TECHNICAL MEMORANDUM South Hartford Conveyance and Storage Tunnel (South Tunnel) Precast FRC Tunnel Segment Design Provision for Ductility

Transcription

1 Technical Memorandum January 24, 2017 Page 1 of 6 TECHNICAL MEMORANDUM South Hartford Conveyance and Storage Tunnel (South Tunnel) Precast FRC Tunnel Segment Design Provision for Ductility 1 PURPOSE This technical memorandum (TM) documents supplementary information and ductility provisions regarding the design of precast FRC tunnel segments for the South Tunnel. This document provides the Metropolitan District (MDC) with design provisions with regard to ductility requirements when precast segments (as structural elements) are not sufficiently reinforced with conventional steel reinforcement and in this case solely reinforced with steel fiber. Technical requirements provided in this memorandum and appendices show that only a fiber product that can satisfy these requirements can be used as sole reinforcement of precast segments. Dramix 4D (80/60BG) provided by Bekaert Maccaferri Underground Solution is the only product in the market that both meet these requirements -by providing an ultimate bending moment higher than the cracking bending moment- and have a proven history of successful applications in tunnels of similar size. Therefore, Engineer designed the fiber reinforcement for precast segments with minimum steel fiber content of 67 pounds per cubic yard in the shape of double hooked ends, with a minimum length of 2-inches, a maximum diameter of inch and aspect ratio (length/diameter) ranging from 65 to 85. Also loose steel fibers were excluded from this design since they can cause balling or clumping during mixing and only fibers glued in clips are acceptable. All these characteristics were mentioned in Contract Documents in Specification Section and on the Contract Drawings Sheet 201 S-532 (Figure 1). Figure 1 Details of fiber reinforcement as in contract documents (excerpt from Plans - Sheet 201 S-532)

2 Technical Memorandum January 24, 2017 Page 2 of 6 Obviously, the alternative to this design is use of conventional steel cages with a detailed design in Contract Drawings (Sheets 201 S-521 through 201 S-531) or use of a hybrid reinforcement system of conventional rebars with any other steel fiber that cannot satisfy the ductility requirements after approval by Engineer. Use of other types of fibers even in a hybrid reinforcement system is contingent to proven history of successful applications in tunnels of similar sizes. 2 BACKGROUND One of the key components of the South Tunnel construction is main conveyance and storage tunnel to be built with tunnel boring machine (TBM). A precast concrete segmental lining system was designed to resist the permanent loads from the ground and groundwater, as well as the temporary loads from production, transportation, and construction. The precast segments were designed to be reinforced to resist the tensile stresses at both the serviceability limit state (SLS) and the ultimate limit states (ULS). Since these components are structural elements, a minimum reinforcement is required to ensure ductility and crack control requirements. Provided reinforcement cannot be lower than a minimum value, so that the ultimate limit state (ULS) can be reached under a yielding moment higher than the cracking moment. Also in the serviceability limit state (SLS), a minimum amount of reinforcement should be provided in tensile zones, in order to reduce the crack width. Minimum reinforcement in conventionally Reinforced Concrete (RC) structural elements are well defined and can be found in Structural Codes such as ACI or fib Model Code For concrete reinforced with steel fibers ONLY, fibers should guarantee ductility requirements by providing an ultimate bending moment higher than the cracking bending moment and also satisfy the cracking serviceability requirements. Otherwise, a hybrid reinforcement solution should be adopted with a combination of conventional reinforcing bar and fiber reinforcement to satisfy these requirements. Precast FRC tunnel segments for the South Tunnel were designed as fiber-reinforced ONLY. Therefore, the ductility requirement must be satisfied solely by fibers, or otherwise the engineer can approve a hybrid FRC-RC solution provided fibers cannot fully satisfy these requirements or by adopting a fully conventional RC solution. 3 DUCTILITY REQUIREMENT FOR ULS Segmental tunnel linings are designed for all the load cases which occur during segment manufacturing, transportation, installation, and service conditions. These load cases include but not limited to load cases during production and transient stages (segment stripping, segment storage, segment transportation, segment handling), construction stages (TBM thrust jack forces, grouting pressure), service stages (earth pressure, groundwater, and surcharge loads, longitudinal joint bursting load). In many of these load cases, precast segments are designed to resist only the maximum bending moment developed due to pure bending action. In ULS, provided reinforcement should be sufficient so that the ultimate limit state can be reached under a yielding moment higher than the cracking moment. Regarding the ultimate state, a minimum amount of steel reinforcement should be introduced in order to avoid the sudden failure of the structural element under bending, due to the formation of a crack in the tensile concrete, and to guarantee a sufficiently ductile behavior before the failure. It is well known that the ultimate state of lightly reinforced beams (not sufficiently reinforced) is characterized by the presence of a single crack in the tensile zone. As shown in

3 Technical Memorandum January 24, 2017 Page 3 of 6 Figure 1, the relationship between the bending moment due to applied load (P) and the midspan deflection ( ) of a three-point bending beam presents a remarkable softening branch during crack growth (Fig. 1b) for plain concrete. Although the crack appears in the ascending branch of the curve, its propagation is initially stable and the bending moment continues to increase up to a peak value. From this point, crack propagation becomes unstable, and the mechanical response displays a reduction of the bending moment (M) with an increase of deflection ( ). After the peak, the crack width exhibits a monotonic increment while the external load decreases. In sufficiently reinforced elements, the unstable crack propagation is only temporary. After the softening branch, the bending moment (M) increases and becomes even higher than effective cracking moment (M cr ). In under reinforced elements when the effective cracking moment (M cr ) is reached, the crack develops in an unstable manner. In this situation there is no increase of bending moment after the softening stage, and brittle failure occurs like in a plain concrete beam. Thus, in under reinforced sections, the effective cracking moment (M cr ) is greater than the ultimate one, (M u ). The condition M cr = M u represents the threshold between brittle and ductile failure, and the corresponding reinforcement ratio is called the minimum reinforcement ratio min (Fig. 1b). Therefore, the minimum reinforcement according to ACI and fib Model Code 2010 is determined by satisfying the ULS ductility requirement presented in the form of Mu > Mcr. For further details, see Technical Paper in Appendix A. Figure 2 The definition of the minimum reinforcement: (a) three-point bending test; (b) bending moment (M) due to applied load (P) vs. mid-span deflection ( ) curves produced by different reinforcement percentages ( ) 3.1 SINGLE-HOOKED VS. DOUBLE-HOOKED FIBERS Steel fibers with hooked-ends have proven history of successful applications in tunnel projects. The reason is that the anchoring of hooks and fiber tensile strength are especially designed to transmit and inhibit cracks in concrete with a width of in ( mm) enabling the fabrication of durable and waterproof structures. The failure mechanism in steel fiber reinforced

4 Technical Memorandum January 24, 2017 Page 4 of 6 concrete is pull-out of fibers from the cementitious matrix in the cracked section. Therefore, the special anchorage of steel fibers in the shape of hooks provide with the most efficient solution for reinforcement of concrete. As shown in Figure 3a, conventional forms of hooked-end fibers are single-hooked. Figure 3b shows typical results of standard beam tests on Dramix 3D 80/60BG (or previously known as RC 80/60BN) with conventional dosage rate of 67 pounds per cubic yard (further details of testing data can be found in Appendix B). The load crack width response provided in this figure under the bending is typical for single hooked-end fibers. Although single-hooked fibers provide significant post-crack residual strength, the ductility requirement in the form of the form of M u > M cr or P u > P cr cannot be satisfied with this type of fiber in conventional dosage rates. Note that according to fib Model Code 2010, for the Ultimate Limit State (ULS) design of FRC section, residual strength or bending moment at crack width opening of CMOD = 2.5 mm should be considered. As one can see, the average residual bending load at this crack opening level in this graph is well below the cracking load. Therefore use of Dramix 3D 80/60BG or other single-hooked fibers as the sole reinforcement (without steel bars) cannot satisfy minimum reinforcement requirement needed for ductility of precast tunnel segments. (a) Pcr Pu (b) Figure 3 (a) Single hooked-end fibers and (b) typical response under standard bending test (Dramix 3D 80/60BG)

5 Technical Memorandum January 24, 2017 Page 5 of 6 In order to provide the engineers with better structural solutions, fiber reinforcement industry has gone through new innovative solutions by improving the fiber anchorage and improved pull-out behavior of steel fibers. As presented in details in Technical Paper in Appendix C, the increase in the number of hooks has a significant impact on the residual stresses during plastic deformation in pull-out tests. This in turn results in a significant improvement in load-deformation or load-crack width response under bending tests. As shown in Figure 4, concrete reinforced with double-hooked Dramix 4D 80/60BG in conventional dosage rate of 67 pounds per cubic yard exhibit a deflection-hardening response during standard bending tests. Further details of testing data are available in an official third-party report in Appendix D. Note that Appendix D also provides satisfactory results of full-scale bending and point-load (simulating TBM thrust forces) tests on full scale tunnel segments reinforced with double-hooked Dramix 4D 80/60BG. As one can see, the ductility requirement in the form of the form of Mu > Mcr or Pu > Pcr can be easily satisfied with this type of fiber in conventional dosage rates. Pu Pcr Figure 4 Results of the beam bending tests on concrete reinforced with double-hooked Dramix 4D 80/60BG 4 DUCTILITY REQUIREMENT FOR SLS Similar to ductility requirement at ULS, in the serviceability limit state (SLS), a minimum amount of reinforcement should be provided in tensile zones, in order to control the crack width. According to fib Model Code 2010 and RILEM TC 162-TDF (2003) recommendation, sections can be designed without conventional reinforcement only if the minimum rebar area required for SLS (As,min) obtained by Equation 1 is zero or negative. A A ct s, min ( kck fctm f Ftsm) (1) s where f ctm is the average concrete tensile strength, f Ftsm is the average residual strength of FRC (MPa), A ct is the area of concrete within tensile zone (mm 2 ), s is the yielding stress of the rebars (MPa), k is the coefficient taking into account non-uniformity of self-equilibrating stresses recommended as 0.8, and k c is defined by Equation 2.

6 Technical Memorandum January 24, 2017 Page 6 of 6 e 0.4h 1 1 k 0.4h c ; if e M / N 0.4 ; k e ; / e c if e M N (2) 1 h h 6e where e is the loading eccentricity due to bending moment (M) in the presence of axial force (N), and h is the section thickness (mm). Technical paper in Appendix E provides detailed design information for case of precast concrete segments reinforced with steel fibers exhibiting a deflection hardening response under bending loading (such as double-hooked Dramix 4D 80/60BG in section 3.1). As mentioned in the reference, minimum rebar area required for SLS (A s,min ) using Equation (1) is negative since FRC segments are designed to exhibit deflection-hardening behavior, confirming a valid design without conventional reinforcement. As concluded in the paper, segments should exhibit deflection-hardening behavior in bending in order to completely replace rebars. 5 CONCLUSIONS Ductility provisions regarding the design of precast FRC tunnel segments as structural elements without conventional reinforcement require a deflection hardening response under standard bending tests. In conventional dosage rates (67 pounds per cubic yard), only double-hooked Dramix 4D 80/60BG fibers with characteristics presented in Contract Documents (Specification Section and Contract Drawings Sheet 201 S-532) can satisfy the ductility requirement needed for sections without conventional reinforcement. The alternative to this design is the use of conventional steel cages with a detailed design in Contract Drawings (Sheets 201 S-521 through 201 S-531) or use of a hybrid reinforcement system of conventional rebars together with any other steel fiber that cannot satisfy the ductility requirements solely, pending the approval by Engineer. 6 REFERENCES 1. ACI Building Code Requirements for Structural Concrete and Commentary. American Concrete Institute Committee fib Model code Bulletin 55: Model Code 2010-First complete draft. Fédération internationale du béton/the International Federation for Structural Concrete. Lausanne, Switzerland. 3. RILEM TC 162-TDF Test and Design Methods for Steel Fibre Reinforced Concrete. Design Method: Final Recommendation. Materials and Structures, V. 36, No. 262, pp

