Val_001a Explicit Geomechanical Solver

Contents

Problem Description

In this test, the column consolidation problem is solved using explicit geomechanical solver, i.e. Solution_algorithm = 4.

The data file for the model is found in: ParaGeo Examples\Validation\Val_001\Data\Val_001a_Terzaghi.dat.

Data File

* Mesh_generation_variables

! ---------------------------------

Node_insert_perturb_fact 0.1

* Units

! --------------------------------------

Stress MPa

Length m

Time s

Temperature Celsius

!----------------------------------------------------------------

! Stratigraphy data

!----------------------------------------------------------------

* Stratigraphy_definition

! --------------------------------------

Unit_names IDM=1

"formation0"

* Stratigraphy_horizon NUM=1

! --------------------------------------

Name "formation0"

Lines IDM=1

* Stratigraphy_surface_load

! --------------------------------------

Applied_stress 2.0

Pore_pressure_flag 1

Time_curve_stress 1

* Time_curve_data NUM=1

! --------------------------------------

Name "load"

Time_curve IDM=2

0.0 1.0

Time_factor IDM=2

1.0 1.0

! ---------------------------------------------------------------

! Group data

! --------------------------------------------------------------

* Group_control_data

! --------------------------------------

Group_numbers IDM=1

Active_geomechanical_groups IDM=1

Active_porous_flow_groups IDM=1

* Group_data NUM=1

! --------------------------------------

Group_name "formation0"

Element_type "QPM4"

Material_name "sediment_elastic"

Surfaces IDM=1

Porous_flow_type 4

!---------------------------------------------------------------

! Material Data

!---------------------------------------------------------------

* Material_data NUM=1

! ---------------------------------

Units IDM=4

MPa

Celsius

Name "sediment_elastic"

! --------------------------------------------------------

Grain_stiffness 38000.0 ! MPa

Grain_density 2650.0

! --------------------------------------------------------

Porosity_model_type 1

Porosity 0.2

! --------------------------------------------------------

Elastic_model_type 1

Isotropic_elastic_properties IDM=2

/"Young's Modulus (E)"/ 10000.0 ! MPa

/"Poisson's Ratio (v)"/ 0.25000

! --------------------------------------------------------

Singlephase_fluid_name "Water"

! --------------------------------------------------------

Permeability_type 1

Permeability 1.00E-15

! --------------------------------------------------------

Biot_type 1

Biot_properties IDM=1

0.825

* Fluid_properties NUM=1

! ---------------------------------

Name "Water"

Fluid_type "Water"

Equation_state_type 0

Stiffness 2000.0 ! MPa

Density 1000.0

Viscosity_type 1

Viscosity 1.00E-9 ! MPa*s

!---------------------------------------------------------------

! Boundary conditions

!---------------------------------------------------------------

* Support_data

! ---------------------------------

Displacement_codes IDM=3 JDM=4

/Set 1/ 1 1 0

/Set 2/ 0 1 0

/Set 3/ 1 0 0

/Set 4/ 0 0 0

Displacement_code_lines IDM=4 JDM=2

/line/ 1 2 3 4

/Assign Set/ 2 3 4 3

!---------------------------------------------------------------

! History data output

!---------------------------------------------------------------

* History_point NUM=1

! ---------------------------------

Name "Base"

Group 1

Output_frequency_increment 10

Point_coordinates IDM=2 JDM=1

0.5 0.0

Displacements IDM=1

"DISP_Y"

Element_data IDM=1

"ELT_PORE"

* History_point NUM=2

! ---------------------------------

Name "Top_surface"

Group 1

Output_frequency_increment 10

Point_coordinates IDM=2 JDM=1

0.5 10.0

Displacements IDM=1

"DISP_Y"

Element_data IDM=1

"ELT_PORE"

* History_global

! ---------------------------------

Output_frequency_time 0.01

Mech_global_energy_data IDM=2

"Kinetic" "Elastic"

