Lesson 1 ADGSE

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Lesson 1
contents
•Rock mass, intact rock and discontinuities
•The geotechnical model
•Discontinuities characterization
•Stereographic representation
1
Rock mass, intact rock and discontinuities
The rock mass is
made up of two
elements: the intact
rock and the
discontinuities.
Discontinuities with
similar attitude,
geological origin and
characteritstics belong
to the same set.
2
3
Chilean tuff
4
Chilean tuff
In the rock mass main 
discontinuities can 
develop, due to 
geological causes (for 
example the faults). 
They usually show a 
complex morpholgy and 
play an important role in 
the rock mass 
behaviour.
5
The rock mass can be considered as a fractured medium
whose behaviour is highly influenced by the mechanical
characteristics of the two elements: intact rock and
discontinuity.
Strength, deformability, permeability, constitutive behaviour
of the rock mass depend on a complex combination of the
contribution of these two main elements and their
interactions.
For these reasons the characterization of a rock mass is not
a simple process: it starts from the laboratory tests for the
measure of mechanical and physical parameters on a small
scale and reaches the real scale parameters by means of
the rock mass classification technique.
The scale effects are not negligible in rock masses.
The transition from small to real scale is based on rock
mass classification.
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7
scale effect
drilling hole
scale effect
tunnel
large underground 
excavation
8
The geotechnical model
The discontinuity sets and the fractures split the rock mass into 
a lot of rock blocks.
On the basis of the ratio between the representative block size
and the size of the engineering structure to be analysed (rock
sample diameter, tunnel diameter, landslide thickness…), a
different geotechnical model should be chosen to represent the
problem:
-Equivalent continuum model, if the block size is small
compared with the structure being analysed
-Discontinuum model, if the size of the block is the same of
that of the structure being analysed or if one of the discontinuity
sets is significantly weaker than the others. In these cases, the
stability of the structure should be analysed by considering
failure mechanisms involving the sliding or rotation of blocks
and wedges defined by intersecting structural features.
9
Transition from an intact to a heavily jointed rock mass with
increasing block size (from Hoek’s corner)
The equivalent continuum model requires to define the rock
mass strength and deformability, that is:
-Constitutive law
-Strength criterion 
-Deformability modulus
The discontinuum model requires to define the strength and 
deformability of the intact rock and the discontinuities, that is:
For the intact rock:
-Constitutive law
-Strength criterion 
-Elastic parameters (Young modulus and Poisson coefficient)
For discontinuities:
-Shear strength criterion
-Normal and tangential stiffness
Discontinuities characterization
The following characteristics are representative of a
rock discontinuity:
•Orientation 
•Spacing
•Persistence
•Roughness 
•Wall strength
•Opening (separation)
•Filling
•Presence of water 
Orientation 
• The orientation of a rock discontinuity in the geographical space
is measured under the assumption that each discontinuity is
represented by a mean plane
• The position of the joint plane is uniquely determined by two
angles:
the dip direction α, that represents the facing direction,
measured clockwise from the north (0°) of the line with
maximum dip in the inclined plane; it is generally expressed
by an angle of 0° to 360°
the dip ψ, that represents the degree of inclination; it is the
acute angle between the plane and the horizontal plane
(measured as the acute angle between the line of maximum
dip in the inclined plane and its horizontal projection); it is
generally expressed by an angle of 0° to 90°
• Discontinuities characterized by similar orientations are
assumed belonging to the same set (family)
12
Dip 
direction, 
α
line of maximum 
dip
13
angolo di 
inclinazione
Dip, ψ
NORD
Spacing 
The spacing is the distance between two adjoining
discontinuities belonging to the same set; it is measured in the
direction orthogonal to the discontinuities.
When a set is defined, it is characterized by the mean value of
the spacing.
14
set
set
set
An example of spacing statistical distribution in a set of 
discontinuities
15
extremely 
close
very
close close moderate wide
very
wide
extremely 
wide
spacing
N
um
be
r 
of
 o
bs
er
va
tio
ns
Persistence
• The persistence of a discontinuity is the size of the contact
area between the discotinuity faces. Usually it is assumed to
be the length of the discontinuity trace observable on an
outcrop.
• The persistence depends on how the discontinuity ends in
the rock mass: it can intersect another discontinuity or end
into the intact rock.
• When a set is defined, it is characterized by a mean value of
the persistence.
16
A scheme of persistence
17
not persistent persistent
Roughness
• The faces of a discontinuity are characterized by a so called
small scale roughness, that is the roughness measured in
the laboratory.
• On a large scale (in situ scale) the discontinuity can show a
waviness. It is measured with respect to the mean plane of
the discontinuity.
