application of qslope to assess the stability of rock
TRANSCRIPT
TECHNICAL NOTE
Application of Qslope to Assess the Stability of Rock Slopesin Madrid Province, Spain
Luis Jorda-Bordehore1
Received: 25 August 2016 / Accepted: 24 March 2017 / Published online: 4 April 2017
� Springer-Verlag Wien 2017
Keywords Empirical approach � Rock mass classification �Slope failure
1 Introduction
Geomechanical classification schemes have been employed
formore than 100 years since Ritter (1879) tried to formalize
an empirical approximation for the design of tunnels (Hoek
2007). These rock mass classification systems are of great
help at preliminary stages of a project, when few data are
available (Hoek 2007). Geomechanical classifications
becamemore popular after the 1970s, with the establishment
of Bieniawski’s Rock Mass Rating (RMR) and Barton’s Q-
index (Barton et al. 1974). The main application and reason
for the development of RMR and Q-index was for the pre-
design of underground works such as tunnels, mines and
caverns (Barton and Bieniawski 2008). The RMR classifi-
cation, although initially applied to underground works,
counted with correction factors for slopes and foundations
(Bieniawski 1989). However, the correction factor for slopes
was almost impossible to be applied due to the extreme range
of correction factors and lack of factor definition in practice
(Romana et al. 2015). Variations of the RMR classification
have been applied to slopes, such as the Mining Rock Mass
Rating (MRMR) classification for mining slopes (Laubscher
1990) or the Slope Mass Rating (SMR) for civil engineering
slopes (Romana 1985); these are probably the most utilized
in practice.
There are several other slope classifications, but the
majority remained unpopular and have been restricted to
specific geological environments or countries: Rock Mass
Strength (RMS, Selby 1980), Slope Rock Mass Rating
(SRMR, Robertson 1988), Chinese Slope Mass Rating
(CSMR, Chen 1995), Natural Slope Methodology (NSM,
Shuk 1994), Continuous Slope Mass Rating (Tomas et al.
2007), Fuzzy Slope Mass Rating (FSMR, Daftaribesheli
et al. 2011), Graphical Slope Mass Rating (GSMR, Tomas
et al. 2012) and Slope Stability Rating (SSR, Taheri and
Tani 2010; Taheri 2012). Most of these classifications are
based on RMR (none based on the Q-index). It must be
highlighted that geomechanical classifications do not sub-
stitute calculations and more complex analyses. Limit
equilibrium analysis, numerical methods or kinematic
assessment (Alejano et al. 2010; Stead and Wolter 2015;
Jorda-Bordehore et al. 2016) can be applied, depending on
the case, to large slopes, complex excavation cycles,
reinforcement projects or slopes with very specific insta-
bilities. In the case of large or complex slopes, geome-
chanical classifications and kinematic approach may not be
sufficient on their own: Numerical models (finite element
or difference) are then required to simulate the global
behavior of the slope and to carry out back analysis (Ale-
jano et al. 2010; Stead and Wolter 2015).
In the case of rock slopes in shallow zones of competent
rocks where stability is structurally controlled, kinematic
assessment methods are habitually employed (Jorda-Borde-
hore et al. 2016). In recent years, SMR has become popular
in the analysis of slopes and is a rock mass classification
with an important kinematic—orientation component in
correction factors (Moon et al. 2001). Kinematic methods
can also be combined with SMR (Umrao et al. 2011).
The stability of shallow rock slopes, except if developed
on poor quality rocks, is structurally controlled by
& Luis Jorda-Bordehore
1 Instituto Geologico y Minero de Espana (IGME), Rios Rosas
23, Madrid 28003, Spain
123
Rock Mech Rock Eng (2017) 50:1947–1957
DOI 10.1007/s00603-017-1211-5
stratification, folds, metamorphic foliation or several types
of discontinuities: joints, veins, etc. Stead and Wolter
(2015) pointed out that […] geological structures such as
folds, faults and discontinuities play a critical role in the
stability and behavior of both natural and engineered rock
slopes. Kinematic assessment precisely considers the shear
strength of discontinuities and its orientations regarding the
slope or cavity generated, whether it is a civil or mining
engineering work. Besides developing a stability study,
kinematic assessment enables the disposition of the nec-
essary reinforcement and there are references for its uti-
lization in mining (Lephatsoe et al. 2014) and civil
engineering works (Gupta and Tandon 2015), as well as in
cultural heritage (YalcinKoca et al. 2011).
