HM_005 Case1 10% shortening at strain rate of 0.2/Ma

In this example a deposition of 4000 m of sediment followed by 10% of shortening at a strain rate of 0.2/Ma (20% of strain per million years) will be simulated.  The deposition will be performed in 10 layers of 400 m height each. The column width is 1000m so that the applied tectonic displacement will be 100m. In order to apply 10% of shortening at 0.2/Ma strain rate the complete displacement should last 0.5 Ma. A detailed description of the deposition data file and restart data file with the tectonic event are shown below.

 

First the depositional stage should be run, and subsequently the restart data file can be executed.

 

Click to expand/collapseBasic Set Up: Sedimentation Data File Description

The initial data file for the project is: HM_005\Data\hm_005_Case1.dat.   The basic data includes:

1Units defining stress in "MPa", length in "m", time in "Ma" and temperature in "Celsius".

2Geometry_set data defining model boundaries.

3Group_control_data activates the geomechanical and porous fields for the pre-existing group and Group_data defines the name, element type, material name, porous flow type and geometry associated with the group.

4Stratigraphy_definition and Stratigraphy_horizon defining stratigraphy data for the pre-existing layer.

5Stratigraphy_surface_load to prescribe conditions at the surface:

(a) A small mechanical load (0.2 MPa) at surface to avoid positive stresses (and material flow in larger geological models.  This is applied with the ParaGeo inbuilt "Step-ramp" curve which is a linear ramp curve.

(b) A prescribed pore pressure of 0 MPa by setting Pore_pressure_flag = 1.

6Material_data to read in the "clay" material properties and the Fluid_properties contained in the external material file "clay_CF040.mat" which defines the material properties of the pre-existing and all sedimentation layers.

7Damping_global_data defining the use of combined damping models (mass proportional damping of 2% and bulk viscosity damping with constant of 0.5).

8Support data (Support_data) defining:

(a)   Geomechanical field: Base fixed vertically and sides fixed horizontally.

9Gravity data (Gravity_data) applied with "Step_ramp" time curve.

10Mesh control (Mesh_control_data) and structured mesh generation data (Structured_mesh_data, Structured_line_set) defining a uniform mesh with 10 x 1 elements per layer.

11Adaptivity control (Adaptivity_control_data) and adaptivity set data (Adaptivity_set_data) specifying a remeshing check set as a very large number 5E8 (to avoid remeshing).  Note that the element size data here are not used - the number of structured divisions for the new sedimented layers are defined in the Sedimentation_parameters.

12Sedimentation_parameters and Sedimentation_data defining the sedimentation data for the new layers.

13Coupling data (Couple_control_data) to define an incremental coupling between the geomechanical and fluid flow fields using the variable group volume strain update algorithm based on undrained conditions (more appropriate for low permeability materials).

14Porous_flow_control_data defining the data specific to the porous flow solution control with solution algorithm defined as nonlinear transient.

15Control_data for the initial and all sedimentation stages except final sedimentation stage defining:

(a)  Incremental transient solution algorithm (Type 4).

(b)  Duration of 4.0 Ma.

(c)  Flow time increment of 0.04 (i.e. coupling time step of 0.04Ma, therefore 100 coupling times for stage duration of 4.0Ma).

(d)  Target number of mechanical steps per coupling step set to 200, therefore total of 200*100=20,000 mechanical steps for stage duration of 4.0Ma.

(e)  Plot file every 1.0 Ma (i.e. four plotfiles per stage).

(f) Screen message output every 10 flow increments.

(g) Output_frequency_restart set to -1 indicating that a new restart file at the end of that stage will be created. The restart file name is "model_name_stage_number.rst"

16In the final sedimentation stage, the control data includes three additional time step data (Maximum_time_increment, End_step_time_increment, Transient_time_step_growth) to allow a gradual reduction of the time step increments to be compatible with the initial time step of the next stage (i.e. tectonic stage).  This is in order to prevent a sudden change of time step increment at the start of the next stage.

17Geometry data (Nodal_data, Geometry_line and Geometry_surface) for definition of the pre-existing layer geometry (1000m x 400m column).

 

The stratigraphy associated with the initial sediment must be defined when the layer sedimentation procedure is used.  This requires

1Defining the existing stratigraphy layer depositional order and the group associated with each layer (via Stratigraphy_definition).

2Defining the topology of the top surface horizon for each stratigraphy layer (via Stratigraphy_horizon).

 

Stratigraphy_definition

The stratigraphy order is specified in order starting from the deepest sediment layer.  Each stratigraphy layer must comprise a single group (see Group_data).  It is recommended that, for each layer,  the stratigraphy unit name, stratigraphy horizon name and group name are identical.  This greatly simplifies data definition and result interrogation, especially when the number of stratigraphy layers becomes large.   If this convention is adopted, ParaGeo will internally identify the required associations between unit, horizons and groups, so that only the unit order is specified on the Stratigraphy_definition data structure.

