The Slope Cube Modulefor HYDRUS (3D)
Simulating Slope Stress and Stability
in Variably-Saturated Hillslopes

Tutorial
Version 1.0

Pan Chen, Alexandra Wayllace, and Ning Lu
August 20, 2019
Soil Water Retention, LLC
Madison, Wisconsin, USA© 2019 Ning Lu. All rights reserved.

DISCLAIMER
The Slope Cube module was developed by the SWR, LLC as a supplemental module of the
HYDRUS (2D/3D) software package to simulate two-dimensional and three-dimensionaltransient fields of soil moisture, soil suction, suction stress, total and effective stresses,
deformation, and local factor of safety. The computational code of the Slope Cube module(written in Fortran) was obtained by coupling the standard computational 2D/3D module of
HYDRUS (flow and transport) with an adopted code from a two-dimensional hydromechanical model (stress and slope stability) developed by Lu et al. (2010) and developed
three-dimensional hydro-mechanical model. While this source code is not available to the
public (and is proprietary/copyrighted), the original source code in Lu et al. (2010) is not
copyrighted, and can be obtained from the senior author. The software has been verified against
selected test cases. However, no warranty is given that the program is error-free. If you do
encounter problems with the code, find errors, or have suggestions for improvement, pleasecontact the senior author at:
Ning Lu
Tel: (303)-995-3980
Soil Water Retention, LLC
www.soilwaterretention.com
Email: ninglu@soilwaterretention.com

i

ii

Table of Contents
DISCLAIMER.......................................................................................................................... i
Table of Contents .................................................................................................................. iii
List of Figures ........................................................................................................................ iv
List of Tables ......................................................................................................................... vii
1. Introduction ...................................................................................................................... 1
2. Example 1: Stability Analysis of a Homogeneous Hillslope under a Constant
Infiltration Rate ................................................................................................................ 2
2.1. Example 1a. Rainfall Scenario 1: Infiltration of 0.05 mm/hour applied for 20

hours .................................................................................................................................. 3
2.2. Example 1b. Rainfall Scenario 2: Infiltration of 0.005 mm/hour applied for 200

hours ........................................................................................................................... 34
3. Example 2: Stability Analysis of a Homogeneous Hillslope under a Time-Varying
Heavy Rainfall Event with a Concentrated Mechanical Load ................................... 40
4. Example 3: Stability Analysis of a Layered Hillslope under a Time-Varying
Heavy Rainfall Event ...................................................................................................... 49
5. Example 4: Shrinkage of a Soil Cake ........................................................................... 69
6. Example 5: Comparison of Measured and Predicted Volumetric Change of a Soil

Cake ................................................................................................................................. 99
References ............................................................................................................................114iii

List of Figures
Figure 1.

Hillslope geometry and boundary conditions for hydrological(in black) and mechanical (in gray) models .................................................. 2

Figure 2.

Project Manager and Project Information windows. ...................................... 3

Figure 3.

Domain Type and Units window. ................................................................... 4

Figure 4.

Main Processes and add-on Modules window. .............................................. 4

Figure 5.

Time Information window. ............................................................................. 5

Figure 6.

Output Information window. .......................................................................... 5

Figure 7.

Iteration Criteria and Initial Conditions window............................................ 6

Figure 8.

Soil Hydraulic Model window. ...................................................................... 7

Figure 9.

Water Flow Parameters and Tensors of Anisotropy window. ........................ 7

Figure 10. Time Variable Boundary Conditions window. ............................................... 8
Figure 11. Slope Cube Parameters window. .................................................................... 9
Figure 12. FE-Mesh Parameters window......................................................................... 9
Figure 13. Graphical user interface. ............................................................................... 10
Figure 14. Steps to insert point coordinates. .................................................................. 11
Figure 15. Lines connecting points in hillslope geometry. ............................................ 12
Figure 16. Surfaces generation for the hillslope. ........................................................... 13
Figure 17. Solids generation for the hillslope. ............................................................... 15
Figure 18. FE-Mesh generation. .................................................................................... 16
Figure 19. FE-Mesh Information window. .................................................................... 16
Figure 20. Initial conditions for water flow. .................................................................. 17
Figure 21. Steps to assign atmospheric boundary condition.......................................... 18
Figure 22. Steps to assign constant head boundary condition. ...................................... 19
Figure 23. Steps to assign X-displacement boundary condition. ................................... 21
Figure 24. Steps to assign Y-displacement boundary condition. ................................... 22iv

Figure 25. Steps to assign XYZ-displacement boundary condition. ............................. 23
Figure 26. Steps to assign XY-displacement boundary condition on the points of
the hillslope. .................................................................................................. 25
Figure 27. Steps to insert observation nodes. ................................................................ 27
Figure 28. Model execution. .......................................................................................... 27
Figure 29. Options for graphical display of results........................................................ 28
Figure 30. Contour plots of pressure head [m] and water content evolution with timefor Example 1a. Results are shown at 0, 4, 12, and 20 hours. .................... 29
Figure 31.

Contour plots of maximum and minimum effective stress [kPa] evolution
with time for Example 1a. Results are shown at 0, 4, 12, and 20 hours. ..... 30

Figure 32.

Contour plots of suction stress [kPa] and field of local factor of safety
evolution with time for Example 1a. Results are shown at 0, 4, 12, and 20
hours............................................................................................................. 31

Figure 33. Graphical display of results on the observation. .......................................... 32
Figure 34. Graphical display of observation nodes. (a) pressure head as a function oftime, (b) suction stress as a function of time, and (c) local factor of safety
as a function of time for the three observation nodes. ................................. 33
Figure 35. Steps to change the infiltration duration. ...................................................... 35
Figure 36. Output Information Window for Example 1b. ............................................. 35
Figure 37. Steps to change infiltration rate. ................................................................... 36
Figure 38. Contour plots of pressure head [m] and water content evolution with timefor Example 1b. Results are shown at 0, 40, 120, and 200 hours.. .............. 37
Figure 39.

Contour plots of maximum and minimum effective stress [kPa] evolution
with time for Example 1b. Results are shown at 0, 40, 120, and 200 hours.
...................................................................................................................... 38

Figure 40.

Contour plots of suction stress [kPa] and field of local factor of safety
evolution with time for Example 1b. Results are shown at 0, 40, 120, and
200 hours...................................................................................................... 39

Figure 41.

Illustration of hillslope geometry and boundary conditions forhydrological (in black) and mechanical (in gray) models for Example 2.... 40

Figure 42. Time-varying rainfall boundary condition used in Example 2. .................... 40v

Figure 43.

Steps to change the infiltration duration and Number of Time-variableboundary records.......................................................................................... 41

Figure 44. Time Variable Boundary Conditions window. .............................................. 42
Figure 45. Steps to assign a mechanical load boundary condition in Slope Cube......... 43
Figure 46.

Contour plots of pressure head [m] and water content evolution with timefor Example 2. Results are shown at 0, 34, 50, and 70 hours. ..................... 44

Figure 47.

Contour plots of maximum and minimum effective stress [kPa] evolution
with time for Example 2. Results are shown at 0, 34, 50, and 70 hours. ..... 45

Figure 48.

Contour plots of suction stress [kPa] and field of local factor of safety
evolution with time for Example 2. Results are shown at 0, 34, 50, and 70
hours............................................................................................................. 46

Figure 49. Graphical display of observation nodes. (a) pressure head as a function oftime, (b) suction stress as a function of time, and (c) local factor of safety
as a function of time for the three observation nodes. ................................. 48
Figure 50. Hillslope geometry and boundary conditions for hydrological (in black)and mechanical (in gray) models ................................................................. 49
Figure 51.

Project Manager and Project Information windows. .................................. 50

Figure 52.

Water Flow Parameters window. ............................................................... 51

Figure 53. Slope Cube Parameters window. .................................................................. 52
Figure 54. Point coordinates displayed in the “Project Navigator-Data” window. ....... 53
Figure 55. Lines connecting points in hillslope geometry (a), and (b) Curves definition
displayed in the “Project Navigator-Data” window.
54
Figure 56. Surfaces generation for the hillslope (a-c) and surfaces definition displayedin the “Project Navigator-Data” window (d). ............................................... 57
Figure 57. Solids generation for the hillslope. ............................................................... 58
Figure 58. FE-Mesh Information window. .................................................................... 59
Figure 59. Assigning two different properties on the hillslope. .................................... 59
Figure 60. Steps to assign water flow boundary conditions. ......................................... 60
Figure 61. Steps to assign displacement boundary conditions. ..................................... 62
Figure 62. Steps to assign XY-displacement boundary condition on the points of
the hillslope. .................................................................................................. 63vi

Figure 63. Steps to insert observation nodes. ................................................................ 64
Figure 64. Contour plots of pressure head [m] and water content evolution with timefor Example 3. Results are shown at 0, 34, 50, and 70 hours. .................... 65
Figure 65.

Contour plots of maximum and minimum effective stress [kPa] evolution
with time for Example 3. Results are shown at 0, 34, 50, and 70 hours. ..... 66

Figure 66.

Contour plots of suction stress [kPa] and field of local factor of safety
evolution with time for Example 3. Results are shown at 0, 34, 50, and 70
hours............................................................................................................. 67

Figure 67. Graphical display of results on the observation. .......................................... 68
Figure 68.

Soil cake geometry and boundary conditions for hydrological (in black)and mechanical (in gray) models. ................................................................ 69

Figure 69. Project Manager and Project Information windows. .................................... 70
Figure 70.

Domain Type and Units window. ............................................................... 71

Figure 71.

Main Processes and add-on Modules window. .......................................... 71

Figure 72.

Time Information window. ......................................................................... 72

Figure 73.

Output Information window. ...................................................................... 72

Figure 74.

Iteration Criteria and Initial Conditions window........................................ 73

Figure 75.

Soil Hydraulic Model window. .................................................................. 74

Figure 76.

