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Int. J. Rock Mech. Mining Sci. VoL 2, pp. 277-304. Pergamon Press Ltd. 1965. Printed in Great Britain.

GRAVITY FLOW OF GRANULAR MATERIALS IN HOPPERS

AND BINS IN MINES--II. COARSE MATERIAL

R U D O L F K V A P I L , (~.S.S.R.'[

Received 21 February 1965

1 . I N T R O D U C T I O N

COARSE m ater i a l ha s t o be dea l t w i th i n coa l and m eta l l if e rous min ing a nd t r anspor t , bo th

i n u n d e r g r o u n d w o r k i n g s , an d i n o p en - cas t w o rk i n gs [ 7] .

The t e rm co ar s e i s u sed fo r g ranu lar mater i a l wh ich i nc ludes par t i c le si zes o f over

8 i n . Min ing opera t i ons o f t en p rodu ce l um ps o f 40 i n . o r mo re i n s ize .

C o a r s e m a t e r ia l m ay o c cu r in m an y f o r ms . F o r t h e s ak e o f i l lu s t r a ti o n F i g . 1 s h o w s f o u r

d i f f e ren t t ypes o f coar se ma ter ia l . F igure 1 (1 ) shows coar se m ater i a l wi th l a rge spher ica l

p i eces o f t h e s am e s i ze an d f o r m, F i g . 1 ( 2 ) r ep r e sen t s co a r s e m a t e r ia l o f p iece s o f th e s ame

s ize bu t d i f f e ren t fo rm, F ig . 1 (3 ) i nd i ca tes coar se m ater i a l cons i s t i ng o f la rge p i eces , ch ip -

p ings and sand . F igure 1 (4 ) i s a schem at i c d i ag ram of a coar se m ix tu re cons i s t ing o f l a rge

p i eces , ch ipp ings , sand and ear th y -c l ay ey cons t it uen t s .

I 3 4

FIG. 1

C o ar s e ma t e r i a l o f th e t y p e s h o w n i n F i g . 1 ( 1 ) h a s t h e g r ea te s t mo b i l it y an d t h a t o f F i g ,

1 (4 ) t he sm al l es t mob i l i ty . Th e ear th y -c l aye y cons t i t uen t s [Fig. 1 (4 ) ] a re l i ab l e t o p l as t i c

defo rm at ion a t a cer t a in m oi s tu re co n ten t , t he y s ti ck t o t he l a rge p ieces and f i ll t he cav i t ies

b e t w een th em . Th i s r e s tr ic t s f r eed o m o f mo v em en t o f t h e l u mp s an d t h e m o b i l i ty o f t h e

co a r s e ma t e r i a l b eco m es le ss . C o a r s e m a t e ri a ls w i th an ap p r ec i ab le p e r cen t ag e o f d am p

ear th y-c l a yey cons t i t uen t s c ause t he g rea t es t op era t i ona l d i ff icu lt ies, no t on ly i n bunk er s

and d i scharge funnel s , bu t a l so i n t he ou t l e t s , on t he bunker o f f t akes and in c rusher s . The

d am p i n g e f fec t o f e a r t h y c l ay ey co n s t it u en t s a l s o r ed u ces t h e cap a c i t y o f c r u sh e r s. A r ed u c -

t i o n o f mo b i l i ty m ay a l s o b e cau s ed b y t h e f o r m o f t h e co a r s e p iece s i n t h a t c e r ta i n s h ap es

a r e l iab l e t o i n t e r lo ck a n d p r o d u ce j am m i n g b e t w een t h ems e l v es .

Coa r se m ater i a l i s r espons ib l e fo r var ious d if ficu lt ies i n se rv i ce , no t on ly b y t he excess ive

* P a r t I p u b l i s h e d i n V o l . 2 , N o . 1 , p p . 2 5 - 4 1 .

t P r e s e n t a d d r e s s : D e p t . o f M i n i n g w i t h M i n e S u r v e y i n g , T h e R o y a l I n s t i t u t e o f T e c h n o l o g y , S t o c k h o l m 7 0 .

