Numerical Methods for Tunneling using ABAQUS

NUMERICAL MODEL The material behavior of the shotcrete shell and inner liner are assumed to be governed by a linear elastic relationship. Furthermore for the shotcrete a yield stress of 20 MN/m² is assumed. All support elements (shotcrete shell and inner liner) are also assumed to be homogenous and isotropic. The shotcrete shell has a uniform thickness of 20 cm and the quality is assumed to be a SpC 25/30-J2 (MPa). The inner liner has a uniform thickness of 30 cm and the quality is assumed to be a C 25/30 (MPa). SpC 25 / 30 - J2 Early strength (ÖVBB, 2004) Characteristic cube compressive strength, after 28 days; (MPa) Characteristic cylinder compressive strength, after 28 days; (MPa) Sprayed concrete or shotcrete C 25 / 30 Characteristic cube compressive strength, after 28 days; (MPa) Characteristic cylinder compressive strength, after 28 days; (MPa) Concrete

Table 1: Physical mechanical properties of ground, shotcrete shell and inner liner

Material GROUND SHOTCRETE SHELL (YOUNG) SHOTCRETE SHELL (HARDENED) INNER LINER

Material Detail

E (MN/m²)

(-)

MARL

500 10,000 15,000 30,500

0.4 + 0.5 0.2 0.2 0.2

SpC 25/30-J2 C25/30

c (MN/m²)

(deg)

(deg)

3.0

35

0

2.3 Contact formulation

For the numerical calculation, contact conditions have to be defined between all elements. An overview of possible contact conditions for the numerical model is provided below:  

ground and shotcrete shell (2.3.1) shotcrete shell and inner liner (2.3.2)

2.3.1 Contact formulation between ground and shotcrete shell

Tangential behavior: 

The Coulomb friction law is assumed with a friction coefficient of µ = 100 ( = 89.43°) and no cohesion. This value (µ = 100) is recommended in the