Barton’s Q-index and Bieniawski’s RMR are the two
most employed geomechanical classifications used for
tunneling design, and until 2015, only RMR had been
applied to slopes. RMR is currently more employed to
slopes thanks to SMR. Nevertheless, the Q-index (applied
to rock mass characterization) could not be applied to
slopes. The Q-index for slopes or Q-slope was conceived
ten years ago, mainly for an immediate application to a
20-km-long hydroelectric project dam-site access road in
the Dominican Republic (Barton and Bar 2015).
However, the first publication on its application only
occurred in 2015 (Barton and Bar 2015). Q-slope was
conceived to be utilized in unsupported road and railway
cuts, individual benches in open-cast mines, but was not
meant to substitute more complex and precise calculations
such as those required in multiple-stage excavation slopes,
inter-ramp or overall slopes in open pits (Bar and Barton
2016), which are carried out employing equilibrium limits,
kinematic or numerical analysis.
Q-slope was created to assess the stability of cut slopes
that develop very fast—e.g., tens of meters per day (Bar
and Barton 2016), in a quick and effective manner. It is a
cost-effective methodology that, in the case of complicated
or very specific slope assessments, should be comple-
mented by kinematic, limit equilibrium or numerical
analyses.
2 Scope
There are no references to the application of the Q-slope
index in Spain. The main objective of the study presented
herein is to apply the Q-slope index to the stability
assessment of several rock slopes in the province of
Madrid, Spain, and verify whether the results of the method
are coherent with what is observed. Studies included
igneous (granite and porphyry), sedimentary (limestone)
and metamorphic (slate, schist and gneiss) rock slopes.
Quarry slopes, small open-pit mines, and road and railway
cut slopes were considered. All analyzed slopes presented
height under 30 m to respect the conditions of the graphic
depicted in Fig. 1 (Barton and Bar 2015). Applicability of
the technique is evaluated, and it is verified whether it
accurately reflects the observed reality of slopes, divided
into stable, quasi-stable and unstable. This study also aims
to contribute to the database built by Bar and Barton
Fig. 1 Slope stability chart using the Q-slope system (Barton and Bar 2015)
1948 L. Jorda-Bordehore
123
(2016), with more data on different terrain and different
types of civil and mining engineering works in Spain.
3 Materials and Methods
The Q-slope is a new rock mass classification that is
specific to rock cuts or slopes and is based on the Q-index.
Q-slope utilizes the same six parameters RQD, Jn, Jr, Ja,
Jw and SRF as the Q-system (Barton and Bar 2015).
The equation that estimates the value of Q-slope shares
two-thirds of its content with the Q-index for underground
works (Barton and Grimstad 2014; Barton and Bar 2015).
The Q-slope equation is (Barton and Bar 2015):
Qslope ¼RQD
Jn� Jr
Ja
� �0
� Jwice
SRFslopeð1Þ
where:
• RQD is the rock quality designation, which varies
between 0 and 100; if its value is B10 (including zero),
then a nominal value of 10 is used to evaluate the Q-
slope (same as with the Q-index).
• Jn is the joint set number that maintains the values
established in the Q-index evaluation.
• Jr and Ja are the joint roughness number and the joint
alteration number, respectively, and maintain the values
of the Q-index (Barton and Grimstad 2014). The factor
Jr
Ja
� �0considers the favorable or unfavorable orienta-
tion of the main discontinuity or of those forming a
wedge by an adjustment factor referred to as the ‘‘O-
factor.’’
• Th eJwice factor is the Environmental and Geological
Condition Number that substitutes the joint water
reduction factor (Jw) of the Q-index.
