problem set solutions mining

7/23/2019 Problem Set Solutions Mining

http://slidepdf.com/reader/full/problem-set-solutions-mining 1/8

Arranz, Christian G.

2009-12463

EM 45 – WFX Pro!"# $"t %1

1.a

Figure 1.a.1 Working Pit

Figure 2.a.2 Final Pit

1.&nt"rra#' An(!"s)

$ta(" 3)

θ IR3=tan

−1 30

(2∗18 )+ 2∗20

tan65+

10

tan 65 *

26.+3

$ta(" 2)

θ IR2=tan−1 60

(3∗18 )+ 2∗20

tan 65+ 2∗10

tan 65 * 32.20



$ta(" 1)θ IR1

=tan−1 70

(3∗6.67 )+ 3∗20

tan 65+

10

tan65 * 53.05

Worin( Pit $!o'" An(!")

¿ tan−1 9∗20

(5∗18)+(2∗25)+(3∗6.67 )+ 20∗7

tan 65+ 4∗10

tan 65 * 36.42

Fina! Pit $!o'" An(!")

¿ tan−1 9∗20

(8∗6.67 )+ (2∗25)+ 20∗7

tan 65+ 4∗10

tan 65 * 43.+6

1.

/h" ina! 'it s!o'" an(!" 43.+6 is st""'"r than th" o'"ratin( 'it s!o'" an(!" 36.42 "as" o

th" transor#ation o th" a!! th" orin( "nh"s into sa"t "nh"s. /his "ss"ntia!! short"ns

th" o#'on"nt o th" s!o'", ths #ain( th" o#'t"7 an(!" st""'"r tri(ono#"tr.

2.



2.a.

Worin( 8i#"nsions o th" $ho"! ar" r"a7 ro# i(r" 2.a

A ≈ 10 meters #ai## 7#'in( h"i(ht

B : 13 meters 7#'in( ra7is at #ai## h"i(ht

D : 15 meters #ai## ttin( h"i(ht o th" sho"!

E ≈ 16 meters #ai## ttin( ra7is

G ≈ 15 meters #ai## 7i((in( ra7is o th" !""! !oor

J ≈ 9 meters !"aran" ra7is o th" oo# 'oint sh"a"s

K ≈ 7.25 meters !"aran" ra7is o r"o!in( ra#"

2. 8"t"r#inin( th" Mini## ;'"ratin( <"nh Wi7th

/h" irst st"' n7"rta"n as th" o#'tation o th" sa"t "r# 7i#"nsions

$in" th" ro!!in( ra7is*1.56#, th" sa"t "r# #at"ria! an(!" o r"'os" * 3=, an7 th"tra'"zoi7a! "r# has a 1# i7" to' as", th" bottom width of the berm i!! "

1+(2 1.56

tan 37°) *5.14 meters.



/h" 7istan" ro# th" r"st to th" tr "nt"r!in" is 7"t"r#in"7 ass#in( 'ara!!"! a!i(n#"nt./h" i7"st 7i#"nsion o th" tr, hih is th" o"ra!! ano' i7th * =.645 #"t"rs, as ta"n

to " th" tr i7th. An7 (iin( a 2 #"t"r !"aran" 7istan" "t""n th" sa"t "r# an7 th"

tr, th" e!ter"i!e to rest dist#!e $%& is¿7.645

2+¿ 5.14>2*10.9625# : 11 meters

/h" sho'e" e!ter"i!e to tr() e!ter"i!e is ass#"7 to " th" 7#'in( ra7is < at #ai## h"i(ht *

13 meters.

/h" desired wor)i!+,o-er#ti!+ be!h dime!sio! /B * / > < > G * 11 > 13 > 15 * 39 meters

/h" width of the (t $/& ass#in( that th" sho"! #o"s a!on( a sin(!" 'ath 'ara!!"! to th" r"st, is

"sti#at"7

/ * 0.90 ? 2? G * 1.+ ?15 ≈ 27 meters hih a''!i"s to th" i7th o th" 'i!" o ro"n #at"ria!.

/h"r"or", to a!!o or s"!! an7 thro o #at"ria! 7rin( !astin(, th" 7"si(n t is !"ss than 2=. A '#"(e

of / * 26 meters is #ss(med.

$a"t "nh * W< - W * 39 – 26 * 13 #"t"rs

Figure 2.b Section view through the working bench



2.

