21 - 26 April 2018 Dubai International Convention

& Exhibition Centre, UAE

ITA - AITES WORLDTUNNEL CONGRESS

POSTER PAPERPROCEEDINGS

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Optimized reinforcement for precast tunnel segments with macro-synthetic fibers

Giuseppe Tiberti1, Giovanni Plizzari2, Ralf Winterberg3, Antonio Conforti4 and Ivan Trabucchi51 University of Brescia, Via Branze n. 43 Brescia (Italy), giuseppe.tiberti@unibs.it (corresponding author)2 University of Brescia, Via Branze n. 43 Brescia (Italy), giovanni.plizzari@unibs.it3 Elasto Plastic Concrete, Temasek Blvd n.9, 038989, Singapore (Singapore), rwinterberg@elastoplastic.com4 University of Brescia, Via Branze n. 43 Brescia (Italy), antonio.conforti@unibs.it5 University of Brescia, Via Branze n. 43 Brescia (Italy), i.trabucchi@unibs.it

ABSTRACT

The use of fiber reinforced concrete (FRC) in tunnel linings, with or without conventional rebars, has increased in the two last decades, especially in segmental linings. Nowadays there is a growing interest in the scientific community on macro-synthetic fibers for use in underground structures. Within this framework, the present study investigates the possibility of using macro-synthetic fiber reinforcement in precast tunnel segments in a possible combination with conventional rebars.An experimental program based on 3 Point Bending Tests was carried out on FRCs characterized by different fiber contents in order to assess their post-cracking nominal residual stresses. The corresponding stress vs. crack opening laws, representative of the FRCs investigated, were calculated through inverse analysis procedure. Then, a typical tunnel lining having small diameter was adopted as reference to optimize the reinforcement solution (macro-synthetic fibers and conventional rebars, i.e. hybrid solution). Particular attention was devoted to the TBM thrust phase, in which high-concentrated forces are introduced in the linings.Key Words: Thrust jack, Splitting phenomena, Fiber reinforced concrete, Macro-synthetic fibers, Numerical analyses.

1. INTRODUCTION

The use of underground space is an appealing solution in order to face and to solve the need of urban mobility which should be always more efficient. To this aim, bored-tunneling is a good solution in order to reduce the hindrance to infrastructure above ground and to the environment. In this regard, excavation process is generally carried out by means of mechanized full face methods. Therefore the excavation is carried out with special machines, the Tunnel Boring Machines (TBMs), or mechanized shields which are able to dig the ground or rock mass, to take it away from the face and to support the tunnel section till the final lining is installed.In the last two decades, Fiber Reinforced Concrete (FRC), with or without conventional rebars, was progressively adopted in several precast tunnel lining projects (ITA report n.2016 ,16; ACI 544.7R2016 ,16-, fib bulletin 2017 ,83). Steel Fiber Reinforced Concrete (SFRC) have been generally used for tunnel linings even though there is a general growing interest in the scientific community on macro-synthetic fibers for use in structural applications (Pujadas et al., 2014; Nitschke A.G. et al., 2016; Conforti et al., 2017). In fact, new types of polypropylene (PP) macro fibers able to impart concrete toughness in order to make it adequate for structural purposes are currently available in the market (Buratti et al., 2011; Banthia et al., 2012).

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The design process of segmental concrete linings in ground conditions is principally governed by the load cases that can be implemented in the so-called ring models (Blom, 2002; Di Carlo et al., 2016), which correspond to the standard load case (embedded ground condition) and the uplift load case (grouting process). Furthermore, other possible mechanisms, occurring during the lining construction process, can result in crack patterns that are frequently observed in practice in tunnel segments. Under this point of view, the application of TBM thrust jack forces is a crucial phase (Tiberti et al., 2015; Liao et al., 2015). Actually, although this phenomenon occurs in the temporary lining building stage, it tends to be normative as well as the final state when the lining is loaded by the ground pressure which interests the entire lining lifetime (Blom, 2002; Groeneweg, 2007).

