Analysis of Rock Mass – Support Interaction &
Investigation of Stabilisation Techniques
CSMM144 Underground Excavation Design
640046848
Dr J.Coggan April 2015
Introduction
This report details the analysis of a planned excavation of a permanent 50m long tunnel,
with a specified cross section of 10m x 5m – at a 1000m depth below surface. Provided
geotechnical information has been incorporated into the design, and used to offer support
recommendations – which have subsequently been further verified through comparisons
with stability results derived from the use of several rock mechanics software programs
(Examine2D, RocSupport, Phase2, UnWedge, RocLab). This investigation has been
conducted for two tunnels of both South East (225o) and South West (135o) orientations; to
evaluate the potential effects of different K-ratios due to a variation in in-situ stress and the
influence held by discontinuities on the changing directions. For clarity, stereonets outlining
the layout of both joint sets, tunnel orientations and bedding have been produced; included
in the appendix (Figure A). Finally, comments related to the final design in terms of tunnel
shape, and specific support recommendations have been provided.
Note: numbered figures (1, 2, 3) are included in this report, and lettered figures (A, B, C) can
be found in the attached appendix.
Rock Mass Classification: Q-System
The supplied geotechnical data included a Q value of 4, which was subsequently assessed
using the Q system - to determine the methodology’s support recommendations for the
excavation. It is assumed that the Q value applies to both tunnel orientations; despite
changing in-situ stresses due to the change in bearing.
Figure 1 shows the Q system graph used in to determine required support. ESR, the
excavation support ratio, was taken as 1.6 to represent a permanent excavation. The span
was taken as 10, giving a span over ESR ratio of 6.25. With the intersection point landing in
category 3 – the corresponding support recommendation is then a combination of 5-6cm of
fibre reinforced shotcrete with systematic rock bolting.
Length of the rock bolts has been calculated as 2.9m in Equation 1 below, with 2.1m spacing
as specified in Figure 1.
Bolt length = 2 + (0.15 ∗
Width
) = 2 + (0.15 ∗ 6.25) = 3m
ESR
EQUATION 1 - ROCK BOLT LENGTH
The recommended support has been considered as adequate for the excavation. The Q
system has a proven history with many cases of successful implementation in the past.
However, a key factor that the system does not consider is the influence of bedding on
potential block caving. Better outlined in Examine2D illustrations included in the appendix
(Figures X and Y), the specific placement of individual rock bolts has the potential to incur a
detachment of a block of weak rock due to the alignment of joints in the local region.
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F IGURE 1 - Q-SYSTEM SUPPORT TABLE (NGI, 2013)
Examine 2D
Examine 2D has been used to model both proposed excavation orientations. In addition to
varying the in-situ stresses, the software allowed for the inclusion of joints and bedding –
input according to the provided dip and dip directions relative to both tunnel orientations.
Excavations were modelled according to the provided data using Hoek-Brown
(UCS,GSI,mi,D) and Barton-Bandis (JCS, JRC, residual friction angle) variables, and were
specified to 1000m depth.
Factor of Safety
Figure B shows the factor of safety analysis for the south western tunnel orientation, with a
K-Ratio of 1.5. The factor of safety has been visualised through a contour system –
highlighting areas of likely potential failure due to the direction and magnitude of the stresses
acting upon the excavation. Expected low stresses in the roof (FoS of 0.2) and to a lesser
extent, the floor (FoS 0.4) can be seen, but a key issue can be seen in the equally low factor
of safety in the right sidewall. It is assumed that this is only not apparent in the left hand side
due to the specific placement of joints – which have been approximated – and that the
sidewall holds potential to be equally threatening. This low factor of safety would lead to
spalling or potentially collapse of the wall, requiring the installation of support.
The south eastern excavation has similar threats to stability as identified in the south west;
shown in Figure C. As before, low stability can be seen in the sidewall as well as the ceiling,
with an additionally unstable floor.
Despite having around 30% less in-situ stress acting on it, the south eastern orientation
appears to be more unstable than the south west – the reverse of what was expected at the
outset of design. This has been attributed to the difference in the dip of the bedding; the SW
drive includes horizontal bedding versus the 15o dipped bedding of the SE drive. This dip
results in the creation of more hazardous local pockets of instability, as the bedding gets into
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more severe angles of intersection with the joints, and in a closer
proximity to the excavation – holding more chance for the creation of
wedges. An example of this wedge creation can be seen in the lower
left hand wall of the south east excavation (Figure 2).
It should again be stated that the joints and bedding input into
Examine2D have been created through approximations, and that the
specific layout of the joints, and thus optimal rock bolt locations, needs
to be physically determined.
Stress Distribution
F IGURE 2 –
W EDGE CREATION
Figures D & E show the distributions of horizontal stress (σ1) in MPa
throughout both excavations.
