Numerical models by the Particle Flow Code (PFC) as well as physical model tests showed that in case of a stable system the stresses in a pillar with a thickness of the radius of two parallel tunnels approach the dead weight of the overburden divided by the pillar thickness. These stresses may rise up to 2.2 times the uniaxial compressive strength without pillar failure. The pillar and the outer sidewalls are fairly equally stressed. In case of rock failure, substantial stress redistributions in the outer sidewalls are possible because there is enough rock mass available. In the pillar, however, stress redistributions are only possible to a limited extent, because rock failure causes a reduction of the load bearing pillar cross-section and consequently an increase in the stresses In these areas. The pillar, therefore, has to be supported as quickly and stiffly as possible, whereas the outer sidewalls and the abutments can be supported more softly.


Collapses during the excavation of tunnels (Baumgartner, 2000), analytical (Vavrovsky, 1987) and numerical models (Roth et al. 2001), together with physical model experiments (Jovanovic & Rulofs, 2005), have shown that single shallow tunnels in soft rock mostly collapse at a critical overburden height of about 1.5 times the tunnel diameter, This paper will investigate the behaviour of soft, homogeneous and isotropic rock around two tunnels under low overburden (rock mass behaviour type; Austrian Society for Geomechanics, 2001).

Rabcewicz (1961) recommended estimating the stresses in the pillar between two tunnels to equal the dead weight of the overburden divided by the pillar thickness Jaeger & Cook (1969) pointed out that the stresses at the surface of the pillar with a thickness of the tunnel radius are close to the stresses at the outer tunnel sidewalls according to analytical analyses by elasticity theory.

The Particle Flow Code (PFC)

The Particle Flow Code (PFC) of the ITASCA Consulting Group (ITASCA, 1999) is modelling the displacements and interactions of loaded assemblies of disc shaped particles (balls) being in or getting into contact with one-dimensional wall elements by the distinct element method (OEM; Cundall, 1987). The particles may be bonded together at their contact points to represent a solid that may fracture due to progressive bond breakage. Fracturing is simulated via progressive bond breakage under load. Every particle is checked on contact with every other particle at every time step. Thus PFC can simulate not only failure mechanisms of the rock around excavations but also complete up to the surface.

For the numerical investigations a particle composited material was generated in a box with a width and a height 4,5 times the tunnel diameter (Fig. I). The overburden of the tunnels is 2,5 times the tunnel diameter and the pillar thickness equals the tunnel radius. After a rough estimation the micro parameters (particle stiffness, inter particle friction, bond strength) were calibrated by back analysis during modelling of the collapse mechanisms.

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