• SRF slope is the stress reduction factor for the slope,
the maximum value between SRFa (which deals with
physical condition), SRFb (which addresses stress,
similarly to the one used in the Q-index) and SRFc,
which considers major discontinuity.
The reader is referred to the work of Barton and Bar
(2015) for a detailed description and weighting of each of
the aforementioned factors. Weighting of factors RQD, Jn,
Jr and Ja remains the same as in the ‘‘classical’’ Q-index
(Barton and Grimstad 2014). The ratio (Jr/Ja)o represents
frictional resistance and is adjusted to take into account the
relative orientation of the major (and eventual minor) joints
that might form potentially unstable wedges. The Jwice and
SRF slope factors originate from the evolution of Jw and
SRF and are applied to the numerator and denominator of
the Qslope equation, respectively.
The graphic depicted in Fig. 1 (Barton and Bar 2015) is
the basis for the application of the method. It is based on a
database of 200 Q-slope back-analyses carried out at the
Dominican Republic, Panama, Australia, Papua New Gui-
nea, Laos and Slovenia, in igneous, sedimentary and
metamorphic terrain (Bar and Barton 2016). Axis X corre-
sponds to Q-slope rock quality and axis Y represents the
slope angle, limited to slopes under 30 m in height. Once
the slope is represented by a point (Q-slope rock mass
quality and angle coordinates), stability is evaluated in
accordance with the graphic zone where it is located. The
graphic (Fig. 1) presents three zones: unstable slopes,
uncertain stability slopes (transition) and stable slopes.
Barton and Bar (2015) established a simple equation for
the steepest angle (b), which does not require reinforce-
ments for slope heights under 30 m:
b ¼ 20 log10 Qslope þ 65� ð2Þ
Equation 2 matches the central data for slope angles
comprised between 35� and 85� (see Fig. 1). For different
Q-slope qualities, the angles shown in Table 1 can be
considered stable.
4 Study Sites
The province of Madrid is situated in the central region of
Spain and the Iberian Peninsula. This zone is constituted by
two great main geological domains: a sedimentary basin—
Cenozoic—where the city of Madrid is located, and a
mountainous system to the north and west, called the Sierra
de Guadarrama, with igneous granite rocks, Paleozoic
metamorphic and Cretaceous sedimentary rocks (Fig. 2).
The following mountain road passes must be highlighted:
Puertos de Navacerrada (1858 m a.s.l.), Cotos (1830 m
a.s.l.), La Morcuera (1796 m a.s.l.), Somosierra (1444 m
a.s.l.), and Puerto de Guadarrama or Alto del Leon
(1511 m a.s.l.). In the mountainous massif, important dams
were built in the nineteenth century to provide water to the
city of Madrid. There are also some quarries and open-pit
mines, as well as several railway tracks. To this end, many
Table 1 Slope angle and Q-slope quality correlations. Adapted from
Bar and Barton (2016)
Q-slope Slope angle (height
under 30 m)
10 85�1.0 65�0.1 45�0.01 25�
Application of Qslope to Assess the Stability of Rock Slopes in Madrid Province, Spain 1949
123
rock slopes have been excavated, with some important
instabilities (some of which have progressed to stability);
however, other areas have required reinforcements or are in
precarious situation (Figs. 3, 4, 5).
Slopes in different zones of the mountainous massif
were studied herein, with different lithology such as
metamorphic (gneiss, schists and slates), igneous granite
and sedimentary (limestone) rocks. Among the civil engi-
neering works studied, there are slopes next to dams,
roadways and railways, quarries and mines (Figs. 4, 5, 6).
