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FRC 2014 Joint ACI-fib International Workshop Fibre Reinforced Concrete: from Design to Structural Applications

Developments in design for fiber reinforced concrete tunnel segments Mehdi Bakhshi, Verya Nasri

AECOM, New York, USA.

Abstract Precast fiber reinforced concrete (FRC) segments are increasingly being adopted in TBM tunnels to take advantage of their potential for production cost saving, improved handling robustness and long-term durability benefits. This paper presents a procedure for structural design of FRC segments. The procedure includes design of FRC lining for production and transitional load cases of demolding, storage, transportation and handling. In addition, construction load cases of TBM thrust jack forces and grouting pressure are discussed. Ground and groundwater loads and force transfer in joints in the final service stage are presented as critical load cases. The proposed design approach is applied to a case of mid-size tunnel. Results show that when the design forces are not relatively large in comparison with the segment cross-section dimension, the use of ﬁbers can lead to elimination or a signiﬁcant reduction of the steel bars, which in turn results in significant construction cost saving.

Keywords Design, fiber, lining, segment, tunnel.

441

FRC 2014 Joint ACI-fib International Workshop Fibre Reinforced Concrete: from Design to Structural Applications

1

Introduction

Precast concrete segments are the predominant support method in Tunnel Boring Machine (TBM) bored tunnels in soft ground and weak fractured rock, providing the initial and final ground support. Conventionally, steel bars are used in concrete segments to resist tensile stresses developed due to all loading cases from the time of casting through service condition. However, there are some issues associated with the use of steel bars including large crack widths, high labor costs and long time for placement of curved bars in manufacturing plant. As an alternative, Fiber Reinforced Concrete (FRC) considerably improves the concrete postcracking behavior, allows for a better crack control and offers plastic shrinkage resistance to the concrete mix and improves the concrete durability. Considering all these benefits, FRC represents a competitive material for tunnel segments. The fiber presence close to segment surface is very advantageous with high tensile stresses developed in this zone induced by TBM thrust jack forces during installation. FRC has been used since 1982 in numerous projects around the world, e.g. water/waste water, gas pipeline, power cable, subway, railway, and road tunnels, as the preferred material for the construction of tunnel precast segmental lining. In most of the projects, small to mid-size tunnels have been reinforced with only steel fibers at a dosage ranging between 25 to 60 kg/m3. Internal diameters of these tunnels range between 2.2-11.4 m and their thicknesses are between 0.15 and 0.4 m. The design has been performed using constitutive laws recommended by international codes and standards such as DBV (2001), RILEM TC 162-TDF (2003), CNR DT 204/2006 (2007), EHE (2008) and fib Model Code (2010). This paper presents a procedure for design of FRC tunnel segments for all load cases happening from the time after casting to the final service condition based on residual tensile strength proposed by ACI 544.FR report (2014) and specified compressive strength. The proposed design approach is applied to a case of mid-size tunnel and key material parameters for design are summarized. Effects of residual strength and different standard constitutive laws on axial force-bending moment interaction diagrams as the key design tools are discussed.

2

Design of FRC tunnel segments by LRFD method

LRFD is a design philosophy that takes into account the variability in the prediction of loads and the behavior of structural elements at ultimate and serviceability limit states. The focus of this paper is on Ultimate Limit State (ULS). Flexural or tensile resistance is calculated based on the residual strength of a standard beam at mid–span deflection of L/150, defined as end-point deflection per ASTM C1609 (2012), where L is distance between the supports (see Figure 1). Due to the overestimation of the fD150 parameter based on elastic approaches, a back-calculation procedure is to be adopted to obtain residual tensile strength, p (Soranakom and Mobasher, 2007). Another approach is to scale standard residual flexural strengths by a factor of 0.33-0.37 (fib, 2010; Bakhshi et al. 2014; Mobasher et al. 2014; Vandewall, 2000). FRC segments are designed for all load cases happening from the time of the casting up to the time when they withstand final service loads. These loads are presented in the following sections. FRC segments are proportioned for adequate strength, using load

442

FRC 2014 Joint ACI-fib International Workshop Fibre Reinforced Concrete: from Design to Structural Applications

factors and strength reduction factors. A strength reduction factor of 0.70 is applied for flexure, compression, shear, and bearing actions of FRC segments to safeguard against uncertainty of material properties.

Figure 1:

3

Definition of residual flexural parameters for FRC beams by ASTM C1609 (2012)

Design for production and transitional stages

The production and transitional loading includes all the loading stages starting from the time of the segment casting up to the time of the segment erection inside TBM shield.

3.1

Segment demolding

This load case represents the effect of lifting systems on stripping precast concrete segments from the molds in the segment manufacturing plant. Figure 2a shows the demolding phase which is modeled by two cantilever beams loaded under its own dead weight. The design is performed with regard to the specified strength when segments are demolded (3-4 hours after casting). Mix proportion for FRC segments (similar to steel fiber reinforced shotcrete) is designed by adjusting accelerator dosage to achieve high early strength, therefore standards beam tests can be conducted at such early hours to obtain residual flexural parameters for design (Bakhshi et al. 2014; Wang and Li, 2006). As shown in Figure 2b, the dead weight is the only force acting on the segment, and therefore, the applied load factor in ULS is 1.4 per ACI 318 (2011). Maximum developed bending moment is compared with provided resistance moment of segment for design check.

