ARTICLE IN PRESS

International Journal of Rock Mechanics & Mining Sciences 44 (2007) 308–320
www.elsevier.com/locate/ijrmms

Technical note

Forecasting potential rock slope failure in open pit mines
using the inverse-velocity method
N.D. Rosea, O. Hungrb, 
a

Piteau Associates Engineering Limited, 215-260 West Esplanade, North Vancouver, B.C., Canada
Department of Earth and Ocean Sciences, University of British Columbia, 6339 Stores Rd., Vancouver, Canada

b

Accepted 28 July 2006
Available online 2 October 2006

Keywords: Inverse-velocity; Displacement monitoring; Slope failure prediction; Contingency planning

1. Introduction
Assessment of rock slope failure mechanisms requires an
understanding of structural geology, groundwater and
climate, rock mass strength and deformability, in situ
stress conditions and seismicity. Stress relief associated
with mining excavation leads to elastic rebound and
ground relaxation displacements that dissipate with time,
a process that is often referred to as time-dependent
deformation [1,2]. With continuing excavation, regressive
slope displacements may occur in a cyclical accelerating/
decelerating fashion. As strain levels increase, strain
softening may lead to plastic (non-recoverable) deformation and progressive failure development [3]. Displacement
rate (velocity) is commonly considered the best indicator of
the failure process.
Monitoring is used in mines in order to anticipate
possible acceleration or failure of a moving slope mass.
Available instruments include precise survey stations and
prisms, wire and rod extensometers, inclinometers, tiltmeters, Global Positioning System (GPS) devices and
geophones to record the intensity of ground noise.
Comprehensive descriptions of surface and subsurface
monitoring, data collection and assessment methods are
included in Dunnicliff [4], Turner and Shuster [5] and
Wyllie and Mah [6]. The common approach towards
interpretation of monitoring data is to convert measurements to rates (velocities), assuming that, in general, a
slope failure will be preceded by increasing rates of
displacement, strain or micro-seismic activity.
 Corresponding author.

E-mail address: oHungr@eos.ubc.ca (O. Hungr).
1365-1609/$ - see front matter r 2006 Elsevier Ltd. All rights reserved.
doi:10.1016/j.ijrmms.2006.07.014

The inverse-velocity method, developed by Fukuzono [7]
in 1985, provides a useful tool for interpretation of
instrument data with the objective of anticipating eventual
slope failure. Astonishingly, even though this approach
was developed based on laboratory tests more than 20
years ago, it does not appear to have been applied for realtime slope failure prediction in the mining industry until
2001 when it was used to predict the first of three largescale slope failures presented in this paper. Experience with
the inverse-velocity approach for large-scale slope movements in poor and fair quality rock masses, has led to
accurate prediction of three large failures ranging in size
from 1 to 18 million cubic metres (M m3). This paper
presents the data and methodology used in these case
histories, but also provides more general discussion of the
inverse-velocity method as a tool for interpreting displacement monitoring results, its advantages and limitations.
The original examples presented here display kinematic
behaviour that is remarkably consistent, making the
application of the method seem rather simple. The authors
recognize that such conditions do not always exist. For this
reason, a detailed discussion has been included of the types
of variation of displacement rates that can precede failure
of large rock slides. The discussion is illustrated by typical
examples drawn from the published literature, involving
mine slopes as well as natural rock slopes.
2. Inverse-velocity method
The concept of inverse-velocity for predicting slope
failure time was developed by Fukuzono [7] based on
previous Japanese work and on large-scale well-instrumented laboratory tests simulating rain-induced landslides in

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309

co-exist and interact, as described in the following
paragraphs (see also [11]).
INVERSE VELOCITY (1/V)

3.1. Measurement error and random ‘‘noise’’

Failure

t0

t

tf

TIME
Fig. 1. Inverse-velocity versus time relationships preceding slope failure—
after Fukuzono [7].

soil. The conditions simulated in the laboratory were
considered to be characteristic of accelerating creep (i.e.,
slow continuous deformation) under gravity loading.
When the inverse of observed displacement time rate
(‘‘inverse-velocity’’) was plotted against time, its values
approached zero as velocity increased asymptotically
towards failure. A trend-line through values of inversevelocity versus time could be projected to the zero value on
the abscissa (x-axis), predicting the approximate time of
failure, as shown in Fig. 1. Fukuzono presented three types
of plots fitted to the laboratory data (i.e., concave, convex
or linear), defined by the following equation:
V  1 ¼ ½Aða   1Þ 1=a 1 ðtf   tÞ1=a 1 ,

(1)

where t is time, A and a are constants and tf is the time of
failure. In the laboratory measurements preceding failure, a
was found to range between 1.5–2.2. As shown in Fig. 1,
the curve of inverse-velocity is linear when a ¼ 2, concave
when ao2 and convex when a42. Based on the results of
laboratory testing, Fukuzono concluded that a linear trend
fit through inverse-velocity data usually provided a reasonable estimate of failure time, shortly before failure.
Several authors showed theoretically that, given ductile,
accelerating creep occurring under constant effective stress
conditions in soil, rock and other materials, the inversevelocity plot would in fact be expected to be linear [8–10].

