bench interramp

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Bench - inter-ramp - overall: A guide to statistically designing a rock slope

James I. Mathis

Zostrich Geotechnical110 W. 6th

Ave. #180

Ellensburg, WA 98926 USAe-mail: [email protected]

ABSTRACT

The proper design and evaluation of the catch bench angle, inter-ramp slope angle,

and overall slope angle, individually as well as in combination, are required for successful

excavation and economic optimization of a rock slope. In many slopes at least one, if notmore, of the above controlling angles are essentially ignored, resulting in a slope properly

designed for one facet of the excavation but ignoring the other components. Bench face

angles can be accurately described statistically utilizing engineering predictions from therock mass discontinuity network and discontinuity shear strengths. Together with the

required bench width, the bench controlled inter-ramp angle is determined. Inter-ramp

angles can be accurately determined by careful construction of a structural geologic model,noting location and orientations of discrete intermediate and large planes of weakness for

the excavation in question. The location and orientation of the overall slope is dependent

upon the slope as determined by the bench controlled inter-ramp angle and the stability

controlled inter-ramp angle. Given advances in data collection and analytical techniquesand continuing moves to increase mining safety while simultaneously attempting to

minimize excavation costs, the only possible way to truly optimize slopes is throughrigorous analytical methods combined with probabilistic techniques.


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tan-1

(15m/(8m+(15m/tan(70))) = 48

tan-1

(150m/(33m+(150m/tan(48))) = 42

INTRODUCTION

A rock slope consists of up to three stability controlled slope components. These

are bench face angle, inter-ramp angle, and overall slope angle (Figure 1). Depending on

the situation, these can be excavation specified or maximum attainable angles. It is,however, critical that the interaction of each of these components is incorporated in the

resulting slope design.

Lets clarify this interaction. Assume an open pit mine with a substantial overall

slope height. Now, assume a bench height of 15m, a required catch bench width of 8m

with a stability determined face angle of 70. Assume the inter-ramp slope has beendetermined to be acceptably stable at an angle of 55 with a ramp width of 33m and a

mean height of 150m. Structural considerations determine that the overall slope shall not

exceed an angle of 44.

What to all these numbers tell us? Well, in order to maintain the required catchbench angle, the inter-ramp angle cannot exceed the geometrical constraints imposed by

the bench geometry. In this case, the bench determined inter-ramp angle is:

(1)

Now, it is obvious that the bench controlled inter-ramp angle (48) is less than the

angle at which the inter-ramp slope has been determined to be stable (55), thus the slope

must be designed to accommodate the required bench geometry.

How about the inter-ramp versus overall slope? The inter-ramp angle cannot

exceed 48, as noted above. If the ramp width is added, the overall slope, as dictated byinter-ramp constraints is:

(2)

The overall slope was determined to be sufficiently stable at 44. Yet, the benchgeometry dictates the inter-ramp angle. This angle, together with the inter-ramp height

and the required ramp width impose an overall slope angle of 42. Therefore, the bench

geometry, for this specific case, dictates the overall slope angle as well.

Of course, some variables can be modified. Bench height can at times beadjusted, as can excavation methods (especially blasting), ramp widths can be adjusted

based on equipment selection, artificial support may be contemplated, etc. In fact, amultitude of possibilities exist to adjust the individual components of the slope geometry.

Still, in order to reach that point one must first understand how one engineers each of thecritical slope components: bench, inter-ramp, and overall slope angles.


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Figure 1 - Bench controlled inter-ramp angle, inter-ramp angle, and overall slope angle

CATCH BENCH DESIGN

The catch bench consists of a bench face and a catch bench. A bench face is the

vertical to intermediate dipping wall created in rock by excavation actions (Figure 2).This wall, or face, will also have the added component of a "bench". This bench, located

at the base of the rock face, will be an area reserved for catching (restraining) rocks thatdetach from the excavated face, thus the term bench face or the face above the bench.

What is bench face design? A basic definition would be the engineering designof a rock face above a bench such that the general standing, stable angle of the face is

quantified. This should incorporate at a minimum the input parameters listed in Figure 2.