Water Flow Parameters and Tensors of Anisotropy window. .................... 75

Figure 77. Slope Cube Parameters window. .................................................................. 75
Figure 78. FE-Mesh Parameters window....................................................................... 76
Figure 79. Graphical user interface................................................................................ 76
Figure 80. Steps to insert point coordinates. .................................................................. 79
Figure 81. Lines connecting points in hillslope geometry. ............................................ 79
Figure 82. Surfaces generation for the hillslope. ........................................................... 81
Figure 83. Solids generation for the hillslope. ............................................................... 83
Figure 84. FE-Mesh generation. .................................................................................... 84vii

Figure 85. FE-Mesh Information window. .................................................................... 84
Figure 86. Initial conditions for water flow. .................................................................. 85
Figure 87. Steps to assign constant water content boundary condition. ........................ 87
Figure 88. Steps to assign Z-displacement boundary condition. ................................... 89
Figure 89. Steps to assign XYZ-displacement boundary condition on the points ofthe soil cake................................................................................................... 91
Figure 90. Steps to insert observation nodes. ................................................................ 93
Figure 91. Model execution. .......................................................................................... 94
Figure 92. Options for graphical display of results........................................................ 95
Figure 93. Contour plots of pressure head [m] and water content evolution with timefor Example 4............................................................................................... 96
Figure 94.

Contour plots of maximum and minimum effective stress [kPa] evolution
with time for Example 4 .............................................................................. 96

Figure 95. Contour plots of suction stress [kPa] evolution with time for Example 4..... 96
Figure 96. Contour plots of XY-deformation, and Z-deformation[m] evolution in XY
and Z directions with time for Example 4 ................................................... 97
Figure 97. Graphical display of results on the observation. .......................................... 98
Figure 98. Graphical display of observation nodes. ...................................................... 99
Figure 99.

Soil cake geometry and boundary conditions for hydrological (in black)and mechanical (in gray) models. .............................................................. 100

Figure 100. Comparison of the measured and fitted SSCC of Denver claystone. ........ 101
Figure 101. Comparison of the measured and fitted Young’s modulus of Denverclaystone. ................................................................................................... 101
Figure 102. Project Information windows. .................................................................. 103
Figure 103.

Steps to insert point coordinates of the soil cake ................................... 105

Figure 104.

Time Information window. ..................................................................... 105

Figure 105.

Output Information window. .................................................................. 106

Figure 106.

Water Flow Parameters and Tensors of Anisotropy window. ................ 107

viii

Figure 107. Slope Cube Parameters window. .............................................................. 108
Figure 108. FE-Mesh Parameters window................................................................... 109
Figure 109. FE-Mesh generation. ................................................................................ 109
Figure 110. Initial conditions for water flow. .............................................................. 110
Figure 111. Steps to assign new constant water content boundary condition. ............ 111
Figure 112. Steps to assign XYZ-displacement boundary condition on the points ofthe soil cake................................................................................................. 112
Figure 113. Pop up window before running the project .............................................. 113
Figure 114. Options for graphical display of results.................................................... 114
Figure 115. Comparison between the simulated and measured porosity..................... 114

ix

List of Tables
Table 1.

Hydro-mechanical parameters used in Example 1 ............................................ 2

Table 2.

Coordinates of points used in hillslope geometry ............................................ 10

Table 1.

Hydro-mechanical parameters used in Example 3

49

Table 4.

Coordinates of points used in hillslope geometry for Example 3

52

Table 2.

Hydro-mechanical parameters used in Example 4

69

Table 3.

Coordinates of points used in soil cake geometry

77

Table 4.

Hydro-mechanical parameters used in Example 5

100

Table 5.

Steps for the water content change used in Example 5

101

Table 6. Coordinates of points used in hillslope geometryx102

1. Introduction
The purpose of this tutorial is to document the use of Slope Stress and Stability, or Slope Cube
module for Hydrus-3D and give users a hands on experience with the software package(version 2.0). Five examples are provided to familiarize the users with the main concepts andprocedures of pre- and post-processing. Three of them focus on the slope stability provided tofamiliarize the users with the main concepts and procedures of pre- and post-processing. Twoof them explain how to solve the deformation problems under the drying conditions. The
measured deformation data in the literature are used to validate the numerical framework.
1. Stability analysis of a homogeneous silty hillslope under a constant rainfall infiltration.
The slope gradient changes from 30o to 60o and is subjected to a constant infiltration
rate. Two cases are considered: a) infiltration rate of 0.05 mm/h is applied for 20 hours,b) infiltration rate of 0.005 mm/h is applied for 200 hours. Users in this example become
familiar with windows in the Water Flow and the Slope Cube modules.
2. Stability analysis of a homogeneous hillslope under a time-varying rainfall and aconcentrated mechanical load at the crest.
The second example considers a homogeneous hillslope subjected to the rainfall
measured during Hurricane Frances when it hit North Carolina in 2004 (Wooten et. al.,2008). A concentrated load of 20 KN is applied to the crest of the slope. Users in thisexample will get familiar with hydrostatic initial conditions, time variable boundary
conditions in the hydrological model, and load boundary conditions in the mechanicalmodel.
3. Stability analysis of a layered sandy and silty hillslope under a time-varying rainfall
infiltration condition. The geometry of the slope is similar with the slope in the Example
2. The top 2-meter depth is sandy soil and the lower layer is silty soil. The rainfall data
are the same as the ones using in the Example 2. Users in this example become familiar
with windows to set different material characteristics in the Water Flow and the Slope
Cube modules.
4. Deformation analysis of a homogeneous clayey soil cake under a drying condition (soilshrinkage). The geometry of the cake: diameter 6.0 cm and height 1.0 cm. The initialwater content of the soil cake is assumed 0.37. The ultimate volumetric water content
is set to 0.25. Users in this example become familiar with windows to analyze
deformation using the Water Flow and the Slope Cube modules.
5. Comparison of measured data and simulated results for soil shrinkage of a clayey soil
is given in this example. The soil cake is initially fully saturated; volumetric changes
due to drying conditions are simulated and compared to measurements using Particle
Image Velocimetry (PIV) (Dong and Lu, 2017).
This tutorial is organized in five sections, one for each example. Each section presents the
problem definition and the step-by-step implementation.

12. Example 1: Stability Analysis of a Homogeneous Hillslope under aConstant Infiltration Rate
The first example demonstrates the stability analysis of a homogeneous three-dimensional silty
hillslope. The geometry and boundary conditions for the Water Flow and the Slope Cubemodels are presented in Figure 1. The slope gradient ranges from 30 to 60 degrees near the toe.
Initial conditions were hydrostatic with the water table set at the base (z=0). Two different
rainfall scenarios are presented as Example 1a and Example 1b respectively. The hillslope
hydro-mechanical parameters are specified in Table 1. Model results are illustrated as thetransient fields of pressure head, water content, minimum and maximum effective stress,
suction stress and local factor of safety.
Back surface, Y=36 m:
No flow
Top surface:
uy=0
AtmosphericFree displacement

Left surface, X=0 m:
No flow
ux=0

Front surface, Y=0 m:
No flow
uy=0

Bottom surface, Z=0 m:
pw =0
uz=0

Figure 1. Hillslope geometry and boundary conditions for hydrological (in black) andmechanical (in gray) models.
Table 1. Hydro-mechanical parameters used in Example 1.

Soil Parameter

Value

Soil type

Silt

[1/m]

3.6

n [-]

1.56

ks [m/h]
[-]

0.10
0.078

[-]

0.430

Gs [-]

2.6

c' [kPa]

12.0

φ' [ ]

45.0

µ [-]

0.30

Ez/Ex

1.0

2

Ed [kPa]

10000

Ew [kPa]

10000

θd

0.1

θw

0.35

m

0.25

2.1 Example 1a. Rainfall Scenario 1: Infiltration of 0.05 m/hour applied for 20 hours
Open Hydrus: Double click on logo
Project Manager (Figure 2)
Button “File”, Button “New”
Name: Example 1a
Description: 3D stability analysis of homogeneous hillslope
Path: (specify)
Working directory: (specify)
Choose “Permanent – remains open when the project is closed”
Button “Next”

(a)

(b)
Figure 2. Project Manager and Project Information windows.
3

Domain Type and Units (Figure 3)
Type of Geometry: 3D-General
Units: m
Button “Next”

Figure 3. Domain Type and Units window.
Main Processes and add-on Modules (Figure 4)
Check “Water Flow”
Check “Slope Cube”
Button “Next”

Figure 4. Main Processes and add-on Modules window.
Time Information (Figure 5)
4

Check “Hours”
Initial Time [hour]: 0
Final Time [hour]: 20
Initial Time Step [hour]: 0.001
Minimum Time Step [hour]: 0.0001
Maximum Time Step [hour]: 1
Check “Time-Variable Boundary Conditions”
Number of Time-Variable Boundary Records: 1
Number of times to repeat the same set of BC records: 1
Button “Next”

Figure 5. Time Information window.
Output Information (Figure 6)
Check “T-Level Information”
Check “Screen Output”
Check “Press Enter at the End”
Count: 20
Button “Update”
Button “Next”

Figure 6. Output Information window.
5

Iteration Criteria (Figure 7)
Maximum Number of Iterations: 10
Water Content Tolerance: 0.001
Pressure Head Tolerance [m]: 0.01
Lower Optimal Iteration Range: 3Upper Optimal Iteration Range: 7
Lower Time Step Multiplication Factor: 1.3
Upper Time Step Multiplication Factor: 0.7
Lower Limit of the Tension Interval: 0.000001
Upper Limit of the Tension Interval: 100
Check Initial Condition “In Pressure Heads”
Button “Next”

Figure 7. Iteration Criteria and Initial Conditions window.
Soil Hydraulic Model (Figure 8)
Check: “van Genuchten-Mualem”
Check: “No Hysteresis”
Button “Next”

6Figure 8. Soil Hydraulic Model window.
Water Flow Parameters and Tensors of Anisotropy window (Figure 9)
Number of Materials: 1
Button “Update”
Name: Silt
Qr: 0.078
Qs: 0.43
Alpha [1/m]: 3.6
n: 1.56
Ks [m/hour]: 0.10
I: 0.5
Button “Next” (Figure 9a)
In the “Tensors of Anisotropy window”, click “Next” (Figure 9b)

Figure 9a. Water Flow Parameters window.