In large open pits, considerable distances may be
required to survey prisms in the direction opposing slope
movement. Optical refraction and diurnal temperature and
pressure effects can result in appreciable error, even with
the most accurate monitoring systems. A certain amount of
filtering is required to differentiate displacement measurements and obtain estimated movement rates, free of
‘‘noise’’. Unfortunately, no general rule regarding the
degree of filtering can be given, as it depends on the
measurement time interval, as well as the type and quality
of the measurements. A reasonable way to approach this
issue, used in Section 4, is to analyse a time series of
measurements to a fixed target positioned at a distance
similar to the survey prisms and determine the optimal
filtering method by trial and error to remove random
variation, without concealing trends.
The simplest filtering, used for the data reported in
Section 4, averages the displacement rate over the last
several (‘‘n’’) readings from a densely sampled time series.
Another method uses linear regression analysis of groups
of measurement points, beginning with the most recent
measurement and counting backwards. The two alternative
algorithms are described in the Appendix A. With either
method, the degree of filtering increases as the chosen
length of interval and number of included measurements
increase. When applied to a fixed reference point, the
corrected displacement rate should tend to zero. When
applied to a group of slope measurements, it will give the
estimated current displacement rate (velocity).
Provisions can also be used to reduce the effect of
instrument error, including:

 
 
 

measurement of slope movements at approximately the
same time of day to reduce diurnal effects;
minimizing the number of surveyors to reduce the
influence of operator error;
using only displacement readings measured in the line of
sight or ‘‘slope distance’’, thereby reducing the influence
of horizontal and vertical angular error of a total
station, which tends to be greater. This is not meant to
diminish the importance of also deriving complete
movement vectors that are useful in aiding interpretation of the movement mechanism. Also, in some cases,
the dominant vector component may not coincide with
the sight distance (e.g., vertical).

3. Variation of displacement rates preceding slope failure
Fukuzono’s experiments were carried out using model
sand slopes under closely controlled laboratory conditions
in a rainfall simulator. Obviously, such conditions rarely
exist in natural or mining rock slopes. Under typical field
conditions, six types of variation of displacement velocity

3.2. Local movements
A large rock slide rarely moves as a completely rigid
block. Fragments of various sizes, often situated around
the perimeter of a central coherent or semi-coherent mass,

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can be subject to localized movements such as minor slides
or topples, bulging or buckling of beds, rotations and
possibly abrupt, local deformation adjustments caused by
crack opening. The result can be random, chaotic
displacement that is of itself unsuitable for detection of
any large-scale trends. It is not unusual for local movements to contradict the movement trend of the main slide
body, both in space and time. Crosta and Agliardi [11],
dealing with a complex natural rock slope failure comprising both sliding and toppling, present several examples of
chaotic displacement records, obviously representing local
deformations. It is necessary to have a sufficiently large
number and wide distribution of measuring devices to
allow those records affected by local movements to be
identified and separated from records that are more
representative of the overall trend. On-going re-assessment
of the failure mechanism and its relation to the geometry
and structure of the slope is important and this also helps
to optimize the placement of instruments in view to
avoiding confusion caused by local movements.
3.3. Periodic variation
Displacement rates will be affected by periodically
changing factors such as precipitation, snowmelt, freezing
of groundwater inflow or discharge paths, mining activity
and blasting vibration. Periodic changes appear as waviness of the record, both on direct velocity-time plots and
inverse-velocity-time plots, superimposed on the longerterm trend line.
Fig. 2 shows the only published example known to the
authors of failure forecast using the Fukuzono inversevelocity method. The example is the 49 M m3 massive
flexural topple at La Clapiére in the Maritime Alps, France
[12]. The landslide exhibited distinct annual cycles, super-

