Val_002a Cylindrical Soil Sample

Contents

Problem Description

This test considers an infinitely long cylinder of radius a, subjected to a sudden fluid pressure load p0 and a stress load -p0at time t = 0 on the boundary r = a.

Val_02_01

Schematic of problem boundary conditions

In this case the model is set up so that:

•Domain consists of a quarter symmetry of the 1 m long radius cylinder discretized in a structured mesh of 2500 triangular elements

•There are rollers on the two symmetry axes.

•The simulation will be coupled (solving of mechanical and fluid flow fields).

•Initial pore pressure and effective stress are 0 MPa.

•A load of 2 MPa of pore pressure and stress is applied instantaneously on the outer boundary. The load is kept constant during the simulation.

•No flow is allowed on the symmetry planes.

•A simulation time of ~100.000 s is considered.

•Relevant material and fluid properties are:

oE = 10 GPa

oν = 0.25

oΦ = 0.2

oKg = 38 GPa

oKf = 2 GPa

ok = 1·10-15 m2 (c = 9.81·10-9 m/s)

oρw = 1000 Kg/m3

Val_02_02

Schematic of model domain

The data file for the model is found in: ParaGeo Examples\Validation\Val_002\Data\Val_002.dat.

Data File

* Geometry_set NUM=1

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

Name "West"

Lines IDM=1

* Geometry_set NUM=2

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

Name "Base"

Lines IDM=1

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

! 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 formation"

Element_type "TPM3V"

Material_name "Poroelastic"

Surfaces IDM=2

1 2

Porous_flow_type 4

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

! Material Data

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

* Material_data NUM=1

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

Name "Poroelastic"

Units IDM=4

MPa

Celsius

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

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 0 0

/Set 2/ 0 1 0

/Set 3/ 1 1 0

/Set 4/ 0 0 0

Displacement_code_geom_set IDM=2

Base

West

Displacement_code_geom_ass IDM=2

2 1

Pore_pressure_codes IDM=1 JDM=2

1 ! Prescribed

0 ! Free

Pore_pressure_code_lines IDM=4 JDM=2

/line/ 2 3 4 5

/Assign Set/ 1 1 1 1

* Global_loads NUM=1

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

Prescribed_pore_pressure IDM=1 JDM=1

2.0 ! MPa

Pres_pore_pressure_lines IDM=4 JDM=2

/lines/ 2 3 4 5

/sets/ 1 1 1 1

* Time_curve_data NUM=1

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

Time_curve IDM=2

0.0 500000.0

Time_factor IDM=2

1.0 1.0

* Global_loads NUM=2

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

Surface_load IDM=2 JDM=1

2.0 0.0 ! MPa (normal tangential)

Surface_load_lines IDM=1 JDM=2

/lines/ 2 3 4 5

/sets/ 1 1 1 1

* Time_curve_data NUM=2

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

Time_curve IDM=2

0.0 500000.0

Time_factor IDM=2

1.0 1.0

* Load_case_control_data

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

Loadcases IDM=2

1 2

Active_load_flags IDM=2

2 2

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

! Mesh data

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

* Mesh_control_data

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

Generation_algorithm 1 ! Structured mesh

* Structured_mesh_data

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

Default_divisions 25

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

! 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"

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

! History data output

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

* History_point NUM=1

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

Name "center"

Group 1

Output_frequency_increment 10

Point_coordinates IDM=2 JDM=1

0.0 0.0

Displacements IDM=1

"DISP_X"

Element_data IDM=1

"ELT_PORE"

* History_point NUM=2

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

Name "outer"

Group 1

Output_frequency_increment 10

Point_coordinates IDM=2 JDM=1

1.0 0.0

Displacements IDM=1

"DISP_X"

Element_data IDM=1

"ELT_PORE"

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

! Stage data (100 flow steps/stage, 100 mech steps/flow step)

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

* Time_scaling_factors

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

Optimal_time_step 1E-8

* Control_data

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

Control_title "Initial"

Duration 1E-4 !s

Solution_algorithm 4

Maximum_number_time_steps 1E8

Initial_time_increment 1E-6 !s

Maximum_number_iterations 5000

Factor_critical_time_step 0.90000

Screen_message_frequency 100

Output_frequency_plotfile -1

Output_time_plotfile 2E-5 !s

* Time_scaling_factors

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

Optimal_time_step 1E-7

* Control_data

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

Control_title "Second"

Duration 1E-3 !s

Solution_algorithm 4

Maximum_number_time_steps 1E8

Initial_time_increment 1E-5 !s

Maximum_number_iterations 5000

Factor_critical_time_step 0.90000

Screen_message_frequency 100

Output_frequency_plotfile -1

Output_time_plotfile 2E-4 !s

* Time_scaling_factors

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

Optimal_time_step 1E-6

* Control_data

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

Control_title "Third"

Duration 1E-2 !s

Solution_algorithm 4

Maximum_number_time_steps 1E8

Initial_time_increment 1E-4 !s

Maximum_number_iterations 5000

Factor_critical_time_step 0.90000

Screen_message_frequency 100

Output_frequency_plotfile -1

Output_time_plotfile 2E-3 !s

* Time_scaling_factors

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

Optimal_time_step 1E-5

* Control_data

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

Control_title "Fourth"

