# Joint Persistence Analysis

Joint **Persistence Analysis** is a feature of the **SWedg***e *Probabilistic Analysis, which allows you to define statistical distributions for joint persistence. For a given wedge size, randomly generated values of persistence can be used as a filter to determine if a wedge can actually form, or to scale the wedge size down according to the allowable persistence.

The Persistence analysis option is a refinement to the **SWedge** Probabilistic analysis. It can be used on its own, or simultaneously with any other Probabilistic analysis options in **SWedge** (i.e. you can define any other input random variables, in addition to the joint persistence). In general, checking for allowable joint persistence in a probabilistic analysis can only DECREASE the calculated probability of failure. The Persistence analysis option should give more realistic estimates of the probability of failure for slopes where the joint planes are not continuous.

To use the Joint Persistence Analysis:

- Select
**Persistence Analysis**from the**Analysis**menu. - Select the Persistence Analysis check box at the top of the dialog.
- Enter the Joint Length and Joint Spacing information as described below.

## Joint Length

**Joint Length** can be defined by either:

- Persistence
- Trace Length

Joint **Persistence** represents the maximum joint length as measured in any direction on a wedge sliding plane.

Joint **Trace Length** represents the exposed trace length of a joint as measured on either the slope face or the upper slope.

## Joint Spacing

Joint Spacing can be defined as either:

- Large spacing
- Small spacing (ubiquitous joints)

### LARGE JOINT SPACING

With the **Large Joint Spacing** option, it is assumed that there is only one trace of joint 1 and one trace of joint 2 on the slope face. The point of intersection of the two joint planes on the slope face is randomly located somewhere between the toe and crest of the slope, resulting in a uniform distribution of wedge height (measured vertically from this intersection point to the slope crest).

If the wedge dimensions exceed the allowable persistence, then the wedge cannot exist. If the wedge dimensions are smaller than the allowable persistence, then the wedge can form and a safety factor is calculated.

The Large Joint Spacing option is a **lower bound solution** for the probability of failure, as the spacing and persistence condition will limit the formation of wedges.

### SMALL JOINT SPACING

The **Small Joint Spacing** option assumes ubiquitous joints (i.e. joints are numerous and may occur at any location). This model will automatically scale down the wedge size until the persistence conditions are met. So a wedge is almost always formed in each simulation if the geometry of the joints and slope creates a kinematically feasible wedge. Its size is dependent on the sampled persistence and the geometry of the bench.

The Small Joint Spacing option is an **upper bound solution** for the probability of failure because a wedge will always be created independent of any spatial location of the joints on the slope face. The only thing that limits the size of the wedge is the geometry of the bench and the persistence of the joints.

## Joint Persistence / Trace Length

According to your selection of Joint Length, you will be able to define statistical distributions for **Persistence** or **Trace Length**, for Joint 1 and/or Joint 2, by selecting the checkboxes and entering the statistical distribution parameters. If a check box is NOT selected, then joint persistence is assumed to be infinite.

For further information and practical examples see:

Tutorial 06 Persistence Analysis

Persistence and Bench Design Theory

## Bench Design

Persistence Analysis is an integral part of the Bench Design option in **SWedge**. When using Persistence Analysis with Bench Design, the Persistence data is input through the Bench Design dialog rather than the Analysis menu.

**Persistence Analysis**option cannot be used in conjunction with the Scale Wedge option. If the Persistence Analysis option is in use, then the

**Scale Wedge**option will NOT be available, and vice-versa.