Design of FRC tunnel segments considering the ductility requirements of the Model Code 2010

TL;DR: In this article, the authors present a critical analysis of the design of FRC segments according to the ductility requirements from the Model Code 2010; an alternative approach is proposed that is compatible with the condition found in some tunnels.

About: This article is published in Tunnelling and Underground Space Technology.The article was published on 2015-03-01 and is currently open access. It has received 65 citations till now.

Summary

1 INTRODUCTION

• Fibre reinforced concrete (FRC) is a composite material used to improve the mechanical response of precast segments for tunnels [1-4], enhancing their ductility and fire resistance as well as their mechanical performance during transient load stages.
• Table 1 [4-6] summarizes some of the main applications already in service or under construction.
• The objective of this paper is to present a critical analysis of the design of FRC segments according to the ductility requirements from the MC 2010 and to propose an alternative approach more compatible with the conditions found in practice.

2 DESIGN PROCEDURE BASED ON THE MC 2010

• In tunnels with large internal diameter, segments are usually subjected to high bending moments during the transient and the service stages - the latter being generally the most unfavourable design condition.
• The SLS and ULS limit conditions considered in the structural verification in each one of these transient situations vary depending on the load pattern applied.
• If fibres are applied as the only reinforcement, the MC 2010 imposes three mechanical criteria based on the load – displacement curve shown in Figure 2a that any FRC structure should fulfil.
• This way, if cracking occurs for the reasons mentioned previously, the segment would still present enough ductility to safely carry the loads applied.

3 METRO L9 OF BARCELONA

• The Metro L9 of Barcelona counts 46 stations and 15 interchanges with a total length of 44 km and connects the airport (El Prat), the justice district (Ciutat de la Justicia) and the high speed railway station (Barcelona Sants Station).
• So far, this is probably one of the most studied TBM-bored tunnels and this is still under construction.
• Experimental and numerical analysis related with the FRC were extensively performed [34-37].
• The Bon Pastor – Can Zam stretch is analysed in the present study.
• The segments were initially designed with a C50/60 concrete reinforced with traditional rebars and 30 kg/m3 of steel fibres.

3.1 Numerical simulations

• The total substitution of the rebars by steel fibres was analysed.
• The results of this analysis were reported in [34].
• This load situation was analysed in detail since this is critical in terms of design and productivity.
• Besides, this is a transient load phase, and once the tunnel is in service, the cracks tend to close due to the compression introduced by the soil.
• The tensile stresses obtained with the model were below 0.785 N/mm2 for the worst – case scenario, meaning that the cross – section of the segments conserve its integrity during the service life unless cracks appear during the stocking or other transient load situations.

3.2.1 Materials

• Once identified with numerical analysis that the critical load occurs in the transient stage during stocking, an experimental program was conducted with real-scale segments in order to verify the substitution of the steel rebars by fibres.
• Mixes were produced with different steel fibre contents (Cf) of 20, 30, 40, 50 and 60 kg/m³ in order to assess the mechanical performance of the FRC with different amounts of fibres [34].
• From each composition, four prismatic specimens with 150x150x600 mm3 were cast and cured under conditions that emulate those experienced of the segments.
• Finally, they were kept under the conditions of the production hall and tested at 28 days according with the standard UNE-EN 14651 [42] to characterize the limit of proportionality fLOP and the residual flexural strengths fR1 and fR3.
• A linear regression of the data included in Figure 7 leads to Equations (6) and (7) for the assessment of the fR1m and fR3m depending on Cf (in kg/m3).

3.2.2 Real scale tests related with the stocking procedure

• The numerical approach proposed to estimate fR3 was compared with the results derived from the experimental program on full-scale tests reproducing the stacking process.
• Even though FRC with a wide range of fibre contents were tested to evaluate the repercussion of the ductility criteria proposed by the MC 2010 in terms of design, segments reinforced with traditional rebars and 30 kg/m3 of fibre and segments reinforced with 60 kg/m³ of fibres were produced for real-scale tests.
• This generates bending moments and, ultimately, damages if Mcr is exceeded.
• Then, the second segment was positioned over the supports that had an eccentricity equal to ee with the axis of the fixed support at the base of the pile.
• The segment with 60 kg/m3 of fibres and an eccentricity e of 0.50 m also cracked when the 6th segment was placed.

4 ANALYSIS OF SECTIONAL RESPONSE

• The structural analysis based on the design approaches presented in Section 2 is used to assess the minimum flexural residual strength that guarantees ductility.
• On the contrary, for eccentricities close to 0.50 m, cracking occurs (SFcr < 1.0) when the number of segments piled is higher than 5.
• The fR3m,min required to meet the ductility condition established in the MC 2010 may be calculated through Equation (4).
• Again, it is observed that the sectional response estimated with the numerical model agrees with the experimental results.
• As this load is also the basis for the assessment of the ductility requirement from the MC 2010, indirectly the minimum residual strength obtained complies with the ULS.

