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Precast segments under TBM hydraulic jacks: Experimental investigation on the local splitting behavior
Tunnelling and Underground Space Technology 50 (2015) 438–450
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Tunnelling and Underground Space Technology journal homepage: www.elsevier.com/locate/tust
Precast segments under TBM hydraulic jacks: Experimental investigation on the local splitting behavior Giuseppe Tiberti, Antonio Conforti ⇑, Giovanni A. Plizzari Department of Civil, Environmental, Architectural Engineering and Mathematics, University of Brescia, Italy
a r t i c l e
i n f o
Article history: Received 25 March 2015 Received in revised form 6 August 2015 Accepted 25 August 2015
Keywords: Thrust jack Splitting phenomena Fiber reinforced concrete Macro-synthetic fibers Fiber orientation
a b s t r a c t The design process of segmental concrete linings in ground conditions generally refers to standard load cases of de-molding, storage, embedded ground condition and grouting process. Nevertheless, the application of the Tunnel Boring Machine (TBM) thrust jack forces is a crucial temporary loading condition during construction, which may govern the design procedure as well as the other stages. Tunnel segments were traditionally reinforced with conventional rebars in order to resist the tensile stresses at both Serviceability (SLS) and Ultimate Limit States (ULS). In the two last decades, Fiber Reinforced Concrete (FRC) has been also used in several precast tunnel segments with or without conventional rebars. For structural purposes, steel fibers are generally used, even though some types of structural macro-synthetic fibers, which are able to impart significant toughness and ductility to concrete, have been recently introduced in the market. For these reasons, an experimental program aimed to investigate the local splitting behavior in the segment regions under the TBM hydraulic jacks was carried out at the University of Brescia. Tests on concrete prisms (with or without fibrous reinforcement) under Line Load (LL) or Point Load (PL) configurations were carried out in order to evaluate the beneficial effects of polypropylene (PP) fibers in controlling typical splitting cracks occurring under the jack loads, which represent one of the most severe loading conditions for tunnel segments. Experimental results show the feasibility of using polypropylene fibers in tunnel segments, since they significantly enhance both the splitting bearing capacity and the ductility. Fibers lead to a stable development of the splitting crack, which allows a redistribution of stresses after cracking. However, the effectiveness of fibers is influenced by the casting direction, which leads to a different fiber orientation. When the latter is favorable (fibers expected to be mainly transversal to the splitting crack) the bearing capacity is higher than in case of an unfavorable casting direction (fibers expected to be mainly parallel to the splitting crack). Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction The employment of Fiber Reinforced Concrete (FRC) in tunnel linings (Chiaia et al., 2009; Tiberti et al., 2014), with or without conventional rebars, has been rising in the two last decades, especially for precast tunnel segmental lining (Liao et al., 2015). Steel Fiber Reinforced Concrete (SFRC) is generally used for these applications even though there is a general growing interest in the scientific community on macro-synthetic fibers for use in structural applications (Conforti et al., 2015; Pujadas et al., 2014a). In fact, in the last decade, important research efforts have been devoted to the development of new types of polypropylene (PP) macro fibers able to enhance concrete toughness in order to make it
⇑ Corresponding author. E-mail addresses: [email protected] (G. Tiberti), [email protected] (A. Conforti), [email protected] (G.A. Plizzari). http://dx.doi.org/10.1016/j.tust.2015.08.013 0886-7798/Ó 2015 Elsevier Ltd. All rights reserved.
adequate for structural purposes (Buratti et al., 2011). Conforti et al. (2014, 2015) showed that these newly developed PP fibers can be used as shear reinforcement in both wide-shallow and deep beams. Pujadas et al. (2014a) demonstrated the feasibility of plastic fibers to be used as reinforcement (without rebars) in slabs under hyperstatic configuration. However, many other structural applications should be investigated, including precast tunnel segments. Referring to precast tunnel linings, it can be underlined that the final state, when the lining is loaded by the surrounding ground, does not represent the worst loading condition since the compressive normal ring force is prevalent and rather low shear forces and bending moments occur. In segmental lining there are several temporary loading conditions such as de-molding and stacking of segments as well as Tunnel Boring Machine (TBM) excavation process that should be carefully considered. In fact, during the lining construction process, after assembly a complete ring, the TBM moves
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Nomenclature a CMOD d fck fcm fctm fLm fR,jm h k
P Pmax Psplitting Rcm Vf
width of loading area crack mouth opening displacement square cross section side of specimens characteristic value of the cylindrical compressive concrete strength mean value of the cylindrical compressive concrete strength mean value of the tensile concrete strength mean value of the limit of proportionality mean value of the residual flexural tensile strength corresponding to CMOD = CMODj height of specimens factor defining the distribution of the transverse tensile stresses along the central line under the external applied load external applied load maximum load splitting crack load mean value of the cubic compressive concrete strength fiber volume fraction
forward by pushing its thrust jacks on the bearing pads of the latest assembled ring; therefore, high thrust jack forces are introduced in the back lining during the excavation process by means of the TBM cutter head. It is worthwhile noticing that the magnitude of these forces depends on several factors, such as the support of ground in front of the TBM, friction forces between ground and shield, cutting force at the front of the TBM (Rijke, 2006). In addition, the force exerted by each jack on the tunnel segment depends also by the numbers of adopted jacks as well as from their configuration (French, German or Japanese (Slenders, 2002)). Therefore, the adopted jack arrangement clearly influences the global segment behavior, which is also related to the stress concentration under the thrust shoes, i.e. local splitting behavior. In fact, the spreading of these forces into the segments leads to a disturbed region (D-region) that has to be carefully analyzed since transverse tensile stresses (defined as splitting or bursting stresses) occur perpendicular to the loading direction. For this reason, local rebars are usually placed in the aforementioned loading areas. Splitting cracks arise especially in areas with reduced segment thickness, as sections with bolt pockets. Most of these cracks will self-heal but larger cracks, which may cause leakage, will always remain. Although there is no danger for collapse, these leaking cracks have to be repaired (e.g. resin injections). Previous research works clearly evidenced the beneficial effects of FRC in presence of load concentrations and splitting phenomena (Schnütgen, 2003; Tiberti, 2014). Plizzari and Tiberti (2007) and Tiberti (2014) have demonstrated, by means of non-linear numerical simulations of tunnel segments, that fibrous reinforcement enables a progressive stable redistribution of splitting stresses, which guarantees the increase of the applied loads after cracking. The authors studied the effects of FRC in tunnel elements both in terms of local behavior (under the TBM thrust jacks) and global behavior of the tunnel segment (Plizzari and Tiberti, 2007; Tiberti, 2014). The latter can be generally investigated by means of advanced non-linear numerical simulations (Plizzari and Tiberti, 2007) or by means of full-scale tests (Caratelli et al., 2011). More recently, Bonalumi et al. (2014) developed full-scale tests on tunnel elements reinforced by polypropylene fibrous reinforcement and conventional rebars (hybrid solution). Nevertheless, there is a lack in literature concerning experimental tests on the
wmax wN,max wS,max wsplitting wN,splitting wS,splitting
rc,max rc,splitting rt rt,max
maximum crack opening (from H1) at Pmax for PL specimens maximum crack opening (from H1) at Pmax on north side for LL specimens maximum crack opening (from H1) at Pmax on south side for LL specimens maximum crack opening (from H1) at Psplitting for PL specimens crack opening (from H1) at Psplitting on north side for LL specimens crack opening (from H1) at Psplitting on south side for LL specimens maximum value of the compressive stress under the loading area value of the compressive stress under the loading area at Psplitting transverse tensile stresses (perpendicular to the loading direction) maximum transverse tensile stress
local segment behavior under high concentrated loads applied, especially for polypropylene fiber reinforced concrete (PFRC) elements. In conventional reinforced tunnel segments this local phenomenon is always taken into account in the design process by means of typical relationships suggested by recommendations for tunnel segments (A.F.T.E.S., 1999; ITA Official Report, 2000; Guglielmetti et al., 2007; DAUB, 2014). As far as FRC is concerned, in spite of its growing use in several tunnel projects (Liao et al., 2015), analytical or semi-empirical relationships are still not available for the prediction of the bearing capacity as well as the expected splitting crack width. In fact, even in the recent A.F.T.E. S. Recommendation (2013), which is specifically focused on the design of SFRC tunnel segments, it is suggested to demonstrate the effectiveness of fibrous reinforcement on the basis of representative tests, taking into account the design arrangements adopted and the procedures for installing FRC, which will determine how the fibers are aligned. Within this framework, the contribution of polypropylene fibrous reinforcement in controlling splitting phenomena was studied at the University of Brescia by means of a broad experimental program. Tests on concrete prisms (with or without fibrous reinforcement) were carried out by considering two different configurations of the applied loads. When using FRC structural elements, it is well known that fiber distribution and fiber orientation (with respect to the expected crack surface) in the concrete matrix considerably influence the structural response (Dupont and Vandewalle, 2005; Ferrara and Meda, 2006). The fiber orientation depends on several factors such as concrete pouring, the geometry of the formwork, the type of vibration and the production method. When steel fibers are used, relatively economic methods for measuring the average fiber orientation are already available (Ferrara et al., 2008; Grünewald, 2004; Laranjerira et al., 2011; Lataste et al., 2008); on the contrary, for PFRC, only few experiences are reported in literature (Pujadas et al., 2014b,c). In the research work presented herein, according to performance approach suggested by Model Code 2010 (2012a, b) (hereafter MC2010) which suggests to consider an adequate orientation factor, two different casting directions (in order to obtain a completely different fiber orientation) were considered for eval-
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uating the different splitting behavior in terms of bearing capacity and ductility. Since the two casting directions are at right angle, the results are expected to provide a wide range on experimental response. 2. Experimental program 2.1. Specimen geometries All experimental tests were carried out by using a prismatic specimen, 750 mm high, with a square cross section having a side (d) of 250 mm (Fig. 1). The latter value was chosen in order to reproduce the thickness of a tunnel segments having a small diameter (e.g. hydraulic tunnel). The chosen height (h) of the specimens was three times the length of the square side (h = 3d = 750 mm) in order to allow a possible redistribution of stresses along specimen height and thus to observe the splitting crack propagation. Moreover, note that no lifting hooks were provided in any specimens. In order to simulate the effects of TBM hydraulic jacks during thrust phase, two different loading configurations were considered: Line Load (LL) and Point Load (PL). LL configuration is characterized by a symmetrical axial load applied on a rectangular strip (Fig. 1a), which mainly leads to a two dimensional problem. In LL configuration, the loading strip was 100 mm wide (a) and 250 mm depth (d), leading to a ratio a/d equal to 0.4 (Fig. 1a). The latter was chosen in order to have the initial splitting crack well before the concrete-crushing failure under the loading strip, which allow to capture the beneficial
effects of fibers since the behavior is completely governed by splitting phenomenon. Moreover, this value of a/d is slightly smaller than the ones generally used in TBM applications (ranging from 0.45 to 0.80), as well as is similar to the one adopted by Schnütgen (2003), i.e. 0.43. PL configuration is subjected to central load which lead to a three dimensional distribution of stresses (Fig. 1b); therefore, PL is a more severe load condition than LL. The same ratio a/d adopted for LL tests was also used in PL configuration, leading to a square loading area of 100 100 mm. In both configurations, the sides of the specimens were identified by cardinal direction (North (N), South (S), West (W), East (E)), as shown in Fig. 1. The experimental program focused the attention on three parameters: loading configuration, material toughness and casting direction. The latter was studied in order to evaluate its influence on splitting bearing capacity and ductility; the casting direction mainly influences the fiber orientation in the structural element. Nine specimens were tested under LL configuration: three in Plain Concrete (PC), three in Polypropylene Fiber Reinforced Concrete made by Vertical casting (PFRC-V) and three in Polypropylene Fiber Reinforced Concrete made by Horizontal casting (PFRC-H). Vertical casting identifies a casting direction identical to loading direction, while horizontal casting identifies a casting direction perpendicular to loading direction (Fig. 2). PC specimens were tested in order to have reference samples. Similarly, nine specimens were tested under PL configuration: three in PC, three in PFRC-V and three in PFRC-H.
