AGH UNIWERSITY OF SCIENCE AND TECHNOLOGY
IN CRACOW
FACULTY OF MINING AND TECHNOLOGY
The project sheet from subcject:
UNDERGROUND CONSTRUCTIONS
Theme:
EVALUATION OF THE QUALITY OF THE ROCK MASS
IN THE VICINITY OF THE TUNNEL (CHAMBER)
WITH THE INITIAL PROPOSAL FOR HOUSING
Prepared by:
Łukasz Ładak
Civil engineering
Year 3, Group 3
Project number: 108
- 2 -
TABLE OF CONTENTS
1.
Project data ........................................................................................................................... - 3 -
2.
Rock Quality Designation – RQD ............................................................................................. - 4 -
3.
Rock Mass Rating System Classification – RMR ....................................................................... - 5 -
3.1.
Basic RMR....................................................................................................................... - 5 -
3.2.
Modified RMR (MRMR) .................................................................................................. - 6 -
3.3.
Uniaxial compressive strength R
crm
................................................................................. - 7 -
3.3.1.
Hoek ....................................................................................................................... - 7 -
3.3.2.
Aydan & Kawamoto ................................................................................................ - 7 -
3.3.3.
Kalamaras & Bieniawski .......................................................................................... - 7 -
3.3.4.
Summary ................................................................................................................ - 8 -
3.4.
Young’s modulus ............................................................................................................ - 8 -
3.4.1.
Bieniawski & Serafim & Pereira ............................................................................... - 8 -
3.4.2.
Hoek & Brown......................................................................................................... - 8 -
3.4.3.
Summary ................................................................................................................ - 8 -
4.
Rock Tunneling Quality Index Q .............................................................................................. - 9 -
4.1.
Rock Tunneling Quality Index calculations ...................................................................... - 9 -
4.2.
Young’s modulus: ........................................................................................................... - 9 -
4.3.
Equiwalent dimention D
e
...............................................................................................- 10 -
4.4.
Support system..............................................................................................................- 10 -
4.4.1.
Preliminary support proposal based on the graph ..................................................- 10 -
4.4.2.
Bolt length .............................................................................................................- 11 -
5.
Correlation between RMR and Q Systems .............................................................................- 11 -
6.
Comments ............................................................................................................................- 12 -
- 3 -
1. Project data
The main aim of the project is to estimate of rock mass quality along with preliminary support
proposal.
Table 1. Initial data
No.
Parameter
Value or description
1.
Shape, dimensions and destinations of tunnel
(chamber)
Underground parking chamber, crossing
rectangular, width 25 m, height 8 m
2.
Average depth, m
30
3.
General characteristic of rock mass in the
region of excavation
Concise, block
4.
Average compressive strength of rock
surrounding tunnel, MPa
70
5.
Average tension strength of rock surrounding
tunnel, MPa
3
6.
RQD, %, core diameter 55 mm
As in the picture
7.
Number and average spacing of discontinuities
sets
Two sets of discontinuities with average
spacing 1.0m
8.
Discontinuities characteristic
Stratas in contact, impermeable natural
filling
9.
Ground water
Driping
10.
Orientation of discontinuities sets to the dip
orientation of tunnel (chamber)
Strike perpendicular to longer chamber
axis; drive against dip, dip 25
o
11.
Way of excavating
Manual and mechanical excavating with
using blasting materials
Figure 1. Drilling core
- 4 -
2. Rock Quality Designation – RQD
Rock Quality Designation index is the borehole core recovery percentage incorporating only
pieces of solid core that are longer than 100 mm in length measured along the centerline of the core.
In this respect pieces of core that are not hard and sound should not be counted though they are 100
mm in length. RQD has considerable value in estimating support of rock tunnels.
Rock Quality Designation index is most often calculated according to the following formula:
=
∑
· 100%
[1]
Where:
∑
–
sum of length of core sticks longer than 100 mm measured along the center line of the core
– total length of core, m.
Therefore there are 4 core piece that are longer than 100 mm and theirs lengths sum up to:
= (20 + 16 + 35 + 14) = 85[
]
As seen in the picture 1, total length of core amounts to:
= 100[
]
In this case the equation [1] for calculating the RQD index was as follows:
=
85
100
· 100% =
.
[%]
According to the estimated RQD value, examined rock mass was classified as good (range
between 75 and 90%).
- 5 -
3. Rock Mass Rating System Classification – RMR
Rock Mass Rating System is a geomechanical classification system for rocks, developed by
Z. T. Bieniawski between 1972 and 1973. The following six parameters are used to classify a rock
mass using the RMR system: uniaxial compressive strength of rock material, RQD, spacing of
discontinuities, condition of discontinuities, groundwater conditions and orientation of
discontinuities. Each of the six parameters is assigned a value corresponding to the characteristics of
the rock. These values are derived from field surveys. The sum of the six parameters is the "RMR
value", which lies between 0 and 100.
