Abstract
Existing design guidelines for concrete hinges are focusing on serviceability limit states. Lack of knowledge about ultimate limit states was the motivation for this work. Experimental data are taken from a testing series on reinforced concrete hinges subjected to eccentric compression up to their bearing capacity. These tests are simulated using the finite element (FE) software Atena science and a material model for concrete implemented therein. The first simulation is based on default input derived from measured values of Young’s modulus and of the cube compressive strength of the concrete. The numerical results overestimate the initial stiffness and the bearing capacity of the tested concrete hinges. Therefore, it is concluded that concrete was damaged already before the tests. A multiscale model for tensile failure of concrete is used to correlate the preexisting damage to corresponding values of Young’s modulus, the tensile strength, and the fracture energy of concrete. This allows for identifying the preexisting damage in the context of correlated structural sensitivity analyses, such that the simulated initial stiffness agrees well with experimental data. In order to simulate the bearing capacity adequately, the triaxial compressive strength of concrete is reduced to a level that is consistent with regulations according to Eurocode 2. Corresponding FE simulations suggest that the ductile structural failure of concrete hinges results from the ductile material failure of concrete at the surface of the compressed lateral notch. Finally, Eurocode-inspired interaction envelopes for concrete hinges subjected to compression and bending are derived. They agree well with the experimental data.
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Abbreviations
- a :
-
Neck width
- \(a_g\) :
-
Maximum aggregate size
- \(b_1\) :
-
Width of the partially loaded area \(A_{c0}\)
- \(b_2\) :
-
Width of the partially loaded area \(A_{c1}\)
- c :
-
Softening parameter
- \(c_1, c_2\) :
-
Coefficients appearing in the crack opening law
- \(c_{ini}\) :
-
Initial value of c
- \(d_1\) :
-
Depth of the partially loaded area \(A_{c0}\)
- \(d_2\) :
-
Depth of the partially loaded area \(A_{c1}\)
- e :
-
Eccentricity of the normal force
- \(e_\sigma \) :
-
Parameter influencing the Menétrey–Willam failure surface in the deviatoric plane
- \({{\varvec{e}}}_x,\,{{\varvec{e}}}_y,\,{{\varvec{e}}}_z\) :
-
base vectors in x, y, and z-direction
- \(f_c\) :
-
Uniaxial compressive strength
- \(f_{c0}\) :
-
Initial elastic limit under uniaxial compression
- \(f_c'\) :
-
Evolving elastic limit under uniaxial compression
- \(f_{cd}\) :
-
Design value of the uniaxial compressive strength
- \(f_{ck}\) :
-
Characteristic value of the uniaxial compressive strength
- \(f_{c,\mathrm{cube}}\) :
-
Mean value of the cube compressive strength
- \(f_{ck,\mathrm{cube}}\) :
-
Characteristic value of the cube compressive strength
- \(f_t\) :
-
Uniaxial tensile strength of the Rankine failure surface
- \(f_t'\) :
-
Uniaxial tensile strength of the Menétrey–Willam failure surface
- \(f_{t,\mathrm{dam}}\) :
-
Uniaxial tensile strength of damaged concrete
- m :
-
Parameter influencing the shape of the Menétrey–Willam failure surface
- \(r_{c}\) :
-
Reduction of uniaxial compressive strength, due to cracks with crack-plane normal vectors orthogonal to the loading direction
- w :
-
Crack opening displacement
- \(w_c\) :
-
Value of w corresponding to the vanishing cohesive stress
- \(w_d\) :
-
Critical compression displacement
- \(w_{\mathrm{dam}}\) :
-
Value of w due to preexisting damage
- x, y, z :
-
Cartesian coordinates