Figure 2 - Anatomy of a bench design


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For a standard bench design, this information is then compiled and the

following conducted:

Identify potential failure modes; Determine the population of potential structural orientations that may occasion

bench failure;

Calculate the stability of the structurally defined failure blocks by standardkinematic analysis;

Adjust the bench face angle until an appropriate safety factor is realized againstsliding and/or;

Calculate potential reinforcement for the sliding blocks, if required; Determine the requisite bench width to retain failed rock from the bench face.

Yet, a variety of questions arise with this standard design. Amongst these are:

Most benches are drilled and blasted vertically. To what minimum angle will thebench fail to and how much material will fall from the crest?

What is the distribution of face angles and how will this distribution of faceangles affect the bench catch width design?

How was the variability of the shear strengths incorporated in the analysis? What is the impact of the discontinuity length and spacing on the face angle and

what is the sensitivity of the design to these parameters?

What would the impact be of utilizing the entire structural orientation distributioninstead of point values?

How much backbreak can be eliminated by drilling angle holes and is itwarranted?

Catch bench face angle design, as conducted by this author, utilizes a rock fabric

simulation to determine bench face angle reliability (2). Discontinuity spatial

characteristics obtained from a rigorous sampling method and obtained either from

physical or photogrammetric mapping are simulated in a three dimensional, Monte Carlogenerated, discontinuity model (Figure 3). The three dimensional model is then cut by a

simulated bench face and statistical failure analyses of wedge and plane shear failures are

conducted on the daylighting features that transect the bench crest. This provides notonly the bench face angle distribution as a function of bench height, but also provides a

large number of simulated face profiles for analysis and allows for the effect of an

excavated face angle of something less than 90.

Rock fall is analyzed using simulated face profiles to determine/verify the

required bench width to accommodate rock fall. Note that rock fall described herein ismaterial physically falling to the bench, not volumetric failure accumulation as

considered by some engineers.


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Figure 3 - Persistence modeling of structures for bench scale analysis

Of course, the analysis incorporates known structural domains (areas of similar

geologic structure including lithologic variations), variations in face orientation (designsectors), and the complete discontinuity shear strength distribution (peak and residual) in

the design. Blasting effects are accommodated as adjustments in the discontinuity spatial

characteristics. At times, rock reinforcement may be considered to modify the bench faceangle distribution.

Once the bench face angles distributions are defined, the reliability of the bench

face angle is utilized for selection of the design bench geometry. The face anglereliability can vary from 70% for areas not often frequented by man or machine to values

>90% for areas where bench failure may substantially impact operations or potentially

endanger personnel. For open pit mines a reliability of 80% appears to be somewhat

standard as this appears to contain most rock that escapes a single bench.

Face angles at the chosen reliability, and segregated by external effects (excellent

vs. poor excavation techniques, etc.) are compiled into a table. This table includes the

structural domain and design sector (face orientation). Note that this table can also

include varying bench height and catch bench width. A geometrically constrained benchcontrolled inter-ramp angle, as noted in the introduction to this article, is then calculated.

Note that the described methodology answers all of the questions posed above,

including the effect of discontinuity length (persistence) and center density (spacing).

Note further these questions can only be answered using probabilistic techniques.

One of the aforementioned points, discontinuity persistence, is absolutely critical

to proper face angle design. As can be seen in Figure 4, discontinuities that are assumedto be continuous through the bench will not honor the rock mass. Continuous structures

would result in a bench face angle that would not change as a function of bench height.

Of course, this is not the case, as double and triple benches are nearly always steeper thansingle benches due to the interaction of discontinuity persistence occasioning failures as

they transect the bench crest. Thus, only a method honoring the mapped discontinuity


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persistence will provide an accurate estimate for bench face design if the discontinuity

persistence is substantially less than the bench height. This variation in bench face

angles is demonstrated for a 10m and 20m bench height utilizing the program Z-Fabric(Zostrich Geotechnical) (Figure 5).

Experience has shown that it is always prudent, as well as good engineering, tovalidate any slope design. Verification of bench scale performance utilizing the above

described methodology has been conducted using a multitude of individual face profilesobtained from surveying as well as photogrammetric techniques. One of the advantages

of utilizing photogrammetric techniques is that the entire imaged slope is available for

face profiling to compare with the analytical bench face and slope angles. While someblind areas may exist due to camera location, the accuracy of the slope topography is far

superior to that obtained by any other easily applied methodology. The verification

process allows one to detect errors in discontinuity data collection, failure mode analysis,and blasting practices such that the bench design may be refined.