277

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  78 RU D O L F K V A PIL

s iz e o f t h e i n d i v i d u a l p i e c e s, b u t a l s o b y a n u m b e r o f o t h e r f a c t o r s . A f a c t o r o f p r i m e i m -

p o r t a n c e i s t h e c o m p o s i t i o n o f t h e c o a r s e m i x t u r e b e c a u s e t h i s g o v e r n s it s m o b i l i ty . T h i s

a l s o d e t e r m i n e s t h e r i s k o f s t i c k in g a n d o f f r e e zi n g o f th e c o a r s e m a t e r i a l.

B a s e d o n t h e o r e t i c a l a n d p r a c t i c a l e x p e r i e n c e , w e c a n s u b d i v i d e c o a r s e m a t e r i a l , d e p e n d -

i n g o n i ts c o m p o s i t i o n , i n t o t h e f o u r g r o u p s 1 t o 4) a c c o r d i n g t o T a b l e 1. T h e d a t a o f t h is

T a b l e p r o v i d e t h e p r i n c i p a l c h a r a c te r i s ti c s f o r th e v a r i o u s g r o u p s o f c o a r s e m a t e r i a l m e t

w i t h i n p r a c t i c e .

TABLE 1 MA IN GROUPS OF COARSE MATERIAL AND THEIR CHARACTERISTICS IN PRACTICE

G roup of coarse material

Num ber o f

group

Am ount of water Risk of Risk of

Com position of absorbed by the sticking freezing

coarse ma terial coarse ma terial

Uniform size distribu-

t ion piece s of same

size and same form

Mixture o f p ieces of

the sam e size but dif-

ferent form

None None None

Almost none Almost none Very small

Mixture o f p ieces of

different siz e and dif- Medium Small, perhaps

ferent form medium

Mixture o f p ieces of

different s ize and form

with earthy-clayey con-

stituents

Medium

Large Large Large

C o a r s e m a t e r i a l o f g r o u p 1 c a u s e s th e l e a s t a n d g r o u p 4 th e g r e a t e s t d if fi cu l ti es . E a c h o f t h e

g r o u p s 1 - 4 i n c lu d e s a s l id i n g s c a le o f v a r i o u s p r o p e r t i e s w h i c h d e p e n d o n m a n y f a c t o r s .

T h e i n f l u e n c e o f t h e m e c h a n i c a l s t r e n g t h a n d t h e s h a p e o f t h e i n d i v i d u a l p i ec e s m a y , f o r

e x a m p l e , b e o f p r i m a r y i m p o r t a n c e . T h e s e p r o p e r t i e s a r e c l o s el y l i n k ed t o t h e q u e s t i o n o f

c r u s h in g o f t h e lu m p s a n d o f t h e d e s t r u c ti o n o f t h e s h a r p c o r n e r s , to t h e c o m m i n u t i o n o f

t h e l a r g e p ie c e s a n d t o t h e f o r m a t i o n o f f in e d u s t y f r a c t i o n s i n t h e g r a v i t y fl o w o f t h e c o a r s e

m a t e r i a l . T h e p r o p e r t i e s o f th e c o a r s e m a t e r i a l m a y c h a n g e a s a f u n c t io n o f th e h e i g h t o f t h e

g r a v i t y f lo w . T h i s c h a n g e i n p r o p e r t i e s is b r o u g h t a b o u t b y t h e f o r m a t i o n o f a l a rg e a m o u n t

o f s m a l l a n d f in e f r a c t io n s i n t h e g r a v i t y f l o w , w h i c h n o t o n l y a l t e rs t h e r a t i o o f th e f r a c t i o n s

b u t a l s o a l te r s t h e m o b i l i t y o f t h e c o a r s e m a t e r i a l a s a r e s u lt o f th e r e d u c t i o n i n p a r t i c l e

s iz e. T h e v a r i a b il i ty o f t h e p r o p e r t i e s b e c o m e s g r e a t e r w i t h a n i n c re a s i n g n u m b e r o f th e

f r a c t i o n s o f t h e m i x t u r e o f c o a r s e m a t e r i a l , w i t h a g r e a t e r v a r i e t y o f t h e s u b s t a n c e o f t h e

i n d i v i d u a l p a r t i c l e s a n d w i t h a g r e a t e r v a r i e t y o f t h e s h a p e o f t h e p a r ti c l e s. C o a r s e m a t e r i a l

o f g r o u p 4 s e e T a b l e t ) h a s t h e r e f o r e t h e g r e a t e s t v a r i a b i l it y .

