Case01 Confined Compression Test

 

This example considers a confined compression test with prescribed pore pressure at the top (0 MPa) and bottom surfaces (1 MPa) to achieve a transient pore pressure distribution within the domain. The geometry considers a 3D slice with displacement constrains in the "North" and "South" surfaces to simulate the problem in plane strain conditions. Note that the model size (12 m x 4 m x 0.2 m) has been chosen arbitrarily rather than being representative of a lab test sample. The top surface of the model is prescribed a downward and slightly westward displacement in order to facilitate strain localisation in a given direction. The material is over consolidated with an initial pre-consolidation pressure of 25 MPa. The confining pressure applied to the East and West boundaries as well as the initial geostatic stress has been set to 2 MPa and applied instantaneously at the beginning of the simulation. The material has a constant permeability of 1E-12 m2. The following cases will be considered:

 

1.Case01a: Fault is predicted based on a plastic strain threshold value of 0.1. Fault elements have permeability multiplied by 100.

2.Case01b: Same case as 01a but plastic strain threshold increased to 5.0 to avoid predicting fault elements and allow for comparisons to highlight the effect of the fault in case 01a.

3.Case01c: Fault is seeded using part geometry at a different location than the fault predicted in Case01a. Both perm enhancement and strength reduction are considered.

4.Case01d: Fault is seeded using part geometry at a different location than the fault predicted in Case01a. Only perm enhancement is considered.

 

 

Ex_010_Case01_01

Initial model, mesh and boundary conditions

 

 

Common to all cases

 

Considering continuum fault flow model requires assignment of the corresponding Fracture_data into the material(s). If no fracture data is assigned to a given material then the continuum fault model will have no effect in such material even if the fault is prescribed.

 

Material_data

Data File

 

 

* Material_data NUM=1

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

 Name                       "Mat_001_sr4"

    (...)

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

 Permeability               1E-12   ! m^2 (1000mD)  

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

 Fracture_set_names  IDM=1

   "Fract01"

 

1For the present examples a single fracture (defined via Fracture_data) named "Fact01" will be considered. Thus it is assigned into the material "Mat_001_sr4" via the keyword Fracture_set_names.

2The present case considers a constant isotropic permeability of 1E-12 m2. Note that it is compulsory to define an isotropic perm law (either constant or a function of porosity) in order to use the continuum fault model (transverse isotropic or orthotropic perm is not allowed).

 

 

 

 

Case01a

 

This case considers that fault is predicted based on a plastic strain threshold value of 0.1. Permeability is enhanced using a multiplication factor of 100. The fault properties are defined within Fracture_data data structure.

 

Fracture_data

Data File

 

 

* Fracture_data NUM=1

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

 Name                       "Fract01"

 Propagation_model_name     "P_strain"

 Propagation_properties  IDM=1

  /Plastic strain/         0.1

 Flow_model_name            "SimpleHydro"

 Conductivity_model_name    "PermMult"

 Permeability_multiplier    100

 Isotropic_perm_flag        1

 

1A single fracture named "Fract01" is defined

2The case considers fault prediction based on plastic strain threshold criteria. Thus Propagation_model_name is defined as "P_strain" and the keyword Propagation_properties is used to define the threshold value which in this case is set to 0.1 (each element that achieves or exceeds such value will be identified as a fault element).

3The perm enhancement for the continuum fault model requires to define the Flow_model_name keyword and set it to "SimpleHydro"

4The present case considers perm enhancement based on a multiplier to the material permeability for fault elements. This is done by setting the keyword Conductivity_model_name to "PermMult" and defining the Permeability_multiplier keyword to set the multiplier value which in this case is set to 100.

5Definition of Isotropic_perm_flag set to 1 is compulsory in order to enhance the perm for predicted fault cases. This applies isotropic perm enhancement in elements identified as fault elements.

 

 

 

Case01b

 

The objective of this case is to provide a reference solution without a fault being predicted to allow comparisons with Case01a and hence facilitate understanding of the effects of the continuum fault flow model. Consequently this case is identical to Case01a but with the plastic strain threshold set to a high value (5.0) in order to prevent prediction of any fault element.

