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REE720S - Rock Engineering 324 - 1st 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
FRIST 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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1.2 Page 2 |
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Instructions: Answer Question I and any 4 other questions. Excess questions will not be marked.
Question I is compulsory.
Time allowed: 3 hours
Question I
(20)
(Short answer questions)
a) Expand the CHILE properties ofrockmass? [l]
b) What kind of roof failure can a truss bolt can prevent? [l]
c) How do the tangential and radial stresses vary as you move away from the boundary of a circular
opening [l]
d) Under low stress environment what kind of support stiffness is required? provide an example [2]
e) What is the function of sill pillar? [ 1]
f) How are the tangential and radial stresses influenced by the internal pressure applied to a circular
opening? [l]
g) When k>0.3 what is the nature stress at the crest of the circular opening? [l]
h) Two openings are made in the underground adjacent to each other and tunnel 1 is under the
influence of tunnel 2, while tunnel 2 is not under the influence of tunnel I. Which one should be
opened first for safe excavation? [ 1]
i) What kind of mesh are used for shotcrete? [I]
j) What is active support and give an example [2]
k) What is critical support pressure? [I]
I) What are the limitations of resign bolts? [2]
m) What is the function of barrier pillars in mines? [I]
n) What are the assumptions behind the pillar design according to tributary theory? [2]
o) What are the conditions for planar slope failure? [2]
Question II
a) A tunnel of 4 m diameter driven at a depth of 500 m in stresses field with k = 0.25. The rock mass (20)
compressive and tensile strengths found from laboratory test are 30 MPa and 2 MPa respectively.
The average density of overburden rock is 27 kN/m 3• Determine the extent of boundary failure.
Question III
a) A tunnel of radius 2.0 excavated in a rock having modulus of elasticity 5 GPa and Poisson's ratio (20)
Of 0.25. The tunnel is subjected to initial hydrostatic stress field of 10 MPa. Assuming c and of
intact rock 3 MPa and 20° and those of broken rock is I MPa and 15° respectively.
i) Determine critical support pressure
ii) Calculate inward displacement of the tunnel when internal support pressure is 5 MPa and 3
MPa
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Question IV
a) A circular tunnel of radius a is constructed in prevailing far-filed stress of O'v and cr1i.Tangential (IO)
stress at point B (a units distance from boundary of the opening) is twice than that of at point A (a
units distance from boundary ofthe opening). Detennine the value ofk.
B
A
b) Discuss the support reinforcement principles used to support underground mine openings
[l OJ
Question V
a) A horizontal strati form ore body at a depth of 150 m below ground surface is planned for extraction ( 14)
using 4.0 m room spans and pillars 7.0 m square in plan. The full stratigraphic thickness of3 mis
to be mined. The unit weight of the overburden rock is 22.5 kN/m 3• Analysis of pillar failures in the
orebody indicates that pillar strength is defined by
s = 10.44h- 0·7w35 ·
Where s is in MPa and pillar height h and width Wp are in m
1. Determine the factor of safety against compressive failure of pillars in the planned layout.
11. The orebody described above is underlain by a clay shale, for which c = 5 MPa, = 28°,
and y = 22 kN/m 3• Determine the factor of safety against bearing capacity failure of the
floor rock.
