opening size and orientation
DESCRIPTION
FragmentationTRANSCRIPT
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OPENING SIZE AND ORIENTATION
In competent rock masses, where rock mass failure is not a dominating factor, failures are
described by geologic structures. If the forces imposed on the block are sufficient to overcome
the shear strength mobilized along the discontinuities, failure occurs. Whether these structural
blocks are described by discrete structures or by families of structures, failure modes are similar.
Wedges and prisms
By far the most common structurally defined failure in hard rock mining is the wedge or prism.
In this case, either a wedge (three sided) or prism (4 or more sides) is defined in the excavation
boundary by geologic structures.
Failure is by one of several modes. These are:
• unidirectional sliding along one plunge line (two faces);
• rotational sliding on one face, and;
• simple detachment under gravity action.
The latter is only applicable in the back (or crown) of an underground opening when the wedge or
prism opens downwards.
Innumerable dissertations exist on the analysis of wedge failure. Hoek and Brown, Brady and
Brown, and Goodman’s work are all good references regarding this topic.
What is important when considering such failures is that:
• a good understanding of the potential shapes and forces involved is understood. An analysis
as conducted in Figure H1 utilizing DIPS and UNWEDGE (RocScience) is highly
recommended. In some cases, an adjustment of the opening shape is all that is required to
reduce or alleviate problems with wedge failure;
• wedge failures increase in volume roughly as the square of the span, thus a minor increase in
span can have a substantial impact on the volume of rock to be reinforced (Figure H2);
All of the above can be analyzed statistically in a fashion similar as that utilized for our slope
stability designs. Rock mass designs can be conducted in a similar statistical fashion.
One useful diagram for determining maximum span is attached as Figure H3. Statistical analysis
of the rock mass properties allows an estimate of the ranges of unsupported spans that may be
attained.
OPEN
ING
BEA
RIN
G
Potential structural orientations Isometric of wedge, looking down
Potential wedge failure geometries
Isometric - back only Section - looking along axis
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FIGURE H1
Stress flow
Clamped block
“Squeezed out” block
Shearzo
ne
Schematic of clamping stresses
After Hutchinson and Diederichs, 1996
Increase of wedge volume
as opening size increase
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FIGURE H2
Diagrams taken from Stewart, S.B, and Forsyth, W.W; The Mathew’s
method for open stope design; CIM Bulletin, July-August 1995.
0.1
0.01
0.0 10 20 30 40 50 60 70 80
1.0
10
ST
AB
ILIT
YN
UM
BE
R,
N
HYDRAULIC RADIUS (FT)
100
1000
Pot
ential
lystab
le
Stab
le
Pote
ntial
lyunst
able
Pote
ntia
l majo
r failure
Pot
entia
l caving
Cavin
g
potentially stable - potentially unstable, modified Mathew’s method
potentially unstable - potential major failure, modified Mathew’s method
potentially major failure - potential caving, modified Mathew’s method
potentially stable - potentially unstable, Laubscher’s RMR converted to N
potentially unstable - unstable transition, Laubscher’s RMR converted to N
unstable transition - potential caving, Laubscher’s RMR converted to N
Note:
This chart has been designed utilizing Stewart and Forsyth’s
modification of Mathew’s method (CIM Bulletin, July 1995) as well
as Laubscher’s (1990) MRMR stability system converted to the Q
system for comparison/useage. Both presented methodologies are
limited for design in weaker rock masses.
Laubscher’s MRMR can be converted to Q’, as utilized in N, the
stability number by the following equation:
The RMR used in this equation should not be adjusted to MRMR
with the exception of blasting conditions. This is due to the fact that
the orientation and stress adjustments take place within Mathew’s
graph. This is also the reason behind extracting the stress reduction
factor (SRF) from Barton’s Q value to obtain Q’. It must also be
noted that the conversion equation given above is not the standard
conversion from Q to RMR. It has been modified to compensate for
the lack of an included SRF in Laubscher’s RMR data collection.
Q’=10^((RMR-42.52)/19.92)
Stab
le
Cavin
g
Potentia
l cavin
g
Stab
le
Cavin
g
Potentia
l cavin
gTra
nsitio
n
Stab
le
P
Cavin
g
ntial ca
ving
Transit
ion
Stab
le
ial ca
vinTransit
ion
Poten
tially
unsta
ble
TRANSITION ZONE KEY
1.0
0.8
0.6
0.4
0.2
0.0
0 5 10 15 20
Fact
or
AF
act
or
C
� ��c i
�c
� induced compressive stress on opening
�i
= uniaxial compressive strength of intact rock
Zone of potential instability (� ��c i
<2)
60o
60o
45o
20o
20o
45o
Orientation
of roof
Orientation
of wallFactor B
1.0
0.8
0.3
0.5
0.4
1.0
8
6
4
2
0
0 20 40 60 80 90
Angle of dip from horizontal (degrees)
Factor C = 8-7*cosine (dip angle)
Q’ = Q*SRF
N = Q’*A*B*C
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FIGURE H3