Journal of Petroleum Geology, Vol.3,
No.2, pp. 209-236>, 1980
©Copyright 2000 Scientific Press,
Ltd.
ON THE THEORY OF GROWTH
FAULTING*
PART II(a): GENESIS OF THE
"UNIT"
W. Crans and G. Mandl
* This research work was carried
out in the Koninklijke/Shell, Exploratie en Produktie
Laboratorium, Rijswijk , The Netherlands, during 1968-1972 by:
Dr. W. Crans, Exploration Consultant, GeoQuest International
Inc./ J. R. Butler and Company, 4605 Post Oak Place, Suite 130,
Houston, Texas 77027, and Dr. G. Mandl, Koninklijke/Shell,
Exploratie en Produktie Laboratorium, Rijswijk, The Netherlands.
Some basic features have been published previously in short notes
by Crans, Mandl and Shippam (1973) and Mandl and Crans (979).
Abstract
A detailed and rigorous
geomechanical analysis of the stability of overpressured, gently
sloping, sediment layers is presented that underlies the
Multi-Unit Delta Model described in Part 1 (Crans, Mandl and
Haremboure, Journ. Petrol. Geol., 2, 3, 1980). That delta model
explains and permits quantitative reproduction of main features
associated with growth faulting. Starting from the equilibrium
equations, the Coulomb-Mohr yield criterion and the proper
initial and boundary conditions, the elastic and plastic stress
fields in the sloping, overpressured layer are derived. The
plastic stress field is calculated on the grid generated by the
"characteristics" of the hyperbolic partial
differential equation for the plastic stress state. These
characteristics, being called in stress analyses "slip
lines", are potential faults. In the case considered, a
parameter equation is derived for one set of slip lines,
(potential growth faults), which may simplify into cycloids under
special conditions. Once the plastic stress field has been
generated, the plastic deformation of the layer can be calculated
by introducing the proper boundary conditions to the flow rules
or plastic "velocity equations" being discussed
extensively. To complete the rheological description, the
behaviour of the sediment layer is described by attributing also
thixotropic properties to the sediment. Although the case
discussed is a very specific one, it illustrates how structural
geological phenomena can be modelled on the computer in an
appropriate geomechanical way. Such a numerical computer model
shows the unique relation between plastic stress state and fault
pattern, and the non-unique relation between plastic stress state
and deformation pattern, being typical for the theory of
plasticity.