- \(A_{c0}\) :
-
Partially loaded area
- \(A_{c1}\) :
-
Distribution area with a similar shape to \(A_{c0}\)
- E :
-
Young’s modulus
- \(E_c\) :
-
Young’s modulus of uncracked concrete
- \(E_{c,\mathrm{dam}}\) :
-
Young’s modulus of damaged concrete
- \(F_{3P}^p\) :
-
Failure function of the Menétrey and Willam criterion
- \(F_{Rdu}\) :
-
Maximum design compressive force
- Fixed :
-
Flag for modeling of crack rotation: \(Fixed=1\) ... no crack rotation
- \(G_f\) :
-
Fracture energy
- \(G_{f,\mathrm{dam}}\) :
-
Fracture energy of damaged concrete
- \(K_{Ic}\) :
-
Fracture toughness
- M :
-
Bending moment
- N :
-
Normal force
- \(\beta \) :
-
Flag for modeling the direction of the plastic flow: \(\beta =0~\dots \) purely deviatoric plastic flow
- \(\varDelta G_f\) :
-
Reduction of fracture energy due to preexisting damage
- \(\varDelta \varphi \) :
-
Rotation angle
- \(\epsilon _c^p\) :
-
Plastic strain at uniaxial compressive strength
- \(\vartheta \) :
-
Lode angle
- \(\lambda _t\) :
-
Auxiliary-to-actual uniaxial tensile strength ratio
- \(\nu \) :
-
Poisson’s ratio
- \(\nu _c\) :
-
Poisson’s ratio of uncracked concrete
- \(\xi \) :
-
Hydrostatic stress invariant
- \(\rho \) :
-
Deviatoric stress invariant
- \(\sigma \) :
-
Softening tensile strength of smeared crack model
- \({\varvec{\sigma }}\) :
-
Cauchy stress tensor
- \(\sigma _1,\sigma _2,\sigma _3\) :
-
Principal stresses
- \(\sigma _\ell \) :
-
Principal normal stress in the loading direction
- \(\sigma _{\ell u}\) :
-
Maximum normal stress in the loading direction
- \(\sigma _y\) :
-
von Mises yield stress of steel
- \(\omega \) :
-
Crack density parameter
References
Austrian Standards Institute: ONR 23303:2010-09-01 Prüfverfahren Beton (PVB)—Nationale Anwendung der Prüfnormen für Beton und seiner Ausgangsstoffe [Test protocol concrete - National application of testing standards for concrete and its raw materials], vol. ONR 23303. Austrian Standards Institute (2010) (in German)
Benveniste, Y.: A new approach to the application of Mori–Tanaka’s theory in composite materials. Mech. Mater. 6(2), 147–157 (1987). https://doi.org/10.1016/0167-6636(87)90005-6
Blom, C.B.M.: Design philosophy of concrete linings for tunnels in soft soils. Doctoral dissertation, Delft University of Technology (2002)
British Standards Institution, CEN European Committee for Standardization: EN 1992-1-1:2015-07-31 Eurocode 2: design of concrete structures—part 1-1: general rules and rules for buildings (2015)
Budiansky, B.: On the elastic moduli of some heterogeneous materials. J. Mech. Phys. Solids 13(4), 223–227 (1965). https://doi.org/10.1016/0022-5096(65)90011-6
Budiansky, B., O’Connell, R.J.: Elastic moduli of a cracked solid. Int. J. Solids Struct. 12(2), 81–97 (1976). https://doi.org/10.1016/0020-7683(76)90044-5
Červenka, J., Papanikolaou, V.K.: Three dimensional combined fracture-plastic material model for concrete. Int. J. Plast. 24(12), 2192–2220 (2008). https://doi.org/10.1016/j.ijplas.2008.01.004
Červenka, V., Jendele, L., Červenka, J.: ATENA program documentation part 1—theory, February 5, 2016 edn. http://www.cervenka.cz/assets/files/atena-pdf/ATENA_Theory.pdf (2016)
Cervenka Consulting, Červenka, V., Jendele, L., Červenka, J., et al.: Build 12562 & Atena 5.1.3. Internet source. http://www.cervenka.cz/download/#atena-gid (2016)
Chen, J., Mo, H.: Numerical study on crack problems in segments of shield tunnel using finite element method. Tunn. Undergr. Space Technol. 24(1), 91–102 (2009). https://doi.org/10.1016/j.tust.2008.05.007
De Waal, R.G.A.: Steel fibre reinforced tunnel segments: for the application in shield driven tunnel linings. Doctoral dissertation, Delft University of Technology (2000)
