rose paper

8/18/2019 Rose Paper

1/11

1Slope Stability Santiago Chile, November 2009

Analysis of Complex DeformationBehaviour in Large Open PitMine Slopes Using the Universal

Distinct Element Code (UDEC)

The design of large open pit mine slopes using conventional limit equilibrium or continuum-based numerical analysis approaches

can often be insufficient in addressing the complex interaction of geologic structure, insitu and induced stresses, groundwater and

rock mass strength conditions. This interaction can be particularly important in environments where strain softening effects from

mining-induced stress relief may lead to progressive slope failure or where design tolerances to slope de formations are low, such

as in areas of permanent mine facilities, critical haulroads or crown pillars.

This document provides a methodology and four case examples of distinct element modeling in large open pit mine slopes usingUDEC in addition to conventional design approaches. UDEC modeling incorporated detailed back analysis of complex slope

deformations by evaluating strain-softening behaviour with bench-by-bench mining to provide multi-point calibration of slope

monitoring data at each excavation stage. Where a high level of input data quality was available, detailed calibration has

provided remarkably accurate predictions of actual slope deformation behavior that was reconciled during and following mining.

These forecasts allowed slope monitoring threshold displacement magnitudes and rates to be developed, providing a basis for

ongoing evaluation of slope stability and development of operational response criteria. In two case examples, slope steepening

was implemented in the latter stages of mining based on predictions of manageable slope conditions.

Abstract

N.D. Rose and M.F. Scholz

Piteau Associates Engineering Ltd.

INTRODUCTION

As open pit mines become progressively deeper and economically more sensitive to stripping ratio, optimization of ore recovery mayrequire acceptance of increased levels of slope deformation or instability, provided that slope conditions can be effectively forecastedand managed. Unfortunately, conventional design methods, such as limit equilibrium analyses, continuum-based numerical analysis, orempirical approaches that rely on historical precedents, are often ineffective in forecasting complex slope deformation behavior, particularlywhen planned ultimate slope heights greatly exceed previous experience. In jointed rock masses where structural geology, groundwater

pressures or rock mass strength conditions play an important or controlling role in slope stability, distinct element modeling using UDECprovides a useful tool to investigate the complex interaction of mining-induced strains and rock mass disturbance (strain softening) onslope deformation behaviour.

This paper presents a UDEC modeling methodology that incorporates detailed back analysis of existing conditions by recreating thehistorical stress-strain path of an open pit slope with bench-by-bench mining and strain softening criteria to simulate rock mass disturbance

related to mining-induced stress relief. Through reconciliation of modeled slope displacements with actual slope monitoring data, andvalidation of model performance at each excavation stage, careful calibration of existing conditions provides greater confidence in forward

predictions of slope behaviour. Four case examples of UDEC modeling in large open pit mine slopes are provided using this approach ina range of geological environments with varying rock mass, structural and groundwater conditions. These examples define a range ofinterramp to overall slope angles, slope heights and potential failure mechanisms.

Case examples are presented from one anonymous open pit mining operation; the Teck Resources Lornex pit, British Columbia, Canada;and two case examples from the Barrick Goldstrike Betze-Post pit, Nevada, USA. For two case examples, predictions of ongoing stabilitydefined from UDEC modeling allowed slope steepening to be considered in the latter stages of mining to maximize ore extraction.Threshold slope monitoring displacements and rates were developed from UDEC modeling results, providing a basis for ongoing evaluationof stability and allowing development of appropriate operational response criteria. These forecasts provided a greater level of confidencein the slope designs than may otherwise have been achieved using a factor of safety approach alone. In all cases, a high level of input

data quality was required.