!---------------------------------------------------------------

! Mesh data

!---------------------------------------------------------------

* Mesh_control_data

! ---------------------------------

Generation_algorithm 1 ! Structured mesh

* Structured_mesh_data

! ----------------------------

Default_divisions 50

List_structured_line_sets IDM=1

* Structured_line_set NUM=1

! ----------------------------

Number_divisions 1

Lines IDM=1

!---------------------------------------------------------------

! Damping data

!---------------------------------------------------------------

* Damping_global_data

! --------------------------------------

Percentage_damping 0.02

!---------------------------------------------------------------

! Coupling control data

!---------------------------------------------------------------

* Couple_control_data

! --------------------------------------

Solution_algorithm "Incremental"

Volume_strain_coupling "Undrained"

Volume_update_model "Variable_group"

Field_names IDM=2

"Geomechanical"

"Porous_flow"

!==============================================================

! Stage data (200 flow steps/stage, 200 mech steps/flow step)

!==============================================================

* Time_scaling_factors

! --------------------------------------

Optimal_time_step 2.50000E-04

* Control_data

! --------------------------------------

Control_title "First"

Duration 10.0

Solution_algorithm 4

Maximum_number_time_steps 1E8

Initial_time_increment 0.05

Maximum_number_iterations 5000

Factor_critical_time_step 0.90

Screen_message_frequency 10

Output_frequency_plotfile -1

Output_time_plotfile 5.0

Output_frequency_restart -1

Output_time_restart 0.00

* Time_scaling_factors

! --------------------------------------

Optimal_time_step 2.50000E-04

* Control_data

! --------------------------------------

Control_title "Second"

Duration 10.0

Solution_algorithm 4

Maximum_number_time_steps 1E8

Initial_time_increment 0.05

Maximum_number_iterations 5000

Factor_critical_time_step 0.90

Screen_message_frequency 10

Output_frequency_plotfile -1

Output_time_plotfile 3.4

Output_frequency_restart -1

Output_time_restart 0.00

* Time_scaling_factors

! --------------------------------------

Optimal_time_step 2.00000E-03

* Control_data

! --------------------------------------

Control_title "Third"

Duration 80.0 !20 to 100

Solution_algorithm 4

Maximum_number_time_steps 1E8

Initial_time_increment 0.4

Maximum_number_iterations 5000

Factor_critical_time_step 0.90

Screen_message_frequency 10

Output_frequency_plotfile -1

Output_time_plotfile 40.0

Output_frequency_restart -1

Output_time_restart 0.00

* Time_scaling_factors

! --------------------------------------

Optimal_time_step 1.00000E-02

* Control_data

! --------------------------------------

Control_title "Fourth"

Duration 400.0 !100 to 500

Solution_algorithm 4

Maximum_number_time_steps 1E8

Initial_time_increment 2.0

Maximum_number_iterations 5000

Factor_critical_time_step 0.90

Screen_message_frequency 10

Output_frequency_plotfile -1

Output_time_plotfile 200.0

Output_frequency_restart -1

Output_time_restart 0.00

* Time_scaling_factors

! --------------------------------------

Optimal_time_step 1.50000E-02

* Control_data

! --------------------------------------

Control_title "Fifth"

Duration 660.0 !500 to 1160

Solution_algorithm 4

Maximum_number_time_steps 1E8

Initial_time_increment 3.0

Maximum_number_iterations 5000

Factor_critical_time_step 0.90

Screen_message_frequency 10

Output_frequency_plotfile -1

Output_time_plotfile 330.0

Output_frequency_restart -1

Output_time_restart 0.00

* Time_scaling_factors

! --------------------------------------

Optimal_time_step 9.00000E-02

* Control_data

! --------------------------------------

Control_title "Sixth"

Duration 4450.0 !1160 to 5610

Solution_algorithm 4

Maximum_number_time_steps 1E8

Initial_time_increment 18.0

Maximum_number_iterations 5000

Factor_critical_time_step 0.90

Screen_message_frequency 10

Output_frequency_plotfile -1

Output_time_plotfile 2220.0

Output_frequency_restart -1

Output_time_restart 0.00

* Time_scaling_factors

! --------------------------------------

Optimal_time_step 1.00000E-01

* Control_data

! --------------------------------------

Control_title "Seventh"

