# Geometry Overview

Rectangular Pillar

A **Rectangular** pillar is defined by it's **length**, **width**, and **thickness (height)**, or **x**, **y**, and **z** values. These are the first 3 items entered in the **Geometry** section of the **Pillar Information** for **Rigid**, **Elastic**, or **Voussoir** analysis methods. (Depending on the relative magnitudes of x, y, and z, the term **pillar**, **beam**, or **plate** may be most applicable, as described at the end of this section. For convenience, the term **pillar** is used most often throughout the Online Help).

Plate with dimensions x = 10, y = 20, z = 1

Plate with dimensions x = 10, y = 20, z = 1; overburden thickness = 1

Plate with dimensions x = 10, y = 20, z = 1; overburden thickness = 1, water height = 2.5

## Polygonal Pillar

A **Polygonal** pillar is defined by a at least three unique **vertices** **(x, y)**, and **thickness **(i.e. height) (**z**) values. The polygon vertices can by input by selecting the **Edit Coordinates** button under the **Geometry** section in **Pillar Information**.

Non-vertical abutments can also be specified by changing the **Abutment Trend** and **Abutment Plunge** under the **Geometry** section in **Pillar Information**.

**NOTE:** Polygon Coordinates option and non-vertical abutments are only available in **Rigid - Polygon** analysis

## Pillars, Beams, and Plates

Depending on the relative magnitudes of x, y, and z, the term **pillar**, **beam**, or **plate** will most correctly describe the geometric model:

- A
**pillar**refers to a model with a**low**span / depth ratio, the**span**being the shorter of the x and y dimensions. - A
**beam**refers to a model with one of the lateral dimensions substantially longer than the other, and a fairly high span / depth ratio (e.g. > 3). Note that the**beam span**is the**short**lateral dimension. - A
**plate**refers to a model where both lateral dimensions are of similar magnitude, and a fairly high span / depth ratio (e.g. > 3).

To model the roof of a long excavation (a **beam**), make one lateral dimension much longer than the other (e.g. x = 10, y = 100). A factor of 10 should suffice, although the user can specify any realistic dimensions (e.g. x = 10000, y = 10).

**NOTE:** The "long" and "short" lateral dimensions can be either the x or the y dimension. Make sure the corresponding lateral stresses are consistent with the chosen x and y directions.

## Is Pillar Permeable?

This option toggles between **Yes** and **No**.

**No** - Water height less than the pillar + overburden thickness will have no effect on the model whatsoever. If water height is greater than the pillar + overburden thickness, then the weight of the free water will have an effect as an extra deadload on the pillar.

**Yes** - Effect of water pressure on lateral effective stress will be taken into account. However, if water height is too high, negative effective stresses will results, and a warning message will appear when attempting to Compute.

## Face Dip

For a Voussoir analysis, the user can specify a dip angle (degrees from horizontal) for the excavation face (>=0 and < 90). Specifying an angle > 0 has the effect of lowering the effective gravitational driving force by a factor of **cos(dip angle)**. Other than this, the analysis procedure is the same as for a zero dip angle.