The FRC post-cracking behaviour can be easily included in the tunnel design process by adopting proper post-cracking tensile laws to be used for the construction of ULS domains (fib Model Code 2012 ,2010) which are based on simplified non-linear analytical methods. These analytical approaches are generally suitable only for studying the previously mentioned embedded tunnel in ground condition and the grouting process. Nevertheless, the distribution of stresses in tunnel elements during the thrust jack phase is significantly complicated and it cannot be easily described by means of analytical non-linear processes; thus, non-linear finite models tend to be necessary in order to study this temporary stage.

Within this framework, the present research work aims to evaluate the possibility of using macro-synthetic fiber reinforcement in precast tunnel segments in a possible combination with traditional rebars by studying a tunnel lining having small diameter. Firstly, fracture properties of two PFRCs (Polypropylene Fiber Reinforced Concretes) were determined. Secondly, non-linear numerical analyses were developed in order to study the TBM thrust jack phase, which strongly affects the optimized reinforcement (fibers + rebars) in precast tunnel segments.

2. MATERIAL PROPERTIES

An experimental campaign was developed for the characterization of PFRCs adequate for use in tunnel elements. Continuous embossed PP fibers 48 mm long with a diameter of 0.70 mm (aspect ratio of 68), tensile strength of 640 MPa and an elastic modulus of 12 GPa were adopted (Table 1). Fibers were added to a base concrete with a target mean cube compressive strength of about 65-60 MPa (typical of precast applications) in two different amount: 6 kg/m3 (PFRC6 series) and 10 kg/m3 (PFRC10 series). Both FRCs were produced by a planetary concrete mixer.

Table 2 shows the mix proportions of concrete PFRC6 and PFR10. It can be observed that they vary only for fiber content and high range polycarboxilated based superplasticizer amount adopted. The latter was adjusted in each concrete type in order to reach a good concrete workability.

For each matrix, twelve small beams 150x150x550mm according to EN 14651 standard (2005) for determining post-cracking behavior and twelve cubes 150x150x150 mm for evaluating concrete compressive strength were produced. Both casting and curing procedures adopted were the same for all specimens. In particular, the curing procedure was characterized by an initial curing with a nonabsorptive sheet, removal from molds 24 hours after casting and storage in a

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moist environment at °2±20C until testing. All experimental tests were carried out between 35 and 40 days after casting.

According to EN 2005) 14651), beams were notched and tested under three point bending test (3PBT). A closed-loop servo-hydraulic machine with a loading capacity of 500 kN (INSTRON 1274) was adopted, as well as a crack control through a clip gauge (which is suggested by EN 2005 ,14651). Linear Variable Differential Transducers (LVDTs) were utilized for measuring also net mid-span deflection (MPD) and crack tip opening displacement (CTOD).

Table 3 shows the mean mechanical properties of the two types of concrete (CV provided in brackets), which were evaluated on the same days as beam tests, in terms of cube and cylinder compressive strength (fc,cube, fc). The cylindrical compressive strength was conventionally assumed as fc=0.83 fc,cube. From Table 3 it can be observed that PFRC6 and PFRC10 were characterized respectively by a fc,cube of 65.8 MPa and 62.6 MPa, as well as a low dispersion of the mechanical properties was obtained.

Table 1. Characteristics of polymer macrofibers.

Table 2. Mix-design of concrete PFRC6 and PFRC10.

Figure 1 represents the nominal stress vs. CMOD (Crack Mouth Opening Displacement) curves of notched small beams of concrete PFRC6 (left) and PFRC10 (right), which were tested, as already underlined, according to EN 2005) 14651). The limit of proportionality fL and the mean values of residual flexure strengths fR,1, fR,2, fR,3, fR,4 (corresponding to CMOD values of 2.5 ,1.5 ,0.5 and 3.5 mm, respectively) are listed in Table 3 as well. A comparable result dispersion in terms of post-cracking mechanical properties can be observed between concretes, i.e. CV ranging from 0.10 to 0.17.

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Table 3. Mean mechanical properties of concretes PFRC6 and PFRC10 measured on standard specimens (CV in brackets).

Figure 1. Nominal stress vs. CMOD curves for concrete PFRC6 (a) and PFRC10 (b).