BACKGROUND

The UDEC analysis code provides the ability to model complex geological structure, rock mass and groundwater conditions, theinteraction of mining activity and related displacement behavior, and the potential for progressive failure development. Modeling of


2/11

2Santiago Chile, November 2009 Slope Stability

the latter two factors is possible based on the dynamic formulation in UDEC that provides a numerically stable solution, even when the

modeled condition is statically unstable. This capability is clearly advantageous for the investigation of slope movements that develop prior

to, and coincident with, a failure condition. Due to the number of input parameters required in UDEC, a high level of site data is required

including the following:

A detailed geological model defining the distribution of major lithologies, faults and/or structural zones;

A comprehensive database of structural discontinuity data defining the orientations (dip and dip direction) of predominant structural

sets, persistence and spacing, and peak/residual shear strength characteristics;Geotechnical properties of the main lithologies derived from geomechanical core logging, mapping and laboratory strength testing

(i.e., uniaxial and triaxial compressive strength, point load index and tensile strength) defining Rock Mass Rating (RMR) according to

Bieniawski (2) or Geological Strength Index (GSI) according to Hoek (3);

A comprehensive database of displacement monitoring data (e.g., survey prisms, extensometer, slope stability radar, inclinometers,

etc.);

A series of staged mine plans showing the development sequence and timing of successive mining phases;Piezometric monitoring and groundwater modeling results defining the distribution of pore pressures during various stages of mine

development; and

Insitu stress testing data defining the pre-mining stress regime, if available.

In considering whether detailed UDEC modeling is appropriate for a particular slope, it is important to first determine whether slope

conditions are complex enough that they cannot be analyzed or explained using conventional design approaches (e.g., structural

kinematics assessments, limit equilibrium modeling, etc.) and whether adequate information exists to construct a meaningful model(as listed above). In environments where design tolerances to slope deformations are low, such as in areas of permanent mine facilities,

critical haulroads or crown pillars, additional investigation effort may be required to develop or obtain high level quality input data.

METHODOLOGY

The overall modeling methodology presented in this paper incorporates a philosophy where the engineering geology, hydrogeology

and mining excavation sequence and geometry are modeled as close as possible to actual conditions, while maintaining a reasonable

compromise between modeling effort and prohibitive model run times. To avoid redundant repetition in the description of the common

methodology used to develop input parameters for each of the case examples presented herein, the following subsections describe the

general process used to generate model geometries, boundary conditions, excavation sequences, material propert ies, rock mass strengths,

discontinuity fabric and properties, insitu stress conditions, groundwater pressures and monitoring histories in the UDEC models.

Model Geometry, Boundary Conditions and Excavation Sequence

Bench excavation geometries are developed from historical mine plans with at least one previous mining phase simulated to limitinertial shock effects (yield) resulting from unrealistically large excavations;

Model dimensions are extended to at least two excavation widths behind the slope crest and one excavation depth below the pit floor

to limit boundary effects;

Horizontal and vertical zero velocity boundaries are applied to the sides and bottom of the model, respectively, whereas

freedom of movement is applied to the top of the model; and

Initial conditions are represented by a pre-mining ground surface followed by bench-by-bench mining under elastic-plastic planestrain conditions.

Material Properties, Rock Mass Strength and Constitutive Models

Rock mass conditions are modeled with the Mohr-Coulomb elastic-plastic constitutive model (Model 3);

Mohr-Coulomb rock mass strengths are derived from the 2002 Hoek-Brown criterion (4) at maximum confining stresses

( σ’3max) in the range of one-third the maximum interramp slope height, or generally between about 1 and 2 MPa for interramp

slopes ranging from about 120 to 240m high;Strain softening criteria are simulated with a FISH routine to update yielded finite difference zone constitutive parameters after each

excavation from peak to disturbed rock mass strengths defined by Hoek-Brown Disturbance (D) factors of 0 and 1.0, respectively,

representing undisturbed to fully disturbed conditions;Rock mass modulus (Em) is estimated from the Hoek-Brown criterion, except in the Basin and Range structural province, USA where

calibration has more successfully been achieved by estimating Em from Serafim and Pereira (5). In these cases, disturbed Em is

estimated as 50% of the peak value;

Depending on rock mass quality, rock mass dilation angle is generally approximated as one-quarter to one-eighth of the rock mass

friction angle, except for fault zones or low quality rock masses where dilation angle is zero; and

Poisson’s ratio is estimated using laboratory testing results or empirical estimates.

