OBSERVATION AND PREDICTION - Introduction to Soft Soil Geotechnique: Content, Context and Application - page 156

There is also a minimum condition for the time step, related to the fact in a given
time step t the storage process should be able to progress over the mesh size x ,

which leads to (see hydrodynamic period equation (6.8) for a mesh size)

x ) 2 t > 2(

c v

If this requirement is not met, the solution may become unstable in space. Both
conditions contradict: no time step suits. By choosing for an implicit time scheme
(Crank-Nicolson) there is no restriction, but for large time steps the accuracy
becomes an issue.

application 9.2
A regional stationary groundwater flow with a well is calculated with a Finite
Difference model with spatial discretisation (mesh size) of x = 25 m and linear

approximation of the potential head in the mesh cells. The calculation result shows
a potential head of = 10 m n the adjacent node. The

well radius is r w = 0.25 m. What is the true potential head in the well?

= 7 m in the well node and

application 9.3
The result of the Direct Simple Shear test, shown in Fig 3.3b, depends on the
initial stress state. This can be shown on the basis of the double sliding model. Two
cases are distinguished: (A) the horizontal stress is smaller than the vertical stress,

yy
or K 0 > 1. In the test, the vertical stress for both cases is kept equal, by adopting a
similar vertical force N . The failure state for both cases, according to the
associative Mohr-Coulomb model, and the corresponding principle stress direction
are presented in Fig 9.12. Obviously, the measured shear force is different in both
cases: T A < T B . The ratio T A /T B is equal to the ratio

xx < yy or K 0 < 1, and (B) the horizontal stress is larger than the vertical, xx >

B , because the total surface
of shear planes are equal in both cases. Fig 9.12 reveals that

A /

A / B = xxA / xxB =

sin 2 )/(1+sin 2 (1 = 30º this ratio becomes 0.6. In the DSS test, care is to

be taken that the stress ratio K 0 =

). For

xx / yy < 1, so that the test result T/N gives a

proper indication for tan .

application 9.4
The previous example shows the stress state at the start of failure. What is the
final stress state in a Direct Simple Shear test (vertical stress is kept constant), if a
conventional Mohr-Coulomb model models the material? Assume

xx yy xy

cos 2 and sin 2

2

m m

with for the radius m of the Mohr-circle complies with