Civil Engineering Reference
In-Depth Information
DEALLOCATE
d at each lift. Then, for each lift the geometry and connectivity can be
calculated and hence the number of equations,
neq
and stiffness matrix diagonal locator
kdiag
, operating at that stage of the construction process. The stiffness matrix and load
vector sizes can then be set by an
ALLOCATE
statement and the viscoplastic algorithm
initiated. The program has the option of applying the gravity loads associated with each
lift in
incs
increments (3 in this case).
The results are shown in Figure 6.31 and plotted in Figure 6.32, showing the progress of
toe displacement as the embankment is raised. For the case shown, in which the foundation
and embankment are both undrained clays, with
14 kN/m
2
, the embankment is seen to
fail when its height reaches approximately 4 m. This is exactly what would be predicted by
Taylor's (1937) charts, which gives, for a 2:1 slope with a depth ratio of
c
u
=
5, a stability
number equal to 0.18, implying a factor of safety very close to unity. The displacement
vectors corresponding to the unconverged solution when the embankment height reached
4 m are shown in Figure 6.33.
D
=
3
.
The final number of elements is: 74
The final number of freedoms is: 452
Lift number 1
There are 288 freedoms
There are 48 elements after 48 were added
Increment 1 took 2 iterations to converge
Increment 2 took 2 iterations to converge
Increment 3 took 2 iterations to converge
Max displacement is 0.1948E-03
Lift number 2
There are 338 freedoms
There are 56 elements after 8 were added
Increment 1 took 2 iterations to converge
Increment 2 took 2 iterations to converge
Increment 3 took 2 iterations to converge
Max displacement is 0.2624E-03
Lift number 3
There are 382 freedoms
There are 63 elements after 7 were added
Increment 1 took 2 iterations to converge
Increment 2 took 2 iterations to converge
Increment 3 took 2 iterations to converge
Max displacement is 0.2806E-03
Lift number 4
There are 420 freedoms
There are 69 elements after 6 were added
Increment 1 took 2 iterations to converge
Increment 2 took 5 iterations to converge
Increment 3 took 7 iterations to converge
Max displacement is 0.3311E-03
Lift number 5
There are 452 freedoms
There are 74 elements after 5 were added
Increment 1 took 15 iterations to converge
Increment 2 took 45 iterations to converge
Increment 3 took 500 iterations to converge
Max displacement is 0.1138E+00
Figure 6.31
Results from Program 6.7 example