Structural Discontinuity Fabric, Properties and Joint Constitutive Models

Peak discontinuity orientations and variability are defined from lower hemisphere equal area projections of structural mapping ororiented core structural data;

Discontinuity spacing is defined from oriented core or structural mapping data;

Persistence and continuity are defined from correlated structural mapping data;

•

•

•

•

••

•

•

•

•

•

•

•

•

•

•

•

•

•

•


3/11


Discontinuity shear strengths are defined from direct shear testing and/or joint profile mapping to derive empirical estimates

based on Joint Roughness Coefficient (JRC) and Joint Compressive Strength (JCS) after Barton and Choubey (6);

Discontinuity conditions are modeled using the Coulomb slip with residual strength constitutive model (Model 5);

Joint normal stiffness(jkn) is approximated as 10% of Em; and

Joint shear stiffness (jks) is approximated from the ratio of bulk to shear modulus multiplied by jkn.

Insitu Stresses and Groundwater Pressures

Insitu stresses are approximated from regional or site testing data, if available. In the absence of stress testing information, insitustresses are assumed to be hydrostatic (i.e., ratio of horizontal to vertical stress equal to 1); and

Groundwater pressures are generally estimated using a series of water tables or pressure distributions if groundwater modeling

results are available.

CASE EXAMPLES

Case Example 1: Anonymous Mine

Case example 1 is from the southwest wall of an anonymous mine (Photo 1). Overall slope heights in the open pit range from 360 to

670m, with plans to deepen the ultimate pit to 750m. The overall slope height of the southwest wall is 390m, with interramp slope angles

of 38 to 40°, defining an overall slope angle of 35°. This case example focuses on back analysis of historical slope conditions on the

southwest wall, but does not address modeling forecasts of future deformation related to mining.

•

•

•

••

•

•

Photo 1 – Southwest Wall of an Anonymous Mine – Looking West

Engineering GeologyThe main rock units at this copper porphyry mine consist of quartz monzonite (QM) and porphyritic quartz monzonite (PQM) that

have intruded a complex Precambrian (PCM) terrain. Up to five modeled mineral zones occur within the deposit, with the majorityof the current pit slopes developed within the hypogene zone.

The structural geology of the deposit is characterized by a predominant major fault orientation that follows a northwest regional strikethat dips steeply to either the southwest or northeast. Another system of major faults strikes northeast and dips steeply to the southeast.The predominant fault trends define orientations susceptible to deep-seated toppling on the southwest wall, while the other system definesrelease surfaces.

Structural relationships represented in the UDEC model were estimated from correlated major faults and structural discontinuity

mapping data. Due to a limited structural database at the time of the study in 2004, only a generalized structural fabric model couldbe developed based on average structural orientations, continuities and spacing. Three discontinuity sets were represented, assummarized in the following:

In-dipping (toppling) faults that dip 75° at an average spacing of 43m;Pitward dipping faults that dip 75° at an average spacing of 38m; and

Pitward dipping joints that dip 40° at an average spacing of 15m.

••

•


4/11


HydrogeologyInterpreted groundwater levels were developed by evaluating historic water levels in exploration drillholes and piezometers installed on

the slope and pit bottom. Groundwater levels are relatively high due to a low horizontal conductivity associated with near-vertical faults

acting as aquitards to groundwater flow. Water levels were interpolated for different periods during mining with draw-down simulated in13 incremental steps to represent water levels achieved with horizontal drainhole drilling.

Rock Mass and Discontinuity Shear Strengths

Table I is a summary of the weighted average geomechanical properties for each geotechnical unit based on geomechanical corelogging, point load index and laboratory testing data. Lower bound disturbed strengths were defined by one standard deviation below the

mean for weighted average core logging parameters.

Peak joint shear strengths are characterized with an effective friction angle ( φ’) of 30° and effective cohesion (c’) of 64 kPa based ondirect shear laboratory testing results. Peak fault shear strengths are defined by a φ’ of 23° and c’ of 40 kPa. Residual shear strengthswere defined with a c’ of zero.

UDEC Model and CalibrationFigure 1 shows the UDEC model geometry for the southwest wall. Mining was simulated with 15m high bench excavations representing

the historic bench-by-bench mining sequence starting in 1991 and leading up to September 2004 with 67 excavations.