3.2

Segment storage

Demolding is followed by stacking the precast segments in the stack yard to gain 28-day strength specified by designer before transportation to the construction site. As shown in Figure 3a, all segments comprising a full ring are piled up within one stack. Designers provide the distance between the stack supports considering an eccentricity of e = 0.1m between the locations of the stacks support for the bottom segment and the supports of above segments. A simply supported beam loaded as in Figures 3b and 3c represent this load case. Applied load factor in ULS is 1.4 per ACI 318 (2011). Maximum developed bending moment is used for design.

443

FRC 2014 Joint ACI-fib International Workshop Fibre Reinforced Concrete: from Design to Structural Applications

(b)

(a)

Figure 2:

a) Demolding in the segment manufacturing plant, b) Forces acting on segments

(a)

(b)

Figure 3:

3.3

(c)

Segments stacking for storage and schematics of forces acting on bottom segment

Segment transportation

Trucks and rail cars transport the precast segments stored in the stack yard to the construction site and TBM trailing gear. Segments may encounter dynamic shock loads during this phase and usually half of the segments of each ring are transported in one car. Wood blockings provide supports for the segments. An eccentricity of 0.1 m is recommended for possible eccentricity. Simply supported beams represent this load case with a dead load factor of 1.4 in ULS per ACI 318 (2011) and a dynamic shock factor of 2.0 applied to the forces.

3.4

Segment handling

Segment handling from stack yard to trucks or rail cars are carried out by specially designed lifting devices or vacuum lifters. Inside the TBM, segment handling is usually carried out using vacuum lifters while other methods may be used occasionally. This load case is simulated similar to segment demolding shown in Figure 2. A dead load factor of 1.4 in ULS per ACI 318 (2011) and a dynamic shock factor of 2.0 are recommended for design.

444

FRC 2014 Joint ACI-fib International Workshop Fibre Reinforced Concrete: from Design to Structural Applications

4

Design for construction stages

The construction loading stages include loading cases starting from the time of segment erection inside the TBM shield up to the time when installation of a ring is completed.

4.1

TBM thrust jack forces

After assembly of a ring, TBM moves forward, as shown in Figure 4, by pushing its jacks on bearing pads placed on the circumferential joints of the newest assembled ring. This action results in development of high compression stresses under the pads, as well as bursting tensile stresses deep in the segment and spalling tensile forces between the pads. Maximum thrust force for each jack pair is obtained by dividing maximum total thrust of TBM over the number of jack pairs. In another approach, jack thrust forces are estimated from the sum of forces required for boring into the rock or acting pressure on cutting face due to earth or slurry pressure, plus friction resistance between the shield surface and the ground, and hauling resistance of trailing gears. In latter approach, average thrust force on each jack pair should be factored by 1.6 times for design at ULS per ACI 318 (2011) recommendation for live loads, while there is no need to apply a load factor on the maximum jack thrust force obtained from former method. Different design methods include ACI 318 (2011) section 18.13 and DAUB (2013) simplified equations, Iyengar diagram (1962) and FE simulations. Residual tensile strength of FRC segment at 28 day is checked against maximum developed bursting tensile stress. hanc

al

(a)

(b)

Figure 4:

4.2

aat

t

a) Thrust jacks pushing on circumferential joints in French configuration, b) Stress distribution schematics under jack shoes (Groeneweg, 2007)

Tail and localized back grouting pressure

This load case presents back grouting or filling the annular space with semi-liquid grouts which is required in order to control and restrict settlement at the surface and to securely lock the lining ring in position. Grout pressure has to be limited to a minimum value which is slightly higher than the water pressure, and a maximum value which is less than the overburden pressure. For the case of tail grouting, vertical gradient of grout pressure is calculated by taking the equilibrium between the upward component of total grout pressure, lining deadweight and tangential component of grout shear strength (Groeneweg, 2007). This load case is modeled by applying radial pressures increasing linearly from the crown to the 445

FRC 2014 Joint ACI-fib International Workshop Fibre Reinforced Concrete: from Design to Structural Applications

invert of tunnel. Deadweight of the lining and grouting pressure are the only loads applied to the tunnel lining and a load factor of 1.25 is applied to both loads in ULS design. In the case of localized backfilling, radial injection through holes provided in the segments is performed where annular gaps exist between the lining extrados and excavation profile after tail grouting. International Tunnel Association guideline (ITA, 2000) is used for simulation of localized backfilling pressure. The lining is modeled as a 2D solid ring with a reduced flexural rigidity due to segment joints. The interaction between lining and surrounding ground or primary hardened grout is modeled by radial springs. Using a structural analysis package, bending moments and axial forces due to the grouting load cases are determined and checked against FRC segment capacity.

5

Design for final service stages

The loading in the final service stage is represented by the long-term interaction of the lining with the ground and groundwater pressure which is discussed further in the next section, as well as other factors specific to an individual tunnel, e.g. additional distortion, earthquake, fire, explosion, and breakouts. Longitudinal joint bursting load due to force transfer in a reduced cross section because of gasket and stress relief grooves (Bakhshi and Nasri, 2013) is another critical load case in the final service stage. Due to similarity to the effect of thrust jack forces, it is not discussed further as similar analysis and design methods are applicable to this load case. The load case of ground, groundwater and surcharge loads is discussed in the following. Precast concrete segments as final lining system withstand different loadings in the service stage including ground (vertical and horizontal) loads, groundwater pressure, dead weight, surcharge and ground reaction loads. Methods of analysis for segmental tunnel linings in conformance with standards and guidelines from various countries in Europe, Asia and America have been presented elsewhere (Bakhshi and Nasri, 2014a; Bakhshi and Nasri, 2014b). These methods include elastic equations, beam-spring model, FE analysis (Figure 5) and Discrete Element method (DEM). Resulting forces on segments are used to design segments and specify compressive and tensile strengths of FRC.

