Engineering Geologist London Bridge Associates Ltd. Stereonets H3.57 afternoon room Tom Robinson Engineering Geologist London Bridge Associates Ltd.

Contents What are stereographic projections? Plotting stereonets - basics Stereonets in engineering geology Practical Exercise

Part 1: What are stereographic projections? 1) 2) Warwick University M.Sc. Course 2014 Geological Investigation & Ground Characterisation.

3D Data in Geology All problems in geology, by definition, are in 3D. We are interested in what happens at depth, even if the depth is only 10’s of m. We need a way plotting 3D data onto a 2D plane, i.e. A sheet of paper. A stereonet is one way of doing this. Stereonets are used by all structural geologists, but have some interesting and unique applications in engineering too.

A note on projections There are two main forms of stereonet used: A Polar Net There are two main forms of stereonet used: Upper hemisphere or polar net. Use these for linear data. Lower hemisphere, or meridional net. Use these for planar and linear data. A Meridional Net The PROJECTION is something different entirely. We will be using equal area projections only. Do not worry about the others!

Great and Small Circles Small circle (projection of a curved surface) Equatorial Circle (horizontal plane) Vertical planes will pass through the origin Great Circle (projection of a plane)

Some definitions Any structure in 3D can be split into lines/curves and planes/surfaces. A stereonet can plot both. A line can be defined by its trend (angle from north) and its plunge (angle from horizontal). Trend ~55° On ANY Stereonet, a line will plot as a point. Plunge ~60°

Some definitions A plane can be defined by three properties: Strike (angle from north to a horizontal line on the plane) Dip (angle from the horizontal plane) Dip direction (angle from north that to where the maximum dip is defined). In engineering, we tend to define a plane by dip and dip direction. Structural geologists use strike and dip. You must be aware of both conventions.

Plotting a simple plane On ANY stereonet, a plane will plot as a great circle. Strike = 045° The dip direction will always precede the strike by 90° Dip = 70° Dip Direction = 135°

Plotting the pole to a plane If we have lots of planar data, the stereonet can get very cluttered with great circles. Plunge ~ 20° This is why we plot the pole normal to the plane, which plots as a point on the stereonet. Trend = 315° Warwick University M.Sc. Course 2014 Geological Investigation & Ground Characterisation.

Plotting the pole to a plane A plane with strike s, dip direction (x = s + 90°), and dip d will define a pole normal to the plane with the following orientation: Trend of pole (t) = s – 90° (add 360° if answer negative) = x – 180° Plunge of pole p = 90° - d

Common Geological Structures If the poles to planes measured in the field look like the points in blue: Rounded fold with shallow dipping limbs The poles in red would correspond to an angular fold, with far steeper sides. Warwick University M.Sc. Course 2014 Geological Investigation & Ground Characterisation.

Engineering Applications Do discontinuity poles exist in any of these zones? Do they daylight? Daylight Envelope Zone of allowable sliding failure Zones of allowable wedge failure Friction Cone Existing rock slope Zone of allowable toppling failure Warwick University M.Sc. Course 2014 Geological Investigation & Ground Characterisation.

Kinematic Analysis The previous slide shows kinematic analysis of a rock slope for sliding, toppling and wedge failure, but it could apply equally to the face or roof of a rock tunnel. Sliding and wedge failure are important failure mechanisms in rock tunnels, and you should be aware of both. Kinematic analysis will tell you if the failure mechanism is allowable based on discontinuity data. It will NOT tell you if the slope or roof will or is likely to fail.

Finally... There are computer programmes now that will plot field orientation data for you, and perform the kinematic analysis automatically: But in order to learn, the best way is the old fashioned way... The Rocscience suite above (DIPS) is a very good example, with limit eqm and finite element software too.

Thank you for listening Any further questions?

Figure References http://maps.unomaha.edu/maher/GPFS/Toadstoolfaultplot.jpg http://www.rockware.com/assets/products/165/features/366/1108/rockworks_structural8.jpg http://www.rocscience.com/assets/files/uploads/8609.jpg