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Mecânica das Rochas para Recursos Naturais e Infraestrutura 
SBMR 2014 – Conferência Especializada ISRM 09-13 Setembro 2014 
© CBMR/ABMS e ISRM, 2014 
 
SBMR 2014 
Hoek & Brown and Barton & Bandis Criteria Applied to a Planar 
Sliding at a Dolomite Mine in Gandarela Synclinal 
 
Felipe Giusepone 
Vale do Rio Doce Company, Belo Horizonte, Brazil, Email: Felipe_g07@hotmail.com 
 
Prof. Dr. Lineu Azuaga Ayres da Silva 
Escola Politécnica da Universidade de São Paulo, São Paulo, Brazil, Email: layres@usp.br 
 
SUMMARY: It was utilized the Hoek & Brown, (1997) rupture criterion (as presented in the 
version of 2000 by Marinos and Hoek ) and the criterion of Barton & Bandis (1982) for the study 
of the slope stability in a Dolomite open pit mine situated in the Gandarela synclinal. The results 
obtained with these criteria were evaluated to verify the compatibility between the two methods. 
 
KEYWORDS: Empirical Design Methods; Hoek & Brown; Barton & Bandis; plane failure; Slope 
Engineering; open pit mines; dolomite 
 
 
1 INTRODUCTION 
 
For the case study was used the Dolomite mine 
situated in Gandarela Synclinal due to the plane 
sliding problems that occurred very frequently in 
the North open pit region. The facility to obtain 
the necessary data for empirical studies was very 
important for the employment of these methods. 
 
 
2 UTILIZATION 
 
2.1 Regional Geology 
 
The area is located in the “Quadrilátero 
Ferrífero”, a very important region of iron 
mining in the center of Minas Gerais state. 
 According to Dorr (1969) the stratigraphic 
column of the “Quadrilátero” is composed of: 
the Basement consisted of gneiss, amphibolites, 
metaultramafics and pegmatites; Super Groups 
“Rio das Velhas”: volcano-sedimentary 
sequence of the type greenstone belt; and the 
Super Group Minas: metasedimentary rocks 
with small volcanic rocks contributions 
consisted of quartzite, phyllite, 
metaconglomerates, iron formations and 
limestones. 
 The Gandarela Formation belongs to the 
Itabira Group and the Super Group Minas. It 
was identified by Dorr (1969) in the 
homonymous Synclinal at East of the 
“Quadrilátero Ferrífero”. This Formation is 
constituted of dolomites, limestones, dolomitic 
phyllites, iron dolomitic formations, phyllites 
and quartzous lenses. 
 The most important lithology for the analysis 
of plane sliding study is the Impure Dolomite 
(DI) that is a constituent of the mine base strata. 
 
2.2 Kinematic Analysis of Rupture 
 
It was used the method of Markland (1972) to 
identify the open pit regions with highest plane 
instability potential. The collection of the 
structural discontinuities attitudes presents in the 
rock mass was located in the field together with 
the proposed final geometry of the open pit 
mine. Four families of discontinuities were 
identified with the following attitudes: 
 Stratification: attitude 244N/S26E/36SE; 
 Family 1: attitude 237N/S32E/82SE; 
 Family 2: attitude 120N/N30E/54NE; 
 Family 3: attitude 94N/N2E/46NE. 
 
 Eighty field measurements were carried out and 
the above values are averages of the measures for 
each family of discontinuity. The possibility of 
plane rupture has been identified in North slope 
of the open pit as shown in Figure 1. 
SBMR 2014 
 The discontinuity involved in analysis of 
rupture is the bedding layer (foliation) and 
lithology DI that remains in the mining final 
configuration. 
 