Figure 5:

446

FEM simulation for tunnel excavation in soft ground

FRC 2014 Joint ACI-fib International Workshop Fibre Reinforced Concrete: from Design to Structural Applications

6

Design example

An example for design of a mid-size TBM tunnel lining with precast FRC segments is presented. It is assumed that internal diameter of the segmental ring is Di = 5.74 m, and the ring composed of 5 large segments and one key segment (one-third of the size of large segments). Width, thickness and curved length at centerline of the large segments are 1.5, 0.3 and 3.4 m, respectively. A stress-strain diagram according to ACI 544.FR report (2014) is adopted. Key design parameters for aforementioned load cases are the specified residual tensile or flexural strength (p or f’D150) and specified compressive strength (f’c). Following the approach of scaling the residual flexural strength obtained by ASTM C1609 (2012) tests, a factor of 0.34 is considered to convert f’D150 to p. Designed early-age and 28-day f’D150 strengths are 2.5 and 4 MPa, respectively. Specified compressive strengths are 15 MPa for early-age and 45 MPa for 28-day FRC segment. As shown in Figure 6, capacity of FRC segments are calculated based on equilibrium conditions assuming a post-crack plastic behavior in the tension zone. First crack flexural strength (f1) is assumed as 4 MPa. Design checks for the production and transitional loads are shown in Table 1. The tunnel is excavated in soft ground. Two-dimensional FEM packages are used for calculation of tunnel lining forces in three different geological reaches defined along the alignment of this tunnel case. Design checks for the load case of the ground and groundwater pressure is shown in Figure 7. In this project, a TBM machine is used with the maximum total thrust of 45,000 kN applied on 16 jack pairs. Maximum thrust forces on each pair is therefore 2.8 MN. The length and width of the contact area between the jack pads and segments, considering a maximum eccentricity of e = 0.025 m, are al = 0.87 m and hanc = 0.2 m, respectively. Dimensions of fully spread stresses are at = 3.4/3 = 1.13 m and h = 0.3 m in tangential and radial directions, respectively. Conforming to simplified equations of ACI 318 (2011), bursting force (Tburst) and its centroidal distance from the face of section (dburst) in radial and tangential directions are: Tangential direction : d burst 0.5 (at 2e) 0.5 (1.13 2 0.025) 0.54 m

Radial direction :

al 0.87 0.25 2.8 (1 Tburst 0.25 Ppu 1 ) 0.105MN 1.08 at 2e d burst 0.5 (h 2eanc ) 0.5 (0.3 2 0.025) 0.125 m hanc 0.2 0.25 2.8 (1 Tburst 0.25 Ppu 1 ) 0.117 MN 0.25 h 2eanc

Using this method of analysis, the maximum bursting stress developed in radial and transverse directions are determined as

Tangential direction : p Radial direction :

p

Tburst 0.105 0.28 MPa d burst 0.7 0.54 Tburst 0.117 1.33 MPa d burst 0.7 0.125

These stresses are less than 28-day specified residual tensile strength of FRC segment as p= 0.34 f’D150 = 1.36 MPa, and the design is valid for load case of TBM thrust jack forces.

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FRC 2014 Joint ACI-fib International Workshop Fibre Reinforced Concrete: from Design to Structural Applications

Figure 6:

Strain and stress distributions through the section as part of it undergoes tension

Table 1:

Segment design checks for production and transitional stages

Phase

Specified Residual Strength (MPa)

Maximum Developed Bending Moment (kNm/m)

Resistance Bending Moment (kNm/m)

Demolding

2.5 (early-age)

5.04

26.25

Storage

4.0 (28 d)

18.01

26.25

Transportation 4.0 (28d)

20.80

42.00

Handling

10.08

42.00

Figure 7:

448

4.0 (28 d)

Design checks for the load case of ground and groundwater pressure

FRC 2014 Joint ACI-fib International Workshop Fibre Reinforced Concrete: from Design to Structural Applications

7 Parametric studies on residual strength and choice of constitutive law Increasing the fiber content in the mix directly results in increase of the residual flexural strengths (f’D150) of FRC. A parametric study on effects of increasing f’D150 from 1 to 5 MPa on the axial force-bending moment interaction diagrams are shown in Figure 8a. Other parameters and segment geometry for this study are similar to the ones presented in previous example. Comparing such diagrams with the results of analyses for aforementioned loading cases (e.g. results shown in Figure 7) results in determining the required residual parameter and the required fiber content based on fiber manufacturer product datasheets. Effect of choice of standard constitutive laws on a similar tunnel segment with a residual strength of 4 MPa is shown in Figure 8b. Results show that choice of constitutive laws shown in Table 2 does not have a significant effect on the axial force-bending moment interaction diagram of FRC segments and subsequently does not affect the design outcome.