Geotechnical Unit Strength

Condition

γ

(kN/m

3

)

RMR/

GSI

σci

(MPa)

mi c’

(kPa)

φ’

(°)Waste Rock Average 19 n/a n/a n/a 0 38

QM II Peak 26 55 73.0 25 822 61.7

(21-40% RQD) Disturbed 50 63.9 25 362 46.7

QM III Peak 26 61 75.0 25 1024 62.9

(41-60% RQD) Disturbed 57 59.2 25 470 51.3

PCM II Peak 26 52 73.4 20 753 59.6

(21-100% RQD) Disturbed 44 67.4 20 291 41.4

Table I – Material Strength Parameters for Case Example 1

Back analysis of September 2004 slope conditions involved seven monitoring locations representing 12 survey prisms near the modelingcross-section. A total of 41 model variations were analyzed by adjusting structural orientation and spacing, prior to achieving calibration

of the actual prism displacements. As seen on Figure 1, reasonable calibration was achieved in the southwest wall UDEC model forhorizontal and vertical displacements and horizontal velocity compared to actual prism displacements and velocities for the period from2000 to 2003. Calibration was achieved with up to 15m of deformation in the upper slope and average monthly model velocities of up

to 75mm/day.

Figure 1 – Back Analysis of UDEC Model (red) versus Actual (grey) Displacements and Velocities for Case Example 1 Showing Contours of Model Horizontal

Displacement


5/11


Case Example 2: West Wall of the Lornex Open Pit, British Columbia, Canada

Case Example 2 is from Teck Resources’ Highland Valley Copper mine in south central British Columbia, Canada. Between 1989 and

1995, mining of the west wall of the Lornex pit experienced up to 45m of complex deep-seated toppling deformation (Photo 2). The

original slope was mined at an interramp angle of 36°. In its final deformed state, the slope comprises an overall slope angle of 29° at

a height of 400m. This case example presents a back analysis of historical slope conditions, but does not present forward predictions of

deformations related to future mining plans.

Photo 2 – West Wall of the Lornex Open Pit in March 2004 – Looking Southwest

Engineering Geology

The west wall occurs mostly in barren, coarse grained Bethsaida granodiorite (BGD) in the upper slope, and altered Skeena quartzdiorite (SQD) in the lower slope. The Lornex Fault Zone (LFZ) is an 80m wide zone of highly fractured and intensely argillically altered

rock that dips west at approximately 80° and defines a lithological contact between BGD and SQD. Other moderately to steeply dipping

faults that trend northeast-southwest occur intermittently throughout the BGD in the hanging wall of the LFZ. The BGD is relatively

competent, but is altered in the vicinity of the fault zones.

Eleven major faults were correlated through the west wall with orientations subparallel to the strike of the slope. Ten of the faults were

characterized by westward dips of 60 to 80° (toppling oriented). One fault (W1-1) dips moderately to the east at dips of 35 to 55°, defining

potential for shearing behind the slope. For the purposes of developing a structural fabric model, structural discontinuity data collected

between 1980 and 1986 was assessed. Although this historical database of 386 fault and 206 joint set measurements represented a

much smaller database than exists for the current slope, it allowed the original structural orientations, spacing and continuity relationships

to be reconstructed prior to significant deformation. Structural fabric orientations were represented by 75° dipping faults dipping both

into and out of the slope. Average fault spacings of 30 and 15m were represented to the west and east of the LFZ, respectively, but were

not extended into the footwall of the W1-1 Fault due to a suspected domain change at the fault boundary. Variability in spacing was notapplied due to limited data.

Hydrogeology

Historical groundwater levels on the west wall were interpreted from drainhole flow and piezometric monitoring records and trends.

Groundwater levels are generally high, despite installation of numerous horizontal drainholes during slope development, due to the low

conductivity of the rock mass and compartmentalization of groundwater between steeply west dipping faults. Groundwater levels in

the UDEC model were simulated in four steps starting from original levels and were incrementally lowered to 1995 conditions.