7 Appendix A Technical Memorandum January 24, 2017

8 Technical Paper Fabio Di Carlo Alberto Meda Zila Rinaldi* DOI: /suco Design procedure for precast fibre-reinforced concrete segments in tunnel lining construction This paper presents a procedure for designing precast tunnel segments for mechanically excavated tunnel linings in fibrereinforced concrete, without any traditional steel reinforcement. Both ultimate and serviceability limit states are considered as well as structural checks at different construction stages of the segment, including demoulding, positioning on floor, storage, transportation, handling and the final stage concerning the loads due to the ground pressure. The structural checks are performed by means of bending moment-axial force interaction envelopes for both the considered limit states, once the constitutive relationship of the material is defined for each stage. Traditional interaction envelopes are drawn for the ultimate limit state check, whereas for the serviceability limit state check, envelopes obtained by limiting the maximum crack opening and maximum concrete compressive stress are proposed. The shear action is also accounted for by reducing the bending moment-axial force envelope. The possibility of having the assistance of a test procedure for particular loading situations is also proposed. Finally, a case study related to a precast steel fibre-reinforced concrete segment is analysed in order to clarify the procedure and show, practically, how to define the actions and evaluate the interaction envelopes. Keywords: precast tunnel segment, fibre-reinforced concrete, ultimate and serviceability checks 1 Introduction The use of fibre-reinforced concrete (FRC) is growing continuously, particularly for pavements, shotcrete and the precast industry. The possibility of totally or partially replacing the traditional reinforcement with FRC offers several advantages, not only in terms of cost reduction, but also related to an improvement in quality and structural performance. These advantages are particularly beneficial in the precast industry. * Corresponding author: rinaldi@ing.uniroma2.it Submitted for review: 20 November 2015; revision: 25 January 2016; accepted for publication: 20 February Discussion on this paper must be submitted within two months of the print publication. The discussion will then be published in print, along with the authors closure, if any, approximately nine months after the print publication. With reference to the structural aspects, the fibre reinforcement improves the performance of the material under tensile actions, increasing the toughness remarkably and enhancing the cracking control [1, 2]. Furthermore, the presence of fibres in the concrete matrix has important effects in increasing fatigue and impact resistance [3, 4]. Recently, the interest in using FRC for the production of precast segments in tunnel linings placed with tunnel boring machines (TBMs) has been growing steadily [5 11]. Different factors have to be considered to support the choice of using FRC as a substitute of the traditional reinforcement in precast tunnel segments. Indeed, not only the cost of the bare materials (i.e. the cost of the omitted reinforcement with respect to the cost of the FRC), but also the reduced labour costs or the enhanced quality of the structure have to be taken into account. As an example, the use of FRC in tunnel segments results in the possibility of omitting the cathodic protection since the fibres are dispersed in the concrete matrix and the absence of contact between them does not allow the transmission of current. Therefore, fibre reinforcement helps to maintain the structural integrity limiting the concrete cracking mainly during the curing and assembly stages, when the segment can be subjected to impact loads during handling and is usually subjected to point loads from the TBM rams. In the last few years, several guidelines and codes covering the design of fibre-reinforced concrete elements have become available [12 14]. Recently the Fib Model Code [15], traditionally a reference document for the design of concrete structures, has been published. This latest version contains a part related to the design of fibre-reinforced concrete structures. The present paper proposes a design and checking procedure for precast FRC tunnel lining segments without any traditional steel reinforcement. Both the provisional and final phases are considered, and the structural checks are performed at the ultimate (ULS) and serviceability (SLS) limit states by means of bending moment-axial force interaction envelopes. This approach was suggested for SLS checks in [16] for cast-in-place tunnels. The shear action is also taken into account. The constitutive relationships of the FRC material at each stage are defined here according to the prescription in [15], but different laws, given by other guidelines, can be adopted Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin Structural Concrete 17 (2016), No

9 F. Di Carlo/A. Meda/Z. Rinaldi Design procedure for precast fibre-reinforced concrete segments in tunnel lining construction Fig. 1. Bending tests to [17] specimen dimensions and test setup As an example, if a 5.0 c material is required, the characteristic value of f R1k should not be less than 5.0 MPa, the f R3k /f R1k ratio should be greater than or equal to 0.9 and the characteristic value of f R3k should not be lower than 4.5 MPa. FRC in compression is characterized by the same tests adopted for plain concrete. Generally, for the typical fibre content used in the precast segments, the fibre reinforcement has no relevant influence on the properties of the material under compression. Fig. 2. Result of bending test to [17] 2 Definition of material characteristics 2.1 FRC material characterization Fibre-reinforced concrete is usually characterized through fracture tests, such as uniaxial tensile tests, three- or fourpoint bending tests, panel tests, etc. According to [17], the tensile characterization of fibre-reinforced concrete can be achieved through threepoint bending tests carried out on small beams with a mm cross-section. A notch 25 mm deep is made in the specimen in order to localize the failure section. Fig. 1 shows the typical test setup. These tests involve taking a series of residual tensile strength f Rj measurements corresponding to different values of crack mouth opening displacement (CMOD) (Fig. 2). Furthermore, a tensile strength defined as the limit of proportionality f L is measured. This quantity is very close to the tensile strength of a plain concrete specimen without fibre reinforcement. The reference stresses for the design, according to [15], are the characteristic values of the limit of proportionality f Lk of the residual strengths f Rlk (measured at CMOD = 0.5 mm) and f R3k (measured at CMOD = 2.5 mm). The FRC material is classified on the basis of the characteristic value of f R1k and of the ratio f R3k /f R1k. For precast tunnel segments without any traditional reinforcement, materials with f R1k ranging from 4.0 to 6.0 MPa are commonly used, combined with an f R3k /f R1k ratio in the ranges 0.9 < f R3k /f R1k < 1.1 or 1.1 < f R3k /f R1k < 1.2 (class c or d respectively according to [15]). 2.2 Additional requirements for FRC in tunnel segments without conventional steel reinforcement According to [15], additional requirements have to be fulfilled when the fibre reinforcement is used without any traditional steel reinforcement. In order to guarantee the ductile behaviour of the material in case of cracking, the following limitations are given for FRC in tension: f Rk 1 f / f > 0.4 Lk / f > 0.5 R3k Rk 1 These conditions, and mainly the first one, can be relevant in the analysed case since concretes with a 28-day compressive strength ranging from 50 to 80 MPa are often used for production purposes (e.g. to speed-up demoulding). As a consequence, high f Lk values can be reached. The further limitations prescribed by [15] are related to the global behaviour of the element, which has to exhibit sufficient structural ductility. As shown in the following, for tunnel segments, these requirements can be fulfilled by choosing the material properties correctly. In particular, according to [15], the ultimate load P u should always be higher than the load at crack initiation P cr (Eq. (3)), in order to avoid brittle failure in case of cracking, and higher than the maximum service load P SLS (Eq. (4)): P > P u cr P > P u SLS (1) (2) (3) (4) 748 Structural Concrete 17 (2016), No. 5

10 F. Di Carlo/A. Meda/Z. Rinaldi Design procedure for precast fibre-reinforced concrete segments in tunnel lining construction In the case of precast tunnel segments according to [10], Eq. (4) rarely governs the design. Eq. (3) can be rewritten in terms of bending moments as follows: M u > M cr where M u and M cr are the ultimate and first cracking bending moments respectively. In solving Eq. (5), a limitation on the f R3 residual strength value is found, as shown in [10]. In conclusion, for tunnel segment design, the structural ductility requirements are fulfilled if the material conditions are satisfied. Furthermore, [15] section 7.7.2, introduces some other limitations in terms of displacements which are meant for statically indeterminate structures but do not apply to the analysed case [10]. 3 Precast segment loading condition The design of a segmental lining requires different verifications for provisional phases and for the loads due to the ground pressure (final stage), considering both the ultimate and serviceability limit states. The TBM thrust phase must also be checked. It is worth noting that, besides the loads, the material properties and the structural schemes can also be different in the different phases, as shown in the following. 3.1 Provisional phases The provisional phase generally includes the stages of demoulding, positioning on floor, storage, transportation and handling. Demoulding and positioning on floor The segments can be demoulded with lifting gear, which results in the structural scheme shown in Fig. 3b (two can- (5) tilevers loaded by the dead weight) adopted for the evaluation of the acting bending moment. Subsequently, the segments are positioned on the floor. The related structural scheme, a beam on two simple supports, is shown in Fig. 4b. These two phases generally take place a few hours after casting and, consequently, the check has to be done with reference to the material strength related to the age at demoulding t d. Storage, transportation and handling For storage purposes, the segments belonging to a single ring can be piled up on top of each other. Fig. 5 shows the structural scheme of the bottom segment for this phase necessary for evaluating the acting bending moments. An eccentricity of the load transmitted by the upper segments to the bottom one, in both the inward and outward directions, can also be introduced to take into account possible positioning errors. Stacks of segments are transported by truck or train. The structural scheme is shown in Fig. 6, considering a stack of three segments. In this phase, a dynamic shock value is applied to the actions, generally in the range (e.g. 2.0 in [18]); again, it is suggested to account for the eccentricity of the load. It is worth remarking that the designer/client can choose the value of the dynamic factor depending on the particular boundary conditions of the segments during transient stages and on the accepted reliability level. The handling of a single segment is supposed to be performed with slings fixed at a defined spacing and with an inclination of 45. The structural scheme is shown in Fig. 7. A dynamic shock value can be considered for the design actions, with the aforementioned considerations. These three phases generally take place 28 days after casting, and then the 28-day material properties are adopted for the safety checks. Fig. 3. a) Lifting gear arrangement for demoulding and b) equivalent structural scheme Fig. 4. a) Positioning of the segment on floor and b) equivalent structural scheme Structural Concrete 17 (2016), No

11 F. Di Carlo/A. Meda/Z. Rinaldi Design procedure for precast fibre-reinforced concrete segments in tunnel lining construction Fig. 6. Loading conditions for the transportation phase and equivalent structural scheme for bottom segment: a) inward load eccentricity, b) outward load eccentricity Fig. 5. Loading conditions for stacked storage and equivalent structural scheme for bottom segment: a) inward load eccentricity, b) outward load eccentricity 3.2 Ground pressure The stress state due to the pressure exerted by the soil and, if applicable, by groundwater and surcharges on the lining rings is provided by the geotechnical design in terms of axial forces and bending moments. In some projects, earthquake, fire, explosion, adjacent tunnels and longitudinal bending moments need to be included. Obviously, the related safety factor has to be properly adopted according to the load combination and the limit states [18]. The safety check is carried out by drawing the M-N interaction envelope for the segment, as described in more detail in section 4. The characteristic values of the compressive and tensile strengths at 28 days have to be adopted at this stage and the coefficient a cc for the long-term load should be taken into account. 4 Segment lining check: ultimate limit state 4.1 Design for flexure N Sd acting on the segment in the different phases are evaluated with reference to the structural schemes described in the previous section and discussed in [9]. The design condition is verified if the point (N Sd ; M Sd) is inside or on the border of the N Rd M Rd envelopes. All the provisional phases (demoulding, positioning on floor, storage, transportation, handling) and the final stage (ground pressure on lining) have to be verified for the ultimate limit state. In order to draw the M-N envelopes related to the ultimate limit state, the hypothesis of planar sections is imposed and a simplified rigid-plastic behaviour (stress block) is assumed for FRC, both in compression and tension (Fig. 8). The design compressive and tensile stresses are evaluated according to [15]. The ultimate strains in compression ε cu and in tension ε fu are equal to 0.35 and 2 % (1 % for constant tensile strain distribution along the cross-section) respectively. Nevertheless, the maximum tensile strain cannot exceed the value related to a maximum crack width w = 2.5 mm. In order to evaluate this limitation, a characteristic length l cs must be defined to derive the strain starting from the crack width according to the following relationship: ε = wl / cs The characteristic length can be assumed to be on the safe side equal to the segment thickness, as suggested in [15] and confirmed in [19]. For this reason, for a linear strain distribution along the section, the ultimate tensile strain ε ULS is given by (6) The safety check for FRC tunnel segments is carried out with axial force-bending moment (N Rd M Rd ) envelopes obtained through translational and rotational equilibrium conditions. The bending moments M Sd and the axial forces ε ULS = min εfu, 2.5 lcs with l cs in mm. (7) 750 Structural Concrete 17 (2016), No. 5

