Letters to the Editor:

One of our customers, Ashley Creighton, Geotechnical Superintendent at Lihir Management Company, New Ireland Province, Papua New Guinea, raises some important issues on probabilistic analyses using Swedge and RocPlane. Rocscience welcomes further feedback on this topic.


From: Ashley Creighton
Subject: Estimating the Probabillity of Failure using Swedge or RocPlane

I am the Geotechnical Superintendent at the Lihir Gold Mine and wish to confirm some issues with the above mentioned software.

Could you please define what a valid wedge is for both Swedge and Rocplane? Does it mean that the wedge is kinematically admissable i.e. the intersection of the planes form a wedge which line of intersection plunges at an angle less than the slope angle? Does it mean that the planes intersect to form a wedge which is both kinematically and non-kinematically feasible?

The reason I ask this is that my understanding from the manual is that the probability of failure, so defined and estimated by the Swedge and Rocplane codes, is not actually the probability of failure as it may not include the entire statistic or population of the orientation combinations for each plane (this is particularly the case for plunges for planes or lines of intersection which are close to the face angle). It is my opinion that to calculate the probability of failure for a wedge in Swedge all combinations should be included in the population, whether or not they are kinematically feasible. I consider that the probability of failure of a wedge, which is a conditional probability, is actually given by:

Prob (Failure) = Prob.(sliding estimated by Swedge)*Prob.(Plunge of Intersection<Slope Angle).

The other issue is with Rocplane. The probability of failure is actually conditional on the strike of the plane being within 20deg. of the face (refer to Hoek and Bray, 3rd Edition Page 150), the probability that the plane dip is less than the face slope and that the shear strengths/water etc result in a mean FoS less than 1.0 i.e.

Prob(Failure)= Prob(sliding estimated by Rocplane)*Prob.(Strike<=20deg)*Prob.(Dip of Plane<Slope Angle)

My concern is that both software codes result in conservative estimates of the Probability of Failure and this becomes progressively pronounced as the plunges of the line of intersection or the plane (in Rocplane) approach the face angle.

For Rocplane, for instance, in using the software the inference is that the plane strikes within 20 deg. of the face. This inference excludes all planes from the statistic that strike greater than 20deg. from the face. These non-kinematically admissible planes should be incorporated in the population for calculation of the Prob. of Failure.

Could you please clarify this for me?

Regards

Ashley Creighton
Geotechnical Superintendent
Lihir Management Company
New Ireland Province, Papua New Guinea

Answer from Rocscience:

We wish to thank Mr. Creighton for the important issues on the probabilistic analyses that he raises in his letter. Such feedback constitutes a critical component of the improvements and advancements continually implemented in Rocscience software. This response will clarify the probability of failure values reported by the Rocscience programs RocPlane and Swedge. It will also briefly outline the broader context within which these probabilities should be applied, and will specify steps planned by Rocscience to address the issues raised.

The two main probabilities of failure that Mr. Creighton mentions – the probability of planar wedge failure and the probability of surface wedge failure – form part of a system. In this system, a wedge on a rock slope can fail in one of the following kinematic modes:

  • Planar failure
  • Wedge failure, or
  • Toppling
Such analyses, which involve multiple failure mechanisms, are sometimes described as system failure analysis. They are generally more complicated than failure analysis of single mechanisms. In the rock wedge system, a wedge is assumed to fail when any one of these failure mechanisms is triggered.

The overall probability of wedge failure comprises the sum
,
where , , and are, respectively, the probabilities of planar failure, surface wedge failure or toppling failure occurring.

As indicated by Mr. Creighton, each of these probabilities is made up of several components. For example, the probability of planar failure, , consists of two primary components: the probability that planar failure conditions exist, , and the probability that sliding will occur on the failure plane, . The probability of planar failure is calculated as the product of the two components, i.e.



Currently, Rocscience supplies individual programs for analyzing two of the three rock wedge failure mechanisms – RocPlane for planar failure analysis and Swedge for surface wedge failure. The company plans to develop a toppling program in the near future.

A basic assumption of RocPlane is that planar failure conditions already exist, i.e. the program does not check whether the strike of a discontinuity is sub-parallel (within 20 degrees) of the strike of a slope face, but assumes that this condition exists. Since the condition of sub-parallelness is not checked for, any prediction made on the probability, , of a kinematically feasible planar wedge forming would not be complete. (Another fundamental assumption in RocPlane is that every discontinuity generated is long enough to span the distance from the toe to the top surface of the slope.)

The probability of failure reported in RocPlane, is the probability that a kinematically feasible planar wedges will fail, i.e. the program outputs .

From the definition of the probability of planar failure provided above, it can be seen that it can be conservatively estimated by equating it to (this assumes the probability to be equal to 1). Presently this is the approach implemented in RocPlane.

Similar to RocPlane, Swedge estimates with the value of the probability of kinematically valid surface wedges failing. As mentioned by Mr. Creighton, under certain conditions these estimates may be too conservative.

The InfoViewers in both RocData and Swedge have information that can be easily used to calculate less conservative values of and . The probability of planar failure, for example, can be estimated as

.

(As noted earlier, this estimate does not take into account the probability of the discontinuity plane striking sub-parallel to the slope face.) The next updates of the programs will automatically compute these values and report them.

As the next step in allowing engineers to more easily calculate the overall probability of wedge failure involving the three major failure modes identified earlier, Rocscience plans to include in RocPlane the capability of checking discontinuity plane strikes being sub-parallel to a slope face. The company’s software developers also intend to implement features that will allow RocPlane and Swedge to read each other’s input data files. Further, Rocscience intends to develop a toppling program, which will also share input data with RocPlane and Swedge.

The ability to read input data across the programs will ensure that after building a model once, the rock slope engineer has the tools to readily assess the probabilities of multiple failure modes. The outlined series of steps will ensure preservation of the power of limit-equilibrium analysis – simplicity. These steps ensure retention of the clarity, ease, and logical structure that makes simple rigid-body analysis of wedges so effective and popular.

Rocscience Inc.

Again, RocNews thanks Ashley Creighton for his very useful comments.