(b) (a)

Figure 8:

Effects of residual strength and choice of constitutive law on the axial forcebending moment interaction diagrams as key design tools

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FRC 2014 Joint ACI-fib International Workshop Fibre Reinforced Concrete: from Design to Structural Applications

Table 2:

Choice of constitutive laws for FRC precast tunnel segments

ACI 544.FR Report

cr = f1 (ASTM C1609) p = 0.34 fD150 (ASTM C1609)

-RILEM TC 162-TDF Recommendation -New Zealand NZS 3101.2 standard

ffctm, fR1, fR4 obtained from EN 14651

DBV (German society of concrete) Recommendation

fbr = fL (EN 14651) br = 0.45 feqm,Ι (fR1 from EN 14651) br = 0.37 feqm,ΙΙ(fR4 from EN 14651)

-fib Model Code 2010 -Italian Guide CNR-DT 204/2006 -Spanish Concrete Code EHE08 -ÖVBB (Austrian society for construction technology) Guide

fFts = 0.45 fR1 (fR1 from EN 14651) fFtu = 0.5 fR3 – 0.2 fR1 (from EN 14651)

-fib Model Code 2010 -Italian Guide CNR-DT 204/2006 -Spanish Concrete Code EHE08

fFtu = 0.33 fR3 (fR3 from EN 14651)

CS (Concrete Society)TR63 Report

f ftd ftd

450

ftd = 0.37 fR3 (fR3 from EN 14651)

FRC 2014 Joint ACI-fib International Workshop Fibre Reinforced Concrete: from Design to Structural Applications

8

Conclusions

Presented procedure for structural design of FRC tunnel segments includes design for production and transitional, construction and final service stages. Application of the design approach to a case of mid-size tunnel indicates that when the design forces are not relatively large in comparison with the segment cross-section dimension, the use of ﬁbers can lead to elimination of steel bars, which in turn results in significant construction cost saving in tunneling industry. Results of analyses indicate that FRC constitutive laws from different guidelines give similar axial force-bending moment interaction diagrams as the key design tools for designing precast tunnel segments.

9

References

ACI 544 Report (under development), Indirect method to obtain a stress-strain diagram for strain softening fiber-reinforced concretes. American Concrete Institute (ACI), Farmington Hills, MI. ACI 318 (2011), Building Code Requirements for Structural Concrete and Commentary. American Concrete Institute (ACI), Farmington Hills, MI. ASTM C1609-12, Standard test method for ﬂexural performance of ﬁber-reinforced concrete (using beam with third-point loading). Bakhshi, M.; Barsby, C.; Mobasher, B. (2014), Comparative evaluation of early age toughness parameters in fiber reinforced concrete. Materials and Structures, Vol. 47, No. 5, pp. 853–872. Bakhshi, M.; Nasri, V. (2013). Practical aspects of segmental tunnel lining design. Proceedings of the World Tunnel Congress (WTC) 2013, Anagnostou, G.; Ehrbar, H. (Eds), Geneva, Switzerland. Bakhshi, M.; Nasri, V. (2014a). Review of international practice on critical aspects of segmental tunnel lining design. Proceedings of the 2014 North American Tunneling (NAT) Conference, Los Angeles, CA. Bakhshi, M.; Nasri, V. (2014b). Guidelines and methods on segmental tunnel lining analysis and design–Review and best practice recommendation. Proceedings of the World Tunnel Congress (WTC) 2014. Iguassu Falls, Brazil. CS-TR 63 (2007), Guidance for the design of steel-fibre-reinforced concrete. Concrete Society (CS), Camberley, UK. CNR-DT 204/2006 (2007), Guidelines for the design, construction and production control of fibre reinforced concrete structures. Italian National Research Council (CNR), Rome, Italy. DAUB (2013), Recommendations for the Design, Production, and Installation of Segmental Rings. German Tunnelling Committee (DAUB), Köln, Germany. DBV Recommendation (2001), Guide to good practice: Steel fibre concrete. German Society for Concrete and Construction Technology (DBV), Berlin, Germany. EHE-08 (2008), Spanish code on structural concrete—Annex 14: Recommendations for using concrete with fibres. Ministry of Public Works and Transport, Madrid, Spain. fib Bulletin 55 (2010), Model code 2010—first complete draft. fédération internationale du béton (fib), Lausanne, Switzerland.

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FRC 2014 Joint ACI-fib International Workshop Fibre Reinforced Concrete: from Design to Structural Applications

Groeneweg, T. (2007), Shield driven tunnels in ultra-high strength concrete: reduction of the tunnel lining thickness. M.Sc. thesis, Delft University of Technology, The Netherlands. ITA Working Group No. 2 (2000), Guidelines for the design of shield tunnel lining. Tunnelling and Underground Space Technology, Vol. 15, No. 3, pp. 303–331. Iyengar, K.T. (1962), Two-dimensional theories of anchorage zone stresses in post-tensioned beams. Journal of the American Concrete Institute, Vol. 59, No. 10, pp. 1443–1466. Mobasher, B.; Bakhshi, M.; Barsby, C. (2014), Backcalculation of residual tensile strength of regular and high performance fiber reinforced. Accepted for Publication. Construction and Building Materials. RILEM TC 162-TDF (2003), – design method—ﬁnal recommendation. Materials and Structures, Vol. 36, No. 262, pp. 560–567. Soranakom, C.; Mobasher, B. (2007), Closed form solutions for flexural response of fiber reinforced concrete beams. ASCE Journal of Engineering Mechanics, Vol. 133, No. 8, pp. 933–941. Vandewall, L. (2000), Cracking behaviour of concrete beams reinforced with a combination of ordinary reinforcement and steel fibers. Materials and Structures, Vol. 33, No. 3, pp. 164-170. Wang, S.; Li, V.C. (2006), High-early-strength engineered cementitious composites, ACI Materials Journal, Vol. 103, No. 2, pp. 97-105.

