the hoek–brown failure criterion mine of geotechinal
TRANSCRIPT
The Hoek–Brown Failure
Criterion Mine of Geotechinal
ABSTRACT The Hoek-Brown failure
criterion for rock masses is
widely accepted and has been
applied in a large number of
projects around the world.
While, in general, it has been
found to be satisfactory, there
are some uncertainties and
inaccuracies that have made
the criterion inconvenient to
apply and to incorporate into
numerical models and limit
equilibrium programs. In
particular, the difficulty of
finding an acceptable
equivalent friction angle and
cohesive strength for a given
rock mass has been a problem
since the publication of the
criterion in 1980.
Group 2 Mining Engineering of Hasanuddin University
The Hoek–Brown Failure Criterion Authors: Angga AL-Amin Husain D621 13 301 [email protected]
Chairul Wahyu Adha D621 13 317
Rizky Isal D621 13 306 [email protected]
Abd. Rahman Sujuthi D621 11 902 [email protected]
Contents ROCK FAILURE DEFINITION ................................................................................................................................ 2
HOEK-BROWN ................................................................................................................................................... 2
HOEK-BROWN FAILURE CRITERION ................................................................................................................... 2
GENERALIZED HOEK-BROWN FAILURE CRITERION ........................................................................................ 3
The Uniaxial Compressive Strength of the intact rock pieces 𝝈𝒄𝒊 .................................................................. 3
Guidelines for estimating disturbance facktor D ........................................................................................... 3
The Geological Strength Index - GSI .............................................................................................................. 4
GSI for heterogeneous rock masses such as flysch .................................................................................... 6
Generation of Mohr-Coulomb parameters from the Hoek-Brown failure criterion: .......................................... 6
Appendix ........................................................................................................................................................... 7
Underground Excavations in Rock by E. Hoek and E.T. Brown Published in 1980. ..................................... 7
Hoek-Brown failure criterion developer : ...................................................................................................... 8
Prof. Evert Hoek, Ph.D., M.Sc. ................................................................................................................... 8
Prof. Edwin Thomas Brown, Ph.D., D.Sc.(Eng.) .......................................................................................... 8
ROCK FAILURE DEFINITION
Failure can involve formation of discrete fracture zones and the more "ductile" or homogeneous deformation.
The latter deformation is caused by a broad distribution of fracture zones or general grain crushing during
compaction. We will not consider deformation caused by plastic strains of the mineral components, as is
common in salt and in calcite at higher temperatures. In our analysis, several assumptions are made (Society
of Petroleum Engineers, 2015):
1. Material is isotropic and homogeneous
2. Stresses are applied uniformly
3. Textural characteristics such as grain size and sorting have no influence
4. Temperature and strain rate are ignored
5. Intermediate stresses are presumed to play no role.
6. Each of these assumptions can be violated, and some have been demonstrated to have major
influences on rock strength.
HOEK-BROWN The Hoek-Brown failure criterion for rock masses is widely accepted and has been applied in a large number of
projects around the world. Stress strain relationships in rocks examined the elastic behavior of rocks, which
was largely reversible. Here we deal with permanent deformation. By rock failure, we mean the formation of
faults and fracture planes, crushing, and relative motion of individual mineral grains and cements.
The original Hoek-Brown failure criterion was developed during the preparation of the book Underground
Excavations in Rock by E. Hoek and E.T. Brown, published in 1980. The criterion was required in order provide
input information for the design of underground excavations. Since no suitable methods for estimating rock
mass strength appeared to be available at that time, the efforts were focussed on developing a dimensionless
equation that could be scaled in relation to geological information. The original Hoek-Brown equation was
neither new nor unique — an identical equation had been used for describing the failure of concrete as early
as 1936.
