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Assessment of the Safety Factor Evolution of the Shotcrete Lining for Different Curing Ages

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Abstract

The behavior of the shotcrete linings during the tunnel construction is complex due to the variability of its mechanical characteristics during the curing time. After the installation of the support structure, the lining is loaded along with the excavation face. A new calculation procedure involving two analytical methods, i.e. the convergence-confinement method and hyperstatic reaction method, have been developed. By means of these two methods, it is possible to assess the evolution of the stress state in the lining, and therefore, also of the safety factor with respect to the failure in compression of the shotcrete. Due to the analysis of the safety factor evolution over time, it is possible to correctly design the lining, to choose the type of sprayed concrete and to define the maximum admissible advance rate of the excavation face, in order not to critically load the lining. In the following paper, after having shown the definition of the safety factor, a parametric analysis is performed, in order to investigate the evolution of the safety factor of the lining for two different rock types, three different shotcrete types and two tunnel advance rates have been considered.

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Abbreviations

b :

Depth of the lining considered, equal to 1 m in the two-dimensional problem taken into consideration

crm peak:

Peak cohesion of the rock mass

crm res :

Residual cohesion of the rock mass

Erm :

Elastic modulus of the rock mass

E SC :

Elastic modulus of the sprayed concrete with varying time t (in hours) after the lining installation in the studied section

\(E_{SC,\infty }\) :

Asymptotic values of the elastic modulus of the sprayed concrete reached for high time values

FS:

Safety factor

\(M_{i,j}\) :

Bending moment in the i-th node, at the load step j-th

\(N_{i,j}\) :

Normal force in the i-th node, at the load step j-th

p 0 :

Lithostatic stress state of the rock mass

t :

Lining thickness

v:

Poisson ratio

α :

Exponent of the exponential equation, which characterizes the curing rate, i.e. the evolution of mechanical parameters (elastic modulus and uniaxial compressive strength) of SC over time

ϕrm peak:

Peak friction angle of the rock mass

ϕrm res:

Residual friction angle of the rock mass

ψ:

Dilatancy

\(\sigma_{n,\hbox{max} ,i,j}\) :

Maximum normal stress acting inside the sprayed concrete in correspondence of a node

σ SC :

Unconfined compressive strength of the sprayed concrete with varying time t (in hours) after the lining installation in the studied section

\(\sigma_{SC,\infty }\) :

Asymptotic values of the unconfined compressive strength of the sprayed concrete, reached for high t values

References

  • Aydan O, Sezaki M, Kawamoto T (1992) Mechanical and numerical modelling of shotcrete. In: Pande G, Pietruszczack S (eds) Numerical models in geomechanics. Taylor and Francis, London, pp 707–7016

    Google Scholar 

  • Bieniawski ZT (1978) Determining rock mass deformability. Int J Rock Mech Min Sci 15:335–343

    Article  Google Scholar 

  • Bryne LE (2014) Time dependent material properties of shotcrete for hard rock tunneling. Ph.D Thesis, Stockholm, Sweden

  • Chang Y, Stille H (1993) Influence of early age properties of shotcrete on tunnel construction sequences. In: Wood DF, Morgan DR (eds) Shotcrete for underground support VI. American Society of Civil Engineers, Reston, pp 110–117

    Google Scholar 

  • Chen WF (1982) Plasticity in reinforced concrete. McGraw-Hill, New York

    Google Scholar 

  • Clements M (2004) Comparison of methods for early age strength testing of sprayed fibre reinforced concrete. In: Bernard ES (ed) Proceedings of the 2nd international conference on engineering developments in sprayed fibre reinforced concrete, Cairns, Queensland, Australia. Taylor, London, pp 81–87

    Google Scholar 

  • Concrete Institute of Australia (2010) Shotcrete in Australia. Concrete Institute of Australia, Rhodes

    Google Scholar 

  • De Belie N, Grosse CU, Kurz J, Reinhardt HW (2005) Ultrasound monitoring of the influence of different accelerating admixtures and cement types for shotcrete on setting and hardening behavior. Cem Concrete Res 35:2087–2094

    Article  Google Scholar 

  • DIN (2014) Spritzbeton - Nationale Anwendungsregeln zur Reihe DIN EN 14487 und Regeln für die Bemessung von Spritzbetonkonstruktionen. Beuth Verlag GmbH, Berlin

    Google Scholar 

  • DiNoia TP, Sandberg PJ (2004) Alkali-free shotcrete accelerator interactions with cement and admixtures. In: 2nd International conference on engineering developments in shotcrete. A.A. Balkema Publishers, Leiden, London, pp 137–144