Table II is a summary of the weighted average geomechanical properties for each geotechnical unit defined from geomechanical core

logging, point load index and laboratory testing data. For fault zones, only disturbed (residual) strengths were applied. Discontinuity shear

strengths for faults were estimated from historical laboratory testing data and back analysis results. Peak and residual φ’’s of 21° were

applied to faults, with peak and residual c’’s of 50 and 0 kPa, respectively.


6/11


Geotechnical Unit Strength Condition γ

(kN/m3)

RMR/

GSI

σci

(MPa) mi

c’

(kPa)

φ’

(°)

BGD Peak 26 51 55.5 28 673 59.8

Disturbed 372 46.7

SQD Peak 26 43 37.9 28 498 55.2

Disturbed 261 38.4

LFZ and BGD Peak 24 30 21.6 28 144 25.2

Fault Zones Disturbed 144 25.2

SQD Peak 24 32 22.3 28 156 26.8

Fault Zones Disturbed 156 26.8

Table II – Material Strength Parameters for Case Example 2

UDEC Model and CalibrationFigure 2 shows the UDEC model geometry incorporating the engineering geology, rock mass strength and hydrogeology conditions

described above. Mining was simulated with 56 individual 12m high bench excavations for slopes excavated up to the current slopeat the end of 1995. An initial pit was first excavated according to a previous layback slope profile from the 1970’s.

Back analysis of current slope conditions was carried out in an iterative process by varying discontinuity orientations and spacingsuntil slope deformations were closely simulated for nine model monitoring histories corresponding to 13 prism locations on the slope. Atotal of 44 models were run before calibration of slope deformations was achieved. Figure 2 shows model (red) and actual (grey) prismdisplacements and velocities versus time for nine monitoring levels on the slope. Reasonable correlation was achieved between model andactual displacements and velocities. About 45m of horizontal displacement is indicated for mining of the current slope up to 1995.

Figure 2 – Back Analysis of UDEC Model (red) versus Actual (grey) Displacements and Velocities for Case Example 2 Showing Contours of Model Horizontal

Displacement


7/11


Modeled velocities were plotted in two ways as follows: i) incremental displacements divided by the period estimated from approximatedates for each excavation (solid red lines); and ii) incremental velocities calculated assuming a mining rate of 120 days per bench (dashedred lines). Both plotting methods provide reasonable calibration of actual velocities experienced during mining. Average model velocitiesup to 50 mm/day are indicated by the UDEC model as compared to a maximum actual daily velocity of greater than 100mm/day for one

monitoring period.

Case Example 3: Northeast Wall of the Betze-Post Open Pit, Nevada, USA.

Case Example 3 is from the northeast wall of the Barrick Goldstrike Betze-Post open pit (Photo 3). This example involves reconciliationof predicted displacements from a UDEC model that was developed in 2001 to forecast complex slope deformations that were occurringduring Northeast Layback mining. These deformations occurred between 2001 and 2003 in response to deep-seated squeezing in

major fault zones and shearing along a low shear strength silty-clay layer in Tertiary Carlin sediments in the upper slope.

Between 2003 and 2005, following completion of mining, slope deformations continued to occur even after large volumes of wastebackfill had been placed in the pit to stabilize the northeast wall. In early 2006, a numerical modeling study was initiated to investigatethe long-term slope deformation behaviour of the northeast wall in response to backfilling and groundwater level recovery by updating the2001 UDEC model.

Photo 3 – Ultimate Wall of the Northeast Layback (March 2003) – Looking North

Background

A comprehensive description of the engineering geology and slope condit ions on the northeast wall is included in Sharon, Rose and

Rantapaa (7). The reader is referred to the previous document for a detailed description of the 2001 UDEC model development and

calibration. Other than the addition of the actual steepened bench geometry that was mined in the lower slope to maximize ore extraction,

water level rises that resulted from the shut down of perimeter pumping wells, and the placement of in-pit waste backfill, no other changes

were made to the original 2001 calibrated UDEC model. This allowed a reconciliation of predicted versus actual displacements over a

period of about four years following original model calibration.