 
 
Figure 1. Kinematic analysis of the possibility of 
breakage in the dolomite configuration of open pit mine 
 
2.3 HOEK & BROWN criterion (1997) 
adapted by Marinos and Hoek (2000) 
 
This criterion is based on the classification 
"Geological Strength Index" (GSI) to 
determine the estimated strength of rock mass. 
 The GSI is determined by abacus (attachment 
1) developed by Marinos and Hoek (2000) and 
depends on the characteristics of 
discontinuities and rock mass structure. These 
characteristics were determined through 
geomechanics description of drill holes and the 
calculation of "Rock Quality Designation 
(RQD) used to assess the degree of rock mass 
natural fracturing and guide to obtaining factor 
GSI on 60 points. 
 This value was obtained by considering the 
structure of the rock very blocky and with 
regular quality of surface discontinuity in 
accordance with the abacus (attachment 1). 
 The parameter mi is obtained according to 
the origin of the rock and determined through 
by the table (attachment 2). This parameter 
was regarded as 9 ± 3 due to the sedimentary 
formation and texture very thin. By means of 
laboratory testing conducted at Escola 
Politécnica da Universidade de São Paulo was 
determined the uniaxial compressive strength of 
rock core samples for DI of 147.80 MPa. The 
rock mass strength is estimated by means of 
equations 1 to 3 which consider the scaling 
factor to correct the lab results. The modeling 
below considers the condition of unweathered 
rock and GSI > 25. 
 
 (1) 
 
 
 For GSI = 60, we have S = 0.0117 
 
 (2) 
 
 
 For mi = 9, we have mb = 2.1569 
 
 Therefore the equation obtained for the rock 
mass using the GSI is: 
 
 
 (3) 
 
 By varying the value of σ3 it is possible to 
determine the shear envelope which 
characterizes the rock mass behavior in the 
presence of requesting efforts, as Figure 2 
demonstrates. 
 
 
 
Figure 2. Rock mass shear envelope obtained by the 
equation GSI 
 
 Therefore, the equation of rupture envelope is 
obtained as described in equation (4) 
 
 (4) 
 
2.3.1 Plane Sliding Analysis 
 
The Figure 3 presents the required geometry 
for the plane rupture in the North slope. 
 
δ 
σ
n 





 

9
100GSI
eS





 

28
100
.
GSI
ib emm
5.0
3
31 0117.0
80.147
1569.2.80.147 






 x
30tan38.11 n 
SBMR 2014 
 
 
Figure 3. Chart for plane rupture analysis 
 
 The safety factor obtained through the Hoek 
and Bray methodology (1981) is calculated by 
means of equation 5. 
 
 
 (5) 
 
 
 Where: 
 
Ψp= Dip angle of the sliding plane (°); 
c
 = cohesion in the rupture surface (Mpa); 

 = angle of friction (°); 
A
= surface length (m); 
U
 = Resultant force of water pressure on the 
plane of discontinuity (tf/m); 
V
 = Resultant force of water pressure on 
tension crack (tf/m); 
W
 = Potentially unstable block weight (tf/m). 
 
 According to the equations 6 to 9 one can 
calculate: 
 
 (6) 
 
 
 (7) 
 
 
 (8) 
 
 
 (9) 
 
 
 The obtained values are: 
 A = 187.14 m 
 W = 6,303.13 tf/m; 
 U = 2,392.46 tf/m; 
 V = zero (without crack tension) 
 It was also considered the contribution of the 
weight of coverage (soil) on the surface of 
rupture using the equation 10.(10) 
 
 
 The achieved value was 1,206.98 tf/m that 
adding to the weight of the potentially unstable 
rock block results in the weight of 7,510.13 
tf/m. Therefore, at the angle of 45° (angle 
provided by the final configuration of the 
proposed open pit), the F.S. of 0.96 was 
obtained, considered unstable and outside the 
safety margin (F.S. ≈ 1.25). 
 General angle alternatives for this face were 
simulated, the obtained data are presented in 
Table 1. 
 
Table 1. Simulations results for calculus of F.S. and 
slope general angle for the open pit North region. 
 
