Comparison of stress between winkler bach theory and ansys finite element met...
Underground Workshop Cavern Design
1. UNDERGROUND WORKSHOP/CAVERN
DESIGN
Rock Mass – Support Interaction
This technical report investigates potential stabilisation techniques that may
be used in a proposed permanent underground workshop facility at 2000m
below surface. This paper summarises the approach taken, key results and
recommendations. The key results will include comparison between rock
mass classification and rock mass, support interaction concepts, and
consideration of support recommendations for long-term stability of the
excavation.
Client: Mr. J. Coggan
Content length: 6 pages
Appendix length: 16 pages
Word Count: 3651
Author: 630024723
2. Underground Workshop/Cavern Design
Introduction 1
TABLE OF CONTENTS
1.0 Introduction ...................................................................................................................................... 2
2.0 Design considerations Q.................................................................................................................. 2
3.0 Design considerations RMR ............................................................................................................ 3
4.0 Excavation design Considerations South West .............................................................................. 3
4.1 Examine 2D.................................................................................................................................. 3
4.2 Roclab .......................................................................................................................................... 4
5.0 Excavation Design Considerations South East ............................................................................... 4
5.1 Examine 2d................................................................................................................................... 4
6.0 Rocsupport SW and SE........................................................................................................................ 5
7.0 Unwedge & Phase 2............................................................................................................................. 7
8.0 Recommendations & Conclusion......................................................................................................... 7
Appendix A – Design Considerations Q&RMR, Geotechnical Information, Equations ............................. 8
Appendix B – Examine 2D........................................................................................................................ 11
Appendix C - Rocsupport.......................................................................................................................... 15
Appendix D – Unwedge ............................................................................................................................ 20
Appendix E – Phase 2 .............................................................................................................................. 21
Appendix F – Stereonet ............................................................................................................................ 23
3. Underground Workshop/Cavern Design
Introduction 2
1.0 INTRODUCTION
The following report highlights key recommendations from calculated results for a proposed excavation.
The workings will be a 6m high, 10 m wide permeant excavation with a 50m length for an underground
workshop. The depth of the project is set to 2000m in “relatively” competent quartzite. A summary of the
geotechnical data can be seen in Appendix A. Information on joint sets is displayed in Appendix B with
stereonets computed using Dips 6.0. The information provided was analysed using examine 2D and
RocLab for visualization of the stresses and strength factor of the surrounding rock mass. Phase 2,
Unwedge and RocSupport have been used to show the support recommendations for the project. The
aim of this software is to provide evidence to support a decision put forward in the conclusion on whether
the working should be orientated in the South West plain or the South East and the support needed.
The K ratio for each orientation has been calculated in section 4.0 and 5.0 for South West and South
East workings respectively. In each of these sections a discussion of the benefits and limitations of the
software can be found. Unwedge and phase 2 have been shown as alternative uses of support software
however focus will be paid to RocSupport as the principal software for computing support
recommendations.
This report will be laid out to discuss each orientation of the workings with all the computational software
and a comparison will be made in section 6.0 the recommendation.
2.0 DESIGN CONSIDERATIONS Q
In the initial stages of ground stabilization investigation calculation of rock mass classification can be
beneficial as a quick way of estimating the required support. From the data provided shown in Appendix
A, it is possible to identify the support required for the potential workings. It mustbe noted these are basic
and quick calculations and may miss out important factors such as joint orientation. The information
provided shows that the rock mass has a Q value of 4. The ESR for a permanent mine working is given
as 1.6. The rock mass quality table shown in Appendix A is able to provide an approximation for the rock
class and the reinforcement for this. Q is taken on a logarithmic scale.
Q= 4
De = 6.25 (See Equation 1)
From the table in Appendix A, it can be shown that the rock quality is fair to poor and the support category
is 4. Which equates to systematic bolting with unreinforced shotcrete, 4-10cm. The calculation for bolt
length is shown in Equation 2 and the spacing is worked out from Langs formula (Equation 3).