Fig. 1. Load configuration: LL (a); PL (b).
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Fig. 2. Specimen casting directions: vertical (a); horizontal (b).
Table 1 Load configuration and geometry characteristics of tested specimens. Specimen designation
Load configuration
Concrete
Casting direction
d (mm)
h (mm)
a (mm)
a/d (–)
LL-PC-1 LL-PC-2 LL-PC-3 LL-PFRC-V-1 LL-PFRC-V-2 LL-PFRC-V-3 LL-PFRC-H-1 LL-PFRC-H-2 LL-PFRC-H-3 PL-PC-1 PL-PC-2 PL-PC-3 PL-PFRC-V-1 PL-PFRC-V-2 PL-PFRC-V-3 PL-PFRC-H-1 PL-PFRC-H-2 PL-PFRC-H-3
Line load Line load Line load Line load Line load Line load Line load Line load Line load Point load Point load Point load Point load Point load Point load Point load Point load Point load
PC PC PC PFRC PFRC PFRC PFRC PFRC PFRC PC PC PC PFRC PFRC PFRC PFRC PFRC PFRC
Vertical Vertical Vertical Vertical Vertical Vertical Horizontal Horizontal Horizontal Vertical Vertical Vertical Vertical Vertical Vertical Horizontal Horizontal Horizontal
250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250
750 750 750 750 750 750 750 750 750 750 750 750 750 750 750 750 750 750
100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100
0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4
All LL and PL tested specimens are summarized in Table 1, in terms of specimen designation, materials, casting direction and main geometrical characteristics. As an example, the designation LL-PFRC-V-1 refers to a splitting sample #1 tested under LL configuration and made in PFRC by vertical casting. In the same way, PL-PFRC-H-2 refers to a splitting sample #2 tested under PL configuration made in PFRC by horizontal casting.
2.2. Materials As already underlined in Section 2.1, two concrete mixtures were used: Plain Concrete (PC) and Polypropylene Fiber Reinforced Concrete (PFRC). The target cylindrical average compressive strength at 28 days, for both PC and PFRC, was about 50 MPa, which is the compressive strength generally adopted in practice for precast tunnel linings. Each matrix was produced with a singular batch by using a planetary concrete mixer. According to Section 2.1, six specimens were made in PC, while twelve were
Table 2 Mix design of PC and PFRC.
Sand 0–4 (kg/m3) Coarse aggregate 4–16 (kg/m3) Maximum aggregate size (mm) Cement type Cement content (kg/m3) Water–cement ratio Super-plasticizer (% on cement content) PP fibers (kg/m3) PP fibers volume fraction (%) Concrete slump (mm)
PC
PFRC
1015 831 16 CEM II/A-LL 42.5R 360 0.50 0.7
1015 831 16 CEM II/A-LL 42.5R 360 0.50 1.2
0 0 200
10 1.10 180
made in PFRC. In any concrete batch nine cubes (150 mm side) were cast for measuring the compressive strength, while three and twelve small beams (150 150 550 mm) were prepared
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for the evaluation of PFRC residual flexural tensile strengths according to EN 14651 (2005), for PC and PFRC, respectively. The mixture proportions of both PC and PFRC are listed in Table 2. The concrete components were the same for both PC and PFRC, except the presence or not of PP fibers and the amount of super-plasticizer, which was 70% greater in PFRC. The water–cement ratio indicated in Table 2 refers to aggregates in saturatedsurface-dry condition. Both mixtures showed a good workability, with a slump of about 180–200 mm (S4 class according to EN 12350-2 (2009)). PFRC contains macro-synthetic PP fibers with a volume fraction (Vf) of 1.10% (10 kg/m3). This amount of fibers was chosen in order to obtain a PFRC with significant post-cracking residual strengths and able to fulfill the requirements of MC2010 for structural application. In particular, embossed PP fibers from a novel polymer resin technology were adopted. Fibers are 54 mm long, with an aspect ratio of 67, tensile strength of 585 MPa and an elastic modulus of 3200 MPa; Table 3 summarizes their main characteristics. Table 4 reports the mechanical properties of concrete: cubic (Rcm) and cylindrical (fcm) mean compressive strength; as mentioned above, nine 150 mm cubes were employed for the determination of Rcm (whose coefficient of variation (CV) is also provided in brackets, see Table 4). The cylindrical compressive strength was assumed as fcm = 0.83 Rcm. The mean value of the cylindrical compressive concrete strength resulted 57.2 MPa and 48.5 MPa for PC and PFRC specimens, respectively. Fig. 3 exhibits the nominal stress vs. CMOD (Crack Mouth Opening Displacement) curves from twelve PFRC and three PC notched small beams (150 150 550 mm), tested for the fracture characterization of concrete, according to EN 14651 (2005). The limit of proportionality (fLm) and the values of the average residual flexure tensile strengths (fR,1m, fR,2m, fR,3m, fR,4m, corresponding to CMOD values of 0.5, 1.5, 2.5 and 3.5 mm, respectively) and their CVs are listed in Table 4 as well. It can be noticed that PFRC exhibits a significant stable post-cracking response, characterized by an increment of about 55% of residual flexural tensile strength from a CMOD equal to 0.5 mm to 3.5 mm; the obtained fracture properties of PFRC fulfill the requirements of MC2010 (2012a,b) for use in structural elements. Moreover, evaluating the characteristic values of the residual flexural tensile strengths according to MC2010, PFRC can be classified as class ‘‘2e”.
2.3. Test set-up and instrumentation Fig. 4a shows the reaction frame system used for both LL and PL configuration. An electro-mechanical screw jack with a loading capacity of 1500 kN was used for all specimens. A displacementcontrolled test was adopted, allowing for a suitable test control during critical steps such as in the case of abrupt cracking phenomena or load drops. The displacement rate (for all specimens) was 0.02 mm/min and was kept constant during the tests up to failure. In the PL configuration, a displacement rate of 0.10 mm/min was used in the softening branch. The applied load was measured by a load cell with a capacity of 2000 kN.
Table 3 Characteristics of PP fibers adopted. Type Shape Length l (mm) Diameter Ø (mm) Aspect ratio l/Ø Minimum tensile strength (MPa) Elastic modulus (MPa) Density (kg/m3)
Polypropylene (PP) Embossed 54 0.81 67 585 3200 910
Table 4 Mechanical properties of PC and PFRC.
Rcm (MPa) fcm (MPa) fLm (MPa) fR,1m (MPa) fR,2m (MPa) fR,3m (MPa) fR,4m (MPa)
6 5
Nominal stress[MPa]
442
PC
PFRC
68.9 (0.04) 57.2 – – – – –
58.4 48.5 4.87 2.40 3.18 3.60 3.76
(0.02) (0.10) (0.17) (0.17) (0.16) (0.16)
Three Point Bending Test EN 14651, 2005
4 3 2 PC
1 0 0.0
PFRC
0.5
1.0
1.5
2.0
2.5
3.0
3.5
CMOD [mm] Fig. 3. PC and PFRC: nominal stress–CMOD curves according to EN 14651 (2005).
All specimens were capped by a thin bed of high strength mortar at top and bottom sides in order to have smooth, parallel and uniform bearing surfaces. Then, the specimens were properly aligned into the reaction frame system in order to avoid any eccentricity. The load was applied at the top surface of the specimens by means of a loading steel plate having sizes of 100 250 mm in LL specimens and 100 100 mm for PL specimens (Fig. 4). The friction between concrete and loading steel plate was reduced by means of a layer of polytetrafluoroethylene (PTFE), having a thickness of 2 mm. The specimens were placed on a square steel plate with a side length of 400 mm, properly leveled by a high strength mortar bed 20 mm thick. The friction between specimens and bottom steel plate was reduced by a PTFE film. Fig. 4b shows a LL specimen while Fig. 4c exhibits a PL sample. On the north and south sides of the LL specimens and in all four faces of PL samples, 50 mm grids were drawn to help in the identification of the crack pattern. Both linear variable differential transducers (LVDTs) and potentiometric transducers (PTs) were installed perpendicular to the loading direction, in order to measure the horizontal crack widths, as reported in Fig. 5. Based on the two-dimensional elastic solution of Iyengar (1962), the instrument H1 was placed where the maximum transverse tensile stress is theoretically reached, i.e. 0.4d = 100 mm. The other instruments (H2, H3, H4 and H5) were distributed along the specimen height in order to capture the propagation of the splitting crack. Therefore, in case of LL configuration (Fig. 5a), two LVDTs and three PTs were used on the two opposite sides of the specimen; for PL configuration, one LVDT and four PTs were used on all four sides of the specimen (Fig. 5b). In addition, in
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Fig. 4. Scheme of loading system (a) and picture of a specimen before testing: LL (b); PL (c).
case of both LL and PL, three LVDTs (V1, V2 and V3) were arranged at 120° around the specimen at the bottom of samples sides (B-region), in order to measure the vertical shortening of the specimen (Fig. 5).
3. Experimental results and discussion 3.1. Specimens under LL configuration All samples subjected to LL configuration showed a splitting failure. Table 5 summarizes all experimental results in terms of failure mode, splitting crack load (Psplitting), crack opening (from H1) at Psplitting on north side (wN,splitting), crack opening (from H1) at Psplitting on south side (wS,splitting), maximum load (Pmax), maximum crack opening (from H1) at Pmax on north side (wN,max), maximum crack opening (from H1) at Pmax on south side (wS,max) and ratio between Pmax and Psplitting. It should be observed that the crack opening measurement includes also the elastic deformation of concrete between the supports of the displacement transducer. Table 5 also reports the mean values as well as the standard deviations (SDs) and the coefficient of variations (CVs); it can be noticed that the latter are in general small, evidencing that the experimental results are consistent. PC samples failed when the principal tensile stress reached the tensile strength of concrete. In fact, PC specimens failed when the splitting crack occurred or shortly afterward (Psplitting = Pmax). The failure, which occurred at an average load of 1044 kN, was very brittle and without any prior warning of impending collapse. At failure the compressive stress under the loading steel plate was about 41 MPa, which is 30% smaller than the compressive strength of PC mixture (fcm = 57.2 MPa). It should be noticed that Psplitting
resulted greater for PC samples than PFRC ones, due to the higher mechanical properties of PC mixture (see Table 4). Concerning PFRC-V samples, it can be observed that PP fibers significantly enhanced the splitting bearing capacity (average Pmax/Psplitting = 1.41) and the ductility (average wmax/wsplitting = 5.70). The specimens failed well after the splitting cracking (Psplitting = 915 kN), reaching higher value of both maximum load and maximum crack opening, which ensures sufficient warning before failure. This is mainly due to the bridging effect of PP fibers, which lead to a stable crack development. The maximum compressive stress under the loading steel plate was about 51 MPa, which is 5% greater than the compressive strength of PFRC mixture (fcm = 48.5 MPa, Table 4), due probably to the lateral confinement that occurs in concrete under the loading steel plate (Iyengar, 1962; Leonhardt and Mönnig, 1973). Also in case of PFRC-H samples, characterized by an unfavorable fiber orientation for splitting cracks, PP fibers were able to enhance the splitting bearing capacity (Pmax/Psplitting = 1.18) and provide ductility (maximum crack opening comparable to PFRC-V specimens). However, these experimental results confirm that the casting direction, which changes the fiber orientation, significantly affects the splitting bearing capacity. On the contrary, the average splitting crack load of PFRC-H samples (Psplitting = 920 kN) was about the same of PFRC-V one, confirming that PP fiber orientation does not influence the tensile strength of concrete. In order to evaluate the reliability of the experimental results on LL specimens, the average splitting crack load (Psplitting) obtained for both PC and PFRC was compared against the prediction of the two-dimensional elastic solution proposed by Iyengar (1962), and well discussed in Leonhardt and Mönnig (1973). Based on this elastic solution, the transverse tensile stresses (rt), which occur in the disturbed region, are defined as:
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Fig. 5. Instrumentation details of: LL (a); PL (b).
