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
Outline • • • • • •
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
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
FRC Precast Tunnel Segments • Used in more than 50 tunnel projects • First FRC tunnel segments: Metrosud (1982)
Reference: ACI 544.AR (2015)—Draft Emerging Technology Report on Design and Construction of FiberReinforced Precast Concrete Tunnel Segments
General Information on FRC Segments Used in Tunnel Projects • 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 Reference: ACI 544.AR (2015)—Draft Emerging Technology Report on Design and Construction of FiberReinforced Precast Concrete Tunnel Segments
Advantages of FRC Segments • 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 Reference: Maccaferri Asia (2013)—Segmental tunnel linings with fibre reinforced concrete, TUTG, Bangkok, 12 September 2013
Spalling/Bursting of Rebar-ReinforcedConcrete at Edges and Corners
Reference: SR99 Alaskan Way Viaduct
Evolution of Design Procedures for FRC Segments • Design by performance testing: before 1992 still being used occasionally in some projects • Design by pioneer tunneling guidelines: from 1992-2003 1. 2. 3.
BV recommendation - German concrete association (1992) Japan railway construction public corporation (1992) Bekaert technical approach for tunnel linings by Moyson (1994)
• Design by recent FRC codes/guidelines: from 2003-present 1. 2. 3. 4. 5. 6.
RILEM TC 162-TDF (2003) Concrete Society TR63 (2007) Italian Standard CNR DT 204/2006 (2007) Spanish Standard EHE-08 (2010) fib Model Code (2010) ACI 544.FR (2015)
Design by Performance Testing Full-scale point load test
TBM
Full-scale bending test
Misalignment
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.
Cantilever load test
Design of FRC Segments By Pioneer Tunneling Guidelines (from 1992-2003) BV recommendation - German concrete association (1992)
Japan railway recommendation (1992)
fbr = fL (EN 14651) bbr = 0.45 feqm,Ι (fR1 from EN 14651) mbr = 0.37 feqm,ΙΙ (fR4 from EN 14651)
-FRC constitutive models provided -Suitable for constructing axial force bending Bekaert moment interaction diagrams method by - Load case of ground & groundwater discussed Moyson (1994) - Presentations of all load cases missing
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 Reference: ACI 544.AR (2015)—Draft Emerging Technology Report on Design and Construction of FiberReinforced Precast Concrete Tunnel Segments
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
Reference: ACI 544.AR (2015)—Draft Emerging Technology Report on Design and Construction of FiberReinforced Precast Concrete Tunnel Segments
Segment Storage • Simulated by simply supported beams loaded under its selfweight 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
* sp is the back calculated residual tensile strength for fiber reinforced concrete
Reference: ACI 544.AR (2015)—Draft Emerging Technology Report on Design and Construction of FiberReinforced Precast Concrete Tunnel Segments
Segment Transportation • Simulated by simply supported beams loaded under its selfweight 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
* sp is the back calculated residual tensile strength for fiber reinforced concrete
Reference: ACI 544.AR (2015)—Draft Emerging Technology Report on Design and Construction of FiberReinforced Precast Concrete Tunnel Segments
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
Handling
Dynamic Shock Factor
Maximum Developed Bending Moment
Key Design Parameters
2.0
w(L2/8-S2/2)+w(L/2+S)f (slings) wa2/2 (others)
sp* and f ’c at 28 d
* sp is the back calculated residual tensile strength for fiber reinforced concrete
Reference: ACI 544.AR (2015)—Draft Emerging Technology Report on Design and Construction of FiberReinforced Precast Concrete Tunnel Segments
TBM Thrust Jack Forces Design checks: • Bursting tensile stresses • Spalling tensile stresses • Compressive stresses Analysis and design methods: • Simplified equations • Analytical methods • Finite Element Analyses (2D/3D) • Non-linear Fracture Mechanics Reference: ACI 544.AR (2015)—Draft Emerging Technology Report on Design and Construction of FiberReinforced Precast Concrete Tunnel Segments
Simplified Equations for TBM Thrust Action
hanc
h-2e
ACI 318 Bursting Design:
DAUB ACI 318 : DAUB :
Compression Design:
ACI 318 :
h Tburst 0.25 Ppu 1 anc ; d burst 0.5 (h 2eanc ) h hanc ; d burst 0.4 (h 2eanc ) Tburst 0.25 Ppu 1 h 2eanc Ppu A s c, j f co 0.85 f c d Aj Aj
Analytical Method for TBM Thrust Action Iyengar (1962) Diagram for Bursting Design
• Bursting stresses (scx) vary from face toward inside segment • Determined as a fraction of fully spread compressive stress (scm = F/ab).