Both mixtures showed a stable post-cracking response, as compared to the typical brittle behavior exhibited by plain concrete. PFRC matrixes are characterized by a softening behavior with a sharp load drop after the peak load, followed by an increment of the residual flexural tensile strength. For larger values of crack width, a soft and progressive decrease of the residual flexural tensile strength is observed. By using higher fiber contents, the load drop (after the peak) decreases and the increment of the residual flexural tensile strength becomes more pronounced (compare PFRC6 response against PFRC10 one in Figure 1). These good post-cracking performances given by the adopted PP fibers are mainly due to their embossed shape, which significantly increases the bond between fiber and matrix and, in addition, to their higher elastic modulus and tensile strength.

The obtained fracture properties of PFRC6 and PFRC10 fulfil the requirements of fib Model Code 2010 (fR,1k/fL,k > 0.4 and fR,3k/fR,1k > 0.5) for use in structural elements, as well as satisfy the requirement of Equation 14-7.7 of Model Code 2010 (fFtuk ≥ 0.08fck2/1 ) allowing to use only PP fibers as minimum shear reinforcement of precast tunnel segments. In fact, considering fR,jk = fR,j (1.64-1∙CV) according to fib Model Code 2012) 2010) the following ratios and characteristic values are obtained: fR,1k/fL,k=0.44, fR,3k/fR,1k=1.33 and fFtuk= 1.01 MPa for PFRC6; fR,1k/fL,k=0.60, fR,3k/fR,1k=1.44 and fFtuk=1.53 MPa for PFRC10.

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3. PRECAST TUNNEL LINING GEOMETRY

A typical precast tunnel lining characterized by a small diameter was considered. In particular, the segmental lining presents an internal diameter of 3200 mm, a thickness of 200 mm (external diameter of 3600 mm), leading to a lining aspect ratio equal to 16. The lining is representative of typical water supply, gas pipeline, waste water or electrical supply tunnels (ITA report n.2016 ,16). Each lining ring is composed by six universal tapered tunnel segments as shown in Figure 2. Hence, the tunnel segment presents an average length of 1780 mm. Two pairs of thrust jacks act on each tunnel segment as well as two bearing pads are positioned on its rear face (ring joint, Figure 2); it was assumed a so-called French thrust jack configuration, where the bearing pads are perfectly aligned with TBM thrust shoes (Groeneweg, 2007). Moreover, the average service thrust load was assumed equal to 1 MN for each TBM shoes. This service load corresponds to a tunnel overburden ranging from 5-4 diameters, according to the simplified model proposed by Rijke (2006) for evaluating the TBM thrust jack forces in ground condition. The maximum thrust load was assumed equal to 1.5 MN for each shoes (Blom, 2002; Groeneweg, 2007).

Based on the experimental evaluation of nominal post-cracking residual strengths of PFRCs (Section 2), it was proven that in both materials (PFRC6 and PFRC10), fiber reinforcement can substitute the minimum transverse shear reinforcement. Furthermore, the post cracking residual strengths are adequate for withstanding local splitting stresses due to high concentrated forces exerted by TBM jacks (Tiberti et al., 2015; ITA report n.2016 ,16). Consequently, in segments with hybrid reinforcement solution, both shear reinforcement and local stirrups for splitting phenomena can be totally replaced or significantly reduced.

Figure 2. Precast tunnel lining geometry.

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Table 4. Reinforcement configurations.

Based on the aforementioned remarks, as summarized in Table 4, the following reinforcement solutions were considered:

- RC segment: typical conventional reinforcement generally adopted in practice corresponding to (6+6)Ø10 curved rebars, stirrups Ø8 with 4 legs@100 mm as shear reinforcement and local stirrups Ø8 with 2 legs@100 mm for splitting stresses.

- RCO+PFRC6 and RCO+PFRC10 segments: hybrid solution based on a combination of PP fibers and conventional reinforcement; (4+4)Ø10 curved rebars were adopted in two connected chords and PP fibers to mainly withstand splitting and shear stresses, as well as to better control spalling phenomenon. Stirrups Ø6 with 2 legs@100 mm were used for each chord.