imposed on a progressive and approximately linear (on the
inverse plot) trend of acceleration. Vibert et al. [12] fitted a
linear trend line to the mean inverse-velocity during the last
two years of observations in mid-1986 and predicted failure
in 1988 or 1989. Target 9 on the slide reached its maximum
velocity of 11 cm day 1 at the low point of the annual cycle
in the fall of 1987. However, by then, an approximately
circular rupture surface developed through the hinge zone
of the toppling, the cumulative displacement approached
100 m, the toe thrust into the soil deposits of the valley
floor and the slide began to self-stabilize [13]. The
movement rate trend reversed at this point, although the
seasonal waves continued.
Another example of a record characterized by cyclic
variation, this time in a shorter time frame, is the 6 M m3
wedge failure at Liberty Pit in Utah, described by [3] and
shown in Fig. 3. A change in trend was observed at 40 days,
corresponding to the onset of the failure process (termed
‘‘progressive’’ stage by Zavodni and Broadbent [3]). The
prominent one to two-week cycles coincided with blasting
activity in the pit and were superimposed on a concave trend
that, nevertheless, pointed to the eventual failure date and
became approximately linear during the last 25 days (Fig. 3c).
Fig. 3 shows that the cycling variation pattern is easier to
interpret on the inverse-velocity plot. The pattern is clear
enough on the direct velocity-time plot (Fig. 3a) and
indicates very significant accelerations in response to
blasting vibration at the beginning of each cycle. However,
only the inverse-velocity plot (Fig. 3b) clarifies the
significance of these accelerations: the amplitude of the
cycles is of the same order as the distance to the horizontal
axis, indicating that each period of blasting had the
potential to trigger failure. The overall trend is also easier
to extrapolate on the inverse plot, as it approaches linearity
within the final weeks before failure.
3.4. Displacement rate trends
While the above-described phenomena complicate the
picture, in many cases a clear trend can be discerned that
allows prediction of the failure date to be made. The
original examples presented in Section 4 later in this paper
illustrate cases in which the trend is dominant and
consistent, over-riding all other types of variability. In
these cases, the trend was also approximately linear over
periods of several days to several weeks preceding failure.
Crosta and Agliardi [11] re-analysed rock slide monitoring
data reported in the literature using a non-linear curve
fitting technique based on Eq. (1), applied over a variety of
time periods and found that for five cases out of seven the
trend line was approximately linear (a 2), while it was
concave (ao2) for the remaining two cases.

Fig. 2. Long-term inverse-velocity plot of displacements, Target 9 on the
La Clapiére slide (data from [12]). The straight dashed line is the
prediction fit used by Vibert et al. [12]. The cross symbols are subsequent
measurements [13].

3.5. Trend changes
A linear inverse-velocity versus. time trend may well be
fundamental for progressive creep failure of rock and other

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An excellent example of a failure process controlled by
observable external factors is the 1963 Vaiont landslide
[14,15]. Fig. 4 summarizes the history of observations over
the last 2 years preceding the slide, based on data presented
by Müller [14]. The time series plotted include precipitation
(a), water level in the reservoir (b), displacement rate (c)
and its inverse (d). The last graph shows that reasonably
systematic trends can be observed, but only within certain
discrete ‘‘compartments’’ of the record. The first acceleration, culminating at 400 days (October, 1962) is clearly
influenced by the second episode of reservoir filling, but
was probably also aggravated by the heavy precipitation at
360 and 370 days (late October, 1962). The trend reversed
with coincident reservoir lowering and decreased precipitation. It is interesting to note from Fig. 4d that a failure
warning of approximately 7 days could have been issued at
that time. The warning would have been subsequently
cancelled, once the trend reversal was confirmed.

Fig. 3. Displacement velocity (a) and inverse-velocity (b) plots from the
liberty pit mine failure (data from [3]), (c) enlargement of the final 25 days
inverse-velocity plot.

materials [9], provided that the failure has a ductile
character and that there are no external conditions
influencing the process. However, the latter condition is
rarely satisfied in rock slopes. The form of any observed
movement trend can be influenced by changes in conditions
occurring in the background. The changes may be sudden,
such as an earthquake or a blast-related shaking episode
that can damage a key element in the structure of a
potential rupture surface, triggering accelerating creep
(cf. Fig. 3 at 40 days). At other times, a change from a
slow, regressive movement trend into progressive accelerating creep can occur without an obvious trigger [3].
A trend change can also set in gradually, as a result of
varying climate or drainage conditions, infiltration of water
into tension cracks, change in slope geometry due to ongoing excavation and similar.

Fig. 4. Synchronized time series of observations over two years before the
catastrophic failure of the Vaiont Slide (data from [14]): (a) precipitation
over 10-day periods; (b) elevation of reservoir water surface; (c)
displacement velocity and (d) inverse-velocity. Vertical lines 1–3 mark
trend changes induced by reservoir filling and precipitation. The arrow
shows the time of failure on October 9, 1963.