fib: fib Model Code for Concrete Structures 2010. Ernst & Sohn, Wiley (2013). https://doi.org/10.1002/9783433604090
Freyssinet, E.: Le pont de Candelier [The bridge of Candelier]. Ann. Ponts Chaussées 1, 165f (1923)
Freyssinet, E.: Naissance du béton précontraint et vues d’avenir [Birth of prestressed concrete and future outlook]. Travaux, pp. 463–474 (1954)
Friswell, M.I., Mottershead, J.E.: Finite Element model updating in structural dynamics, vol. 38. Springer (1995). https://doi.org/10.1007/978-94-015-8508-8
Gladwell, G.M.: Contact problems in the classical theory of elasticity. Springer (1980). https://doi.org/10.1007/978-94-009-9127-9
Grassl, P., Jirásek, M.: Damage-plastic model for concrete failure. Int. J. Solids Struct. 43(2223), 7166–7196 (2006). https://doi.org/10.1016/j.ijsolstr.2006.06.032
Hefny, A.M., Chua, H.C.: An investigation into the behaviour of jointed tunnel lining. Tunn. Underg. Space Technol. 21(34), 428 (2006). https://doi.org/10.1016/j.tust.2005.12.070. In: Safety in the Underground Space—Proceedings of the ITA-AITES 2006 World Tunnel Congress and 32nd ITA General Assembly
Hlobil, M., Göstl, M., Burrus, J., Hellmich, C., Pichler, B.: Molecular-to-macro upscaling of concrete fracture: theory and experiments. J. Mech. Phys. Solids, under revision (2017)
Hordijk, D.A.: Local Approach to Fatigue of Concrete, vol. 210. Doctoral dissertation, Delft University of Technology, The Netherlands (1991). ISBN 90/9004519-8
Janßen, P.: Tragverhalten von Tunnelausbauten mit Gelenkstübbings [Structural behavior of segmented tunnel linings]. Ph.D. thesis, Technical University of Braunschweig (1986)
Jusoh, S.N., Mohamad, H., Marto, A., Yunus, N.Z.M., Kasim, F.: Segment’s joint in precast tunnel lining design. J. Teknol. 77(11), 91–98 (2015). https://doi.org/10.11113/jt.v77.6426
Kalliauer, J.: Insight into the structural behavior of concrete hinges by means of finite element simulations. Master thesis, TU Wien, Karslplatz 13, 1010 Wien (2016)
Klappers, C., Grübl, F., Ostermeier, B.: Structural analyses of segmental lining—coupled beam and spring analyses versus 3D-FEM calculations with shell elements. Tunn. Undergr. Space Technol. 21(3–4), 254–255 (2006). https://doi.org/10.1016/j.tust.2005.12.116
Kupfer, H., Hilsdorf, H.K., Rusch, H.: Behavior of concrete under biaxial stresses. J. Proc. 66(8), 656–666 (1969)
Leonhardt, F.: Mainbrücke Gemünden—Eisenbahnbrücke aus Spannbeton mit 135 m Spannweite [Bridge over the river Main at Gemünden—prestressed railway bridge with a span of 135 m]. Beton Stahlbetonbau 81(1), 1–8 (1986). https://doi.org/10.1002/best.198600010
Leonhardt, F., Reimann, H.: Betongelenke: Versuchsbericht, Vorschläge zur Bemessung und konstruktiven Ausbildung. Kritische Spannungszustände des Betons bei mehrachsiger, ruhender Kurzzeitbelastung [Concrete hinges: test report, recommendations for structural design. Critical stress states of concrete under multiaxial static short-term loading], vol. 175. Ernst und Sohn, Berlin (1965) (in German)
Maidl, B., Herrenknecht, M., Maidl, U., Wehrmeyer, G.: Mechanised Shield Tunnelling. Wiley-Blackwell (2012). https://doi.org/10.1002/9783433601051
Majdi, A., Ajamzadeh, H., Nadimi, S.: Investigation of moment–rotation relation in different joint types and evaluation of their effects on segmental tunnel lining. Arab. J. Geosci. 9(7), 1–15 (2016). https://doi.org/10.1007/s12517-016-2538-z
Marx, S., Schacht, G.: Betongelenke im Brückenbau [Concrete hinges in bridge construction], vol. 18. Deutscher Beton- und Bautechnik-Verein e.v. (2010) (in German)
