REE720S - Rock Engineering 324 - 2nd Opp - Nov 2022


REE720S - Rock Engineering 324 - 2nd Opp - Nov 2022



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nAmlBIA UnlVERSITY
OF SCIEnCE Ano TECHnOLOGY
FACULTY OF ENGINEERING AND THE BUILT ENVIRONMENT
DEPARTMENT OF CIVIL MINING AND PROCESS ENGINEERING
QUALIFICATION : BACHELORS OF ENGINEERING IN MINING ENGINEERING
QUALIFICATION CODE: 08BMIN LEVEL: 7
COURSE CODE: REE720S
COURSE NAME: ROCK ENGINEERING
SESSION: NOVEMBER 2022
PAPER: THEORY
DURATION: 3 HOURS
MARKS: 100
SECOND OPPORTUNITY QUESTION PAPER
EXAMINER(S) Mallikarjun Rao Pillalamarry
MODERATOR: Prof. Mapani Benjamin
INSTRUCTIONS
1. Answer all questions.
2. Read all the questions carefully before answering.
3. Marks for each question are indicated at the end of each question.
4. Please ensure that your writing is legible, neat and presentable.
PERMISSIBLE MATERIALS
I. Examination paper.
2. Tracing paper
3. Mathematical Instruments
THIS QUESTION PAPER CONSISTS OF 08 PAGES (Including this front page)

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Instructions: Answer Question 1 and any 4 other questions. Excess questions will not be marked.
Question 1 is compulsory.
Time allowed: 3 hours
Question I
(20)
Short answer questions
a) What is pulp density of backfill? [I]
b) Why is the extraction ratio maintained at less than 0.75 in room and pillar mining? [I]
c) What are the conditions for wedge failure [2]
d) How are the crown holes (subsidence) formed? [I]
e) What is the optimum pulp density with respect to slurry back fill? [I]
f) What is the function of rib pillar? [I]
g) What factors influence the amount of subsidence tilt? [3]
h) Which rock.mass parameters influence the stability of slopes? [2]
i) What are the different types of toppling failure? [3]
j) Which is the cheapest of backfills used in underground mines? [I]
k) What type oftest is used to measure the bearing capacity ofrockbolt? [I]
1) What is the point of inflexion with respect to subsidence? [I]
m) The sliding plane must 'daylight' in the slope face. What does this statement mean? [I]
n) Which one of these supports (rock bolts, steel sets and shotcrete) Figure I is stiffer?
2.S
"-
Q.
1.S
o.s
--Rock Bolts
--o-Seel Sets
-<>-Shotcrete
0
o
0.002
o.004
0.006
0.008
0.01
o on
0.014
0.016
0.018
Deformation (m)
Figure I
2

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Question II
a) A 2 m radius vertical shaft is to be excavated through a sandstone in which in situ stresses are 4 and (20)
6 MPa. A vertical discontinuity at its closest point A, located a distance of 6 m from shaft wall. The
discontinuity has Coulomb shear strength parameters C is 0.05 MPa, angle of internal friction(~) is
20°. Determine the factor of safety of discontinuity at point B shown in Figure 2.
I I l ~· 4MPa "'~
6MPa-
i Il
~MPa
Figure 2
Question III
a) A metalliferous surface mine is operated with a bench as shown in Figure 3. The height of the bench (13)
is IO m. The cohesion and angle of internal friction of failure plane are I 5 kPa and 20° respectively.
Density of water and the rockmass is 1000 kg/m 3 and 3000 kg/m3 (29.43 kN/m 2) respectively.
Detennine the effect water pressure in the crack on the factor of safety of the slope.
B
TensionCrack _.
.C
!2.5m
!Om
A
Figure 3
b) State the assumptions behind the derivation of Krisch equations used to determine stresses around (7)
underground openings.
Question IV
a) Determine the subsidence tilt between the distance of 30-40 m from rib side under the following ( I0)
working conditions assuming that pre-subsidence profile is flat
Depth of working I00 m
Length of panel 150 m
• Mining height is 4 m
b) Briefly describe subsidence mechanism in high extraction mining
(10)
3

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Question V
a) A tunnel of 3 m radius excavated in a rock is subjected to a hydrostatic stress field of IO MPa. (20)
Modulus of elasticity and Poisson's ratio of rockmass was estimated to be 600 MPa and 0.25
respectively. Assuming cohesion and angle of internal friction ofrockmass is 2.42 MPa and 30°
1. Estimate longitudinal deformation 2 m away from the tunnel face
11. Determine the factor of safety ofshotcrete applied on to the surface of the tunnel at 2 m away
from tunnel face with following specifications
Concrete Young's Modulus (Ee)= 20.7 GPa
Poisson's Ratio(n) = 0.25
Lining thickness (tc) = 0.3 m
Uni axial compressive strength (sec)= 34.5 MPa
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
Deformation (m)
Figure 4: Tunnel support characteristics curve
Question VI
a) What are the properties of backfill and how does pore pressure influences the stability of backfill? (I 0)
b) Compare mechanical anchored bolts with grouted rock bolts
(I 0)
4