5 Results
Geomechanical stations/geotechnical observation points
were established at 33 slopes, where data were gathered on
orientation (dip-dir and dip), joint properties (infilling,
roughness, continuity, spacing, etc.), slopes (height, incli-
nation, orientation) and failure modes observed. Other data
were also collected, such as JRC and JCS, which can be
utilized in posterior kinematic studies. The slopes studied
herein were visited between the months of June and August,
2016, and are located within a 100-km radius of Madrid, to
the north, in mountainous zone. Table 2 shows the param-
eters used to calculate RQD, Ja, Jr/Ja, O-factor, Jwice and
SRF, and consequently Q-slope. Data on geometry, lithol-
ogy, height and inclination of each studied slope are also
shown in Table 2, along with the types of failure (circular,
planar, wedge or toppling). Figure 7 summarizes the dif-
ferent types of slope failures. Herein ‘‘quasi-stable slopes,’’
and ‘‘failed’’ slopes have been merged into a single category
named ‘‘unstable’’—indicated by crosses in Figs. 8 and 9.
Figure 3 depicts some of the stable slopes studied. The
characteristics of these slopes are highlighted in Table 3.
Figure 4 shows several slopes with small instabilities.
These slopes could be considered as ‘‘quasi-stable slopes’’
by Barton and Bar (2016 figures), represented by squares.
Figure 5 depicts failed slopes, and some still remain
unstable. Figure 8 summarizes the results for each ana-
lyzed slope, with values of inclination, rock quality and
stability: unstable or stable. The original figure is from
Barton and Bar (2015), over which the points representing
the studied slopes were marked (based on their Q-slope and
inclination coordinates). The points are represented by two
different codes: crosses represent failed–unstable slopes
and triangles represent stable slopes. This representation is
different from Barton and Bar (2015), in which a third
category was present: quasi-stable, represented by squares.
The research presented herein has improved the existing
database with Spanish slopes and lithology. The Q-slope
Fig. 2 Geological scheme of the study zone
1950 L. Jorda-Bordehore
123
Fig. 3 Stable slopes at the study zone: a Bustarviejo railway station, b El Villar dam, c Atazar lockout, d Valgallego road
Fig. 4 Uncertain stability slopes at the study zone: these are included in the ‘‘unstable slopes’’ category: a El Berrueco road, b Verdadera pit,
c Venturada quarry, d El Villar dam parking-road, e Reguerillo quarry, f San Eusebio quarry
Application of Qslope to Assess the Stability of Rock Slopes in Madrid Province, Spain 1951
123
geomechanical classification was effective for the charac-
terization of the studied slopes and described in a fast and
preliminary manner its degree of stability, as shown in
Fig. 8. The 33 studied cases were added to the 200 initial
cases (Barton and Bar 2015). Overall, the existing graphic
(Fig. 1) correctly represented the observed reality, although
some refinements could be made to the limits of some
zones in the graphic. The result of implementing these
Fig. 5 Failed or unstable slopes at the study zone: a La Cabrera-Cabanillas road, b El Molar street-road, c Valgallego road, d Cantos Negros pit,
e La Montanesa mine-crown pillar failure
Fig. 6 Histogram of the studied lithologies
1952 L. Jorda-Bordehore
123
Table
2Resultsofthemainparam
etersforeach
slope
Studysite
#Location
Lithology
Height,
inmeters
Slopeangle,
indegrees
Q-slopevaluecalculationfactors
Stability:
