RocSupport
version 4.0
Tutorial 4 | Using the Vrakas and Anagnostou Method
Topics Covered:
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Duncan Fama Solution Method
Vrakas and Anagnostou Method
Deterministic Analysis
Custom Support
RocSupport v. 4.0 Tutorial Manual
Tutorial 4: Using the Vrakas and Anagnostou Method
Introduction
This problem was taken from Vrakas and Anagnostou (2014). It compares the results of finitestrain and infinitesimal solutions for tunnel convergence for a problem with a significant final
wall displacement. The problem uses material properties corresponding to the Sedrun section
of the Gotthard Base Tunnel in Switzerland, which passes through heavily squeezing ground.
This problem will compare Vrakas and Anagnostou’s finite strain method with the DuncanFama classical small-strain solution.
Method 1: Duncan-Fama
Open RocSupport and select New File from the toolbar or the File menu.
We will start by studying the Duncan-Fama solution method.
Open the Project Settings dialog and in the General tab, change the Solution Method to
Duncan-Fama (1993). Notice the text on the right updates to give a small description of the
small strain method. We will assume all input values are exact values (deterministic). Click OK.
Open the Tunnel Parameters dialog from the toolbar or the Analysis menu. Enter the following
data into the dialog:
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Tunnel Radius = 5 m
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In-Situ Stress = 22.5 MPa
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Young’s Modulus = 2000.00 MPa
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Poisson’s Ratio = 0.25
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Cohesion = 0.25 MPa
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Friction Angle = 23 degrees
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Dilation Angle = 3 degree
The dialog should look as follows:
Select Apply and then Close. Switch to the Tunnel Section View from the toolbar or the
Analysis menu. Your screen should look as follows.
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RocSupport v. 4.0 Tutorial Manual
Tutorial 4: Using the Vrakas and Anagnostou Method
The textbox on the left corner of the screen confirms that the tunnel convergence is 100%.
This means that the tunnel walls were displaced by 5 meters (the length of the radius) into the
tunnel. Therefore, this problem can clearly be classified as a large-strain problem. We will now
see what results we get using the Vrakas and Anagnostou (2014) Solution Method.
Method 2: Vrakas and Anagnostou
Open the Project Settings dialog and in the General tab, change the Solution Method to Vrakas
and Anagnostou (2014). Notice the text on the right updates to give a small description of the
large strain method. Select OK.
Immediately the textbox on the left corner of the screen updates the results to show that the
tunnel convergence is now approximately 50%. The Ground Reaction curve should look as
follows:
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RocSupport v. 4.0 Tutorial Manual
Tutorial 4: Using the Vrakas and Anagnostou Method
This demonstrates the importance of using the Vrakas and Anagnostou Method for a large
strain model.
We will now add support to the tunnel.
Custom Support
Open the Support Parameters dialog using the button on the toolbar or the Analysis menu. We
will add a custom steelset support to the tunnel. Click on the steelsets tab and check the Add
Support box. Then check the Custom box in the same tab.
Here, we can define the properties of our custom steelset. Alternatively, we can select a custom
support from the table of custom support types. Select the Types button in the tab. You should
see the Reinforcement dialog.
We will apply the default steelset. Select OK. The information is now loaded in the dialog. Select
Apply and Close.
Switch to the Tunnel Section View from the toolbar or the Analysis menu.
We can see from the textbox that the radius of the plastic zone has decreased from 30 m to 17
m. The tunnel convergence has also been reduced to 11%.
However, the tunnel will need further reinforcement. This will be left as an exercise to the user.
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RocSupport v. 4.0 Tutorial Manual
Tutorial 4: Using the Vrakas and Anagnostou Method
References
A. Vrakas, G. Anagnostou. (2014) A finite strain closed-form solution for the elastoplastic
ground response curve in tunnelling, International Journal for Numerical and Analytical Methods in
Geomechanics 38(11): 1131-1148.
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