• To determine the geometrical contour, photografic and
photogrammetric methods, as well as laser or mechanical
profilometers, are used.
• When a set is defined, it is characterized by a mean value of
the roughness.
18
Small scale (1 and 2) 
and large scale roughness
19
The roughness profile is obtained by means of a mechanical 
profilometer (Barton comb, a sliding needles comb):
or a laser profilometer
20
Typical roughness
profiles and suggested
terminology
• The length of each
profile can vary
between 1 and 10 m
• The horizontal scale is
equal to the vertical
one
21
rough
smooth
slick
rough
smooth
slick
rough
smooth
slick
flat
wavy
segmented
typical roughness 
profiles and 
corresponding JRC 
values
22
JRC estimation
Wall strength
• The wall strength is the compressive strength of the
discontinuity faces. It can be lower than the uniaxial
compressive strength of the intact rock because of the
exposure to atmospheric agents and alteration of the
discontinuity walls.
• To measure the wall strength the sclerometer (Schmidt
hammer) is used.
• When a set is defined, it is characterized by a mean value of
the wall strength.
23
24
Schmidt hammer and 
correlation chart: examples
JCS estimation
It is possible to distinguish four conditions of discontinuities:
1. If the walls of the discontinuity are not weathered, JCS is
assumed equal to the uniaxial compressive strength of the
intact rock, σci
2. If the walls are weathered, JCS<σci
3. If the alteration process affects the rock mass, JCS further
decreases
4. If the rock mass is at an advanced stage of alteration, the JCS
value can thus be obtained as follows:
• uniaxial compressive tests or point load tests on rock samples (1
and 4)
• Schmidt hummer tests on interface walls (2)
• uniaxial compressive tests or point load tests on rock samples
taken from the alterated part of rock mass (3)
25
Opening 
• The opening of a discontinuity is the distance between its
faces. The gap between the two faces of the interface can
be filled with air, water or other materials.
26
examples of rock 
discontinuity 
opening
closed discontinuity open discontinuity
filled discontinuity
opening
Filling
The filling material disjoins the two faces of the discontinuity. 
It can be constituted of sand, silt, clay, breccia…
27
Examples of filled 
discontinuities
Presence of water
The water flow occurs in the discontinuities, as their
permeability is greater than that of the intact rock.
In a fault area the flow can occur into the rock mass.
28
The number and orientation of the joint sets define the shape of the 
rock blocksin the rock mass
The spacing of the discontinuities and their mutual intersections
define the volume of the rock blocks
29
one main set of 
discontinuities
three main sets of 
discontinuities
30
examples of rock mass geometry: a) blocky; b) 
irregular; c) tabular; d) columnar 
Stereographic representation
The data obtained by a geomechanical survey allow to
define the main discontinuities sets of the rock mass and
their mean orientation.
The definition of the main sets is usually done on the
basis of the orientation data.
These data must be interpreted with a statistical
approach.
To represent the great number of orientation data the
stereographic projections are available.
The following characteristics of the discontinuities are
collected during a geomechanical survey:
• Number
• Type
• Spacing
• Persistence
• Orientation
• Filling
• Water presence
• Litology
• Wall strength
• Opening
• Shape
• Roughness
Stereographic representation of the discontinuities
big circle reference sphere
mean plane representing 
the discontinuity
The discontinuity plane is projected on the horizontal plane 
as pole and big circle. The lower hemisphere is chosen as 
reference hemisphere.
big circle projectionpole projection 
discontinuity plane
Equatorial grid
The reference hemisphere is covered by a grid of parallels and
meridians in such a way as the equatorial plane is perpendicular to
the Nord-South direction.
The projection of the grid on the horizontal plane is the equatorial
grid.
equatorial plane 
trace
The reference hemisphere is covered by a grid of parallels and
meridians in such a way as the equatorial plane is horizontal.
The projection of the grid on the horizontal plane is the polar grid.
Polar grid
equatorial plane 
trace
Reticolo polare
Proiezione equivalente
Reticolo equatoriale
Proiezione equivalente
POLAR GRID EQUATORIAL GRID
Pseudo-horizontal: 
close to the grid 
boundary
Pseudo-vertical: close 
to the grid centre
pole
Characteristic orientation of discontinuity sets: an example
Set 
Orientation 
(DIP/DIP DIR)
K1 020°/80°
K2 154°/78°
K3 044°/80°
str 310°/20°
K4 090°/80°
str K4
K1
K2 K3
K1 K2
str
K3
K4
K1 K2
K3
K4
str
Characteristic orientation of 
discontinuity sets: an example
When the main sets of discontinuities are identified, every
other characteristic can be interpreted statistically by means of
the istograms
Example of the spacing distribution for a certain set (set 1)