Key points to note are the areas of low stress and in the case of the SE excavation; negative
(tension) forces in the floor and near the lower left corner. This is due to the displacement of
the walls due to deformation (discussed below), pulling the rock in towards the centre of the
excavation. This is important, as rock is substantially weaker in tension than it is in
compression, so the requirement for these areas to be properly identified and subsequently
rock bolted (strong in tension) is vital.
Additionally, joints experiencing both shear and tension forces have been highlighted in
purple and red respectively. Holding the potential to slip, these should ideally be rock bolted
if in the immediate surrounding area of the excavation to prevent the knock on effects which
could occur (rock fall).
Displacement
Examine2D is also capable of displaying the total expected displacement of the rock –
shown in Figures F & G. For a clearer analysis, the maximum values for each excavation
area have been tabulated and converted into mm (Table 1).
Although sidewall deformations are relatively similar,
differences in the roof and floor can be seen. While the
SE drive has less overall vertical movement, the majority
of it is in the floor, due to tensional stress forces and the
shearing of surrounding joints. Creating a complex
situation to deal with - the greater but simpler roof
deformation within the SW drive, shown in this case,
would be easier to prevent via a standard support setup
of rock bolts and shotcrete.
T ABLE 1 - MAXIMUM
DISPLACEMENTS
Limitations
A key limitation of the Examine 2D software is that it can only create a simulation in one
direction; it is not wholly representative of actual conditions. However, in this unique situation
this mostly does not affect the analysis due to the perpendicular alignment of the tunnel &
and joint orientations. While the program does well in outlining the issue of potential sidewall
spalling and areas of low factor of safety around the excavation – it is not able to incorporate
the effect of adding support, subsequently being unable to provide clarification as to the
potential influence of a reinforcement design.
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RocSupport
The use of the RocSupport software provided an initial limitation in that it only supports
circular excavations. While the specific shape of the access tunnel has not been defined, the
change of a 10m x 5m excavation to a circular version is considered too great a change to
recommend with only fundamental knowledge about the tunnel use requirements. However,
the program was still used as a tool for comparison through analysing correlations between
the conclusions drawn for a similar sized circular excavation in the same ground conditions.
The size of the excavation was taken as a circle of 4m radius, which gives an area of
50.27m2; essentially equivalent to the 50m2 area of the specified excavation. A separate
model was created for both individual orientations – the fundamental difference being in the
in-situ stress. From the provided geotechnical data, the 37.5MPa stress was taken as acting
on the south western tunnel, and the 26.0MPa stress on the south eastern tunnel. These
correspond to K-Ratios of 1.50 and 1.04 respectively.
In both cases, the distance to which support was installed from the face was found to
substantially affect the calculated factors of safety – a factor not included in other systems.
This is due to the reactionary stress forces from excavation works requiring time to
redistribute throughout the surrounding rock; installing support too early would entrap this
unnecessary additional stress. With consideration to this, a distance of 2m was incorporated
to allow adequate stress redistribution; shown in Figures I & K. From the graphs, the support
can be seen to only begin acting once the gradient of stress redistribution has begun to
relax.
The support in both directions was similar to the Q system recommendations for an easier
comparison between the two support designs; using a combination of 5cm thick shotcrete
and systematic rock bolting – though the length of these is only input as a visual factor, and
does not affect the stability, unlike in Q.
South West Orientation
The south west drive originally saw much instability due to the higher in-situ stress –
resulting in an original factor of safety of around 0.16; creating a plastic zone with a radius of
5.31m around the tunnel with an in-situ stress of 37.5MPa (K Ratio =1.5). Both shotcrete
(50mm thick, 35MPa) and rockbolts (0.63MPa maximum pressure, 17mm bolts) spaced at
1.1m throughout the perimeter of the circular tunnel) were designed (Figure H). This gave a
new sampled factor of safety of 1.61, meeting the target of 1.5 for long term stability. While
the program does not factor in bolt length to the strength factor, it would need to be ensured
that the bolts pass through the plastic layer to access suitably strong rock.
South East Orientation
Starting with an approximate 0.26 factor of safety with a plastic zone radius of 4.86m and an
in-situ stress of 26MPa (K Ratio = 1.04), the south east orientation appears to be stable via
the installation of shotcrete alone. As before, 50mm thick shotcrete - with a UCS of 35MPa –
was used (Figure J); increasing the factor of safety to 1.51. Further analysis would be
required to identify any potentially weak areas which would require rock bolting; especially
because the presence of joints has not been taken into account. However, the shotcrete
alone acts to bolster the factor of safety regarding the surrounding rock mass enough to only
warrant spot bolting in determined weak spots due to discontinuities.