7

Figure 10b. Tensors of Anisotropy window.
Time Variable Boundary Conditions (Figure 10)
Precip. [m/hour]: 0.05 for the step.
Button “Next”

Figure 10. Time Variable Boundary Conditions window.
Slope Cube Parameters (Figure 11)
Specific gravity: 2.6
Cohesion [kPa]: 12
Friction angle[o]: 45
Poisson ratio: 0.3
Ratio between Young modulus in z-direction and Young modulus in x-direction Ez/Ex: 1.0
Young modulus at dry state [kPa]: 10000
Young modulus at wet state [kPa]: 10000
Water content at dry state [-]: 0.1
Water content at wet state [-]: 0.35
Power law parameter m [-]: 0.25
Button “Next”

8Figure 11. Slope Cube Parameters window.
FE-Mesh Parameters (Figure 12)
Un-Check: “Automatic”, and set the size of element Ts = 2.0 m
Check: “Tetrahedral”
Button “Next”
Button “OK” to warning window

(a)

(b)

Figure 12. FE-Mesh Parameters window.
GRAPHICAL MODE
In this mode the user can:
- Specify the geometry of the model- Generate the FE-mesh- Specify material distribution, observation nodes, regions and sub-regions
9

- Specify boundary conditions
These steps can be performed through the two main windows “Project Navigator – Data” and“Edit Bar” or through the Main Menu (Figure 13).

Figure 13. Graphical user interface.
Geometry Settings
In the Project Navigator-Data select “Geometry”->”Points”.
Select “Point” () in the Edit Bar and insert the coordinates of the 22 points in Table 2.
Click “Apply” after each point. Click “Stop” when done (Figure 14).
Another way of doing this is Insert->Domain Geometry->Points->Graphically. Then use thecursor to click on locations where you would like the points.
Table 2. Coordinates of points used in hillslope geometry.
Point

X [m]

Y [m]

Z [m]

P1

0.00

0.00

0.00

P2

36.52

0.00

0.00

P3

32.13

18.00

0.00

P4

0.00

18.00

0.00

P5

0.00

36.00

0.00

P6

27.73

36.00

0.00

P7

0.00

0.00

15.00

P8

10.00

0.00

15.00

P9

11.00

0.00

14.76

P10

12.00

0.00

14.36

P11

13.00

0.00

13.80

P12

14.00

0.00

13.00

P13

0.00

18.00

20.39

10

P14

10.00

18.00

20.39

P15

11.00

18.00

20.15

P16

12.00

18.00

19.75

P17

13.00

18.00

19.19

P18

0.00

36.00

25.78

P19

10.00

36.00

25.78

P20

11.00

36.00

25.54

P21

12.00

36.00

25.07

P22

13.00

36.00

24.58

Figure 14a. Steps to insert point coordinates.

Figure 14b. Point coordinates displayed in the “Project Navigator-Data” window.
11Select the “Line-Connected Segments” command () from the Edit Bar (or Insert->Domain
Geometry-> Curves->Polylines->Graphically).
Connect the points to define the geometry (Figure 15). To finish the polyline press “Escape”.

Figure 15a. Lines connecting points in hillslope geometry.

Figure 15b. Curves definition displayed in the “Project Navigator-Data” window.
12Select the “Planar surface Boundary” command ( ) from the Edit Bar. Alternatively, it canbe selected via Insert->Domain Geometry->Surface->Planar->Graphically.
Select the boundary curves to generate a Surface. Using this command generate surfaces 1-5
as follows:
Surface 1: Y= 0 (Figure 16a).
Surface 2: Y= 18 (Figure 16b).
Surface 3: Y= 36 (Figure 16b).
Select the “Curved surface - Quadrangle” command ( ) from the Edit Bar. Select theboundary curves to generate a Surface. Using this command generate surfaces 1-5 as follows:
Surface 4: Slope face, Y=0-18 (Figure 16c).
Surface 5: Slope face, Y= 18-36 (Figure 16c).
Select the “Planar surface Boundary” command ( ) from the Edit Bar. Alternatively, it canbe selected via Insert->Domain Geometry->Surface->Planar->Graphically.
Select the boundary curves to generate a Surface. Using this command generate surfaces 6-11
as follows (Figure 16d):
Surface 6: X= 0, Y = 0-18.
Surface 7: X=0, Y= 18-36.
Surface 8: Z=0, Y= 0-18.
Surface 9: Z=0, Y=18-36.
Surface 10: Top face, Y= 0-18.
Surface 11: Top face, Y= 18-36.
Select the boundary curves of Surface 6 (X=0), Surface 6 is generated (Figure 16d).
Repeat the above steps to generate Surfaces 7-9 and 10-11 (Figures 16d).

Surface 3

Surface 2

Surface 1

(a)

(b)

13

Surface 9Surface 8

(c)

(d)

(e)
Figure 16. Surfaces generation for the hillslope (a-d) and surfaces definition displayed in the“Project Navigator-Data” window (e).
Select the “Solid - Boundary surfaces” command ( ) from the Edit Bar. Click on “Pick
Boundary Surfaces” (Figure 17a) and select the boundary surfaces of Solid 1 (Surfaces 1, 2, 4,
6, 8, 10), Solid 1 is generated (Figure 17b).
Select the boundary surfaces of Solid 2 (Surfaces 2, 3, 5, 7, 9, 11), Solid 2 is generated (Figure
17c).

14

(a)

(b)

(c)

Figure 17. Solids generation for the hillslope.
Define FE-Mesh
Click on the “FE-Mesh” folder in the Project Navigator-Data.
Click “Generate FE-Mesh command () from the Edit Bar (or Edit->FEMesh->Generate FE-Mesh). (Figure 18).

15

Figure 18. FE-Mesh generation.
Click on Mesh->Mesh parameters in the “Project Navigator – Data”
Click on “Next” in the pop-up “FE-Mesh Information” and “OK” in the pop-up window withwarning for the next steps (Figure 19).

(a)

(b)
Figure 19. FE-Mesh Information window.
Domain Properties
All nodes are automatically assigned to Material 1.
16Water Flow Initial Conditions
Click on the “Initial Conditions” folder in the Project Navigator-Data.
In the Edit Bar click on “New Pressure Head Initial Condition” (). Select“Equilibrium from the lowest located nodal point” and specify “Bottom Pressure Head IC” to
0.0 m (Figure 20). Click “OK”

Figure 20. Setting of initial conditions for water flow.
Water Flow Boundary Conditions
Click on the “Boundary Conditions” folder in the Project Navigator-Data.
Click on “Water Flow”
Click on the “New Boundary Condition” command () from the Edit Bar.
In the “New Water Flow Boundary Condition” pop up window select “Atmospheric
Boundary”.
Click on “Atmospheric Boundary” in the Edit Bar and with the cursor select the top boundary
surfaces of the hillslope (Figure 21).

17

(a)

(b)

(c)
Figure 21. Steps to assign atmospheric boundary condition.
18

Click on the “New Boundary Condition” command () from Edit Bar.
In the “New Water Flow Boundary Condition” pop-up window select “Constant Head”. And
Give the Pressure Head Value = 0.000 m at the left.
Click on “Constant Head” in the Edit Bar
Click on “Section” in the left Bar
Choose “Geo-Sections” from “Options – Section”
Choose “Surface No.8 and 9” from “Geo-Sections” lists
Using the cursor select the bottom surface boundary (Figure 22).

(a)

(b)
Figure 22. Steps to assign constant head boundary condition.
19

Slope-Cube Boundary Conditions
Click on the “Boundary Conditions” folder in the Project Navigator-Data.
Click on “Slope Cube.”
Click on the “New Slope Cube Boundary Condition” command from the Edit Bar.
In the “New Slope Cube Boundary Condition” pop-up window select “X-displacement” andset it to 0 m.
Click on “X-displacement” in the Edit Bar.
Click on “Section” in the left Bar
Choose “Geo-Sections” from “Options – Section”
Choose “Surface No. 6 and 7” from “Geo-Sections” lists
Using the cursor select the left two surfaces and giving X-displacement = 0 (Figure 23).

(a)

(b)
20

(c)
Figure 23. Steps to assign X-displacement boundary condition.
Click on the “New Slope Cube BDRC” command from the Edit Bar.
In the “New Slope Cube Boundary Condition” pop-up window select “Y-displacement” andset it to 0 m.
Click on “Y-displacement” in the Edit Bar
Click on “Section” in the left Bar
Choose “Geo-Sections” from “Options – Section”
Choose “Surface No. 1 and 3” from “Geo-Sections” lists
Using the cursor select the two surfaces and giving Y-displacement = 0 (Figure 24).

(a)
21

(b)
Figure 24. Steps to assign Y-displacement boundary condition.
Click on the “New Boundary Condition” command from the Edit Bar.
In the “New Slope Cube Boundary Condition” pop-up window select “XYZ-displacement”
and set it to 0 m (X=0, Y=0, Z=0).
Click on “XYZ-displacement” in the Edit Bar
Click on “Section” in the left Bar
Choose “Geo-Sections” from “Options – Section”
Choose “Surface No. 8 and 9” from “Geo-Sections” lists
Using the cursor select the two surfaces and giving XYZ-displacement = 0 (Figure 25).

(a)
22

(b)
Figure 25. Steps to assign XYZ-displacement boundary condition.
Click on the “Edit conditions on FE-mesh” command from the Edit Bar.
Click on “XY-displacement” in the Edit Bar.
Click on “Section” in the left Bar
Choose “Geo-Sections” from “Options – Section”
Choose “Surface No. 1” from “Geo-Sections” lists
Choose the point (X=0, Y=0) on the mesh of the hillslope
In the “Slope Cube Boundary Condition” pop-up window select “XY-displacement”.
Set X-value, and Y-value to 0 m, respectively.
Click “OK” to set the boundary condition on the points of the mesh (Figures 26a, b, c).
According to the same steps to set the “XY-displacement” on “Surface No. 3” (Figure 26d).

