5 - Successive Failure

1.0 Introduction

Successive failure of a rock slope refers to a phenomenon where multiple failures occur in a rock slope in quick succession, leading to a large-scale slope failure. This type of failure can occur when initial failures trigger additional failures as blocks are further destabilized. This analysis is important for many reasons including:

Identifying key blocks. A key block is a block whose removal is required for the subsequent destabilization of larger masses of blocks. If key blocks are stabilized, then the slope is stabilized.
Identifying the total failure depth behind key blocks. Bolt supports must have adequate length to anchor blocks into competent rock mass.
Identifying extent of failure volumes due to successive failure of the slope.

This tutorial covers how to utilize the Successive Failure analysis options in RocSlope3, and view the failure iteration and failure depth of blocks.

Finished Product

The finished product of this tutorial can be found in the Tutorial 05 Successive Failure folder. All tutorial files installed with RocSlope3 can be accessed by selecting File > Recent Folders > Tutorials Folder from the RocSlope3 main menu.

2.0 Opening the Starting File

Select File > Recent > Tutorials Folder.
Go to the Tutorial 05 Successive Failure folder and open the file Tutorial 05 Successive Failure.rocslope_model.

This model already has the following defined and provides a good starting point to start computing blocks:

Project Settings
Material Properties
External Geometry
Joint Properties
Measured Joints

3d view of starting geometry — 3D View of Successive Failure file with Measured Joints

In the starting model, Measured Joints are defined over the west extents of open pit. The size of the joints are relatively large (Radius = 500 m) so blocks have the potential of forming deep behind the free surface of the slope, some completely behind daylighting blocks.

2.1 Project Settings

Review the Project Settings.

Select Analysis > Project Settings
Select the Units tab. Ensure Units are Metric, stress as MPa.

Units tab in Project Settings dialog
Select the Analysis tab.

Ensure Design Factor of Safety = 1.5.
Ensure Successive Failure is ON. We will be analyzing successive failures by iterating through each stage of failed blocks until no more blocks can be removed.

analysis tab in project settings — Analysis tab in Project Settings dialog

Click Cancel to exit the dialog.

2.2 Material Properties

Review the Material Properties.

Select Materials > Define Materials
One (1) material property is defined in the Define Materials dialog. The Schist material property has:

Unit Weight = 0.026 MN/m3.
No Water Surface applied.

define materials dialog schist property — Schist Material Property in Define Materials dialog

Click Cancel to exit the dialog.

2.3 External Geometry

The External is of a pit shell and composed of one volume assigned with the Schist material property.

2.4 Joint Properties

Review the Joint Properties.

Select Joints > Define Joint Properties . Two (2) joint properties are defined.
The Smooth joint property has:

Strength Type = Mohr-Coulomb
Cohesion = 0 MPa
Phi = 10 degrees
Waviness = 0 degrees

smooth joint property — Smooth Joint Property Strength tab in Define Joint Properties dialog

Water Pressure Method = Dry

smooth joint property water parameters — Smooth Joint Property Water Parameters tab in Define Joint Properties dialog

The Rough joint property has:

Strength Type = Mohr-Coulomb
Cohesion = 0 MPa
Phi = 30 degrees
Waviness = 0 degrees.

rough joint property strength tab — Rough Joint Property Strength tab in Define Joint Properties dialog

Water Pressure Method = Dry

rough joint property water parameters — Rough Joint Property Water Parameters tab in Define Joint Properties dialog

Click Cancel to exit the dialog.

2.5 Measured Joints

Review the Measured Joints.

Select Joints > Define Measured Joints . 40 Measured Joints are defined.

Listed in order of Dip, Dip Direction, X, Y, Z, Radius, and Joint Property:

Dip	Dip Direction	X	Y	Z	Radius	Joint Property
59	48	-390	-115	1018	500	Rough
77	131	-319	-337	1004	500	Rough
78	123	-313	-157	1003	500	Rough
78	313	-486	128	1037	500	Rough
61	13	-793	-447	1099	500	Rough
89	255	-272	-65	994	500	Smooth
51	341	-375	-594	1015	500	Smooth
67	107	-548	47	1050	500	Smooth
57	86	-281	91	996	500	Smooth
82	105	-758	33	1092	500	Smooth
53	62	-546	-100	1049	500	Smooth
46	84	-665	-224	1073	500	Smooth
55	79	-772	-386	1094	500	Smooth
29	223	-798	-400	1100	500	Smooth
50	82	-305	193	1001	500	Smooth
34	33	-699	-504	1080	500	Smooth
39	57	-348	-272	1010	500	Smooth
81	36	-258	-51	992	500	Smooth
58	314	-544	-193	1049	500	Smooth
39	211	-744	-599	1089	500	Smooth
81	268	-797	108	1099	500	Smooth
65	336	-455	104	1031	500	Smooth
78	317	-575	-54	1055	500	Smooth
62	133	-656	-479	1071	500	Smooth
27	283	-769	-258	1094	500	Smooth
30	167	-458	-465	1032	500	Smooth
33	132	-253	-539	991	500	Smooth
60	336	-580	80	1056	500	Smooth
30	39	-583	168	1057	500	Smooth
28	76	-362	-30	1012	500	Smooth
17	101	-362	-432	1012	500	Smooth
10	249	-511	-162	1042	500	Smooth
19	343	-631	112	1066	500	Smooth
45	58	-789	-329	1098	500	Smooth
26	213	-628	60	1066	500	Smooth
84	351	-516	-421	1043	500	Smooth
51	162	-339	-320	1008	500	Smooth
49	178	-253	-309	991	500	Smooth
77	291	-403	114	1021	500	Smooth
54	51	-417	-421	1023	500	Smooth

define measured joints dialog — 40 Joints in Define Measured Joints dialog

Click Cancel to exit the dialog.