3.1. Basic RMR
Table 2. Rock Mass Rating System (after Bieniawski 1989)
No.
Parameter
Value
Rating
Comments
1
Strength of intact rock material
(uniaxial compressive strength)
70 MPa
7
Linear adjustment
2
Drill core quality (RQD)
85 %
18
Linear adjustment
3
Spacing of discontinuities
1.0 m
13
Linear adjustment
4
Condition of
discontinuities
Discontinuity
length
(persistence)
< 1 m
6
Envisaged value
Separation
(aperture)
< 0.1 mm
5
Envisaged value,
stratas in contact
Roughness
Very rough
6
Envisaged value
Infilling (gouge)
Hard filling < 5 mm
4
Envisaged value,
natural filling
Weathering
Unweathered
6
Envisaged value,
RQD=85%
5
Groundwater
Dripping
4
Lack of data about
inflow
6
Dip direction and orientation
Strike perpendicular to
longer chamber axis;
drive against dip with
25
o
dip
-10
Unfavorable
= 7 + 18 + 13 + 6 + 5 + 6 + 4 + 6 + 4 − 10 =
According to the estimated RMR value, examined rock mass was classified as fair
(class III, range between 41 and 60 points).
- 6 -
3.2. Modified RMR (MRMR)
Calculation of Modified Rock Mass Rating in the present project is not necessary. The MRMR
describes decrease of rock mass strength and other parameters under influence of specified factors.
However, these differences are related only to the rock mass in close neighborhood of excavation
area. In present project, the whole surrounding rock mass is being investigated and this is why there
is no need to calculate MRMR.
Nevertheless, for educational and comparative reasons, the MRMR will be calculated.
Modified Rock Mass Rating index is calculated according to the following formula:
=
·
· S ·
[2]
Each parameter was explained in table 3 below.
Table 3. Adjusted Rock Mass Rating System
No.
Parameter
Value
Comments
1
Blasting damage
adjustment
A
B
0,8
Manual and mechanical
excavating with using
blasting materials
2
In-situ stress and change
of stress adjustment
A
S
1
Average value of parameter
3
Major faults and fractures
S
1
Two sets of discontinuities
with average spacing
1.0 m
In this case the equation [2] for calculating the modified RMR index was as follows:
= 59 · 1 · 1 · 0.8 =
According to the estimated RMR value, examined rock mass was classified as fair
(class III, range between 41 and 60 points).
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3.3. Uniaxial compressive strength R
crm
3.3.1. Hoek
= √ ·
,
[3]
Where:
– material constant,
– average compressive strength of rock surrounding tunnel, MPa.
Tunnel width was estimated from the following equation:
=
[4]
Therefore:
=
= 0.01051
According to equation [3] uniaxial compressive strength amounts to:
,
= √0.01051 · 70 = .
[
]
3.3.2. Aydan & Kawamoto
= 0.0016 ·
.
,
[5]
Therefore:
,
= 0.0016 · 59
.
=
,
[
]
3.3.3. Kalamaras & Bieniawski
=
·
,
[6]
Therefor:
,
=
70
2
·
59 − 15
85
=
.
[
]
- 8 -
3.3.4. Summary
Table 4. Uniaxial compressive strength of rock mass values
Uniaxial compressive strenght of rock mass
Value
Hoek
7.18 MPa
Aydan & Kawamoto
24.78 MPa
Kalamaras & Bieniawski
18.12 MPa
3.4. Young’s modulus
3.4.1. Bieniawski & Serafim & Pereira
For
> 50 Young’s modulus is calculated from the equation below:
= 2 ·
− 100,
[7]
Therefore:
,
= 2 · 59 − 100 =
.
[
]
3.4.2. Hoek & Brown
=
· 10
,
[8]
Therefore:
,
=
√70
10
· 10
=
.
[
]
3.4.3. Summary
Table 5. Young’s module values
Young’s module
Value
Bieniawski & Serafim & Pereira
18.00 GPa
Hoek & Brown
14.05 GPa
- 9 -
4. Rock Tunneling Quality Index Q
4.1. Rock Tunneling Quality Index calculations
Rock Tunneling Quality Index ‘Q’ was estimated from the equation below:
=
·
·
[9]
Where:
– Rock Quality Designation,
– joint set number,
– joint roughness number,
– joint alternation number,
– joint water reduction factor,
– stress reduction factor.
Table 6. Statement of Tunneling Quality Index ‘Q’ parameters
No. Parameter Value
Comments
1
RQD
85
-
2
J
n
4
Two discountinuity sets
3
J
r
1,5
Rough or irregular, planar
4
J
a
0.75
Tightly healed, hard, non-softening
impermeable filling
5
J
w
0.33
Large inflow or high pressure
6
SRF
1
Medium stress
In this case the equation [8] for calculating the Rock Tuneling Quality Index ‘Q’ was as follows:
=
85
4
·
1.5
0.75
·
0.33
1
=
.