Finite Element (FE) Simulations for TBM Thrust Action
Transverse Bursting and Spalling Stresses
Compressive Stresses
Reference: ACI 544.AR (2015)—Draft Emerging Technology Report on Design and Construction of FiberReinforced Precast Concrete Tunnel Segments
Tail Skin Grouting Pressure • 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 sg = 225 kPa
Axial Forces sg = 245 kPa 1573 kN
114 kN.m
Bending Moments
sg = 264.5 kPa
Reference: ACI 544.AR (2015)—Draft Emerging Technology Report on Design and Construction of FiberReinforced Precast Concrete Tunnel Segments
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 max sg = 225 kPa distributed triangularly over a 36o
-159 kN.m 1734 kN
36O
Axial Forces
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)
Ground and Groundwater Loads (Beam-Spring Method Simulation) 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 Axial Forces
-1,666 kN
Bending Moments
156 kN.m
Interaction spring stiffness calculated by US Army Corps of Engineers (USACE) method
Ground and Groundwater Loads ( 2D FEM Simulations) Recommended by ÖVBB & AFTES for Tunnels in Soft Ground
• 2D Continuum Analyses with FEM Usually Sufficient for Tunnels without Sudden Changes in Cross Section or Concentrated Load Intensities 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) Recommended for Tunnels in Fractured Rock
• 2D Discontinuum Analyses • Intact Rock & Joint Set Properties Used for Modeling • Bending Moment Distribution is Different than in Soft Ground
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.
Longitudinal Joint Bursting Forces Design checks: • Bursting tensile stresses • Compressive stresses Analysis and design methods: • Simplified equations DAUB (2013) • Finite Element Analyses (2D/3D) • Analytical methods Tensile Stress
Compressive Stresses
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 • • • • • • • • • • •
• Ring composed of 5+1 Di = 5.5 m (18 ft) segments b = 1.5 m (5 ft) • The tunnel is excavated in h = 0.3 m (12 in) fractured rock 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
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
Reference: ACI 544.AR (2015)—Draft Emerging Technology Report on Design and Construction of FiberReinforced Precast Concrete Tunnel Segments
Design Checks for Different Load Cases
ACI 318 Tangential direction :
sp
1.2 Tburst 1.2 17.32 1000 174 psi (1.2 MPa) hanc d burst 0.7 8 1.77 12
Radial direction :
sp
1.2 Tburst 1.2 17.55 1000 177 psi (1.22 MPa) al d burst 0.7 34 5
Phase Demolding Storage Transportation Handling
Specified Residual Strength, MPa (psi) 2.5 (360) 2.5 (360) 4.0 (580) 4.0 (580)
Maximum Bending Moment kNm/m (kipf-ft/ft) 5.04 (1.13) 18.01 (4.05) 20.80 (4.68) 10.08 (2.26)
Bending Moment Strength, kNm/m (kipf-ft/ft) 26.25 (5.91) 26.25 (5.91) 42.00 (9.44) 42.00 (9.44)
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 Start
Assume structural dimensions of members
Determine design load
Structural analysis
Examine stresses
Examine deformation
Examine cracks
Check
NG
OK
End
Reference: JSCE. 2007. Standard Specifications for Tunneling: Shield Tunnels. Japan Society of Civil Engineers.
Design Checks & Limiting Values for SLS of Tunnel Segments SLS States Stress
Deformation Cracking
Location
Items to Check Stress in concrete Segment section Stress in reinforcement Stress in concrete Segment joints Stress in connectors Segmental ring Ring deformation Joint opening Segment joints Joint offset Flexural crack width Segment section Shear force
Limiting Values Allowable compressive stress of concrete Allowable tensile stress of steel bars Allowable compressive stress of concrete Allowable stress of connecting bolts Allowable deformation Allowable gap between segments joints Allowable offset between segments joints Allowable concrete crack width Shear crack capacity
Reference: JSCE. 2007. Standard Specifications for Tunneling: Shield Tunnels. Japan Society of Civil Engineers.