12 F. Di Carlo/A. Meda/Z. Rinaldi Design procedure for precast fibre-reinforced concrete segments in tunnel lining construction Fig. 7. Handling phase: a) sling arrangement, b) equivalent structural scheme Fig. 8. Simplified constitutive relationships for FRC for evaluating ultimate loads As mentioned in section 2, it is assumed that the fibre reinforcement has no relevant influence on the properties of the material in compression. Therefore, the design compressive strength of the concrete f cd (t), depending on the time t at which the check is performed, can be evaluated as follows: where f R3k (t) is the tensile strength related to a CMOD of 2.5 mm (Fig. 2) at time t (i.e. when the check is performed) and γ f is the safety coefficient for FRC in tension, whose value is the same as for the concrete in compression γ c. The characteristic compressive strength f ck at different curing times is usually available (e.g., in Eurocode 2, for a curing temperature of 20 C). However, the variation in the residual tensile strength f R3k with the curing time can be determined with experimental tests, since it deα f fcd() t = γ where: f ck (t) characteristic compressive strength at time t a cc coefficient taking into account long-term load (usually 0.85) γ c safety coefficient for concrete (usually 1.5, even if a value of 1.4 can be used in several countries for precast production carried out with quality control) The coefficient a cc is assumed to be equal to 1 in all the provisional phases. According to [15], the design tensile strength is f Ftud cc ck c () t 1 f t () t = R3k() γ 3 f (8) (9) Fig. 9. Variation in (mean) tensile strength f R3 with time pends not only on the concrete properties, but also on the fibre characteristics and content. Fig. 9 shows a typical pattern of the mean value of the tensile strength f R3, determined experimentally in a precast plant. 4.2 Design for shear The presence of the fibres provides additional shear strength and contributes to shear cracking control. The models and formulations available for evaluating the shear capacity enhancement given by the fibres, in the presence of conventional steel rebar reinforcement, was recently summarized in [20]. Very few studies are available on the shear capacity of fibre-reinforced structures without traditional reinforcement. A procedure is suggested in [21], leading to a reduction in the M-N envelopes. In particular, the proposed approach is based on the application of Mohr s circles in concrete plasticity and on the definition of a reduced value of the tensile strength f red Ftud in order to account for the presence of the shear V: f red Ftud with σ = τ σ 2 I 1 σ I I (10) = f Ftuk = f γ Ftud and τ = V, where A is the cross- A f sectional area. It is clear from Eq. (10) that the maximum allowable tangential stress must be less than f Ftud. The strength f red Ftud is adopted for constructing the bending moment-axial force M-N interaction envelopes Structural Concrete 17 (2016), No

13 F. Di Carlo/A. Meda/Z. Rinaldi Design procedure for precast fibre-reinforced concrete segments in tunnel lining construction and therefore the shear check is included within the classical verifications for flexural and axial forces. 5 Serviceability limit state check Checking the segment at the serviceability limit state consists of verifying that the following two conditions are fulfilled: 1. The maximum stress in compression must be not greater than the maximum serviceability stress σ csls (assumed to be 0.6 f ck in [22]); as a consequence, the limit to the strain ε csls is σ csls /E c, where E c is the Young s Modulus of the concrete. 2. The maximum crack opening must be not greater than the design value, which depends on different factors, such as environmental conditions ([23]) and client restrictions, and generally ranges between 0 and 0.3 mm. The SLS safety check is then carried out by drawing M-N interaction envelopes, which are obtained by imposing the attainment of one or both of the two conditions described above. In order to define the envelopes simply, the strain related to the required maximum crack opening must be evaluated using Eq. (6) (section 4.1): ε w (11) where l cs is the characteristic length. The M-N interaction envelopes can be obtained through translational and rotational equilibrium conditions. In particular, as already discussed, the serviceability conditions are attained when the fibre-reinforced concrete reaches the strain ε csls in compression and/or the strain ε w in tension. With this aim, the compressive constitutive relations valid for plain concrete also apply to FRC, whereas the tensile FRC constitutive laws at SLS must be defined. In particular, according to [15], three different cases can be distinguished. For softening materials at SLS (CASE (I), Fig. 10) the same constitutive relationship adopted for plain concrete in uniaxial tension is used up to the peak strength f ct. In the post-cracking stage, a bilinear relation applies. In particular, the post-peak propagation branch (BC in Fig. 10a) can be described as with = w l max cs σ fct ε ε = P 0.2f f ε ε ε Q ct ct Gf = f l ct cs Q P 0.8 f + ε ct P E for ε ε ε (12) (13) where E c is the Young s modulus for concrete and G f the fracture energy of plain concrete, which is defined, according to [15], as 0.18 G = f 78 fcm Nm c P C (14) where f cm is the mean value of the concrete strength in compression (in MPa). For softening materials, the residual strength (fourth branch, DE in Figs. 10a and 10b) is defined by two points corresponding to the SLS stage (ε SLS, f Fts ) and ULS stage (ε ULS, f Ftu ). In particular, The effects of the TBM thrust on the segments can lead to a severe stress field in the element, with subsequent cracks that can jeopardize the structural durability. For this reason, to this phase should be given the same attention as to the others and a suitable check should be carried out. It should be remarked that in the simple design procedure, the actions transmitted by the TBM are considered as a single point load acting on the segment s circumferential side. This model is far from the actual field conditions, mainly for two reasons: the action is not actually a point load, (the dimensions of the thrusting pads usually used allow a distributed pressure) and more loads (thrusting pads) are present on the segment. Consequently, their relatively small spacing implies a reciprocal interε = CMOD / l and f = 0.45f f SLS 1 cs Fts R1 Ftu (15) (16) with w u = ε ULS l cs and ε ULS from Eq.(7). For materials characterized by a stable propagation up to ε SLS with a tensile strength f Fts > f ct, two cases can be considered: CASE (II): The cracking process becomes stable up to the SLS strain and four branches again define the constitutive relationship. The first two branches remain the same as those corresponding to plain concrete, while the third branch (BD in Fig. 10b) is described analytically as The design value f Ftsd is obtained from (17) (18) with γ f = 1 for the serviceability limit state ([15]) and where f Fts is the serviceability residual strength, defined as the post-cracking strength for serviceability crack openings and evaluated with Eq. (15). CASE (III): Cracking remains stable up to the SLS strain and three branches define the constitutive relationship. The second branch (AD in Fig. 10c) is defined as (19) where σ A and ε A are on the elastic branch for a stress equal to 0.9 f Fts (Fig. 10c). 6 TBM thrust ( Fts R3 R1) w = f u Fts + CMOD f 0.5 f 0.2 f 0 σ fct ε ε = P f f ε ε f Ftsd Ftsd ct f = γ Fts f σ σ A f σ Ftsd A SLS 3 P ε ε = A ε ε SLS A for ε ε ε P for ε ε ε A SLS SLS 752 Structural Concrete 17 (2016), No. 5

14 F. Di Carlo/A. Meda/Z. Rinaldi Design procedure for precast fibre-reinforced concrete segments in tunnel lining construction Fig. 10. Stress-strain relationships at SLS for softening (a) and softening or hardening (b, c) behaviour of FRC [15] Fig. 11. TBM thrust: a) Model geometry, b) typical crack pattern action and does not allow the situation of a single load to be considered. For this reason, the check for this phase has to be performed with numerical models and/or full-scale experimental tests in order to simulate, as closely as possible, the actual actions on the segment and to point out the concrete cracking phenomena and predict the crack opening. This aspect is very important because in this kind of structure the crack opening limit has to be complied with [10, 24 25]. With this aim, non-linear numerical models can be adopted [5, 26] with reference to the single segment and the whole ring. The three-dimensional geometry of the segment can be drawn, including holes for the connection and erection systems, in order to evaluate the stress state accurately. Particular attention has to be paid to modelling the boundary and loading conditions, reproducing as faithfully as possible the effective restraint and loading schemes. In order to investigate the cracking phenomena, the precast Structural Concrete 17 (2016), No

15 F. Di Carlo/A. Meda/Z. Rinaldi Design procedure for precast fibre-reinforced concrete segments in tunnel lining construction Fig. 12. Test setup for simulating TBM thrust [9, 26] Demoulding and positioning on floor phases The bending moments and shear forces related to the phases of demoulding and positioning on floor are evaluated with the structural schemes of Figs. 3 and 4 by assuming a length L = L tot /4 = 875 mm for both (Table 4). In this particular case, the value of the maximum bending moment, and the related shear, coincides in the two schemes. The values of the uniformly distributed load g (Figs. 3 and 4) due to the self-weight of the segment are summarized in Table 4. The design bending moment M Sd and shear V Sd are evaluated by assuming the partial safety factor γ G = 1.35 according to [15] and are also listed in Table 4. The axial force is neglected. The comparison between the bending actions evaluated with the above schemes and the structural resistsegment can be modelled by adopting a non-linear mechanical approach for the concrete based on the smeared crack model in which the crack is considered to be spread over an area that belongs to an integration point of the mesh. The crack starts when the principal tensile stress exceeds the value of the tensile strength of the material. Subsequently, during the computational process, the orientation of the crack can co-rotate with the axes of principal strain if a rotating concept is adopted. The post-cracking tensile behaviour is described through a tension softening stress-strain diagram significantly affected by the crack bandwidth parameter, which represents the width over which the crack is smeared. This parameter is strictly connected to the size of the mesh and can affect the results of the performed numerical analyses. Anyway, in the author s opinion, an experimental survey is very useful (and almost essential) for the model calibration and validation. Full-scale tests can be performed with an ad hoc loading system aiming to simulate the TBM thrust, as shown in Fig. 12 [9, 26]. Particular care has to be devoted to the definition of the test setup and procedure in order to reproduce the actual condition of the segment during the TBM thrust phase. With this aim, the segment should be loaded with the same number of jacks acting in the field, and with the same steel pads used with the TBM (Fig. 12). 7 Case study The case study analysed here relates to a precast steel FRC segment without traditional reinforcement. The aim is to show the practical procedure for defining the M-N envelopes for the phases cited above. Owing to the different check mode based on a numerical and/or experimental analysis, as already discussed, the TBM thrust phase is not treated here. A typical segment geometry is considered, with a section characterized by a thickness th = 300 mm, width h = 1500 mm and length L tot = 3500 mm. The ring is intended to be built from six segments. A fibre-reinforced concrete of class 5c (i.e. f R1k 5 MPa, 0.9 f R3k /f R1k 1.1, according to [15]) was adopted. The strength related to a CMOD of 2.5 mm (f R3 ) was assumed to be 4.5 MPa. The characteristic strength in compression after 28 days (f ck ) was set equal to 40 MPa. According to [15], the FRC material can be adopted for segments without traditional steel reinforcement since all the requirements described in section 2.2 are fulfilled, as shown in Table Ultimate limit state check The ULS safety check is carried out for all the phases described in section 3. The design values of the compressive and tensile strengths (at 28 days) are summarized in Table 2; the ones to be used for the provisional phases (according to section 3) are given in Table 3. The design actions are evaluated and compared with the relative M-N interaction envelopes, constructed taking into account shear action (section 4.2). Table 1. Requirements according to [15] Requirement Case study Values of parameters Check f R1k /f Lk > 0.4 f R3k /f R1k > 0.5 f R1k = 5MPa = 2 f f 3 = f 2.95 MPa * R1k /f Lk = 1.7 > 0.4 Lk f R3k = 4.5MPa f R1k = 5MPa ( ck) f R3 /f R1k = 0.9 > 0.5 M M u M cr ** u = 138.5kNm M M cr = 94.7kNm u M cr *f Lk is assumed to be equal to the characteristic flexural tensile strength of the matrix and evaluated according to [15] **Mean values 754 Structural Concrete 17 (2016), No. 5