Table 5 Main experimental results of LL tests. Specimen designation
Type of failure
Psplitting (kN)
wN,splitting (mm)
wS,splitting (mm)
Pmax (kN)
wN,max (mm)
wS,max (mm)
Pmax/Psplitting (–)
PC LL-PC-1 LL-PC-2 LL-PC-3 Mean SD CV
Splitting Splitting Splitting – – –
1152 1011 970 1044 95 0.09
0.289 0.121 0.179 0.196 0.085 0.43
0.124 0.129 0.101 0.118 0.015 0.13
1152 1011 970 1044 95 0.09
0.289 0.121 0.179 0.196 0.085 0.43
0.124 0.129 0.101 0.118 0.015 0.13
1.00 1.00 1.00 1.00 – –
PFRC-V LL-PFRC-V-1 LL-PFRC-V-2 LL-PFRC-V-3 Mean SD CV
Splitting Splitting Splitting – – –
1020 840 885 915 94 0.10
0.110 0.136 0.225 0.157 0.060 0.38
0.113 0.291 0.123 0.176 0.100 0.57
1439 1271 1160 1290 140 0.11
0.701 1.236 1.148 1.028 0.287 0.28
0.633 1.070 0.899 0.867 0.220 0.25
1.41 1.51 1.31 1.41 0.10 0.07
PFRC-H LL-PFRC-H-1 LL-PFRC-H-2 LL-PFRC-H-3 Mean SD CV
Splitting Splitting Splitting – – –
938 836 985 920 76 0.08
0.150 0.113 0.148 0.137 0.021 0.15
0.071 0.154 0.093 0.106 0.043 0.41
1072 1163 1022 1086 71 0.07
0.461 0.704 1.248 0.804 0.403 0.50
0.363 0.954 1.120 0.812 0.398 0.49
1.14 1.39 1.04 1.18 0.18 0.15
rt ¼ k P=d2
ð1Þ
where k is a factor defining the distribution of the transverse tensile stresses along the central line under the external applied load, P; d, as already underlined, is the side length of the square cross section of the sample. Considering a/d = 0.4 (as in the present experimental program), the maximum value of k, at which corresponds the
maximum transverse tensile stress (rt,max), resulted equal to 0.26 and it occurs at a distance of 0.4d from the sample top surface. Moreover, the splitting crack load in a concrete sample is reached when the maximum transverse tensile stress resulted equal to the tensile strength of concrete (fctm); the latter, both for PC and PFRC, can be evaluated by equation 5.1–3a of MC2010 (2012a,b):
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f ctm ¼ 0:3 f ck
ð2Þ
where fck is the characteristic compressive strength of concrete. The latter was calculated according to equation 5.1–1 of MC2010, subtracting, as a first approximation, 8 MPa to the mean value of the cylindrical compressive strength of PC and PFRC (see Table 4). Therefore, the tensile strength of concrete, evaluated by means of Eq. (2), resulted equal to 4.03 MPa and 3.53 MPa for PC and PFRC, respectively. Therefore, the splitting crack load of the tested specimens, having d = 250 mm, can be evaluated by the following equation: 2
Psplitting ¼ f ctm d =0:26
ð3Þ
The splitting crack load evaluated by means of Eq. (3) resulted equal to 970 kN for PC and 850 kN for PFRC; these values are just 7% smaller than the experimental ones (see Table 5), confirming the reliability of the LL experimental results. It is worthwhile noticing that the elastic solution, previously mentioned, is generally adopted by designers for evaluating the risk of cracking in tunnel elements during the TBM thrust phase. Moreover, in segments with conventional reinforcement, the proper bearing capacity is guaranteed by means of local stirrups placed under the TBM footplates. This local reinforcement is generally designed by means of simplified strut-and-tie model. From this point of view, the experimental tests have provided the maximum bearing capacity as well as the ductility exhibited by PFRC elements. Concerning the influence of casting direction on the splitting behavior, Figs. 6 and 7 report the load vs. crack-opening curves measured at south side (a) and load vs. crack-depth curve (b) for specimens LL-PFRC-V-3 and LL-PFRC-H-2, respectively. The splitting crack depth was evaluated from the sample top surface, considering both the horizontal instrumentation curves (a significant change in slope identifies the cracking) and the images that were captured continuously throughout the tests (10 s interval). The specimen LL-PFRC-V-3 showed a stable propagation of the splitting crack, with a continuous increase in bearing capacity, even after each crack development along the specimen height. In fact, the splitting crack developed in three steps up to 2d (500 mm), causing just a slightly decrease of slope of the load vs. crack opening curve (Fig. 6a). On the contrary, in specimen LL-PFRC-H-2, the splitting crack developed in two steps along the specimens, causing a plateau in the load vs. crack opening curves, at each crack propagation (Fig. 7a). Therefore, the samples having an unfavorable casting direction (and the consequent fiber orientation; PFRC-H) showed a splitting behavior more unstable and less controlled. The beneficial effects of PP fibers on the splitting behavior of specimen under LL configuration is well depicted also in Fig. 8a,
1800 Load 1600 [kN]
which shows the load vs. crack opening curves (from H1) for PC, PFRC-H and PFRC-V specimens; the low dispersion of the experimental results allowed to consider the mean values. The main aspects previously pointed out can be observed in Fig. 8a. In addition, it should be noticed that both PFRC-V and PFRC-H specimens, in spite of a very different splitting crack propagation, reached the maximum bearing capacity at a comparable maximum crack opening (i.e. 0.8–1.0 mm at H1 level – see also Table 5). However, after reaching the maximum load, a softening branch was observed in both PFRC-V and PFRC-H samples, even if PFRC-V exhibited much higher ductility. In fact, generally, PFRC-V samples reached an ultimate crack opening 65% larger than the one from PFRC-H specimens. Fig. 8b exhibits the load vs. splitting crack depth (from sample top surface) curve for PFRC-V and PFRC-H LL samples, showing the propagation of the splitting cracks along the specimen height. PP fibers provides a post-cracking residual tensile strength across the splitting crack, allowing the specimen the possibility to find a new stress distribution and equilibrium along the specimen height. Consequently, the splitting crack progressively increases in PFRC samples, as it is well evidenced in Fig. 8b. However, the development of the splitting crack clearly depends on the post-cracking toughness of FRC. In fact, in order to find a new equilibrated configuration, the specimen cast horizontally (PFRC-H, with an unfavorable fiber orientation) required a deeper splitting crack than PFRC-V samples. On the other hand, in PC samples a sudden increase of the splitting crack depth occurred due to the brittle post-cracking behavior of PC. This stress redistribution in FRC confirm the numerical results obtained by Plizzari and Tiberti (2007) and Tiberti (2014). Fig. 9 shows the final crack patterns of LL-PC-1, LL-PFRC-V-3 and LL-PFRC-H-2 specimens; these crack patterns clearly show the splitting failure, as well as the different propagation of the splitting crack. Fig. 9a clearly evidences, once again, the sudden and brittle failure occurred for PC samples, where the specimens were divided into two separate parts. Moreover, all specimens showed a single splitting crack at the center and the crack pattern on the north and south sides was very similar. Concerning possible practical implications, the experimental evidences confirmed that a high bearing capacity is achieved in presence of PP fibrous reinforcement, which means higher safety factor or the possibility of completely substituting or reducing the local splitting conventional reinforcement generally adopted. Nevertheless, no specific relationships are currently available for taking into account this contribution and consequently experimental tests on full-scale specimens are usually adopted (Caratelli
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Fig. 6. LL-PFRC-V-3: load vs. crack-opening curves measured at south side (a) and load vs. splitting crack depth curve (b).
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Fig. 7. LL-PFRC-H-2: load vs. crack-opening curves measured at south side (a) and load vs. splitting crack depth curve (b).
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Fig. 8. LL: mean experimental curves of load vs. H1 crack-opening for PC, PFRC-V and PFRC-H (a) and load vs. splitting crack depth curves for PFRC-V and PFRC-H (b).
Fig. 9. Final crack patterns of: LL-PC-1 (a); LL-PFRC-V-3 (b); LL-PFRC-H-2 (c).
et al., 2011). From this point of view, the LL configuration could be a possible simple method for evaluating the local splitting behavior of FRC. However, further experimental programs should be carried out in order to provide a simplified analytical method for the prediction of the splitting bearing capacity in case of FRCs.
3.2. Specimens under PL configuration Referring to PL tests, Table 6 lists the experimental results in terms of failure mode, splitting crack load (Psplitting), compressive stress under the loading steel plate at Psplitting (rc,splitting), maximum
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a b c
Specimen designation
Type of failure
Psplitting (kN)
rc,splitting (MPa)
wsplitting (mm)
Pmax (kN)
rc,max (MPa)
wmax (mm)
Pmax/Psplitting (–)
PC PL-PC-1 PL-PC-2 PL-PC-3 Mean SD CV
Splittinga Splittinga Splittinga – – –
950 949 931 943 11 0.01
95.0 94.9 93.1 94.3 1.1 0.01
0.380 (S) 0.196 (N) 0.252 (S) – – –
950 949 931 943 11 0.01
95.0 94.9 93.1 94.3 1.1 0.01
0.380 (S) 0.196 (N) 0.252 (S) – – –
1.00 1.00 1.00 1.00 – –
PFRC-V PL-PFRC-V-1 PL-PFRC-V-2 PL-PFRC-V-3 Mean SD CV
Splittingb Splittingb Splittingb – – –
822 811 742 792 43 0.05
82.2 81.1 74.2 79.2 4.3 0.05
0.073 (E) 0.088 (S) 0.066 (N) – – –
898 917 843 886 38 0.04
89.8 91.7 84.3 88.6 3.8 0.04
0.491 (E) 0.543 (N) 1.083 (W) – – –
1.09 1.13 1.14 1.12 0.02 0.02
PFRC-H PL-PFRC-H-1 PL-PFRC-H-2 PL-PFRC-H-3 Mean SD CV
Splittingc Splittingc Splittingc – – –
765 786 731 761 28 0.04
76.5 78.6 73.1 76.1 2.8 0.04
0.123 (W) 0.110 (S) 0.184 (W) – – –
805 834 765 801 35 0.04
80.5 83.4 76.5 80.1 3.5 0.04
0.268 (W) 0.276 (S) 0.324 (W) – – –
1.05 1.06 1.05 1.05 0.01 0.01
Uncontrolled loss of confinement after splitting. Progressive and stable loss of confinement after splitting. Loss of confinement after splitting.
crack opening (from H1) at Psplitting (wsplitting), maximum load (Pmax), maximum compressive stress under the steel plate at Pmax (rc,max), maximum crack opening (from H1) at Pmax (wmax) and ratio between Pmax and Psplitting. Mean values, SDs and CVs are also reported. All PC samples showed, also under PL configuration, a very brittle splitting failure (Psplitting = Pmax), which occurred, once again, when the principal tensile stress exceeded tensile concrete strength; this was observed at an average load of 943 kN. Contrarily to LL tests, failure occurred with a compressive concrete stress (under the loading steel plate) that was 65% higher than the compressive strength of PC mixture, i.e. 95 MPa. This can be explained by considering concrete confinement due to a triaxial state of compressive stress under the loading steel plate (Iyengar, 1962; Leonhardt and Mönnig, 1973). However, the uncontrolled loss of confinement at splitting cracking led the failure of PC samples under PL configuration to be even more explosive than in LL samples, as proved in the final crack pattern of sample PL-PC-2 shown in Fig. 10.