2 . P R E S S U R E T R A N S M I S S IO N , S T R E S S D I S T R I B U T I O N A N D A R C H I N G I N

C O A R S E M A T E R I A L

C o a r s e m a t e r i a l c a n b e te r m e d a c o m p l e x h e t e r o g e n e o u s m a s s . T h e c a v i ti e s b e t w e e n t h e

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GRAVITY FLOW OF GRANULAR MATERIALS IN HOPPERS AND BINS IN M1NFS II 79

individual pieces may be empty or be filled by various substances stone chippings, pebbles,

gravel, sand, earth, day, etc.).

The contact between the individual pieces may be direct see Fig. 2) or indirect so that

other filler substances e.g. pebbles and sand--S and clay--T) may be present between the

coarse pieces see Fig. 3).

FIG. 2

FIG. 3

Indirect contact of the pieces is essential in coarse material of group 3 and 4 according

to Table 1.

Direct contact of the large pieces may be point-like, along an edge, or flat, depending

not only on the shape of the pieces, but also on the strength of their substance. It is possible

for all three types of contact to occur in the same coarse material. Coarse material may

have various types and qualities of contact.

Pressures are transmitted in coarse material at the points of contact. The pressure trans-

mission may take many forms because the grouping of the coarse material may be quite

random and variegated.

The transmission of pressure may be relatively complex even in the very simple coarse

material consisting of spherical particles group 1 from Table 1) as can be seen from Fig.

4 a). This picture shows a plane photo-elastic stress model of such a material.

R.M. T

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2 8 0 R U D O L F K V A P IL

FIG. 4 a)

FIG. 4 b )

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GRAVITY FLOW OF GRANULAR MATERIALS IN HOPPERS AND BINS IN MI NE S II 281

T h e t r an s m i s s io n o f p re s s u re c a n b e j u d g e d f r o m t h e p a t t e r n a n d c o n c e n t r a t i o n o f t h e

s tr e ss e s w h i c h a r e d e f i n e d b y i s o c h r o m a t i c li n es a n d r e p r o d u c e d i n F i g . 4 a ) a s d o t t e d

l in e s . F i g u r e 4 b ) is a s c h e m a t i c d i a g r a m o f t h e p r e s s u r e t r a n s m i s s i o n .

O n e o f t h e p i e c e s i n th e m o d e l w a s l o a d e d o n t h e s u r f a ce b y a p o i n t c o n t a c t [ m a r k e d i n

F i g . 4 a ) b y a t h i c k a r r o w ] . T h e d i s t r i b u t i o n o f t h e s t r e ss e s in F i g . 4 a ) c l e a r l y i n d i c a t e s

t h a t t h e l o a d i s c o n c e n t r a t e d o n a f e w p ie c e s. T h i s i s, o f c o u r se , a c c o m p a n i e d b y a r e a s i n

w h i c h t h e p i e c e s a r e n o t l o a d e d a t a ll . T h e r e m a y e v e n b e c a v it ie s [ m a r k e d b y N i n F i g . 4 a )

a n d 4 b )] a b o v e w h i c h t h e r e m a y b e a r c h e s f o r m e d b y c o a r s e pi ec e s.

T h e t r a n s m i s s i o n o f p r es s u r es i n t h e a c t u a l p r o t o t y p e t a k e s p l a c e i n s p a c e a n d w i ll , t h e r e -

f o r e , e x h i b i t s t i l l g r e a t e r v a r i e t i e s t h a n a r e s h o w n o n F i g . 4 a ) a n d 4 b ) .

T h e g r e a t e s t o p e r a t i o n a l d if fi cu l ti es w i t h c o a r s e m a t e r i a l a r e c a u s e d b y a r c h i n g a b o v e t h e

o u t l e t o p e n i n g . U n d e r c e r t a i n c i rc u m s t a n c e s t h e i n d i v i d u a l p ie c e s o f th e c o a r s e m a t e r i a l

m a y b e g r o u p e d i n s u c h a p a t t e r n t h a t a r c h i n g t a k e s p l a ce . T h e m a i n c a u s e o f t h is is th e

r e s t r i c t i o n i n t h e g r a v i t y f l o w o f t h e c o a r s e m a t e r i a l w h i c h e x i st s a t t h e o u t l e t o p e n i n g .