unstable,orstable
Failure
mode
RQD
JnJr Ja��
0J w
ice
SRFslope
Qslopevalue
1LaCabrera—Cabanillas
Gneiss
880
70
15
0.39
0.7
80.16
Unstable
Wedge
2Lacabrera—Cabanillas
Gneiss
10
85
80
15
1.125
0.85
2.5
2Unstable
Wedge
3ElBerrueco
Slate
860
10
61.125
0.65
2.5
0.49
Unstable
Planar
4ElBerrueco
Slate
860
10
61.5
0.65
2.5
0.65
Unstable
Planar
5Valgallego
Lim
estone
450
85
90.75
0.7
40.13
Unstable
Planar
6Valgallego
Lim
estone
460
85
93
0.85
2.5
9.6
Stable
–
7Venturadaquarry
Lim
estone
30
60
95
60.75
0.7
51.66
Unstable
Planar
8Venturadanaturalslope
Lim
estone
30
15
95
60.75
0.7
51.66
Stable
–
9Reguerillo
quarry
Lim
estone(karstified)
10
80
70
12
0.76
0.85
50.75
Unstable
Wedge
10
Atazardam
village
Slate
660
70
90.76
0.7
50.83
Unstable
Wedge
11
Bustarviejo
railway
station
Granite
890
100
12
0.75
0.90
2.5
2.25
Stable
–
12
Atazarlockout
Slate
550
55
12
0.76
0.65
50.45
Stable
–
13
ElVillardam
Gneiss
30
40
100
91.5
0.7
111.7
Stable
–
14
ElVillardam
Gneiss
30
90
100
91.5
0.7
111.7
Stable
–
15
ElVillardam
parking
Gneiss
870
65
12
0.38
0.85
2.5
0.7
Unstable
Wedge
16
Verdaderapit
Gneiss
680
80
12
1.125
0.7
2.5
2.1
Unstable
Wedge
17
Sardineraminetrench
Gneiss
12
90
80
12
1.125
0.85
16.4
Stable
–
18
CantosNegrosW
pit
Granite
590
100
12
0.175
0.7
80.13
Unstable
Wedge
19
Liebre
copperquarry
Gneiss
640
40
15
0.375
0.6
50.12
Stable
–
20
MontanesaBamine
Baritedikeandgranite
10
90
65
12
0.019
0.4
10
0.004
Unstable
Toppling
21
Montanesamine
naturalslope
Bariteandgranite
10
20
65
12
0.019
0.4
10
0.004
Stable
–
22
CruzVerdemagnesitemine
Serpentiniteandmarble
20
65
50
12
0.25
0.4
10
0.04
Unstable
Circular
23
San
Eusebio
Fmine
Granodiorite
10
80
85
90.25
0.7
50.33
Unstable
Toppling
24
San
Eusebio
quarry
Porfides—granodiorite
15
90
90
90.375
0.85
50.64
Unstable
Toppling
25
ElMolar
Schists
380
10
12
0.56
0.6
40.07
Unstable
Circular
26
Road
quarry
Bustar
Gneiss
750
60
15
0.75
0.65
2.5
0.78
Stable
–
27
Road
cutBustarviejo
Gneiss
554
10
12
0.375
0.65
2.5
0.08
Stable
–
28
Road
cutBustarviejo
Gneiss
545
10
15
0.375
0.65
2.5
0.065
Stable
–
29
Road
cutBustarviejo
Gneiss
866
75
90.375
0.65
50.4
Unstable
Wedge
30
Road
cutBustarviejo
Gneiss
870
55
90.25
0.65
50.2
Unstable
Wedge
31
Navazales
quarry
Granite
890
100
31.5
0.85
142.5
Stable
–
32
Fte
Milanoroundabout
Porphyr
852
100
90.50
0.85
50.94
Unstable
Wedge
33
Fte
Milanoroundabout
Porphyr
848
90
90.75
0.85
2.5
2.55
Stable
–
Italic
values
indicatedatarepresentedin
Fig.8
Application of Qslope to Assess the Stability of Rock Slopes in Madrid Province, Spain 1953
123
improvements is shown in the graphs of Figs. 8 and 9,
which are a better fit for this situation.
Prior to this study, there were no available data for the
lower left zone of Fig. 1, which corresponded to low-
quality rock (Q-slope\ 0.01) and slope angles\30�. Thiszone originally appeared as an uncertain stability slope
(Figs. 1 and 8). One case was found herein, and the result
was stable (see point 21 Figs. 8 and 9). A section could be
added to this zone, ‘‘stable slopes’’ for rock slopes that,
despite low quality, are stable with low inclinations. For
example, a slope located on very bad quality rock but with
10�–15� inclination would rarely be unstable, except in
Fig. 7 Histogram with failure modes present in the studied slopes
Fig. 8 Results for the studied slopes, following criteria of Barton and
Bar (2015) and Bar and Barton (2016). Crosses indicate failed slopes,
squares represent quasi-stable slopes, and triangles correspond to
stable slopes (on Barton’s and Bar’s 2015 original graphic).