North
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Referring to PFRC-V samples, PP fibers were able to enhance the splitting bearing capacity of about 12%; this value is much smaller than the one obtained in case of LL test due to the loss of confinement after splitting (the compressive stress under the loading steel plate was about 80% higher than the compressive uniaxial strength of concrete). In fact, the splitting crack seemed to propagate into the compressive zone of the disturbed region, probably causing the loss of confinement. The maximum bearing capacity (Pmax) was reached at a H1 crack opening greater than the one measured at Psplitting. Afterwards, PP fibers lead to a progressive loss of confinement after splitting, with respect to PC samples. It is worth noticing that, as a consequence of the higher mechanical properties of PC matrix (see Table 4), also in PL tests Psplitting resulted smaller for PFRC samples as compared to PC ones. The same behavior of PFRC-V samples was observed in PFRC-H ones, even if the maximum splitting capacity was smaller and the post-cracking behavior was more unstable. In fact, the ratio Pmax/Psplitting resulted equal to 1.05 (Table 6) and only half of the
West
Fig. 10. Final crack pattern of sample PL-PC-2.
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South
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Fig. 13. Final crack pattern of sample PL-PFRC-V-1.
Table 7 Comparison between average splitting crack load of LL and PL samples. Designation
LL Psplitting (kN)
PL Psplitting (kN)
Psplitting,PL/Psplitting,LL (–)
PC PFRC-V PFRC-H
1044 915 920
943 792 761
0.90 0.87 0.83
crack opening at Pmax of PFRC-V samples was reached. PL experimental results confirms, once again, that casting direction significantly affects both the splitting behavior and the splitting bearing capacity. Moreover, according to experimental results on LL specimens, the average splitting crack load of PL-PFRC-H specimens resulted about the same of the one of PL-PFRC-V samples (i.e. 761 kN).
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North
South
West
East
Fig. 14. Final crack pattern of sample PL-PFRC-H-1.
Table 7 summarizes the average splitting crack load experimentally observed (Psplitting) in case of LL and PL tests, and their ratio (Psplitting,PL/Psplitting,LL); the latter resulted smaller than one, pointing out that the splitting crack load is of about 15% smaller in case of PL tests. This tendency is in accordance with the experimental results of Schnütgen (2003) and it is probably due to the more complicated stresses distribution which develops in PL configuration. Fig. 11a exhibits the comparison of all PL experimental tests, in which the experimental curves of load vs. crack-opening (H1) are shown in terms of mean values. Fig. 11b shows a zoom up to 3 mm of crack opening (H1); the aforementioned experimental observations can be clearly observed (in particular, the softening branch detected in both PFRC-V and PFRC-H samples as well as the sudden failure of PC samples). In order to better understand the different splitting crack propagation in PL specimens with different fiber orientation, Fig. 12 shows the load vs. crack opening (H1) curves up to 3 mm for PL-PFRC-V-1 and PL-PFRC-H-1 samples; in addition, Figs. 13 and 14 show their final crack patterns, respectively. In specimen PL-PFRC-V-1, the splitting crack occurred at a load of 822 kN (Psplitting) along a north–south plane. After that, the bridging effect of PP fibers allowed the increment of the external load up to 898 kN (Pmax), when a new splitting crack appeared also along a east–west plane. Eventually the loss of confinement led the sample in the softening branch. Therefore, the final crack pattern of PL-PFRC-V-1 is characterized by clear splitting cracks on all four sides. On the other hand, sample PL-PFRC-H-1 did not show splitting cracks on all four sides, but just on two opposite sides (north and south sides in Fig. 14). In fact, the smallest toughness of the PFRC, due to casting direction, did not allow a significantly increment of the bearing capacity after cracking, and thus the loss of confinement occurred before the appearance of the splitting crack also along the east–west plane. This different behavior between PFRCV and PFRC-H was observed in all samples underlining, once again, the significant influence of the casting direction on the splitting behavior of FRC elements. It is worthwhile noticing that the key role of concrete confinement under the loading steel plate probably not allowed a complete evaluation of fiber resistant contribution with respect to splitting phenomenon, as demonstrated by the not regular crack propagation along the specimen height on the two expected
cracking planes. Consequently, the PL configuration provides less practical information for designers compare to LL one. 4. Conclusions In the present paper the local splitting behavior in the segment regions under the Tunnel Boring Machine (TBM) hydraulic jacks was investigated by means of experimental tests on prismatic specimens under Line Load (LL) and Point Load (PL) configurations. Tests were carried out on twelve samples in polypropylene fiber reinforced concrete (PFRC) as well as on six reference specimens made of plain concrete (PC). The effect of the casting direction in PFRC specimens, that influences fiber orientation, was also investigated. Based on this experimental study, the following conclusion can be drawn: (1) Splitting failure of plain concrete samples is very brittle. (2) The presence of fibers lead to an enhancement of both splitting bearing capacity and ductility by means of a progressively increase of splitting crack length, which probably allows the elements to find a new stress distribution along the specimen height in equilibrium to the external load (stress redistribution). (3) A total amount of 10 kg/m3 (volume fraction Vf = 1.10%) of macro-synthetic polypropylene fibers significantly enhance the splitting behavior and the bearing capacity of a concrete prism (up to +40%), as well as the specimen ductility; this aspect was especially underlined in LL tests. Therefore, PFRC can be successfully used in concrete tunnel segments since it guarantees a higher bearing capacity and stable development of splitting cracks. (4) The casting direction of structural elements influences the splitting development and the bearing capacity of the specimens, since it leads to a different fiber orientation. When the latter is favorable (with fibers expected to be mainly transversal to loading direction and to the splitting crack), the LL bearing capacity increased of about 40% while, with an unfavorable casting direction (with fibers expected to be mainly parallel to the splitting crack), the LL bearing capacity increased of about 18%. (5) The splitting crack starts developing slightly earlier in PL configuration with respect to LL.
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Acknowledgements The Authors are grateful to BASF Construction Chemicals Italy for the financial support; a special acknowledgement goes to Dr. Emmanuel Attiogbe and to Dr. Sandro Moro. Finally, the help from Engineers Bernardelli Vincenzo and Uberti Aurelio, as well as from the technicians Luca Martinelli, Augusto Botturi, Domenico Caravaggi and Andrea Delbarba, for the assistance in performing the experimental program, is gratefully acknowledged. References Bonalumi, P., Di Prisco, M., Meda, A., 2014. Indagine sperimentale su conci di tunnel in calcestruzzo fibrorinforzato con macro-fibre polimeriche. Atti del 20°convegno CTE, Collegio Tecnici dell’Edilizia, pp. 367–378 (in Italian). Buratti, N., Mazzotti, C., Savoia, M., 2011. Post-cracking behaviour of steel and macro-synthetic fibre-reinforced concretes. Constr. Build. Mater. 25, 2713– 2722. Caratelli, A., Meda, A., Rinaldi, Z., Romualdi, P., 2011. Structural behaviour of precast tunnel segments in fiber reinforced concrete. Tunn. Undergr. Space Technol. 26, 284–291. http://dx.doi.org/10.1016/j.tust.2010.10.003. Chiaia, B., Fantilli, A.P., Vallini, P., 2009. Combining fiber-reinforced concrete with traditional reinforcement in tunnel linings. Eng. Struct. 31 (7), 1600–1606. Conforti, A., Minelli, F., Tinini, A., Plizzari, G.A., Moro, S., 2014. Structural applicability of polypropylene fibres: deep and wide-shallow beams subjected to shear. In: FRC 2014 Joint ACI-fib International Workshop, Montreal, Canada, pp. 341–356. Conforti, A., Minelli, F., Tinini, A., Plizzari, G.A., 2015. Influence of polypropylene fibre reinforcement and width-to-effective depth ratio in wide-shallow beams. Eng. Struct. 88, 12–21. http://dx.doi.org/10.1016/j.engstruct.2015.01.037, ISSN 0141-0296. Dupont, D., Vandewalle, L., 2005. Distribution of steel fibres in rectangular sections. Cem. Concr. Compos. 27, 391–398. EN 12350-2, 2009. Testing Fresh Concrete – Part 2: Slump-Test. EN 14651, 2005. Precast Concrete Products – Test Method for Metallic Fibre Concrete – Measuring the Flexural Tensile Strength. European Standard. Ferrara, L., Meda, A., 2006. Relationships between fibre distribution, workability and the mechanical properties of SFRC applied to precast roof elements. Mater. Struct. 39 (4), 411–420. Ferrara, L., Park, Y., Shah, S.P., 2008. Correlation among fresh state behavior, fiber dispersion and toughness properties of SFRCs. J. Mater. Civ. Eng. 20 (7), 493–501. fib Bulletin 65, 2012a. ‘‘Model Code 2010 – Final Draft”, vol. 1, 350 p (ISBN 978-288394-105-2). fib Bulletin 66, 2012b. Model Code 2010 – Final Draft”, vol. 2, 370 p (ISBN 978-288394-106-9). Grünewald, S., 2004. Performance-based Design of Self-compacting Fibre Reinforced Concrete. PhD Thesis, Delft University of Technology, Delft University Press (ISBN 90-407-2487-3). Guglielmetti, V., Grasso, P., Mahtab, A., Xu, S., 2007. Mechanized tunneling in urban areas: design methodology and construction control. CRC Press, Taylor & Francis Group, p. 507, ISBN 9780415420105. Iyengar, K.T.S.R., 1962. Two-dimensional theories in anchorage zone stresses in post tensioned prestressed beams. J. Am. Concr. Inst. 59 (10), 1443–1446.