Figure 4 - effect of discontinuity persistence as a function of bench height

Figure 5 - comparison of bench face distributions as a function of bench height


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INTER-RAMP DESIGN

As was discussed previously, bench scale design is, for most part, predicated on

relatively simple failure modes with low applied stresses on the sliding surfaces. The

controlling geologic structures (rock fabric) can be dealt with statistically as has beendone above.

However, inter-ramp slope design is more much complex, incorporating

intermediate faults, rock fabric, and at times, rock mass strength characteristics. Due to

this varying height of the inter-ramp slope, the required slope analyzes can fall anywhere

between fabric stability analyzes for benches and the individual failure analyzes requiredfor overall slope stability.

The inter-ramp portion of a pit slope is that slope between:

The crest of the excavation and any intermediate ramp; Between two sections of ramp, or; The ramp and the base of the excavation

A term that has come into common usage in the last few years is stack height or

the continuous vertical stack of benches that will maintain stability given specific

design parameters and engineering analyses. This term is essentially synonymous withthe inter-ramp height as it is specifically addressed in inter-ramp design as slope height.

Stability of the inter-ramp slope is generally still, as for benches, controlled byrelatively simple structural failure modes. Yet, when attempting to proceed utilizing

similar logic as for bench design, two major problems immediately arise:

Stability constraints. The frequency, continuity, and location of the geologicstructures that may control any potential inter-ramp scale failures must be defined

for analysis. The output of potential number of failures together with theirassociated size, defined not only by the expected number but a probable range, is

available only through statistical analysis.

Economic constraints. Unlike bench design, the operator must decide when aninter-ramp scale failure occasions economic impact on the operation. Other than

the obvious safety concerns, which must be addressed, this latter actually dictatesthe inter-ramp slope angle chosen for design. Again, as the input to any economic

analysis of this sort requires a range of failure occurrences and volumes this willonly lend meaningful results through probabilistic stability analyses.

Stability constraints

Inter-ramp stability analyses examine the stability of potential failure geometries

greater than one bench up to, and including, the entire inter-ramp height. As noted


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previously, the inter-ramp height can at times be the entire rock slope, at which point the

inter-ramp is equivalent to the overall slope.

Similar input values are required as for bench design (Figure 2) with the

substitution of the inter-ramp height and bearing for the equivalent bench values.

Adjustments may be required in the discontinuity shear strengths, as fault values may berequired. Assessments of rock mass strength values may be required as well.

One of the greatest differences between inter-ramp and bench design is that

equivalent structure defining the failure geometry must generally be greater than the

height of the bench in persistence. However, such structures are difficult if notimpossible to map as a single feature as they traverse multiple benches in an existing pit

or transect outcrop in natural terrain prior to mining. Extrapolation of fabric mapping

data for such analysis is possible but somewhat unproven. Further, some assessment ofthe feature density (spacing) must be provided as well. At present, geologic structural

interpretation is required to fulfill this requirement.

The requisite structural interpretation is extensive requiring pit wall/outcrop

mapping of continuous structures and intermediate faults, drillhole interpretation of

faults/broken zones, and a comprehensive assessment of the entire structural picture (3).Note this is not a standard geologic interpretation, but has been developed as a function

of advances in photogrammetric and modeling software. This provides the structural

underlay for geotechnical assessment (Figure 6).

For a pushback, or additional excavation immediately behind an existing wall oroutcrop, the mapped structures together with their physical characteristics can be

projected directly onto the wall. Multiple failure geometries can be analyzed together

with exterior influences such as water and blasting. This allows slope geometries to beadjusted, rock mass strength influence assessed, and potential rock reinforcementconsidered. Such an analysis indirectly addresses persistence as the projection of the

geologic structures is not large given their persistence. This is the preferred inter-ramp

slope design environment. Note that the related stability analyses, even for discretestructures, utilize the shear strength distributions on the defining structural features. In

addition, as noted above, variations in water level, statistical representations of release

structures, etc. can and should be included in the design if they exhibit a demonstrableeffect.

