Abstract
Tunnels are structures which have vital roles in the development of societies. In the numerical models of underground cavities, such as tunnels, loading due to zone elimination is induced instantaneously in the soil mass, and it might cause a disturbance in the stress state especially around the excavation area. However, this is not compatible with the principles of elastoplastic constitutive models used in soil behavior simulations. Besides, the predicted load on the tunnel liner will be larger than the actual value in this kind of modeling. In other words, it causes the so-called overestimated design. Using an appropriate constitutive model could lead the numerical analyses to accurate results. In this research, loading increment in the simulation of soil behavior is evaluated according to experimental data. Next, a correct way for numerical simulation related to underground excavation is described according to gradually eliminating (incremental) stress around tunnels based on the numerical modeling in the finite-difference code called FLAC. Hence, the effect of releasing the stress on the results is illustrated by the stress paths and deformations around a tunnel. Finally, the installation time of the tunnel liner and its impact on the numerical results are considered based on some experimental and field data. It is concluded that the use of software default in modeling the tunnel issues might lead to extreme oscillations in the stress paths, and it could affect the numerical results. Therefore, it is reasonable to utilize a proper way to release the stress around the excavation area gradually.
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(triaxial test data taken from (Gasparre 2005))
(triaxial test data taken from (Gasparre 2005))
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Acknowledgements
This work has been financially supported by the research deputy of Shahrekord University. The Grant Nos. were 97GRN1M1829 and 97GRN1M1709.
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Appendix: The algorithm Used in FLAC by FISH Programming to Release the Stress
Appendix: The algorithm Used in FLAC by FISH Programming to Release the Stress
The general steps of the numerical model for the gradual release of the stress around the excavation region in the FLAC software.
For this purpose, it is necessary to use the possibility of programming in the FLAC software, which is executed in the FISH language. The intended algorithm has been listed as follows:
- 1.
First, the overall soil medium (mass) is defined and run to reach the initial equilibrium.
- 2.
The excavation region becomes vacant.
- 3.
The nodes numbers on the boundary of the excavation region are specified.
- 4.
The nodes on the excavation boundary along the x- and y- axes should be fixed.
- 5.
Again, an analysis is performed to be formed (created) the reactions into the supports placed on the tunnel’s boundary nodes mentioned in the step 4.
- 6.
The nodes on the tunnel’s boundary became free (the supports placed on the tunnel’s boundary are removed).
Note: It could be easily implemented in the FLAC software and does not require coding with FISH programming until step (6). Next steps should be done with coding by FISH language programming.
- 7.
Two additional grid variables are intended for each node on the excavation boundary. For example, ex_1(i,j) and ex_2(i,j) are defined to save the horizontal and vertical forces of the nodes placed on the excavation boundary, respectively (that are calculated in step 5). The indices i and j are represented the coordinates of zones and grid-points (nodes) in x and y directions, respectively.
- 8.
Also, the horizontal and vertical external forces of each node (which are calculated in step 5 and used in step 7) are stored in two other new variables such as xfa and yfa. These forces are applied to the corresponding nodes by command and apply commands in FISH programming.
- 9.
After applying the opposite of the external forces computed in step 8 (xfa and yfa) to the boundary nodes, an analysis is performed to reach the initial equilibrium. Now, the system is ready to begin the unloading (excavation).
- 10.
The number of steps (stages) to release the stress of the soil around the tunnel is specified.
- 11.
Considering the number of the stages to release the stresses, the external forces of each boundary nodes are reduced. Then, the reduced forces are applied to the boundary nodes for each stage of the stress release.
- 12.
In each stage, after applying the reduced forces on each node, the problem is analyzed to achieve equilibrium.
- 13.
This operation is performed until the end of the loading (i.e. the reduced forces to be zero).
It should be noted that from step 11 onwards, it could be placed in a loop. In addition, if the tunnel liner should also be considered, it can be controlled that the liner should be installed after releasing a certain (intended) percentage of the stress. In this way, it is possible to install the tunnel liner at the intended time (after a certain percentage of the stress release).
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Heidarzadeh, H., Kamgar, R. Evaluation of the Importance of Gradually Releasing Stress Around Excavation Regions in Soil Media and the Effect of Liners Installation Time on Tunneling. Geotech Geol Eng 38, 2213–2225 (2020). https://doi.org/10.1007/s10706-019-01158-8
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DOI: https://doi.org/10.1007/s10706-019-01158-8