ITA, International Tunneling Association, Official Report, 2000. Guidelines for the design of shield tunnel lining. Tunnel. Undergr. Space Technol. 15 (3), 303–331. Laranjerira, F., Grünewald, S., Walraven, J., Blom, C., Molins, C., Aguado, A., 2011. Characterization of the orientation profile of steel fiber reinforced concrete. Mater. Struct. 44 (6), 1093–1111. Lataste, J.F., Behloul, M., Breysse, D., 2008. Characterisation of fibres distribution in a steel fibre reinforced concrete with electrical resistivity measurements. NDT&E Int. 41, 638–647. Leonhardt, F., Mönnig, E., 1973. Vorlesungen uber Massivbau. Springer, Berlin (Italian version: Leonhardt F, Mönnig E (1986) Casi speciali di dimensionamento nlle costruzioni in c.a. e c.a.p., vol. 2, Edizioni di Scienza e Tecnica, Milano). Liao, L., De la Fuente, A., Cavalaro, S., Aguado, A., 2015. Design of FRC tunnel segments considering the ductility requirements of the Model Code 2010. Tunn. Undergr. Space Technol. 47, 200–210. Plizzari, G.A., Tiberti, G., 2007. Structural behaviour of SFRC tunnel segments. In: Proceedings of the 6th International Conference on Fracture Mechanics of Concrete and Concrete Structures (FraMCos), vol. 3, pp. 1577–1584 (ISBN 9780-415-44066-0). Pujadas, P., Blanco, A., Cavalaro, S.H.P., Aguado, A., 2014a. Plastic fibres as the only reinforcement for flat suspended slabs: experimental investigation and numerical simulation. Constr. Build. Mater. 57, 92–104. Pujadas, P., Blanco, A., Cavalaro, S.H.P., De la Fuente, A., Aguado, A., 2014b. Multidirectional double punch test to assess the post-cracking behaviour and fibre orientation. Constr. Build. Mater. 58, 214–224. Pujadas, P., Blanco, A., Cavalaro, S.H.P., De la Fuente, A., Aguado, A., 2014c. Fibre distribution in macro-plastic fibre reinforced concrete slab-panels. Constr. Build. Mater. 64, 496–503. Recommendations of A.F.T.E.S., 1999. Recommendations for Design, Sizing, and Construction of Precast Segments Installed at the Rear of Tunnel Boring Machine. English Version. Recommendations of A.F.T.E.S. n.GT38R1A1, 2013. Design, dimensioning and execution of precast steel fibre reinforced concrete arch segments. Tunn. espace souterrain 238, 312–324. Recommendations of DAUB, 2014. Recommendations for the Design, Production and Installation of Segmental Rings. DAUB (German Tunneling Committee) Working Group ‘‘Lining Segment Design”. English Version. Rijke, Q.C. de, 2006. Innovation of Stress and Damage Reduction in Bored Tunnels during Construction Based on a Shield Equilibrium Model. Graduate Thesis, Utrecht, Delft University of Technology and Holland Railconsult. Schnütgen, B., 2003. Design of precast steel fiber reinforced tunnel elements. In: Proceedings of the RILEM TC 162-TDF Workshop, Test and Design Methods for Steel Fiber Reinforced Concrete – Background and Experiences, Bochum, Germany, pp. 145–152. Slenders, B.M.A., 2002. Modellering van boortunnels. Thesis, Delft University of Technology and Projectorganisatie HSL-Zuid, Utrecht (Dutch). Tiberti, G., 2014. Concrete tunnel segments with combined traditional and fiber reinforcement: optimization of the structural behavior and design aspects. Ph. D. Thesis, Department of Civil, Environmental, Architectural Engineering and Mathematics, University of Brescia, ISBN 978-88–548-7005-5, Aracne editrice s. r.l., Roma, Italy, 396 p. Tiberti, G., Minelli, F., Plizzari, G.A., 2014. Reinforcement optimization of fiber reinforced concrete linings for conventional tunnels. Compos. Part B: Eng. 58, 199–207. http://dx.doi.org/10.1016/j.compositesb.2013.10.012, ISSN: 13598368.
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Tunnelling and Underground Space Technology journal homepage: www.elsevier.com/locate/tust
Precast segments under TBM hydraulic jacks: Experimental investigation on the local splitting behavior Giuseppe Tiberti, Antonio Conforti ⇑, Giovanni A. Plizzari Department of Civil, Environmental, Architectural Engineering and Mathematics, University of Brescia, Italy
a r t i c l e
i n f o
Article history: Received 25 March 2015 Received in revised form 6 August 2015 Accepted 25 August 2015
Keywords: Thrust jack Splitting phenomena Fiber reinforced concrete Macro-synthetic fibers Fiber orientation
a b s t r a c t The design process of segmental concrete linings in ground conditions generally refers to standard load cases of de-molding, storage, embedded ground condition and grouting process. Nevertheless, the application of the Tunnel Boring Machine (TBM) thrust jack forces is a crucial temporary loading condition during construction, which may govern the design procedure as well as the other stages. Tunnel segments were traditionally reinforced with conventional rebars in order to resist the tensile stresses at both Serviceability (SLS) and Ultimate Limit States (ULS). In the two last decades, Fiber Reinforced Concrete (FRC) has been also used in several precast tunnel segments with or without conventional rebars. For structural purposes, steel fibers are generally used, even though some types of structural macro-synthetic fibers, which are able to impart significant toughness and ductility to concrete, have been recently introduced in the market. For these reasons, an experimental program aimed to investigate the local splitting behavior in the segment regions under the TBM hydraulic jacks was carried out at the University of Brescia. Tests on concrete prisms (with or without fibrous reinforcement) under Line Load (LL) or Point Load (PL) configurations were carried out in order to evaluate the beneficial effects of polypropylene (PP) fibers in controlling typical splitting cracks occurring under the jack loads, which represent one of the most severe loading conditions for tunnel segments. Experimental results show the feasibility of using polypropylene fibers in tunnel segments, since they significantly enhance both the splitting bearing capacity and the ductility. Fibers lead to a stable development of the splitting crack, which allows a redistribution of stresses after cracking. However, the effectiveness of fibers is influenced by the casting direction, which leads to a different fiber orientation. When the latter is favorable (fibers expected to be mainly transversal to the splitting crack) the bearing capacity is higher than in case of an unfavorable casting direction (fibers expected to be mainly parallel to the splitting crack). Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction The employment of Fiber Reinforced Concrete (FRC) in tunnel linings (Chiaia et al., 2009; Tiberti et al., 2014), with or without conventional rebars, has been rising in the two last decades, especially for precast tunnel segmental lining (Liao et al., 2015). Steel Fiber Reinforced Concrete (SFRC) is generally used for these applications even though there is a general growing interest in the scientific community on macro-synthetic fibers for use in structural applications (Conforti et al., 2015; Pujadas et al., 2014a). In fact, in the last decade, important research efforts have been devoted to the development of new types of polypropylene (PP) macro fibers able to enhance concrete toughness in order to make it
⇑ Corresponding author. E-mail addresses: [email protected] (G. Tiberti), [email protected] (A. Conforti), [email protected] (G.A. Plizzari). http://dx.doi.org/10.1016/j.tust.2015.08.013 0886-7798/Ó 2015 Elsevier Ltd. All rights reserved.
adequate for structural purposes (Buratti et al., 2011). Conforti et al. (2014, 2015) showed that these newly developed PP fibers can be used as shear reinforcement in both wide-shallow and deep beams. Pujadas et al. (2014a) demonstrated the feasibility of plastic fibers to be used as reinforcement (without rebars) in slabs under hyperstatic configuration. However, many other structural applications should be investigated, including precast tunnel segments. Referring to precast tunnel linings, it can be underlined that the final state, when the lining is loaded by the surrounding ground, does not represent the worst loading condition since the compressive normal ring force is prevalent and rather low shear forces and bending moments occur. In segmental lining there are several temporary loading conditions such as de-molding and stacking of segments as well as Tunnel Boring Machine (TBM) excavation process that should be carefully considered. In fact, during the lining construction process, after assembly a complete ring, the TBM moves
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Nomenclature a CMOD d fck fcm fctm fLm fR,jm h k
P Pmax Psplitting Rcm Vf
width of loading area crack mouth opening displacement square cross section side of specimens characteristic value of the cylindrical compressive concrete strength mean value of the cylindrical compressive concrete strength mean value of the tensile concrete strength mean value of the limit of proportionality mean value of the residual flexural tensile strength corresponding to CMOD = CMODj height of specimens factor defining the distribution of the transverse tensile stresses along the central line under the external applied load external applied load maximum load splitting crack load mean value of the cubic compressive concrete strength fiber volume fraction
forward by pushing its thrust jacks on the bearing pads of the latest assembled ring; therefore, high thrust jack forces are introduced in the back lining during the excavation process by means of the TBM cutter head. It is worthwhile noticing that the magnitude of these forces depends on several factors, such as the support of ground in front of the TBM, friction forces between ground and shield, cutting force at the front of the TBM (Rijke, 2006). In addition, the force exerted by each jack on the tunnel segment depends also by the numbers of adopted jacks as well as from their configuration (French, German or Japanese (Slenders, 2002)). Therefore, the adopted jack arrangement clearly influences the global segment behavior, which is also related to the stress concentration under the thrust shoes, i.e. local splitting behavior. In fact, the spreading of these forces into the segments leads to a disturbed region (D-region) that has to be carefully analyzed since transverse tensile stresses (defined as splitting or bursting stresses) occur perpendicular to the loading direction. For this reason, local rebars are usually placed in the aforementioned loading areas. Splitting cracks arise especially in areas with reduced segment thickness, as sections with bolt pockets. Most of these cracks will self-heal but larger cracks, which may cause leakage, will always remain. Although there is no danger for collapse, these leaking cracks have to be repaired (e.g. resin injections). Previous research works clearly evidenced the beneficial effects of FRC in presence of load concentrations and splitting phenomena (Schnütgen, 2003; Tiberti, 2014). Plizzari and Tiberti (2007) and Tiberti (2014) have demonstrated, by means of non-linear numerical simulations of tunnel segments, that fibrous reinforcement enables a progressive stable redistribution of splitting stresses, which guarantees the increase of the applied loads after cracking. The authors studied the effects of FRC in tunnel elements both in terms of local behavior (under the TBM thrust jacks) and global behavior of the tunnel segment (Plizzari and Tiberti, 2007; Tiberti, 2014). The latter can be generally investigated by means of advanced non-linear numerical simulations (Plizzari and Tiberti, 2007) or by means of full-scale tests (Caratelli et al., 2011). More recently, Bonalumi et al. (2014) developed full-scale tests on tunnel elements reinforced by polypropylene fibrous reinforcement and conventional rebars (hybrid solution). Nevertheless, there is a lack in literature concerning experimental tests on the
wmax wN,max wS,max wsplitting wN,splitting wS,splitting
rc,max rc,splitting rt rt,max
maximum crack opening (from H1) at Pmax for PL specimens maximum crack opening (from H1) at Pmax on north side for LL specimens maximum crack opening (from H1) at Pmax on south side for LL specimens maximum crack opening (from H1) at Psplitting for PL specimens crack opening (from H1) at Psplitting on north side for LL specimens crack opening (from H1) at Psplitting on south side for LL specimens maximum value of the compressive stress under the loading area value of the compressive stress under the loading area at Psplitting transverse tensile stresses (perpendicular to the loading direction) maximum transverse tensile stress
local segment behavior under high concentrated loads applied, especially for polypropylene fiber reinforced concrete (PFRC) elements. In conventional reinforced tunnel segments this local phenomenon is always taken into account in the design process by means of typical relationships suggested by recommendations for tunnel segments (A.F.T.E.S., 1999; ITA Official Report, 2000; Guglielmetti et al., 2007; DAUB, 2014). As far as FRC is concerned, in spite of its growing use in several tunnel projects (Liao et al., 2015), analytical or semi-empirical relationships are still not available for the prediction of the bearing capacity as well as the expected splitting crack width. In fact, even in the recent A.F.T.E. S. Recommendation (2013), which is specifically focused on the design of SFRC tunnel segments, it is suggested to demonstrate the effectiveness of fibrous reinforcement on the basis of representative tests, taking into account the design arrangements adopted and the procedures for installing FRC, which will determine how the fibers are aligned. Within this framework, the contribution of polypropylene fibrous reinforcement in controlling splitting phenomena was studied at the University of Brescia by means of a broad experimental program. Tests on concrete prisms (with or without fibrous reinforcement) were carried out by considering two different configurations of the applied loads. When using FRC structural elements, it is well known that fiber distribution and fiber orientation (with respect to the expected crack surface) in the concrete matrix considerably influence the structural response (Dupont and Vandewalle, 2005; Ferrara and Meda, 2006). The fiber orientation depends on several factors such as concrete pouring, the geometry of the formwork, the type of vibration and the production method. When steel fibers are used, relatively economic methods for measuring the average fiber orientation are already available (Ferrara et al., 2008; Grünewald, 2004; Laranjerira et al., 2011; Lataste et al., 2008); on the contrary, for PFRC, only few experiences are reported in literature (Pujadas et al., 2014b,c). In the research work presented herein, according to performance approach suggested by Model Code 2010 (2012a, b) (hereafter MC2010) which suggests to consider an adequate orientation factor, two different casting directions (in order to obtain a completely different fiber orientation) were considered for eval-
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uating the different splitting behavior in terms of bearing capacity and ductility. Since the two casting directions are at right angle, the results are expected to provide a wide range on experimental response. 2. Experimental program 2.1. Specimen geometries All experimental tests were carried out by using a prismatic specimen, 750 mm high, with a square cross section having a side (d) of 250 mm (Fig. 1). The latter value was chosen in order to reproduce the thickness of a tunnel segments having a small diameter (e.g. hydraulic tunnel). The chosen height (h) of the specimens was three times the length of the square side (h = 3d = 750 mm) in order to allow a possible redistribution of stresses along specimen height and thus to observe the splitting crack propagation. Moreover, note that no lifting hooks were provided in any specimens. In order to simulate the effects of TBM hydraulic jacks during thrust phase, two different loading configurations were considered: Line Load (LL) and Point Load (PL). LL configuration is characterized by a symmetrical axial load applied on a rectangular strip (Fig. 1a), which mainly leads to a two dimensional problem. In LL configuration, the loading strip was 100 mm wide (a) and 250 mm depth (d), leading to a ratio a/d equal to 0.4 (Fig. 1a). The latter was chosen in order to have the initial splitting crack well before the concrete-crushing failure under the loading strip, which allow to capture the beneficial
effects of fibers since the behavior is completely governed by splitting phenomenon. Moreover, this value of a/d is slightly smaller than the ones generally used in TBM applications (ranging from 0.45 to 0.80), as well as is similar to the one adopted by Schnütgen (2003), i.e. 0.43. PL configuration is subjected to central load which lead to a three dimensional distribution of stresses (Fig. 1b); therefore, PL is a more severe load condition than LL. The same ratio a/d adopted for LL tests was also used in PL configuration, leading to a square loading area of 100 100 mm. In both configurations, the sides of the specimens were identified by cardinal direction (North (N), South (S), West (W), East (E)), as shown in Fig. 1. The experimental program focused the attention on three parameters: loading configuration, material toughness and casting direction. The latter was studied in order to evaluate its influence on splitting bearing capacity and ductility; the casting direction mainly influences the fiber orientation in the structural element. Nine specimens were tested under LL configuration: three in Plain Concrete (PC), three in Polypropylene Fiber Reinforced Concrete made by Vertical casting (PFRC-V) and three in Polypropylene Fiber Reinforced Concrete made by Horizontal casting (PFRC-H). Vertical casting identifies a casting direction identical to loading direction, while horizontal casting identifies a casting direction perpendicular to loading direction (Fig. 2). PC specimens were tested in order to have reference samples. Similarly, nine specimens were tested under PL configuration: three in PC, three in PFRC-V and three in PFRC-H.