5 REPERCUSSION OF DUCTILITY CRITERIA

• To evaluate the repercussion of the two approaches discussed in this study, the minimum average fR3m estimated following each of them was translated into a required fibre content (Cf).
• The latter was then used in Equation 7 to assess Cf. Figure 12 shows the curves that relate Cf and e for the critical situation of a pile composed by 7 segments plus the key.
• This value is difficult to justify from the technical, practical and economic point of view taking into account the specific circumstances of Line 9 of Barcelona.
• The direct application of the requirement from the MC 2010 would render the use of fibres as the only reinforcement almost unviable for the example considered.

6 CONCLUSIONS

• The analysis performed in this study sheds light on a fundamental aspect related to the design of FRC tunnel segments that might have a direct practical repercussion.
• The following conclusions may be derived from the present work.
• In tunnels with segmental linings subjected mainly to compression in service and designed not to crack in the transient stages, the direct application of the ductility requirements from the MC 2010 may lead to a fR3 higher than the required value for the ULS.
• The ductility obtained on this way will be more compatible with the load observed in the transient stages.
• On the contrary, in the alternative approach proposed in this study, a minimum average fR3 equal to 3.2 N/mm² is obtained.

Figures

Figure 8. Test simulating the effects of the eccentricity in a pile of (a) 3 segments and (b) 7 segments plus a key

Figure 7. Average residual flexural tensile strength depending on fibre content

Figure 10. Bending moment diagrams for self-weight (a) and segments stocked (b)

Figure 9. Detail of a) average crack width measured and b) expected brittle failure of segment reinforced only with 60 kg/m3 of fibres and subjected to eccentricities of 0.50 m

Figure 1. Temporary load stages of a segment: (a) demoulding; (b) stocking; (c) transport and (d) jack’s thrust

Figure 2. P-δ curve for a FRC structure (a) and M-χ diagram for different sectional responses (b)

Figure 12. Curves Cf - e depending on the approach selected

Figure 11. Variation of SFcr (a) and fR3m,min (b) depending on eccentricity

Figure 4. Age – dependency of the required fR3m,min for concrete classes (a) C30, (b) C50, (c) C70 and dependency of h on fR3m,min at 7 days (d)

Figure 3. FRC cross – section of a precast segment subjected to axial stresses

Table 1. Applications of precast FRC segments in tunnels (u.c.: under construction)

Table 2. Composition of concrete

Figure 5. Ring dimensions of the Can Zam – Bon Pastor Stretch of Barcelona’s Metro L9

Figure 6. Dimensions of the jacks and eccentricity considered for the numerical analysis

Frequently asked questions

Q1. What have the authors contributed in "Design of frc tunnel segments considering the ductility requirements of the model code 2010" ?

The objective of this paper is to present a critical analysis of the design of FRC segments according to the ductility requirements from the MC 2010 ; an alternative approach is proposed that is compatible with the condition found in some tunnels. The study suggests that the alternative approach may be applied under certain conditions, leading to a reduction in the fibre consumption. 

Q2. How many jacks are used to advance the ring?

The advance of the TBM during construction is accomplished by means of 15 jacks that have a contact area of 1.374 x 0.350 m2 and introduce a total force of 90 MN in the segmented lining. 

Q3. What is the first requirement about the ultimate load?

The first requirement about the ultimate load is a condition established in most reinforced concrete codes that intend to avoid the brittle failure in case of cracking (Pu ≥ Pcr). 

Q4. What is the ductility requirement for the tunnel?

In tunnels with segmental linings subjected mainly to compression in service and designed not to crack in the transient stages, the direct application of the ductility requirements from the MC 2010 may lead to a fR3 higher than the required value for the ULS. 

Q5. What are the attractive solutions for a tunnel?

In these cases, mixed reinforcement configurations consisting of a minimum amount of steel bars (that provide resistant capacity in ULS) and a moderate dosage of fibres (that control the crack width in SLS) are attractive solutions. 

Q6. What is the reason for the ductility limitation in tunnels?

if cracking due to imperfections or other damages occur, they may be detected and corrected before construction of the tunnels with small or even no repercussion to the performance of the structure and to the safety of workers. 

Q7. What is the minimum amount of reinforcement required?

To determine the minimum amount of fibre reinforcement required, the condition Mu ≥ Mcr must be solved by using nonlinear sectional analysis (Fig. 3) and by imposing the constitutive equations suggested in the MC 2010. 

Q8. What is the probable scenario for cracking?

If cracking occurs, the most probable scenario is that it will be the result of thermo-hygrometric induced stresses or a dynamic load very limited in time. 

Q9. What are the main problems of tunnels with smaller internal diameters?

On the other hand, tunnels with smaller internal diameter tend to be predominantly compressed during service, these being less sensible to either asymmetric loads derived from the soil or other discontinuities. 

Q10. What is the main reinforcement used in the tunnel?

As a result, the main reinforcement usually consists of a minimum amount ofrebars established in codes to avoid brittle failure of the segments that might occur during the transient load situations. 

Q11. What is the probability of cracking for a load of 7 segments?

They show that for an eccentricity of 0.25 m, the probability of cracking is low since SFcr reaches values close to 1.5 for the maximum load (7 segments + key).