 Ψf (o) 
 Cohesion 
(MPa) 
 A (m) W (tf/m) 
U 
(MPa) 
 Θ (o) F.S. 
 38 11.38 187.14 1,560.46 2,392.46 30 1 1,61 
 40 11.38 187.14 3,145.07 2,392.46 30 1,20 
42 11.38 187.14 4,725.65 2,392.46 30 1,06 
45 11.38 187.14 7,510.12 2,392.46 30 0,96 
50 11.38 187.14 10,449.74 2,392.46 30 0,92 
65 11.38 187.14 17,998.24 2,392.46 30 0,87 
 
 Evaluating table 1 one can verify that the 
angle of 38° to 40° is the best option for the 
open pit general angle in the North slope 
according to the methodology of Hoek and 
Brown (1997). 
 
2.4 BARTON & BANDIS Criterion (1982) 
 
This criterion was developed for the exclusive 
study of the plane sliding analysis and correlates 
the uniaxial compressive rock strength (drill 
hole) with the rock mass uniaxial compressive 
strength by means of "tilt tests" and sclerometer 
Schmidt. 
 As well as the GSI is important to determine 
the characteristics of the discontinuities of the 
Rock slope 
plane 
Soil slope plane 
Descontinuit
y bedding 
plane 
 
pp
pp
VsenW
senVUWcA
SF 

cos..
tan..cos.
..



  peczHA cos.
pWW ecHU  cos...
4
1 2

2
..
2
1
ww zV 
   



  1cot.cot.cot.1...
2
1 22
fppH
zHW 
csss HW  cot...
2
1 2

SBMR 2014 
studied rock mass, the Barton and Bandis 
criterion (1982) uses the compressive surface 
strength obtained by means of the Schmidt 
sclerometer to determine these characteristics 
using the JCS parameter (coefficient of 
superficial compressive strength) and the JRC 
(coefficient of the discontinuities roughness). 
 The JCS is obtained directly from the 
sclerometer test performed on a cut surface 
(sawn). It was considered JCS = 66.14 MPa. 
The JCR is calculated by the equation 11. 
 
 (11) 
 
 
 The residual friction angle (Φr) is obtained by 
means of the equation 12. 
 
 
 (12) 
 
 The angle (Φ bbb) is the angle of friction 
between two surfaces cut (sawn), as Figure 4 
illustrates the "Tilt Test." 
 It was considered Φ bbb = 32˚. The correction 
parameter (r/R) is obtained by calculating the 
ratio between the superficial compressive 
strengths on the weathered discontinuity (r) on 
the sawn surface (R). This parameter was 
estimated at 1.0313. 
 
 
 
Figure 4. Representation of the "Tilt Test." 
 
 So according to the equation (12) Φr = 
32.63˚, the difference between α – Φr can be 
characterized as the increment in friction angle 
arising from "asperity" of the discontinuity 
surface. This value was estimated by means of 
the experiment of "Tilt Test" subtracting values 
between natural and sawn surfaces (cut). It was 
considered i = α – Φr = 8°. 
 The normal stress (σns) is determined by 
means of the weight of the tested sample ("Tilt 
Test") and the contact surface between these 
samples. The σns value was estimated at 0.0036 
MPa. Finally using the equation 11, one has JRC 
= 9.52 MPa. 
 Barton and Bandis (1982) correct the values 
obtained in the laboratory to get the interested 
field values using the scaling factor based on the 
relationship between the length of the tested 
samples (14.5cm) and the length of the 
discontinuity susceptible to plane sliding in the 
field (187.14m). The parameters JRC and JCS 
are corrected employing the equations 13 and 14. 
 
 
 (13) 
 
 
 (14) 
 
 
 Thus: JRC = 78.56 MPa and JCS = 250.57 
MPa. 
 
2.4.1 Plane sliding Analysis 
 
Figure 3 shows the required geometry for the 
plane sliding in the North slope. The safety 
factor obtained by means of Barton and Bandis 
criterion (1982) is calculated using equation 15. 
 
 
 (15) 
 
 
 
 The weight of the rock block (W) and the 
uniaxial compression strength (σ) are the same 
as considered by the criterion of Hoek & Brown. 
So for the angle of 44° it was obtained the F.S. 
of 1.26. 
 