Bolt length calculated (m) = 2.9375m or 3.0m (1sf)
Bolt spacing Calculated (m) = 1.5m (interpolated from the graph spacing is 2.5m)
For economic purposes it is probable that a bolt length of 2.9375m will not be found and therefore 3.0m
will be sufficient. The Q system canbe comparedlater to the RocSupport softwareto see if the calculation
will provide the best factor of safety. The Q system is limited by engineering judgement and cannot
reliably replace the software that will be covered in the following sections. It is ideal however for
predictions and quick calculations.
4. Underground Workshop/Cavern Design
Design considerations RMR 3
3.0 DESIGN CONSIDERATIONS RMR
RMR can be calculated using data collected in the field similar to Q (See Appendix A for the Table 1).
However a lack of ground investigation information prohibits us from calculating RMR using the tables
therefore from information provided by the client RMR is equal to 75 (seeEquation 4). Table 2 in Appendix
A shows for a RMR of 75 we expect good rock quality requiring support of bolt length 3.0m spaced 2.5m
apart. Shotcreting the crown with a thickness of 50mm. Support should be constructed 20m from the
face. Compared to Q this is similar. Length of bolt required is the same and spacing is the same. Q does
not specify where from the face the support should be installed but RMR does. Again this interpretation
is designated by engineering judgement and bias can be considered. When compared to Roc support
this report can conclusively see if the predictions made by RMR and Q will provide a sufficient factor of
safety for the excavations.
4.0 EXCAVATION DESIGN CONSIDERATIONS SOUTH WEST
The coefficient of earth pressure at rest or the K ratio can be calculated using Equation 5. The k ratio
provides a number for the horizontal stress and the out of plane stress that can be put into the
computational software to aid in the design of the excavation, show the stresses around the excavation
and help design the support for the workings. The in-situ stresses are as follows:
σv= 50MPa (vertical)
σh= 40MPa (045 degrees bearing)
σH= 60MPa (135 degrees bearing)
The K ratio for the in plane horizontal stress equals; 1.2, the K ratio for the out of plane stress is equal
to; 0.8.
4.1 EXAMINE 2D
Examine 2D software provides a simple and quick elastic analysis for investigating the different K ratios
and changes to in situ stress of the rock mass from the excavation. It also has the ability to measure the
changes in stresses dueto the appearance of discontinuities in the rock. Stress contour patterns highlight
the induced stresses surrounding the working. Using the parameters of quartzite and those set by the
client this report was able to analyze the strength factor and the in plane stress. The following figures will
be analyzed for the south west tunnel design:
Figure 4.1.A – Strength factor South West(see Appendix B)
Figure 4.1.B – Sigma 1 stress South West(see Appendix B)
The contours for strength factor represent a ratio of material strength to the induced stress. A value less
than one represents failure of the material. It can be clearly seen in Figure 4.1.A that failure will occur
under the conditions set. The contours for the sigma 1 stress represent the horizontal stresses and how
the shape and size of the tunnel redistributes around the working. Figure 4.1.B shows that the stress will
be redistributed to the corners of the excavation.
The effect of discontinuities on the structure can be shown in figures:
Figure 4.1.C - Strength factor South Westwith jointing (see AppendixB)
Figure 4.1.D - Sigma 1 stress South West with jointing (see AppendixB)
5. Underground Workshop/Cavern Design
Excavation design Considerations South West 4
Shown in Figure 4.1.C and D are the worst case scenarios for the discontinuities represented in the data.
Each strike of the joint runs parallel with the tunnel direction. The one joint set characterized is shown to
spaced 3m apart from the other. As can be seen in the Figures in Appendix B the discontinuities have an
effect on the strength factor and Sigma 1 stress plane. In Figure 4.1.C it is clear that there are less zones
where the strength factor is less than one and therefore less zones of potential failure. Figure 4.1.D shows
the horizontal stresses are not focused on the corners of the excavation anymore but show reduced
stresses in the roof and floor of the tunnel. When designing support recommendations it is important to
design for the worst case scenario. As the exact jointing is unknown it is seen as best practice to account
for the maximum possible number of joints in the set.
- The limitations of examine 2D?