Comparison of Predicted Versus Actual Encountered Displacements

Figure 3 is a plot of the northeast wall UDEC model showing the predicted versus actual displacements at two monitoring locations

behind the pit crest. As shown on the upper left graph on Figure 3, model predictions in red provide close agreement with actual prism

slope distance monitoring displacements in blue. Total vector prism displacements in grey are less comparable due to monitoring station

resets in the data.


8/11


Figure 3 – Case Example 3 UDEC Model Showing Predicted (red) versus Actual (blue and grey) Prism and GPS Displacements (inset graphs) and Contours of

Model Horizontal Displacements over Four Years Following Original Model Calibration

On the upper right graph on Figure 3, monitoring data from a GPS monitoring grid (grey) located 225m behind the pit crest is seen

to provide close agreement with predicted model displacements (red). During mining, both actual and model displacements follow a

subsidence trend, then following mining, approximately 6 cm of ground rebound is both predicted and documented. These results provide

a compelling example of the capabilities of UDEC as a predictive design tool, with model predictions remaining accurate up to four years

following original model calibration.

Case Example 4: South Wall of the Betze-Post Open Pit, Nevada, USA

Case Example 4 is from the south wall of the 11th West Layback at the Barrick Goldstrike Betze-Post pit (Photo 4). This case history

involves both the calibration of complex slope deformations using UDEC, as well as reconciliation of predicted model results with actual

slope monitoring data. Mining on the south wall of the 11th West Layback began in 2006 and was completed in late May 2009. Interramp

angles range from 38 to 44° defining an overall slope angle of 34° at a height of 450m.

Photo 4 – South wall of the 11th West Layback (September 2008) – Looking East


9/11


Background

In late 2006, mining on the 11th West Layback exposed a low shear strength lithological contact approximately 100m below the pit

crest. In September 2007, the S-07-B failure occurred after a series of smaller instabilities related to the exposure of the contact. Failure

debris was contained on stepouts at the 4960 and 4840 levels that were implemented to control raveling and rockfall (Photo 4). As

mining continued, large-scale slope deformation began to result in tension cracking across the entire width of the south wall and slope

displacements began to follow a relatively slow, but consistent acceleration trend. In June 2008, after approximately one year of continued

acceleration, a UDEC modeling study was initiated to investigate the long-term stability of the south wall and to optimize ore extractionwhile maintaining adequate slope stability.

Engineering Geology

The Devonian metasedimentary units exposed on the south wall consist of fractured argillite, sandstone and interbedded siltstone of

the Rodeo Creek (DRC) Formation, and limestone, siltstone and related rocks of the Popovich (DP) Formation. The contact between the

DP/DRC formations comprises low shear strength carbonaceous black claystone (CBC). Bedding orientations within the metasedimentary

stratigraphy dips adversely toward the pit at an average dip of about 15°.

Structural discontinuity relationships for the various lithological units represented in the UDEC model were developed from open pit

structural mapping data. The average dips of the main structural sets were estimated from peak orientations on lower hemisphere equal

area projections for each structural domain. Average spacing and continuity relationships for each structural set were derived from

open pit structural mapping data, field observations and adjustments during model calibration. Table III summarizes the various pitward

(north) and in-dipping (south) structural sets incorporated in the UDEC model. For each geotechnical domain, the average and modeled

variability of the dip, spacing and continuity of each discontinuity type (i.e., faults, bedding and joints) are provided.

Domain Pitward Dipping Structures In-Dipping Structures

Type Dip Spac. Cont. Type Dip Spac. Cont.

(°) (m) (m) (°) (m) (m)

Buzzard- Fault 80 23±3 1500±10 Fault 75 23 1500

DRC Bedding 15±1.5 6±1.5 200±100 ±3 ±3 ±10

Buzzard- Fault 40±3 46±23 200±50 Joint 75 23 150

DP Joint 80±3 23±3 200±100 ±3 ±3 ±50

Bedding 15±3 12±3 200 ±100

West Joint 80±3 23±3 200±100 Fault 75 46 1500

Bazza-DP Bedding 15±3 12±3 200±100 ±3 ±3 ±10

Table III – Summary of UDEC Model Discontinuity Orientation. Spacing and Continuity for Case Example 4

Hydrogeology

Deep perimeter well dewatering at the Betze-Post pit has resulted in depressurized conditions in the metasedimentary units on the

south wall to approximately 160m below the base of the pit. Perched groundwater above the CBC layer was simulated with a water table

12m above the DP/DRC contact. In the DP-UM unit below the contact, a constant pore pressure of 120 kPa was modeled to simulate the

strong downward gradient towards fully depressurized conditions in the DP units below.


