# Theory Knowledge Base

• Why does the Factor of Safety not increase when the wedge weight increases?

The fact that the Factor of Safety is independent of the wedge weight is likely due to the fact that there is no cohesion defined for your joint planes. Think of a block on an inclined plane with only friction; the FS is equal to tan(phi)/tan(alpha) where phi is the friction angle and alpha is the failure plane angle. Note that the FS is independent of the weight of the block.

If you add cohesion, you’ll probably see a change in the FS for different wedge weights.

• Once movement occurs, does UnWedge continue to calculate the Factor of Safety based on the buoyant weight of the block?

The program does not assume that once there is movement there is a drop in water pressure and the Factor of Safety reverts to a dry case. If there is water pressure, the Factor of Safety calculated always accounts for this pressure.

For more details on how the Factor of Safety is calculated with and without water pressure, see the UnWedge Factor of Safety Theory Manual.

• When including a constant joint water pressure in UnWedge, does the reported Factor of Safety consider the buoyant weight or the dry weight?

The Factor of Safety limit equilibrium equations are derived in terms of total forces, so the program uses the rock unit weight you define in the Input Data dialog to determine the wedge weight.

You would enter the saturated unit weight if the wedge was below the water table, although in rock there is usually very little difference between the dry and saturated unit weights. Effective stresses are computed on the joint planes for use in strength calculations by subtracting the pore pressure from the total normal stress. The effective stresses are not computed by first computing a buoyant unit weight and using this, although you could formulate the limit-equilibrium equations this way and get an identical result.

To summarize, the program properly accounts for the fact that the wedge is below the water table.

• What is the difference between shear force and resistance force?

The shear force is simply the driving force resolved in the direction of sliding. This is a driving force due to all active forces (wedge weight, water pressure, etc.) on the wedge. The shear resistance is a resistance force due to the strength of the joints.

• What is the significance of zero pressure on the boundary in UnWedge?

Zero pressure on the boundary means that the boundary is free draining and there is no pore pressure allowed to develop on the tunnel surface. If this is off, it is as if drainage is prevented due to blockage of the drainage system and pore pressure is allowed to build-up to the hydrostatic condition at all points on the joint surface. It's the worst-case situation and you'll find that, in general, it gives a lower Factor of Safety.

• How can water pressure increase the Factor of Safety in UnWedge?

If the water pressure increases the Factor of Safety, then it is most likely associated with a change in the mode of failure.

For example, if the wedge is sliding on one plane, then water pressure is added in such a way as to cause the wedge to slide on two planes, then the shear strength on the second plane can be enough to increase the Factor of Safety. This is particularly the case if there is cohesion on the second plane.

• How are bolts implemented in UnWedge and what failure modes are supported?

UnWedge is a limit-equilibrium (LE) analysis program, so bolts are converted to an equivalent support force that is added into the LE solution process. This process computes a Factor of Safety of the wedge using force equilibrium. It does not compute whether a bolt fails or not. So when you see a failure mode indicated, this does not mean that the bolt is failing. This means that if the bolt was to fail, it would most likely fail by that mechanism, and the available amount of support force is computed using this failure mode. For more information, see the Bolt Force Diagram section of the Online Help.

Bolt force diagrams are used in a LE analysis to determine the amount of force a bolt element can put back into the force equations used in the LE analysis. If the wedge has a Factor of Safety less than 1, then this infers that the support has failed. If the FS is greater than 1, then the support has not failed.

UnWedge considers six-bolt failure modes:

• Pullout
• Tensile
• Stripping
• Shear
• User-defined
• Compression

• Is the input bolt tensile capacity the ultimate bolt capacity or the yield stress?

It is up to you whether you use the ultimate, yield, allowable, or working capacity of the bolt. Many codes stipulate which to use and what factor to apply.

• What does the statement, "effect of stress cannot reduce FS from value computed without stress", mean?

On page 23 of the UnWedge Theory Manual, in the section on Field Stress theory, it states the following:

It should be noted that the effect of stress cannot reduce the Factor of Safety from the value computed without stress in section 7. The reasoning for this is that once any movement of the wedge occurs, contact with the rock mass is lost, and the Factor of Safety reverts to the unstressed value. As a result of stress included in the analysis, both the unstressed and the stressed factors of safety are calculated and the maximum of the two is reported.

If the effect of stress is causing a decrease in Factor of Safety, then the reported Factor of Safety will stay the same (i.e. the program will be reporting the unstressed Factor of Safety). If you only want to report the stressed Factor of Safety, go to the Field Stress option and select the Advanced option. Toggle on the option to report only the stressed Factor of Safety. In this way, you can see what the stress is doing to the Factor of Safety. • Where do you look up values for cable bond strength, anchor capacity, and plate capacity?

A good reference for bolt properties is: Cablebolting in Underground Mines (by D.J. Hutchinson & M.S. Diederichs 1996, BiTech Publishers)

• I have a binder from DYWIDAG that contains specs for various bolts and anchors but I cannot locate values for the parameters requested in UnWedge. Why?

The properties you use for UnWedge parameters depend on the type of bolts/cables you use. For DYWIDAG bars they give you a sheet with ultimate loads in kN. For the mechanically anchored type use this load for the capacities of the anchor/steel/plate and use an anchored bolt unless you have some reason to think that the plates or anchor will not give you the same capacity as the steel. If you're grouting then you need to find the bond strength, which is a function of the water-cement ratio or resin type.