Examine 2D assumes that the material modeled is isotropic, consistent and linearly elastic. It is however
the case that in reality this is very unlikely. Although the excavation is 2000m deep in quartzite it is wrong
to assume that this rock mass is homogenous. For deformation, the data produced by examine 2D is
only shows elastic distortion. What is missing is plastic deformation that the excavation causes. It is
unclear whether in a real life scenario the plastic deformation zones would have much effect on the
excavation, but at a depth of 2km they should not be ignored. The lack of 3D representation does not
take into account the real stress flow around the ends of the excavation. With the knowledge that the
excavation is 50m long this can be modelled using examine 3D. The main problem with examine 2D is it
only models in two dimensions and assumes the length is therefore infinite with no ends.
4.2 ROCLAB
This software is used in conjunction with examine 2D in order to evaluate the young’s modulus (Em) by
inputting the parameters shown in Appendix A. It was possible to calculate a value of Em which works out
as 30000Mpa (1sf). This is the same for both South West orientation and South East.
5.0 EXCAVATION DESIGN CONSIDERATIONS SOUTH EAST
The K ratio for the in plane horizontal stress equals 0.8 and the out of plane stress ratio is 1.2.
5.1 EXAMINE 2D
In section 4.1 the limitations and introduction to examine 2D can be seen, this section will only focus on
the data collected from the software and the data when discontinuities are taken into account. Shown
below are a list of the figures discussed in this section:
Figure 5.1.A - South Eaststrength factor, Examine 2D
Figure 5.1.B - South EastSigma 1 plane stress,Examine 2D
Figure 5.1.C - South East strength factor with added discontinuities,Examine 2D
Figure 5.1.D - South East Sigma 1 plane stress with added discontinuities,Examine 2D
The strength factor shown in Figure 5.1.A shows for the South Easterly orientation there is more chance
of failure in the side wall of the excavation, this is also supported by figure 5.1.B where the horizontal
stress is less in value compared with the South West orientation. With a dominant vertical stress there
are zones of reduced stress in the roof and foot of the excavation, the blue contouring in figure 5.1.B
shows this. There are similarities to the South Western orientation where the highest zones of stress are
the corners of the excavation. It is probable that the corners of the tunnel will be rounded to reduce these
6. Underground Workshop/Cavern Design
6.0 Rocsupport SW and SE 5
zones of stress and areas of failure. The biggest difference shown between figures 4.1.A and 5.1.A is the
strength factor shows failure in the roof and sidewalls through strength factor where by the strength factor
is less than 1.00 in value.
When the discontinuities are added the worst case scenario is once again taken into account. As can be
seen in figure 5.1.C and 5.1.D there are two joint sets opposing one another. This creates wedges in the
roof and sidewall. The effect that these discontinuities have on the strength factor and sigma 1 stress is
drastic compared to the discontinuities in the South Westernalignment. In Figure 5.1.C the strength factor
shows zones of failure in the left side of the excavation where a small wedge and large wedge meet. It is
assumed that this area will suffer wedge failure and subsequent support will be needed to prevent this
undesired effect. There is also likely to be large wedge failure in the roof. For this worst case scenario it
is also assumed that the wedge runs for the length of the cavern therefore there is a chance of large
wedge failure across the entire length of the working. The two joint sets increase the zone of relaxation
in the roof and floor of the excavation when comparing figures 5.1.B and 5.1.D.
6.0 ROCSUPPORT SW AND SE
Rocsupport estimates deformation in circular tunnels. This report is looking into support parameters for
a rectangular 6mx10m tunnel. Therefore this report has had to convert the area of 60m2
into a circular
shape which gives a tunnel with a diameter of 4.37m. The software can work to find different solution
based upon the solution input. For the purpose of this study the chosensolution is Carranza-Torres based
on Hoek-Brown failure criterion. The software allows this report to compare support methods for different
scenarios. The support methods include: Shotcrete, Rock bolts, Steelsets and a custom option. Because
the software cannot distinguish orientation and jointing the following section will show a table (Table 4)
comparing support parameters in a variety of scenarios but negating the SW and SE orientation. The
print screens in Appendix E show:
The ground reaction curves both long term and standard for each scenario. This is the relationship
between the interior pressure and the deformation of the walls. It is shown as a blue line for standard
and black for long term.