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Developments in design for fiber reinforced concrete tunnel segments Mehdi Bakhshi, Verya Nasri

AECOM, New York, USA.

Abstract Precast fiber reinforced concrete (FRC) segments are increasingly being adopted in TBM tunnels to take advantage of their potential for production cost saving, improved handling robustness and long-term durability benefits. This paper presents a procedure for structural design of FRC segments. The procedure includes design of FRC lining for production and transitional load cases of demolding, storage, transportation and handling. In addition, construction load cases of TBM thrust jack forces and grouting pressure are discussed. Ground and groundwater loads and force transfer in joints in the final service stage are presented as critical load cases. The proposed design approach is applied to a case of mid-size tunnel. Results show that when the design forces are not relatively large in comparison with the segment cross-section dimension, the use of ﬁbers can lead to elimination or a signiﬁcant reduction of the steel bars, which in turn results in significant construction cost saving.

Keywords Design, fiber, lining, segment, tunnel.

441

FRC 2014 Joint ACI-fib International Workshop Fibre Reinforced Concrete: from Design to Structural Applications

1

Introduction

Precast concrete segments are the predominant support method in Tunnel Boring Machine (TBM) bored tunnels in soft ground and weak fractured rock, providing the initial and final ground support. Conventionally, steel bars are used in concrete segments to resist tensile stresses developed due to all loading cases from the time of casting through service condition. However, there are some issues associated with the use of steel bars including large crack widths, high labor costs and long time for placement of curved bars in manufacturing plant. As an alternative, Fiber Reinforced Concrete (FRC) considerably improves the concrete postcracking behavior, allows for a better crack control and offers plastic shrinkage resistance to the concrete mix and improves the concrete durability. Considering all these benefits, FRC represents a competitive material for tunnel segments. The fiber presence close to segment surface is very advantageous with high tensile stresses developed in this zone induced by TBM thrust jack forces during installation. FRC has been used since 1982 in numerous projects around the world, e.g. water/waste water, gas pipeline, power cable, subway, railway, and road tunnels, as the preferred material for the construction of tunnel precast segmental lining. In most of the projects, small to mid-size tunnels have been reinforced with only steel fibers at a dosage ranging between 25 to 60 kg/m3. Internal diameters of these tunnels range between 2.2-11.4 m and their thicknesses are between 0.15 and 0.4 m. The design has been performed using constitutive laws recommended by international codes and standards such as DBV (2001), RILEM TC 162-TDF (2003), CNR DT 204/2006 (2007), EHE (2008) and fib Model Code (2010). This paper presents a procedure for design of FRC tunnel segments for all load cases happening from the time after casting to the final service condition based on residual tensile strength proposed by ACI 544.FR report (2014) and specified compressive strength. The proposed design approach is applied to a case of mid-size tunnel and key material parameters for design are summarized. Effects of residual strength and different standard constitutive laws on axial force-bending moment interaction diagrams as the key design tools are discussed.

2

Design of FRC tunnel segments by LRFD method

LRFD is a design philosophy that takes into account the variability in the prediction of loads and the behavior of structural elements at ultimate and serviceability limit states. The focus of this paper is on Ultimate Limit State (ULS). Flexural or tensile resistance is calculated based on the residual strength of a standard beam at mid–span deflection of L/150, defined as end-point deflection per ASTM C1609 (2012), where L is distance between the supports (see Figure 1). Due to the overestimation of the fD150 parameter based on elastic approaches, a back-calculation procedure is to be adopted to obtain residual tensile strength, p (Soranakom and Mobasher, 2007). Another approach is to scale standard residual flexural strengths by a factor of 0.33-0.37 (fib, 2010; Bakhshi et al. 2014; Mobasher et al. 2014; Vandewall, 2000). FRC segments are designed for all load cases happening from the time of the casting up to the time when they withstand final service loads. These loads are presented in the following sections. FRC segments are proportioned for adequate strength, using load

442

FRC 2014 Joint ACI-fib International Workshop Fibre Reinforced Concrete: from Design to Structural Applications

factors and strength reduction factors. A strength reduction factor of 0.70 is applied for flexure, compression, shear, and bearing actions of FRC segments to safeguard against uncertainty of material properties.

Figure 1:

3

Definition of residual flexural parameters for FRC beams by ASTM C1609 (2012)

Design for production and transitional stages

The production and transitional loading includes all the loading stages starting from the time of the segment casting up to the time of the segment erection inside TBM shield.

3.1

Segment demolding

This load case represents the effect of lifting systems on stripping precast concrete segments from the molds in the segment manufacturing plant. Figure 2a shows the demolding phase which is modeled by two cantilever beams loaded under its own dead weight. The design is performed with regard to the specified strength when segments are demolded (3-4 hours after casting). Mix proportion for FRC segments (similar to steel fiber reinforced shotcrete) is designed by adjusting accelerator dosage to achieve high early strength, therefore standards beam tests can be conducted at such early hours to obtain residual flexural parameters for design (Bakhshi et al. 2014; Wang and Li, 2006). As shown in Figure 2b, the dead weight is the only force acting on the segment, and therefore, the applied load factor in ULS is 1.4 per ACI 318 (2011). Maximum developed bending moment is compared with provided resistance moment of segment for design check.

