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DISROC 5 -  Example: Other Examples

Fracture zone around tunnels

As it is well known, shear softening can lead to strain localization on shear bands which can represent mode II fractures. This example illustrates Disroc's ability to simulate this phenomenon.

The model ANELVIP (31430) of the Disroc Materials Catalog covers elastoplastic materials with softening plasticity. The cohesion, friction angle and tensile strength decrease with plastic deformation.

Softening Equations

The following diagram shows the stress-strain curve of the material under uniaxial compressive load. A softening behavior is observed, with or without a positive hardening phase before the peak stress, and with different softening rates (brittleness) and different residual stresses, for different values of the constitutive parameters.

Fig.1: Softening plasticity in ANELVIP

Now, consider the excavation of a tunnel in quasi-brittle rock represented by the ANELVIP model with softening. The mesh and the boundary conditions used in Disroc to simulate this excavation problem are shown in the following figures.

Mesh - Boundary Conditions Fig.2a: Mesh and boundary conditions

Mesh details
Fig.2b: Mesh zoom near the tunnel wall

The excavation of the tunnel is modeled by controlling the boundary forces on the tunnel wall and decreasing them from their initial values, corresponding to the in situ stresses, to zero. This process is described by the parameter λ varying from λ =0 at the initial state of in situ stresses to λ =1 for the totally deconfined tunnel.

The in situ stresses considered here are σH = 16 MPa and σV = 12 MPa. The rock strength is given by the Mohr-Coulomb criterion with cohesion C=7.2 MPa and φ=12. The softening behavior leads to a residual cohesion of 0.3*C=2.16 MPa and a residual friction angle of 0.2*φ=2.4.

The following figures show the shear fractures developed around the tunnel by this excavation action for different values of the deconfinig parameter λ.

Lambda = 0.5 Figure 3.a: Shear fractures for λ=0.5 Lambda = 0.6 Figure 3.b: Shear fractures for λ=0.6 Lambda = 0.7 Figure 3.c: Shear fractures for λ=0.7
Lambda = 0.8 Figure 3.d: Shear fractures for λ=0.8 Lambda = 0.9 Figure 3.e: Shear fractures for λ=0.9 Lambda = 1.0 Figure 3.f: Shear fractures for λ=1.0

The state of the vertical stress σyy and vertical displacement uy at the final stage of excavation are given below.

Vertical stress field Figure 4.a: Contour of σyy (MPa) after excavation Vertical displacement field Figure 4.b: Contour of vertical displacement (m) after excavation

The deformed shape of the fractured excavation zone with shear bandes representing the shear fractures is given in the following figure.

Click on the figure for video animation

Deformaed shear bands
Figure 5: Shear fractures around the tunnel in deformed geometry after excavation