 

Fracture_data

Data File

 

 

* Fracture_data NUM=1

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

 Name                       "Fract01"

 Propagation_model_name     "P_strain"

 Propagation_properties  IDM=1

  /Plastic strain/         5.0

 Flow_model_name            "SimpleHydro"

 Conductivity_model_name    "PermMult"

 Permeability_multiplier    100

 Isotropic_perm_flag        1

 

1Case identical to Case01a but plastic strain threshold defined with a value of 5.0 in order to avoid identification of fault elements.

 

 

 

   Case01c

 

The present case considers a fault being prescribed in a higher location that the fault predicted in Case01a. Both perm enhancement and strength reduction will be considered thus creating a preferential localisation pathway which different from the one predicted in Case01a. For prescribing a fault the following data structures are required:

 

•Fracture_data with an assigned Coordinate_system (compulsory)

•Fault_set linking the Fracture_data with the Part_geometry_set which defines the fault pathway as well as defining the seeding properties for the fault.

•Fault_insertion to request fault seeding (prescribe the fault)at the elements intersecting the part geometry.

 

 

Fracture_data

Data File

 

* Fracture_data NUM=1

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

 Name                       "Fract01"

 Propagation_model_name     "PreExist"

 Flow_model_name            "SimpleHydro"

 Conductivity_model_name    "PermMult"

 Permeability_multiplier    100

 Isotropic_perm_flag        1

 Coordinate_system          1

 

 

* Coordinate_system  NUM=1

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

 Name   "Fracture direction" ! 52.96 in Y axis

 Direction_cosines  IDM=3  JDM=3

   0.6024        0.0000        0.7982

   0.0000        1.0000        0.0000

   -0.7982        0.0000        0.6024

 

1For prescribed faults through fault seeding Propagation_model_name must be set to "PreExist".

2Definition and assignment of a Coordinate_system  is compulsory for cases with prescribed faults. Nonetheless setting of Isotropic_perm_flag to 1 ignores the coordinate system and considers isotropic perm enhancement (if Isotropic_perm_flag is set to 0 the assigned coordinate system would be used to determine the perm enhancement in each direction).

3Even though the Coordinate_system is going to be ignored (because isotropic perm enhancement is assumed) the Direction_cosines have been defined to be consistent with the fault angle (52.96 º with the horizontal along the Y axis).

 

 

Part geometry

Data File

 

* Part_geometry_set         NUM=1

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

 Name           "Fault01_part"  

 Part_type      "Fault"

 Part_surfaces  IDM=1

   1

 

* Part_surface              NUM=1

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

 Facets      IDM=3  JDM=2

   1 2 4

   2 3 4

 

* Part_nodal_data         NUM=1

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

 Nodes      IDM=4

   1 2 3 4

 Coordinates   IDM=3 JDM=4

   0   0.3   4.7

   0  -0.1   4.7

   4  -0.1  10.0

   4   0.3  10.0

 

1Part_geometry_set, Part_surface and Part_nodal_data are used to define an inclined plane with similar slope than the fault predicted in Case01a but at a higher location. Such part geometry is going to be used to seed the fault at the intersected elements.

2The part geometry is named "Fault01_part"

3The node numbers and the facets of the part geometry are defined according the schematic picture below, with the facets following counter-clockwise direction (all facets must be defined following the same direction which in this case could been either clockwise or counter-clockwise direction)

 

Ex_010_Case01_07

Schematic of part surface facet topology

 

 

Fault_set

Data File

 

* Fault_set  NUM=1

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

 Name                     "Fault01"

 Fracture_assignment      "Fract01"

 Insertion_type           "Seeded"          

 Geometry_set             "Fault01_part"

 Seeding_variables  IDM=1  

   "P_strnv"

 Seeding_values  IDM=1

   0.05

 

1The Fault_set is named Fault01.

2The fracture data named "Fract01" is assigned to the fault

3The part geometry named "Fault01_part" is assigned to the fault via the keyword Geometry_set. Such part geometry will be used to seed the fault at the intersected elements.

4Seeding_variables and Seeding_values keywords are defined in order to consider strength decrease in fault elements. This introduces a reduction in pre-consolidation pressure according to the value of imposed plastic volumetric strain (P_strnv) following the hardening data of the material. In this case a plastic volumetric strain of 0.05 is considered.

5If Seeding_variables and Seeding_values are not defined in Fault_set then only perm enhancement would be considered for the seeded fault.