3.2

Segment storage

Demolding is followed by stacking the precast segments in the stack yard to gain 28-day strength specified by designer before transportation to the construction site. As shown in Figure 3a, all segments comprising a full ring are piled up within one stack. Designers provide the distance between the stack supports considering an eccentricity of e = 0.1m between the locations of the stacks support for the bottom segment and the supports of above segments. A simply supported beam loaded as in Figures 3b and 3c represent this load case. Applied load factor in ULS is 1.4 per ACI 318 (2011). Maximum developed bending moment is used for design.

443

FRC 2014 Joint ACI-fib International Workshop Fibre Reinforced Concrete: from Design to Structural Applications

(b)

(a)

Figure 2:

a) Demolding in the segment manufacturing plant, b) Forces acting on segments

(a)

(b)

Figure 3:

3.3

(c)

Segments stacking for storage and schematics of forces acting on bottom segment

Segment transportation

Trucks and rail cars transport the precast segments stored in the stack yard to the construction site and TBM trailing gear. Segments may encounter dynamic shock loads during this phase and usually half of the segments of each ring are transported in one car. Wood blockings provide supports for the segments. An eccentricity of 0.1 m is recommended for possible eccentricity. Simply supported beams represent this load case with a dead load factor of 1.4 in ULS per ACI 318 (2011) and a dynamic shock factor of 2.0 applied to the forces.

3.4

Segment handling

Segment handling from stack yard to trucks or rail cars are carried out by specially designed lifting devices or vacuum lifters. Inside the TBM, segment handling is usually carried out using vacuum lifters while other methods may be used occasionally. This load case is simulated similar to segment demolding shown in Figure 2. A dead load factor of 1.4 in ULS per ACI 318 (2011) and a dynamic shock factor of 2.0 are recommended for design.

444

FRC 2014 Joint ACI-fib International Workshop Fibre Reinforced Concrete: from Design to Structural Applications

4

Design for construction stages

The construction loading stages include loading cases starting from the time of segment erection inside the TBM shield up to the time when installation of a ring is completed.

4.1

TBM thrust jack forces

After assembly of a ring, TBM moves forward, as shown in Figure 4, by pushing its jacks on bearing pads placed on the circumferential joints of the newest assembled ring. This action results in development of high compression stresses under the pads, as well as bursting tensile stresses deep in the segment and spalling tensile forces between the pads. Maximum thrust force for each jack pair is obtained by dividing maximum total thrust of TBM over the number of jack pairs. In another approach, jack thrust forces are estimated from the sum of forces required for boring into the rock or acting pressure on cutting face due to earth or slurry pressure, plus friction resistance between the shield surface and the ground, and hauling resistance of trailing gears. In latter approach, average thrust force on each jack pair should be factored by 1.6 times for design at ULS per ACI 318 (2011) recommendation for live loads, while there is no need to apply a load factor on the maximum jack thrust force obtained from former method. Different design methods include ACI 318 (2011) section 18.13 and DAUB (2013) simplified equations, Iyengar diagram (1962) and FE simulations. Residual tensile strength of FRC segment at 28 day is checked against maximum developed bursting tensile stress. hanc

al

(a)

(b)

Figure 4:

4.2

aat

t

a) Thrust jacks pushing on circumferential joints in French configuration, b) Stress distribution schematics under jack shoes (Groeneweg, 2007)

Tail and localized back grouting pressure

This load case presents back grouting or filling the annular space with semi-liquid grouts which is required in order to control and restrict settlement at the surface and to securely lock the lining ring in position. Grout pressure has to be limited to a minimum value which is slightly higher than the water pressure, and a maximum value which is less than the overburden pressure. For the case of tail grouting, vertical gradient of grout pressure is calculated by taking the equilibrium between the upward component of total grout pressure, lining deadweight and tangential component of grout shear strength (Groeneweg, 2007). This load case is modeled by applying radial pressures increasing linearly from the crown to the 445

FRC 2014 Joint ACI-fib International Workshop Fibre Reinforced Concrete: from Design to Structural Applications

invert of tunnel. Deadweight of the lining and grouting pressure are the only loads applied to the tunnel lining and a load factor of 1.25 is applied to both loads in ULS design. In the case of localized backfilling, radial injection through holes provided in the segments is performed where annular gaps exist between the lining extrados and excavation profile after tail grouting. International Tunnel Association guideline (ITA, 2000) is used for simulation of localized backfilling pressure. The lining is modeled as a 2D solid ring with a reduced flexural rigidity due to segment joints. The interaction between lining and surrounding ground or primary hardened grout is modeled by radial springs. Using a structural analysis package, bending moments and axial forces due to the grouting load cases are determined and checked against FRC segment capacity.

5

Design for final service stages

The loading in the final service stage is represented by the long-term interaction of the lining with the ground and groundwater pressure which is discussed further in the next section, as well as other factors specific to an individual tunnel, e.g. additional distortion, earthquake, fire, explosion, and breakouts. Longitudinal joint bursting load due to force transfer in a reduced cross section because of gasket and stress relief grooves (Bakhshi and Nasri, 2013) is another critical load case in the final service stage. Due to similarity to the effect of thrust jack forces, it is not discussed further as similar analysis and design methods are applicable to this load case. The load case of ground, groundwater and surcharge loads is discussed in the following. Precast concrete segments as final lining system withstand different loadings in the service stage including ground (vertical and horizontal) loads, groundwater pressure, dead weight, surcharge and ground reaction loads. Methods of analysis for segmental tunnel linings in conformance with standards and guidelines from various countries in Europe, Asia and America have been presented elsewhere (Bakhshi and Nasri, 2014a; Bakhshi and Nasri, 2014b). These methods include elastic equations, beam-spring model, FE analysis (Figure 5) and Discrete Element method (DEM). Resulting forces on segments are used to design segments and specify compressive and tensile strengths of FRC.