    Chapter  Google Scholar 

  • Do NA, Dias D, Oreste P, Djeran-Maigre I (2014a) A new numerical approach to the hyperstatic reaction method for segmental tunnel linings. Int J Numer Anal Meth Geomech 38:1617–1632

    Article  Google Scholar 

  • Do NA, Dias D, Oreste P, Djeran-Maigre I (2014b) The behavior of the segmental tunnel lining studied by the hyperstatic reaction method. Eur J Environ Civ Eng 18(4):489–510

    Google Scholar 

  • Fahimifar A, Hedayat A (2008) Determination of ground response curve of the supported tunnel considering progressive hardening of shotcrete lining. In: Proceedings of the 5th Asian rock mechanics symposium, Tehran, Iran, November 24–26

  • Fahimifar A, Hedayat A (2010) Elasto-plastic analysis in conventional tunnelling excavation. Proc Inst Civ Eng Geotech Eng 163(1):37–45. https://doi.org/10.1680/geng.2010.163.1.37

    Article  Google Scholar 

  • Feenstra PH, de Borst B (1993) Aspects of robust computational models for plain and reinforced concrete. Heron 48(4):5–73

    Google Scholar 

  • Graziani A, Boldini D, Ribacchi R (2005) Practical estimate of deformations and stress relief factors for deep tunnels supported by shotcrete. Rock Mech Rock Eng 38(5):345–372

    Article  Google Scholar 

  • Hellmich C, Ulm FJ, Mang HA (1999) Multisurface chemoplasticity II: numerical studies on NATM-tunneling. J Eng Mech-ASCE 125(6):702–714

    Article  Google Scholar 

  • Iwaki K, Hirama A, Mitani K, Kaise S, Nakagawa K (2001) A quality control method for shotcrete strength by pneumatic pin penetration test. NDT and E Int 34(6):395–402

    Article  Google Scholar 

  • Kotsovos MD, Newman JB (1978) Generalized stress-strain relation for concrete. J Eng Mech-ASCE 104:845–856

    Google Scholar 

  • Melbye T (1994) Sprayed concrete for rock support. MBT International Underground Construction Group, Zürich

    Google Scholar 

  • Meschke G (1996) Elasto-viskoplastische Stoffmodelle fur numeriscbe Simulationen mittels der Methode der Finiten Elemente. Habilitationsschrift, TU Wien

  • Mohajerani A, Rodrigues D, Ricciuti C, Wilson C (2015) Early-age strength measurement of shotcrete. J Mater. https://doi.org/10.1155/2015/470160

    Article  Google Scholar 

  • Moussa AM (1993) Finite element modelling of shotcrete in tunnelling. Ph.D thesis, University of Innsbruck, Austria

  • Neuner M, Schreter M, Unteregger D, Hofstetter G (2017) Influence of the constitutive model for shotcrete on the predicted structural behavior of the shotcrete shell of a deep tunnel. Materials 10:577. https://doi.org/10.3390/ma10060577

    Article  Google Scholar 

  • Neville AM, Dilger WH, Brooks JJ (1983) Creep of plain and structural concrete. Construction Press, Harlow

    Google Scholar 

  • Oreste P (2003) Procedure for determining the reaction curve of shotcrete lining considering transient conditions. Rock Mech Rock Eng 36(3):209–236. https://doi.org/10.1007/s00603-002-0043-z

    Article  Google Scholar 

  • Oreste P (2007) A numerical approach to the hyperstatic reaction method for the dimensioning of tunnel supports. Tunn Undergr Sp Technol 22:185–205

    Article  Google Scholar 

  • Oreste P (2009) The convergence-confinement method: roles and limits in modern geomechanical tunnel design. Am J Appl Sci 6(4):757–771

    Article  Google Scholar 

  • Oreste P (2014) The Determination of the tunnel structure loads through the analysis of the Interaction between the void and the support using the convergence-confinement method. Am J Appl Sci 11(11):1945–1954

    Article  Google Scholar 

  • Oreste P, Spagnoli G, Luna Ramos CA, Sebille L (2018) The hyperstatic reaction method for the analysis of the sprayed concrete linings behavior in tunneling. Geotech Geol Eng 36(4):2143–2169. https://doi.org/10.1007/s10706-018-0454-6