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A slightly concave accelerating trend began with the
third cycle of reservoir filling at 520 days, its beginning
marked by the vertical line number 1 on the figure (May,
1963). Its concavity may reflect the convex shape of the
filling curve within this period. A distinct reduction in the
slope of the trend line occurred when the filling stopped
(vertical line 2). The new, slower trend continued for 50
days, but was sharply interrupted by the arrival of heavy
rains at 650 days, marked by line 3 (August, 1963).
The new trend turned abruptly towards the axis, moderated slightly with the desperate attempt to lower the
reservoir during the last 20 days, but then progressed to
failure at 23:39 on October 9, 1963, with well-known
catastrophic consequences. The trend of the final 50 days
could be reasonably well represented by a linear fit [16].
These monitoring results lend further support to the
conclusion of Hendron and Patton [15] that the final
trigger was a combination of high-reservoir level and high
precipitation.
Not all processes influencing the shape of the inversevelocity graph can be as easily visualized as those at Vaiont
and some driving factors of this type may remain hidden.
However, this case history illustrates that attempting to
find a ‘‘universal’’ equation to fit a trend over long periods
of time is unlikely to succeed. Any ‘‘fit’’ to the inversevelocity curve is valid only within its specific compartment
and must be modified as soon as a trend change is
confirmed. The authors recommend linear extrapolation of
data over varying lengths of time, looking for a consistent
trend and noting and re-evaluating any departures from it,
combined with observation of various controlling factors
and the developing failure mechanism. In other words, firm
‘‘prediction’’ of the failure time probably cannot be made
over a long period of time. But the inverse-velocity method
provides a powerful means to examine developing trends,
make and systematically revise interim predictions and
rapidly and quantitatively assess the significance of
apparent trend changes.
3.6. Brittle failure
All of the above discussion relates to cases where largescale, ductile failure occurred, involving high stress levels
relative to rock strength. Brittle rock failure in tension or
shear may be a controlling factor in other cases, especially
at lower stress levels in smaller slides and involving strong
rock mass. A good example is the 1971 slide of a 50,000 m3
wedge of quartzitic argillite at Libby Dam in Montana [17].
A set of extensometer displacement records reproduced in
Fig. 5 shows three step-like, nearly instantaneous displacements on centimetre scale over a four year period, followed
by sudden failure. The failure mechanism involved shearing
of a highly strength-asymmetric wedge comprising smooth
and rough discontinuities, combined with tensile failure
at the head of the slide. The timing of this type of
failure cannot be anticipated by means of displacement
monitoring.

Fig. 5. Displacement record of four extensometers on the Libby Dam
abutment wedge failure (data from [8]). The lines end on the date of
sudden, extremely rapid failure of the wedge in early 1970.

4. Case examples of predicted failure time using inversevelocity
Three case examples are presented from two large open
pit mines that illustrate the use of inverse-velocity for
predicting failure time. Examples 1 and 3 occurred in 2001
and 2005 at Barrick Gold’s Betze-Post open pit mine
located in the Carlin Trend, northeastern Nevada. Example 2 occurred at another large mining operation in western
United States. Each of these cases involved instabilities
that were monitored using manual and robotic total station
survey of reflective prisms, and wireline extensometers. In
each case, failure predictions approximated the failure time
to the day of the actual failure. Predictions of failure time
for the 1, 2 and 18 M m3 failures were forecasted 2 weeks, 5
days and 3 months prior to failure, respectively.
At both mining operations, survey distances of over 1 km
resulted in accuracies in survey measurements of about
710–15 mm, or greater. As a result, different methods of
data smoothing were required to provide reasonable
resolution of slope movement trends.
4.1. Case Example 1
Example 1 involves a 550 m high slope failure on the
southeast wall of the Betze-Post open pit in August 2001.
The southeast wall is situated in Jurassic granodiorite rocks
that are argillically (clay) altered along major gouge-filled
faults and shear zones. As a result, groundwater is highly
compartmentalized and has a significant influence on slope
stability. A description of the structural geology and
hydrogeology of the southeast wall is included in [18].
Complex wedge deformations on the upper southeast
wall began as early as 1993. The failure mechanism

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involved shearing along deep wedge intersections that
plunged moderately towards the open pit, causing upward
heaving along shallow in-slope dipping faults that were
oriented obliquely to the slope face. Stability analyses were
carried out to define the required slope geometry to
maintain a minimum factor of safety (FOS) of 1.2 under
partially depressurized conditions. Between 1993 and 1998,
slope stability was managed on the First East and Second
East Laybacks on the southeast wall with a combination of
engineered waste rock buttresses, offload cuts, step-outs,
horizontal drain holes and vertical wells.
In 1998, a re-design of the southeast wall was required
due to instability that had occurred in two adjacent areas
of the southeast wall. A detailed description of the redesign for one of those areas is presented in [18]. As part of
the 2SE Layback design, 12 nested complex wedges ranging
in size from approximately 1–10 M m3 were analysed using
a three-dimensional version of Bishop’s simplified method
[19] to satisfy a minimum FOS of 1.2 for the ultimate slope.