- PFRC6 and PFRC10 segments: PP fiber reinforcement only. Flexural, shear, spalling and splitting stresses are withstood by fibers only.

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4. NUMERICAL MODELLING

The numerical analyses were performed by means of the finite element code DIANA 2016) 10.1). The main aim was to evaluate the behaviour of segments with different reinforcement solutions (Table 4) during TBM operations. The numerical simulations were carried out by adopting the characteristic mechanical properties of material as suggested by fib bulletin 2017) 83). In fact, with regard to the thrust jack forces acting on FRC lining (during the construction process), an optimum use of material properties can be achieved by a change in the design philosophy. In fact, contrarily to plain concrete, after cracking, FRC is able to significantly redistribute stresses.

4.1. Material modellingA stress vs. crack opening law, representative of the PFRC investigated, was calculated by means of inverse analysis (Roelfstra and Wittmann, 1986). A discrete concrete crack model was used and a tri-linear post-cracking law was adopted. The latter has been progressively calibrated in order to fit the experimental results showed in Section 2, which were obtained from three point bending tests (3PBTs). In particular, the characteristic experimental curves of 3PBTs were calculated for PFRC6 and PFRC10 in order to retrieve the corresponding uni-axial post-cracking laws, whose parameters are reported in Table 5. Based on the mean values of cylindrical compressive strengths, the corresponding characteristic values were estimated (fck, see Table 5). The elastic modulus (Ec) and characteristic tensile strength, fctk are reported as well; the latter were estimated according to fib Model Code 2012) 2010). The uniaxial compressive behavior of concrete was described by means of the model proposed by Thorenfeldt (1987). Moreover, the increase of compressive strength due to lateral confinement was considered by means of the model introduced by Selby and Vecchio (1993). Steel B450C (Eurocode ,2 2004) was adopted as both transverse and longitudinal reinforcement. In numerical analyses a yielding and ultimate tensile strength equal to 475 MPa and 572 MPa were considered; a Von-Mises yielding criterion with strain-hardening was assumed.

Table 5. Main parameters adopted in the numerical analyses.

4.2. Precast tunnel segment modelling

A three dimensional numerical model of one single tunnel segment with two pairs of actuators was adopted (Figure 3). Twenty-nodes iso-parametric solid brick elements were used in combination with interface elements. The latter were used to simulate the support through radial joints provided by the adjacent rings; in-plane and out-of-plane stiffness of interface elements were opportunely calibrated (Trabucchi,

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2015). It should be noticed that supports provided by previous assembled ring were localized on the bearing pads surfaces (Figure 3).The application of TBM forces was simulated by means of a uniform pressure applied on the top side of the thrust shoes steel plate.

A total strain rotating smeared crack model was used for concrete behavior after cracking. Hence, the stress vs. crack opening laws of PFRCs investigated (Table 5) must be transformed in stress vs. strain relationships by referring to a crack bandwidth (h) equal to the average dimension of the element (about 52 mm), as suggested by Rots (1988). Steel reinforcing rebars were simulated with embedded reinforcement; the total amount of fiber and traditional rebars were previously listed in Table 4.

Figure 3. Mesh adopted for the 3D solid finite element model of the precast tunnel segment.

4.3. Numerical results

The bearing capacity of tunnel segments, as well as the safety factor with respect to the service load (s.l.), were investigated by increasing progressively the load in order to evaluate the correspondent development of stresses and crack patterns. In Figure 4, the typical crack pattern exhibited by segments in numerical analyses is schematically reported.

The first crack appears between the loading surfaces (Figure 4a) at a load level of about 0.54 times the service load. This crack, generally defined as spalling crack, arises as a result of the curved shape assumed locally by the segment. The spalling crack development was evaluated by considering the relative displacement between two points astride the crack and assuming, for the sake of simplicity, a single crack. The corresponding base of measurement is about 315 mm, and the resulting diagram is shown in Figure 4b for the RC configuration. Splitting cracks due to local radial tensile stresses occur under the TBM shoes at about 1.48 s.l.; subsequently, when reaching 1.65 times the service load also tangential splitting cracks appear in the segment.

