| Application | PLAXIS 2D |
| Version | PLAXIS 2D 2024.1 |
| Date created | 8 July 2024 |
| Date modified | 3 March 2025 |
| Original author | Richard Witasse - Principal Application Engineer |
| Keywords | PLAXIS 2D, Rock, Tunnel closure, Plastic radius, Rock bolts, Shotcrete, Mohr-Coulomb, Field stress |
This example demonstrates the practical application of PLAXIS for the calculation of the tunnel deformation and the effectiveness of the proposed tunnel support. It has been inspired by an article from Hoek (1998). The problem involves a 10 m span modified horseshoe-shaped tunnel driven through very poor-quality rock at a depth of 250 m. It is assumed that the rock mass properties and the ratio of the in-situ stresses remain constant. The horizontal stress is assumed to be 1.3 times the vertical stress.
The rock mass is a graphitic phyllite with a uniaxial compressive strength of σci = 15 MPa. The rock mass is described as 'disintegrated', consisting of a poorly interlocked mixture of angular and rounded pieces, and 'poor' with slickensides and highly weathered surfaces corresponding to an approximate Geological Strength Index GSI = 25. The uniaxial compressive strength of the rock mass is estimated as σcm = 1 MPa (deducted from the equivalent cohesive strength ceq = 330 kPa and equivalent friction angle φeq = 24.9° obtained by curve fitting as shown in Figure 1.
Figure 1: Converting Hoek-Brown Strength Envelope to Mohr Coulomb failure line
To limit the strain development within acceptable limit (between 2% and 5%), a support providing 1.6 MPa is required (see Figure 2). This can be easily achieved using a 1 m x 1 m pattern of 34 mm diameter rock bolts together with a 200 mm thick shotcrete lining.
Figure 2: Considered tunnel support system