Tunnel in a Jointed Anisotropic Elastic Material (FLAC3D)

Note

The project file for this example is available to be viewed/run in FLAC3D.[1] The project’s main data file is shown at the end of this example.

The plane strain problem of a tunnel under anisotropic in-situ stress is considered. The material is model by the Columnar-Basalt (COMBA) Model model. The tunnel has a radius of 1m. Orthogonal joint sets are considered for the simulations. Ubiquitous joints 1 and 3 are normal to the plane of study (their dip direction is 90°). A series of simulations is considered whereby the dip angle of joint 3 is rotated in 15° increments, between 0° and 90°, whilst joint 1 is kept normal to joint 3. The in-situ horizontal stress is 8 MPa in the horizontal x-direction, and 12 MPa in the vertical direction; the stress in the out of plane direction is 10 MPa. Roller boundary conditions are applied at the far boundaries. Full symmetry is used for the simulations. The material anisotropic elastic properties are listed in Table 1. The dilation for the joints is 0°, tensile strength is set to a high value. The joint strength properties are shown in Table 2.

Table 1: Elastic Properties for the Tunnel Simulation

\(E\)

\(\nu\)

\(K_{1n}\)

\(K_{2n}\)

\(K_{3n}\)

\(K_{1s}\)

\(K_{2s}\)

\(K_{3s}\)

60 GPa

0.3

1200 GPa/m

1200 GPa/m

300 GPa/m

1200 GPa/m

1200 GPa/m

50.4 GPa/m
Table 2: Strength Properties for the Tunnel in Ubiquitous Joint Material Simulation

joint-cohesion-1

5 MPa

joint-friction-1

0°

joint-cohesion-2

1e20 MPa

joint-friction-2

0°

joint-cohesion-3

5 MPa

joint-friction-3

10°

Displacement contours at the end of the simulations from dip-3 = 0°, 15°, 30°, …, and 165° are shown followed:

dip = 0 ../../../../../_images/disp-015.png ../../../../../_images/disp-030.png ../../../../../_images/disp-045.png ../../../../../_images/disp-060.png ../../../../../_images/disp-075.png ../../../../../_images/disp-090.png ../../../../../_images/disp-105.png ../../../../../_images/disp-120.png ../../../../../_images/disp-135.png ../../../../../_images/disp-150.png ../../../../../_images/disp-165.png

The displacement contours look reasonable; the model appears to be well-behaved for the cases investigated.

The plastic state at the end of the simulations from dip-3 = 0°, 15°, 30°, …, and 165° are shown followed:

dip = 0 ../../../../../_images/state-015.png ../../../../../_images/state-030.png ../../../../../_images/state-045.png ../../../../../_images/state-060.png ../../../../../_images/state-075.png ../../../../../_images/state-090.png ../../../../../_images/state-105.png ../../../../../_images/state-120.png ../../../../../_images/state-135.png ../../../../../_images/state-150.png ../../../../../_images/state-165.png

The simulations predict shear localization around the tunnel; the pattern and extent of the yielding zone shows a rather complex interplay of influences of the anisotropic in-situ stress state, and the strength and orientation of the joints. However, the results exhibit an expected pattern of symmetry as the joints are rotated.

Data File

tunnel.dat

;---------------------------------------------------------------------
;            numerical solution for a long tunnel in pre-stressed
;            anisotropic material - plane strain
;---------------------------------------------------------------------
model large-strain off

zone create radial-cylinder size 1 1 50 50 ratio 1 1 1 1.1 point 1 20 0 0 ... 
     point 2 0 0.2 0 point 3 0 0 20 dimension 1 1 1 1
zone reflect normal -1 0 0 origin 0 0 0
zone reflect normal 0 0 -1 origin 0 0 0
;
zone cmodel assign columnar-basalt
zone property flag-matrix-plastic false
zone property young=60e3 poisson=0.30
zone property space-1=0.1 space-2=0.1 space-3=0.1
zone property stiffness-normal-1=1200e3 stiffness-normal-2=1200e3 stiffness-normal-3=300e3 
zone property stiffness-shear-1=1200e3 stiffness-shear-2=1200e3 stiffness-shear-3=50.4e3
zone property dip-1 [dip1] dip-direction-1 90
zone property normal-x-2 0 normal-y-2 1 normal-z-2 0
zone property dip-3 [dip3] dip-direction-3 90
zone property joint-cohesion-1 5.0  joint-friction-1 5  joint-dilation-1 0 joint-tension-1 1e20
zone property joint-cohesion-2 1e20 joint-friction-2 0  joint-dilation-2 0 joint-tension-2 1e20
zone property joint-cohesion-3 5.0  joint-friction-3 10 joint-dilation-3 0 joint-tension-3 1e20
;
zone initialize stress-xx -8
zone initialize stress-yy -10
zone initialize stress-zz -12
zone gridpoint fix velocity-z range position-z -20.1 -19.9
zone gridpoint fix velocity-z range position-z 19.9 20.1
zone gridpoint fix velocity-x range position-x -20.1 -19.9
zone gridpoint fix velocity-x range position-x 19.9 20.1
zone gridpoint fix velocity-y
;
zone history displacement-x position 1 0 0
zone history velocity-x position 1 0 0
zone history unbalanced-force-y position 1 0 0
zone history unbalanced-force-z position 1 0 0
history interval 20

model solve
model save [savefile]

Endnote