COMPUTATIONAL GEOMECHANICS GeoEE 557 Instructor Derek Elsworth 231 Hosler elsworth psu edu Shugang Wang 230A Hosler szw138 psu edu Content Modeling deformation flow and transport using finite element finite difference and boundary element methods Coupled processes of flow deformation and heat mass and reactive transport Objectives To gain an appreciation of numerical methods through exposure to finite element finite difference and boundary element codes The course is designed for potential users and developers of domain and integral numerical methods that are ubiquitously applied in hydrology and atmospheric sciences mining civil mechanical and petroleum engineering and the geologic and materials sciences Prerequisites Matrix algebra elementary calculus elementary programming in MatLab Location T Th 4 40 5 55 218 Hosler 3 credits 1 Overview of Coupled Processes 1 1 Uncoupled systems 1 2 Coupled processes Thermo Hydro Mechanical Chemical T H M C 1 3 Balances of Mass Momentum and Energy 1 4 Interaction and Onsager Processes 1 5 Building representative systems incorporating couplings 1 6 Preliminary examples of THM processes 1 7 Key couplings 1 8 Dependent variables their selection and modes of coupling 2 Mechanical Behavior M 2 1 Conservation of momentum and Hooke s law 2 1 1 Principle of virtual work 2 2 Finite element representation 2 2 1 1 dimensional elements 2 2 2 2 dimensional behavior 2 2 2 1 CST elements 2 2 2 2 Isoparametric elements 2 3 Variational procedures Deformation 3 Hydraulic Behavior H 3 1 Conservation of mass and Darcy s law 3 2 Steady behavior 3 2 1 1 dimensional elements 3 2 2 2 dimensional behavior 2 D triangular and 2 D isoparametric elements 3 3 Transient behavior 3 3 1 Time stepping methods 3 4 Dual porosity flows 4 Hydro Mechanical Coupling H M 4 1 Stiffness and conductance terms 4 2 Coupling terms and symmetry 4 3 Time stepping Flow 4 4 1 dimensional examples 4 5 Dual porosity behavior 5 Mass Chemical Transport C 5 1 Conservation of mass and Fick s law 5 2 Steady behavior 5 3 Transient behavior 5 4 Considerations of local equilibrium Transport 6 Hydro Mechanical Chemical Coupling H M C 6 1 Stiffness conductance and advective terms 6 2 Coupling terms and symmetries 7 Thermal Transport T 7 1 Conservation of Energy and Fourier s law 7 2 Steady behavior 7 3 Transient behavior 8 Thermo Hydro Mechanical Coupling T H M 8 1 Stiffness conductance and advective terms 8 2 Coupling terms and symmetry 8 3 Time stepping 8 4 1 dimensional examples 9 Thermo Hydro Mechanical Chemical Coupling T H M C 9 1 Stiffness conductance and advective terms 9 2 Coupling terms and symmetries 10 Summary Behaviors 11 Boundary Element Methods Introduction 11 1 Indirect method General principles 11 1 1 Groundwater mechanics 11 1 2 Elasticity 11 2 Direct Method General principles 11 2 1 Groundwater mechanics 11 2 2 Elasticity 11 3 Coupled FEM BEM analysis 12 Overview and Summary Selected texts on reserve in the EMS library Lecture Overheads and Course Notes available online Grading 20 80 Participation Final project Transport TITLE Tentative Topic 1 Introduction 6 References 2 1 Governing Equations 2 2 Formulation 2 3 Solution 3 Validation 4 Parametric Study 5 Conclusions 0 Abstract and 10 min Presentation ACTIVITY Assign Select Problem Research topic and complete and report literature review Define conservation equations constitutive relations and boundary and initial conditions Formulate model Solve using model Validate Complete parametric study Distill significant results Complete paper and present results DELIVERABLE Oral report One page narrative and at least 20 references 10 DUE J 21 J 29 One page max plus figures 10 F 12 One page max plus figures One page max plus figures One page max plus figures One page max plus figures One page max plus figures 10 minute presentation with one slide for each of 1 2 1 2 2 2 3 3 4 5 seven slides 10 10 10 10 10 30 F 26 M 19 A2 A9 Academic Conduct Penn State s policy on academic integrity applies to all aspects of course deliverables Students are encouraged to work together in groups but to submit independent work Further details are available at http www ems psu edu students integrity index html A 22