313

Approximately 6 months after the start of the 2SE
Layback, slope deformations began to develop in the mid
to upper slope and continued for another two years,
through to completion of the ultimate wall. Nine survey
prisms were used to monitor the main complex wedge area
with locations shown in Fig. 6. Total displacements of up
to 1 m were encountered in the upper slope over the course
of mining, defining an average movement rate of about
2 mm day 1. Slope deformations responded cyclically to
mining and seasonal precipitation, but remained regressive
throughout mining. No remedial changes were required to
the 2SE Layback mine plan and ore recovery was
successfully completed in January 2001 to one additional
bench below the final bottom target elevation.
Approximately 5 months after mining was completed,
the southeast wall began to exhibit signs of progressive
failure development, as was recognized from weak accelerations in the slope monitoring data. Inverse-velocity
graphs were developed and the potential slope failure time

Fig. 6. Example 1: Map of upper southeast wall showing complex wedge geometries, prism locations (solid dots), mean azimuth and plunge angles of
displacement vectors (short solid lines) and plane intersections of the interpreted multi-planar complex wedge rupture surface (dashed lines).

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1.0

35

Predicted velocity curv es (based
on inverse-velocity fits ) compared
with actual velocity data

VELOCITY (cm/day)

30
0.9

INVERSE VELOCITY (days/cm)

0.8
0.7

25
20
15
10
5

0.6

0
-45

0.5

-40

-35 -30 -25 -20 -15 -10 -5
TIME BEFORE FAILURE (DAYS)

0

0.4
S-189
S-190
S-205
S-219
S-220
S-221
S-249
S-262
S-265

0.3
0.2
0.1

Regression coefficient (R2) =99%
for all inverse-velocity fits

0.0
45

40

35

30

25

20

15

10

5

0

TIME BEFORE FAILURE (DAYS)
18-Jul-01

25-Jul-01

1-Aug-01

8-Aug-01

15-Aug-01

22-Aug-01

29-Aug-01

DATE
Fig. 7. Example 1: Plot of 6-day average inverse-velocity and velocity (predicted curves versus actual values on inset graph) versus time for nine prisms
(time 0 was the observed time of failure). Prism numbers correspond to Fig. 6.

was initially predicted to occur approximately 2–3 months
later. As displacement rates increased, a clear inversevelocity trend developed and began to converge on a failure
time of August 29, 2001. Fig. 7 is a plot of inverse-velocity
versus time showing the trends of nine survey prisms
located at various elevations on the slope (Fig. 6) over the
last 6 weeks of data prior to failure. Targets were
monitored using a robotic total station at 2 h intervals.
Data filtering was achieved by calculating six-day average
slope distance velocities to reduce the effects of instrument
error in low-level velocity values (i.e., n ¼ 72 in Eq. (A1) in
the Appendix A). Linear regression was then applied to the
entire data set of inverse-velocities. The regression coefficients (R2) were 99% for all nine prisms, indicating a
consistent, linear trend. The data began to diverge from the
best-fit lines closer to the failure time (Fig. 7). But, since
this was an optimistic change, it was decided to base the
predictions conservatively on projecting the best-fit linear
trends through 2–4 weeks of data rather than adjusting
predictions based on the shorter-term trend.
An 18 M m3 (47 million ton) failure occurred on the
southeast wall of the Betze-Post pit on August 29, 2001.
The failure initiated in a 345 m high section of the upper
bedrock slope. Prior to failure, the maximum overall slope

angle (crest-to-toe) was 271 over a slope height of 450 m.
The failure encompassed an overall slope height of 550 m.
The angle defined from the original crest to the toe was 241.
The failure episode lasted several hours as a series of nested
complex wedge failures and rock avalanches. Fig. 6
illustrates the total vector displacements for nine survey
prisms approximately one week before failure. Following
failure, a maximum total displacement of about 400 m was
estimated for the failure mass. The Fahrböschung angle,
defined from the crest of the back-scarp to the toe of the
landslide deposit, was estimated at 22.51. The failure
occurred on an ultimate pit wall approximately 8 months
after completion of mining and had no adverse impacts on
the open pit mining operation.
4.2. Case Example 2
Example 2 involves a failure of a 365 m high slope, with
210 m of consolidated tertiary alluvial sediments overlying
weathered and altered intrusive bedrock. High groundwater conditions, a highly fractured rock mass and the
occurrence of steeply in-slope dipping faults, resulted in
deep-seated toppling deformations that propagated into
the overlying sediments. Slope deformations had occurred

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0.14

VELOCITY (cm/day)

250

INVERSEVELOCITY(days/cm)

0.12

0.10

200

Predicted velocity curves (based
on inverse-velocity fits) compared
with actual velocity data

150
100
50

0.08
0
15 14 13 12 11 10 9 8 7 6 5 4 3 2 1

0

TIME BEFORE FAILURE (DAYS)

