Analysis

Analysis can be performed on unit blocks and, as an option, combined blocks. Successive Failure analysis is currently only available for unit blocks and not combined blocks.

Successive Failure of Unit Blocks

The Successive Failure algorithm employed by RocSlope3 involves the following steps:

1. Determine all valid unit blocks formed by the intersection of joints with the geology.
2. Identify unit blocks which have a free face (i.e., daylights) on the geology.
3. For each daylighting unit block, determine its removability based on the constraints of its joint pyramid (Goodman and Shi, 1985)
4. For each removable unit block, compute the kinematics, taking into account self-weight, shear resistance along sliding joints, loading, water pressure, and supports. If the factor of safety of the block is less than the Design Factor of Safety defined in Project Settings, then the block is considered failed.
5. For each failed unit block, determine if any other unit blocks are face-face adjacent to it. The removal of failed blocks may present opportunities for blocks which are beside or behind (and in some cases, not immediately daylighting) to become removable due to the reduction of constraints forming its joint pyramid as well as reduction of shear resistance along the joint(s) (i.e., what was formerly a joint surface is now a free surface).
6. Repeat steps 3-5 until no further failed unit blocks are found.

If Successive Failure is turned off, then only immediately removable blocks which daylight are analyzed (i.e., steps 1-4). This is identical to the first iteration only of a Successive Failure analysis.

ASSUMPTIONS

Applications of various loads and supports with Successive Removal:

• If bolts intersect a failed daylighting block in a given failure iteration, then it is removed with the failed block and has no impact on block kinematics in subsequent failure iterations. The assumption is that the bolt has failed (pullout, stripping/failure of plate, tensile failure) and no longer provides any capacity. This is a conservative assumptions since in reality, some bolt capacity may still remain.
• Loads applied to the free surface do not transfer to the blocks below once the daylighting blocks are removed.
• Support pressures applied to the free surface do not transfer to the blocks below once the daylighting blocks are removed.
• Shotcrete applied to the free surface does not provide any capacity to blocks beyond the initial failure iteration. The assumption is that the shotcrete has failed, and the shotcrete along the shared edges between the failed blocks and the blocks in the next failure iteration is lost. This is a conservative assumption since in reality, some shotcrete capacity may still remain along intact edges.
• Ponded water level on the free faces is unaffected by removal of blocks. If a joint becomes a free surface due to elimination of failed blocks in preceding failure iterations, then the free surface is subjected to ponded water pressure forces (if any), and zero water pressure otherwise.
• Joint water pressure (with the exception of joints which become free surfaces) remain unchanged. The assumption is that the failure is immediate and water pressure does not have time to dissipate with the elimination of failed blocks in preceding failure iterations.

Successive Failure takes into account the possibility of key blocks whereby the stability of the entire slope may depend on them. When Successive Failure is turned on, RocSlope3 analyzes the progressive failure of the blocks, starting from blocks which are immediately removable and unstable on the surface of the slope and allowing the slope to 'unravel' subsequent to the elimination of unstable adjacent blocks.

Combined block Analysis

In Combined block analysis, RocSlope3 searches for critical block clusters consisting of at least two (2) unit blocks. Note that “criticality” is user defined, as the significance of a combined block could be for its removability, size, safety factor, and/or required support pressure, etc. The combined block search criterion currently adopted by RocSlope3 is to find the largest removable combined blocks given all possible block sliding directions. This means that the combined block search is prioritized by volume and geometric removability, and not by factor of safety or distribution of forces.

The largest removable combined block algorithm employed by RocSlope3 involves the following steps:

1. Determine all valid unit blocks formed by the intersection of joints with the geology.
2. Determine the range of possible block sliding directions based on the joints intersecting through a block cluster.
3. For every increment of possible sliding direction, determine the largest removable combined block. The search always starts from the combined block of the largest possible volume, only decreasing in size if removability is not possible. Once the largest removable combined block is found for the current sliding direction, the algorithm immediately moves on to the next increment of sliding direction and step 3 is repeated.
4. Report all combined blocks found from steps 1-3, disregarding any largest removable block that is a unit block. All reported combined blocks consist of at least two (2) unit blocks.

Design Factor of Safety

The Design Factor of Safety defines the threshold for what is considered a “safe” or “failed” block. It applies to all analysis types, including:

• Unit block and Combined block analyses
• Successive failure and non-successive failure analyses in unit blocks
• Deterministic and Probabilistic analyses

The Design Factor of Safety is applied as follows:

• A unit block or combined block with a Factor of Safety equal to or greater than the Design Factor of Safety is considered safe.
• A unit block or combined block with a Factor of Safety less than the Design Factor of Safety is considered failed.
• In a Successive Failure of unit blocks, the Design Factor of Safety is used to determine the collection of failed unit blocks in each failure iteration.
• In a Probabilistic Analysis, the Design Factor of Safety is used to determine the Probability of Failure (i.e., PF = number of failed blocks with FS < Design FS / number of sampled blocks) in each location.