16 Table 2. Characteristic and design strengths in compression and tension (28 days after casting) F. Di Carlo/A. Meda/Z. Rinaldi Design procedure for precast fibre-reinforced concrete segments in tunnel lining construction Characteristic strength Material safety factor Design strength Compression f ck = 40 MPa γ c = 1.5 f cd = 0.85 f ck /γ c = 22.7 MPa Tension f R3 = 4.5 MPa f Ftu = f R3 /3 = 1.5 MPa γ f = 1.5 (ULS) f Ftud = f Ftu /γ f = 1.0 MPa Table 3. Characteristic and design strengths in compression and tension (provisional phases) Phase Segment demoulding (6 h) Positioning on floor (6 h) Storage (28 days) Transportation (28 days) Handling (28 days) f ck [MPa] f cd [MPa] f R3 [MPa] f ctd [MPa] ance, defined through M-N interaction envelopes and obtained with the material properties of Table 2, is shown in Fig. 13. The shear action is accounted for, as described in section 4.2, even if its influence is negligible in these two phases. Storage phase Each ring, composed of six segments, is piled up in one stack. The bending moments and shear forces are evaluated with reference to the structural scheme of the segment at the bottom, shown in Fig. 5. Axial load is neglected. According to [18], an eccentricity of the support equal to 100 mm is considered for the lower segment, as shown in Fig. 5. This value can be accepted as a reference if no other indications are available. The uniformly distributed load g, due to the self-weight of the bottom segment, and the forces F, due to the weight of the stacked segments, are summarized in Table 5. The same table also gives the design bending moment M Sd and shear V Sd evaluated with reference to the worst condition of the two eccentricity cases considered (a and b in Fig. 5) and the most highly stressed section. A partial safety factor γ G = 1.35 is assumed according to [15]. Transportation phase The transportation of the segments is considered as a stack of three segments on a truck or train. The distance between the two bearing sleeves is assumed to be L tot /4 = 875 mm. The structural scheme is presented in Fig. 6. An eccentricity of the support equal to 100 mm is considered for the lower segment. Furthermore, a dynamic shock coefficient of 2.0 ([18]) is applied. The values of the uniformly distributed load g, due to the self-weight of the segment at the bottom, and the forces F (Fig. 6), due to the weight of the transported segments, are summarized in Table 5. The design bending moment M Sd and shear V Sd are evaluated with reference to the worst condition of the two eccentricity cases considered (a and b, Fig. 6) and to the most highly stressed section, by assuming the partial safety factor γ G = 1.35 according to [15]. Handling phase Finally, the handling of a single segment is considered. The slings are fixed at a distance of 2/4 (L tot ) = 1750 mm with an inclination of 45. The structural scheme is illustrated in Fig. 7. A dynamic shock value of 2.0 is considered. The values of the uniformly distributed load g, due to the self-weight of the segment, and the forces F (Fig. 7), are Table 4. Demoulding and positioning on floor phases design actions Structural scheme g [kn/m] M Sd [knm] V Sd [kn] g = γ cls th h g = = M = γ g L 2 = 5.8 Sd G 2 V Sd = γ G (g L) = 13.3 Structural Concrete 17 (2016), No

17 F. Di Carlo/A. Meda/Z. Rinaldi Design procedure for precast fibre-reinforced concrete segments in tunnel lining construction ues of the compressive and tensile strengths related to a 28-day curing age and taking into account the coefficient a cc = 0.85 for the long-term load ([15]). Fig. 15b clearly shows that the points related to the design actions are inside the bending moment-axial force interaction envelope. 7.2 Serviceability limit state check Fig. 13. ULS safety check-demoulding and positioning on floor summarized in Table 5. The design bending moment M Sd and shear V Sd, listed in Table 5, are evaluated with reference to the most highly stressed section by assuming a partial safety factor γ G = 1.35 according to [15]. The design bending moments and axial forces are finally compared with the structural resistance, evaluated through M-N interaction envelopes, computed with the design strength values of Table 2 and by assuming the long-term coefficient a cc = 1. The shear action is taken into account as described in section 4.2, and for this reason, specific M-N envelopes are drawn for each different phase, shown in Fig. 14, even if the same material properties (related to 28 days after casting) are considered. In the case study analysed, all the ULS checks were satisfied. Ground pressure In the proposed case study, for the sake of simplicity, only the pressure exerted by the ground is examined and evaluated with the FLAC program. In particular, a clay soil is considered and a Mohr-Coulomb failure criterion adopted, characterized by a cohesion c = 0.01 N/mm 2 and an internal friction angle φ = 27. The specific weight of the soil is assumed to be γ = 20 kn/m 3. The tunnel geometry is shown in Fig. 15a and the results obtained in terms of axial forces and bending moments are highlighted in Fig. 15b. The design actions are evaluated by applying a load safety factor equal to The M-N interaction envelope for the segment is drawn with the characteristic val- Finally, the serviceability limit state (SLS) check is carried out with reference to the storage, transport and handling phases. The main values of the strengths and of the strains required for defining the constitutive relationship, evaluated according to section 5, are summarized in Table 6. In the proposed example, the characteristic maximum crack opening w max is assumed to be 0.15 mm, in agreement with [23], assuming an class XD1. The same table also gives the limit strain in tension ε w (Eq. (11)), evaluated with w max = 0.15 mm, which is necessary for the construction of the M-N envelopes. The complete constitutive relationship of the FRC in tension, obtained according to [15], considering the characteristic values of residual strengths f ct, f R1 and f R3, falls within socalled case I, (section 5, Fig. 10a), being f Fts < f ct, and is plotted in Fig. 16a. A detail of the σ ε diagram to be adopted for the check, limited to the strain ε w, is shown in Fig. 16b. The related M-N envelope is highlighted in Fig. 17. The design actions, evaluated with the safety factor γ G = 1, are marked in the same figure. Since all the dots are inside the envelope, the check for the three phases is satisfied. 8 Conclusions An analytical procedure for designing and checking steel fibre-reinforced precast segments, without any traditional steel reinforcement, for mechanically excavated tunnel linings is presented in this paper and applied to a case study. The main outcomes of the research can be summarized as follows: The proposed design and checking procedure is a useful tool for the analysis of both the provisional phases (including demoulding, positioning on floor, storage, transportation and handling) and the final stage concerning the loads due to the ground pressure. The methodology Table 5. Loads and design actions for storage, transportation and handling phases g [kn/m] F [kn] M Sd [knm] V Sd [kn] Storage phase 5 W M = γ F = n g L 2 Sd G + F e = 98.4 = n= 1 2 V Sd = γ G (g L F) = 146 Transport phase g = γ cls th h g = = W n = γ cls th h L = 39.4 W F = 2 n = M = γ γ g L 2 Sd G din + F e 2 = 22.3 V Sd = γ G γ din (g L F) = 133 Handling phase M = γ γ g L 2 Sd G din 2 = 11.6 V Sd = γ G γ din (g L) = Structural Concrete 17 (2016), No. 5

18 F. Di Carlo/A. Meda/Z. Rinaldi Design procedure for precast fibre-reinforced concrete segments in tunnel lining construction Fig. 14. ULS safety check: a) storage; b) transportation; c) handling Fig. 15. Ground pressure: a) soil action on ring, b) check by the way of interaction domain is not applicable to the TBM thrust phase, which requires suitable numerical and/or experimental models in order to faithfully simulate the actual restraint and loading schemes of the segment and to properly represent the concrete cracking phenomena and predict the crack opening. The structural checks can be carried out by means of bending moment axial force interaction envelopes for both the ultimate and serviceability limit states, once the constitutive relationship of the material is defined for each stage. In SLS checks, both the concrete maximum compressive stress and the maximum crack opening have to be limited. Table 6. Strength and strain values for SLS constitutive relationship in tension f ct [MPa] F Fts [MPa] F Ftu [MPa] ε SLS [ ] ε ULS [ ] ε w [ ] Structural Concrete 17 (2016), No

19 F. Di Carlo/A. Meda/Z. Rinaldi Design procedure for precast fibre-reinforced concrete segments in tunnel lining construction Fig. 16. SLS stress-strain relationships: a) complete relationship up to ε ULS, b) limited to ε w Fig. 17. SLS: M-N interaction envelope f R1k f R3k g h l s t th t d w w max w u characteristic residual strength measured at CMOD (0.5 mm) characteristic residual strength measured at CMOD (2.5 mm) uniformly distributed load segment width characteristic length time segment thickness age at demoulding maximum crack width maximum crack opening (SLS) maximum crack opening accepted in structural design The presence of the shear action can be properly taken into account in both the considered limit states by reducing the bending moment axial force interaction envelopes according to the procedure suggested in [21]. The analysed case study highlights how the proposed checking tool can be easily and quickly applied and interpreted. Notation Roman lower-case letters c cohesion of soil e load eccentricity f cd (t) design cylinder compressive strength f ck (t) characteristic cylinder compressive strength f cm mean value of compressive strength f ct peak tensile strength of plain concrete f ctd design tensile strength of plain concrete f Fts serviceability residual strength f Ftsd design value of post-cracking strength for serviceability crack opening f Ftu ultimate residual strength f Ftud (t) design value of post-cracking strength f red Ftud reduced value of design tensile strength f Ftuk characteristic value of post-cracking strength f L limit of proportionality f Lk characteristic value of limit of proportionality f Rj residual flexural tensile strength corresponding to CMOD = CMODj Roman capital letters A cross-sectional area CMOD j crack mouth opening displacement E c Young s modulus of concrete F forces due to weight of stacked segments G f fracture energy of plain concrete L length of cantilever section of segment L tot segment length M bending moment M cr first cracking bending moment M Sd design value of applied bending moment M Rd design value of resistant bending moment M u ultimate bending moment N axial force N Sd design value of applied axial force N Rd design value or resistant axial force P cr load at crack initiation P SLS maximum service load P u ultimate load V shear force V Sd design value of shear force weight of nth segment W n Greek lower-case letters a cc long-term load coefficient for concrete in compression γ specific weight of soil γ c partial safety factor for concrete material properties specific weight of concrete γ cls 758 Structural Concrete 17 (2016), No. 5