O b s e r v a t i o n s i n p r a c t ic e a n d r e s e a r c h in t h e l a b o r a t o r y h a v e i n d i c a t e d t h a t w e c a n c la s si fy

a r c h e s o f c o a r s e m a t e r i a l a s

p r bolic

i n f o r m .

T h e h e i g h t h o f th e a r c h d e p e n d s m a i n l y o n t h e p r o p e r t i e s o f t h e c o a r s e m a t e r i a l , o n t h e

w a y i n w h i c h t h e a r c h i s s u p p o r t e d a t it s b a s e i. e. o n t h e i n c l in a t i o n o f th e a b u t m e n t a r e a

o f th e a r c h ) a n d o n t h e f r i c t io n a l o n g th e a b u t m e n t a r e a .

A s s u m e t h e a b u t m e n t a r e a s o f t h e a r c h t o b e h o r i z o n t a l a n d t h e a n g l e o f i n t e r n a l f r ic t io n

o f th e c o a r s e m a t e r i a l t o b e ~b = 4 5 °. T h e m a x i m u m h e i g h t o f t h e a r c h u n d e r t h e s e c o n d i t i o n s

i s g i v e n b y

h = l × 1.66 × co t ~b 1)

w h e r e h = h e i g h t o f a r c h

l = i t s s pa n

= t h e a n g l e o f i n t e r n a l fr i c ti o n .

T h e a c t u a l h e i g h t o f a r c h e s o f c o a r se m a t e r i a l i n p r a c t i c a l c o n d i t io n s i s u s u a ll y m u c h

s m a l l e r th a n t h e v a l u e c a l c u la t e d f r o m e q u a t i o n 1 ) b e c a u s e t h e h e i g h t o f t h e a r c h i s i n -

f l u e n c e d b y t h e i n c l i n a t i o n o f t h e w a ll s o f t h e b u n k e r o r d i s c h a r g e f u n n e l o n w h i c h t h e a r c h

res t s .

F i g u r e 5 s h o w s a p h o t o - e l a s t i c st re s s m o d e l o f a s e c t i o n o f a n a r c h w h i c h is s u p p o r t e d o n

t h e i n c l i n e d w a l l o f a d i s c h a r g e h o p p e r . T h e w a l l is i n c l i n e d a t a n a n g l e a .

T h e e f f e c t o f t h e i n c l i n a t i o n o f t h e w a l l o n t h e h e i g h t o f t h e a r c h c a n , i n p r i n c i p le , b e

e x p r e s s e d a s f o l l o w s :

T h e h e i g h t h o f t h e a r c h c a n b e s m a l le r i f t h e w a ll o f t h e d i s c h a r g e h o p p e r s is s t ee p e r , i. e.

i f t h e a n g l e a i s g r e a t e r . T h e s t r e s s i m p a r t e d b y t h e a r c h t o t h e i n c l i n e d w a l l o f t h e d i s c h a r g e

h o p p e r a l s o c h a n g e s a s a f u n c t i o n o f th e a n g l e a [2 , 3 , 8, 9, 1 1].

F i g u r e 6 i n d i ca t e s d i a g r a m m a t i c a l ly t h e d i s t r ib u t i o n o f th e f o r c e s u n d e r n e a t h t h e f o o t

o f a h i g h a r c h o f c o a r s e m a t e r i a l . T h e l e g e n d i s a s f o l lo w s : q = s t re s s d u e t o c o a r s e m a t e r i a l ,