Fig. 1. Load configuration: LL (a); PL (b).
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Fig. 2. Specimen casting directions: vertical (a); horizontal (b).
Table 1 Load configuration and geometry characteristics of tested specimens. Specimen designation
Load configuration
Concrete
Casting direction
d (mm)
h (mm)
a (mm)
a/d (–)
LL-PC-1 LL-PC-2 LL-PC-3 LL-PFRC-V-1 LL-PFRC-V-2 LL-PFRC-V-3 LL-PFRC-H-1 LL-PFRC-H-2 LL-PFRC-H-3 PL-PC-1 PL-PC-2 PL-PC-3 PL-PFRC-V-1 PL-PFRC-V-2 PL-PFRC-V-3 PL-PFRC-H-1 PL-PFRC-H-2 PL-PFRC-H-3
Line load Line load Line load Line load Line load Line load Line load Line load Line load Point load Point load Point load Point load Point load Point load Point load Point load Point load
PC PC PC PFRC PFRC PFRC PFRC PFRC PFRC PC PC PC PFRC PFRC PFRC PFRC PFRC PFRC
Vertical Vertical Vertical Vertical Vertical Vertical Horizontal Horizontal Horizontal Vertical Vertical Vertical Vertical Vertical Vertical Horizontal Horizontal Horizontal
250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250
750 750 750 750 750 750 750 750 750 750 750 750 750 750 750 750 750 750
100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100
0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4
All LL and PL tested specimens are summarized in Table 1, in terms of specimen designation, materials, casting direction and main geometrical characteristics. As an example, the designation LL-PFRC-V-1 refers to a splitting sample #1 tested under LL configuration and made in PFRC by vertical casting. In the same way, PL-PFRC-H-2 refers to a splitting sample #2 tested under PL configuration made in PFRC by horizontal casting.
2.2. Materials As already underlined in Section 2.1, two concrete mixtures were used: Plain Concrete (PC) and Polypropylene Fiber Reinforced Concrete (PFRC). The target cylindrical average compressive strength at 28 days, for both PC and PFRC, was about 50 MPa, which is the compressive strength generally adopted in practice for precast tunnel linings. Each matrix was produced with a singular batch by using a planetary concrete mixer. According to Section 2.1, six specimens were made in PC, while twelve were
Table 2 Mix design of PC and PFRC.
Sand 0–4 (kg/m3) Coarse aggregate 4–16 (kg/m3) Maximum aggregate size (mm) Cement type Cement content (kg/m3) Water–cement ratio Super-plasticizer (% on cement content) PP fibers (kg/m3) PP fibers volume fraction (%) Concrete slump (mm)
PC
PFRC
1015 831 16 CEM II/A-LL 42.5R 360 0.50 0.7
1015 831 16 CEM II/A-LL 42.5R 360 0.50 1.2
0 0 200
10 1.10 180
made in PFRC. In any concrete batch nine cubes (150 mm side) were cast for measuring the compressive strength, while three and twelve small beams (150 150 550 mm) were prepared
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for the evaluation of PFRC residual flexural tensile strengths according to EN 14651 (2005), for PC and PFRC, respectively. The mixture proportions of both PC and PFRC are listed in Table 2. The concrete components were the same for both PC and PFRC, except the presence or not of PP fibers and the amount of super-plasticizer, which was 70% greater in PFRC. The water–cement ratio indicated in Table 2 refers to aggregates in saturatedsurface-dry condition. Both mixtures showed a good workability, with a slump of about 180–200 mm (S4 class according to EN 12350-2 (2009)). PFRC contains macro-synthetic PP fibers with a volume fraction (Vf) of 1.10% (10 kg/m3). This amount of fibers was chosen in order to obtain a PFRC with significant post-cracking residual strengths and able to fulfill the requirements of MC2010 for structural application. In particular, embossed PP fibers from a novel polymer resin technology were adopted. Fibers are 54 mm long, with an aspect ratio of 67, tensile strength of 585 MPa and an elastic modulus of 3200 MPa; Table 3 summarizes their main characteristics. Table 4 reports the mechanical properties of concrete: cubic (Rcm) and cylindrical (fcm) mean compressive strength; as mentioned above, nine 150 mm cubes were employed for the determination of Rcm (whose coefficient of variation (CV) is also provided in brackets, see Table 4). The cylindrical compressive strength was assumed as fcm = 0.83 Rcm. The mean value of the cylindrical compressive concrete strength resulted 57.2 MPa and 48.5 MPa for PC and PFRC specimens, respectively. Fig. 3 exhibits the nominal stress vs. CMOD (Crack Mouth Opening Displacement) curves from twelve PFRC and three PC notched small beams (150 150 550 mm), tested for the fracture characterization of concrete, according to EN 14651 (2005). The limit of proportionality (fLm) and the values of the average residual flexure tensile strengths (fR,1m, fR,2m, fR,3m, fR,4m, corresponding to CMOD values of 0.5, 1.5, 2.5 and 3.5 mm, respectively) and their CVs are listed in Table 4 as well. It can be noticed that PFRC exhibits a significant stable post-cracking response, characterized by an increment of about 55% of residual flexural tensile strength from a CMOD equal to 0.5 mm to 3.5 mm; the obtained fracture properties of PFRC fulfill the requirements of MC2010 (2012a,b) for use in structural elements. Moreover, evaluating the characteristic values of the residual flexural tensile strengths according to MC2010, PFRC can be classified as class ‘‘2e”.
2.3. Test set-up and instrumentation Fig. 4a shows the reaction frame system used for both LL and PL configuration. An electro-mechanical screw jack with a loading capacity of 1500 kN was used for all specimens. A displacementcontrolled test was adopted, allowing for a suitable test control during critical steps such as in the case of abrupt cracking phenomena or load drops. The displacement rate (for all specimens) was 0.02 mm/min and was kept constant during the tests up to failure. In the PL configuration, a displacement rate of 0.10 mm/min was used in the softening branch. The applied load was measured by a load cell with a capacity of 2000 kN.
Table 3 Characteristics of PP fibers adopted. Type Shape Length l (mm) Diameter Ø (mm) Aspect ratio l/Ø Minimum tensile strength (MPa) Elastic modulus (MPa) Density (kg/m3)
Polypropylene (PP) Embossed 54 0.81 67 585 3200 910
Table 4 Mechanical properties of PC and PFRC.
Rcm (MPa) fcm (MPa) fLm (MPa) fR,1m (MPa) fR,2m (MPa) fR,3m (MPa) fR,4m (MPa)
6 5
Nominal stress[MPa]
442
PC
PFRC
68.9 (0.04) 57.2 – – – – –
58.4 48.5 4.87 2.40 3.18 3.60 3.76
(0.02) (0.10) (0.17) (0.17) (0.16) (0.16)
Three Point Bending Test EN 14651, 2005
4 3 2 PC
1 0 0.0
PFRC
0.5
1.0
1.5
2.0
2.5
3.0
3.5
CMOD [mm] Fig. 3. PC and PFRC: nominal stress–CMOD curves according to EN 14651 (2005).
All specimens were capped by a thin bed of high strength mortar at top and bottom sides in order to have smooth, parallel and uniform bearing surfaces. Then, the specimens were properly aligned into the reaction frame system in order to avoid any eccentricity. The load was applied at the top surface of the specimens by means of a loading steel plate having sizes of 100 250 mm in LL specimens and 100 100 mm for PL specimens (Fig. 4). The friction between concrete and loading steel plate was reduced by means of a layer of polytetrafluoroethylene (PTFE), having a thickness of 2 mm. The specimens were placed on a square steel plate with a side length of 400 mm, properly leveled by a high strength mortar bed 20 mm thick. The friction between specimens and bottom steel plate was reduced by a PTFE film. Fig. 4b shows a LL specimen while Fig. 4c exhibits a PL sample. On the north and south sides of the LL specimens and in all four faces of PL samples, 50 mm grids were drawn to help in the identification of the crack pattern. Both linear variable differential transducers (LVDTs) and potentiometric transducers (PTs) were installed perpendicular to the loading direction, in order to measure the horizontal crack widths, as reported in Fig. 5. Based on the two-dimensional elastic solution of Iyengar (1962), the instrument H1 was placed where the maximum transverse tensile stress is theoretically reached, i.e. 0.4d = 100 mm. The other instruments (H2, H3, H4 and H5) were distributed along the specimen height in order to capture the propagation of the splitting crack. Therefore, in case of LL configuration (Fig. 5a), two LVDTs and three PTs were used on the two opposite sides of the specimen; for PL configuration, one LVDT and four PTs were used on all four sides of the specimen (Fig. 5b). In addition, in
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443
Fig. 4. Scheme of loading system (a) and picture of a specimen before testing: LL (b); PL (c).
case of both LL and PL, three LVDTs (V1, V2 and V3) were arranged at 120° around the specimen at the bottom of samples sides (B-region), in order to measure the vertical shortening of the specimen (Fig. 5).