Table IV is a summary of the weighted average geomechanical properties for each geotechnical unit from 2007 geotechnical drilling

and laboratory testing results. For fault zones, disturbed strengths incorporated a cohesion of half the peak strength. Discontinuity

shear strengths for joints and bedding consisted of peak φ’’s of 30 to 32° and a residual φ’ of 25°. Faults were assigned a peak and

residual φ’ of 20°. Peak and residual c’’s of 48 and 0 kPa, respectively, were applied to all discontinuity types.


10/11


Geotechnical Unit Strength Condition γ

(kN/m3)

RMR/

GSI

σci

(MPa) mi

c’

(kPa)

φ’

(°)

Lower RC Peak 23.5 46.1 24.1 12 369 46.0

Disturbed 186 29.6

DP-UM Peak 25.1 50.6 38.0 17 523 53.7

Disturbed 278 39.3DP-SD Peak 25.1 62.3 37.4 16 731 55.7

Disturbed 411 45.6

Lower DP Peak 25.1 62.7 46.8 7 997 49.5

Disturbed 475 39.7

CBC Contact Peak 22 - - - 48 25

Disturbed 48 16

Faults Peak 22 - - - 48 20

Disturbed 24 20

Table IV – Material Strength Parameters for Case Example 4

UDEC Model and Calibration

Figure 4 shows the UDEC model geometry incorporating the engineering geology, rock mass strength and hydrogeology conditions

described above. Mining was simulated in UDEC with 78 individual 12m high bench excavations for slopes excavated during two previous

laybacks and up to the end of the 11th West Layback in May 2009.

Back analysis of current slope conditions was carried out in an iterative process by varying model input parameters until slope

deformations were closely simulated for nine model monitoring histories corresponding to 13 prisms on the slope. By adjusting structure

continuity, spacing and shear strengths, a total of 22 model variations were run before calibration of slope deformations was achieved.

Figure 4 shows model predicted (red) versus actual prism displacements and velocities (grey) used for back analysis.

UDEC Model Prediction and Reconciliation

The results of the UDEC modeling study indicated that slope accelerations, that had been occurring for approximately one year prior to

mid August 2008, would begin to decelerate in mid to late September 2008, and would continue to decelerate until mining was completed

on the south wall. In addition to this, the modeling results indicated that the interramp slope angle could be steepened from 40 to 44°

in the lower slope, without having a significant impact on overall slope stability. This was supported by a UDEC factor of safety of 1.16

for the final slope, which was corroborated by parallel anisotropic limit equilibrium analyses that defined a factor of safety of 1.18, as

summarized in Armstrong and Rose (8). These results were predicated by improved rock mass and structural conditions in the West

Bazza-DP structural domain in the lower slope, as well as reduced mining excavation rates in ore at the pit bottom.

Figure 4 – Case Example 4 UDEC Model Showing Modeled (red) versus Actual (grey) Displacements and Velocities, and Contours of Model Horizontal

Displacement


11/11


Based on modeling predictions, average monthly slope monitoring threshold levels were developed using average warning and hazard

threshold velocities of 4 and 6 mm/day, respectively. These threshold velocities were selected to maintain overall slope displacement

magnitudes below an empirical total threshold of about one metre that had been empirically derived from a number of progressive bedding

shear failures that were documented during slope development.

As seen on Figure 4, close agreement exists between the model ing predictions made for horizonta l displacement and velocity. Model

vertical displacement for the upper monitoring level overestimates the actual monitored vertical displacements. However, a much

better match occurs for the modeled versus actual vertical displacements for the lower monitoring location. Predicted deceleration for

monitoring points closely follows actual deceleration defined by the slope monitoring data. In fact, the maximum prism velocity trend in

the upper graph almost precisely matches the predicted velocity trend starting at the end of the calibration period.

