Civil Engineering Reference
In-Depth Information
There are 294 equations and the skyline storage is 10521
step disp load(av) load(react) moment iters
1 0.2000E-04 0.1097E+02 0.1197E+02 0.3678E+01 2
2 0.4000E-04 0.1194E+02 0.1311E+02 0.4023E+01 2
3 0.6000E-04 0.1292E+02 0.1425E+02 0.4368E+01 4
4 0.8000E-04 0.1385E+02 0.1535E+02 0.4676E+01 31
5 0.1000E-03 0.1477E+02 0.1644E+02 0.4971E+01 19
6 0.1200E-03 0.1569E+02 0.1752E+02 0.5262E+01 10
7 0.1400E-03 0.1660E+02 0.1860E+02 0.5548E+01 14
8 0.1600E-03 0.1751E+02 0.1968E+02 0.5833E+01 8
9 0.1800E-03 0.1842E+02 0.2076E+02 0.6115E+01 13
10 0.2000E-03 0.1933E+02 0.2183E+02 0.6397E+01 4
11 0.2200E-03 0.2021E+02 0.2288E+02 0.6656E+01 32
12 0.2400E-03 0.2107E+02 0.2392E+02 0.6904E+01 23
13 0.2600E-03 0.2193E+02 0.2495E+02 0.7148E+01 13
14 0.2800E-03 0.2279E+02 0.2597E+02 0.7384E+01 22
15 0.3000E-03 0.2363E+02 0.2698E+02 0.7614E+01 16
16 0.3200E-03 0.2444E+02 0.2796E+02 0.7819E+01 30
17 0.3400E-03 0.2523E+02 0.2884E+02 0.8004E+01 32
18 0.3600E-03 0.2601E+02 0.2970E+02 0.8186E+01 13
19 0.3800E-03 0.2675E+02 0.3048E+02 0.8355E+01 40
20 0.4000E-03 0.2744E+02 0.3120E+02 0.8519E+01 44
21 0.4200E-03 0.2810E+02 0.3187E+02 0.8676E+01 28
22 0.4400E-03 0.2866E+02 0.3243E+02 0.8815E+01 40
23 0.4600E-03 0.2918E+02 0.3293E+02 0.8945E+01 29
24 0.4800E-03 0.2961E+02 0.3330E+02 0.9068E+01 64
25 0.5000E-03 0.3001E+02 0.3363E+02 0.9180E+01 29
26 0.5200E-03 0.3029E+02 0.3387E+02 0.9264E+01 44
27 0.5400E-03 0.3043E+02 0.3403E+02 0.9313E+01 45
28 0.5600E-03 0.3056E+02 0.3416E+02 0.9353E+01 18
29 0.5800E-03 0.3067E+02 0.3427E+02 0.9387E+01 11
30 0.6000E-03 0.3076E+02 0.3437E+02 0.9414E+01 13
31 0.6200E-03 0.3085E+02 0.3447E+02 0.9439E+01 7
32 0.6400E-03 0.3092E+02 0.3455E+02 0.9459E+01 11
33 0.6600E-03 0.3099E+02 0.3463E+02 0.9474E+01 14
34 0.6800E-03 0.3105E+02 0.3468E+02 0.9486E+01 12
35 0.7000E-03 0.3110E+02 0.3474E+02 0.9497E+01 3
Figure 6.20
Results from Program 6.4 example
the force builds up to a maximum value of around 31 kN/m when using average stresses.
This is in close agreement with the closed form Rankine solution of 30 kN/m, despite the
relatively crude mesh. The higher result obtained by nodal reactions is commonly observed
in analyses of this type, due in part to the high shear stress concentration at the bottom
edge of the wall. The displacement vectors of the mesh corresponding to passive failure
of the soil behind the wall are shown in Figure 6.22. The Rankine passive mechanism
outcropping at an angle of 30
◦
to the horizontal is reproduced.
The initial stress algorithm presented in this program will tend to overestimate collapse
loads, especially if the displacement (load) steps are made too big. Users are recommended
to try one or two different increment sizes to test the sensitivity of the solutions. The
problem is caused by incremental “drift” of the stress state at individual Gauss points into
illegal stress space, in spite of apparent numerical convergence. Although not included
in the present work, various strategies are available (e.g. Nayak and Zienkiewicz, 1972)
for drift correction. In the next section, more complicated “stress-return” procedures are
illustrated which ensure stresses at each Gauss point return accurately to the yield surface.