3. Experimental results and discussion 3.1. Specimens under LL configuration All samples subjected to LL configuration showed a splitting failure. Table 5 summarizes all experimental results in terms of failure mode, splitting crack load (Psplitting), crack opening (from H1) at Psplitting on north side (wN,splitting), crack opening (from H1) at Psplitting on south side (wS,splitting), maximum load (Pmax), maximum crack opening (from H1) at Pmax on north side (wN,max), maximum crack opening (from H1) at Pmax on south side (wS,max) and ratio between Pmax and Psplitting. It should be observed that the crack opening measurement includes also the elastic deformation of concrete between the supports of the displacement transducer. Table 5 also reports the mean values as well as the standard deviations (SDs) and the coefficient of variations (CVs); it can be noticed that the latter are in general small, evidencing that the experimental results are consistent. PC samples failed when the principal tensile stress reached the tensile strength of concrete. In fact, PC specimens failed when the splitting crack occurred or shortly afterward (Psplitting = Pmax). The failure, which occurred at an average load of 1044 kN, was very brittle and without any prior warning of impending collapse. At failure the compressive stress under the loading steel plate was about 41 MPa, which is 30% smaller than the compressive strength of PC mixture (fcm = 57.2 MPa). It should be noticed that Psplitting
resulted greater for PC samples than PFRC ones, due to the higher mechanical properties of PC mixture (see Table 4). Concerning PFRC-V samples, it can be observed that PP fibers significantly enhanced the splitting bearing capacity (average Pmax/Psplitting = 1.41) and the ductility (average wmax/wsplitting = 5.70). The specimens failed well after the splitting cracking (Psplitting = 915 kN), reaching higher value of both maximum load and maximum crack opening, which ensures sufficient warning before failure. This is mainly due to the bridging effect of PP fibers, which lead to a stable crack development. The maximum compressive stress under the loading steel plate was about 51 MPa, which is 5% greater than the compressive strength of PFRC mixture (fcm = 48.5 MPa, Table 4), due probably to the lateral confinement that occurs in concrete under the loading steel plate (Iyengar, 1962; Leonhardt and Mönnig, 1973). Also in case of PFRC-H samples, characterized by an unfavorable fiber orientation for splitting cracks, PP fibers were able to enhance the splitting bearing capacity (Pmax/Psplitting = 1.18) and provide ductility (maximum crack opening comparable to PFRC-V specimens). However, these experimental results confirm that the casting direction, which changes the fiber orientation, significantly affects the splitting bearing capacity. On the contrary, the average splitting crack load of PFRC-H samples (Psplitting = 920 kN) was about the same of PFRC-V one, confirming that PP fiber orientation does not influence the tensile strength of concrete. In order to evaluate the reliability of the experimental results on LL specimens, the average splitting crack load (Psplitting) obtained for both PC and PFRC was compared against the prediction of the two-dimensional elastic solution proposed by Iyengar (1962), and well discussed in Leonhardt and Mönnig (1973). Based on this elastic solution, the transverse tensile stresses (rt), which occur in the disturbed region, are defined as:
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Fig. 5. Instrumentation details of: LL (a); PL (b).
Table 5 Main experimental results of LL tests. Specimen designation
Type of failure
Psplitting (kN)
wN,splitting (mm)
wS,splitting (mm)
Pmax (kN)
wN,max (mm)
wS,max (mm)
Pmax/Psplitting (–)
PC LL-PC-1 LL-PC-2 LL-PC-3 Mean SD CV
Splitting Splitting Splitting – – –
1152 1011 970 1044 95 0.09
0.289 0.121 0.179 0.196 0.085 0.43
0.124 0.129 0.101 0.118 0.015 0.13
1152 1011 970 1044 95 0.09
0.289 0.121 0.179 0.196 0.085 0.43
0.124 0.129 0.101 0.118 0.015 0.13
1.00 1.00 1.00 1.00 – –
PFRC-V LL-PFRC-V-1 LL-PFRC-V-2 LL-PFRC-V-3 Mean SD CV
Splitting Splitting Splitting – – –
1020 840 885 915 94 0.10
0.110 0.136 0.225 0.157 0.060 0.38
0.113 0.291 0.123 0.176 0.100 0.57
1439 1271 1160 1290 140 0.11
0.701 1.236 1.148 1.028 0.287 0.28
0.633 1.070 0.899 0.867 0.220 0.25
1.41 1.51 1.31 1.41 0.10 0.07
PFRC-H LL-PFRC-H-1 LL-PFRC-H-2 LL-PFRC-H-3 Mean SD CV
Splitting Splitting Splitting – – –
938 836 985 920 76 0.08
0.150 0.113 0.148 0.137 0.021 0.15
0.071 0.154 0.093 0.106 0.043 0.41
1072 1163 1022 1086 71 0.07
0.461 0.704 1.248 0.804 0.403 0.50
0.363 0.954 1.120 0.812 0.398 0.49
1.14 1.39 1.04 1.18 0.18 0.15
rt ¼ k P=d2
ð1Þ
where k is a factor defining the distribution of the transverse tensile stresses along the central line under the external applied load, P; d, as already underlined, is the side length of the square cross section of the sample. Considering a/d = 0.4 (as in the present experimental program), the maximum value of k, at which corresponds the
maximum transverse tensile stress (rt,max), resulted equal to 0.26 and it occurs at a distance of 0.4d from the sample top surface. Moreover, the splitting crack load in a concrete sample is reached when the maximum transverse tensile stress resulted equal to the tensile strength of concrete (fctm); the latter, both for PC and PFRC, can be evaluated by equation 5.1–3a of MC2010 (2012a,b):
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f ctm ¼ 0:3 f ck
ð2Þ
where fck is the characteristic compressive strength of concrete. The latter was calculated according to equation 5.1–1 of MC2010, subtracting, as a first approximation, 8 MPa to the mean value of the cylindrical compressive strength of PC and PFRC (see Table 4). Therefore, the tensile strength of concrete, evaluated by means of Eq. (2), resulted equal to 4.03 MPa and 3.53 MPa for PC and PFRC, respectively. Therefore, the splitting crack load of the tested specimens, having d = 250 mm, can be evaluated by the following equation: 2
Psplitting ¼ f ctm d =0:26
ð3Þ
The splitting crack load evaluated by means of Eq. (3) resulted equal to 970 kN for PC and 850 kN for PFRC; these values are just 7% smaller than the experimental ones (see Table 5), confirming the reliability of the LL experimental results. It is worthwhile noticing that the elastic solution, previously mentioned, is generally adopted by designers for evaluating the risk of cracking in tunnel elements during the TBM thrust phase. Moreover, in segments with conventional reinforcement, the proper bearing capacity is guaranteed by means of local stirrups placed under the TBM footplates. This local reinforcement is generally designed by means of simplified strut-and-tie model. From this point of view, the experimental tests have provided the maximum bearing capacity as well as the ductility exhibited by PFRC elements. Concerning the influence of casting direction on the splitting behavior, Figs. 6 and 7 report the load vs. crack-opening curves measured at south side (a) and load vs. crack-depth curve (b) for specimens LL-PFRC-V-3 and LL-PFRC-H-2, respectively. The splitting crack depth was evaluated from the sample top surface, considering both the horizontal instrumentation curves (a significant change in slope identifies the cracking) and the images that were captured continuously throughout the tests (10 s interval). The specimen LL-PFRC-V-3 showed a stable propagation of the splitting crack, with a continuous increase in bearing capacity, even after each crack development along the specimen height. In fact, the splitting crack developed in three steps up to 2d (500 mm), causing just a slightly decrease of slope of the load vs. crack opening curve (Fig. 6a). On the contrary, in specimen LL-PFRC-H-2, the splitting crack developed in two steps along the specimens, causing a plateau in the load vs. crack opening curves, at each crack propagation (Fig. 7a). Therefore, the samples having an unfavorable casting direction (and the consequent fiber orientation; PFRC-H) showed a splitting behavior more unstable and less controlled. The beneficial effects of PP fibers on the splitting behavior of specimen under LL configuration is well depicted also in Fig. 8a,
1800 Load 1600 [kN]
which shows the load vs. crack opening curves (from H1) for PC, PFRC-H and PFRC-V specimens; the low dispersion of the experimental results allowed to consider the mean values. The main aspects previously pointed out can be observed in Fig. 8a. In addition, it should be noticed that both PFRC-V and PFRC-H specimens, in spite of a very different splitting crack propagation, reached the maximum bearing capacity at a comparable maximum crack opening (i.e. 0.8–1.0 mm at H1 level – see also Table 5). However, after reaching the maximum load, a softening branch was observed in both PFRC-V and PFRC-H samples, even if PFRC-V exhibited much higher ductility. In fact, generally, PFRC-V samples reached an ultimate crack opening 65% larger than the one from PFRC-H specimens. Fig. 8b exhibits the load vs. splitting crack depth (from sample top surface) curve for PFRC-V and PFRC-H LL samples, showing the propagation of the splitting cracks along the specimen height. PP fibers provides a post-cracking residual tensile strength across the splitting crack, allowing the specimen the possibility to find a new stress distribution and equilibrium along the specimen height. Consequently, the splitting crack progressively increases in PFRC samples, as it is well evidenced in Fig. 8b. However, the development of the splitting crack clearly depends on the post-cracking toughness of FRC. In fact, in order to find a new equilibrated configuration, the specimen cast horizontally (PFRC-H, with an unfavorable fiber orientation) required a deeper splitting crack than PFRC-V samples. On the other hand, in PC samples a sudden increase of the splitting crack depth occurred due to the brittle post-cracking behavior of PC. This stress redistribution in FRC confirm the numerical results obtained by Plizzari and Tiberti (2007) and Tiberti (2014). Fig. 9 shows the final crack patterns of LL-PC-1, LL-PFRC-V-3 and LL-PFRC-H-2 specimens; these crack patterns clearly show the splitting failure, as well as the different propagation of the splitting crack. Fig. 9a clearly evidences, once again, the sudden and brittle failure occurred for PC samples, where the specimens were divided into two separate parts. Moreover, all specimens showed a single splitting crack at the center and the crack pattern on the north and south sides was very similar. Concerning possible practical implications, the experimental evidences confirmed that a high bearing capacity is achieved in presence of PP fibrous reinforcement, which means higher safety factor or the possibility of completely substituting or reducing the local splitting conventional reinforcement generally adopted. Nevertheless, no specific relationships are currently available for taking into account this contribution and consequently experimental tests on full-scale specimens are usually adopted (Caratelli
1800 Load 1600 [kN]
LL PFRC-V-3 South Side
1400
1400
1200
1200
1000
1000
800
400 200 0 0.00
800
H1 H2 H3 H4 H5
600
LL PFRC-V-3
600 400
Crack opening [mm]
200
Splitting crack depth from top surface [x d]
0 0.50
1.00
1.50
(a)
2.00
2.50
3.00
0.0
0.5
1.0
1.5
2.0
2.5
3.0
(b)
Fig. 6. LL-PFRC-V-3: load vs. crack-opening curves measured at south side (a) and load vs. splitting crack depth curve (b).
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1800 Load 1600 [kN]
1800 Load 1600 [kN]
LL PFRC-H-2 South side
1400
1400
1200
1200
1000
1000
800
800
H1 H2 H3 H4 H5
600 400 200
600 400 200
Crack opening [mm]
0 0.00
0 0.50
1.00
1.50
LL PFRC-H-2
2.00
2.50
3.00
Splitting crack depth from top surface [x d] 0.0
0.5
1.0
1.5
2.0
2.5
3.0
(b)
(a)
Fig. 7. LL-PFRC-H-2: load vs. crack-opening curves measured at south side (a) and load vs. splitting crack depth curve (b).