According to the estimated Rock Tuneling Quality Index ‘Q’ value, examined rock mass was
classified as good (range between 10 and 40 points).
4.2. Young’s modulus:
= 10 ·
·
,
[10]
Therefore:
= 10 ·
14.025 ·
70
3
=
. [
] = .
[
]
- 10 -
4.3. Equiwalent dimention D
e
=
,
[11]
Where:
– excavation diameter, m,
– Excavation Support Ratio (for underground parking assumed
= 1.2).
=
25
1.2
=
[ ]
4.4. Support system
Figure 2. Estimated support categories based on the Tunneling Quality Index ‘Q’
4.4.1. Preliminary support proposal based on the graph
According to the graph, chamber in examined rock mass belongs to the 4
rd
reinforcement
category.
- 11 -
Proposed support solution for examined conditions is systematic bolting and unreinforced
shotcrete with following parameters:
Bolt spacing (in unshotcreted area) – 1.0 ÷ 1.6 m
Bolt length (only predicted value) – value close to 5.0 m
Shotcrete thickness – 4 ÷ 10 cm
4.4.2. Bolt length
It is possible to estimate bolts length from the graph above but only for ESR value equal 1.
Although, there is analytical way to calculate needed length of bolts. The equations that were used
are represented below:
=
.
·
,
[12]
Therefore:
=
2 + 0.15 · 25
1.2
= . [ ]
5. Correlation between RMR and Q Systems
Table 7. Correlation between RMR and Q Systems under Different Conditions
Correlation
Source of case
studies
Source of case studies,
Comments
RMR value
RMR = 13,5·log(Q) +43
New Zealand
Civil engineering tunnels
58.483
RMR = 9·ln(Q) +44
Diverse origin
Civil engineering tunnels
65.127
RMR = 12.5·log(Q) +55.2
Spain
Civil engineering tunnels
69.536
RMR = 5·ln(Q) +60.8
South Africa
Civil engineering tunnels
74.004
RMR = 43.89 - 9.19·ln(Q)
Spain
Mining tunnels, soft rock
19.621
RMR = 10.5·ln(Q) +41.8
Spain
Mining tunnels, soft rock
69.699
RMR = 12.11·log(Q) +50.81
Canada
Mining tunnels, soft rock
64.699
RMR = 8.7·ln(Q) +38
Canada
Civil engineering tunnels,
sedimentary rocks
60.975
RMR = 10·ln(Q) +39
Canada
Mining tunnels, hard rocks
65.408
According to the results, the closest value to the basic RMR is the one from correlation
= 13.5 · log( ) + 43, therefore supposed localization of the underground parking is
New Zeland.
- 12 -
6. Comments
Using RMR index the rock mass was classified as class III – fair rock. However, established
RMR value (59 points) is very close to the brackets’ border, which is 60-61 points. According to the
Rock Tunneling Quality index ‘Q’ value (14 points) rock mass taken under consideration is good but
here the ‘Q’ index value is close to fair rock bracket (4-10 points). In summary, these two methods
gave us similar results. It can be said, that the rock mass examined in this project may be recognized
as a rock between fair and good.
Some different results were obtained using RMR modified index (MRMR). That method also
ranked rock mass into class III – fair rock but with lower score - 47 points. The main reason of that
assignment is using A
B
factor value equal 0.8, which is caused by using blasting materials in
excavating process. However, as it was said above, that value reflects the rock mass strength only in
close neighborhood of the excavation area.
There are sizable discrepancies in Young’s modulus and the Uniaxial compressive strenght of
rock mass values. Quite big differences shows up comparing Young’s modulus calculated for RMR
and ‘Q’ index. Values obtained from formulas for RMR (14 GPa and 18 GPa) are very higher than
value calculated for ‘Q’ index (6.89 GPa). Uniaxial compressive strenght of rock mass was calculated
using formulas for RMR and here were also some diffrent values obtained, depenging on which
formula was used. The maximum difference is noticed between Hoek’s method (7.18 MPa) and
Aydan’s & Kawamoto‘s method (24.78 MPa).
In both classifications there are some factors that have the major influence at final result.
They are RQD value, ground water conditions, spacing and conditions of discontinuities.
In my opinion RMR method is more precise. It contains more parameters obtained in
research than ‘Q’ index. On the other hand we have not got any information about some of them and
we have to estimate or predict them basing on our subjective opinion, so it could reduce precision of
RMR.
Score of ‘Q’ index imposes preliminary support which contains systematic bolting with bolt
spacing between 1.0 ÷ 1.6 m. According to figure 2, unreinforced shotcreted support 4 ÷ 10 cm thick
is also needed. Bolts’ length red from the figure 2 amounts about 5 m but that is the value for
= 1. The precise bolts’ length for
= 1.2 were calculated from analytical formula and gave
us the value equal 4.8 m.
Correlation between RMR and Q-system pointed out supposed localization of civil
engineering tunnel – New Zeland.