Waste Rock Back Analysis

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Courtesy of SoilVision Systems Ltd.

On October 4, 2004, during field measurements collected in trench LFG-008, a crack developed in the middle of the trench. This occurred during the destruction of the Goat Hill North (GHN) rock pile at the Questa site. The crack varied in width up to a maximum of 100 mm and extended in an arc pattern around the pushed out section of the slope.

The slope had been pushed in a convex arc out from the original slope of the mountain in order to ultimately flatten the slope of the GHN pile and reduce a slope failure risk. Trenches were excavated through undisturbed zones of the original rock pile during the slope destruction process in order to provide insitu field testing / sampling opportunities for the Questa Waste Rock Pile Weathering Study. The crack formed an arc through the excavated trenches in a manner opposite to the lip of the slope. A view of the crack as highlighted from a position directly above the slope may be seen in Figure 1.


Figure 1: Location of the crack as viewed from 
up the 2:1 slope

The purpose of the back analysis was to identify possible soil strata/soil property scenarios that would produce a slip surface and failure condition at the location measured in the field. For this analysis it was assumed that the crack as observed in the field represents failure. It is noted the crack could possibly represent displacement that might not have ultimately represented failure conditions.

The following points were noted about the site:

  • A bulge at the base of the slope was observed but the precise location was undetermined
  • From survey points and field photographs it was possible to identify the geometry of the upper level rock pile
  • The location of the exit point of the crack could not be determined
  • It was estimated the crack exited at a distance greater than 150 ft from the crest of the slope
  • The exact exit location could not be safely measured
  • Moist conditions existed along the top of the crack at the time of failure

In order to proceed with the analysis it was necessary to recognize the following assumptions:

  • The shear strength of the rock pile material is homogenous
  • The slip surface does not go through the bedrock
  • The shear strength of the bedrock is significantly higher than that of the rock pile material
  • There is a weak soil layer between the bedrock and the rock pile material.
  • The shear strength of the rubble zone is less than that of the rock pile material
  • Shear box testing estimated waste rock phi between 36-47 degrees (slope should not fail!)
  • Colluvium and the rubble zone are combined into a single layer.

The assumptions resulted in the developed 2D geometry as shown in Figure 2

Figure 2: Established geometry of the 2D cross-section through the center of the slope failure

Analysis

Four scenarios were developed based on differing assumptions regarding the slope geometry of the rock pile. Only circular slip surfaces were considered in this analysis.

Case 1: Fixed Entry of Failure Surface - Strong rock pile material and weak rubble zone

In the Case 1 scenario it is assumed that the rock pile material has strength values which are consistent with field measurements.The strength of the rubble zone is then reduced until the factor of safety of the critical slip surface falls below 1.0. An entry and exit trial-and-error methodology was used to identify the location of the critical slip surface.

Rock Pile Material: Cohesion = 15 kPa, Friction angle = 36 degrees

  1. Entry and exit trial-and-error methodology was used to identify the location of the critical slip surface
  2. Entry point: Survey Data
  3. Exit point: approximate based on a combination of field observations of a bulge at the toe as well as a sensitivity slope stability analysis regarding the likely location of the slip surface

Given the deep location of the slip surface it appears unlikely that a cohesion value of less than 10 kPa is possible since a reasonable amount of cohesion is needed to force the CSS to have reasonable depth.

Based upon the analysis, the material properties required in the rubble zone in order to achieve failure conditions are:

Figure 3: Typical results of analysis of a potential failure through the rubble zone

Case 2: Fixed Entry of Failure Surface - Homogeneous model

In Case 2 scenario, it was assumed that the soil parameters of the rock pile material and the rubble zone are the same. The entry and exit points of the slip surface were fixed and a circular slip surface was assumed. The radius and center of the assumed slip surface was allowed to vary based on a series of increments related to the assumed entry and exit points.

Soil parameters: rock pile material and the rubble zone are the same

  1. Entry and exit points: fixed and a circular slip surface was assumed
  2. Radius and center of the assumed slip surface allowed to vary based on a series of increments related to the assumed entry and exit points
  3. Cohesion was assumed to be zero and the effective friction angle allowed to vary until a factor of safety just below 1.0 was achieved.
  4. Cohesion was subsequently added in the additional model runs and the effective friction angle varied until failure conditions were achieved.