20 F. Di Carlo/A. Meda/Z. Rinaldi Design procedure for precast fibre-reinforced concrete segments in tunnel lining construction γ din γ f γ G ε ε cu ε csls ε fu ε SLS ε ULS ε w σ σ csls σ I τ φ References dynamic shock value partial safety factor for FRC in tension partial safety factor for load strain ultimate strain in compression maximum compressive strain (SLS) ultimate strain in tension serviceability tensile strain (SLS) ultimate tensile strain (ULS) maximum tensile strain (SLS) stress maximum compressive stress (SLS) normal stress shear stress internal friction angle of soil 1. Romualdi, P., Batson, G. B.: Mechanics of Crack Arrest in Concrete. ASCE Journal of Engineering Mechanics, 1963, 89, pp Walraven, J.: The evolution of Concrete. Structural Concrete, 1999, 1, pp Di Prisco, M., Plizzari, G. A., Felicetti, R.: Proceedings of the 6 th RILEM Symposium on Fiber Reinforced Concretes (FRC), Varenna (Italy), September 20-22, RILEM PRO 39, Bagneaux (France), Cadoni, E., Meda, A., Plizzari, G. A.: Tensile behaviour of FRC under high strain-rate. Materials and structures, 2009, 42, pp Plizzari, G. A., Tiberti, G.: Steel fibers as reinforcement for precast tunnel segments. Tunnelling and Underground Space Technology, 2008, 21(3 4). 6. Kasper, T., Edvardsen, C., Wittneben, G., Neumann, D.: Lining design for the district heating tunnel in Copenhagen with steel fibre-reinforced concrete segments. Tunnelling and Underground Space Technology, 2008, 23(5), pp Caratelli, A., Meda, A., Rinaldi, Z., Romualdi, P.: Structural behaviour of precast tunnel segments in fiber reinforced concrete. Tunnelling and Underground Space Technology, 2011, 26(2), pp De la Fuente, A., Pujadas, P., Blanco, A., Aguado, A.: Experiences in Barcelona with the use of fibres in segmental linings. Tunnelling and Underground Space Technology, 2012, 27(1), pp Caratelli, A., Meda, A., Rinaldi, Z.: Design according to MC2010 of a fibre-reinforced concrete tunnel in Monte Lirio, Panama. Structural Concrete 2012, 13(3), pp Liao, L., De La Fuente, A., Cavalaro, S., Aguado, A.: Design of FRC tunnel segments considering the ductility requirements of the Model Code Tunnelling and Underground Space Technology, 2015, 47, pp Liao, L., De La Fuente, A., Cavalaro, S., Aguado, A., Carbonari, G.: Experimental and analytical study of concrete blocks subjected to concentrated loads with an application to TBM-constructed tunnels. Tunnelling and Underground Space Technology, 2015, 49, pp RILEM: Final Recommendations, TC-162-TDF: Test and design methods for steel fibre-reinforced concrete: sigma-epsilon-design method. Mater. Struct., 2003, 36, pp CNR DT 204/2006: Guidelines for the Design, Construction and Production Control of Fibre-reinforced Concrete Structures, Italian National Research Council, CNR, DAfStb-Richtlinie: Stahlfaserbeton, Deutscher Ausschuss für Stahlbeton, Berlin, fib Model Code for Concrete Structures 2010, Ernst & Sohn, Buratti, N., Ferracuti, B., Savoia, M.: Concrete crack reduction in tunnel linings by steel fibre-reinforced concretes. Construction and Building Materials, 2013, 44, pp EN 14651: Test method for metallic fibre concrete Measuring the flexural tensile strength, ACI 544.7R-16: Report on Design and Construction of Fibre-Reinforced Precast Concrete Tunnel Segments, ACI Committee 544, Jan Di Prisco, M., Colombo, M., Dozio, D.: Fibre-reinforced concrete in fib Model Code 2010: principles, models and test validation. Structural Concrete, 2013, 14(4). 20. fib Bulletin No. 57: Shear and punching shear in RC and FRC elements, Coccia, S., Meda, A., Rinaldi, Z.: On shear verification according to the fib Model Code 2010 in FRC elements without traditional reinforcement. Structural Concrete 2015, DOI: /suco (available online). 22. EN /2005, Eurocode 2: Design of Concrete Structures Part 1-1: General Rules and Rules for Buildings, CEN. 23. AFTES Recommendation No. GT38R1A1: Design, dimensioning and execution of precast steel fibre-reinforced concrete archsegments. Tunnels et Espace Souterrain 238, Jul/ Aug Burgers, R., Walraven, J., Plizzari, G. A, Tiberti, G.: Structural behaviour of SFRC tunnel segments during TBM operations. World Tunnel Congress ITA-AITES, Prague, Tiberti, G., Conforti, A., Plizzari, G. A.: Precast segments under TBM hydraulic jacks: Experimental investigation on the local splitting behavior. Tunnelling and Underground Space Technology, 2015, 50, pp Cignitti, F., Sorge, R., Meda, A., Nerilli, F., Rinaldi, Z.: Numerical analysis of precast tunnel segmental lining supported by full-scale experimental tests. 7th Intl Symp. on Geotechnical Aspects of Underground Construction in Soft Ground, Rome, May 2011, pp Fabio Di Carlo Postdoctoral Fellow, Department of Civil Engineering and Computer Science Engineering University of Rome Tor Vergata via del Politecnico 1, 00133, Rome, Italy di.carlo@ing.uniroma2.it Alberto Meda Associate Professor, Department of Civil Engineering and Computer Science Engineering University of Rome Tor Vergata via del Politecnico 1, 00133, Rome, Italy alberto.meda@uniroma2.it Zila Rinaldi Associate Professor, Department of Civil Engineering and Computer Science Engineering University of Rome Tor Vergata Via del Politecnico, 1, Rome, Italy Tel.: Fax: rinaldi@ing.uniroma2.it Structural Concrete 17 (2016), No

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27 Appendix C Technical Memorandum January 24, 2017

28 9th RILEM International Symposium on Fiber Reinforced Concrete - BEFIB September 2016, Vancouver, Canada PULL-OUT RESPONSE OF DISCRETE INNOVATIVE HOOKED-END STEEL FIBRE SHAPE AND GEOMETRY EMBEDDED IN SELF COMPACTING CONCRETE Clifford A O Okeh 1, David W Begg 2, Stephanie J Barnett 3, Nikos Nanos 4 1 Mr. University of Portsmouth and Southampton Solent University, UK, clifford.okeh@port.ac.uk 2 Dr. University of Portsmouth, UK, stephanie.barnett@port.ac.uk 3 Dr. University of Portsmouth, UK, david.begg@port.ac.uk 4 Dr. University of Portsmouth, UK. nikos.nanos@port.ac.uk ABSTRACT Distinct types of steel fibres embedded in concrete have been shown to generate a range of values for bond stress and different slip behaviour between concrete matrix and fibre interface under applied load. Single hook end steel fibre produces both higher peak load and dissipated energy during pull-out compared to straight fibres as a result of increased anchorage mechanism. However, the fibre behaviour during pull-out is predominantly influenced by mobilisation and straightening of the hook resulting in improved mechanical properties of steel fibre concrete if fully utilised. This on-going study aims to investigate the pull-out behaviour of new innovative steel fibres with single and multiple hooked-end shape and geometry on the peak pull-out load, dissipated energy, stiffness and bond strength. A laboratory single fibre pull-out investigation was carried out using three types (S1, M1 and M2) of new innovative hooked-end steel fibres with 10mm, 20mm and 30mm embedded depth at 0 0 inclination angle in self-compacting concrete (f cu =64MPa). The results stipulate that alteration of hooked-end steel fibre shape and geometry increased the anchorage efficiency up to 161% from single to multiple hooks, thereby improving the anchorage mechanism, resulting in higher peak load and dissipated energy. The load-slip behaviour during plastic deformation is modified, hence increased average bond stresses. Keywords: Pull-out load and dissipated energy, Single and multiple hooked-end steel fibres, Self- Compacting concrete, Bond stress, Slip dependent shear stress. Clifford Okeh University of Portsmouth School of Civil Engineering & Surveying Portland Building, Portsmouth PO1 3AH United Kingdom clifford.okeh@port.ac.uk +44 (0)

29 9th RILEM International Symposium on Fiber Reinforced Concrete - BEFIB September 2016, Vancouver, Canada 1. INTRODUCTION Steel fibre reinforced self-compacting concrete (SFRSCC) is one of the recent cementitious materials used in the construction industry due to the benefits (sustainability, health and safety) that selfcompacting concrete offers. Its main structural advantage is the improvement in pre and postcracking behaviour such as increase in first crack load, ultimate peak load and toughness as a result of more uniform steel fibre distribution and orientation along the casting direction provided by selfcompacting properties [1] however, it effectiveness is based on the application method adopted. Apart from improvement in steel fibre distribution and orientation, research has shown that other factors such as fibre geometric characteristics, fibre material properties, concrete properties and fibre volume accounts for further improvements in post cracking process [2;3;4,5]. These improvements are as a result of increase in the concrete matrix strength and/or enhanced fibre matrix bond interface which influences the bridging efficiency across the cracks [6] hence optimising the bond stress slip behaviour [7]. Different steel fibre geometry (straight, hooked, twisted, crimpled etc) presents different bond characteristics when used in concrete thereby influencing the behaviour in the pre and post cracking zone [8]. Their behaviour during pull-out test differs significantly, such as de-bonding after peak load for straight fibres; increase in pull-out force after de-bonding for deformed fibres due to mechanical anchorage; and a progressive mobilisation and straightening of the hooks after peak pull-out load for hooked end steel fibre which is mainly controlled by frictional resistance after approximately 4.5mm displacements [6]. The use of hooked end steel fibres is most common in the construction industry with 67% of sold fibre consisting of hooked type [9], its effectiveness in concrete depends on the embedment length across the crack which should be greater than the hooked end length [10]. This accounts for the additional frictional force generated due to straightening of the hooks in addition to the increase in matrix adhesion [11]. This leads to higher frictional pull-out force [6] when compared to straight fibres hence improving the mechanical performance of the concrete. The behaviour of hooked end steel fibres on pull-out parameters during a single pull-out test can be assessed based on three criterion; the bond-slip hardening characteristics with relationship to wedge effect of the abraded particle, scratching of the fibre surface and end deformation of the fibre as suggested by [7]. The additional frictional resistance and anchorage interlock mechanism generated as a result of the embedment length is caused by the bond stresses at the straight part and hooked region τ 1 and τ 2 respectively which are complicated to calculate as defined by [12]. These stresses are used to determine the hook efficiency determined by using their ratio to obtain the anchorage coefficient (K an ). The benefits of single hooked end steel fibre when compared to straight steel fibre during pull-out test is again recently emphasised by [1] and [6] but there is still the need to investigate the effect of shape and geometric characteristics on the pull-out response of new innovative multiple hooked end steel fibres with increase in hook number, hook depth and tensile strength at different embedment depths on the pull-out parameters when used in self-compacting concrete. 2. EXPERIMENTAL PROGRAMME AND TESTING 2.1 Material characteristics and specimen preparation Three types of hooked end steel fibre types with different shape, geometric and tensile strength properties were investigated in this study. See Figure 1 and Table 1 for hooked end steel fibre details. These hooked end steel fibres were embedded in plain self-compacting concrete (without fibres) with an average compressive strength of 64MPa and slump flow value of 835mm. The embedment depths of 10mm, 20mm and 30mm were investigated at 0 0 inclination angles. The mix design incorporated Fosroc Auracast.200 high range water reducing superplasticizer admixture, Portland Cement CEM I 52.5R with high cement content similar to [13] and [9] for selfcompacting concrete (SCC). See Table 2 for material details. Sea-won flint with no fraction of clay or 331

30 9th RILEM International Symposium on Fiber Reinforced Concrete - BEFIB September 2016, Vancouver, Canada fine silt with maximum size of 6mm was used as the fine aggregates and coarse aggregate composed of sea-won flint gravel, with maximum size of 10mm. The aggregate s contents were fixed and by modifying only the water-powder ratio and superplasticiser dosage, self-compatibility was achieved [13]. The concrete mix has a water/cement ratio of 0.27 with 0.69% cement mass of superplasticizer admixture in order to obtain comparable rheological and mechanical parameters. Fly ash or silica fume was not added to the mix design since the focus has been on the effect of various hooked end steel fibre types within a concrete matrix rather than the use of fly ash and silica fume to compliment the cement in order to prevent variation of physical and chemical properties to improve strength [9]. Figure 1: New Innovative S1, M1, M2 macro steel fibres. [3] Type 1 (S1) Type 2 (M1) Type 3 (M2) Figure 1: Shape of hooked-end macro steel fibres [14] Table 1: Geometry details and mechanical properties of hooked end steel fibres (S1, M1 and M2) Fibre Shape Type Length (mm) Diameter (mm) Aspect ratio Effective Hooked-end Region Length (mm) Depth of Hooked End Region (mm) Tensile Strength (N/mm 2 ) No of Fibres/kg Young Modulus N/mm 2 Single Hooked end Double Hooked end Double Hooked end S (+/-7.5%) M (+/-7.5%) M (+/-7.5%)