0.06

0.04

0.02

Regression coefficient (R2) = 83 to 99%
for all inverse-velocity fits

0.00
15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

TIME BEFORE FAILURE (DAYS)
Fig. 8. Example 2: Plot of inverse-velocity and velocity (predicted curves versus actual values on inset graph) versus time for five prisms and one wireline
extensometer (line) (time 0 was observed time of failure).

in a regressive fashion in response to mining over a one
year period before signs of progressive failure were
recognized.
Fig. 8 is a plot of data for five survey prisms and one
wireline extensometer, showing linear best-fit trends
projecting to a failure time that was forecasted from one
to two weeks prior to failure. Velocities for five prisms were
calculated based on incremental total vector survey readings. The wireline extensometer was measured at 15-min
intervals via radio telemetry, but velocities were calculated
on a 24-h basis (n ¼ 96) to reduce the effect of error and
instrument resets. The wireline extensometer data provided
the most accurate prediction of slope failure time. The R2
linear regression coefficient for the wireline extensometer
data was 99%, as compared to 83–99% for the five survey
prisms.
Mining activities were successfully stopped with advanced warning of impending slope failure. No adverse
impacts were experienced by the mining operation. The
failure occurred on an interim slope and contingency
planning provided alternate mining faces.
Approximately 1 M m3 (2 million ton) of material from
the upper slope was deposited by the landslide on the
working level, forming a debris lobe that extended
approximately 100 m from the toe of the slope. Prior to
failure, the slope was mined at an interramp slope angle

(IRA) of 441. The head scarp of the failure extended
approximately 50–75 m behind the pit crest, defining a
Fahrböschung angle of 351. Boulders of up to 3 m in
diameter rolled to a maximum distance of 130 m from the
original toe of the slope, but were arrested by a safety
impact berm. The total duration of the failure stage was
several minutes.
4.3. Case Example 3
Example 3 involves a 2 M m3 (5 million ton) failure that
occurred over a 120 m slope height on the southwest wall of
the Betze-Post pit on May 22, 2005. The failure occurred
approximately two weeks after a low shear strength
lithologic contact was daylighted with an average dip of
about 171 towards the open pit. The final trend was
progressive in nature and followed 115 mm of rain in 11
days, and a peak rainfall event of 53 mm in 24 h, 6 days
prior to failure. The failure occurred as a result of the
adverse orientation of low shear strength materials at the
lithologic contact and pore pressures associated with
infiltration of up to 4000 l per minute of surface water in
tension cracks at the pit crest. As shown in Fig. 9,
consistent inverse-velocity trends were defined 4–5 days
before failure, based on 2-day average inverse-velocity
values, based on slope distance survey measurements taken

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0.25
VELOCITY (cm/day)

300

INVERSE VELOCITY (days/cm)

0.20

Predicted velocity curves (based
on inverse-velocity fits) compared
with actual velocity data

200

100

0.15
0
4

3

2

1

0

TIME BEFORE FAILURE (DAYS)
0.10

0.05

Regression coefficient (R2) = 73 to 91%
for all inverse-velocity fits
0.00
4

3

2

1

0

22-May-05

23-May-05

TIME BEFORE FAILURE (DAYS)

18-May-05

19-May-05

20-May-05

21-May-05
DATE

Fig. 9. Example 3: Plot of inverse-velocity and velocity (predicted curves versus actual values on inset graph) versus time for three prisms (time 0 was the
observed time of failure).

at 2 h intervals (n ¼ 24). Prior to this, slope movements had
behaved in a regressive fashion so that only a relatively
short interval provided a consistent trend, which was,
nevertheless used for a failure prediction.
Fig. 10 is a photo approximately 2 months after the
failure. The failure occurred on an interim wall and had no
adverse impacts on mining activities. Remediation included
diversion of surface water near the pit crest and a stepout
at the failure toe. Preceding failure, the slope was mined at
an IRA of 381. The Fahrböschung angle was determined to
be 271, and the maximum runout distance from the original
mined toe was about 90 m. The maximum total displacement of the failure mass was estimated to be about 140 m.
The failure event, observed from a distance, occurred over
a period of about 1 min.
4.4. Case Example 4
A fourth case example is presented that illustrates the use
of inverse-velocity to plan and implement remedial
measures to mitigate possible slope failure, using selected
threshold movement rates based on forecasted failure
times. This example involves a 3–10 M m3 (5–18 million

ton) instability on the northeast wall of the Betze-Post open
pit that developed in late 2000 and continued to deform at
controlled rates, through to completion of mining in
January 2003. During mining, slope deformations were
managed by implementing well placed offloading cuts,
step-outs, mid-slope waste rock buttresses and temporarily
splitting Layback development. A detailed account of the
engineering geology, hydrogeology, design and development of the Northeast Layback is included in [20].
From early May to the end of June 2002, slope
movements within the Midnight/Pats complex wedge
exhibited slope accelerations. Slope movements were
related to low angle shearing along the low shear strength
(i.e., f ¼ 91, c ¼ 35 kPa) Carlin waxy silt unit. Fig. 11 is a
graph of inverse-velocity versus time for six prisms located
on the upper slope. Again, a consistent linear inversevelocity trend was identified, with an indicated potential
failure time of early to mid August 2002.
Based on this observation, a decision was made to
stabilize the slide by unloading the active part of the
complex wedge. Stability analyses carried out using the
three-dimensional Bishop’s simplified method (Fig. 12)
were used to determine the volume of material required to