23

(a)

(b)

24

(c)

(d)
Figure 26. Steps to assign XY-displacement boundary condition on a point of the hillslope.
Observation Nodes
Click on the Domain Properties Tab under the View Window.
On the Navigator Bar click on Domain Properties-Observation Nodes (or Insert->Domain
Properties->Observation Nodes).
25

Click on Edit Properties on FE-Mesh command () on the Edit Bar, thenInsert Observation Node command ().
Click on “Section” in the left Bar. And choose “Geo-Sections” from “Options – Section”
Choose “Surface No. 1” from “Geo-Sections” lists.
Choose a point from the mesh of the hillslope, then Observation Node 1 is listed in Observation
Nodes Bar.
According to the above method, specify another two observation points on the Surfaces 2 and3, respectively (Figure 27).

(a)

(b)
26

(c)
Figure 27. Steps to insert observation nodes.
Save
Save the project using the Save command () on the Toolbar File->Save).

Run Calculations
Click the ‘Calculate Current Project” command (>Calculate Current Project) (Figure 28).

Figure 28. Model execution.
27) on the Toolbar (or Calculation-

OUTPUT
Click on the Results Tab under the View Window or Click on the “Results-Graphical Display”
folder in the Project Navigator-Data (Figure 29).
Graphical Display includes contour distribution for:- Pressure Heads- Water Content- Velocity- Velocity Vectors- Streamlines- Maximum Total Stress- Minimum Total Stress- Maximum Effective Stress- Minimum Effective Stress- Suction Stress- Field of Local Factor of Safety- XY - Stress- YZ - Stress- XZ - Stress- Intermediate Effective Stress

Figure 29. Options for graphical display of results.
Evolution in time of pressure head, water content, minimum and maximum effective stress,
suction stress, and local factor of safety are shown in Figures 30-32. Pressure head, suction
stress, and local factor of safety as a function of time at the observation nodes are shown in
Figure 33-34.

28

Pressure head [m]Water content [-]Time: 0 [h]Time: 0 [h]Time: 4 [h]Time: 4 [h]Time: 12 [h]Time: 12 [h]Time: 20 [h]Time: 20 [h]Figure 30. Contour plots of pressure head [m] and water content evolution with time for
Example 1a. Results are shown at 0, 4, 12, and 20 hours.
29Maximum effective stress [kPa]

Minimum effective stress [kPa]

Time: 0 [h]Time: 0 [h]Time: 4 [h]Time: 4 [h]Time: 12 [h]Time: 12 [h]Time: 20 [h]Time: 20 [h]Figure 31. Contour plots of maximum and minimum effective stress [kPa] evolution withtime for Example 1a. Results are shown at 0, 4, 12, and 20 hours.

30Suction stress [kPa]

Field of local factor of safety [-]Time: 0 [h]Time: 0 [h]Time: 4 [h]Time: 4 [h]Time: 12 [h]Time: 12 [h]Time: 20 [h]Time: 20 [h]Figure 32. Contour plots of suction stress [kPa] and field of local factor of safety evolution
with time for Example 1a. Results are shown at 0, 4, 12, and 20 hours.

31Click on the “Results – Other Information” folder in the Project Navigator-Data (Figure 33).
Click on “Observation Points” to show the results on the observation.

Figure 33. Graphical display of results on the observation.
In the pop-up window “Observation Nodes”, The evolution of Pressure head, Water content,
Maximum Total Stress, Minimum Total Stress, Maximum Effective Stress, Minimum
Effective Stress, Suction Stress, Local of Factor of Safety can be shown (Figure 35).

(a)

32

(b)

(c)

(d)
Figure 34. Graphical display of observation nodes. (a) pressure head as a function of time, (b)water content as a function of time, (c) suction stress as a function of time, and (d) local
factor of safety as a function of time for the three observation nodes.
332.2 Example 1b. Rainfall Scenario 2: Infiltration of 0.005 m/h applied for 200 hours
Implementing the second rainfall scenario to Example 1a requires the following modifications:
Close the Example 1a Project (click Save Project at the Toolbar)
Project Manager
Select Example 1a project
Button “Copy”
Name: Example 1b
Description: Change infiltration rate and duration
Button “OK”
Need to open new project (Example 1b) in Project Manager and then Close Project Manager(click red “x” in upper right corner or “close” in lower right corner). To avoid confusions, it’salso worth closing the previous project (Example 1a).
In the Project Navigator Data click on the “Flow and Transport Parameters” folder.
Click on “Time Information.”
Specify “Final Time” to 200 hours.
Click “Next.” (Figure 35).

(a)

34

(b)
Figure 35. Steps to change the infiltration duration.
On the pop-up “Output Information” window:
Set “Count” to 10.
Click “Default.”
Click “Update.”
Click “OK” (Figure 36).

Figure 36. Output Information Window for Example 1b.
In the Project Navigator Data click on the “Flow and Transport Parameters” folder.
Click on “Water Flow”
Click on “Variable Boundary Cond.”
Make sure “Time” set to 200 hours
Set “Precip” to 0.005 m/h for the 200 hours.
Click on “OK” (Figure 37).

35

3

(a)

(b)
Figure 37. Steps to change infiltration rate on the top surfaces.
Save project
Run Calculations
Click the ‘Calculate Current Project” command (>Calculate Current Project)) on the Toolbar (or Calculation-

OUTPUT
Click on the Results Tab under the View Window or Click on the “Results-Graphical
Display” folder in the Project Navigator-Data. Results for Example 1b are provided in
Figures 38-40.
36

Pressure head [m]Water content [-]Time: 0 [h]Time: 0 [h]Time: 40 [h]Time: 40 [h]Time: 120 [h]Time: 120 [h]Time: 200 [h]Time: 200 [h]Figure 38. Contour plots of pressure head [m] and water content evolution with time for
Example 1b. Results are shown at 0, 40, 120, and 200 hours.

37Maximum effective stress [kPa]

Minimum effective stress [kPa]

Time: 0 [h]Time: 0 [h]Time: 40 [h]Time: 40 [h]Time: 120 [h]Time: 120 [h]Time: 200 [h]Time: 200 [h]Figure 39. Contour plots of maximum and minimum effective stress [kPa] evolution withtime for Example 1b. Results are shown at 0, 40, 120, and 200 hours.

38Suction stress [kPa]

Field of local factor of safety [-]Time: 0 [h]Time: 0 [h]Time: 40 [h]Time: 40 [h]Time: 120 [h]Time: 120 [h]Time: 200 [h]Time: 200 [h]Figure 40. Contour plots of suction stress [kPa] and field of local factor of safety evolution
with time for Example 1b. Results are shown at 0, 40, 120, and 200 hours.

393. Example 2: Stability Analysis of a Homogenous Hillslope under a Timevarying Heavy Rainfall Event with a Concentrated Mechanical Load.
Example 2 demonstrates the stability analysis of a homogenous hillslope subject to the hourly
averaged rainfall measured during the Hurricane Frances that hit North Carolina in September
2004 (Wooten et al., 2008). The example also includes a concentrated mechanical load of 20
kN applied to the crest of the hillslope. The hillslope geometry and boundary conditions forthe water flow and the Slope Cube models are presented in Figure 41. The hillslope hydromechanical parameters are specified in Table 1. The rainfall time series used as the tophydrologic boundary condition is shown in Figure 42 and it is provided in the file
Rainfall_Example2.csv with the complimentary material to this tutorial. Model results areillustrated as the transient fields of pressure head, water content, minimum and maximum
effective stress, shear stress, suction stress and local factor of safety.
20 KN

Left surface, X=0 m:
No flow
ux=0Back surface, Y=36 m:
No flow
uy=0
Top surface:
AtmosphericFree displacement

Front surface, Y=0 m:
No flow
uy=0

Bottom surface, Z=0 m:
pw =0
uz=0

Figure 41. Illustration of hillslope geometry and boundary conditions for hydrological (inblack) and mechanical (in gray) models for Example 2.

Figure 42. Time-varying rainfall boundary condition used in Example 2.

40

This example has similar initial settings to Example 1a; therefore, the user can open Example
1a and perform the following modifications:
Project Manager (File->Project Manager)
Select Example 1a project
Button “Copy”
Name: Example 2
Description: a slope under time-variable rainfall and mechanical load
Button “Open”
Time Information (Project Navigator-Data-> Flow and Transport Parameters-> Time
Information).
Specify “Final Time” to 80 hours.
Set “Number of Time-Variable Boundary Records” to 80
Click “Next.” (Figure 43)

Figure 43. Steps to change the infiltration duration and Number of Time-variable boundary
records.
Output Information
Count: 80.
Click “Default.”
Click “Update.”
Click “OK.”Variable Boundary Conditions (Project Navigator-Data->Flow and Transport Parameters>Variable Boundary Cond).
Set “Precip” to values provided in Rainfall_Example2.csv. You can copy and paste the values.
Click “OK”

41

Figure 44. Time Variable Boundary Conditions window.
Slope Cube Boundary Conditions (Figure 45). (Project Navigator-Data->Boundary
Conditions->Slope Cube)
Click on the “Edit Conditions on FE-mesh” command () from the Edit Bar.
Click on “Z-force” in the Edit Bar.
Double click on the node where the force will be applied Figure 45b).
In the pop-up “Slope Cube Boundary Condition” window, select “Z-force” and specify a Zvalue of -20 KN.
Click “OK.”

(a)

42

(b)

(c)
Figure 45. Steps to assign a mechanical load boundary condition in Slope Cube.
Save project.
Run Calculations
Click the ‘Calculate Current Project” command (>Calculate Current Project)) on the Toolbar (or Calculation-

OUTPUT
Click on the Results Tab under the View Window or Click on the “Results-Graphical Display”
folder in the Project Navigator-Data. Results for Example 2 are provided in Figures 46-48.

43

Pressure head [m]Water content [-]Time: 0 [h]Time: 0 [h]Time: 34 [h]Time: 34 [h]Time: 50 [h]Time: 50 [h]Time: 70 [h]Time: 70 [h]Figure 46. Contour plots of pressure head [m] and water content evolution with time for
Example 2. Results are shown at 0, 34, 50, and 70 hours.

