Fig 1.
Flow chart of the application of the variational criterion.
Fig 2.
Sketch and numerical model of the tunnel portal.
Fig 3.
Curves between displacements and SRFs for nodes when .
Fig 4.
Curves between displacements and SRFs for nodes when .
Fig 5.
Curves between displacements and SRFs for nodes when .
Fig 6.
Pictures of failure elements under different SRFs when .
Fig 7.
Pictures of failure elements under different SRFs when .
Fig 8.
Pictures of failure elements under different SRFs when .
Fig 9.
Pictures of the shear strain increment of the model under different commands when .
Fig 10.
Pictures of the shear strain increment of the model under different commands when .
Fig 11.
Pictures of the shear strain increment of the model under different commands when .
Fig 12.
Curves between elastic and plastic zone energy values and SRFs.
Table 1.
Variational values and SRFs when .
Table 2.
Variational values and SRFs when .
Table 3.
Variational values and SRFs when .
Table 4.
FOSs under different criteria.
Table 5.
FOSs under different mesh densities.
Table 6.
FOSs under different geometric dimensions.
Table 7.
FOSs under different strength reduction factor intervals.
Table 8.
FOSs under adjusted mechanical parameters.
Table 9.
FOSs under adjusted convergence criteria.
Table 10.
Variational values and SRFs when the slope-tunnel system is under natural conditions.
Table 11.
Variational values and SRFs when the slope-tunnel system is with the anti-slide pile reinforcement.
Table 12.
Results under different criteria.
Fig 13.
Nephograms of the slope-tunnel system engineering example when the failure occurs.
Fig 14.
Curves between elastic energy increment values and SRFs for the slope-tunnel system engineering example.
Note: the elastic energy is calculated by referencing the method in papers [17,18], and it yields more ideal results.
Table 13.
Results of examples from the manual of Rocscience.