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stabilize the wedge. It was estimated that up to 360,000 ton
of material would have to be excavated at the pit crest, and
approximately 90,000 ton placed at the daylight level of the

317

Carlin waxy silt unit to stabilize the slope. It was estimated
that up to one month could be required to implement the
remedial measures, without causing significant disruption
to the mine plan. Threshold movement rates were selected
for remediation activities such that construction and
operation would be completed with a two-week buffer
period prior to failure, if it were to occur.
Approximately 3 days after construction started, a
significant trend change could be discerned in the inversevelocity plot of the monitoring data, as the slope began
decelerating. A threshold movement rate of about
2.5 cm day 1, or an inverse-velocity of about 0.4 days/cm,
was used to schedule construction and excavation. As seen
on Fig. 11, remediation continued over a period of about
three weeks until slope displacement rates stabilized to
acceptable levels. Periodically throughout the remainder of
mining, additional crest offloading was required to maintain velocities below threshold values. Fig. 13 is a photo
showing the upper portion of the Midnight/Pats complex
wedge (see Fig. 12) as crest offload mining was taking
place. The Northeast Layback was successfully completed
in January 2003. Failure of the upper northeast wall was
mitigated by implementing the remedial measures discussed above.

Fig. 10. Example 3: Photo of 2 M m3 Southwest wall failure at the BetzePost open pit that occurred May 22, 2005 (case Example 3).

2

Stabilization of Slope Displacements

INVERSEVELOCITY(days/cm)

1.5

Buttress and Offload
Remedial Measures
1

0.5

Regression Coefficient( R2) = 96 to 99%
for all Inverse-Velocity Fits.
0
105 100 95

90

85

80

75

70

65

60

55

50

45

40

35

30

25

20

15

10

5

0

TIME BEFORE FAILURE (DAYS)

1-May-02

16-May-02

31-May-02

15-Jun-02

30-Jun-02

16-Jul-02

31-Jul-02

15-Aug-02

DATE
Fig. 11. Example 4: plot of inverse-velocity versus time for six prisms on the upper northeast wall. Note the trend change in inverse-velocity in response to
slope remediation.

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Midnight Fault

Pats Fault

Carlin waxy silt unit

Scale
100m
Fig. 12. Example 4: Complex wedge on the upper northeast wall of the Betze-Post open pit involving the Midnight/Pats faults and Carlin waxy silt
(3 M m3).

observation that the inverse-velocity plot often approaches
linearity, especially during the final stages before failure,
enhances the utility of the technique. In principle, the same
approach can be used for extrapolating any unstable
phenomena, for example the frequency of micro-seismic
events recorded during the onset of a rock slope failure.
The following general rules are suggested for use of the
method.

Fig. 13. Example 4: Photo of the upper northeast wall of the Betze-Post
open pit showing the location of crest offloading in the Midnight/Pats
complex wedge.

5. Conclusion
Can the time of rock slope failure be predicted from
displacement monitoring results? Obviously, in view of the
mix of review and original data presented in this paper, we
cannot answer an unequivocal ‘‘yes’’. However, Fukuzono’s inverse-velocity method is a powerful tool that
significantly improves our ability to interpret monitoring
data and estimate the timing of the failure process. The
primary advantage of the method is that inverse-velocitytime plots, whether linear or not, are much easier to
extrapolate towards the failure limit than the usual
hyperbolic curves recorded by accelerating deformations
prior to failure, trending to a vertical asymptote. The

(a) The method must not be applied in isolation, without
being accompanied by qualitative observations of slope
behaviour, collection of data and on-going analysis of
the structure of the slope, rock mass condition, stress
and groundwater regime. Displacement monitoring is
only one component of a complex process that
comprises slope stability management.
(b) The method cannot be used for rock slides dominated
by brittle failure, although the identification of such
cases is at present a matter of judgment. Particular care
should be exercised when dealing with relatively small
failures in strong rock.
(c) The monitoring data must be processed to remove the
effects if instrument error (see Appendix A) and
eliminate records distorted by local movements.
(d) Failure forecasting relies on the identification of
consistent trends. The possibility of trend changes,
driven by observable or unknown factors, must always
be kept in mind. Monitoring must be continued as long
as possible prior to failure. The results must be
constantly re-evaluated and any established best-fit
functions must be revised in view of the latest data. If a
stable trend exists, as shown in the four original
examples presented in Section 4, predictions can be