1800 Load 1600 [kN]
H1 LVDT PC fcm=57.2 MPa; PFRC fcm=48.5 MPa
1400 1200
1800 Load 1600 [kN]
LL: Mean Experimental Curves
1400
PFRC-V
PC
1000
1200 1000
PFRC-H
800
800
600
600
400
400
200 0 0.00
LL: Crack depth comparison
Crack opening [mm]
PFRC-V PFRC-H
200
Splitting crack depth from top surface [x d]
0 0.50
1.00
1.50
2.00
2.50
3.00
(a)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
(b)
Fig. 8. LL: mean experimental curves of load vs. H1 crack-opening for PC, PFRC-V and PFRC-H (a) and load vs. splitting crack depth curves for PFRC-V and PFRC-H (b).
Fig. 9. Final crack patterns of: LL-PC-1 (a); LL-PFRC-V-3 (b); LL-PFRC-H-2 (c).
et al., 2011). From this point of view, the LL configuration could be a possible simple method for evaluating the local splitting behavior of FRC. However, further experimental programs should be carried out in order to provide a simplified analytical method for the prediction of the splitting bearing capacity in case of FRCs.
3.2. Specimens under PL configuration Referring to PL tests, Table 6 lists the experimental results in terms of failure mode, splitting crack load (Psplitting), compressive stress under the loading steel plate at Psplitting (rc,splitting), maximum
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a b c
Specimen designation
Type of failure
Psplitting (kN)
rc,splitting (MPa)
wsplitting (mm)
Pmax (kN)
rc,max (MPa)
wmax (mm)
Pmax/Psplitting (–)
PC PL-PC-1 PL-PC-2 PL-PC-3 Mean SD CV
Splittinga Splittinga Splittinga – – –
950 949 931 943 11 0.01
95.0 94.9 93.1 94.3 1.1 0.01
0.380 (S) 0.196 (N) 0.252 (S) – – –
950 949 931 943 11 0.01
95.0 94.9 93.1 94.3 1.1 0.01
0.380 (S) 0.196 (N) 0.252 (S) – – –
1.00 1.00 1.00 1.00 – –
PFRC-V PL-PFRC-V-1 PL-PFRC-V-2 PL-PFRC-V-3 Mean SD CV
Splittingb Splittingb Splittingb – – –
822 811 742 792 43 0.05
82.2 81.1 74.2 79.2 4.3 0.05
0.073 (E) 0.088 (S) 0.066 (N) – – –
898 917 843 886 38 0.04
89.8 91.7 84.3 88.6 3.8 0.04
0.491 (E) 0.543 (N) 1.083 (W) – – –
1.09 1.13 1.14 1.12 0.02 0.02
PFRC-H PL-PFRC-H-1 PL-PFRC-H-2 PL-PFRC-H-3 Mean SD CV
Splittingc Splittingc Splittingc – – –
765 786 731 761 28 0.04
76.5 78.6 73.1 76.1 2.8 0.04
0.123 (W) 0.110 (S) 0.184 (W) – – –
805 834 765 801 35 0.04
80.5 83.4 76.5 80.1 3.5 0.04
0.268 (W) 0.276 (S) 0.324 (W) – – –
1.05 1.06 1.05 1.05 0.01 0.01
Uncontrolled loss of confinement after splitting. Progressive and stable loss of confinement after splitting. Loss of confinement after splitting.
crack opening (from H1) at Psplitting (wsplitting), maximum load (Pmax), maximum compressive stress under the steel plate at Pmax (rc,max), maximum crack opening (from H1) at Pmax (wmax) and ratio between Pmax and Psplitting. Mean values, SDs and CVs are also reported. All PC samples showed, also under PL configuration, a very brittle splitting failure (Psplitting = Pmax), which occurred, once again, when the principal tensile stress exceeded tensile concrete strength; this was observed at an average load of 943 kN. Contrarily to LL tests, failure occurred with a compressive concrete stress (under the loading steel plate) that was 65% higher than the compressive strength of PC mixture, i.e. 95 MPa. This can be explained by considering concrete confinement due to a triaxial state of compressive stress under the loading steel plate (Iyengar, 1962; Leonhardt and Mönnig, 1973). However, the uncontrolled loss of confinement at splitting cracking led the failure of PC samples under PL configuration to be even more explosive than in LL samples, as proved in the final crack pattern of sample PL-PC-2 shown in Fig. 10.
North
South
Referring to PFRC-V samples, PP fibers were able to enhance the splitting bearing capacity of about 12%; this value is much smaller than the one obtained in case of LL test due to the loss of confinement after splitting (the compressive stress under the loading steel plate was about 80% higher than the compressive uniaxial strength of concrete). In fact, the splitting crack seemed to propagate into the compressive zone of the disturbed region, probably causing the loss of confinement. The maximum bearing capacity (Pmax) was reached at a H1 crack opening greater than the one measured at Psplitting. Afterwards, PP fibers lead to a progressive loss of confinement after splitting, with respect to PC samples. It is worth noticing that, as a consequence of the higher mechanical properties of PC matrix (see Table 4), also in PL tests Psplitting resulted smaller for PFRC samples as compared to PC ones. The same behavior of PFRC-V samples was observed in PFRC-H ones, even if the maximum splitting capacity was smaller and the post-cracking behavior was more unstable. In fact, the ratio Pmax/Psplitting resulted equal to 1.05 (Table 6) and only half of the
West
Fig. 10. Final crack pattern of sample PL-PC-2.
East
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1800 Load 1600 [kN]
1800 Load 1600 [kN]
PL: Mean Experimental Curves H1 LVDT PC fcm=57.2 MPa; PFRC fcm=48.5 MPa
1400 1200
1200
PC
H1 LVDT PC fcm=57.2 MPa; PFRC fcm=48.5 MPa
1400
1000
PL: Mean Experimental Curves
PC
1000 PFRC-V
800
PFRC-V
800
600
600
400
400
PFRC-H
200
PFRC-H
200
Crack opening [mm]
Crack opening [mm]
0
0 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0
0.0
0.5
1.0
(a)
1.5
2.0
2.5
3.0
(b)
Fig. 11. PL: mean experimental curves of load vs. H1 crack-opening curves for PC, PFRC-V and PFRC-H (a) and their zoom up to 3 mm of H1 crack opening (b).
1800 Load 1600 [kN]
1800 Load 1600 [kN]
PL PFRC-V-1 H1 North H1 South H1 West H1 East
1400 1200 1000
1400
H1 North H1 South H1 West H1 East
1200 1000
800
800
600
600
400
400
200 0
PL PFRC-H-1
200
Crack opening [mm] 0.0
0.5
1.0
1.5
2.0
2.5
3.0
0
Crack opening [mm] 0.0
0.5
1.0
1.5
2.0
2.5
3.0
(b)
(a)
Fig. 12. Load vs. H1 crack-opening curves up to 3 mm for PL-PFRC-V-1 (a) and PL-PFRC-H-1 (b).
North
South
West
East
Fig. 13. Final crack pattern of sample PL-PFRC-V-1.
Table 7 Comparison between average splitting crack load of LL and PL samples. Designation
LL Psplitting (kN)
PL Psplitting (kN)
Psplitting,PL/Psplitting,LL (–)
PC PFRC-V PFRC-H
1044 915 920
943 792 761
0.90 0.87 0.83
crack opening at Pmax of PFRC-V samples was reached. PL experimental results confirms, once again, that casting direction significantly affects both the splitting behavior and the splitting bearing capacity. Moreover, according to experimental results on LL specimens, the average splitting crack load of PL-PFRC-H specimens resulted about the same of the one of PL-PFRC-V samples (i.e. 761 kN).
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North
South
West
East
Fig. 14. Final crack pattern of sample PL-PFRC-H-1.
Table 7 summarizes the average splitting crack load experimentally observed (Psplitting) in case of LL and PL tests, and their ratio (Psplitting,PL/Psplitting,LL); the latter resulted smaller than one, pointing out that the splitting crack load is of about 15% smaller in case of PL tests. This tendency is in accordance with the experimental results of Schnütgen (2003) and it is probably due to the more complicated stresses distribution which develops in PL configuration. Fig. 11a exhibits the comparison of all PL experimental tests, in which the experimental curves of load vs. crack-opening (H1) are shown in terms of mean values. Fig. 11b shows a zoom up to 3 mm of crack opening (H1); the aforementioned experimental observations can be clearly observed (in particular, the softening branch detected in both PFRC-V and PFRC-H samples as well as the sudden failure of PC samples). In order to better understand the different splitting crack propagation in PL specimens with different fiber orientation, Fig. 12 shows the load vs. crack opening (H1) curves up to 3 mm for PL-PFRC-V-1 and PL-PFRC-H-1 samples; in addition, Figs. 13 and 14 show their final crack patterns, respectively. In specimen PL-PFRC-V-1, the splitting crack occurred at a load of 822 kN (Psplitting) along a north–south plane. After that, the bridging effect of PP fibers allowed the increment of the external load up to 898 kN (Pmax), when a new splitting crack appeared also along a east–west plane. Eventually the loss of confinement led the sample in the softening branch. Therefore, the final crack pattern of PL-PFRC-V-1 is characterized by clear splitting cracks on all four sides. On the other hand, sample PL-PFRC-H-1 did not show splitting cracks on all four sides, but just on two opposite sides (north and south sides in Fig. 14). In fact, the smallest toughness of the PFRC, due to casting direction, did not allow a significantly increment of the bearing capacity after cracking, and thus the loss of confinement occurred before the appearance of the splitting crack also along the east–west plane. This different behavior between PFRCV and PFRC-H was observed in all samples underlining, once again, the significant influence of the casting direction on the splitting behavior of FRC elements. It is worthwhile noticing that the key role of concrete confinement under the loading steel plate probably not allowed a complete evaluation of fiber resistant contribution with respect to splitting phenomenon, as demonstrated by the not regular crack propagation along the specimen height on the two expected
cracking planes. Consequently, the PL configuration provides less practical information for designers compare to LL one. 4. Conclusions In the present paper the local splitting behavior in the segment regions under the Tunnel Boring Machine (TBM) hydraulic jacks was investigated by means of experimental tests on prismatic specimens under Line Load (LL) and Point Load (PL) configurations. Tests were carried out on twelve samples in polypropylene fiber reinforced concrete (PFRC) as well as on six reference specimens made of plain concrete (PC). The effect of the casting direction in PFRC specimens, that influences fiber orientation, was also investigated. Based on this experimental study, the following conclusion can be drawn: (1) Splitting failure of plain concrete samples is very brittle. (2) The presence of fibers lead to an enhancement of both splitting bearing capacity and ductility by means of a progressively increase of splitting crack length, which probably allows the elements to find a new stress distribution along the specimen height in equilibrium to the external load (stress redistribution). (3) A total amount of 10 kg/m3 (volume fraction Vf = 1.10%) of macro-synthetic polypropylene fibers significantly enhance the splitting behavior and the bearing capacity of a concrete prism (up to +40%), as well as the specimen ductility; this aspect was especially underlined in LL tests. Therefore, PFRC can be successfully used in concrete tunnel segments since it guarantees a higher bearing capacity and stable development of splitting cracks. (4) The casting direction of structural elements influences the splitting development and the bearing capacity of the specimens, since it leads to a different fiber orientation. When the latter is favorable (with fibers expected to be mainly transversal to loading direction and to the splitting crack), the LL bearing capacity increased of about 40% while, with an unfavorable casting direction (with fibers expected to be mainly parallel to the splitting crack), the LL bearing capacity increased of about 18%. (5) The splitting crack starts developing slightly earlier in PL configuration with respect to LL.
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