segmental linings, IoM3 UDCC 2015, 11 - 12 September, 2015 - Hong Kong

Constructing Axial Force-Bending Moment Interaction Diagram

Zones 1 & 2

Zone 3


Design Checks for Different Load Cases

Phase Specified Residual Strength, MPa (psi)

Maximum Bending Moment kNm/m (kipf-ft/ft)

Bending Moment Strength, kNm/m (kipf-ft/ft)

Demolding 2.5 (360) 5.04 (1.13) 26.25 (5.91)

Storage 2.5 (360) 18.01 (4.05) 26.25 (5.91)

Transportation 4.0 (580) 20.80 (4.68) 42.00 (9.44)

Handling 4.0 (580) 10.08 (2.26) 42.00 (9.44)

ACI 318

)22.1(1775347.0

100055.172.12.1:

)2.1(1741277.187.0

100032.172.12.1:

MPapsida

TdirectionRadial

MPapsidh

TdirectionTangential

burstl

burstp

burstanc

burstp

s

s

Reference: Bakhshi & Nasri (2015)—New ACI report on design of fiber reinforced concrete tunnel segmental linings, IoM3 UDCC 2015, 11 - 12 September, 2015 - Hong Kong

Design for Serviceability Limit States (SLS)

Design Flowchart for SLS

Reference: JSCE. 2007. Standard Specifications for Tunneling: Shield Tunnels. Japan Society of Civil Engineers.

OK

NG

Start

Assume structural dimensions of members Determine design load

Structural analysis

Examine cracks Examine deformation Examine stresses

Check

End

Design Checks & Limiting Values for SLS of Tunnel Segments

Reference: JSCE. 2007. Standard Specifications for Tunneling: Shield Tunnels. Japan Society of Civil Engineers.

SLS States Location Items to Check Limiting Values

Stress

Segment section Stress in concrete Allowable compressive stress of concrete

Stress in reinforcement Allowable tensile stress of steel bars

Segment joints Stress in concrete Allowable compressive stress of concrete

Stress in connectors Allowable stress of connecting bolts

Deformation

Segmental ring Ring deformation Allowable deformation

Segment joints Joint opening Allowable gap between segments joints

Joint offset Allowable offset between segments joints

Cracking Segment section Flexural crack width Allowable concrete crack width

Shear force Shear crack capacity

Calculation of Flexural Crack Width for Reinforced Concrete Segments

- ACI 224.1R (2007) - JSCE (2007) - EN 1992-1-1 (2004)

33 10011.0 Adfw csb

22

22

sd

E

fw c

s

s b

s

sr

s

s

cm

s

s

effct

ts

rE

fs

E

A

A

E

E

A

A

fkf

sw 6.0

)1(

max,

,

max,

)(7.0487

)2(57.0

20

1555.0;

sd

n

n

fs

E

fsw c

c

csd

s

s

Allowable SLS Crack Width

Reference: ÖVBB Guideline, 2011, “Guideline for Concrete Segmental Lining Systems”, Austrian Society for Concrete and Construction Technology.

Requirement Class

Designation Application Requirement

Allowable Crack Width

AT1 Largely dry - One-pass lining with very tight waterproofing requirements - Portal areas

Impermeable 0.20 mm (0.008 in)

AT2 Slightly moist

- One-pass lining for road and railway tunnels with normal waterproofing requirements (excluding portals)

Moist, no running water in tunnel

0.25 mm (0.010 in)

AT3 Moist - One-pass lining without waterproofing requirements - two-pass lining systems

Water dripping from individual spots

0.30 mm (0.012 in)

AT4 Wet - One-pass lining without waterproofing requirements - two-pass lining as drained system

Water running in some places

0.30 mm (0.012 in)

Concrete Codes: - ACI 224.1R (2007): 0.3 mm (0.012 in) - EN 1992-1-1 (2004): 0.3 mm (0.012 in) - fib Model Code (2010): 0.2 mm (0.008 in)

Tunnel Codes: - LTA (2007): 0.3 mm (0.012 in) - DAUB (2013): 0.2 mm (0.008 in) - JSCE (2007): 0.004 dc

- ÖVBB (2011):

Current and Future Research Studies

Current Studies: Reinforcement Alternatives for SLS of Cracking

Reference: Bakhshi & Nasri (2015). Design of Segmental Tunnel Linings for Serviceability Limit State. Proc of the World Tunnel Congress (WTC) 2015. May 22-28, 2015, Dubrovnik, Croatia.

Alternatives: 1- Conventional Reinforcement 2- Fiber Reinforcement

Service Loads: M = 239 kN.m (177 kips-ft) N = 2,068 kN (465 kips)

top

strains

ftop = 17.1 MPa (2.48 ksi)

stresses

Fiber properties:

f’D150 = 4 MPa (0.58 ksi)

sp = 0.34 x 4 MPa = 1.36 MPa (0.197 ksi)

1524 mm (60 in)

305 mm (12 in)

x=179 mm

(7.04 in)

fc,t

sp = 1.36 MPa (0.197 ksi)

top

st

sb

strains

ftop = 18.45 MPa

(2.676 ksi)

Fst = 1,956 kN (440 kips)

stresses

10 #4 (Asb = 1290 mm2)

10 #4 (Ast = 1290 mm2)

38 mm (1.5 in)

1524 mm (60 in)

229 mm (9 in)

305 mm (12 in)

x=148 mm

(5.8 in)

38 mm (1.5 in)

Fsb = 2,122 kN (477 kips)

Current Studies: Design for Cracking Serviceability Limit States


Steps for FRC segments: 1- Determination of neutral axis

2- Determination of compressive/tensile strains at extreme fibers

3- Calculation of crack width using gauge length concept

hwDTCNR

CodeModelfib

tfc,:)2007(2006/204

&)2010(

)(:)2003(162 , xhwTDFTCRILEM tfc

tfcwDAfStb ,14.0:)2012(

Current Studies: Comparing Fibers vs. Rebars for Cracking Under Service Loads

Maximum Crack Width in RC Segments Maximum Crack Width in FRC Segments

ACI 224.1R (2007) - Gergely & Lutz

0.10 mm (0.0039 in)

fib Model Code (2010) CNR-DT 204 (2006)

0.10 mm (0.0040 in)

ACI 224.1R (2007) - Frosch 0.14 mm (0.0056 in) RILEMTC 162-TDF (2003) 0.04 mm

(0.0017 in)

JSCE (2007) 0.14 mm (0.0053 in)

DAfStb (2012) 0.047 mm (0.0018 in)

EN 1992-1-1 (2004) 0.07 mm (0.0028 in)


• Optimized hybrid (fiber+rebar) design for large- diameter tunnels > 24 ft (7.3 m)

Future Research Studies

• Minimum FRC characteristics as sole reinforcement for ductility requirement and crack control


)540(8.3 psiMPafL )580(41 psiMPafR

• Allowable crack width for segmental tunnel linings considering tunnel infiltration/exfiltration (flow)


Flow through parallel plates

Conclusion

• In mid-size tunnels use of fibers in segment can lead to elimination of steel bars at the ultimate limit state (ULS), which in turn results in significant construction cost saving.

• Use of fiber in tunnel segments results in reduction of crack width in under the service load for Serviceability Limit State (SLS) design.

• Different standard FRC constitutive laws give similar axial force-bending moment interaction diagrams as the key design tool for designing precast tunnel segments.

Thank you

design of segmental tunnel linings for serviceability...

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