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N.D. Rose, O. Hungr / International Journal of Rock Mechanics & Mining Sciences 44 (2007) 308–320

given and their reliability can be confirmed by
continuing to evaluate the most recent data until the
time of failure. If trend changes occur, the predictions
must be promptly revised. It must be accepted that false
alarms may occasionally be given. ‘‘Optimistic’’ trend
changes can sometimes be deliberately ignored as
shown in Example 1 of Section 4. ‘‘Pessimistic’’ trend
changes must be evaluated and acted upon promptly.
(e) The treatment of cyclic changes depends on the
magnitude of their amplitude, relative to the distance
from the horizontal axis on the inverse-velocity plot. If
the ratio between these two quantities is high, it may be
necessary to assume that the low point of any given
cycle may produce sudden rupture.
(f) Data fitting using non-linear inverse-velocity trend
lines may provide a more accurate assessment of some
longer-term trends, but is more complex, which may
limit practical use. The authors recommend the use of
linear fits, updated on an ongoing basis to identify
trend curvature or to signal the onset of trend changes.
Since trend curvature may result from a particular
manner of change of unknown driving factors, it does
not seem advisable to look for a uniquely shaped
mathematical function. Linear fits facilitate easy
prediction of anticipated displacements, which can
then be used for rapid confirmation of a consistent
trend (or otherwise). The prediction equations are
derived in the second part of the Appendix A.
Possibly for the first time in the published literature,
successful a priori forecasts of large mine rock slope
failures using the inverse-velocity method have been
documented. As a tool helping interpretation of displacement monitoring results, the Fukuzono method appears to
be indispensable for rock slide cases of the kind described
in Section 4 and very helpful for many other cases.
6. Experience database
In an ongoing effort to increase the database of
experience with the inverse-velocity approach, the authors
of this paper would like to extend an invitation for others
to share their experience using this method. If necessary,
confidentiality can be maintained by omitting reference to
the location or source of the data. Correspondence to this
effect can be made via electronic mail to Mr. Nick Rose at
nrose@piteau.com or Dr. Oldrich Hungr at ohungr@
eos.ubc.ca.
Acknowledgements
The authors of this paper are grateful to the management
of Barrick Goldstrike Mines Ltd., Barrick Gold Corp. and
the anonymous mining company that provided permission
to present the slope monitoring data and information
included in this paper. Recognition is given to the staff at
both mines that collected the slope monitoring data and

319

contributed to the sound engineering judgment that was
used in the successful application of this approach.
Particular thanks are given to Bob Sharon, Mark Rantapaa,
Tracey Miller, John Cash, Dave Pierce, Joe Gallegos and
Jorge Armstrong. Critique by an anonymous reviewer has
led to an improvement of the manuscript.
Appendix A
Part 1: Two alternative data filtering methods
Displacement monitoring results are collected as a time
series, t1yti, d1ydi, where ti and di are the most recent
time and displacement, respectively. The simplest filtering
method consists of using only every nth observation to
calculate rate. Thus, the current displacement rate is
vi ¼

d i   d i n
.
ti   ti n

(A.1)

The second method calculates velocity as the slope of a
linear regression line, plotted through the last n observation points:
std
vi ¼
,
(A.2)
s1
where

2
i
1 4X
1
s1 ¼
t2j  
n   1 j¼i n
n

i
X

!2 3
tj 5

and

"
i
X
1
1
std ¼
tj d j  
n   1 j¼i n
n

(A.3)

j¼i n

i
X
j¼i n

!
tj

i
X

!#
dj

.

(A.4)

j¼i n

Part 2: Anticipated displacement data, based on a linear
trend
Linear extrapolation has the advantage of being easy to
execute and to modify when deviations occur. Once linear
trends are identified in slope movement data and fit with a
line with a slope A and intercept v0, predicted failure time
can be calculated as follows:
tf ¼

1
þ t0 .
Av0

(A.5)

Predicted velocities can be plotted versus time by taking
the inverse of Eq. (A.5), such that:
 
  1
1
vPredicted ¼
  Aðt   t0 Þ .
(A.6)
v0
By integrating the above equation, predicted relative
displacements can be calculated as follows:
     
 
  
1
1
d Predicted ¼ ln
  Aðt   t0 Þ .
(A.7)
  ln
v0
v0

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Predicted velocity and relative displacement curves can
be compared to the actual slope monitoring data to
determine whether the predicted trend is stable or whether
changes in slope behaviour may be occurring.
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