OBSERVATION AND PREDICTION - Introduction to Soft Soil Geotechnique: Content, Context and Application - page 142

small strain) (undrained situations), oedometer test, triaxial tests (complete history
of the degradation of soil stiffness with increase in strain level), simple shear test
(lower reliability), and correlations with Atterberg limits (lower reliability). The
initial conditions within the ground ( K 0 , OCR, water conditions, etc.) are important
to consider when using non-linear constitutive models for the soil.
For further detailed information on the application of numerical methods
reference is made to many textbooks (a.o. Potts and Zdravkovi), and in particular
to the outcome of the EU-project GeoTechNet/design tools. 44

Numerical and physical peculiarities
In the field of reservoir engineering numerical and physical aspects of the
simulation of the mechanical interaction of pore fluids and the porous matrix is
extensively studied. Basic concepts for space-time discretisation, solution
techniques, numerical stability and accuracy of non-linear equations, equally
valuable in geo-mechanical simulation, can be found in the work of Khalid Aziz et
al. Some specific intriguing phenomena are outlined next.

Artificial dispersion
Numerical dispersion is an undesired non-physical effect inherently present in
discrete time-space domain algorithms. It appears in the numerical treatment of
hyperbolic or parabolic partial differential equations, e.g. for transport or dynamics
in porous media. It aggravates, if processes are non-linear and at discontinuities
(interfaces with a large contrast in a certain property). For time and space
discretisation, Taylor series expansions are used, which have multiple terms.
Generally, only the first derivative term in the expansion is used for differencing
and the higher order derivative terms are neglected. Control of numerical
dispersion can be accomplished by limiting the size of time steps and by increasing
spatial discretisation. Also, there are numerical techniques to improve
representation of the derivatives.
As an example, consider the heat transport equation (14.1)

2

2 T T T

D v (9.9)

x t

x

L v is the dispersion coefficient and v the convective velocity. For the
spatial derivative Taylor series is used with spatial distance d

Here, D =

2

T T ( x d ) T ( x ) d T

2

O ( d ) (9.10)

2

x d 2

x

44

In GeoTechNet, a EU-project during 2001-2005, 40 members of 17 countries participated
in the development of a geotechnical database and in gaining insight in EC7, design tools,
human and environmental impact and natural disasters in the geotechnical profession.