Case 02 Joint Normal Displacement with Bandis Model (Spacing 0.25m)

Contents

In this case, the joint spacing is reduced to 0.25m resulting in 4 joints within the simulation element. Results are compared with the 1-joint element in Case 01. Note that the data file for this Case02 differs from the Case01 data file in just the Fracture_spacing value in the Fracture_data data structure.

$fract_003_case02_fig1$

Fig. 1 Prescribed loading on element with embedded continuum fracture

Material Properties

The properties used in this simulation test are listed below.

Property	Value
Young's Modulus	2000 MPa
Poisson's Ratio	0.20
Porosity	0.35

The additional material parameters related to the embedded continuum fracture are:

Contact Surface Properties	Value
Normal stiffness	1000 MPa
Initial aperture	0.01m
Initial porosity	0.04
Maximum joint stiffness	30000 MPa
Spacing	0.25 m

Data File Description

The data file for the example is in: fract_003\Data\fract_003_case02.dat. The basic data includes:

1Material_data defines the material properties of the model, including the fracture set associated with the embedded fracture.

2Fracture_data assigns the properties of embedded fracture as well as the fracture spacing and local coordinate system.

3Global_loads prescribes axial displacement on the element top surface.

4History_point outputs displacement, stress values, and fracture state variables at every 0.01s.

Note that only key data structures are described below.

Material_data

Material_data defines the material properties of the model, including the fracture set associated with the embedded fracture.

Data File

*Material_data NUM=1

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

Material_name "Sample"

Units IDM=4

/Stress/ "MPa"

/Length/ "m"

/Time/ "s"

/Temperature/ "Celsius"

Grain_stiffness 3.0000E+10

Grain_density 2710.00

Porosity_model_type 1

Porosity 0.35000

Elastic_model_type 1

Isotropic_elastic_properties IDM=2

/Young's Modulus (E)/ 2000

/Poisson's Ratio (V)/ 0.20000

Fracture_set_names IDM=1

"fract_set1"

1Material name, units and grain stiffness are defined as listed.

2Density is defined as 2710 kg/m3.

3Constant porosity type model is used. The value is defined as 0.35.

4Young’s modulus and Poisson’s ratio are defined as 2000MPa and 0.2, respectively.

5The material data structure is associated with fracture set “fract_set1”.

Fracture_data

Fracture_data assigns the properties of the embedded fracture as well as the fracture spacing and local coordinate system.

Data File

* Fracture_data NUM=1

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

Name "fract_set1"

Units IDM=4

/Stress/ "MPa"

/Length/ "m"

/Time/ "s"

/Temperature/ "Celsius"

Propagation_model_name "PreExist"

Fracture_spacing 0.25

Coordinate_system_name "Fracture_Set1"

Normal_stiffness_model "Bandis"

Normal_stiffness_properties IDM=3

/Joint Stiffness/ 1000

/Initial Aperture/ 0.01

/Maximum Joint Stiffness/ 300000

Normal_strength_model "Elastic"

1Fracture data name and units are defined as listed.

2The propagation model type is defined as “PreExist”, indicating the embedded fracture as a pre-existing entity.

3Fracture spacing is defined as 0.25m.

4The fracture data is associated with coordinate system named “Fracture_Set1”.

5The fracture normal stiffness model is defined as Bandis model.

6The input values for Bandis model are defined, including joint stiffness, initial aperture and maximum joint stiffness.

7Elastic normal strength model is defined, indicating no formal failure criterion is applied.

Global_loads

Global_loads prescribes axial displacement on the element top surface.

Data File

* Global_loads NUM=1

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

Prescribed_displacement IDM=3 JDM=1

/Set 1/ 0.0 0.0 -0.025

Pres_displacement_geom_set IDM=1

"Top"

Pres_displacement_geom_ass IDM=1

1Geometry set “Top” is prescribed with downward axial displacement of 0.025m.

History_point

History_point outputs displacement, stress values, and fracture state variables at every 0.01s.

Data File

* History_point NUM=1

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

Name "Set1"

Group 1

Output_frequency_time 0.01

Point_coordinates IDM=3 JDM=1

1.0 1.0 1.0

Displacements IDM=1

"DISP_Z"

Stresses IDM=3

"STRS_XX" "STRS_YY" "STRS_ZZ"

Fracture_state_variables NUM=2

"F_kn" "F_dispn"

1The History_point data structure is associated with Group 1.

2The history data is output at an interval of 0.01s throughout the simulation time.

3The history data is monitored at coordinate point (1,1,1).

4Displacement, stresses and fracture state variables as listed are output at the monitored history point.

Results

The result files for this example is available in directory: fract_003\Results. These results are compared with Case01 which contains only 1 embedded joint. Figure 2 shows the element with 4 embedded joints exhibits even lower tangent modulus in the fracture closure stage due to higher fracture compliance accumulated from all 4 joints. The presence of multiple joints results in lower overall fracture stiffness (Figure 3), and thus the total joint normal displacement is higher in the 4-joint element (Figure 4). This can be explained by the inverse relationship between joint displacement and fracture stiffness, provided that the prescribed load is constant. It should be noted that higher value of total joint normal displacement does not imply higher individual joint normal displacement compared to the 1-joint model. This is observed in Figure 4. In terms of porosity, 4-joint element has higher initial value due to higher number of joints (Figure 5). The porosity reduces linearly due to linear reduction of total joint normal displacement. The reduction is around 50% from 0.04.

Although not shown here, the following results do not change when smaller (finer) elements were used.

$fract_003_case02_fig2$

Fig. 2 Comparison of axial stress with intact sample

$fract_003_case02_fig3$

Fig. 3 Comparison of fracture stiffness

$fract_003_case02_fig4$

Fig. 4 Comparison of axial and fracture displacement

$fract_003_case02_fig5$

Fig. 5 Reduction of porosity due to joint closure