3.0 Compute

RocSlope3 has a two-part compute process.

3.1 Compute Blocks

The first step is to compute the blocks which may potentially be formed by the intersection of joints with other joints and the intersection of joints with the free surface.

To compute the blocks:

Navigate to the Compute workflow tab
Select Analysis > Compute Blocks

As compute is run, the progress bar reports the compute status. Once compute is finished, the Results node is added to the Visibility Tree and All Valid Blocks are blocks are shown in the viewport. The Results node consists of the collection of valid blocks and the socketed slope. The original External and Measured Joints visibility is turned off.

compute blocks 3d view — 3D View of all Valid Blocks

Once compute is finished, the blocks are coloured according to the Block Color option (Random Colors) set in the Results node's Property pane.

Compute Blocks only determines the geometry of the blocks. In order to obtain other information such as the factor of safety, Compute Kinematics needs to be run.

3.2 Compute Kinematics

The second and final compute step is to compute the removability, forces, and factor of safety for each of the valid blocks.

To compute the block kinematics:

Ensure that the Compute workflow tab is the active workflow.
Select Analysis > Compute Kinematics

As compute is run, the progress bar reports the compute status. By default, after Compute Kinematics is run, only Removable Blocks are shown.

compute kinematics 3d view — 3D View of Removable Blocks only

In a Successive Failure mode of analysis, several Failure Iterations may be performed. In the first Failure Iteration, only immediately removable daylighting blocks are analyzed. Any blocks which have a factor of safety less than the Design Factor of Safety (set in Project Settings) is considered "failed". These blocks are also known as "key blocks". The stability of key blocks control the global stability of the slope. As key blocks fail and are detached from the slope, potential constraints in joint faces (in regards to removability and valid sliding direction) are removed and become free faces which no longer support the block or provide shear resistance to sliding. As such, the failure proceeds in a successive manner. See the Analysis topic for more information on Successive Failure.

Successive Failure analysis in RocSlope3 does not model the interaction between blocks; the unravelling mechanism is much more complex. Instead, RocSlope3 looks at each block in isolation during each Failure Iteration.

4.0 Interpreting Results

Once both blocks and kinematics are computed, all block results can be viewed in a table format.

4.1 Block Information

To view all block results:

Navigate to the Results workflow tab
Select Interpret > Block Information

Visualizing blocks can be difficult when the slope extents are large compared to the block extents.

To zoom into all blocks:

Select Interpret > Zoom To All Blocks

The Block Information pane shows the collection of blocks according to the Results Set settings. The Results Set shown can be selected in the Results tab of the Display Options, or the Properties pane for the Results Node. By default, only Removable Blocks are coloured. In the case of Successive Failure, it may be more beneficial to only colour the failed blocks. Failed blocks are blocks which have a factor of safety less than the Design Factor of Safety.

To colour Failed Blocks Only:

Select View > Display Options
Navigate to the Results tab in the Display Options dialog.
Set Results Set = Failed Blocks (FS < Design FS)
Click OK to close the dialog.

Select the Results node from the Visibility Tree.
In the Results node Properties pane, set Results Set = Failed Blocks (FS < Design FS).

Failed Blocks Only are now coloured according to Random Colors.

failed block information — Block Information pane showing only Failed Blocks

A failed block is inherently geometrically removable, but a removable block may not fail. The removability is geometry-dependent, while factor of safety is force-dependent.

Note that the Failure Iteration column is visible for a Successive Failure analysis. The Failure Iteration indicates the the step in which the block fails. It is not a true representation of the complex unraveling mechanism, but rather for notation and filtering.

4.2 Edit Filters

To see the progressive unravelling of the slope, we can toggle the Failure Iteration quick filter under the Filter Options > Edit Filters section.

At the top of the Block Information pane, click Filter Options
Expand the Edit Filters section.
For the Failure Iteration quick filter, increase the minimum value from 1 to 2 and hit ENTER. All blocks which are immediately removable and have failed (i.e., key blocks) are filtered out and hidden in the viewport.

block information filtered — 3D View and Block Information pane showing Failed Blocks with key blocks filtered out

Step 2 can be repeated to show the successive failure of the slope.
Select the Clear Filter button to remove the filter.

Alternatively:

Hover the mouse over the Failure Iteration header in the Block Information listing and click the small filter symbol that appears.
In the Filter Rules tab, set the operator to Is greater than and the value to 1; OR
In the Filter Values tab, select all checkboxes except leave 1 unchecked. The key blocks are hidden.
Select the Clear Filter button in the pop-out dialog to remove the filter.

4.3 Contour Blocks

In RocSlope3, blocks can be contoured by several metrics. In a Successive Failure analysis, the Failure Iteration and Failure Depth are especially relevant.

To show block contours:

Select Interpret > Contour Blocks
From the Contour pane on the right of the screen, select Failure Iteration. Blocks are coloured by the failure iteration that it belongs to. This is also an easy way to quickly identify key blocks and visually see the effects of block failures on adjacent blocks.

3D View of Failed Blocks contoured by Failure Iteration
From the Contour pane on the right of the screen, select Failure Depth. The daylighting blocks are contoured by the maximum Failure Depth, measured from the free surface to the deepest failed block, in a direction normal to the free surface. This metric is a good indicator of the minimum bolt length required to anchor into competent rock if bolts are installed normal to the slope surface.

3D View of Failed Blocks contoured by Failure Depth

When visualizing All Valid Blocks or Removable Blocks results sets, some blocks may have a Failure Depth of 0. Blocks with a Failure Depth of 0 are either non-daylighting blocks or daylighting blocks which are safe (i.e., Factor of Safety >= Design Factor of Safety)

This concludes Tutorial 05.

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