31 9th RILEM International Symposium on Fiber Reinforced Concrete - BEFIB September 2016, Vancouver, Canada Table 2: Self compacting concrete mix design Material Quantity (Kg/m3) Cement Sand Gravel Water Superplasticiser Mixing procedure, manufacture and testing of specimens All mixing operation during experimental work has been carried out using a drum tilting mixer. The mixing procedure and time started with 30 seconds wet mixing of coarse aggregate using 70% of measured water. Fine aggregate added and allowed to mix for a further 1 minute. Cement was then added and mixing carried on for a further 2.5 minutes after which the remaining 30% of water containing superplasticiser was slowly added. Mixing continued for a further 9 minutes to allow the effect of the superplasticiser to kick-in. Total mixing time was 13 minutes. This procedure was adopted throughout the experimental programme. 27 cubes (100mm x 100mm x 100mm) specimens were manufactured in disposable polystyrene moulds. Three numbers of each hooked end steel fibre types were carefully inserted into one concrete cube specimen to the desired embedment depth (10mm, 20mm or 30mm) as marked on the steel fibres. This insertion was done in the wet state to allow for adequate adhesion and interlock between fibre, aggregate and cement paste as the concrete self-compacts. A 4in1 level plumb square ruler measuring 12in x 12in was used to ensure 0 0 inclination angle is achieved with fibre inserted perpendicular to top surface of the cube specimen. Specimens were demoulded after 24 hours and placed in a curing tank at 20 C 2 for 28 days. The pull-out test was carried out using a 30KN Lloyd instrument testing machine with suitable grip as shown in Figure 2. Load cell measurements were recorded against displacement under closed loop load control operation with a speed rate of 2mm/min. Figure 2: Lloyd instrument 30 KN test machine (Southampton Solent University, 2014) 333

32 3. EXPERIMENTAL RESULTS AND DISCUSSIONS Data analysis has been carried out and evaluated using test results recorded from pull-out test on S1, M1 and M2 hooked end steel fibres. Average cube compressive strength of 64MPa has been obtained with plain self-compacting concrete cube specimens. Discussions focused on effect of steel fibre hooked end shape on load slip curve, fibre efficiency, slip dependent shear stress and slip displacement at peak load, pull-out force, pull-out energy dissipated, and fibre anchorage coefficient. 3.1 Effect of steel hooked end shape on load slip curve Figure 3 shows the load displacement relationship for a typical S1, M1 and M2 hooked end steel fibre types during a pull-out test at 0 0 inclination angles. Emphasis is made to the effect on the anchorage mechanism provided by each fibre type due to the number of hooks rather than the embedment length as this is more dominant as stated by [6]. The result indicates that the increase in hook number affects the behaviour after the peak load (when debonding occurs) during the plastic deformation process as a result of straightening of the hooks. The softening behaviour of the plastic deformation region shows a series of load increase, this account for the straightening of the individual hooks at various residual stresses. When comparing the increase in load at these displacement points for M1 and M2 steel fibres, the results shows a steep rise with M1 steel fibre type when compared to M2. The steep rise can be attributed to the hook end depth (M1 = 6mm and M2 = 4mm) which affects the residual stresses during stress degradation and as such alters the softening behaviour during plastic deformation. This trend is also similar when compared to single hooked end steel fibre (S1) th RILEM International Symposium on Fiber Reinforced Concrete - BEFIB September 2016, Vancouver, Canada Force (N) S1 M1 M Slip (mm) Figure 3: A typical load - slip curve for S1, M1 & M2 hooked end steel fibres 334

33 9th RILEM International Symposium on Fiber Reinforced Concrete - BEFIB September 2016, Vancouver, Canada 3.2 Hooked end steel fibre efficiency The hooked end steel fibre efficiency has been calculated using the formula stated by [6]: Fibre efficiency = σ max /f y (1) Where σ max is the tensile stress in the fibre and f y is the yield strength of the steel fibre. The steel fibre efficiency is attributed to the utilisation of the fibre tensile capacities in relation to fibre rupture or slip behaviour during pull-out test. The result in Figure 4 shows that 100% of S1 and M2 steel fibres did not rupture (break) during the pull-out test because of the slip behaviour before reaching its steel tensile strength of 1100MPa and 2300MPa respectively. However, the result indicates 33% of M1 steel fibre ruptured, the rupture occurred just after the peak load during plastic deformation. The behaviour associated with M1 fibre failure could be as a result of the high stress generated to cause slip as well as the stress required to straighten the hook (influenced by fibre shape and depth of hook). The high stress generated for M1 hook shape can be attributed to its design with no straight part in the hook geometry (see Figure 1) accounting for bond stress τ 1 as suggested by [12] see Figure [5]. But its design allows for bond stress τ 2 (bond stresses in the hook) to be generated immediately on application of pull-out force as well as the effect of increase in hook depth thus, providing additional anchorage interlock between the fibre and the concrete matrix which result in fibre rupture. The result also shows that steel fibre efficiency increased with increase in embedment depth when considering mean values. This increase can be as a result of increase in the surface area of the steel fibre in contact with the concrete matrix (increase in wedge effect of the abraded particle and adhesion resistance) thereby providing additional resistance to slip hence increasing the slip displacement Figure 7 and pull-out load Figure 8. The scatter of steel fibre efficiency also decreased with increase in embedment depth for all fibre types although in some cases with respect to M1 steel fibre type the scatter ranged above 100% steel fibre efficiency. This indicates that the 33% of M1 steel fibres that ruptured during the pull-out test exceeded their yield strength. This failure mode is more pronounced with increase in embedment depth Fibre Efficiency (%) Embedded Depth (mm) Specimen Type M M S1 30 Figure 4: Graph of steel fibre efficiency against embedded depth and specimen type 335

34 9th RILEM International Symposium on Fiber Reinforced Concrete - BEFIB September 2016, Vancouver, Canada Figure 5: Single hooked end steel fibre total bond stresses τ ƒ ( τ 1 = bond stresses in the straight part of the fibre Ɩ 1 and τ 2 = bond stresses in the hook Ɩ 2 ) cited in [12] 3.3 Slip dependent shear stress and slip displacement at peak load The slip dependent shear stress τ (s) has been calculated based on the slip at the peak pull-out load using the formula suggested by [7] given as: τ (s) = p (s) / π x d f x (L E s) (2) Where p (s) is load at any slip, d f is the diameter of the fibre, L E is the initial embedment length and s is the slip during pull-out. Figure 6 shows the slip dependent shear stress at peak load which can be referred to as the ultimate bond stress before debonding, Figure 7 shows a corresponding slip displacement at peak load of each steel fibre type at various embedment depths. The result indicates that there is an increase in slip dependent shear stress at peak load when S1 steel fibre is compared to M1 and M2 irrespective of embedment depth. The increase in slip stress can be attributed to the increase in the interlock mechanism that is provided by the multiple hooked end steel fibres (M1 and M2) compared to the single hook end steel fibre S1 with the concrete matrix. The behaviour is very complex to analyse due to a combination of various factors (hook end depth, number of hooks and shape). However, one obvious factor causing the additional interlock efficiency is the effective linear length of the hooked end region (S1 = 3mm; M1 = 8mm and M2 = 10mm) embedded in the concrete. The effective linear length accounts for the increase in total bond stress (stress in straight part of steel fibre and stress in the hook). Comparison between M1 and M2 steel fibre shows no significant improvement in the slip dependent shear stress as a result of the scatter but an increase of up to 41% with mean values. The effect of increase in embedment depth decreases the slip dependent shear stress and increases the slip displacement for all steel fibre types indicating a better performance in shear resistance at greater depths. This behaviour is due to the increase in adhesion bond and wedge effects caused by the additional steel fibre surface in contact with the concrete matrix. No significant influence of steel fibre types on the slip displacement at peak load except at 30mm embedment depth when S1 is compared to M1 and M2. This indicates increase in bond stresses attributed to the increase in interlock mechanism and adherence bond caused by the effective linear length and shape effect in contact with the concrete matrix. 336

35 9th RILEM International Symposium on Fiber Reinforced Concrete - BEFIB September 2016, Vancouver, Canada The scatter of the slip dependent shear stress and slip displacement at peak load is observed to decrease with increase in embedment depth for all fibre types. This trend can be attributed to the accuracy of the steel fibre insertion to the required depth in the concrete during manufacture 60 Slip DependentShear Stress(MPa) Embedded Depth (mm) Specimen Type M M S1 30 Figure 6: Graph of slip dependent shear stress against embedded depth and specimen type 5 Slip Displacement at Peak (mm) Embedded Depth (mm) Specimen Type M M S1 30 Figure 7: Graph of slip displacement at peak load against embedded depth and specimen type 337

36 9th RILEM International Symposium on Fiber Reinforced Concrete - BEFIB September 2016, Vancouver, Canada 3.4 Pull-out force and dissipated energy The pull-out force and pull-out dissipated energy were derived from the load-displacement curve. The energy has been calculated as the area under the load slip curve as emphasised by [7]. The test results as presented in Figures 8, 9 and 10 indicates that alteration of steel fibre hooked end shape and geometry (adjusting hook number and hook depth) increases the pull-out force and pull-out dissipated energy up to a maximum of 160% from S1 to M2 as embedment depth increases. There is a direct relationship between the pull-out force and pull-out dissipated energy. The behaviour in pull-out parameters can be assessed based on the bond-slip hardening characteristics with relationship to wedge effect of the abraded particle, scratching of the fibre surface and end deformation of the fibre as suggested by [7]. Improvements obtained in this experiment clearly indicate a link to the effect of the fibre end deformation of the hook. The hook number, hook depth and tensile strength of the steel fibres accounts for the additional frictional resistance and bond anchorage interlock between fibre and concrete matrix. The bond mechanism generated is caused by the bond stresses at the straight and hook parts τ 1 and τ 2 respectively as defined by [12]. These stresses can be used to determine the hook efficiency from their ratio towards obtaining the anchorage coefficient (K an ). Furthermore, it is important to highlight on the effect of each steel fibre type on the scatter as shown in Figures 8 and 9. The graph shows a reduction in the scatter as embedment depth increases. This trend may again be attributed to the in-accuracy when inserting the fibres into the concrete during manufacture, thereby affecting the efficiency of the fibre Peak Pull-out Load (N) Embedded Depth (mm) Specimen Type M M S1 30 Figure 8: Graph of maximum pull-out force against embedded depth & fibre type 338

37 9th RILEM International Symposium on Fiber Reinforced Concrete - BEFIB September 2016, Vancouver, Canada Dissipated Energy (Nmm) Embedded Depth (mm) Specimen Type M M S1 30 Figure 9: Graph of pull-out dissipated energy against embedded depth & fibre type Peak Pull-out Load (N) Specimen Type M1 M2 S Dissipated Energy (Nmm) Figure 10: Graph of peak pull-out load against pull-out dissipated energy & fibre type 339

38 9th RILEM International Symposium on Fiber Reinforced Concrete - BEFIB September 2016, Vancouver, Canada 4. CONCLUSION The study investigated pull-out parameters of single and multiple hooked end steel fibres from a single pull-out test with embedment depths of 10mm, 20mm and 30mm at 0 0 inclination angle. The test results evaluated led to the following conclusions: The increase in the number of hooks affects the residual stresses during plastic deformation, hence the softening behaviour during stress degradation is modified. There is a direct relationship between the pull-out force and pull-out dissipated energy with alteration of hooked end shape and geometry from single to multiple as expected. Alteration of steel fibre hooked end shape and geometry by increasing the hook number and adjusting hook depth, increases the pull-out force and pull-out dissipated energy up to a maximum of 160% from S1 to M2 as embedment depth increases. Increase in embedment depth reduces the scatter of pull-out parameters irrespective of hooked end steel fibre type. This may be attributed to increased accuracy during manufacturing. There is no significant influence at short embedment depth except at 30mm on the slip displacement at peak load and slip dependent shear stress when single hook end steel fibre is compared to multiple hooks. This is as a result of the increased adherence bond caused by the increase in linear effective length in contact with the concrete matrix as well as the shape effect. 5. REFERENCES 1. Cunha, V. M. C. F., Barros, J. A. O., & Sena-Cruz, J. M. (2010). Pullout behaviour of steel fibres in self compacting concrete. Journal of materials in Civil Engineering, 22 (1), Akcay, B., & Tasdemir, M. (2012). Mechanical behaviour and fibre dispersion of hybrid steel fibre self-compacting concrete. Construction and Building Materials, 28 (1), Barros, J. A. O., Lourenco, L., Soltanzadeh, F., & Taheri, M. (2013). Steel fibre reinforced concrete for elements failing in bending and shear. Advances in Concrete Construction, 1 (1), Dupont, D. (2003) Modelling and experimental validation of the constitutive law (σε) and cracking behaviour of steel fibre reinforced concrete. Catholic University of Leuven, Belgium. 5. Sorelli, L. G., Meda, A., & Pizzari, G. A. (2006). Steel fibre concrete slabs on ground: A structural matter. ACI Structural Journal, 103 (4), Breitenbücher, R., Meschke, G., Song, F., & Zhan, Y. (2014). Experimental, analytical and numerical analysis of the pull-out behaviour of steel fibres considering different fibre types, inclinations and concrete strengths. Structural Concrete Journal of the fib, 15 (2), Wille, K., & Naaman, A. E. (2010) Bond stress-slip behavior of steel fibers embedded in ultra high performance concrete, In: Proc. 18th European Conf. on Fracture and Damage of Advanced Fiber-Reinforced Cement-Based Materials. Contribution to ECF 18, V. Mechtcherine & M. Kaliske (eds.), (pp99 111). Dresden, Germany. 8. Lok, T., & Pei, J. (1998). Flexural behaviour of steel fibre reinforced concrete. Journal of Materials in Civil Engineering, 10 (2), Pajak, M., & Ponikiewski, T. (2013). Flexural behaviourof self-compacting concrete reinforced with different types of steel fibres. Construction and Building Materials, 47,

