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.