Alternatively, where the design slope is substantially behind the mapping slope orin areas where no structural projections may be made, the designer is forced to utilize

statistical representations of structural populations. The orientation distribution for the

design structure population is relatively simple to obtain, either by projection of fabricmapping data, analysis of major features, or both. However, two critical parameters for

the stability analyses are persistence and density (spacing).

Density (spacing): The spacing of the major geologic structures impacting inter-ramp stability can be obtained from analysis of the local structural interpretation,


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Figure 7 - Effect of multiple structural intersections on probability of failure geometry

occurrence

The rapid change in wall curvature at a pit bottom (Figure 8), or a nose

developed in a pit wall can also be analyzed statistically. Where these two special slope

cases have often been described as being more, or less, stable because of degrees offreedom of motion that is only partially true. As the plan curvature of the slope wall

increases, it is more difficult to create a viable geometry as the release structures must be

found in a specific locale and have a substantial, and increasing, persistence for a viable

failure block to be defined. Alternatively, for a nose, the requirements for persistence andlocation of the release structures are substantially reduced. These can both be addressed

analytically, using probabilistic methods, with the aforementioned interpretative

structural work thus improving slope stability assessments.

Economic constraints

An inter-ramp slope analysis, if conducted using statistical methods, will be either

expressed as a probability of failure, the expected number of failures, or both. Thelocation and extent of the failure will have some economic impact on the operation.

For example, if the inter-ramp scale failure is on a slope where it will have little

impact either on mining operations, traffic, or facilities, then the economic impact ofinter-ramp failure is minimal. The probability of failure can likely be quite high without

substantial economic consequences.

However, if the design inter-ramp slope is below a haul road to the bottom of a

pit with no alternative methods for access if the ramp is obliterated by failure, the failure

is an end of mine life event with large economic consequences. In this situation, theprobability of failure, including the accuracy of the failure estimate, must be carefully

considered. Slope angles may be flattened to account for this risk in specific portions of

the pit specifically to address this factor.


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Once these values have been determined for all structural domains and slope

angles, the slope should be re-optimized. This may result in substantial slope translation

from the original design if those estimates were in error.

However, this design stage provides for an optimization and accommodation of

individual geologic structures and structural zones that may actually improve the slope.For example, as seen in Figure 6, the structural interpretation indicates the design slope

falls along a major structure. However, stepping the slope back slightly into the wallbehind the structure allows a portion of the slope to be excavated steeper than the

original design allowed as the rock fabric has been accommodated in the bench design.

Whether this is economic is unknown, but it certainly should be compared againstreducing the slope angle in front of the existing structure. Similar analyses should be

made regarding changes in wall orientation, bench height, ramp location, etc. Economic

benefits of such result analyses/combinations/adjustments can be substantial. In order torealize such benefits, active participation of a knowledgeable geotechnical engineer who

recognizes potential opportunities and pitfalls is required in the planning process.

OVERALL SLOPE DESIGN

Of the three stability controlled slope components, the overall slope is generally

the simplest in terms of conceptual framing and analysis.

This comment is not made without considered examination of its implications.

Let us examine what we have already conducted to arrive at the overall slope design:

The overall slope design should only be conducted after the bench and inter-rampdesigns have been conducted, with final interactions of both considered. Thus,

slopes have been adjusted to reflect inter-ramp and bench stability concerns,including major structures and zones of low rock mass strength.

Inter-ramp design requires a detailed structural geologic interpretation for theinter-ramp areas. As these encompass the entire design pit, a detailed structural

model is available for the overall slope design.

Thus, a piecewise stable slope has been designed, with the location of these individualslope components being generally correct spatially. In other words, there is no real

guesswork as to final location of the slope compared to overall wall failure geometries.

The complete structural and lithologic model for the design slope is then examined forpotential failure geometries. It makes no difference as to the analytical methods utilized,as these are dependent upon the failure modes and stresses involved. As long as the

designer incorporates the uncertainty in the model within the analytical process, the

probability of failure for any portion of the design pit may be calculated. This variabilityis, of course, more easily accommodated in simpler models as compared to three-

dimensional numeric models. Even in the latter case, the structural and strength

variability can, and must, be incorporated in the final analysis.


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