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UnWedge: Vertical Shaft Handling, Bolt Supports and More

One of the many concerns for practitioners excavating tunnels in rock masses is the possibility of wedge instabilities created by intersecting discontinuities. For addressing issues like these Rocscience has the software UnWedge, a 3D modelling program that provides users with the tools to perform comprehensive wedge stability analyses of tunnels and shafts.

UnWedge works by allowing users to define a 2D section which is then extruded along the tunnel axis to a finite or infinite length. The program identifies wedges formed by three joints and the tunnel face and calculates the resulting factor of safety and required support pressure to achieve the design factor of safety.

To predict and avoid potential critical failure in a user’s design, the software comes with a variety of powerful tools including the Tunnel Orientation Analyzer and the Support Designer. The Tunnel Orientation Analyzer shows the user the critical values (i.e., min factor of safety, max required support pressure, etc.) of a tunnel at multiple orientations while considering every possible joint combination at each orientation. Based on the required support pressure, users can then use the Support Designer to integrate various support combinations into their design. With the Support Designer users can select specific support products from numerous manufacturers and UnWedge will auto-populate their properties directly from the manufacturers’ specifications.

New features: Improved Bolt Patterns and Vertical Shaft Handling

With the new UnWedge release coming this late July, the support design process is getting even better. Users adding bolt patterns and spot bolts to their design now have more options for defining the geometry of their bolts. Users can now input the local trend and plunge angles manually when adding bolts. This expansion of design options allows practitioners more precise control over the design of their supports and as well as a speedier overall design process.

In addition to these new support design options, an exciting new feature has been added for defining the geometry of vertical shafts. As mentioned previously, models are created in UnWedge by defining a 2D section and extruding this along the tunnel axis. In the case of vertical shafts, this process has been made even better with the new option to apply a ground surface to the top end/roof of the shaft. The addition of this ground surface above the roof of the shaft provides a realistic boundary for wedge and support extents. This option has been enhanced even further as well with the option to define a water surface along the height of the shaft.

Comparative analysis: Vertical Shaft in UnWedge and RS3

While UnWedge on its own is a fantastic LEM program for analyzing wedge stability in rock mass excavations, performing a fully comprehensive analysis of any underground excavation often means using multiple analysis methods to verify your critical failure results. A great companion tool for performing such analyses is the 3D FEM program RS3. Finite Element programs like RS3 allow users to consider other factors beyond wedge stability such as displacement and joint stiffness when analyzing the stability of a model. In the following example, we perform such a comparative analysis by first using UnWedge to analyze a vertical shaft with a circular cross-section, and then comparing the results in RS3.

UnWedge Analysis

The UnWedge model shown below consists of a vertical shaft with a tunnel trend of 0 degrees, a plunge of 90 degrees, and a circular cross-section with a diameter of 6m.

A wedge analysis using UnWedge is suitable for this case since we are dealing with an underground excavation in rock containing intersecting structural discontinuities. These discontinuities are assumed to possess significantly lower shear strength and negligible tensile strength, compared to the surrounding intact rock mass. The three joint orientations that make up the resultant wedges have Dip/Dip Directions = 85/0, 45/125, 48/240 deg, respectively. The joints’ shear strength follows a Mohr-Coulomb model, with a friction angle = 30 deg, and zero cohesion and tensile strength.

Four perimeter wedges are formed along the shaft. Here, we will only look at a 10m-long segment of the shaft and skip the computation of the end wedges (i.e., roof and floor wedges). A truncation surface is added (trend = 45 deg) at an offset of approximately 0.54 m away from the tunnel. The truncation surface acts as a realistic boundary (i.e., discontinuity, wall, etc.) for the North West wedge, by reducing its apex and overall volume.

UnWedge: Vertical shaft with circular cross section
UnWedge: Vertical shaft with circular cross section

In order to achieve a Factor of Safety of at least 1.5 for the shaft design, we will stabilize the wedges with mechanically anchored rock bolts. The bolt has a Tensile Capacity, Plate Capacity, and Anchor Capacity = 0.1 MN and Shear Strength = 0.01 MN. The bolts are 1.5 m in length which exceeds the maximum apex height of the perimeter wedges. Since these wedges can technically form anywhere spatially along the height of the shaft, we design a bolt pattern spaced at 1m by 1m to ensure an adequate number of intersecting bolts per wedge, regardless of the spatial location.

UnWedge - Shaft with bolt supports
UnWedge: Vertical shaft with bolt support

After placing the supports, we see that the Factor of Safety is well above 1.5 for all four perimeter wedges.

RS3 Analysis

To verify these results, we then performed a non-shear strength reduction (SSR) analysis of the same shaft in RS3. To do this, the excavation and joint geometries were imported from UnWedge into the RS3 program. The rock mass was modelled as elastic and the joint strength was modelled as plastic to explicitly model only wedge failure mechanisms. The joints had the same Mohr-Coulomb strength parameters as the UnWedge example as well as the same unit weight (0.027 MN/m3). Gravitational in situ stress was modelled in UnWedge. Finally, a very low horizontal stress ratio of 0.01 was applied to minimize clamping effects from the stress state around the shaft.

RS3: Total displacement of wedges
RS3: Total displacement of wedges on vertical shaft


The SSR analysis showed that the factor of safety from RS3 can exactly match UnWedge results under certain joint stiffness parameters (primarily shear stiffness). This joint stiffness had the most notable impact on results, where stiff joints increase the factor of safety and soft joints reduce it. Generally, high differences (orders of magnitude changes) are required to see significant differences in results.

What we learn from this observation is that while stiffness (deformation) properties are not considered in UnWedge, that does not mean that they are unimportant or do not influence behaviour. What this specifically means for UnWedge users is that to mimic rigid block failure in RS3, it appears that the ratio of rock Young’s modulus to joint stiffness, particularly shear stiffness, must be high.

RS3: Vertical shaft with bolt supports
RS3: Vertical shaft with bolt supports

In addition to the learnings regarding stiffness, RS3 was also able to show the total displacement results of the wedges (shown in the previous image) as well as the resulting total displacement when supports are applied (shown above) which verifies the results found in UnWedge.

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