Limitations
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RocSupport offers a good means of comparison between the issues outlined by Examine2D
and the effectiveness of the standard support systems recommended by rock classification
systems (Q). However, it does not have the capacity to determine the extent to which the
support is a success in smaller, specific regions which would experience instability due to
jointing. This would need further analysis both numerically and on-site to provide optimal
support design. Again, a further key limitation is in the circular only geometry. The
comparison with Q does identifiy similarities – especially in success using similar
reinforcement – however variations such as the exclusion of bolt length in RocSupport do
cause issue.
Phase2 & UnWedge
Two alternative software programs which could offer valuable insight into the stability of the
final excavation are the finite element analysis programs Phase 2 and UnWedge.
UnWedge
UnWedge acts to provide stability analysis and visualisations of the intersecting structural
discontinuities in the form of wedges – which could be useful in further design analysis.
Factors of safety for each wedge are also provided with the ability to input support. A quick
setup of both excavation orientations has been included in the appendix; Figures L and M.
The key advantage of the program is that it considers the specific development locations and
sizes of wedges in the roof and spalling on the sidewalls; information lacking in the Q system
which can be used to compare with Examine2D to best design specific bolt placements.
The results correlate with the conclusions drawn from Examine2D; that sidewall spalling,
shown in the form of wedges here, is likely to occur due to the stress influence held by the
joint discontinuities. While it is difficult to accurately compare exact reinforcement designs
(specific instability locations and bolt placements vary), some brief investigation proves that
the program does suggest that these ‘danger areas’ can be satisfactorily dealt with the use
of rock bolt support.
Phase2
Phase 2 is an in-depth finite element analysis program, particularly useful in parametric
studies by allowing results shown for multiple tabs of a changing variable value. With
regards to further design of the excavation, Phase 2 could be used to assess the influence
the young’s modulus of the surrounding rock has on the safety of the tunnel. This could
extend to ensuring that prepared support will hold the strength to stabilise the tunnel even if
the modulus drops in areas of the excavation. Examples have been included in the
appendix, in Figures X Y AND Z.
Orientation and shape of access tunnel
Considering the differences outlined by Examine2D regarding the stresses, displacements
and factors of safety expected to act upon the two potential tunnel orientations; it is
recommended to excavate the tunnel towards the South-West – at a bearing of 225o.
Despite having a 30% higher in-situ stress, the horizontal bedding planes do not threaten the
excavation to the same degree as those dipped at 15o which hold much more potential for
wedge creation in the roof and sides.
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With regards to the shape of the tunnel, it is unrealistic to assume
that the excavation can and should be driven with right angled
corners, as suggested in the Examine 2D examples. The program
itself has issues with calculating stresses around such sharp edged
corners, and a drill and blast operation would not be expected to
blast out right angled corners. Instead, it is expected that the actual
access tunnel would form more of an oval shape, which is much
more accepting of stress. This is additionally beneficial with regards
to reducing floor heave, which is encouraged by sharp corners which
can encourage tension. Curved corners act to reduce this effect –
which can be seen in Figure 3.
While a circular tunnel would be most beneficial with regards to
stress redistribution and safety, the desired 10m by 5m excavation
size would require a substantial change to convert it into a circular
tunnel. Instead, a wide version of the rounded horseshoe seen in the
bottom of Figure 3 is recommended to better meet the specified size.
F IGURE 3 - TUNNEL
SHAPE VS HEAVE
Comparison of access tunnel support
In addition to ensuring stability in the excavation walls, it is vital that support also ensures the
stability of the rock in close proximity to the excavation. Figure B shows the extent of low
factor of safety extends beyond the excavation ceiling – approximately 2.5m (while the
program does not provide a measurement, the space between beddings is also 2.5m. The
final rock bolt design should then be 3m, for full reach.
The use of cable bolts to bypass the bedding was considered, to bypass the weakened
layers due to bedding near the excavation. However, a cable bolt would be substantially less
effective in reinforcing the surrounding rock – also highlighted in Figure D – unlike the
standard rock bolt.
Shotcrete set to the 5cm thickness suggested by the Q system is accepted as satisfactory in
all cases.
Conclusion and Recommendations
Several conclusions can be drawn from this analysis, in relation to the final tunnel design:



The rock mass consists of fairly competent sandstone which will only need general
reinforcement in the form of shotcrete and systematic rock bolting. This is suggested
by both the Q – system and RocSupport software.
The combination of joint sets and bedding poses a sizeable threat with regards to
areas of instability and potential rock fall. It is vital that these are properly assessed
before work begins – and are continually monitored during and after construction with
suitable spot bolting installed.
This investigation only looked to setup a general design – further detailed analysis
should be carried to fully investigate the suitability of the excavation once support is
installed, potentially incorporating the use of Phase 2 software.
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