Duration 1E-1 !s

Solution_algorithm 4

Maximum_number_time_steps 1E8

Initial_time_increment 1E-3 !s

Maximum_number_iterations 5000

Factor_critical_time_step 0.90000

Screen_message_frequency 100

Output_frequency_plotfile -1

Output_time_plotfile 2E-2 !s

* Time_scaling_factors

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

Optimal_time_step 1E-4

* Control_data

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

Control_title "Fifth"

Duration 1E-0 !s

Solution_algorithm 4

Maximum_number_time_steps 1E8

Initial_time_increment 1E-2 !s

Maximum_number_iterations 5000

Factor_critical_time_step 0.90000

Screen_message_frequency 100

Output_frequency_plotfile -1

Output_time_plotfile 2E-1 !s

* Time_scaling_factors

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

Optimal_time_step 1E-3

* Control_data

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

Control_title "Sixth"

Duration 10 !s

Solution_algorithm 4

Maximum_number_time_steps 1E8

Initial_time_increment 0.1 !s

Maximum_number_iterations 5000

Factor_critical_time_step 0.90000

Screen_message_frequency 100

Output_frequency_plotfile -1

Output_time_plotfile 2.0 !s

* Time_scaling_factors

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

Optimal_time_step 0.01

* Control_data

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

Control_title "Seventh"

Duration 100 !s

Solution_algorithm 4

Maximum_number_time_steps 1E8

Initial_time_increment 1.0 !s

Maximum_number_iterations 5000

Factor_critical_time_step 0.90000

Screen_message_frequency 100

Output_frequency_plotfile -1

Output_time_plotfile 20.0 !s

* Time_scaling_factors

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

Optimal_time_step 0.1

* Control_data

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

Control_title "Eight"

Duration 1000 !s

Solution_algorithm 4

Maximum_number_time_steps 1E8

Initial_time_increment 10.0 !s

Maximum_number_iterations 5000

Factor_critical_time_step 0.90000

Screen_message_frequency 100

Output_frequency_plotfile -1

Output_time_plotfile 200.0 !s

* Time_scaling_factors

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

Optimal_time_step 1

* Control_data

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

Control_title "Ninth"

Duration 100000 !s

Solution_algorithm 4

Maximum_number_time_steps 1E8

Initial_time_increment 100.0 !s

Maximum_number_iterations 5000

Factor_critical_time_step 0.90000

Screen_message_frequency 100

Output_frequency_plotfile -1

Output_time_plotfile 20000.0 !s

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

END DATA

! Geometry Definition

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

! Point Definition

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

* nodal_data

node_numbers IDM=10

1 2 3 4 5 6 7 8 9 10

coordinates IDM=2 JDM=10

0 0

1 0

0.980785280 0.195090322

0.923879533 0.382683432

0.831469612 0.555570233

0.707106781 0.707106781

0.555570233 0.831469612

0.382683432 0.923879533

0.195090322 0.98078528

0 1

! Surface Data

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

* geometry_surface NUM=1

lines IDM=4

1 2 3 7

* geometry_surface NUM=2

lines IDM=4

7 4 5 6

! Line Data

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

* geometry_line NUM=1

line_type 1

points IDM=2

1 2

* geometry_line NUM=2

line_type 2

points IDM=3

2 3 4

* geometry_line NUM=3

line_type 2

points IDM=3

4 5 6

* geometry_line NUM=4

line_type 2

points IDM=3

6 7 8

* geometry_line NUM=5

line_type 2

points IDM=3

8 9 10

* geometry_line NUM=6

line_type 1

points IDM=2

10 1

* geometry_line NUM=7

line_type 1

points IDM=2

1 6

1Three node plane strain elements are defined for the domain

2Porous_flow_type is set to 4 (coupled)

3Material and fluid properties are defined

4Displacement fixities are assigned via Support_data:

a.No perpendicular displacement to "Base" and "West" geometry sets

b.Free displacement in outer boundary

5Pore pressure will be prescribed in the outer boundary (lines 2, 3, 4 and 5) as specified in Support_data

6A pore pressure of 2 MPa will be instantaneously applied in the outer boundary and will be kept constant during the simulation. This is defined in Global_loads NUM=1 with its corresponding Time_curve_data NUM=1

7A stress load of 2 MPa will be instantaneously applied in the outer boundary and will be kept constant during the simulation. This is defined in Global_loads NUM=2 with its corresponding Time_curve_data NUM=2. Note that the stress load is defined in the local coordinate system of the facet so that a positive value means that the load is pointing towards the center of the element.

8The mesh is defined so there are 25 default number of divisions for all lines. No additional data is specified

9Couple_control_data is defined to couple geomechanical and porous flow fields

10Two history points are defined at the center and at the outer boundary of the model.

11Several 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 100 flow steps and c.a. 100 mechanical steps per flow step (c.a. 10.000 mech steps per stage). Note that the flow step size is defined via Initial_time_increment within Control_data structure whereas the mechanical time step is defined via Time_scaling_factors data structure.

Results

The result files for the project are in directory: ParaGeo Examples\Validation\Val_002\Results. History results are plotted into 00 - Val_002 Results.xlsx sheet.

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

Val_02_03

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

Val_02_04

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