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1
Stress Path & Engineering Failure
John A Hudson
Some diagrams with the help of
Prof John P. Harrison, University of Toronto
Lecture 3
F1
F2
F3
Fn
Fractures
Intact rock
Boundary
conditions
Excavation
Water flow
We now need to
be able to
predict what will
happen when
the tunnelling
engineer makes
an excavation in
this mechanical
environment
2
Wuhan – Feb 2008 – Unsolved Problems in Rock Mechanics and Rock Engineering
The main mechanical stability problems are related to the
release of rock blocks and stress induced spalling
Illustration from Prof Derek Martin, University of Alberta
3
Pictures of underground rock failure
in the next slides are from
Table 7.7 in this book
4
The
6
Let us think about
what happens to a
point in the rock
mass which becomes
a point on the surface
of an underground
excavation
7
The three primary effects of excavation are:
a) displacements occur because stressed
rock has been removed, allowing
the remaining rock to move (due to
unloading);
(b) there are no normal and shear stresses
on an unsupported excavation surface and
hence the excavation boundary must be a
principal stress plane with one of the
principal stresses (of magnitude zero) being
normal to the surface. Generally, this will
involve a major perturbation of the pre-
existing stress field, both in the principal
stress magnitudes and their orientations;
and
(c) at the boundary of an excavation open to
the atmosphere, any previous fluid pressure
existing in the rock mass will be reduced to
zero (or more strictly, to atmospheric
pressure). This causes the excavation to act
as a 'sink', and any fluid within the rock
mass will tend to flow into the excavation.
8
9
10
The rock properties required
for design are those of the
rock mass after, rather than
before, excavation.
Thus, if during excavation
the intact rock deteriorates,
the redistribution of stress
damages the rock, and water
flow weakens fractures, the
local host rock mass will be
weaker than anticipated.
There can be complex
variations in the stress paths.
Major
principal
stress,
1
Minor principal stress, 3
Wuhan – Feb 2008 – Unsolved Problems in Rock Mechanics and Rock Engineering 11
Rock mass
Stress state at a pointbefore excavation
1
3
Rock mass
Excavation
Stress state at the sameexcavationpoint after
1
Failure criterion
Actual stress path
Assumed stress path
1
3
Initial stress state
Final stress state
Wuhan – Feb 2008 – Unsolved Problems in Rock Mechanics and Rock Engineering 12
Direct stress path
Direct stress path
1
1
3
3
Initial stress state
Final stress state
Final stress state
Failure criterionFailure criterion
Indirect constrainedstress path
1
3
Initial stress state
Initial stress state
Final stress state
Indirect stress path
1
3
Initial stress state
Final stress state
1 3
1 3
1 3
1 3
(a) in elastic materials stress paths are unconstrained
(b) in inelastic materials, stress paths are constrained by the failure locus
Illustration from Prof John P Harrison, University of Toronto
Wuhan – Feb 2008 – Unsolved Problems in Rock Mechanics and Rock Engineering 13
3
1
2
failure locus surface
c
1 2 3
Changes in principal
stress magnitudes
000
00
00
2
1
Principal stresses are parallel and perpendicularto open fracture surfaces and excavation surfaces
1
2
,
3 = 0
14
Trend
Plunge
For a line:
Trend and plunge
For a plane:
Dip and
Dip direction
Wuhan – Feb 2008 – Unsolved Problems in Rock Mechanics and Rock Engineering 15
a b cd
e
a
b
c
de
a
b
c
d
e
3
2
1 90°
great circlerepresenting planeof excavation surface
NChanges in principal
stress orientations
Illustration prepared by Prof John P Harrison, University of Toronto
At all locations and times during excavation,
the principal stresses remain orthogonal
1 2 3
16
Illustration from
Prof John P
Harrison,
University of
Toronto
Wuhan – Feb 2008 – Unsolved Problems in Rock Mechanics and Rock Engineering 17
Principles of stress paths in the context of
excavation for rock engineering
1. The stress path is defined as the variations in
magnitudes and orientations of the three principal
stresses in the stress tensor as a result of natural or
engineering-induced changes.
The term stress path has been used (e.g. Lambe
and Whitman, 1979) to refer to the sequence of
loading in a laboratory test. Here we use the term in
a more general sense to refer to the changes in the
stress tensor with time.
Wuhan – Feb 2008 – Unsolved Problems in Rock Mechanics and Rock Engineering 18
2. Stress paths are geometrically constrained
by two factors.
One is the convention that, 1 2 3 ,
which has the effect that only part of the entire
stress space can be traversed by the stress path.
The other constraint is that certain states are not
sustainable in an engineering context, due to the
fact that rock follows a failure criterion, and hence
the traversable region of space is limited.
Wuhan – Feb 2008 – Unsolved Problems in Rock Mechanics and Rock Engineering 19
3. In an elastic material, by definition failure
does not occur, and so the stress path is
unconstrained in terms of failure and is of
no practical significance.
Wuhan – Feb 2008 – Unsolved Problems in Rock Mechanics and Rock Engineering 20
4. In an inelastic material, the stress path
does have practical significance, because if
it reaches the failure initiation locus, not
only will the properties of the material
change, but the final stress state will be
different from that based on elasticity.
Wuhan – Feb 2008 – Unsolved Problems in Rock Mechanics and Rock Engineering 21
5. Time is considered to be the independent
variable for the stress path, although this
can often be correlated directly to a spatial
variable, such as tunnel advance.
Wuhan – Feb 2008 – Unsolved Problems in Rock Mechanics and Rock Engineering 22
6. The stress path ̶ in terms of changes in
the principal stress magnitudes ̶ can be
plotted directly in principal stress space.
The stress path in terms of changes in
principal stress orientations can be plotted
directly on an hemispherical projection.
To plot both, magnitudes and orientations,
on the same diagram requires a hybrid
presentation.
Wuhan – Feb 2008 – Unsolved Problems in Rock Mechanics and Rock Engineering 23
7. Because rock is an inelastic material,
the stress path should be tracked in all
analyses of stress redistribution, to account
properly for those circumstances when the
stress path reaches the failure locus.
Wuhan – Feb 2008 – Unsolved Problems in Rock Mechanics and Rock Engineering 24
8. Different excavation sequences will give
rise to different stress paths, some of which
may reach the failure locus.
It may be possible to ameliorate, reduce
the effect of, (or exacerbate, make worse)
this effect for engineering purposes by
considerations of the excavation sequence.
Wuhan – Feb 2008 – Unsolved Problems in Rock Mechanics and Rock Engineering
In underground excavations, the major principal stress
reaches a maximum parallel to unsupported rock
surfaces ̶ where the stress perpendicular to the
excavated surface is zero, 3 = 0.
1
2
0 0
0 0
0 0 0
Principal stress perpendicular to
excavation surface
Principal stresses parallel to excavation
surface 1
2
,
3 = 0
25
a b cd
e
a
b
c
de
a
b
c
d
e
3
2
1
90°
90°
90°
N
3
1
2
failure locus surface
c
1 2 3
a b cd
e
a
b
c
de
a
b
c
d
e
3
2
1 90°
great circlerepresenting planeof excavation surface
N
Principles of the
stress path
26 Illustration from Prof John P Harrison, University of Toronto
27
Illustration from Prof John P Harrison, University of Toronto
28
The stress path principles hold whatever the type of
excavation, e.g. during the block caving method of mining
End of Lecture 3
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