 
 
 
ns
r
JCS
JRC


10log


   
R
r
br .2020  
003.0
0
0.
JRC
n
L
L
JCSJCS










senW
JCS
JRCW
SF
r
n
.
log.tan.cos.
..
10


















002.0
0
0.
JRC
n
L
L
JRCJRC








SBMR 2014 
3 RESULTS 
 
The criteria of Hoek & Brown (1997) adapted by 
Marinos & Hoek (2000) and Barton & Bandis 
(1982) showed consistency for the analysis of 
plane sliding. 
 The figure 5 presents the values obtained 
using these two criteria. 
 
 
 
Figure 5. Relation of FS obtained using the criteria of 
Hoek-Brown (1997) and Barton and Bandis (1982). 
 
 The probable stability of this slope occurs 
between the angles of 38° to 40° and 42° to 44° 
according to the criteria of Hoek & Brown and 
Barton & Bandis respectively for F.S. around 
1.25. This difference of 2° to 4° can be 
considered insignificant in the field and of 
difficult verification in large mineral slopes. The 
two criteria determined the angle of 50° as the 
limit value for stability (F.S. = 1.0). 
 Considering the project angles occur 
significant differences between the 
methodologies of analysis, such as: the angle of 
40° presents F.S. = 1.45 in accordance with the 
criterion of Barton and Bandis and F.S. = 1.20 
according to Hoek and Brown. There is a 
difference of 21%. 
 
 
4 CONCLUSION 
 
According to Hoek and Brown (1997) the 
methodology GSI should not be used in rock 
masses where the problems of instabilities are 
caused by planes bedding. 
 The ISRM recommends the use of the 
criterion of Barton and Bandis (1982) in these 
cases. 
 This article raise the possibility of further 
studies to confirm the recommendation of the 
ISRM and the possibility to assert compatibility 
between these methods. This compatibility 
should be tested and confirmed in research and 
future studies. 
 
 
REFERENCES 
 
Barton, N; Bandis, S. Effect of block size on the shear 
behavior of jointed rock [Keynote lecture]. In: U.S. 
SYMPOSIUM ON ROCK MECHANICS, 23rd., 
1982, Berkeley, Cal. Proceedings. New York: Soc of 
Min Eng of AIME, 1982. p. 739-760. 
Dorr, J.V.N. Physiographic, stratigraphic and structural 
development of the quadrilátero ferrífero, Minas 
Gerais, Brazil. Washington, D.C., 1969. 110 p. (U.S. 
Geological Survey Professional Paper, 641-A). 
Hoek, E.; Bray J. Rock slope engineering. London: The 
Institution of Mining and Metallurgy, 1981. 358 p. 
Hoek, E.; Brown, E.T. Practical estimates of rock mass 
strength. Intnl. J. Rock Mech.& Mining Sci. & 
Geomechanics Abstracts. 1997. p.1165-1186. 
Marinos, P.; Hoek, E. GSI: a geologically friendly tool for 
rock mass strength estimation. In: INTERNATIONAL 
CONFERENCE ON GEOTECHNICAL & 
GEOLOGICAL ENGINEERING, 2000, Melbourne. 
GeoEng2000. Lancaster: Technomic, 2000. p. 1422-
1489. 
Markland, J.T. A useful technique for estimating the 
stability of rock slopes when the rigid wedge sliding 
type of failure is expected. London: Imperial College, 
1972. 10 p. (Imperial College Rock Mechanics 
Research Report, n. 19). 
 
0 
0.2 
0.4 
0.6 
0.8 
1 
1.2 
1.4 
1.6 
1.8 
38 40 42 45 50 60 65 
Slope plane angle 
Security factor (F.S) 
Barton_Bandis Hoek _Brown 
SBMR 2014 
 
 
Attachment 1. Abacus to Obtain the Dolomite GSI, 
Reference: Marinos and Hoek (2000) 
 
 
 
 
Attachment 2. Values Of The Constant mi for Intact 
Rock, by Rock Group
4
. Reference: Marinos And Hoek 
(2000)