 

Data File

 

 

* Stratigraphy_definition

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

 Units  IDM=1

     "clay"

 

1Only one layer is present in the initial model.

2In general ParaGeo allows different names to be used for the Group, Stratigraphy Horizon and Stratigraphy Unit.  In such case, in addition to Units,  the Stratigraphy Horizon Number (Horizon_numbers) and Group number (Group_numbers) for each unit must be provided.

3For this example, a consistent naming of the group  "clay",  horizon "clay"  and unit "clay"  is adopted.   Consequently, only the unit order is required and the Unit->Group->Horizon association is automatically established by ParaGeo.

 

 

Stratigraphy_horizon

The stratigraphy horizon defines the top surface of each pre-existing stratigraphy unit.  It is defined by a set of geometry lines in 2-D or a set of geometry surfaces in 3-D. A Stratigraphy_horizon data structure must be defined for each stratigraphy unit.

 

Data File

 

 

* Stratigraphy_horizon NUM=1

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

 Name         "clay"

 Geometry_set  "Top"

   

 

1The stratigraphy horizon for unit "clay" must be defined.

2For consistency it is also named "clay".

3The top surface of the unit (i.e. line #3) is defined by the geometry set named "Top".

 

Layer sedimentation is defined using a single data structure for each sedimented layer:

1Sedimentation_parameters and Sedimentation_data define the control data for deposition of a single layer; e.g. stratigraphy unit name, material, sedimentation type, etc.

 

Sedimentation Data

Sedimentation_data is the primary data structure for definition of sedimentation of a new stratigraphy unit.  One data structure is required for each new layer and the sedimentation process is associated with a single analysis stage (step).   Consequently in the current problem, where ten additional layers are deposited on the pre-existing layer, the analysis consists of 11 stages - an initialisation stage and 10 sedimentation stages, each one with a Sedimentation_data structure.

 

As all the sedimentation steps are identical with the exception of the stratigraphy unit name, the data structure Sedimentation_parameters may be used to define the common parameters of sedimentation and only the definition of the stratigraphy unit name would be required in Sedimentation_data.

 

Data File

 

 

* Sedimentation_parameters

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

 Sedimentation_type          "Drape"

 Material_name                "clay"

 Duration                       4.0

 Reference_thickness          400.0

 Num_struct_divisions            10

 Output_flag                      1

 

 

* Sedimentation_data

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

 Stratigraphy_unit_name     "Layer1"

 

The sedimentation data for stratigraphy layer 1 is defined before the Control_data for Stage 2 Unit "Layer1".  The definition of all Sedimentation_parameters is as described here:

1 Sedimentation type is "Drape".

2 The material for the new layer is "clay".

3 The gravity for the layer deposited is applied over 4 Ma which is equal to the stage duration.

4 The thickness of the deposited layer before consolidation due to gravity is 400 m.

5 Num_struct_divisions defines the number of element divisions through the deposition depth.

6 Output_flag is set to 1 to output a plot file on sedimentation.

 

7 Sedimentation_data only includes the stratigraphy unit name of each sedimented layer.  The first layer is named "Layer1".

 

 

 

During the tectonic stage which lasts 0.5Ma, our target number of flow steps for this duration is 100, i.e. a time step increment of 0.005.  However, the time step increments defined for the sedimentation stages are 0.04 which is an 8-fold increase. In order to prevent a sudden change of time step increment at the start of the tectonic stage following on from the final sedimentation stage, it is recommended to allow a gradual reduction of the time step increments for the final sedimentation stage to be compatible with the initial time step of the next stage (i.e. tectonic stage).  To this end, the final sedimentation control stage includes three additional time step data (Maximum_time_increment, End_step_time_increment, Transient_time_step_growth) to facilitate this gradual reduction.

 

 

Data File

 

 

* Control_data

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

 Control_title                "Layer10"

 Solution_algorithm                4  

 Target_number_time_steps        200

 Duration                        4.0

 Initial_time_increment         0.04

 Maximum_time_increment         0.04

 End_step_time_increment       0.005

 Transient_time_step_growth     1.02

 Screen_message_frequency         10

 Output_time_plotfile            1.0

 Output_frequency_plotfile        -1

 Output_frequency_restart         -1                        1

 

The following describes the three additional control data which facilitates gradual reduction of time step increments between successive control stages:

1 Maximum_time_increment defines the maximum allowable time increment.  This is set to 0.04, same as the Initial_time_increment used for the sedimentation stages.

2 End_step_time_increment defines the time increment targeted at the end of the stage.  This is recommended to be set same as the Initial_time_increment used in the next control stage (i.e. tectonic stage).

