Tunnel Excavation

This example studies the behavior of soil during a tunnel excavation. The surface settlement and the width of the plastic region around the tunnel are important parameters required to predict the reinforcements that are required during the excavation. This verification example is adapted from Ref. 1 and Ref. 2.

In order to calculate in-situ stresses, use two studies. In the first study compute the stress state of the soil before the excavation of the tunnel. In the second study compute the elastoplastic behavior once the soil is removed. This requires incorporation of the stress response calculated in the first study. The soil removal is modeled using the activation feature in the linear elastic material model.

In order to speed up the calculation consider the soil in the first step as elastic, and in the second step, add the Drucker-Prager soil plasticity model. The example is solved in 2D plane strain.

Model Definition

The geometry consists of a soil layer that is 45 m deep and 90 m wide. A tunnel of 10 m in diameter is placed at the symmetry axis, 20 m below the surface. A bed rock, 45 m below the surface, constrains the displacement in the vertical direction, and a roller boundary is used to model the infinite extension of the soil in the lateral direction.

Figure 1: Dimensions and boundary conditions for the tunnel excavation example.

Soil Properties

The soil properties are adapted from Ref. 2.

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Young’s modulus, E = 12 MPa and Poisson’s ratio ν = 0.495.

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Cohesion c = 130 kPa and angle of internal friction φ = 30 degrees.

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Use the Drucker-Prager criterion and match the material parameters to the Mohr-Coulomb criterion.

Constraints and Loads

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At the lower boundary, fix the displacement with a fixed Constraint.

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Use symmetry condition at the left boundary, and roller condition at the right boundary.

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Add a node to account for gravity effects.

Results and Discussion

Figure 2 shows the stress distribution due to gravity. The roller and symmetry boundaries create a linear vertical variation of the stress.

Figure 2: The von Mises stress in the soil layer before excavation of the tunnel.

Figure 3 shows the stress distribution after excavating the tunnel. Note the increase in the equivalent stress around the tunnel.

Figure 3: The von Mises stress in the soil layer after excavation of the tunnel.

In the second step, besides removing the tunnel domain, a soil plasticity feature is included. In Figure 4, the region that experience plastic deformation is shown.

Figure 4: Plastic deformation in the zone near the tunnel after the excavation.

The horizontal displacement and the settlement of the top surface due to the excavation is shown in Figure 5 and Figure 6.

Figure 5: The horizontal displacement at the top surface.

Figure 6: The surface settlement.

References

1. D. Potts and L. Zdravkovic, Finite Element Analysis in Geotechnical Engineering, Thomas Telford Publishing, 2001.

2. H. Schweiger, “Results from Numerical Benchmark Exercises in Geotechnics,” Proc. 5th European Conference on Numerical Methods in Geotechnical Engineering, pp. 305–314, 2002.

Geomechanics_Module/Soil/tunnel_excavation

Modeling Instructions

From the menu, choose .

New

In the window, click

Model Wizard

In the window, click

In the tree, select .

Click .

Click

In the tree, select .

Click

Geometry 1

Rectangle 1 (r1)

In the toolbar, click

In the window for , locate the section.

In the text field, type 90.

In the text field, type 45.

Locate the section. In the text field, type -45.

Click

Circle 1 (c1)

In the toolbar, click

In the window for , locate the section.

In the text field, type 5.

In the text field, type 180.

Locate the section. In the text field, type -20.

Locate the section. In the text field, type 270.

Click

Form Union (fin)

In the window, click .

In the window for , click

Use the full geometry and a linear elastic material in the first step.

Solid Mechanics (solid)

Linear Elastic Material 1

Since in this example, the Poisson’s ratio is 0.495, use a mixed formulation to avoid locking effects.

In the window, under click .

In the window for , locate the section.

From the list, choose .

Symmetry 1

In the toolbar, click

and choose .

Select Boundaries 1 and 3–5 only.

Fixed Constraint 1

In the toolbar, click

and choose .

Select Boundary 2 only.

Roller 1

In the toolbar, click

and choose .

Select Boundary 7 only.

Gravity 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Linear Elastic Material 1

In the window, click .

Soil Plasticity 1

In the toolbar, click

and choose .

In the window for , locate the section.

Select the check box.

Add an node and enable it only in the second study in order to get in-situ stresses due to gravity.

Linear Elastic Material 1

In the window, click .

Initial Stress and Strain 1

In the toolbar, click

and choose .

In the window for , locate the section.

In the S0 table, enter the following settings:


withsol('sol1', solid.sx)	withsol('sol1', solid.sxy)	withsol('sol1', solid.sxz)
withsol(’sol1’, solid.sxy)	withsol('sol1', solid.sy)	withsol('sol1', solid.syz)
withsol(’sol1’, solid.sxz)	withsol(’sol1’, solid.syz)	withsol('sol1', solid.sz)

Add an node to the linear elastic material in order to model the soil removal. The activation expression set to zero in order to deactivate the material. The elastic stiffness of the soil material is multiplied by activation scale factor.

Linear Elastic Material 1

In the window, click .

Activation 1

In the toolbar, click

and choose .

Select Domain 2 only.

In the window for , locate the section.

In the text field, type 1e-9.

Materials

Material 1 (mat1)

In the window, under right-click and choose .

In the window for , locate the section.

In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Young’s modulus	E	12e6	Pa	Basic
Poisson’s ratio	nu	0.495	1	Basic
Density	rho	2000	kg/m³	Basic
Cohesion	cohesion	130e3	Pa	Mohr-Coulomb
Angle of internal friction	internalphi	30[deg]	rad	Mohr-Coulomb