One of the keys to understand rock mechanics is to understand the joint patterns within the rock. Critically important in understand the joint pattern is to understand the orientation of the joints. To do this we use Dip, Dip Direction and the related measurements.

The first concept to understand is the dip of a joint. We shall initially consider a single planar joint within the rock such as a shear or fault. To define the direction of the joint in three dimensional space we typically use two values. By doing this we can use the conventional 360 degrees that is commonly used to define angles and directions. The two angles typically used are called Dip and Dip Direction.

To consider Dip and Dip Direction we need to consider a line on the plane of the joint. Imagine a grid of lines on this plane, with one set of lines running across the plane at the same height, effectively forming contours not rising or falling across the plane. The second set of lines on this grid will run perpendicular to the contours. This second set of lines would be the steepest line that could be formed on the plane. This line is the key line from which we measure Dip and Dip Direction.

The Dip Direction can be determined by viewing the plane and the line we have drawn on plan. The orientation of the line can be specified using the 360 degrees of a compass bearing. At this point it is worth noting that this value is not absolute, but that the baseline needs to be specified. Normally the baseline orientation is North but this could be true north, grid north or magnetic north.

Having specified the direction of the line, we need to specify how steep the line is. We do this using the Dip of the joint. To obtain the dip we have to cut the plane of the joint along the Dip Direction of the joint. Having cut the joint plane the Dip of the joint can be measured by measuring the angle from the horizontal of the plan of the joint. This means that a steeper dip gives a steeper joint up to a maximum of 90 degrees. Typically dip is only measured as a positive angle between 0 and 90 degrees.
Dip and Dip Direction are the typical values that are quoted to give the joint orientation. There are however a few other dimensions that are used to specify the orientation of features. Strike is a value used instead of Dip Direction. The Strike is a line at 90 degrees to the Dip Direction. Referring back to our original diagram the Strike follows the contour lines running parallel to the slope. Strike and Dip Direction are therefore interrelated. It is important to note that Strike may not be defined using the conventional 360 degree compass, but may be defined as being an angle East or West of North such as N72E, 72 degrees East of North. Strike can be represented on a plan by a long line following the direction of the strike and a short bar at 90 degrees showing the direction of the dip.

Another method of defining Dip and Dip Direction is Trend and Plunge. Trend and plunge tend to be used with linear features such as tunnels, shafts or roads. Trend tends to follow the centreline of these features such as the axis of a tunnel and is defined in the same way as Dip Direction. The plunge is then defined in the same way as the dip so the steeper the plunge the steeper the slope of the tunnel.

It is important to understand Dip and Dip Direction when designing rock structures. When using these measurements of the orientation of joints you must clarify how it has been defined by the geologist to ensure that you are applying the measurements in the same manner as they have been defined.

Tags: Analysis, Dip, Dip direction, Geology, Joint Sets, Logging, Plunge, Rock mechanics, Strike, Trend

UDEC is an incredibly powerful tool for analysing complex problems in rock mechanics. Not only is it capable of modelling the behaviour of deformable blocks, but it has tools for generating semi-random block patterns so it can model complex systems of jointing within the rock mass.

The power of this tool can however be a problem. There is always a temptation to just input measured or estimated quantities into UDEC with a suitably high variability, run the model a number of times and then take the worst case result. This is particularly the case with joint sets in a rock mass. A common convention is to simply obtain the joint sets from DIPS, adjust the joint orientations to give the apparent dips of the joints on the face of the model and then input all of the joint sets into the model and run it. This is however an overly simplistic method of generating the joint sets.

The key to understanding how to work with joint sets in UDEC is to understand a key limitation of UDEC; it can only model failure in two dimensions, normal to the face that is modelled in UDEC. To consider this point I want to consider a few different cases with different combinations of joint sets and joint orientations.

Let us first consider the simple case with a single joint set potentially causing a failure. The dip of the joint set is parallel to the dip of the slope as shown in the diagram. In this case the key joint set can be readily modelled in UDEC.

The next stage is to consider what happens when the dip of the joint set is rotated by 45 degrees to the dip of the slope. Assuming that we only have one joint set, then slip of the joints would not occur, as another release pane would be needed.

So let us consider the case with two joint sets oriented with dip directions of +45 degrees and -45 degrees and both having the same dip. In this case it is relatively simple to show that the direction of slide of a wedge that is released will be perpendicular to the slope face. Again, UDEC will model this situation appropriately because the direction of failure is perpendicular to the plane of the face being modelled in UDEC.

It becomes more complex when the dip and dip direction of the joint sets relative to the slope face are different. When this occurs, the dip direction may not be parallel to the dip of the slope. The implication of the this is that a simple UDEC model normal to the to the dip direction of the slope may not give us an appropriate solution.

So how do we model this more complex problem? The fundamental requirement is to understand what is happening to the slope prior to the analysis using UDEC. If you can understand the dominant failure mechanisms then you can adjust the UDEC models to deal with them. I will give to examples of how UDEC models can be adjusted to potentially give a more representative solution for the problem. None of these methods are guaranteed to give the correct solution, they all have problems. The reality of the assumption of a two dimensional problem in UDEC is that in most rock mechanics problems, it can only give an indication of the behaviour of the system.

The first simplified approach to the solution is to simply model the problem along the dip direction of a dominant joint set. By using this approach the angle of dip of the dominant joint set is correct. The factor of safety against sliding along these dominant joint sets will be correct. However all other joint sets will not be correct, and the installed support in the UDEC model will have to be corrected because it will typically not be oriented along the dip direction of the dominant joint set. Whilst this approach is effective in modelling failure along a single dominant joint set, it does not consider failure along two joint sets.

The second approach therefore is to assess the dip direction and dip of the sliding direction of a block. This can be done using analysis programmes such as UNWEDGE and SWEDGE. The joint sets in UDEC can therefore be adjusted to model the dip and dip direction of the sliding surface rather than the joints themselves. This may not directly solve the problem because the dip direction of the sliding plane may still not be parallel to the dip direction of the slope. There will also be geometric problems in the model as UDEC models prismatic blocks and we are actually trying to model pyramid shaped blocks. Support, applied forces and other adjustments to the models may therefore be necessary.

A final note of warning. If you model two joint sets in UDEC dipping in the same direction, it is possible that the joint sets could cross. This could lead to composite failure through both joint sets which may be appropriate but not in all cases. Two joints sets in a UDEC model may be dipping in the same direction, however the actual dip direction of these joint sets may be very different. If this is the cases, then composite failure through these two joint sets would not be appropriate. The UDEC model could therefore significantly over predict the size of a failure zone by forming composite failures.

The generation of joint sets for modelling slopes in UDEC can clearly be a complex problem. I hope these techniques and observations might help improve the use of UDEC. So far I have only dealt with slopes; tunnels and caverns are even more complex so I hope to deal with these in a future post.

Tags: Block Stability, Dip, HC Itasca, Joint Sets, Rock mechanics, Slope stability, SWEDGE, UDEC, UNWEDGE