Nonlinear Time-Dependent Analysis of the Load-Bearing Capacity of a Single Permanent Shotcrete Lining at the Brenner Base Tunnel

Figures & data

Fig. 1: Longitudinal view and cross-section of the investigated tunnel section, together with the dimensions, tunnel support structure and partial excavation scheme

Fig. 2: Illustration of the geology in the investigated section

Fig. 3: 2D plane strain model of the emergency tunnel, with the boundary and initial conditions and the excavation profile: top heading and bench (excavated simultaneously) and invert

Fig. 4: Finite element mesh after excavation of the top heading and the bench (left) and after excavation of the invert and placement of the complete shotcrete lining (right)

Fig. 5: Assumed time-dependent stress release layout after excavation of the top heading and the bench in the 2D finite element model

Table 1: Shotcrete composition used for the permanent shotcrete lining in the emergency tunnel

Ingredient	Quantity	Unit
Water	203	kg/m^3
CEM I 52.5N	380	kg/m^3
Limestone sand (0/4)	1031	kg/m^3
Crushed limestone aggregates (4/8)	694	kg/m^3
Fluasit (hydraulically binding admixture)	40	kg/m^3
Accelerator Mapequick 043 FFG	7.5–8.5	%

Fig. 6: Molds for spraying directly cylindrical specimens (left), molds and spray boxes placed at the tunnel site (center), and spraying of cylindrical specimens at the tunnel face (right)

Fig. 7: Sprayed shotcrete specimen, unmolded 6 h after spraying (left), unsealed specimen for determining the uniaxial compressive strength (center), and sealed specimen mounted in a hydraulic creep test bench (right)

Table 2: Calibrated material parameters for the shotcrete damage plasticity (SCDP) model

Young's modulus at 1 day	$E^{\left(1\right)}$	13,943 MPa	Ratio of uniaxial tensile strength to compressive strength	$f_{\mathrm{tu}}/f_{\mathrm{cu}}$	0.1
Young's modulus at 28 days	$E^{\left(28\right)}$	21,537 MPa	Ratio of biaxial to uniaxial compressive strength	$f_{\mathrm{bu}}/f_{\mathrm{cu}}$	1.16
Creep compliance parameter	$q_4$	34 × 10^−6 1/MPa	Ultimate shrinkage strain	${ϵ}_{\mathrm{shr}}^{\mathrm{\infty }}$	−0.0013
Poisson’s ratio	$\nu$	0.21	Shrinkage half-time	$t_{\mathrm{shr}}^{50}$	8645 h
Creep exponential modulus	$e^{\mathrm{flow}}$	1.22	Plastic strain at peak in uniaxial compression at 1 h	${ϵ}_{\mathrm{cpu}}^{p\left(1\right)}$	−0.06
Uniaxial compressive strength at 1 day	$f_{\mathrm{cu}}^{\left(1\right)}$	18.56 MPa	Plastic strain at peak in uniaxial compression at 8 h	${ϵ}_{\mathrm{cpu}}^{p\left(8\right)}$	−0.0014
Uniaxial compressive strength at 28 days	$f_{\mathrm{cu}}^{\left(28\right)}$	40.85 MPa	Plastic strain at peak in uniaxial compression at 24 h	${ϵ}_{\mathrm{cpu}}^{p\left(24\right)}$	−0.0007
Ratio of uniaxial yield stress to compressive strength	$f_{\mathrm{cy}}/f_{\mathrm{cu}}$	0.1	Specific mode I fracture energy at 28 days	$G_{\mathrm{fI}}^{\left(28\right)}$	0.1 N/mm

Fig. 8: Predicted evolution of the uniaxial compressive strength (left) and the Young's modulus (right): experimentally determined values from Ref. [17] and additional experimental data from 2018,¹⁹ and predictions by the calibrated shotcrete damage plasticity (SCDP) model

Fig. 9: Predicted evolution of the vertical displacement at the crown and horizontal displacement at the side wall, and statistical bandwidth according to geodetic measurements

Fig. 10: Predicted evolution of the circumferential stress at the rock–shotcrete interface and the free surface at the crown and the side wall

Fig. 11: Predicted evolution of the longitudinal stress at the rock–shotcrete interface and the free surface at the crown and the side wall

Fig. 12: Predicted circumferential stress (left) and longitudinal stress (right) along the shotcrete lining at the rock–shotcrete interface and the free surface for t = 54 h and t = 108 h

Fig. 13: Contour plot of the circumferential stress ${\sigma }_{\mathrm{C}}$ (left) and the longitudinal stress ${\sigma }_{\mathit{L}}$ (right) acting in the shotcrete lining 132 h after excavation of the top heading and the bench, i.e. 24 h after placement of the lower part of the lining

Neuner M, Cordes T, Drexel M, Hofstetter G. Time-dependent material properties of shotcrete: experimental and numerical study. Materials 2017; 10(9), 1067. doi: 10.3390/ma10091067

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Dummer A. Numerische Modellierung und experimentelle Untersuchung des Materialverhaltens von jungem Spritzbeton mit Anwendung für den Brenner Basistunnel (Master Thesis, in German). Universität Innsbruck, 2019.

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