Dealing with corners and changing geometry - The Boundary Element Method with Programming - page 345

Note that the resulting traction to be applied at the new excavation surface for load
case 4 is the sum of tractions obtained by internal stress evaluation for load cases 1 to 3
plus the tractions due to the virgin stress field. For the analysis of the next load case, the
mesh of the single infinite region representing the excavated tunnel surface is changed
by removing the face elements and adding a row of elements representing the next stage
of excavation.

Figure 12.18 Vertical displacements at tunnel crown

0

LC1 NEW
LC2 NEW
LC3 NEW
LC4 NEW
LC5 NEW
LC1 REF
LC2 REF
LC3 REF
LC4 REF
LC5 REF

LC1

-0.005

LC2

-0.01

LC3

-0.015

-0.02

LC4

-0.025

LC5

-0.03

0 3 6 9 12 15

chainage [m]

Figure 12.19 Vertical displacements at tunnel crown
The results of vertical displacements along the crown of the tunnel are shown in Figure
12.19 for load cases 1 to 5. These results are compared with the reference solution.
There is some difference and this can be attributed to approximation made for the stress
distribution near the corners. It seems that the resultant excavation force is not