Civil Engineering Reference
In-Depth Information
This program allows excavations over general shapes of meshes, so it is the user's
responsibility to provide the global coordinates
g coord
and element numbering
g num
of the original unexcavated configuration as data. Figure 6.38 shows a truncated data set in
the interests of a compact presentation. The same concept of a “local” node freedom array
lnf
as in the previous program is used again. In a preliminary loop, labelled
elements 0
the ground is stressed by its own weight. The soil model allows for 7 properties read as
usual into the array
prop
. Note that due to the simplicity of the constitutive model, a very
limited range of
K
o
values could be achieved automatically, so
K
o
is input as data as the
7th property read into the array
prop
.
Following the coordinates, element numbering, and boundary condition data, the data
requires the number of nodes at which output will be required
nouts
, followed by the
output node numbers
no
, the plastic tolerance
tol
, the iteration ceiling
limit
, the number
of load increments per excavation
incs
, and the number of excavations
layers
.
The final block of data gives the excavation sequence. For each of the excavation steps,
the number of elements to be removed
noexe
and the element numbers
exele
must be
read. The subroutine
exc nods
computes the node numbers removed at each excavation
step. Excavated “air” elements are given a stiffness of zero (
0) and the excavated
nodes are automatically fully restrained and hence removed from the assembly process.
As in the previous program, for each “layer” the geometry is modified and a new
stiffness matrix and load vectors formed. Arrays that change their size from one excavation
to the next therefore involve
ALLOCATE
and
DEALLOCATE
statements.
For the case considered, the vertical excavation (case
E
=
) is to occur in two steps
layers=2
leading to a cut of depth 2 m. As can be seen from the data, the first excavation
removes elements 9 and 13, and the second excavation, removes elements 10 and 14.
The output (for case B) shown as Figure 6.39 and plotted in Figure 6.40, indicates that
B
The initial number of elements is: 16
The initial number of freedoms is: 96
Excavation number 1
There are 86 freedoms
There are 14 elements after 2 were removed
Increment 1 took 2 iterations to converge
Increment 2 took 2 iterations to converge
Increment 3 took 2 iterations to converge
Increment 4 took 2 iterations to converge
Increment 5 took 2 iterations to converge
Node x-disp y-disp
29 0.7635E-05 -0.5876E-04
30 0.9240E-04 -0.3784E-04
31 0.8605E-04 -0.1057E-04
32 0.1102E-03 -0.1652E-05
Excavation number 2
There are 76 freedoms
There are 12 elements after 2 were removed
Increment 1 took 2 iterations to converge
Increment 2 took 2 iterations to converge
Increment 3 took 5 iterations to converge
Increment 4 took 22 iterations to converge
Increment 5 took 250 iterations to converge
Node x-disp y-disp
29 -0.3073E-03 -0.1641E-02
30 0.9790E-03 -0.1531E-02
31 0.2371E-02 -0.1282E-02
32 0.4044E-02 -0.7897E-03
Figure 6.39
Results from Program 6.8 example