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(a) (b)Figure 4. Typical final crack pattern occurring in the investigated tunnel

segment (a); development of spalling crack in the RC segment (b).

0.54 times the s.l.: tangential spalling cracks

1.48 times the s.l.: radial splitting cracks

1.65 times the s.l.: tangential splitting cracks

2.03 times the s.l.: tangential splitting cracks more

developed.

2.83 times the s.l.: final crack pattern

Figure 5. Numerical analyses: crack pattern development in theRC segment.

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By referring to the RC configuration, the progressive development of the crack pattern is showed in Figure 5 by means of contours; it should be noticed that small discs are used as a graphical expedient for representing the crack planes. Moreover, the number of discs depends on the integration points; thus it is a qualitative representation, which is very useful especially for capturing the spatial development of crack planes. In this regard, it can be noticed that, up to about 1.65 times the service loads, the three cracked regions due to spalling, radial and tangential splitting can be clearly pointed out but they are distributed on rather small areas. On the contrary, when reaching progressively the load up to 2 times the service load, the spalling crack and tangential splitting crack tend to develop on a larger area. At two times the service load, it can be appreciated (Figure 4b) a sudden increase of both spalling crack and tangential splitting crack (Figure 5). This tendency is probably due to a mutual interaction between tangential splitting cracks occurring under TBM shoes and spalling one, since their crack planes are similar oriented (Figure 5). In order to better investigate this phenomenon, the development of tangential splitting crack was evaluated by considering the relative displacement between two points astride the crack (the corresponding base of measurement is about 330 mm long).

In Figure 6 the local development of spalling and splitting cracks are plotted for all the configurations considered. It is worth noticing that, in both diagrams, a small contribution due to elastic deformations is included. The diagrams clearly evidenced that all configurations exhibited a satisfactory behavior at service load and up to the maximum thrust load (equal to 1.5 s.l.). The segments PFRC6 and PFRC10 exhibit a maximum load of about 2 times the service load. As previously mentioned, at that load level, a sudden development of spalling and tangential splitting crack occur as clearly pointed out in Figure 6a and b, respectively. The optimized combination of local rebars and PP fibers (RCO+PFRC6 and RCO+PFRC10) enables to further increase the safety factor even though larger crack widths appear. In fact, both local spalling and splitting cracks are lower than 0.2 mm for load levels smaller than 2 times the service load.

(a) (b)

Figure 6. Comparison between different reinforcement solutions: spalling crack opening (a) and splitting crack opening (b).

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5. CONCLUSIONS

The main purpose of this research was the evaluation of macro-synthetic fibers as possible reinforcement solution in precast tunnel segments characterized by a small diameter (3.2 m) in combination or not with traditional rebars. Based on a numerical study developed by considering the TBM thrust phase, the following conclusions can be drawn:

- PFRCs and RCO+PFRCs segments guarantee the required structural performance at both service and maximum TBM thrust loads;

- spalling and tangential splitting crack phenomena are well controlled by PP fibers. The corresponding estimated crack widths through the numerical model remain below 0.2 mm up to a load level of about two times the service load;

- a mutual interaction is clearly pointed out between tangential splitting cracks occurring under TBM shoes and spalling one (even though the latter occur earlier), since their crack planes are similar oriented;

- the combination of conventional rebars and fiber reinforcement (RCO+PFRC), which led to a rebar reduction of about %61 with respect to RC solution, is particular effective also for high load levels, by guaranteeing higher safety factor and the same behaviour of reference RC solution.

6. ACKNOWLEDGEMENTS

The Authors would like to thank Engineers Daniele Rivetta and Andrea Piardi, as well as the technicians Luca Martinelli, Augusto Botturi, Domenico Caravaggi and Andrea Delbarba, for the assistance in performing the experimental program. A special acknowledgement goes to Engineer Antonio Mudadu for the assistance in performing the numerical analyses.