39 9th RILEM International Symposium on Fiber Reinforced Concrete - BEFIB September 2016, Vancouver, Canada 10. Robins, P., Austin, S., & Jones, P. (2002). Pull-out behaviour of hooked steel fibres. Material Structures, 35 (251), Benaicha, M., Jalbaud, O., Hafidi, A. A., & Burtschell, Y. (2013). Rheological and mechanical characterisation of fibre-reinforced self-compacting concrete. International Journal of Engineering and Innovative Technology, 2 (7), Remigijus, S., & Gediminas, M. (2010) Influence of fibre shape on the strength of steel fibre reinforced concrete. In: Proc. 10th Int. Conf. on Modern Building Materials, Structures and Techniques (pp ). Vilnius, Lithuania. 13. Okamura, H., & Ouchi, M. (2003) Applications of Self-Compacting Concrete in Japan. In: Proc. 3rd Int. RILEM Symposium on Self-Compacting Concrete (pp.3-5). Reykjavik, Iceland. 14. Vandekerokhore, & Devos. (2012) Dramix: Reinforcing the future. Bekaert SA, Belgium 341

40 Appendix D Technical Memorandum January 24, 2017

41 Università degli Studi di Roma Tor Vergata CIVIL ENGINEERING AND COMPUTER SCIENCE DEPARTMENT TERC TUNNELLING ENGINEERING RESEARCH CENTRE TECHNICAL REPORT TESTS ON PRECAST TUNNEL SEGMENT IN CONCRETE NEWLY HIGH TENSILE STRENGTH STEEL FIBERS DRAMIX 4D 80/60BG Draft CUSTOMER: BMUS February 2015 Prof. Alberto Meda Prof. Zila Rinaldi

42 Doc: TR_BMUS_4D.docx TESTS ON Dramix 4D 80/60BG Date: 22/12/2014 Page: 2/31 INDEX INTRODUCTION SEGMENT GEOMETRY MATERIAL SEGMENT TESTING PROCEDURE Bending Test Point load test BENDING TEST: RESULTS CONCLUSIONS TERC TUNNELLING ENGINEERING RESEARCH CENTRE University of Rome Tor Vergata

43 Doc: TR_BMUS_4D.docx TESTS ON Dramix 4D 80/60BG Date: 22/12/2014 Page: 3/31 INTRODUCTION The loading tests, object of the present report, are carried out on precast tunnel segments in fiber reinforced concrete produced in the Laboratory of Materials and Structures of the Civil Engineering Department of the Rome University Tor Vergata. The segments were cast by using segment moulds typically used in hydraulic tunnels. The tests were conducted by the Laboratory of Materials and Structures of the Civil Engineering Department of the University of Rome Tor Vergata. Responsible of the tests are Prof. Alberto Meda and Prof. Zila Rinaldi. Two different kinds of tests were performed, as described in the following: a test simulating the point loads effects on the segments, produced by the TBM machine during the digging phase and a flexural test simulating the behaviour of the segments when loaded under bending. In total, 2 segments have been tested. The tests were performed on elements made in concrete without traditional reinforcement, with a fiber content equal to 40 kg/m 3. The adopted fiber are Dramix 4D 80/60BGwith a length of 60 mm. This mix design is typical in precast segment production in terms of cost and performance. TERC TUNNELLING ENGINEERING RESEARCH CENTRE University of Rome Tor Vergata

44 Doc: TR_BMUS_4D.docx TESTS ON Dramix 4D 80/60BG Date: 22/12/2014 Page: 4/31 1 SEGMENT GEOMETRY The tests have been carried out on precast segments characterized by a thickness of 250 mm, a length of about 1670 mm and a width of about 1200 mm (Fig. 1.1). Figure 1.1. Segment geometry The reinforcement is constituted by steel fibers Bekaert Dramix 4D 80/60BG, with a content of 40 Kg/m 3. No traditional steel reinforcement in rebars is present. TERC TUNNELLING ENGINEERING RESEARCH CENTRE University of Rome Tor Vergata

45 Doc: TR_BMUS_4D.docx TESTS ON Dramix 4D 80/60BG Date: 22/12/2014 Page: 5/31 2 MATERIAL The segments were cast in moulds available at the laboratory of the Rome University Tor Vergata (Fig. 2.1). The concrete was prepared in a truck mixer. The adopted moulds have electrical vibrators in order to compact the concrete. Both the segments were made from the same batch, as well as beams and cubes for the material characterization. The mix design of the concrete adopted for the segment preparation is shown in Table 2.1. Steel fibers Bekaert Dramix 4D 80/60BGwere added with a content of 40 Kg/m 3. The casting phase is shown in Figure 2.1. Table 2.1. Concrete mix design Component kg/m 3 Cement 42.5 R 480 Natural sand (0-4 mm) 422 Crushed sand (0-4 mm) 423 Crushed aggregate (4-16 mm) 519 Crushed aggregate (16-25 mm) 350 Plasticiser 4.8 Water 170 Steel fiber 40 Figure 2.1. Segment cast The average compressive strength of the fiber reinforced material, measured on 8 cubes having 150 mm side, was equal to MPa. The tensile behaviour was characterized through bending tests on nine 150x150x600 mm notched specimens (Fig. 2.2) according to the EN (Fig. 2.3). The diagrams of the nominal stress versus the crack mouth opening displacements (CMOD) are plotted in Figure 2.4. Furthermore, in Table 2.2 are summarised the values of the stress related to the TERC TUNNELLING ENGINEERING RESEARCH CENTRE University of Rome Tor Vergata

46 Doc: TESTS ON Dramix 4D 80/60BG TR_BMUS_4D.docx Date: 22/12/2014 Page: 6/31 proportionality limit (fl) and the residual nominal strengths related to four different crack openings - CMOD (0.5, 1.5, 2.5 and 3.5 mm), named fr1, fr2, fr3, fr4. The material can be classified as 5e according to Model Code 2010 (Fig. 2.5). In fact the characteristic value of fr1k is higher than 5 MPa and the ration between fr3k and fr1k is equal to 1.37, so higher than 1.3. Figure 2.2. Tensile behaviour: beam specimens. 150 hsp=125 Section A-A A A b= L=500 Figure 2.3. Tensile behaviour: bending test set-up (EN 14651). TERC TUNNELLING ENGINEERING RESEARCH CENTRE University of Rome Tor Vergata

47 Doc: TESTS ON Dramix 4D 80/60BG fr2 TR_BMUS_4D.docx Date: 22/12/2014 Page: 7/31 fr3 fr CMOD4 CMOD3 CMOD2 CMOD1 Nominal stress [MPa] fr CMOD [mm] Figure 2.4. Results of the beam bending tests Table 2.2 Results of the beam bending tests fl [Mpa] fr1 [MPa] fr2 [MPa] fr3 [MPa] fr4 [MPa] Beam_01 Beam_02 Beam_03 Beam_04 Beam_05 Beam_06 Beam_07 Beam_08 Beam_ Average Characteristic TERC TUNNELLING ENGINEERING RESEARCH CENTRE University of Rome Tor Vergata

48 TESTS ON Dramix 4D 80/60BG Doc: TR_BMUS_4D.docx Date: 22/12/2014 Page: 8/31 F(# ',+&&"AH# =?/# (A# *M4# +#,"./+%# /,+&="'# B/?+1"(G%# '+.# B/# +&&GD/!C# BH# =?/# '?+%+'=/%"&="'# A,/IG%+,# %/&"!G+,# 1+,G/&# =?+=# +%/# A(%# &/%1"'/+B","=H# # Of R1k P# +.!# G,="D+=/# Of R3k P# '(.!"="(.&E# K.# J+%="'G,+%# =N(# J+%+D/=/%&C#.+D/,H# f R1k #O%/J%/&/.=".@#=?/# &=%/.@=?#".=/%1+,P#+.!#+#,/==/%#+C#BC#'C#!#(%#/#O%/J%/&/.=".@#=?/#f R3k )f R1k #%+="(PE# F?/#&=%/.@=?#".=/%1+,#"&#!/A"./!#BH#=N(#&GB&/WG/.=#.GDB/%&#".#=?/#&/%"/&># 9E:C#9E6C#;E:C#;E6C#RE:C#TE:C#6E:C#8E:C#UE:C#<E:C#X#Y3$+Z# N?",/#=?/#,/==/%& ac#bc#cc#d, e#'(%%/&j(.!#=(#=?/#%/&"!g+,#&=%/.@=?#%+="(&># a#"a#:e6# #f R3k )f R1k # #:EU# b#"a#:eu# #f R3k )f R1k # #:EV# c#"?#:@a# f R3k )f R1k # #9@9# B6@879C# d#"?#9@9# #f R3k )f R1k # #9@D# e#"?#9@d# #f R3k )f R1k # EF/#!/&"G./%# F+&# =(# &H/'"?I# =F/# %/&"!J+,# &=%/.G=F# ',+&&# +.!# =F/#? )? # Figure 2.5. Model Code 2010 classification. TERC TUNNELLING ENGINEERING RESEARCH CENTRE University of Rome Tor Vergata

49 Doc: TR_BMUS_4D.docx TESTS ON Dramix 4D 80/60BG Date: 22/12/2014 Page: 9/31 3 SEGMENT TESTING PROCEDURE One Point load and one flexural tests are carried out, as discussed in detail in the following 3.1 Bending Test The test was performed with the loading set-up illustrated in Figures 3.1 and 3.2, in displacement control, by adopting a 1000kN electromechanical jacket, with a PID control and by imposing a stroke speed of 10 µm/sec. The segments were placed on cylindrical support with a span of 1200 mm and the load, applied at midspan, was transversally distributed be adopting a steel beam as shown in Figure 3.3. Figure 3.1: Bending test set-up TERC TUNNELLING ENGINEERING RESEARCH CENTRE University of Rome Tor Vergata

50 Doc: TR_BMUS_4D.docx TESTS ON Dramix 4D 80/60BG Date: 22/12/2014 Page: 10/31 Left side Right side Figure 3.2 Segments under bending test Figure 3.3 Loading distribution system During the test, the following measures were continuously registered: the load F, measured by means of a 1000kN load cell with a precision of 0.2%; the midspan displacement measured by means of three potentiometer wire transducers placed along the transverse line (Fig. 3.4); the crack opening at midspan, measured by means of two LVDTs (Fig. 3.4). TERC TUNNELLING ENGINEERING RESEARCH CENTRE University of Rome Tor Vergata

51 Doc: TR_BMUS_4D.docx TESTS ON Dramix 4D 80/60BG Date: 22/12/2014 Page: 11/31 Furthermore, the crack pattern was recorded at different step, with the help of a grid plotted on the intrados surface (100x100mm). LVDT left LVDT right Wire transducer w1 (left) Wire transducer w3 right Wire transducer w2 (middle) Figure 3.4. Bending test instrumentation 3.2 Point load test The point load test was performed by applying two point loads at the segment, by adopting the same steel plates used by the TBM machine (Fig. 3.5). A uniform support is considered, as the segment is placed on a stiff beam suitably designed. Every jack, having a loading capacity of 2000 kn, is inserted in a close ring frame made with HEM 360 steel beams and 50 mm diameter Dywidag bars (Fig. 3.5). The load was continuously measured by pressure transducers. Four potentiometer transducers (two located at the intrados and two at the extrados) measure the vertical displacements, while one LVDT transducers is applied between the load pads, in order to measure the crack openings. (Figs. 3.6 and 3.7). TERC TUNNELLING ENGINEERING RESEARCH CENTRE University of Rome Tor Vergata