b) State the advantages of rock bolts
( 6)
Question VI
a) What are the different types of backfill considered in mining operations and briefly describe about ( I 0)
the crushed waste fill
b) Data for a potential wedge failure by sliding down the line of intersection are given below
(10)
Plane
Dip
direction
Plane A
-30
Plane B
120
Slope Face
45
Upper slope
100
Height of wedge = 30 m
Dip
60
60
60
10
Cohesion (kPa)
70
35
Friction angle(~)
29
23
1. Determine dip and azimuth of the line of intersection of joint plane A and B [6]
ii. Check whether basic conditions for wedge failure are satisfied [4]
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Equal Area Net
(Schmidt Net)
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Additional Information
Exam (REE720S-2022)
Stresses around circular openings
ur.r =~p2 { (l+k)
( 1--
a2)
r2
-(1-k)
( 1-4-+3ra2-2
a4)
r4
cos20
}
<Joe= P2o { (1 + k) ( 1 + ::) + (1- k) ( 1 + 3 ::) cos 20}
rer =~
p
2
{
(l-k)
( 1+2--3ra2-2
Displacement around circular openings
a4)
r4
sin20
}
2
Ur= p4°Ga r {(l+k)-(l-k)
( 4(1-v)-r a22) cos20 }
2
ue = p4°Ga r {(1- k) ( 2(1- 2v) + ra22) sin 20 }
Stresses around circular openings with internal pressure
-p·){ ( = <Jrr Pi + (p0 2 t (1 + k') 1 - raZ2) - (1 - k') ( 1 - r42a2 + 3 ar44) cos 20}
-p·){ ( = <Jee Pi + (p0 2 t (1 + k') 1 + ra22) + (1 - k') ( 1 + 3 ar44) cos 20}
-p·){ ( 2 4
= 're
(p 0
2i
(1 - k')
1 + r22a -
3 ra4 ) sin 20}
k' = kpo -pi
Po-Pi
Stresses around circular openings at infinite distance
<Jee=p0 [l + k + 2(1- k) cos 20]
Stress transformation
'n = 're
cos 2a -
1
2 (<Jrr-
<Jee)sin 2a
Support System Characteristics
= = <J' 2c cos¢ k 1+sin¢
c 1-sin!ll
1-sin(ll
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2 Pages 11-20 |
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Inward elastic displacement
Radius of plastic zone around the tunnel
Total inward displacement
Longitudinal displacement
Ratio of maximum plastic zone radius to tunnel radius
1
rp = [2(p 0 (k - 1) + O"c)](k-1)
r0
(1 + k)uc
Displacement at tunnel face
Maximum displacement
The tunnel wall displacement ahead of the face (x < O) is
U l. -- U·lf exfro
The tunnel wall displacement behind the face (x > O) is
(-3x/r 0)
= ui Uim - ( Uim - Uit )e (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
= + Psmax
Uiy Ufo
s
FS = Psmax
Pse
Shotcrete support
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Rock bolts
Average pillar stress
= = Psbmax
Tbf
sl sc ; Ksb
E5 n:dt
4ls l sc
Pillar design
Bearing capacity of roof/floor with square pillar
qb
=
1
2ywpNy
+ cNc
(i) (!)] Ne = (Nq - 1) cotcp; Ny= l.S(Nq - 1) tancp; = Nq en:tan<J, tan 2 [ +
Bearing capacity of roof/floor with rib pillar
qb
=
1
zYWpNySy
+ c cotcp NqSq -
c cotcp
o.4(Wp/lp); Sy= 1-
Sq= 1 +sin</J(Wp/lp)
Maximum subsidence
Subsidence
Subsidence at a distance x from the rib side
Sx = O.SSm[tanh (; - 1.645) + 1]
Slope Stability
Planar slope failure
cA + w cos t/Jptan cp
FoS=
w sin t/Jp
Slope with Tension Crack in upper slope surface (From equations)
FoS = _cA_+ (.w.;.._w.c._o._ssitn/"Jt-p/--J-pU+---V-~.Vc-o.-ssitn/Jt/pJpt)an cp
1
A
= (H. -,,z,)
sm 'l'p
;
U
= zYwZswm. (H,'l',p,-
z) ; V = -2l Ywza,
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Weight of sliding block (Slope with Tension Crack in upper slope surface)
Weight of sliding block (Slope with Tension Crack in a slope face)
Factor of safety of the slope in dimensionless form (from Figures)
F=(-2-c/-y-H-).--P-+--Q(-Q+-.-cRo-.St-lc/-Jop-t-l-/RJp(P +S))tan c/>
P
=--(-;1s-in
z/ H)
1/Jp
R
=-.Y-y.w-;
zw
z
z
H
S=-.-z.zwsmlHzjJ
.
P
Slope with Tension Crack in the upper slope surface
Slope with Tension Crack in the slope face
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