44Maximum effective stress [kPa]

Minimum effective stress [kPa]

Time: 0 [h]Time: 0 [h]Time: 34 [h]Time: 34 [h]Time: 50 [h]Time: 50 [h]Time: 70 [h]Time: 70 [h]Figure 47. Contour plots of maximum and minimum effective stress [kPa] evolution withtime for Example 2. Results are shown at 0, 34, 50, and 70 hours.

45Suction stress [kPa]

Field of local factor of safety [-]Time: 0 [h]Time: 0 [h]Time: 34 [h]Time: 34 [h]Time: 50 [h]Time: 50 [h]Time: 70 [h]Time: 70 [h]Figure 48. Contour plots of suction stress [kPa] and field of local factor of safety evolution
with time for Example 2. Results are shown at 0, 34, 50, and 70 hours.
46

(a)

(b)

(c)

47

(d)
Figure 49. Graphical display of observation nodes. (a) pressure head as a function of time, (b)water content as a function of time, (c) suction stress as a function of time, and (d) local
factor of safety as a function of time for the three observation nodes.

48

4. Example 3: Stability Analysis of a Layered Hillslope under a Timevarying Heavy Rainfall Event.
The third example demonstrates the stability analysis of a layered three-dimensional silty toclay hillslope. The geometry is similar to Example 2. However, the 2-meter top layer is the silt
being different from the lower clayey layer. The same rainfall data used in Example 2 are also
used in this case. The hillslope geometry and boundary conditions for the water flow and the
Slope Cube models are presented in Figure 50. The hillslope hydro-mechanical parameters are
specified in Table 3. The rainfall time series used as the top hydrologic boundary condition is
the same shown in Figure 42. Model results are illustrated as the transient fields of pressure
head, water content, minimum and maximum effective stress, suction stress and local factor ofsafety.
Back surface, Y=36 m:
No flowu y =0Top surface:
AtmosphericFree displacement

Left surface, X=0 m:
No flow
ux=0

Bottom surface, Z=0 m:
pw =0
uz=0

Front surface, Y=0 m:
No flow
uy=0

Figure 50. Hillslope geometry and boundary conditions for hydrological (in black) andmechanical (in gray) models.
Table 51. Hydro-mechanical parameters used in Example 3.
Soil Parameter

Value

Soil type

Silt

Clay

[1/m]

3.6

1.9

n [-]

1.56

1.31

ks [m/h]
[-]

0.10

0.01

0.078

0.095

[-]

0.430

0.410

Gs [-]

2.6

2.7

c' [kPa]

12.0

20.0

φ' [ ]

45.0

30.0

Ez/Ex

1.0

1.0

Ed [kPa]

15000

10000

49

Ew [kPa]

15000

10000

θd

0.10

0.10

θw

0.35

0.35

m

0.25

0.25

Project Manager
Select Example 2 project
Button “Copy”
Name: Example 3
Description: Layered 3D slope stability analysis
Button “OK”

Figure 51. Project Manager and Project Information windows.
Need to open new project (Example 3) in Project Manager and then Close Project Manager.
Water Flow Parameters and Tensors of Anisotropy window (Figure 52)
In the Project Navigator Data click on the “Water Flow” – “Soil-Hydraulic Params” folder. On
the pop-up window “Water Flow Parameters”
Number of Materials: 2
Button “Update”
Material 1:
Name: Silt
Qr: 0.078
Qs: 0.43
Alpha [1/m]: 3.6
n: 1.56
Ks [m/hour]: 0.10
I: 0.5Material 2:
Name: Clay
Qr: 0.095
Qs: 0.4150

Alpha [1/m]: 1.9
n: 1.31
Ks [m/hour]: 0.01
I: 0.5
Button “OK”

Figure 52. Water Flow Parameters window.
Slope Cube Parameters (Figure 53)
In the Project Navigator Data click on the “Water Flow” – “Slope Cube Stress Parameters”
folder.
On the pop-up window “Slope Cube Parameters”, Click “1- Silt” in the Materials window
Specific gravity: 2.6
Cohesion [kPa]: 12
Friction angle[o]: 45
Poisson ratio: 0.3
Ratio between Young modulus in z-direction and Young modulus in x-direction Ez/Ex: 1.0
Young modulus at dry state [kPa]: 15000
Young modulus at wet state [kPa]: 15000
Water content at dry state [-]: 0.10
Water content at wet state [-]: 0.35
Power law parameter m [-]: 0.25
Click “2- Clay” in the Materials window
Specific gravity: 2.7
Cohesion [kPa]: 20
Friction angle[o]: 30
Poisson ratio: 0.3
Ratio between Young modulus in z-direction and Young modulus in x-direction Ez/Ex: 1.0
Young modulus at dry state [kPa]: 10000
Young modulus at wet state [kPa]: 10000
Water content at dry state [-]: 0.10
Water content at wet state [-]: 0.35
Power law parameter m [-]: 0.25
Button “OK”

51

(a) Silt(b) Clay
Figure 53. Slope Cube Parameters window.
GRAPHICAL MODE
Geometry Settings
Delete all the curves.
In the Project Navigator-Data select “Geometry”->”Points”.
Select “Point” () in the Edit Bar and insert the coordinates of added 12 points (P23 – P34)
in Table 4.
Click “Apply” after each point. Click “Stop” when done. All the points are listed here (Figure
54).
52

Another way of doing this is Insert->Domain Geometry->Points->Graphically. Then use thecursor to click on locations where you would like the points.
Table 4. Coordinates of points used in hillslope geometry for Example 3.
Point

X [m]

Y [m]

Z [m]

P1

0.00

0.00

0.00

P2

36.52

0.00

0.00

P3

32.13

18.00

0.00

P4

0.00

18.00

0.00

P5

0.00

36.00

0.00

P6

27.73

36.00

0.00

P7

0.00

0.00

15.00

P8

10.00

0.00

15.00

P9

11.00

0.00

14.76

P10

12.00

0.00

14.36

P11

13.00

0.00

13.80

P12

14.00

0.00

13.00

P13

0.00

18.00

20.39

P14

10.00

18.00

20.39

P15

11.00

18.00

20.15

P16

12.00

18.00

19.75

P17

13.00

18.00

19.19

P18

0.00

36.00

25.78

P19

10.00

36.00

25.78

P20

11.00

36.00

25.54

P21

12.00

36.00

25.07

P22

13.00

36.00

24.58

P23

0.00

0.00

13.00

P24

10.00

0.00

13.00

P25

14.00

0.00

11.00

P26

0.00

18.00

18.39

P27

10.00

18.00

18.39

P28

13.00

18.00

17.19

P29

0.00

36.00

23.78

P30

10.00

36.00

23.78

P31

13.00

36.00

22.58

P32

36.52

0.00

2.00

P33

32.13

18.00

2.00

P34

27.73

36.00

2.00

53

Figure 54. Point coordinates displayed in the “Project Navigator-Data” window.
Select the “Line-Connected Abscissae” command () from the Edit Bar (or Insert->Domain
Geometry-> Curves->Polylines->Graphically).
Connect the points to define the geometry (Figure 55). To finish the polyline press “Escape”.

Figure 55a. Lines connecting points in hillslope geometry.

54

Figure 55b. Curves definition displayed in the “Project Navigator-Data” window.
Select the “Set new planar surface with arbitrary boundary lines graphically” command ( )from the Edit Bar. Alternatively, it can be selected via Insert->Domain Geometry->Surface>Planar->Graphically. Select the boundary curves to generate a Surface. Using this command
generate surfaces 1-5 as follows:
Surface 1-2: Y= 0 (S1-S2);
Surface 3-4: Y= 18 (S3-S4);
Surface 5-6: Y= 36 (S5-S6) (Figure 56a).
Surface 7-10: X= 0 (S7-S10);
Surface 11-12: Z= 0 (S11-S12);
Surface 13-14: X= 27-36 (S13-S14) (Figure 56b).
Select the “Set new planar surface with arbitrary boundary lines graphically” command ( )from the Edit Bar. Alternatively, it can be selected via Insert->Domain Geometry->Surface>Planar->Graphically. Select the boundary curves to generate a Surface. Using this command
generate surfaces four top surfaces as follows:
Surface 15: Z= 13-18, Y = 0-18 (S15);
Surface 17: Z=18-23, Y= 18-36 (S17).
Surface 19: Z=15-20, Y= 0-18 (S19).
55

Surface 21: Z=20-25, Y=18-36 (S21) (Figure 56c).
Select the “Set new Quadrangle” command ( ) from the Edit Bar. Select the boundary curves
to generate a Surface. Using this command generate other four surfaces as follows:
Surface 16: Y = 0-18 (S16);
Surface 18: Y= 18-36 (S18).
Surface 20: Slope surface, Y= 0-18 (S20).
Surface 22: Slope surface, Y=18-36 (S22) (Figure 56c).
The generated surfaces are listed in Figure 56d.
S5

S3

S6

S4
S1

S2

(a)
S9

S7
S10
S8

S12

S14

S11
S13
(b)

56

S19

(c)

(d)
Figure 56. Surfaces generation for the hillslope (a-c) and surfaces definition displayed in the“Project Navigator-Data” window (d).
Select the “Set new solid defined by boundary surfaces” command ( ) from the Edit Bar.
Click on “Pick Boundary Surfaces” and select the boundary surfaces of Solid 1 (Surfaces 1, 3,
7, 13, 15, 16, 19, 20), Solid 1 is generated (Figure 57a).
Select the boundary surfaces of Solid 2 (Surfaces 3, 5, 9, 14, 17, 18, 21, 22), Solid 2 is generated(Figure 57b).
Select the boundary surfaces of Solid 3 (Surfaces 2, 4, 8, 11, 15, 16), and Solid 4 (Surfaces 4,6, 10, 12, 17, 18), two solids are generated (Figure 57c).
All he generated solids are listed in Figure 57d.