7. REFERENCES

ACI Committee 2016) .544). Report on Design and Construction of Fiber Reinforced Precast Concrete Tunnel Segments, ACI 544.7R16-, American Concrete Institute, pp. 36.Banthia N., Bindiganavile V., Jones J. and Novak, J. (2012). Fiber-reinforced concrete in precast concrete applications: Research leads to innovative products. PCI Journal, 3) 57), pp. 46-33.Buratti N., Mazzotti C. and Savoia M. (2011). Post-cracking behaviour of steel and macro-synthetic fibre-reinforced concretes, Construction and Building Materials, Vol. 25, pp. 2722-2713.Conforti, A., Minelli, F., Plizzari, G.A., and Tiberti, G. (2017). Comparing test methods for the mechanical characterization of fiber reinforced concrete. Structural Concrete, 14-1, https://doi.org/10.1002/suco.201700057.Di Carlo F., Meda A., Rinaldi Z. (2016). Design procedure of precast fiber reinforced concrete segments for tunnel lining construction, Structural Concrete, under press, doi: 10.1002/suco.201500194.DIANA – Finite Element Analysis (2016). User’s Manual release 10.1. TNO DIANA BV, Delft, The Netherlands. Edited by Jonna Manie and Wijtze Pieter Kikstra.EN 2005) 14651). Precast concrete products – test method for metallic fibre

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concrete – Measuring the flexural tensile strength. European Standard.Eurocode 2004) 2). Design of concrete structures. European Standard.fib Bulletin 2017) 83). Precast tunnel segments in fibre-reinforced concrete, W.P. 1.4.1 Tunnels in fiber reinforced concrete, ISSN 3610-1562, ISBN -88394-2-9786-123.Groeneweg T.W. (2007). Shield driven tunnels in ultra high strength concrete, reduction of the tunnel lining thickness, Graduate Thesis, Delft University of Technology, The Netherlands, January, 2007.ITA report n. 2016) 16). Twenty years of FRC tunnel segments practice: lessons learnt and proposed design principles, April 2016, pp. 71, ISBN -1013-970-2-9782-5.Liao L., De la Fuente A., Cavalaro S. and Aguado, A. (2015). Design of FRC tunnel segments considering the ductility requirements of the Model Code 2010, Tunnelling and Underground Space Technology, Vol. 47, pp. 210-200.Model Code 2010 - Final draft (2012). fib Bulletin 65. Volume 1, pp. 350, ISBN -9782-105-88394-2; fib Bulletin 66. Volume 2, pp. 370, ISBN 9-106-88394-2-978.Nitschke A. G. and Winterberg R. (2016). Performance of macro-synthetic fiber reinforced tunnel linings. In: Proceedings of the World Tunnel Congress 2016, San Francisco (U.S.A.), 28-22 April, 2016, full-paper available on usb-stick, 10 p.Pujadas P., Blanco A., Cavalaro S. and Aguado A. (2014). Plastic fibres as the only reinforcement for flat suspended slabs: experimental investigation and numerical simulation, Construction and Building Materials, Vol. 57, pp. 104-92.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.Roelfstra P. E .and Wittmann F.H. (1986). Numerical method to link strain softening with failure of concrete, in Fracture Toughness and Fracture Energy, Edited by F.H. Wittmann, Elsevier, London.Rots J.G. (1988). Computational modeling of concrete fracture, Ph. D Thesis, Delft University of Technology, The Netherlands, pp. 132.Selby R.G. and Vecchio F.J. (1993). Three dimensional constitutive relations for reinforced concrete, Univ. Toronto, Civil. Eng., Toronto, Canada.Thorenfeldt E., Tomaszewicz A. and Jensen J. J. (1987). Mechanical properties of high-strength concrete and applications in design. In Proc. Symp. Utilization of High-Strength Concrete, Stavanger, Norway.Tiberti G., Conforti A. and Plizzari G.A. (2015). Precast segments under TBM hydraulic jacks: Experimental investigation on the local splitting behavior, Tunnelling and Underground Space Technology, Vol. 50, August 2015, pp. 450-438, doi: http://dx.doi.org/10.1016/j.tust.2015.08.013.Trabucchi I. (2015). Studio numerico di rivestimenti per gallerie realizzati in conci prefabbricati, Master Thesis, University of Brescia, pp. 250.

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