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Additional Information
Exam (REE720S-2022)
Stresses around circular openings
arr =~p2 { (l+k)
( 1--
a2)
r2
-(l-k)
( 1-4-+3ar2-2
a4)
r4
cos20
}
= (j 99 ~o {(1 + k) ( 1 + ;:) + (1 - k) ( 1 + 3 ;:) cos 20}
•r0=~p2 { (l-k) ( 1+2--3ar2-2
Displacement around circular openings
a4)
r4
sin20
}
2
2
Ur= -p40G-ar { (1 + k) - (1- k) ( 4(1- v) - -ra2) cos 20 }
U9 = p4°Ga2r{ (l-k) ( 2(1-2v)+
Stresses around circular openings with internal pressure
ra22) sin20 }
2
2
r2 = (lrr
Pi + (p0
-
2
p·1)
{
(1
+
k')
( 1-
ar 2)
-
(1 - k') ( 1 - 4a
+ 3 ra44) cos 20}
-p·){ ( 2
= (l99 Pi + (p0 2 1 (1 + k') 1 + ar 2) + (1 - k') ( 1 + 3 ra44) cos 20}
24
•re
= (po
-2
p·)
i
{
(1
-
k') ( 1 + 2ra2
-
3 ra4 ) sin 20 }
k' = kpo -pi
Po-Pi
Stresses around circular openings at infinite distance
(l99 = Po[l + k + 2(1- k) cos 20]
Stress transformation
=2 2 1
1
(ln C(lrr + (l99) + C(lrr - (l99) cos 2a +•resin 2a
•n
= •re
cos 2a -
1
C(lrr -
(l99)
sin 2a
2
Support System Characteristics-·
2c ros0 k 1+si110· -
(j c ---- 1-sin0
---- 1-sin0
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Inward elastic displacement
2po - <le
Per= l + k
Radius of plastic zone around the tunnel
](k-1) 1
r, -
P-
r.0
[ (1
2(p 0(k
+ k)((k
-
-
1) + <Tc)
l)Pi + <Tc)
Total inward displacement
Longitudinal displacement
Ratio of maximum plastic zone radius to tunnel radius
Displacement at tunnel face
1
= + Tp [2(p 0 (k - 1) <Tc)](k-1)
r0
(1 + k)<lc
Maximum displacement
The tunnel wall displacement ahead of the face (x < O) is
Ul. -- U·lf ex/ro
The tunnel wall displacement behind the face (x > O) is
(-3x/r 0)
= )e ui Uim - ( Uim - Uit (zrp/ro)
Rock Support Interaction
The displacement of the tunnel at support yield is given by
The factor of safety (FS)of the support
Steel Support
Uiy = Ufo + -P-smya-x
s
FS = Psmax
Pse
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Shotcrete support
Rock bolts
Average pillar stress
Pillar design
Bearing capacity of roof/floor with square pillar
Ne= (Nq - 1)cot¢;
qb
=
1
2 ywpNy
+
cNc
(i) (t)] = Ny= 1.S(Nq - 1)tanq,; Nq e7rtan<f> tan 2 [ +
Bearing capacity of roof/floor with rib pillar
qb
=
1
2ywpNySy
+
c
cottp
NqSq
-
c cottp
Sy = 1 - 0.4 (W/zpp); Sq = 1 + sin tp(W/zpp)
Maximum subsidence
Subsidence
Subsidence at a distance x from the rib side
Sx = O.SSm[tanh (: - 1.645) + 1]
Slope Stability
Planar slope failure
FoS
=
cA + w cos t/Jptan q,
w sin t/Jp
Slope with Tension Crack in upper slope surface (From equations)
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FoS =-c-A-+--(-w-'.w-c-.o-ss-ti-/nJ~tp/--J-pU+-V.Vco.ssitn/Jtp/Jp)tan</>
1
A = (sHm. -.,,,,Pz,) ; U =. zYwZsmw. (.,H,,P,,- z) ; V =-12.Ywzi
Weight of sliding block (Slope with Tension Crack in upper slope surface)
Weight of sliding block (Slope with Tension Crack in a slope face)
½rH W= 2 {( 1 - (z/H/)cost/Jp{cott/Jp.tan t/Jr- 1)}
Factor of safety of the slope in dimensionless form (from Figures)
F=-(~2c-f-yH--).--P--+-Q-(-Q+-.Rco.Sttc/Jopt-tR/Jp(P + S))tan <J,
( 1 - z/ H)
Yw zw z
P= sint/Jp ;R=y·7·H;S=7·H·
zw z sm. t/Jp
Slope with Tension Crack in the upper slope surface
Slope with Tension Crack in the slope face
Q = {(1- (Z/H)2) cost/Jp(cott/Jp.tan t/Jr- 1)}
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