Mining on the south wall of the 11th West Layback was successfully completed in late May 2009 with average monthly threshold

monitoring rates remaining below the hazard level of 6 mm/day, but periodically exceeding the warning threshold level of 4 mm/day

for short durations in local areas of the slope. Since mining was completed, in-pit waste backfill is being placed at the toe of the

slope to improve the long-term stability of the south wall.

CONCLUSIONS

The four case studies presented in this paper provide examples of a detailed UDEC modeling methodology that approximates the

actual stress-strain path of a slope by simulating bench-by-bench mining with strain-softening criteria. Through a process of careful

reconciliation between model displacements and actual slope monitoring data, detailed model calibration is achieved, thus allowing

forward modeling predictions to be made with greater confidence. By simulating the bench-by-bench mining sequence, predictions of

incremental displacements and velocities are made possible. In the latter two case examples presented, the modeling predictions have

stood the test of time with actual slope performance matching closely with model predictions for periods of one to four years after original

calibration. In all cases a high level of input data was required.

Although not discussed directly in this paper, the percentage of yielded finite difference zones defined by undisturbed-disturbed strain

softening relationships, and peak-residual relationships defined by model discontinuity slip, can be used to approximate the zonation of

Hoek-Brown D factor as a function of depth for use in limit equilibrium analysis. An example of comparative limit equilibrium modeling to

the UDEC model presented in Case Example 4 is included in Armstrong and Rose (8).

ACKNOWLEDGEMENTS

The authors of this paper would like to thank Barrick Goldstrike Mines Inc., Highland Valley Copper and the anonymous mining company

for their permission to include the background information and UDEC modeling results presented in case examples from each mine site.

Particular thanks are given to J. Armstrong, K. Testerman, M. Rantapaa, R. Sharon, M. Penick, D. Merber, L. Shwydiuk, S. Daly, S. Fortin, P.

Witt, W. Newcommen, C. Maggs and M. Yan for engineering and geological support during the numerical modeling investigations and/or

efforts in obtaining permission to publish the information included in this paper.

REFERENCES

1. Itasca, 2004. Universal Distinct Element Code (UDEC) User’s Guide, Version 4.0. Itasca Consulting Group, Inc., Minneapolis,

Minnesota, November.

2. Hoek, E. 1994. Strength of rock and rock masses, ISRM News Journal, 2(2), 4-16.

3. Bieniawski, Z.T., 1976. “Rock Mass Classification in Rock Engineering.” Proceedings Symposium on Exploration for Rock Engineering,

ed. Z.T. Bieniawski, Balkema, Rotterdam, pp. 97-106.

4. Hoek, E., Carranza-Torres, C. and Corkum, B., 2002. “Hoek-Brown Failure Criterion – 2002 Edition.” Proc. North American Rock

Mechanics Society Meeting, Toronto, July, 7p.

5. Serafim, J.L. and Pereira, P., 1983. “Considerations of the Geomechanical Classification of Bieniawski.” Proceedings International

Symposium on Engineering Geology and Underground Construction, Vol. 1, Balkema, Rotterdam, pp. 1133-1142.

6. Barton, N. and Choubey, V., 1977. “The Shear Strength of Rock Joints in Theory and Practice.” Rock Mechanics, Vol. 10, pp. 1-54.

7. Sharon, R., Rose, N. and Rantapaa, M., 2005. “Design and Development of the Northeast Layback of the Betze-Post Open Pit.”

Proceedings, SME Annual Meeting, Salt Lake City, Utah, Society for Mining, Metallurgy, and Exploration, Inc., Pre-print 05-09, 10p.

8. Armstrong, J. and Rose, N.D., 2009. “Mine Operation and Management of Progressive Slope Deformation on the South Wall of theBarrick Goldstrike Betze-Post Open Pit.” Proceedings of the Slope Stability 2009 Conference, Santiago, November.

rose paper

Documents