Val_001b Implicit Geomechanical Solver

Problem Description

 

In this test, the column consolidation problem is solved using implicit geomechanical solver, i.e. Solution_algorithm = 7.

 

Click to expand/collapseData File Description

The only difference between the current and previous data file is that we set Solution_algorithm to 7 here, and define the displacement norm tolerance value under Control_data. Users may refer to Val_001a to familiarise with the  parameters used in the analytical solution. The data file for the model is found in: ParaGeo Examples\Validation\Val_001\Data\Val_001b_Terzaghi.dat.

 

Data File

 

 

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

!

! 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                       7

 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

 Displacement_norm_tolerance           0.01

 

 

* Time_scaling_factors

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

 Optimal_time_step               2.50000E-04

 

 

* Control_data

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

 Control_title                      "Second"

 Duration                              10.0

 Solution_algorithm                       7

 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

 Displacement_norm_tolerance           0.01    

 

 

* Time_scaling_factors

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

 Optimal_time_step               2.00000E-03

 

 

* Control_data

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

 Control_title                      "Third"

 Duration                              80.0 !20 to 100

 Solution_algorithm                       7

 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

 Displacement_norm_tolerance           0.01      

 

 

* Time_scaling_factors

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

 Optimal_time_step               1.00000E-02

 

 

* Control_data

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

 Control_title                      "Fourth"

 Duration                             400.0 !100 to 500

 Solution_algorithm                       7

 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

 Displacement_norm_tolerance           0.01  

 

 

* Time_scaling_factors

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

 Optimal_time_step               1.50000E-02

 

 

* Control_data

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

 Control_title                      "Fifth"

 Duration                             660.0 !500 to 1160

 Solution_algorithm                       7

 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

 Displacement_norm_tolerance           0.01

 

 

* Time_scaling_factors

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

 Optimal_time_step               9.00000E-02

 

 

* Control_data

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

 Control_title                      "Sixth"

 Duration                            4450.0 !1160 to 5610

 Solution_algorithm                       7

 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

 Displacement_norm_tolerance           0.01

 

 

* Time_scaling_factors

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

 Optimal_time_step               1.00000E-01

 

 

* Control_data

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

 Control_title                     "Seventh"

 Duration                            5000.0 !5610 to 10610

 Solution_algorithm                       7

 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

 Displacement_norm_tolerance           0.01      

 

 

* Time_scaling_factors

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

 Optimal_time_step               2.00000E-00

 

 

* Control_data

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

 Control_title                      "Eight"

 Duration                           90000.0 !10610 to 100610

 Solution_algorithm                       7

 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  

 Displacement_norm_tolerance           0.01

 

* Time_scaling_factors

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

 Optimal_time_step              10.00000E-00

 

 

* Control_data

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

 Control_title                      "Ninth"

 Duration                          399390.0 !10610 to 100610

 Solution_algorithm                       7

 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  

 Displacement_norm_tolerance           0.01    

 

 

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

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

 

 

1Because we use implicit geomechanical solver in this test, the Solution_algorithm is set to 7, along with the addition of Displacement_norm_tolerance value. The remaining settings are inherited from the previous cases.

 

 

 

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_05b

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

 

Val_01_06b

 

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

 

 

Val_01_07b

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