Support reaction curves for each scenario. Characterized as the relationship between support
pressure and the strain of the support methods used. This is shown as purple line.
The Tunnel section views showing the cross sections of the tunnel diameter for all the scenarios. This
includes the plastic zone radius and added support.
For the purpose of comparison there is a scenario with no support. Long term scenario is taken into
account because the working is permanent. Rocsupport makes many assumptions, the circular tunnel is
one already mentioned. It also assumes the K ratio is 1 or the in situ stress field is hydrostatic and
therefore as mentioned before doesn’t account for tunnel direction. The support modelled in the software
is set to a uniform internal pressure around the circumference.Rockbolts and cables are fitted in a regular
design and shotcreteing is a closed ring around the entire tunnel. In a real life scenario this may not be
needed. The factor of safety calculated by Rocsupportcan only compute when support is added a certain
distance from the face. If the support is added to far away factor of safety rises to large amount that are
unfeasible. Therefore for the purposes of continuity the support for all scenarios shown in Table 4 will be
set 1m from the face.
7. Underground Workshop/Cavern Design
6.0 Rocsupport SW and SE 6
Scenario Support added Convergence Long term
Convergence
Factor of safety
(ST/LT)
1 None 0.29% 0.32% N/A
2 - 34mm Rockbolts at a
spacing of 1.5m.
- 100mm Shotcrete
thickness
0.27% 0.30% 1.46 (ST) / 1.18 (LT)
3 - 34mm Rockbolts at a
spacing of 1.5m.
- 50mm shotcrete ().5
day curing time)
- 150mm Steelsets at
32kg/m
0.28% 0.32% 1.37 (ST) / 1.09 (LT)
4 - 34mm Rockbolts at a
spacing of 1.0m.
- 1000mm shotcrete
- 307mm Steelsets at
97kg/m with a 0.1m
out of plane spacing
0.22% 0.23% 2.37 (ST) / 1.96 (LT)
5 (1.35m from face) - 34mm Rockbolts at a
spacing of 1.0m.
- 307mm Steelsets at
97kg/m with a 1.1m
out of plane spacing
- 300mm shotcrete
0.25% 0.28% 1.9 (ST) / 1.51
Table 4: Comparison table for the five scenarios (See Appendix C)
Figures used:
- Figure 5.2.A: Graph and diagram with no support(Scenario 1)
- Figure 5.2.B: Graph and diagram using parameters setby Q (maximum) (Scenario 2)
- Figure 5.2.C: Graph and diagram for minimum maxsupportpressure(Scenario 3)
- Figure 5.2.D: Graph and diagram for bestsupportsolution.(Scenario 4)
- Figure 5.2.E: Graph and diagram for the mostpractical supportsolution (Scenario 5)
Although scenario one has a small convergence long term and short term it is still likely to fail. If it is
added to the examine 2d data the report has shown that in both orientations there is chance of failure. It
is to this reports conclusion that the cavern will require support. Scenario 2 uses the maximum Q values
calculated in section 2.0. There is no specification on rock bolt diameter so for the purpose of worst case
scenario this report has compared the maximum diameter available on the software of 34mm. The Q
system scenario does show a small change in long term convergence but a long term factor of safety of
1.18 is too small. A factor of safety of 1.00 is technically deemed safe, however practically the design of
the excavation needs to have a long term factor of safety above 1.5. Scenario 3 is there to compare the
minimum max support pressure for all of the support. Its long term convergence is the same as
unsupported and factor of safety of 1.09. This scenario is unpractical for those reasons. Scenario 4 looks
at using all the support at maximum max support pressure with small spacing’s between supports. It
gives the best convergence value and the change between long term and short term convergence is
negligible (0.23% and 0.22% respectively). The factor of safety is also sufficient for the tunnel being 1.96
for long term. In reality this scenario is probably too expensive with all the support and inefficient with all
the small spacing’s. Scenario 5 is most likely the best option. Factor of safety in the long run is above 1.5
8. Underground Workshop/Cavern Design
7.0 Unwedge & Phase 2 7
and convergence is 0.28% long term, the second best option shown in table 4. It will be cheaper to install
the support in this scenario compared with scenario 4.