Calculation of Flexural Crack Width for Reinforced Concrete Segments - ACI 224.1R (2007)
- JSCE (2007)
w 0.011b f s 3 d c A 10
3
f s 2 w 2 s b dc Es 2
2
f 15 5(n 2) ; s 0.55 w s s csd 0.7 4 d c 0.7 ( s ) Es f c 20 7n 8
- EN 1992-1-1 (2004)
f s kt w sr ,max
f ct ,eff
(1
As A Es
E s As ) Ecm A f sr ,max 0.6 s Es
Allowable SLS Crack Width 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) Requirement Class
Designation
AT1
Largely dry
AT2
Slightly moist
AT3
Moist
AT4
Wet
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):
Application - One-pass lining with very tight waterproofing requirements - Portal areas - One-pass lining for road and railway tunnels with normal waterproofing requirements (excluding portals) - One-pass lining without waterproofing requirements - two-pass lining systems - One-pass lining without waterproofing requirements - two-pass lining as drained system
Requirement
Allowable Crack Width
Impermeable
0.20 mm (0.008 in)
Moist, no running water in tunnel
0.25 mm (0.010 in)
Water dripping from individual spots
0.30 mm (0.012 in)
Water running in some places
0.30 mm (0.012 in)
Reference: ÖVBB Guideline, 2011, “Guideline for Concrete Segmental Lining Systems”, Austrian Society for Concrete and Construction Technology.
Current and Future Research Studies
Current Studies: Reinforcement Alternatives for SLS of Cracking Alternatives: 1- Conventional Reinforcement 2- Fiber Reinforcement
Service Loads: M = 239 kN.m (177 kips-ft) N = 2,068 kN (465 kips)
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.
Current Studies: Design for Cracking Serviceability Limit States top
Steps for FRC segments:
x=179 mm (7.04 in)
Fiber properties:
f’D150 = 4 MPa (0.58 ksi)
sp = 0.34 x 4 MPa = 1.36 MPa (0.197 ksi)
305 mm (12 in)
sp = 1.36 MPa
1- Determination of neutral axis 2- Determination of compressive/tensile strains at extreme x=148 mm (5.8 in) fibers 3- Calculation of crack width using gauge length concept
ftop = 17.1 MPa (2.48 ksi)
(0.197 ksi)
1524 mm (60 in)
fc,t 38 mm (1.5 in)
stresses
strains
ftop = 18.45 MPa (2.676 ksi)
top st 10 #4 (Ast = 1290 mm2)
Fst = 1,956 kN (440 kips)
305 mm (12 in) 229 mm (9 in)
10 #4 (Asb = 1290 mm2)
1524 mm (60 in)
sb
strains
Fsb = 2,122 kN (477 kips)
stresses
38 mm (1.5 in)
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.
Current Studies: Comparing Fibers vs. Rebars for Cracking Under Service Loads RILEM TC 162 TDF (2003) :
w fc ,t (h x)
DAfStb (2012) :
w 0.14 fc ,t
fib Model Code (2010) & CNR DT 204 / 2006 (2007) :
w fc,t h
Maximum Crack Width in RC Segments
Maximum Crack Width in FRC Segments
ACI 224.1R (2007) - Gergely 0.10 mm & Lutz (0.0039 in)
fib Model Code (2010) CNR-DT 204 (2006)
0.10 mm (0.0040 in)
RILEMTC 162-TDF (2003)
0.04 mm (0.0017 in)
DAfStb (2012)
0.047 mm (0.0018 in)
ACI 224.1R (2007) - Frosch
0.14 mm (0.0056 in)
JSCE (2007)
0.14 mm (0.0053 in)
EN 1992-1-1 (2004)
0.07 mm (0.0028 in)
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.
Future Research Studies • Optimized hybrid (fiber+rebar) design for largediameter tunnels > 24 ft (7.3 m)
Future Research Studies • Minimum FRC characteristics as sole reinforcement for ductility requirement and crack control f 3.8MPa (540 psi ) L
f R1 4 MPa (580 psi )
Future Research Studies • 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