57

Solid 2

Solid 1(a)(b)

Solid 4

Solid 3(c)(d)

Figure 57. Solids generation for the hillslope.
Define FE-Mesh
Click on the “FE-Mesh” folder in the Project Navigator-Data.
Click “Generate FE-Mesh command () from the Edit Bar (or Edit->FEMesh->Generate FE-Mesh).
Click on Mesh->Mesh parameters in the “Project Navigator – Data”
Click on “Next” in the pop-up “FE-Mesh Information” and “OK” in the pop-up window withwarning for the next steps (Figure 58).

58

(a)
Figure 58. FE-Mesh Information window.

(b)

Domain Properties
Generally, all the solids are assigned to silt (Figure 59a). Click the lower layers are assigned tothe material “clay” (Figure 59b).

(a)

(b)
Figure 59. Assigning two different properties on the hillslope.
59

Water Flow Boundary Conditions
Click on the “Boundary Conditions” folder in the Project Navigator-Data.
Click on “Water Flow”
Click on “Atmospheric Boundary” in the Edit Bar and with the cursor select the top boundary
surfaces of the hillslope (Figure 60a).
Click on “Constant Head” in the Edit Bar
Click on “Section” in the left Bar
Choose “Geo-Sections” from “Options – Section”
Choose “Surface No.8 and 9” from “Geo-Sections” lists
Using the cursor select the bottom surface boundary to assign the constant head condition(Figure 60b).

(a)

(b)
Figure 60. Steps to assign the water flow boundary conditions.
60

Slope-Cube Boundary Conditions
Click on the “Boundary Conditions” folder in the Project Navigator-Data.
Click on “Slope Cube.”
Click on “X-displacement” in the Edit Bar.
Using the cursor select the left two surfaces (Surface No. 7-10 and 13-14) and giving Xdisplacement = 0, respectively (Figure 61a).

(a)
Click on “Y-displacement” in the Edit Bar
Click on “Section” in the left Bar
Choose “Geo-Sections” from “Options – Section”
Choose “Surface No. 1-2 and 5-6” from “Geo-Sections” lists
Using the cursor select the two surfaces and giving Y-displacement = 0, respectively (Figure
61b).

61

(b)
Click on “XYZ-displacement” in the Edit Bar
Click on “Section” in the left Bar
Choose “Geo-Sections” from “Options – Section”
Choose “Surface No. 8 and 9” from “Geo-Sections” lists
Using the cursor select the two surfaces and giving XYZ-displacement = 0 (Figure 61c).

(c)
Figure 61. Steps to assign displacement boundary conditions.
62

Click on the “Edit conditions on FE-mesh” command from the Edit Bar.
Click on “XY-displacement” in the Edit Bar. Click on “Section” in the left Bar
Choose “Geo-Sections” from “Options – Section”
Choose “Surface No. 1-2” from “Geo-Sections” lists
Choose the points on the mesh of the hillslope (Figures 62a).
In the “Slope Cube Boundary Condition” pop-up window select “XY-displacement”.
Set X-value, and Y-value to 0 m, respectively.
Click “OK” to set the boundary condition on the points of the mesh (Figures 62a).
According to the same steps to set the “XY-displacement” on “Surface No. 5-6” (Figure
62b).

Figure 62. Steps to assign XY-displacement boundary condition on a point of the hillslope.
Observation Nodes
Click on the Domain Properties Tab under the View Window.
On the Navigator Bar click on Domain Properties-Observation Nodes (or Insert->Domain
Properties->Observation Nodes).
Click on Edit Properties on FE-Mesh command () on the Edit Bar, thenInsert Observation Node command ().
Click on “Section” in the left Bar. And choose “Geo-Sections” from “Options – Section”
Choose “Surface No. 1” from “Geo-Sections” lists.
Choose a point from the mesh of the hillslope, then Observation Node 1 is listed in Observation
Nodes Bar.
According to the above method, specify another two observation points on the Surfaces 2 and3, respectively (Figure 63).

63

Figure 63. Steps to insert observation nodes.
Save
Save the project using the Save command () on the Toolbar File->Save).

Run Calculations
Click the ‘Calculate Current Project” command (>Calculate Current Project).

) on the Toolbar (or Calculation-

OUTPUT
Evolution in time of pressure head, water content, minimum and maximum effective stress,
suction stress, and local factor of safety are shown in Figures 64-66. Pressure head, suction
stress, and local factor of safety as a function of time at the observation nodes are shown in
Figure 67.

64

Pressure head [m]Water content [-]Time: 0 [h]Time: 0 [h]Time: 34 [h]Time: 34 [h]Time: 50 [h]Time: 50 [h]Time: 70 [h]Time: 70 [h]Figure 64. Contour plots of pressure head [m] and water content evolution with time for
Example 3. Results are shown at 0, 34, 50, and 70 hours.

65Maximum effective stress [kPa]

Minimum effective stress [kPa]

Time: 0 [h]Time: 0 [h]Time: 34 [h]Time: 34 [h]Time: 50 [h]Time: 50 [h]Time: 70 [h]Time: 70 [h]Figure 65. Contour plots of maximum and minimum effective stress [kPa] evolution withtime for Example 3. Results are shown at 0, 34, 50, and 70 hours.

66Suction stress [kPa]

Field of local factor of safety [-]Time: 0 [h]Time: 0 [h]Time: 34 [h]Time: 34 [h]Time: 50 [h]Time: 50 [h]Time: 70 [h]Time: 70 [h]Figure 66. Contour plots of suction stress [kPa] and field of local factor of safety evolution
with time for Example 3. Results are shown at 0, 34, 50, and 70 hours.
67

(a)

(b)
Figure 67. Graphical display of observation nodes: (a) suction stress as a function of time,and (b) local factor of safety as a function of time for the three observation nodes.

685. Example 4: Shrinkage of a Soil Cake
The fourth example demonstrates the deformation analysis of a homogeneous soil cake undera drying condition. The geometry and boundary conditions for the Water Flow and the Slope
Cube models are presented in Figure 68. The initial water content of the soil cake is assumed
0.37. The ultimate volumetric water content is set to 0.25. The hydro-mechanical parametersof the soil are specified in Table 5. Model results are illustrated as the transient fields ofpressure head, water content, minimum and maximum effective stress, suction stress and local
factor of safety. Comparison between failure surface evolutions is provided.

Figure 68. Soil cake geometry and boundary conditions for hydrological (in black) andmechanical (in gray) models.
Table 69. Hydro-mechanical parameters used in Example 4.
Soil Parameter

Value

Soil type
α [1/m]
n [-]

Clay
2.70
1.23

ks [m/h]0.03

θ r [-]
θs [-]

0.10
0.38

c′ [kPa]φ′ [ ]

10.0

Gs [-]

2.7

Ed [KPa]4700

θd [-]

0.10

Ew [KPa]990

θ w [-]

0.38

m [-]
µ [-]

0.96
0.25

30.0

69

Open Hydrus: Double click on logo
Project Manager (Figure 69)
Button “File”, Button “New”
Name: Example 3
Description: 3D Shrinkage of a Soil Cake
Path: (specify)
Working directory: (specify)
Choose “Permanent – remains open when the project is closed”
Button “Next”

(a)

(b)
Figure 69. Project Manager and Project Information windows.
Domain Type and Units (Figure 70)
Type of Geometry: 3D-General
Units: m, DP: 4
Button “Next”
70Figure 70. Domain Type and Units window.
Main Processes and add-on Modules (Figure 71)
Check “Water Flow”
Check “Slope Cube”
Button “Next”

Figure 71. Main Processes and add-on Modules window.
Time Information (Figure 72)
Check “Hours”
Initial Time [hour]: 0
Final Time [hour]: 571

Initial Time Step [hour]: 0.0001
Minimum Time Step [hour]: 0.00001
Maximum Time Step [hour]: 1
Button “Next”

Figure 72. Time Information window.
Output Information (Figure 73)
Check “T-Level Information”
Check “Screen Output”
Check “Press Enter at the End”
Count: 20
Button “Update”
Input the time series on the right as follows: 0.001, 0.002, 0.005, 0.01, 0.02, 0.05, 0.1, 0.15,
0.2, 0.3, 0.5, 0.8, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4, 5.
Button “Next”

Figure 73. Output Information window.
Iteration Criteria (Figure 74)
Maximum Number of Iterations: 10
Water Content Tolerance: 0.001
Pressure Head Tolerance [m]: 0.0172

Lower Optimal Iteration Range: 3Upper Optimal Iteration Range: 7
Lower Time Step Multiplication Factor: 1.3
Upper Time Step Multiplication Factor: 0.7
Lower Limit of the Tension Interval: 0.000001
Upper Limit of the Tension Interval: 100
Check Initial Condition “In Water Contents”
Button “Next”

Figure 74. Iteration Criteria and Initial Conditions window.
Soil Hydraulic Model (Figure 75)
Check: “van Genuchten-Mualem”
Check: “No Hysteresis”
Button “Next”

73Figure 75. Soil Hydraulic Model window.
Water Flow Parameters (Figure 76)
Number of Materials: 1
Button “Update”
Name: Clay
Qr: 0.10
Qs: 0.38
Alpha [1/m]: 2.7
n: 1.23Ks [m/hour]: 0.0288
l: 0.5
Button “Next” (Figure 76a).
On pop up “Tensors of Anisotropy” window, click “Next” (Figure 76b).

Figure 76a. Water Flow Parameters window.

74

Figure 76b. Tensors of Anisotropy window.
Slope Cube Parameters (Figure 77)
Specific gravity: 2.7
Cohesion [kPa]: 10
Friction angle[o]: 30
Poisson ratio: 0.25
Ez/Ex [-]: 1.0
Young modulus at dry state [kPa]: 4700
Young modulus at wet state [kPa]: 990
Water content at dry state [-]: 0.10
Water content at wet state [-]: 0.38
Power law parameter m [-]: 0.25
Button “Next”

Figure 77. Slope Cube Parameters window.
FE-Mesh Parameters (Figure 78)
Uncheck: “Automatic”, and set the size of element Ts = 0.0025 m
Check: “Tetrahedral”
75Button “Next”
Button “OK” to warning window(a)Figure 78. FE-Mesh Parameters window.