Figure 5:

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FEM simulation for tunnel excavation in soft ground

FRC 2014 Joint ACI-fib International Workshop Fibre Reinforced Concrete: from Design to Structural Applications

6

Design example

An example for design of a mid-size TBM tunnel lining with precast FRC segments is presented. It is assumed that internal diameter of the segmental ring is Di = 5.74 m, and the ring composed of 5 large segments and one key segment (one-third of the size of large segments). Width, thickness and curved length at centerline of the large segments are 1.5, 0.3 and 3.4 m, respectively. A stress-strain diagram according to ACI 544.FR report (2014) is adopted. Key design parameters for aforementioned load cases are the specified residual tensile or flexural strength (p or f’D150) and specified compressive strength (f’c). Following the approach of scaling the residual flexural strength obtained by ASTM C1609 (2012) tests, a factor of 0.34 is considered to convert f’D150 to p. Designed early-age and 28-day f’D150 strengths are 2.5 and 4 MPa, respectively. Specified compressive strengths are 15 MPa for early-age and 45 MPa for 28-day FRC segment. As shown in Figure 6, capacity of FRC segments are calculated based on equilibrium conditions assuming a post-crack plastic behavior in the tension zone. First crack flexural strength (f1) is assumed as 4 MPa. Design checks for the production and transitional loads are shown in Table 1. The tunnel is excavated in soft ground. Two-dimensional FEM packages are used for calculation of tunnel lining forces in three different geological reaches defined along the alignment of this tunnel case. Design checks for the load case of the ground and groundwater pressure is shown in Figure 7. In this project, a TBM machine is used with the maximum total thrust of 45,000 kN applied on 16 jack pairs. Maximum thrust forces on each pair is therefore 2.8 MN. The length and width of the contact area between the jack pads and segments, considering a maximum eccentricity of e = 0.025 m, are al = 0.87 m and hanc = 0.2 m, respectively. Dimensions of fully spread stresses are at = 3.4/3 = 1.13 m and h = 0.3 m in tangential and radial directions, respectively. Conforming to simplified equations of ACI 318 (2011), bursting force (Tburst) and its centroidal distance from the face of section (dburst) in radial and tangential directions are: Tangential direction : d burst 0.5 (at 2e) 0.5 (1.13 2 0.025) 0.54 m

Radial direction :

al 0.87 0.25 2.8 (1 Tburst 0.25 Ppu 1 ) 0.105MN 1.08 at 2e d burst 0.5 (h 2eanc ) 0.5 (0.3 2 0.025) 0.125 m hanc 0.2 0.25 2.8 (1 Tburst 0.25 Ppu 1 ) 0.117 MN 0.25 h 2eanc

Using this method of analysis, the maximum bursting stress developed in radial and transverse directions are determined as

Tangential direction : p Radial direction :

p

Tburst 0.105 0.28 MPa d burst 0.7 0.54 Tburst 0.117 1.33 MPa d burst 0.7 0.125

These stresses are less than 28-day specified residual tensile strength of FRC segment as p= 0.34 f’D150 = 1.36 MPa, and the design is valid for load case of TBM thrust jack forces.

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FRC 2014 Joint ACI-fib International Workshop Fibre Reinforced Concrete: from Design to Structural Applications

Figure 6:

Strain and stress distributions through the section as part of it undergoes tension

Table 1:

Segment design checks for production and transitional stages

Phase

Specified Residual Strength (MPa)

Maximum Developed Bending Moment (kNm/m)

Resistance Bending Moment (kNm/m)

Demolding

2.5 (early-age)

5.04

26.25

Storage

4.0 (28 d)

18.01

26.25

Transportation 4.0 (28d)

20.80

42.00

Handling

10.08

42.00

Figure 7:

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4.0 (28 d)

Design checks for the load case of ground and groundwater pressure

FRC 2014 Joint ACI-fib International Workshop Fibre Reinforced Concrete: from Design to Structural Applications

7 Parametric studies on residual strength and choice of constitutive law Increasing the fiber content in the mix directly results in increase of the residual flexural strengths (f’D150) of FRC. A parametric study on effects of increasing f’D150 from 1 to 5 MPa on the axial force-bending moment interaction diagrams are shown in Figure 8a. Other parameters and segment geometry for this study are similar to the ones presented in previous example. Comparing such diagrams with the results of analyses for aforementioned loading cases (e.g. results shown in Figure 7) results in determining the required residual parameter and the required fiber content based on fiber manufacturer product datasheets. Effect of choice of standard constitutive laws on a similar tunnel segment with a residual strength of 4 MPa is shown in Figure 8b. Results show that choice of constitutive laws shown in Table 2 does not have a significant effect on the axial force-bending moment interaction diagram of FRC segments and subsequently does not affect the design outcome.