Duration 5000.0 !5610 to 10610

Solution_algorithm 4

Maximum_number_time_steps 1E8

Initial_time_increment 20.0

Maximum_number_iterations 5000

Factor_critical_time_step 0.90

Screen_message_frequency 10

Output_frequency_plotfile -1

Output_time_plotfile 2500.0

Output_frequency_restart -1

Output_time_restart 0.00

* Time_scaling_factors

! --------------------------------------

Optimal_time_step 2.00000E-00

* Control_data

! --------------------------------------

Control_title "Eight"

Duration 90000.0 !10610 to 100610

Solution_algorithm 4

Maximum_number_time_steps 1E8

Initial_time_increment 400.0

Maximum_number_iterations 5000

Factor_critical_time_step 0.90

Screen_message_frequency 10

Output_frequency_plotfile -1

Output_time_plotfile 45000.0

Output_frequency_restart -1

Output_time_restart 0.00

* Time_scaling_factors

! --------------------------------------

Optimal_time_step 10.00000E-00

* Control_data

! --------------------------------------

Control_title "Ninth"

Duration 399390.0 !10610 to 100610

Solution_algorithm 4

Maximum_number_time_steps 1E8

Initial_time_increment 2000.0

Maximum_number_iterations 5000

Factor_critical_time_step 0.90

Screen_message_frequency 10

Output_frequency_plotfile -1

Output_time_plotfile 200000.0

Output_frequency_restart -1

Output_time_restart 0.00

!===============================================================

END DATA

! Geometry Definition

!=============================================================

! Point Definition

! -------------------------------

* nodal_data

node_number IDM=4

1 2 3 4

coordinates IDM=3 JDM=4

0.0 0.0 0.0

1.0 0.0 0.0

1.0 10.0 0.0

0.0 10.0 0.0

! Surface Data

! -------------------------------

* geometry_surface NUM=1

surface_type 1

lines IDM=4

1 2 3 4

! Line Data

! -------------------------------

* geometry_line NUM=1

line_type 1

points IDM=2

1 2

* geometry_line NUM=2

line_type 1

points IDM=2

2 3

* geometry_line NUM=3

line_type 1

points IDM=2

3 4

* geometry_line NUM=4

line_type 1

points IDM=2

4 1

1The boundary conditions for top surface are applied via the Stratigraphy_surface_load data structure:

a.2 MPa stress load

b.0 MPa prescribed pore pressure (Pore_pressure_flag = 1 with no value specified)

2The Time Curve NUM=1 is defined so that the load applied is instantaneous

34 node plane strain elements are defined for the domain

4Porous_flow_type is set to 4 (coupled)

5Material and fluid properties are defined

6Displacement fixities are assigned via Support_data:

a.No vertical displacement at the base (line 1)

b.No horizontal displacement at the sides (lines 2 and 4)

c.Free displacement on top surface (line 3)

7Two history points are defined at the base and at the top surface of the model.

8The mesh is defined so there are 50 default number of divisions for all lines but divisions for base (and consequently top surface) are set to 1 via the Structured_line_set data structure

9Several stages with different durations are defined. For each stage time steps have been defined in such a way so that each stage is solved with 200 flow steps and c.a. 200 mechanical steps per flow step (c.a. 40.000 mech steps per stage). Note that the flow step size is defined via Initial_time_increment.

Results

The result files for the project are in directory: ParaGeo Examples\Validation\Val_001\Results. The Plots Over Line exported from ParaView are provided in CSV format and pasted into Val_001_Terzaghi.xlsx sheet.

The results show that ParaGeo calculations match the analytical solution very well:

Val_01_05

Normalized pore pressure vs normalized depth. Comparison of ParaGeo explicit results (dots) with the analytical solution (lines) at different times.

Val_01_06

Normalized pore pressure at the base of the model as a function of normalized time. Comparison of ParaGeo explicit results (dots) with the analytical solution (lines).

Val_01_07

Normalized displacement at the top of the model as a function of normalized time. Comparison of ParaGeo explicit results (dots) with the analytical solution (lines).