3 Transient_time_step_growth defines the maximum time step growth between successive increments.  This growth should not be too excessive as it could lead to instability.  For this example, it is set as 1.02.

 

 

 

 

Click to expand/collapseBasic Set Up: Restart File with Tectonic Event Description

The Restart data file for the project is: HM_005\Case1\Data\Restart_hm_005_Case1_Tectonic.dat.   The basic data includes:

1Restart_read_data to specify the restart file that will be read.

2Global_loads data structure to define a prescribed displacement of -100 m (10% of shortening) on the right hand boundary defined by the Geometry_set named "East".

3Time_curve_data that defines the time curve for the tectonic event, i.e. linear ramp over a time duration of 0.5 Ma.

4Load_case_control_data to define the Global_load associated with the tectonic event as active.

5Couple control (Couple_control_data) and control data (Control_data). The coupling algorithm is set to Undrained (more appropriate for low permeability materials).

6Control_data for the tectonic stage defining:

(a)  Incremental transient solution algorithm (Type 4).

(b)  Duration of 0.5 Ma.

(c)  Flow time increment of 0.005 (i.e. coupling time step of 0.005 Ma, therefore 100 coupling times for stage duration of 0.5 Ma).

(d)  Target number of mechanical steps per coupling step set to 1500, therefore total of 1500*100=150,000 mechanical steps for stage duration of 0.5 Ma.

(e)  Plot file every 0.1 Ma (i.e. five plotfiles).

 

In order to restart a simulation the Restart_read_data structure must be used and the Restart_file_name must be provided.

 

Restart_read_data

Restart_read_data is the primary data structure for reading a restart file. Restart_file_name must be provided in order to specify which restart file will be read. No additional files are required to run the simulation. Note that the restart file (.rst) must be placed in the same directory as the restart data file.  

 

Data File

 

 

* Restart_Read_data

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

 Restart_file_name      "hm_005_Case1_stage_11.rst"

 

The Restart_read_data is used to restart the simulation after the sedimentation of the column is completed and to define the subsequent tectonic event. The Restart_file_name is used to specify the file ("hm_005_Case1_stage_11.rst") that contains the results to be read by the code and carry forward the simulation from that time.

 

 

 

    The shortening event is defined via a prescribed displacement on the right hand boundary ("East") using the Global_loads data structure.

 

Global_loads

Global_loads is the primary data structure for definition of any type of load (boundary condition) in the model. The load must be defined via a load set (e.g. Prescribed_displacement) as well as the geometry entities to which the load will be applied (e.g. Pres_displacement_geom_set). Each Global_loads data structure has an associated Time_curve_data that by default is identified with the same ID number. Load_case_control_data defines the activation state of the Global_loads.

 

Data File

 

 

* Global_loads NUM=1

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

 Name          "Displacement"

 Prescribed_displacement IDM=2 JDM=1

  /Set 1/  -100.0    0.0

 Pres_displacement_geom_set        IDM=1

   "East"

 Pres_displacement_geom_ass        IDM=1

    1

 

* Time_curve_data NUM=1

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

 Name          "Displacement"

 Time_curve    IDM=2

   44.0  44.5

 Load_factor   IDM=2

   0.0   1.0

 

* Load_case_control_data

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

 Loadcases         IDM=1

  1

 Active_load_flags IDM=1

  2

 

The tectonic event is described via a prescribed displacement on the right hand boundary. Global_loads number 1 is defined for that purpose. Note that:

1 Prescribed_displacement is used to specify the lateral displacement of -100 m in the X coordinate and 0 m in the Y coordinate.

2 Pres_displacement_geom_set and Pres_displacement_geom_ass are used to assign the displacement Set 1 to the Geometry_set named "East" which comprises all geometry lines on the right hand boundary.

3 The Time_curve_data number 1 defines that the shortening will be applied linearly from time 44 Ma to 44.5 Ma.

4 The Load_case_control_data defines the load number 1 as active (flags are: 0=Inactive, 1=Delete, 2=Active).

 

Note that the data definition Geometry_set "East" initially comprise a single geometry line #3 for the right hand boundary of the pre-existing layer. When new layers are deposited, the new right hand boundary lines are automatically added to the data definition Geometry_set "East".

 

 

Click to expand/collapseResults

The result files for the project are in directory: HM_005\Case1\Results.  This directory also contains the excel file 00_hm_005_Case01.xlsx which contains ParaView plot over line results at time 44 Ma and 44.5 Ma as shown graphically below.

 

The effects of the tectonic event can be visualized below:

- increase in overpressure,

- decrease in porosity,

- increase in Sxx', decrease in Syy' and Szz',

- increase in deviatoric stress, increase in effective mean stress at depths above 1000 m and decrease in effective mean stress at depths below 1000m.

 

HM_005_Case01_001

 

Parameters vs depth before and after the tectonic event