Maximum height is 30 m
1954 L. Jorda-Bordehore
123
serpentinite or talc rocks. Therefore, in this zone a more
generous range of ‘‘stable’’ zone could be introduced,
encompassing the region near location #21 of Fig. 8. This
modification is presented in Fig. 9.
An unstable rock slopewith a slope under 20� is quite rare,and one can only imagine weathered lignite with planar
failure, layers of clay or talc. For future reinterpretations of
the chart, a horizontal limit is proposed for stable–unsta-
ble slopes under 20� and very low quality rock mass.
In the central zone of the graphic, for qualities between
0.03 and 0.6, the distribution of sectors coincides and the
database presented herein matches Barton and Bar (2015).
Fig. 9 Modification proposal for limit lines separating stability categories, at least for the study zone. Modifications applied to the original
figure from Barton and Bar (2015)
Table 3 Data from the pictures of some representative slopes
Figure Slope # Type of slope/use Stability/unstable kinematic failure Slope angle degrees Qslope value
Figure 3a 11 Railway Stable 90 2.25
Figure 3b 13–14 Dam Stable 40–90 11.7
Figure 3c 12 Roadway Stable 50 0.45
Figure 3d 6 Roadway Stable 60 9.6
Figure 4a 3–4 Roadway Planar 60 0.49–0.65
Figure 4b 16 Mine pit Wedge 80 2.1
Figure 4c 7 Quarry Planar 60 1.66
Figure 4d 15 Parking—roadway Planar 70 0.7
Figure 4e 9 Quarry Rock detachments due to karst weathering 80 0.75
Figure 4f 24 Quarry Rock detachments due to ice 90 0.64
Figure 5a 1 Roadway Wedge 80 0.16
Figure 5b 25 Street Rotational rock mass 80 0.07
Figure 5c 5 Roadway Planar 50 0.13
Figure 5d 18 Mine pit Toppling 90 0.13
Figure 5e 20 Mine pit—underground Toppling—crown pillar failure 90 0.004
Application of Qslope to Assess the Stability of Rock Slopes in Madrid Province, Spain 1955
123
Regarding the right half of the graphic, with rock qualities
Q-slope[0.6, differences were found when comparing
data with Barton and Bar (2015). There is coincidence with
the ‘‘unstable zone,’’ but further research is necessary to
better limit the stable zone. Several slopes were not entirely
unstable, nor completely failed, and could be referred to as
‘‘quasi-stable slopes’’ or located in an uncertain stability
slope region (see slopes #4, 7, 10 and 32 in Fig. 8). In the
rock slope database presented herein, several slopes with
qualities between 0.6 and 2 and inclinations between 60�and 90� were unstable. Therefore, the zone ‘‘uncertain
stability slopes,’’ could be widened. This modification is
shown in Fig. 9, as a suggestion for further research.
From rock qualities Q-slopes[3, all slopes of the
database studied herein and from Barton and Bar (2015)
were stable, even with inclinations of 90�. For these
qualities, the left limit of the stable zone (see Fig. 1 and 8)
could be a vertical line. Figure 9 depicts these new possible
zones.
Further studies are required, in other geographies and
with other types of lithology, to fine-tune the limits of the
different empirical zones of the graphic.
6 Conclusions
The objective of this study was not to change empirical
graphics for each case, but rather suggest limits that could be
implemented once more data are available, e.g., for a pos-
terior version of the graphic that includes more field data.
The new Q-slope geomechanical classification has been
applied herein to several mining and civil slopes in the
Guadarrama mountain range—north of Madrid, Spain.
Different lithology was considered, such as slates, granite
and limestones as well as different slope uses (civil, min-
ing, etc.). The new Q-slope has been useful to characterize
the stability of slopes under 30 m and was successfully
applied to back-analyze roadway, railway and mining
engineering slopes.
Some modifications are proposed to the empirical graph
developed by Barton and Bar (2015), which can provide
better fit to specific cases of either very good or very bad
quality rocks.
Acknowledgements The authors kindly thank Dr Adrian Riquelme
from the University of Alicante, Spain, for the review and suggestions
for the manuscript.
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