52 Doc: TR_BMUS_4D.docx TESTS ON Dramix 4D 80/60BG Date: 22/12/2014 Page: 12/31 Figure 3.5. Point load test LVDT Transducer transducer P1 transducer P3 Figure 3.6. Test set up for segments subjected to compression: intrados TERC TUNNELLING ENGINEERING RESEARCH CENTRE University of Rome Tor Vergata

53 Doc: TR_BMUS_4D.docx TESTS ON Dramix 4D 80/60BG Date: 22/12/2014 Page: 13/31 transducer P4 transducer P2 Figure 3.7. Test set up for segments subjected to compression: extrados TERC TUNNELLING ENGINEERING RESEARCH CENTRE University of Rome Tor Vergata

54 Doc: TR_BMUS_4D.docx TESTS ON Dramix 4D 80/60BG Date: 22/12/2014 Page: 14/31 4 BENDING TEST: RESULTS The test set up for the segment subjected to bending test is shown in Figure 4.1. Figure 4.1. Bending test set up It is worth remarking that the test is carried out in displacement control, with an electromechanical jack, up to the collapse. The cracking phase is highlighted during the test. The displacements measured by the 3 wire transducers (Fig. 3.4) are plotted versus the load in Figure 4.2. No appreciable torsion was found, as the three wire transducers measured almost coincident displacements. The maximum load was about 254 kn. TERC TUNNELLING ENGINEERING RESEARCH CENTRE University of Rome Tor Vergata

55 Doc: TR_BMUS_4D.docx TESTS ON Dramix 4D 80/60BG Date: 22/12/2014 Page: 15/ Load (kn) W1 W2 W Displacement (mm) a) 300 Load (kn) W1 W3 W Displacement (mm) Figure 4.2. Bending test: load-mean displacement. a) total graph; b) detail up to 10 mm displacement The first crack appears for a load value of about 170 kn, at the intrados surface close to the midspan of the segment and propagates on the lateral surfaces. The crack pattern is shown in Figure 4.3. The maximum crack width is about 0.05 mm (Fig. 4.4). TERC TUNNELLING ENGINEERING RESEARCH CENTRE University of Rome Tor Vergata

56 Doc: TR_BMUS_4D.docx TESTS ON Dramix 4D 80/60BG Date: 22/12/2014 Page: 16/31 a) b) c) Figure 4.3. Bending test: load level 170 kn: crack pattern: a) right lateral surface, b) intrados surface, c) left lateral surface Figure 4.4. Bending test. Load level 170 kn; maximum crack width. TERC TUNNELLING ENGINEERING RESEARCH CENTRE University of Rome Tor Vergata

57 Doc: TR_BMUS_4D.docx TESTS ON Dramix 4D 80/60BG Date: 22/12/2014 Page: 17/31 For a load level of 200 kn a new crack forms at the intrados surface, and propagates on the right lateral face (in blue in Fig. 4.5). Furthermore a widening and lengthening of the already formed crack takes place (Fig. 4.5). The maximum crack width is about 0.25 mm (Fig. 4.5d). a) b) c) d) Figure 4.5. Bending test. Load level 200 kn; a) intrados face; b)right face; c) left face.; d) maximum crack width The crack pattern for a load level of 225 kn is highlighted in Figure 4.6. New cracks form at the intrados surface (in green in Fig. 4.6a), spreading towards the lateral faces (Fig. 4.6b, c). A lengthening and/or widening of the already formed cracks takes place (Figs. 4.6a, b, c). The maximum crack width on the lateral surfaces is about 0.4 mm (Fig. 4.7). TERC TUNNELLING ENGINEERING RESEARCH CENTRE University of Rome Tor Vergata

58 Doc: TR_BMUS_4D.docx TESTS ON Dramix 4D 80/60BG Date: 22/12/2014 Page: 18/31 a) b) c) Figure 4.6. Bending test. Load level 140 kn; a) intrados face; b) right face; c) left face. Figure 4.7. Bending test. Load level 225 kn, maximum crack width on the lateral surfaces. TERC TUNNELLING ENGINEERING RESEARCH CENTRE University of Rome Tor Vergata

59 Doc: TR_BMUS_4D.docx TESTS ON Dramix 4D 80/60BG Date: 22/12/2014 Page: 19/31 Further cracks form for the peak load of 253 kn, at the intrados and lateral surfaces, as shown in pink in Figures 4.8 and 4.9, respectively. The maximum crack width on the lateral surfaces is about 0.9 mm (Fig. 4.10). Figure 4.8. Bending test. Load level 253kN, intrados surface. a) b) Figure 4.9. Bending test. Load level 253 kn, a) right face, b) left face. TERC TUNNELLING ENGINEERING RESEARCH CENTRE University of Rome Tor Vergata

60 Doc: TR_BMUS_4D.docx TESTS ON Dramix 4D 80/60BG Date: 22/12/2014 Page: 20/31 Figure Bending test. Load level 253 kn; maximum crack width on the lateral surfaces. The state of the segment for a displacement close to the maximum one, equal to about 47 kn, is shown in Figures 4.11, 4.12 and In particular, in Figure 4.11 the evolution of the crack pattern, from the peak to the maximum displacement, is highlighted. a) b) Figure Bending test. intrados surfaces; evolution of the crack pattern; a) peak displacement; b) maximum displacement; TERC TUNNELLING ENGINEERING RESEARCH CENTRE University of Rome Tor Vergata

61 Doc: TR_BMUS_4D.docx TESTS ON Dramix 4D 80/60BG Date: 22/12/2014 Page: 21/31 Figure Bending test. Maximum displacement; right face. a) b) Figure Bending test. Load level 177 kn; a) right surface; b) left surface. Finally the segment at the end of the tests is shown in Figure 4.14, and the detected crack pattern is summarised in Figure TERC TUNNELLING ENGINEERING RESEARCH CENTRE University of Rome Tor Vergata

62 Doc: TR_BMUS_4D.docx TESTS ON Dramix 4D 80/60BG Date: 22/12/2014 Page: 22/31 Figure Bending test. End of the test. TERC TUNNELLING ENGINEERING RESEARCH CENTRE University of Rome Tor Vergata

63 Doc: TR_BMUS_4D.docx TESTS ON Dramix 4D 80/60BG Date: 22/12/2014 Page: 23/ kn 200 kn 225 kn 255 kn Figure Bending test. Crack pattern The crack width on the intrados is evaluated on the basis of the two LVDTs measures. In Figure 4.16 the LVDTs displacements are plotted versus the load. It is worth noting that two or three cracks passes through the instruments lengths (Figs. 4.11, 4.12, 4.13 and 4.14), and then the measure is related to the sum of their crack widths. TERC TUNNELLING ENGINEERING RESEARCH CENTRE University of Rome Tor Vergata

64 TESTS ON Dramix 4D 80/60BG Doc: TR_BMUS_4D.docx Date: 22/12/2014 Page: 24/ Load (kn) LVDT A right LVDT LVDT left R Displacement (mm) a) LVDT left LVDT R LVDT right LVDT A Load (kn) Displacement (mm) Figure Bending test. LVDTs measures b) TERC TUNNELLING ENGINEERING RESEARCH CENTRE University of Rome Tor Vergata

65 Doc: TR_BMUS_4D.docx TESTS ON Dramix 4D 80/60BG Date: 22/12/2014 Page: 25/31 5 POINT LOAD TEST: RESULTS The segment under the point load test is reported in Figure 5.1. F 1 F 2 Figure 5.1. Set up of the point load test The loading process is summarised in Figure 5.2 through the load time diagram. It is worth remarking that in this report the term load will refer to the single shoe. TERC TUNNELLING ENGINEERING RESEARCH CENTRE University of Rome Tor Vergata

66 Doc: TR_BMUS_4D.docx TESTS ON Dramix 4D 80/60BG Date: 22/12/2014 Page: 26/ F 1 =F Load (kn) Time (s) Figure 5.2. Load on the single shoe vs Time The displacements measured by the four potentiometer transducers (Figs. 3.6, 3.7) are plotted in Figure 5.3. The maximum measured displacement is about 0.48 mm P1 P2 P3 P Load (kn) Displacement (mm) Figure 5.3. Load displacement of the slabs (wire transducers) The first crack appeared for a load level of 1000 kn (for each steel pad) between the two shoes at the top and extrados surface (Fig. 5.4a). This spalling (splitting) crack propagates in the following steps through the extrados and intrados surfaces, as highlighted in Figures 5.4b, c, d and 5.7. Up to the load level of 1750 kn, the maximum crack width was lower than 0.05 mm. TERC TUNNELLING ENGINEERING RESEARCH CENTRE University of Rome Tor Vergata

67 Doc: TR_BMUS_4D.docx TESTS ON Dramix 4D 80/60BG Date: 22/12/2014 Page: 27/31 For a load level of about 2000 kn a bursting crack opens under the point load named F2 (see Figure 5.5a). This crack extended, in the following steps for a length of about 80 cm at the intrados surface and about 100 cm at the extrados side (Figs. 5.5b, 5.5c, 5.7). The maximum crack width measured with a crack gauge during the test was equal to about 0.35 mm (Fig. 5.5d). The maximum crack width at the end of the test, after the complete unloading, was about 0.05 mm (Fig. 5.6). a) b) c) Figure 5.4. a) First crack formation (F1=F2= 1000 kn); b) F1=F2=1150 kn; c) F1=F2= 1350; intrados, extrados faces; d) F1=F2=1750; intrados, extrados faces d) TERC TUNNELLING ENGINEERING RESEARCH CENTRE University of Rome Tor Vergata

68 Doc: TR_BMUS_4D.docx TESTS ON Dramix 4D 80/60BG Date: 22/12/2014 Page: 28/31 a) b) c) d) Figure 5.5. a) F1=F2= 2000 kn; bursting crack formation; b) F1=F2= 2500 kn; crack evolution, intrados surface; c) F1=F2= 2500 kn; crack evolution, extrados surface; ) F1=F2= 2500 kn; maximum crack width. TERC TUNNELLING ENGINEERING RESEARCH CENTRE University of Rome Tor Vergata

69 Doc: TR_BMUS_4D.docx TESTS ON Dramix 4D 80/60BG Date: 22/12/2014 Page: 29/31 Figure 5.6. Total unloading (end of the test); maximum crack width. The final crack pattern is summarised in Figure 5.7 and the crack widths measured during the test are reported in table kn 1750 kn 1150 kn 2000 kn 1350 kn 2250 kn 1500 kn 2500 kn Figure 5.7. Point load test; Crack pattern TERC TUNNELLING ENGINEERING RESEARCH CENTRE University of Rome Tor Vergata

70 Doc: TR_BMUS_4D.docx TESTS ON Dramix 4D 80/60BG Date: 22/12/2014 Page: 30/31 Table 5.1. Crack width Crack name (Fig. 5.7) Crack width [mm] 1000 [kn] 1150 [kn] 1350 [kn] 1500 [kn] 1750 [kn] 2000 [kn] 2250 [kn] 2500 [kn] 0 [kn] 1 <0.05 <0.05 < <0.05 <0.05 < < < <0.05 <0.05 <0.05 < < <0.05 < Finally, the crack width, measured by the LVDT placed between the steel pads (Fig. 3.6) is plotted versus the load (of the single pad) in Figure 5.8. It is worth remarking that two cracks pass through the instrument length Load (kn) Displacement (mm) Figure 5.8. Load displacement diagrams (LVDT measures) TERC TUNNELLING ENGINEERING RESEARCH CENTRE University of Rome Tor Vergata