(b)

GRAPHICAL MODE
In this mode the user can:
- Specify the geometry of the model- Generate the FE-mesh- Specify material distribution, observation nodes, regions and sub-regions- Specify boundary conditions
These steps can be performed through the two main windows “Project Navigator – Data” and“Edit Bar” or through the Main Menu (Figure 79).

76

Figure 79. Graphical user interface.
Geometry Settings
In the Project Navigator-Data select “Geometry”->”Points”.
Select “Set new circle graphically using three points” () in the Edit Bar and insert thecoordinates of the 3 points (P1-P3) in Table 6.
Click “Apply” when the first three points input. Click “Stop” when done (Figure 80a, b).
According the same method, draw the other two circles with the points in Table 6 (P4-P6, P7P9), Click “Stop” when done (Figure 80c, d).
Another way of doing this is Insert->Domain Geometry->Points->Graphically. Then use thecursor to click on locations where you would like the points.
Table 80. Coordinates of points used in soil cake geometry.
Point

X [m]

Y [m]

Z [m]

P1

0.030

0.000

0.000

P2

0.000

0.030

0.000

P3

-0.030

0.000

0.000

P4

0.030

0.000

0.005

P5

0.000

0.030

0.005

P6

-0.030

0.000

0.005

P7

0.030

0.000

0.010

P8

0.000

0.030

0.010

P9

-0.030

0.000

0.010

77

(a)

(b)

78

(c)

(d)
Figure 80. Steps to insert point coordinates.
Select the “Line-Connected Abscissae” command () from the Edit Bar (or Insert->Domain
Geometry-> Curves->Polylines->Graphically).
Connect the points to define the geometry (Figure 81).

79

Figure 81. Lines connecting points in the geometry.
Select the “Generates surfaces from selected curves lying in the plane” command (the Edit Bar.
Select the boundary curves of Surface 1 (Z=0), Surface 1 is generated.
On the pop on window, click “OK” (Figure 82a).
Generate Surfaces 2 (Z=0.005) and 3 (Z=0.01) (Figure 82b).

) fromSelect the “Set new Quadrangle” command ( ) from the Edit Bar.
Input the boundary curves 1 (Z=0), 4, 2 (Z=0.005), and 4, Click “Surfaces”, then click “Apply”.
Surface 4 is generated (Figure 82c).
Input the boundary curves 2, 5, 3, and 5, Click “Surfaces”, then click “Apply”. Surface 5 isgenerated (Figure 82d).
Click “Stop”

80Surface 1(a)Surface 3
Surface 2(b)81Surface 4(c)Surface 5(d)Figure 82. Surfaces generation for the hillslope.

Select the “Set new solid defined by boundary surfaces” command ( ) from the Edit Bar.
Select the boundary surfaces of Solid 1, Solid 1 is generated (Figure 83a).
Repeat the above steps to generate Solid 2 (Figure 83b).

82

(a)

(b)

83

(c)

(d)
Figure 83. Solids generation for the hillslope.
Define FE-Mesh
Click on the “FE-Mesh” folder in the Project Navigator-Data.
84

Click “Generate FE-Mesh command (Mesh->Generate FE-Mesh). (Figure 84).

) from the Edit Bar (or Edit->FE-

Figure 84. FE-Mesh generation.
Click on “Next” in the pop-up “FE-Mesh Information” and “OK” in the pop-up window withwarning for the next steps (Figure 85).

(a)

(b)
Figure 85. FE-Mesh Information window.

85

Domain Properties
All nodes are automatically assigned to material “Clay.”
Water Flow Initial Conditions
Click on the “Initial Conditions” folder in the Project Navigator-Data.
Click on “1 - Constant, th=0.25” under the “Water Content”. Select “Constant” and specify“Water Content IC” to 0.37 (Figure 86). Click “OK”

Figure 86. Initial conditions for water flow.
Water Flow Boundary Conditions
Click on the “Boundary Conditions” folder in the Project Navigator-Data.
Click on “Water Flow”
Click on the “New Water Flow BDRC” command () from the Edit Bar.
In the “New Water Flow Boundary Condition” pop up window select “Constant Water
Content”. And Give “Water Content Value” = 0.25 m at the left.
Click on “Constant Flux” in the Edit Bar and with the cursor select the top boundary surfacesof the hillslope (Figure 87).

86

(a)

(b)

87

(c)
Figure 87. Steps to assign constant water content boundary condition.
Slope-Cube Boundary Conditions
Click on the “Boundary Conditions” folder in the Project Navigator-Data.
Click on “Slope Cube.”
Click on the “New Boundary Condition” command from the Edit Bar.
In the “New Slope Cube Boundary Condition” pop-up window select “Z-displacement” andset it to 0 m.
Click on “Z-displacement” in the Edit Bar.
Click on “Section” in the left Bar
Choose “Geo-Sections” from “Options – Section”
Choose “Surface No. 6 and 7” from “Geo-Sections” lists
Using the cursor select the bottom surface and giving Z-displacement = 0 (Figure 88).

88

(a)

(b)

89

(c)
Figure 88. Steps to assign Z-displacement boundary condition.
Click on the “Edit conditions on FE-mesh” command from the Edit Bar.
Click on “XYZ-displacement” in the Edit Bar.
Click on “Section” in the left Bar
Choose “Geo-Sections” from “Options – Section”
Choose “Surface No. 1” from “Geo-Sections” lists
Choose the point (X=0, Y=0, Z=0) on the mesh of the soil cakeIn the “Slope Cube Boundary Condition” pop-up window select “XYZ-displacement”.
Set X-value, Y-value, and Z-value to 0 m, respectively.
Click “OK” to set the boundary condition on the point of the mesh. (Figure 89).

90

(a)

(b)

91

(c)
Figure 89. Steps to assign XYZ-displacement boundary condition on the point of the soil
cake.
Observation Nodes
Click on the Domain Properties Tab under the View Window.
On the Navigator Bar, click on “Domain Properties-Observation Nodes” (or Insert->Domain
Properties->Observation Nodes).
Click on “Edit Properties on FE-Mesh” command () on the Edit
Bar, then Insert Observation Node command ().
Click on “Section” in the left Bar. And choose “Geo-Sections” from “Options – Section”
Choose “Surface No. 2” from “Geo-Sections” lists.
Choose a point from the mesh of the hillslope, then Observation Node 1 is listed in Observation
Nodes Bar.
According to the above method, specify another two observation points on the Surfaces 2 and3, respectively (Figure 90).

92

(a)

Observation
Node 1(b)

93

Observation
Node 2

Observation
Node 3Observation
Node 4(c)Figure 90. Steps to insert observation nodes.
Save
Save the project using the Save command () on the Toolbar File->Save).

Run Calculations
Click the ‘Calculate Current Project” command (>Calculate Current Project) (Figure 91).

Figure 91. Model execution.
94) on the Toolbar (or Calculation-

OUTPUT
Click on the Results Tab under the View Window or Click on the “Results-Graphical Display”
folder in the Project Navigator-Data (Figure 92).
Graphical Display includes contour distribution for:- Pressure Heads- Water Content- Velocity- Velocity Vectors- Streamlines- Maximum Total Stress- Minimum Total Stress- Maximum Effective Stress- Minimum Effective Stress- Suction Stress- Field of Local Factor of Safety- XY - Stress- YZ - Stress- XZ - Stress- Intermediate Effective Stress

Figure 92. Options for graphical display of results.
Evolution in time of pressure head, water content, minimum and maximum effective stress,
suction stress, XY-deformation, and Z-deformation of the Surface 2 (middle circle surface) are
shown in Figures 93-96.

95

Time: 0 [h]

0.1 [h]0.8 [h](a) Pressure head [m]Time: 0 [h]

0.1 [h]0.8 [h]Figure 93. Contour plots of pressure head [m] and water content evolution with time for
Example 4. Results are shown at 0, 0.1, and 0.8 hours.

Time: 0 [h]

0.1 [h]0.5 [h](a) Maximum effective stress [kPa]
Time: 0 [h]

0.1 [h]0.5 [h](b) Minimum effective stress [kPa]
Figure 94. Contour plots of maximum and minimum effective stress [kPa] evolution withtime for Example 4. Results are shown at 0, 0.1, and 0.5 hours.

96Time: 0 [h]

0.1 [h]0.8 [h]Suction stress [kPa]
Figure 95. Contour plots of suction stress [kPa] evolution with time for Example 4. Results
are shown at 0, 0.1, and 0.8 hours.

Time: 0 [h]

0.1 [h]0.8 [h](a) XY-deformation [m]Time: 0 [h]

0.1 [h]0.8 [h](b) Z-deformation [m]Figure 96. Contour plots of XY-deformation, and Z-deformation[m] evolution in XY and Z
directions with time for Example 4. Results are shown at 0, 0.1, and 0.8 hours.
Click on the “Results – Other Information” folder in the Project Navigator-Data (Figure 97).
Click on “Observation Points” to show the results on the observation.

97

Figure 97. Graphical display of results on the observation.
In the pop-up window “Observation Nodes”, the evolution of Pressure head, Water content,
Maximum Total Stress, Minimum Total Stress, Maximum Effective Stress, Minimum
Effective Stress, Suction Stress, Local of Factor of Safety can be shown. For example, theevolution of Pressure head, Water content, Maximum Effective Stress, and Suction Stress on
Node 1 are shown here (Figure 98).

(a)

98

(b)

(c)

(d)
Figure 98. Graphical display of observation nodes. (a) pressure head as a function of time, (b)water content as a function of time, (c) maximum effective stress as a function of time, and(d) suction stress as a function of time for the three observation nodes.
996. Example 5: Comparison of Measured and Predicted Volumetric Change
of Soil Cake
This example simulates an experiment using the drying cake method (Lu and Kaya, 2013).
Results from the numerical simulation are compared to experimental results obtained by Dongand Lu in 2017. The set up consists of a soil cake made out of claystone of 2.00 cm in heightand 7.62 cm in diameter; the sample was compacted to a porosity of 0.47, initially fully
saturated, and subjected to drying conditions. Volumetric water content decreased from 0.47
to 0.21; changes in diameter and height were measured at ten different times and are presented
in Table 13. The geometry and boundary conditions are presented in Figure 99; hydrologicalconditions are labeled in black, while mechanical boundary conditions are labeled in gray. A
comparison between the measured and simulated suction stress characteristic curves (SSCC)
is provided in Figure 100. Young modulus was obtained experimentally at each step byapplying a constant strain and measuring the stress in the soil sample. For the numericalsimulation, the Young modulus values at different water contents were obtained using thepower law equation developed by Lu and Kaya in 2013. A comparison between the measured
and predicted Young modulus values is presented in Figure 101. Soil parameters are provided
in Table 7.