HOEK-BROWN FAILURE CRITERION
One of the early difficulties arose because many geotechnical problems, particularly slope stability issues, are
more conveniently dealt with in terms of shear and normal stresses rather than the principal stress
relationships of the original Hoek-Brown criterion, defined by the equation:
𝝈′𝟏 = 𝝈′𝟑 + 𝝈𝒄𝒊 (𝒎𝒃
𝝈′𝟑𝝈𝒄𝒊
+ 𝑺)
𝒂
Where:
▪ ’1 and ’3 are maximum and minimum effective stresses at failure
▪ mb is the value of the Hoek-Brown constant m for the rockmass
▪ s and a are constants which depend upon the rockmass characteristics
▪ ci is the uniaxial compressive strength of the intact rock pieces
GENERALIZED HOEK-BROWN FAILURE CRITERION Where mb is a reduced value of the material constant mi and is given by :
𝑚𝑏 = 𝑚𝑖 𝑒𝑥𝑝 (𝐺𝑆𝐼 − 100
28 − 14𝐷)
s and a are constants for the rock mass given by the following relationships:
𝑠 = 𝑒𝑥𝑝 (𝐺𝑆𝐼 − 100
9 − 3𝐷)
𝑎 =1
2+1
6(𝑒−𝐺𝑆𝐼/15 + 𝑒−20/3)
The Uniaxial Compressive Strength of the intact rock pieces 𝝈𝒄𝒊
Guidelines for estimating disturbance facktor D D is a factor which depens upon the degree of disturbance to which the rock mass has been subjected by blast
damage and stress relaxation. It varies from 0 for undisturbed in situ rock masses to 1 for very disturbed rock
masses. Guidelines for the selection of D are discussed in a later section.
The Geological Strength Index - GSI The Geological Strength Index (GSI) system, proposed in 1995, is used for the estimation of the rock mass
strength and the rock mass deformation modulus.
The GSI system concentrates on the description of two factors:
▪ Rock structure, and
▪ Block surface conditions.
Excellent quality controlled blasting or excavation by Tunnel Boring Machine results in minimal disturbance to the confined rock mass
surrounding a tunnel.D=0 .0
Mechanical or hand excavation in poor quality rock masses (no blasting) results in minimal disturbance to
the surrounding rock mass. D=0.0
Where squeezing problems result in significant floor heave, disturbance can be severe unless a temporary invert, as shown in the photograph, is placed. D=0.5
Very poor quality blasting in a hard rock tunnel results in severe local damage, extending 2 or 3 m, in the
surrounding rock mass. D=0.8
Small scale blasting in civil engineering slopes results in modest rock mass damage, particularly if controlled blasting is used as shown on the left hand side of the
photograph. However, stress relief results in some disturbance. D=0.7-1.0
Very large open pit mine slopes suffer significant disturbance due to heavy production blasting and also due to stress relief from overburden removal. D=1.0
In some softer rocks excavation can be carried out by ripping and dozing and the degree of damage to the
slopes is less. D=0.7
The guidelines given by the GSI system are for the estimation of the peak strength parameters of jointed rock
masses. There are no guidelines given by the GSI, or by any other system, for the estimation of the rock mass’
residual strength that yield consistent results.
Characterisation of rock masses on the basis of interlocking and joint
alteration:
GSI for heterogeneous rock masses such as flysch
Generation of Mohr-Coulomb parameters from the Hoek-Brown failure criterion: Use Equation:
𝝈′𝟏 = 𝝈′𝟑 + 𝝈𝒄𝒊 (𝒎𝒃
𝝈′𝟑𝝈𝒄𝒊
+ 𝑺)
𝒂
to generate triaxial test results. Statistical curve fitting of data, using Equation :
𝝉 = 𝑨𝝈𝒄𝒊 (𝝈′𝒏 − 𝝈𝒕𝒎
𝝈𝒄𝒊)
𝑩
Where:
A and B are material constants; ’n is the normal effective stress; tm is the ‘tensile’ strength of the rockmass :
𝝈𝒕𝒎 =𝝈𝒄𝒊𝟐(𝒎𝒃 − √𝒎𝒃
𝟐 + 𝟒𝒔)
reflecting the fact that the rock particles are interlocked and not free to dilate
Appendix
Underground Excavations in Rock by E. Hoek and E.T. Brown
Published in 1980.
Hoek-Brown failure criterion developer :
Prof. Evert Hoek, Ph.D., M.Sc.
Senior Consultant: Evert Hoek Consulting Engineer Inc.
Prof. Edwin Thomas Brown, Ph.D., D.Sc.(Eng.)
Senior Consultant: Golder Associates Pty Ltd