(b) (a)

Figure 8:

Effects of residual strength and choice of constitutive law on the axial forcebending moment interaction diagrams as key design tools

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FRC 2014 Joint ACI-fib International Workshop Fibre Reinforced Concrete: from Design to Structural Applications

Table 2:

Choice of constitutive laws for FRC precast tunnel segments

ACI 544.FR Report

cr = f1 (ASTM C1609) p = 0.34 fD150 (ASTM C1609)

-RILEM TC 162-TDF Recommendation -New Zealand NZS 3101.2 standard

ffctm, fR1, fR4 obtained from EN 14651

DBV (German society of concrete) Recommendation

fbr = fL (EN 14651) br = 0.45 feqm,Ι (fR1 from EN 14651) br = 0.37 feqm,ΙΙ(fR4 from EN 14651)

-fib Model Code 2010 -Italian Guide CNR-DT 204/2006 -Spanish Concrete Code EHE08 -ÖVBB (Austrian society for construction technology) Guide

fFts = 0.45 fR1 (fR1 from EN 14651) fFtu = 0.5 fR3 – 0.2 fR1 (from EN 14651)

-fib Model Code 2010 -Italian Guide CNR-DT 204/2006 -Spanish Concrete Code EHE08

fFtu = 0.33 fR3 (fR3 from EN 14651)

CS (Concrete Society)TR63 Report

f ftd ftd

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ftd = 0.37 fR3 (fR3 from EN 14651)

FRC 2014 Joint ACI-fib International Workshop Fibre Reinforced Concrete: from Design to Structural Applications

8

Conclusions

Presented procedure for structural design of FRC tunnel segments includes design for production and transitional, construction and final service stages. Application of the design approach to a case of mid-size tunnel indicates that when the design forces are not relatively large in comparison with the segment cross-section dimension, the use of ﬁbers can lead to elimination of steel bars, which in turn results in significant construction cost saving in tunneling industry. Results of analyses indicate that FRC constitutive laws from different guidelines give similar axial force-bending moment interaction diagrams as the key design tools for designing precast tunnel segments.

9

References

ACI 544 Report (under development), Indirect method to obtain a stress-strain diagram for strain softening fiber-reinforced concretes. American Concrete Institute (ACI), Farmington Hills, MI. ACI 318 (2011), Building Code Requirements for Structural Concrete and Commentary. American Concrete Institute (ACI), Farmington Hills, MI. ASTM C1609-12, Standard test method for ﬂexural performance of ﬁber-reinforced concrete (using beam with third-point loading). Bakhshi, M.; Barsby, C.; Mobasher, B. (2014), Comparative evaluation of early age toughness parameters in fiber reinforced concrete. Materials and Structures, Vol. 47, No. 5, pp. 853–872. Bakhshi, M.; Nasri, V. (2013). Practical aspects of segmental tunnel lining design. Proceedings of the World Tunnel Congress (WTC) 2013, Anagnostou, G.; Ehrbar, H. (Eds), Geneva, Switzerland. Bakhshi, M.; Nasri, V. (2014a). Review of international practice on critical aspects of segmental tunnel lining design. Proceedings of the 2014 North American Tunneling (NAT) Conference, Los Angeles, CA. Bakhshi, M.; Nasri, V. (2014b). Guidelines and methods on segmental tunnel lining analysis and design–Review and best practice recommendation. Proceedings of the World Tunnel Congress (WTC) 2014. Iguassu Falls, Brazil. CS-TR 63 (2007), Guidance for the design of steel-fibre-reinforced concrete. Concrete Society (CS), Camberley, UK. CNR-DT 204/2006 (2007), Guidelines for the design, construction and production control of fibre reinforced concrete structures. Italian National Research Council (CNR), Rome, Italy. DAUB (2013), Recommendations for the Design, Production, and Installation of Segmental Rings. German Tunnelling Committee (DAUB), Köln, Germany. DBV Recommendation (2001), Guide to good practice: Steel fibre concrete. German Society for Concrete and Construction Technology (DBV), Berlin, Germany. EHE-08 (2008), Spanish code on structural concrete—Annex 14: Recommendations for using concrete with fibres. Ministry of Public Works and Transport, Madrid, Spain. fib Bulletin 55 (2010), Model code 2010—first complete draft. fédération internationale du béton (fib), Lausanne, Switzerland.

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Groeneweg, T. (2007), Shield driven tunnels in ultra-high strength concrete: reduction of the tunnel lining thickness. M.Sc. thesis, Delft University of Technology, The Netherlands. ITA Working Group No. 2 (2000), Guidelines for the design of shield tunnel lining. Tunnelling and Underground Space Technology, Vol. 15, No. 3, pp. 303–331. Iyengar, K.T. (1962), Two-dimensional theories of anchorage zone stresses in post-tensioned beams. Journal of the American Concrete Institute, Vol. 59, No. 10, pp. 1443–1466. Mobasher, B.; Bakhshi, M.; Barsby, C. (2014), Backcalculation of residual tensile strength of regular and high performance fiber reinforced. Accepted for Publication. Construction and Building Materials. RILEM TC 162-TDF (2003), – design method—ﬁnal recommendation. Materials and Structures, Vol. 36, No. 262, pp. 560–567. Soranakom, C.; Mobasher, B. (2007), Closed form solutions for flexural response of fiber reinforced concrete beams. ASCE Journal of Engineering Mechanics, Vol. 133, No. 8, pp. 933–941. Vandewall, L. (2000), Cracking behaviour of concrete beams reinforced with a combination of ordinary reinforcement and steel fibers. Materials and Structures, Vol. 33, No. 3, pp. 164-170. Wang, S.; Li, V.C. (2006), High-early-strength engineered cementitious composites, ACI Materials Journal, Vol. 103, No. 2, pp. 97-105.

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