1 FEM study of the faults activation Technische Universität München Joint Advanced Student School (JASS) St. Petersburg Polytechnical University Author: Ulanov Alexander

2 Problem significance Geomechanics application: - Subsidence of rocks - Sliding of bed near oil well

3 Аrea of study Faults activation in deforming saturated porous medium.

4 Particularity Examples of the elastic bodies (3D case and 2D case) with the possible surfaces of slipping. Interface (contact) element concept Parameters of the media may discontinue Nonlinear problem

5 Goals and objectives Simulation of joint transient process of diffusion porous pressure and stress state calculation in saturated porous medium.

6 Our estimates Еstimates: Saturation porous medium - combination of pore space, deformable skeleton and moving fluid. - Darcy's law for fluid. - Fluid is compressible. - Porous medium is isotropic and linear. - Small deflection. Examples:sandstone,clay.

7 Continuity equation: Equilibrium equation: p - pore pressure u - displacement vector k - coefficient of permeability μ - viscosity of the pore fluid Coupled solution for saturated one-phase flow in a deforming porous medium G - shear modulus Biot 1955

8 Variational formulation (part 1) Ω – domain in 2D(3D) space; S - boundary; n – external normal Variational formulation of equilibrium equation

9 Variational formulation of continuity equation Variational formulation (part 2)

10 Sc – surface of contact Interface model

11 Characteristics of interface layer elements: - infinitesimal thickness - permeability D - stiffness C Interface element concept Goodman 1968

12 Slip computation Slipping condition (Mohr-Coulomb) : σ n - normal stress σ s - shear stress K - friction coefficient С H - cohesion stress Iterative process: Stiffness С: If contact element is sliding Cs = 0 1 Calculation of strain state. 2 Slip conditional test. 3 Calculation of strain with new stiffnesses form.

13 Program structure Geometry and Grid generation - Ansys ICEM - Gambit Solution of problem - FEM solver - Optimization of data ( sparce-matrix ) - Iteration lib (ITL MTL) Processing and result аnalysis - GID - Tecplot10

14 Mesh generation in Gambit (format.CDB ) GID output Domain example (1)

15 Domain example (2) Mesh quality adaptation

16 Results No interface (slip) zone Modelling of sliding - Diffusion effect -Influence of cohesion Coh -Influence of permeability k -Influence of nonuniform permeability D

17 No interface (slip) zone. Diffusion effect - Pressure on lateral side is fixed - Zero-initial condition for pressure - No fluid flux in normal direction Establishment of linear pressure distribution

18 Influence of cohesion (Coh) C ohesion Count of elements Fixed pressure - Fixed permeability k - External load - Slipping condition Relative displacement of interface layer

19 Influence of permeability k - Fixed value of cohesion - Diffusion effect ( P = constant ) - Different value of permeability k permeability k СohNumber of elements External load

20 Effect of nonuniform permeability Destruction of rock in contact layer – Slip zone in contact layer k is – isotropic permeability ( no slip case ) k slip – additional component ( appear in slip case )

21 - Different value of Ds - Establishment of linear pressure distribution - Zero-initial condition for pressure - Zero displacement - Sliding on all contact layer Influence of nonuniform permeability ( part 1 )

22 Influence of nonuniform permeability ( part 1 ) Ds=1 Ds=10Ds=100

23 Influence of nonuniform permeability ( part 2 ) - Establishment of linear pressure distribution - Zero-initial condition for pressure - External load - Ds=100

24 Conclusions The model of coupled solution for saturated one-phase flow in a deforming porous medium is considered. Influence of various parameters on sliding is investigated. Goodman interface element concept is used.

25 Thank you for your attention !