Figure 99. Soil cake geometry and boundary conditions for hydrological (in black) andmechanical (in gray) models.

100

104
Suction stress (-kPa)

Denver claystone

103

SSCC

102

101

100
0.0

0.1

0.2

0.3

0.4

0.5

Volumetric water content
Figure 100. Comparison of the measured and fitted SSCC of Denver claystone.

Figure 101. Comparison of the measured and fitted Young’s modulus of Denver claystone.

101Table 102. Hydro-mechanical parameters used in Example 5.
Soil Parameter

Value

Soil type
α [1/m]n [-]Denver claystone
0.29431.29

ks [m/h]

0.0003

θ r [-]
θs [-]

0.04
0.47

c′ [kPa]

10.0

φ′ [ ]
Gs [-]

30.0
2.7

Ed [KPa]2391

θd [-]

0.04

Ew [KPa]196

θ w [-]

0.47

m [-]
µ [-]

1.59
0.25

Table 103. Steps for the water content change used in Example 5.
Step
0
1
2
3
4
5
6
7
8
9
10

Volumetric watercontent
0.470
0.457
0.442
0.421
0.401
0.366
0.344
0.314
0.282
0.247
0.206

This example has similar initial settings to Example 4; therefore, the user can open Example 4
and perform the following modifications:
Open Hydrus: Double click on logo
Project Manager (File->Project Manager) (Figure 102)
Select Example 4 project
Button “Copy”
Name: Example 5
Description: Comparison of measured and simulated 3D Shrinkage of a Soil Cake
102

Button “Open”

Figure 102. Project Information windows.
Geometry Settings
In the Project Navigator-Data select “Geometry”->”Points”.
Modify the coordinates of the nine points in the three circles, listed in Table 9.
Click the first point and modify the coordinates in X, Y, and Z in the bottom circle. Click “OK”
when done. (Figure 103a).
Click Points 2 and 3, modify the coordinates, respectively. Click “OK” when done (Figure103b).
Modify the coordinates of points 4-6, and 7-9, redraw the other two circles with these points inTable 9 (P4-P6, P7-P9), Click “Stop” when done (Figure 103c).
Table 103. Coordinates of points used in hillslope geometry.
Point

X [m]

Y [m]

Z [m]

P1

0.03810.00000.0000P2

0.00000.03810.0000P3-0.03810.00000.0000P4

0.03810.00000.0100P5

0.00000.03810.0100P6-0.03810.00000.0100P7

0.03810.00000.0200P8

0.00000.03810.0200P9-0.03810.00000.0200

103

(a)

(b)

104

(c)
Figure 103. Steps to insert point coordinates of the soil cake.
Time Information (Figure 104)
Check “Hours”
Initial Time [hour]: 0
Final Time [hour]: 50
Initial Time Step [hour]: 0.0001
Minimum Time Step [hour]: 0.00001
Maximum Time Step [hour]: 1
Button “Next”

Figure 104. Time Information window.
105

Output Information (Figure 105)
Check “T-Level Information”
Check “Screen Output”
Check “Press Enter at the End”
Count: 13
Button “Update”
Input the time series on the right as follows: 0.01, 0.02, 0.05, 0.1, 0.2, 0.5, 1, 2, 5, 10, 20, 30,
50.
Button “Next”

Figure 105. Output Information window.
Water Flow Parameters (Figure 106). (Project Navigator-Data->Flow and TransportParameters->Water Flow->Soil-Hydraulic Parameters).
Number of Materials: 1
Material 1:
Name: Denver claystone
Qr: 0.04
Qs: 0.47
Alpha [1/m]: 0.2943
n: 1.29
Ks [m/hour]: 0.0003
I: 0.5
Button “Next”
A dialogue box may appear asking confirmation to delete the simulation results. Click “OK.”On pop up “Tensors of Anisotropy” window, click “Next” (Figure 106b).

106

Figure 106a. Water Flow Parameters window.

Figure 106b. Tensors of Anisotropy window.
Slope Cube Parameters (Figure 107) ((Project Navigator-Data->Flow and TransportParameters->Slope Cube Stress Parameters).
Specific gravity: 2.7
Cohesion [kPa]: 10
Friction angle[o]: 30
Poisson ratio [-]: 0.25
Ez/Ex ratio [-]: 1.0
Young modulus in x, y-direction [kPa]: 2391
Young modulus in z-direction [kPa]: 196
Water content at dry state [-]: 0.04
Water content at wet state [-]: 0.47
Power law parameter, m [-]: 1.59
Button “Next”

107Figure 107. Slope Cube Parameters window.
FE-Mesh Parameters (Figure 108)
Un-Check: “Automatic”, and set the size of element Ts = 0.0050 m
Check: “Tetrahedral”
Button “Next” (Figure 108a)
On the pop-on window Button “OK” (Figure 108b)
On the pop-on window Button “Yes” (Figure 108c)

(a)

108

(b)

(c)
Figure 108. FE-Mesh Parameters window.
Define FE-Mesh
The information and the generated mesh are shown in Figures 109a, b.

(a)

109

(b)
Figure 109. FE-Mesh generation.
Domain Properties
All nodes are automatically assigned to material Denver claystone.
Water Flow Initial Conditions
Click on the “Initial Conditions” folder in the Project Navigator-Data.
Click on “1 - Constant, th=0.38” under the “Water Content”. In the “Edit Water Flow Boundary
Condition” pop up window, modify “Water Content IC” to 0.47 (Figure 110). Click “OK”

Figure 110. Initial conditions for water flow.
Water Flow Boundary Conditions
110

Click on the “Boundary Conditions” folder in the Project Navigator-Data.
Click on “Water Flow”
Click on the boundary condition “Constant Water Content; 0.25”, In the “Edit Water Flow
Boundary Condition” pop up window, modify “Water Content Value” to 0.457 (Figure 111).

Figure 111. Assign new constant water content boundary condition.
Slope-Cube Boundary Conditions
Click on the “Boundary Conditions” folder in the Project Navigator-Data.
Click on “Slope Cube.”
Click on the “Edit conditions on FE-mesh” command from the Edit Bar.
Click on “Section” in the left Bar
Choose “Geo-Sections” from “Options – Section”
Choose “Surface No. 1” from “Geo-Sections” lists
Choose the point (X=0, Y=0, Z=0) on the mesh of the soil cakeIn the “Slope Cube Boundary Condition” pop up window, click “OK” to set the boundary
condition on the point of the mesh. (Figures 112a, b).

111

(a)

(b)
Figure 112. Steps to assign XYZ-displacement boundary condition on the point of the soil
cake.
Observation Nodes
Click on the Domain Properties Tab under the View Window.
On the Navigator Bar click on Domain Properties-Observation Nodes (or Insert->Domain
Properties->Observation Nodes). There are three observation nodes on the geometry. Make
sure these observation nodes are correct. The observation nodes can be changed and redraw ifnecessary.
112

Save project.
Save the project using the Save command () on the Toolbar File->Save).

Run Calculations
Click the ‘Calculate Current Project” command (>Calculate Current Project).
In the pop up window, Click “Yes”. (Figure 113a).
In the pop up window, Click “Yes”. (Figure 113b).

) on the Toolbar (or Calculation-

(a)

(b)
Figure 113. Pop up window before running the project.
OUTPUT
Click on the Results Tab under the View Window or Click on the “Results-Graphical Display”
folder in the Project Navigator-Data. Evolution in time of pressure head, water content,
maximum and minimum total stress, maximum and minimum effective stress, suction stress,
Field of Local Factor of Safety, XY-deformation, and Z-deformation can be shown (Figure
114).

113

Figure 114 Comparison between the simulated and measured porosity.
The volumetric change can be calculated by the software at each step of water content. Figure
115 shows the comparison between the simulated and measured porosity of Denver claystone
by the project (data from Dong and Lu, 2017).

Denver claystone

0.5

Porosity

0.4

0.3

0.2

Measured
Predicted

0.1
0.0

0.1

0.2
0.3
0.4
Volumetric water content

Figure 115 Comparison between the simulated and measured porosity.

114

0.5

References
Dong, Y. and Lu, N. (2017). “Measurement of suction-stress characteristic curve under dring
and wetting conditions.” Geotech. Test. J., 40(1), 107-121.
Lu, N., Godt, J. W., and Wu, D. T. (2010). “A closed-form equation for effective stress inunsaturated soil.” Water Resour. Res., 46(5), W05515, 1-14.
Lu, N., and Kaya, M. (2013). “A drying cake method for measuring suction stresscharacteristic curve, soil-water retention, and hydraulic conductivity function.” Geotech.
Test. J., 36, 1–19, doi:10.1520/GTJ20120097.
Lu, N., and Kaya, M. (2014). “Power law for elastic moduli of unsaturated soil.” J. Geotech.
Geoenviron. Eng., 140(1), 46–56.
Šimůnek, J., van Genuchten M.T., and Sejna, M. (2012). “The HYDRUS software package forsimulating the two- and three-dimensional movement of water, heat, and multiple solutes
in variably-saturated porous media, version 2.0.” PC Progress, Prague, Czech Republic.
Wooten, R. M., Gillon, K. A., Witt, A. C., Latham, R. S., Douglas, T. J., Bauer, J. B.,
Fuemmeler, S. J., Lee, L. G. (2008). “Geologic, geomorphic, meteorological aspects ofdebris flows triggered by hurricanes Frances and Ivan during September 2004 in thesouthern Appalachian Mountains of Macon County, North Carolina (southeastern USA).”
Landslides, 5(1), 31–44.

115