Gi"n th" s'"ii (rait o host ro to " 2.=, h" n#"r o !! !oa7 trsass#in( 100@

"ii"n that n""7 to " i!!"7 to #in" a 30 #"t"r !on( t is o#'t"7 as)

density of host rock , γ =2.7∗density of water

(1

metric ton

m3

)γ =2.7

metric ton∨tonnes

m3

Volume of cut =widthof cut ∗benchheight ∗length of cut =27∗15∗30=12,150m3

Mass of cut =volume of cut ∗density of host rock =12,150m3∗2.7

tonnes

m3 =32,805

t

$in" th" no#ina! 'a!oa7 a'ait o th" tr * 1+1 tonn"s, th"n

32,805

181 =181.24 trucks

3.

Figure 3.a Dimensions and forces in a rock slope with a potential failure plane (Hustrulid, 2! from Hoek, 1"#a$

Wh"r"

Fator o $a"t *

Force tending

Resisting Force( R)¿

induce sliding¿=cA+cos! tan ∅

sin! ,

t sin" #ini## "nh a" an(!" i is 7"sir"7,

Fator o $a"t * 1, #ain( sin!=cA+cos! tan∅

3.1

< tri(ono#"tr, !"t % " th" !"n(th o th" ai!r" '!an" in ross s"tion i" 'ara!!"! to th"

r"sistin( or", an7 l " th" thin"ss o th" ai!r" '!an" into th" 'a(". /h"n,

sin != "

# -B #= "

sin ! ,



th"r"or", th" Ar"a o th" ai!r" '!an", A=l#=l∗ "

sin ! 3.2

A!so, o#'tin( or th" o!#" o th" trian(!ar 'ris# ro s!o'"s!a,

Volume=1

2bhl=

1

2 " ( 1

tan !−

1

tani )∗ " ∗l 3.3

Dsin( W"i(ht, W in !s an7 8"nsit, inlbs

ft 3 , =¿ 8"nsito!#" * ? 3.4

$stittin( 3.2 or th" Ar"a, A

an7 ons""nt! sstittin( 3.3 an7 3.4 to 3.1, th"n

sin!=cA+cos! tan∅ 3.1

-Bγ ∗1

2 " ( 1

tan !−

1

tan i )∗ " ∗l∗sin!=c( l∗ "

sin ! )+ γ ∗1

2 " ( 1

tan !−

1

tan i )∗ " ∗l∗cos ! tan∅

-Bγ ∗1

2 " ( 1

tan !−

1

tan i )∗ " ∗l∗sin!=c( l∗ "

sin ! )+ γ ∗1

2 " ( 1

tan !−

1

tan i )∗ " ∗l∗cos ! tan∅

-Bγ"

2 ( 1

tan !−

1

tan i ) sin!=( c

sin ! )+ γ"

2 ( 1

tan !−

1

tan i )cos ! tan∅

-Bγ"

2 ( 1

tan !−

1

tan i )[sin!−cos!tan∅]=( c

sin ! )

-B ( 1

tan !−

1

tan i )=2( c

sin ! )[ sin!−cos!tan∅ ]∗γ"

-B

(

1

tani

)=

−2( c

sin ! )[ sin!−cos!tan

∅

]∗γ"

+ 1

tan !

-B ( 1

tan i )=−[( 2c

sin ! )∗tan ! ]+ [(sin!−cos!tan∅)∗γ" ]

[ sin!−cos!tan ∅ ]∗γ" tan !



-B

!

( 2c

sin ! )∗tan ¿

¿¿

tan i=−[ sin!−cos!tan∅ ]∗γ" tan !

¿

-Bi=tan

−1 −[ sin!tan!−sin!tan∅ ]∗γ"

( 2c

cos ! )+ [ sin!−cos!tan ∅ ]∗γ"

4.

Dsin(, Ho"-<ron ass#in( no (ron7at"r 7ata is aai!a!"

$ =γ"

c =

2650 kg

m3∗1000m

86000 kg

m3

, h"r" γ =2.65∗density of water(1000kg /m3)

$ =30.81395

Fin7in( th" "ia!"nt a!" o X, sin( th" '!ot that r"!at"s th" s!o'" h"i(ht an7 s!o'" an(!"

ntions or '!an" ai!r" in a 7rain"7 s!o'" Hstr!i7, 2006 ro# Ho", 19=0a s"" i(r"

4.a)



Figure &.a 'elationship etween the slope height and slope angle functions for plane failure in a drained slope(Hustrulid, 2! from Hoek, 1"#a$ and the suse)uent retrie*al of +, when -3.13"/

/h" a!" o X as 7"t"r#in"7 to " X : 24.3,

$stittin( to th" "ation % =2√ (i− ! )( !−∅) , (i"n I * 43hi(h"st 7i' an(!" o a!t

ithin th" s"tion ith th" 'ossi!" '!anar ai!r" an7 ∅=¿ 35 an(!" o int"rna! rition o

An7"sit"

24.3=2√ (i−43° ) (43°−35° )

i=61.45°

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