Computational strategies for predictive geology with reference to salt tectonics

Abstract This work is concerned with aspects of computational strategies for predictive geology with particular reference to the field of salt tectonics. The computational approach is based on the Lagrangian methodology incorporating: (i) large deformations of inelastic solids at finite strains, (ii) constitutive models for generic inelastic materials suitable for description of simultaneously active elasto-plastic, viscoplastic and viscoelastic behaviour, (iii) an adaptive strategy for modelling of large deformations of inelastic solids at finite strains. Apart from its economic importance, salt tectonics, and in particular formation of salt diapirs, is considered to be representative for many geological processes in the Earth’s crust. A number of numerical simulations are provided to illustrate the scope and benefits of the developed computational approach. These include the formation of the salt diapirs due to (i) compression and folding, (ii) thin skinned extension, and (iii) simulation of salt diapirism due to progradation on a basin scale.

[1]  D. Peric,et al.  A computational model for generalized inelastic materials at finite strains combining elastic, viscoelastic and plastic material behaviour , 2003 .

[2]  Martin P. A. Jackson,et al.  External shapes, strain rates, and dynamics of salt structures , 1986 .

[3]  Antonio Orlando,et al.  Analysis of transfer procedures in elastoplasticity based on the error in the constitutive equations: Theory and numerical illustration , 2004 .

[4]  Klaus-Jürgen Bathe,et al.  A hyperelastic‐based large strain elasto‐plastic constitutive formulation with combined isotropic‐kinematic hardening using the logarithmic stress and strain measures , 1990 .

[5]  T. Belytschko,et al.  Computational Methods for Transient Analysis , 1985 .

[6]  Donald E. Carlson,et al.  The derivative of a tensor-valued function of a tensor , 1986 .

[7]  Christian Miehe,et al.  Computation of isotropic tensor functions , 1993 .

[8]  J. Brackbill,et al.  A continuum method for modeling surface tension , 1992 .

[9]  David R. Owen,et al.  On error estimates and adaptivity in elastoplastic solids: Applications to the numerical simulation of strain localization in classical and Cosserat continua , 1994 .

[10]  J. C. Simo,et al.  Algorithms for static and dynamic multiplicative plasticity that preserve the classical return mapping schemes of the infinitesimal theory , 1992 .

[11]  P. Perzyna.  Fundamental Problems in Viscoplasticity , 1966 .

[12]  J. C. Simo,et al.  On a fully three-dimensional finite-strain viscoelastic damage model: Formulation and computational aspects , 1987 .

[13]  Stéphane Zaleski,et al.  Numerical simulation of Rayleigh-Taylor instability for single and multiple salt diapirs , 1992 .

[14]  L. L. Nettleton.  Recent Experimental and Geophysical Evidence of Mechanics of Salt-Dome Formation , 1943 .

[15]  S. Reese,et al.  A theory of finite viscoelasticity and numerical aspects , 1998 .

[16]  Klaus-Jürgen Bathe,et al.  Error indicators and adaptive remeshing in large deformation finite element analysis , 1994 .

[17]  David R. Owen,et al.  Transfer operators for evolving meshes in small strain elasto-placticity , 1996 .

[18]  S. Chandrasekhar.  Hydrodynamic and Hydromagnetic Stability , 1961 .

[19]  M. Ortiz,et al.  Lagrangian finite element analysis of Newtonian fluid flows , 1998 .

[20]  Cv Clemens Verhoosel,et al.  Non-Linear Finite Element Analysis of Solids and Structures , 1991 .

[21]  L. L. Nettleton.  Fluid Mechanics of Salt Domes , 1934 .

[22]  David R. Owen,et al.  On adaptive strategies for large deformations of elasto-plastic solids at finite strains : computational issues and industrial applications , 1999 .

[23]  O. Hassager,et al.  An algorithm for the use of the Lagrangian specification in Newtonian fluid mechanics and applications to free-surface flow , 1985, Journal of Fluid Mechanics.

[24]  N. Cristescu,et al.  Time effects in rock mechanics , 1998 .

[25]  James A. Sethian,et al.  Level Set Methods and Fast Marching Methods , 1999 .

[26]  Djordje Peric,et al.  On a class of constitutive equations in viscoplasticity : formulation and computational issues , 1993 .

[27]  David R. Owen,et al.  Finite-element applications to the nonlinear mechanics of solids , 1998 .

[28]  Michael Ortiz,et al.  Adaptive mesh refinement in strain localization problems , 1991 .

[29]  B. Vendeville,et al.  The fall of diapirs during thin-skinned extension , 1992 .

[30]  Wing Kam Liu,et al.  Nonlinear Finite Elements for Continua and Structures , 2000 .

[31]  C. Talbot.  INCLINED AND ASYMMETRIC UPWARD-MOVING GRAVITY STRUCTURES , 1977 .

[32]  O. Stephansson,et al.  Diapirism theory and experiment , 1972 .

[33]  Christian Miehe,et al.  Superimposed finite elastic–viscoelastic–plastoelastic stress response with damage in filled rubbery polymers. Experiments, modelling and algorithmic implementation , 2000 .

[34]  D. Owen,et al.  A model for finite strain elasto-plasticity based on logarithmic strains: computational issues , 1992 .

[35]  J. C. Simo,et al.  Associated coupled thermoplasticity at finite strains: formulation, numerical analysis and implementation , 1992 .

[36]  M. Ortiz,et al.  A material‐independent method for extending stress update algorithms from small-strain plasticity to finite plasticity with multiplicative kinematics , 1992 .

[37]  C. Talbot.  Centrifuged models of Gulf of Mexico profiles , 1992 .

[38]  D. Waltham.  Why does salt start to move , 1997 .

[39]  M. Aubertin,et al.  A unified representation of the plasticity, creep and relaxation behavior of rocksalt , 2000 .

[40]  J. F. Besseling,et al.  Mathematical Modelling of Inelastic Deformation , 1994 .

[41]  S. Stewart,et al.  Synthesis of salt tectonics in the southern North Sea, UK , 1995 .

[42]  Wei Shyy,et al.  Computational Fluid Dynamics with Moving Boundaries , 1995 .

[43]  L. Anand,et al.  Finite deformation constitutive equations and a time integrated procedure for isotropic hyperelastic—viscoplastic solids , 1990 .

[44]  Hemin Koyi,et al.  The shaping of salt diapirs , 1998 .

[45]  M. M. Rashid,et al.  Material state remapping in computational solid mechanics , 2002 .

[46]  E. A. de Souza Neto,et al.  A new computational model for Tresca plasticity at finite strains with an optimal parametrization in the principal space , 1999 .

[47]  W.-D. Woidt,et al.  Finite element calculations applied to salt dome analysis , 1978 .

[48]  H. Ramberg.  Gravity, deformation and the earth's crust : in theory, experiments, and geological application , 1981 .

[49]  E. A. de Souza Neto,et al.  A computational framework for a class of fully coupled models for elastoplastic damage at finite strains with reference to the linearization aspects , 1996 .

[50]  H. Koyi,et al.  Salt diapirs of the southwest Nordkapp Basin : analogue modelling , 1993 .

[51]  Geoffrey J. Frank,et al.  A viscoelastic–viscoplastic constitutive model for glassy polymers , 2001 .

[52]  K. Bathe.  Finite Element Procedures , 1995 .