 

 

Fault_insertion

Data File

 

* Fault_insertion  NUM=1

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

 Insertion_type      "Seeded"

 Faults  IDM=1

   "Fault01"

 Seeding_variables IDM=1

   "P_strnv"

 Seeding_values  IDM=1

   0.02

 Element_size     0.2

 

1Fault_insertion data structure is defined in order to seed (prescribe) each fault listed in Faults keyword (in this case Fault01). Note that only a single Fault_insertion data structure per stage is allowed with the seeding being performed at the beginning the stage (after sedimentation in case of a deposition stage).

2Definition of Seeding_variables and Seeding_values is compulsory in Fault_insertion data structure. Note however that the values specified in Fault_set are the ones that will be used to calculate strength (pc) decrease.

3Definition of Element_size allows to decrease the element size at the location of the fault. In this case the size has been decreased to 0.2.

 

 

 

 

   Case01d

 

This case is identical to Case01c but without considering strength decrease at the fault. Consequently only the data that has changed is highlighted.

 

Fault_set

Data File

 

* Fault_set  NUM=1

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

 Name                     "Fault01"

 Fracture_assignment      "Fract01"

 Insertion_type           "Seeded"          

 Geometry_set             "Fault01_part"

 

1This case is identical to Case01c but Seeding_variables and Seeding_values are not being defined in order to not consider any effect on the material strength upon fault seeding (only perm enhancement is considered). Note that in Fault_insertion Seeding_variables and Seeding_values are defined as they are compulsory but this will have no effect in the strength.

 

 

 

 

 

 

 

Results

A selection of result files for the project are provided in directory: ParaGeo Examples\General Examples\Ex_010\Case01\Results.

 

In the figure below the evolution of plastic strain and the active flag for the elements identified as being Fract01 for Case01a is shown. Note that the plastic strain maximum range is limited to the same input value as the one used to predict a fault (0.1) in order to highlight the correlation between the red elements in the plastic strain contours and the elements having a value of 1 of active fracture flag. As can be seen the model has predicted a strain localization dipping to the West boundary due to the imposed displacement on the top boundary. The strain localization initiated the bottom corner of the west boundary where the pore pressure values are higher at the time that deformation starts to take place.

 

Ex_010_Case01_02

Evolution of Plastic Strain and Fract01 Active Flag (values of 1 indicate that the element is identified as such fault) for Case01a. Note that plastic strain range has been limited to 0.1 to highlight the correlation with the elements predicted as faults. Note that the finer element size in the fault is due to the data defined in Adaptivity_set_data.

 

 

 

The results below at the end of the simulation show the predicted plastic strain, the elements being identified as fault elements, the enhanced perm in the fault elements and the pore pressure distribution for case01a. Note how the enhanced perm facilitated fluid flow along the fault resulting in a stronger pore pressure gradient in the eastern boundary than in the west boundary.

 

Ex_010_Case01_03

Results at the end of the simulation for Case01a.

 

 

 

The pictures below show the final results for case01b in which the data has been defined so that no fault elements are predicted (the plastic strain threshold has been set to 5.0 whereas the maximum predicted plastic strain value is 0.8). Note the horizontal pore pressure contours as the flow is mostly vertical because no preferential flow pathway has been created.

Ex_010_Case01_04

Results at the end of the simulation for Case01b.

 

 

 

The figures below show the initial state and the final results for Case01c. In this case part geometry has been used to seed a fault decreasing the pre-consolidation pressure (strength) and enhancing the permeability in the fault elements. Due to the decreased strength at the prescribed fault pathway the strain localization is preferentially predicted at such location. The pore pressure contours reflect the perm enhancement at the prescribed location as well.

 

Ex_010_Case01_05

Pre-consolidation pressure decreased at seeded elements before any deformation has taken place at time 0.25 (left) and results at the end of the simulation (right) for Case01c.

 

 

 

The figures below show the results for case01d which considers a prescribed fault at the same location as case01c but in the present case only perm enhancement at the fault location is considered (no strength reduction of the fault elements). As can be seen the strain localisation is predicted at the same location as Case01a due to the homogeneous strength in the domain although the preferential flow pathway occurs at the location where the fault is prescribed due to the perm enhancement.

 

Ex_010_Case01_06

Results at the end of the simulation for Case01d.