An example of the critical slip surface may be seen in Figure 4.

Figure 4: Example location of the critical slip surface for Case 2

Since cohesion is needed for the slip surface to remain deep in the slope it is assumed that a minimum amount of cohesion is needed in this case.

What is problematic in this scenario is the fact the friction angle of the material is required to be between 27-33 degrees in order to achieve failure conditions. This range of friction angles is significantly different than the 36-47 degrees friction angle measured. It is therefore considered unlikely this scenario is realistic.

Case 3: Variable Critical Slip Surface (CSS) location - Strong rock pile material and weak rubble zone

In the Case 3 and 4 analyses the location of the potential slip surface is unrestrained. Material parameters for the angle of internal friction and cohesion are then varied manually in order to cause the location of the critical slip surface (CSS) to replicate field observations.

The selected slip surface location shown in Figure 5 is based on an approximate match of entry and exit points and results in the following material parameters:

  • Rock Pile Material:
    • Cohesion = 15 kPa
    • Friction angle = 36 degrees
  • Colluvium/Rubble:
    • Cohesion = 7 kPa
    • Friction angle = 24 degrees

The identified material parameters are reasonable and provide a level of continuity with measured laboratory and field results. The measured friction angles for in situ tests showed a lower limit value of 36 degrees. The friction angle for the colluvium / rubble zone is also consistent with the properties of the colluvium determined in the Norwest (2004) study.

Figure 5: Location of slip surface for weak rubble / colluviums

Case 4: Variable CSS location - Homogeneous model

Case 4 represents the scenario when the rock pile and rubble regions are given the same material parameters. The location of the critical slip surface is allowed to freely vary within the confines of the grid and radius search technique. The material parameters were adjusted until the upper entry point of the critical slip surface location matched field observations and the calculated factor of safety was approximately equal to 1.0.

The resulting critical slip surface is very similar in location to the critical slip surface determined in Case 3 and may be seen in Figure 6. The soil parameters used to achieve this critical slip surface are quite different than obtained for Case 3 and are given below:

  • Rock Pile Material:
    • Cohesion = 150 kPa
    • Friction angle = 18 degrees

These parameters are unrealistic in comparison to site-measured parameters. The high cohesion values are needed in order to cause the CSS location to be deeper in the pile and match the observed exit point of the slip surface. It is reasonable to conclude the rock pile and rubble zones do not have the same material properties.

Figure 6: Resulting slip surface from a homogeneous model

Conclusions and Recommendations

The back-analysis of the slope failure at Goat Hill North in October, 2004 indicates that there are two possible modes of failure. These modes of failure are:

  1. A deep-seated failure through a relatively weak layer of rubble or colluvium layers and
  2. Failure through the rock pile material.

The results of the various failure cases analyzed indicate that case 3 represents the most likely failure condition and is represented as determined by the back-analysis.

Case 3: Strong rock pile material and weak rubble zone: If the observed failure surface was initiated by a deep weak layer then it is the indication of this analysis that reasonable material parameters of rubble/colluviums are as determine by the back-analysis.

CSS Location Variable: In this case the rock pile material parameters are fixed with a friction angle of 36 and a cohesion value of 15 kPa. It is worthy of note that the colluvium/rubble properties are consistent with the properties obtained by Norwest (2004). The rubble properties obtained for the assumed failure conditions are as follows:

  • Friction angle: 24
  • Cohesion: 7 kPa

The following points summarize the findings:

  • It appears unlikely that the crack observed on October, 2004, is due to a failure plane through rock pile material alone. If this were the case, the resulting model-determined soil parameters (Φ= 18°, cohesion = 150kPa) differ significantly from the in situ testing program.
  • It appears likely that the observed slope failure was the result of sliding along a deep-seated weak layer beneath the rock pile material and above the bedrock layers. When this hypothesis is considered, the resulting material parameters needed to produce failure conditions are consistent with existing field observations.

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