    Article  Google Scholar 

  • Oreste P, Spagnoli G, Luna Ramos CA (2019) The elastic modulus variation during the shotcrete curing jointly investigated by the convergence-confinement and the hyperstatic reaction methods. Geotech Geol Eng 37(3):1435–1452. https://doi.org/10.1007/s10706-018-0698-1

    Article  Google Scholar 

  • Pan YW, Huang ZL (1994) A model for the time dependent interaction between rock and shotcrete support in a tunnel. Int J Rock Mech Min Sci 31(3):213–219

    Article  Google Scholar 

  • Pöttler R (1990) Time-dependent rock: shotcrete interaction a numerical shortcut. Comput Geotech 9(3):149–169

    Article  Google Scholar 

  • prEN 934-5 (2003) Admixtures for concrete, mortar and grout—part 5: admixtures for sprayed concrete—definitions, requirements and conformity

  • Prudencio LR Jr (1998) Accelerating admixture for shotcrete. Cem Concr Compos 20:213–219

    Article  Google Scholar 

  • Qiu Y, Ding B, Gan J, Guo Z, Zheng C, Jiang H (2017) Mechanism and preparation of liquid alkali-free liquid setting accelerator for shotcrete. IOP Conf Ser Mater Sci Eng 182:012034. https://doi.org/10.1088/1757-899X/182/1/012034

    Article  Google Scholar 

  • Rispin M, Howard D, Kleven OB, Garshol K, Gelson J (2009) Safer, deeper, faster: sprayed concrete: an integral component of development mining. Australian Centre for Geomechanics

  • Rokhar RB, Zachow R (1997) Ein neues Verfahren zur taglichen Kontrolle der Auslastung einer Spritzbetonschale. Felsbau 15(6):430–434

    Google Scholar 

  • Schädlich B, Schweiger HF (2014) A new constitutive model for shotcrete. In: Hicks MA, Brinkgreve RBJ, Rohe A (eds) Numerical methods in geotechnical engineering. Taylor & Francis, Oxam, pp 103–108

    Chapter  Google Scholar 

  • Schütz R (2010) Numerical modelling of shotcrete for tunneling. Ph.D. thesis, Imperial College London, UK

  • Schütz R, Potts DM, Zdravkovic L (2011) Advanced constitutive modelling of shotcrete: model formulation and calibration. Comput Geotech 38(6):834–845

    Article  Google Scholar 

  • Spagnoli G, Oreste P, Lo Bianco L (2016) New equations for estimating radial loads on deep shaft linings in weak rocks. Int J Geomech 16(6):06016006. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000657

    Article  Google Scholar 

  • Spagnoli G, Oreste P, Lo Bianco L (2017) Estimation of shaft radial displacement beyond the excavation bottom before installation of permanent lining in nondilatant weak rocks with a novel formulation. Int J Geomech 17(9):04017051. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000949

    Article  Google Scholar 

  • Thomas A (2009) Sprayed concrete lined tunnels. Taylor & Francis, Oxon

    Google Scholar 

  • Weber JW (1979) Empirische Formeln zur Beschreibung der Festigkeitsentwicklung und der Entwicklung des E-moduls von Beton. Betonwerk-und-Fertigteiltechnik, pp 753–759

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Authors and Affiliations

  1. Department of Environmental, Land and Infrastructural Engineering, Politecnico di Torino, Corso Duca Degli Abruzzi 24, 10129, Turin, Italy

    Pierpaolo Oreste

  2. BASF Construction Solutions GmbH, Dr.-Albert-Frank-Straße 32, 83308, Trostberg, Germany

    Giovanni Spagnoli

  3. Faculty of Engineering, Universidad Mariana, Calle 18 No. 34-104, Pasto, Colombia

    Cesar Alejandro Luna Ramos

  4. Department of Civil and Environmental Engineering, Colorado School of Mines, 1500 Illinois Street, Golden, CO, 80401, USA

    Ahmadreza Hedayat

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  1. Pierpaolo Oreste
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  2. Giovanni Spagnoli
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  3. Cesar Alejandro Luna Ramos
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  4. Ahmadreza Hedayat
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Correspondence to Giovanni Spagnoli.

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Cesar Alejandro Luna Ramos: Formerly at Department of Environmental, Land and Infrastructural Engineering, Politecnico di Torino, Corso Duca Degli Abruzzi 24, 10129 Torino, Italy.

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Oreste, P., Spagnoli, G., Luna Ramos, C.A. et al. Assessment of the Safety Factor Evolution of the Shotcrete Lining for Different Curing Ages. Geotech Geol Eng 37, 5555–5563 (2019). https://doi.org/10.1007/s10706-019-00990-2

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