One of the biggest limitations with the software is the in ability to separate the spacing’s of support. In a
practical solution this would be different. It is important to compare the data from Rocsupport with
Unwedge and phase 2 which have been explained in the next sections.
7.0 UNWEDGE & PHASE 2
UnWedge
3 dimensional representation of excavation with discontinuities, wedges and joints can be easily seen with
color coding (Appendix D)
Support mechanisms can be input on the 3d diagram and easily visualised, also takes into account
orientation.
Safety factors and weight (tonnes) can be calculated and shown for individual wedges.
The data from the file shows the wedges in the South west orientation are smaller, require less support
and tunnel has better safety factor.
Phase 2
The Phase2 consists of three program components: Model, Compute and Interpret.
Support structures can be added separately.
A wider variety of support mechanisms that can be modelled compared with RocSupport.
In Appendix E the phase two computation and interpretation can be seen for the South East orientation.
The interpretation offers a similar view to the Examine 2D software, therefore it is easy to analyse the
data. The added support reduces the sigma 1 stress around the excavation drastically. No south West
file was found therefore there can be no comparison.
8.0 RECOMMENDATIONS & CONCLUSION
Tunnel orientation mustbe in the South Westdirection; Examine 2D showedbetter strength factor
and responses to sigma 1 stress with discontinuities.
Discontinuities in South East orientation have potential to form large wedges (see UnWedge and
examine 2D)
South West tunnel requires less support (See Appendix D)
The South West tunnel will ideally need systematic rock bolts spaced 1.0m apart with a diameter
of 34mm and a length of 3m. It will require 300mm of shotcrete and 307mm Steelsets spaced
1.1m apart. This will reduce the long term convergence from 0.32% to 0.28% and the factor of
safety to 1.51.
In reality the Q system support parameters calculated will be sufficient for the cavern. The factor
of cost will be the decision between the two scenarios in the conclusion.
The solutions presented in this report should not be taken as absolute and support must be
dynamic with advance of the excavation. These figures and results should be used for planning
and construction design.
All the software discussed has limitations the two focused in this report (Examine 2D and
Rocsupport) the main limitation being not taking into account plastic deformation.
11. Underground Workshop/Cavern Design
10
Table 2: Guidelines for excavation and support of 10 m span rock tunnels in accordance with the RMR
system, after Bieniawski 1989.
Table3: Geotechnical
data.
(Below)
Stress and joint sets
12. Underground Workshop/Cavern Design
Appendix B – Examine 2D 11
APPENDIX B – EXAMINE 2D
Figure 4.1.A – South West strength factor, Examine 2D
Figure 4.1.B – South West Sigma 1 plane stress, Examine 2D
13. Underground Workshop/Cavern Design
Appendix B – Examine 2D 12
Figure 5.1.A – South East strength factor, Examine 2D
Figure 5.1.B – South East Sigma 1 plane stress, Examine 2D
14. Underground Workshop/Cavern Design
Appendix B – Examine 2D 13
Figure 4.1.C - South West strength factor with added discontinuities, Examine 2D
Figure 4.1.D - South West Sigma 1palne stress with added discontinuities, Examine 2D
15. Underground Workshop/Cavern Design
Appendix B – Examine 2D 14
Figure 5.1.C - South East strength factor with added discontinuities, Examine 2D
Figure 5.1.D - South East Sigma 1 plane stress with added discontinuities, Examine 2D
16. Underground Workshop/Cavern Design
Appendix C - Rocsupport 15
APPENDIX C - ROCSUPPORT
Figure 5.2.A – Unsupported tunnel diagram and ground characteristic curve
18. Underground Workshop/Cavern Design
17
Figure 5.2.C – Support parameters and ground characteristic curve for all support at minimum max
support pressure.