Marx, S., Schacht, G.: Concrete hinges—historical development and contemporary use. 3rd fib International Congress, 2010, pp. 1–21 (2010)
Marx, S., Schacht, G.: Gelenke im Massivbau [Hinges in concrete structures]. Beton Stahlbetonbau 105(1), 27–35 (2010). https://doi.org/10.1002/best.200900061. (in German)
Menétrey, P., Willam, K.J.: Triaxial failure criterion for concrete and its generalization. ACI Struct. J. 92(3), 311–318 (1995). https://doi.org/10.14359/1132
Morgenthal, G., Olney, P.: Concrete hinges and integral bridge piers. J. Bridge Eng. 21(1), 06015,005 (2016). https://doi.org/10.1061/(ASCE)BE.1943-5592.0000783
Mori, T., Tanaka, K.: Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metall. 21(5), 571–574 (1973). https://doi.org/10.1016/0001-6160(73)90064-3
Sallenbach, H.H: Betongelenke beim Hardturm-Viadukt [Concrete hinges for the Hardturm-Viadukt]. Schweizer Bauzeitung 85 (1967)
Schacht, G., Marx, S.: Unbewehrte Betongelenke—100 Jahre Erfahrung im Brückenbau [Unreinforced concrete hinges—100 years of experience in bridge construction]. Beton Stahlbetonbau 105(9), 599–607 (2010). (in German)
Schacht, G., Marx, S.: Concrete hinges in bridge engineering. Proc. Inst. Civ. Eng. Eng. Hist. Herit. 168(2), 65–75 (2015). https://doi.org/10.1680/ehah.14.00020
Schlappal, T., Schweigler, M., Gmainer, S., Peyerl, M., Pichler, B.: Creep and cracking of concrete hinges: insight from centric and eccentric compression experiments. Mater. Struct. 50(6), 244 (2017). https://doi.org/10.1617/s11527-017-1112-9
Teachavorasinskun, S., Chub-uppakarn, T.: Influence of segmental joints on tunnel lining. Tunn. Undergr. Space Technol. 25(4), 490–494 (2010). https://doi.org/10.1016/j.tust.2010.02.003
Zaoui, A.: Continuum micromechanics: survey. J. Eng. Mech. 128(8), 808–816 (2002). https://doi.org/10.1061/(asce)0733-9399(2002)128:8(808)
Zhang, W., Jin, X., Yang, Z.: Combined equivalent & multi-scale simulation method for 3-D seismic analysis of large-scale shield tunnel. Eng. Comput. 31(3), 584–620 (2014). https://doi.org/10.1108/EC-02-2012-0034
Ziegler, F.: Mechanics of solids and fluids, 2nd edn. Springer (1995). https://doi.org/10.1007/978-1-4612-0805-1
Acknowledgements
Open access funding provided by Austrian Science Fund (FWF). Financial support by the Austrian Ministry for Transport and Technology (bmvit), the Austrian Research Promotion Agency (FFG), ÖBB-Infrastruktur AG, ASFINAG Bau Management GmbH, provided within the VIF-project 845681 “Optimierte Bemessungsregeln für dauerhafte bewehrte Betongelenke” and corresponding discussions with Michael Schweigler (TUWien), Susanne Gmainer and Martin Peyerl (Smart Minerals GmbH), Alfred Hüngsberg (ÖBB-Infrastruktur AG), Erwin Pilch and Michael Kleiser (ASFINAG Bau Management GmbH) are gratefully acknowledged. Additional interesting discussions regarding the use of concrete hinges inmechanized tunneling, carried out within theAustrian Science Fund (FWF) project P 281 31-N32 “Bridging theGap by means ofMultiscale Structural Analysis” with Yong Yuan (Tongji University) and Jiaolong Zhang (TU Wien/Tongji University) are also gratefully acknowledged.
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This paper is dedicated to the memory of Franz Ziegler
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Kalliauer, J., Schlappal, T., Vill, M. et al. Bearing capacity of concrete hinges subjected to eccentric compression: multiscale structural analysis of experiments. Acta Mech 229, 849–866 (2018). https://doi.org/10.1007/s00707-017-2004-3
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DOI: https://doi.org/10.1007/s00707-017-2004-3