P = p r e s s u r e c o m p o n e n t o f f o o t o f a r c h , R = f r i c ti o n f o r c e , T = s h e a r a n d N = n o r m a l

f o r c e o f p re s s u r e a r c h . T h e t a n g e n t t o t h e m e d i a n l in e a t t h e f o o t o f t h e a r c h i n t e r se c t s th e

a x is o f s y m m e t r y o f t h e a r c h i n a c e r ta i n p o i n t . A h o r i z o n t a l l in e d r a w n t h r o u g h t h i s p o i n t

i n c lu d e s w i t h t h e t a n g e n t t h e a n g l e ft. T h e i n c l i n a t i o n o f t h e w a l l o f t h e d i s c h a r g e h o p p e r is a

a n d t h e a n g l e i n c l u d e d b y t h e c o m p o n e n t s o f N i s d e s i g n a t e d b y ~ . F o r a h i g h a r c h t h e s e

a n g l es r , v a n d y a r e g i v e n t h e i n d e x 1 a n d t h o s e f o r a f la t a r c h t h e i n d e x 2 . T h e d i s t r i b u t i o n

o f t h e f o r c e s u n d e r n e a t h t h e f o o t o f a f la t a r c h is s h o w n s c h e m a t i c a ll y i n F i g . 7 .

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282 RUDOLF KVAPIL

FIG 5

= g O - - 3 1

FIG 6

\ , . . C r + - .~ ~ I /

• i • e o ° = -

~ . ~ . - . ~ - " /

~- ~ =~:

Flo 7

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G R A V I T Y F L O W O F G R A N U L A R M A T E R I A L S I N H O P P E R S A N D B I N S I N

MINES II 283

I f w e a s s u m e t h a t t h e a r c h is o f p a r a b o l i c f o r m w e c a n c a l c u l a te t h e h o r i z o n t a l c o m -

p o n e n t H o f th e p r e s su r e e x e r t e d b y t h e a r c h b y t h e f o r m u l a

q×l

H - - 2 x~ t an f l 2 )

T h e c o a r s e p ie c e s m a y b e a s s e m b l e d i n a r a n d o m p a t t e r n s o t h a t t h e h e i g h t h o f t h e a r c h

m a y v a r y w i t h th e s a m e i n c l i n a t io n o f t h e h o p p e r w a l l. I n o u r c a s e, t h e c h a r a c te r i st i c s o f

t h e a r c h c a n b e e x p r e s s e d b y t h e a n gl e /3 . T e s t s h a v e p r o v e d t h a t t h e h e i g h t o f th e a r c h m a y

v a r y b e t w e e n c e r t a i n l im i t s c o r r e s p o n d i n g t o f lm a x >~ f l >~ flm tn w i t h o u t d i s t u r b i n g t h e

e q u i l i b r i u m c o n d i t i o n s o f t h e a r c h .

I n t h e c a s e o f h i g h a r c h e s , a c c o r d i n g t o F i g . 6 , th e f o o t o f t h e a r c h is k e p t i n i ts p o s i t i o n

b y t h e f r i c t i o n f o r c e R w h i c h a c ts i n a n u p w a r d s d i r e c ti o n , R b e i n g g r e a t e r t h a n T .

T h e e q u i l i b r i u m o f th e f l a t a r c h , a c c o r d i n g t o F i g . 7 , a t th e s a m e i n c l i n a t io n o f t h e h o p p e r

w a l l is b r o u g h t a b o u t b y t h e f r i c ti o n f o r c e ac t in g d o w n w a r d s , R a g a i n b e i n g g r e a t e r t h a n T .

I n a c c o r d a n c e w i t h t h e d e s i g n a ti o n s o f F i g s. 6 a n d 7 w e c a n s t a te f o r h i g h a r c h e s

f l l = 90 ° - - Ctl + 01 and fo r f l a t a rche s /32 = 90 ° - - ~1 - - z~2.

W h e n t h e v a l u e s f o r T a n d R a r e e q u a l , t h e e q u a t i o n s i n T a b l e 2 a r e v a li d f o r th e d e t e r -

m i n a t i o n o f t h e m a x i m u m a n d m i n i m u m a n g l e/ 3 o f a r c h es f r o m c o a r s e m a t er ia l , a ls o f o r

t h e m a x i m u m a n d m i n i m u m h o r i z o n t a l fo r c e H e x e r te d b y th e a r c h o n t h e w a l l o f t h e d is -

c h a r g e h o p p e r .

T A B L E 2

/

max

\ \

/ H m a x

M a x i m u m h e ig h t o f a r c h f r o m c o a r se M i n i m u m h i g h t o f a r c h f r o m c o a r s e

m a t e r i a l m a t e r i a l

8 m a x = 9 0 ° - a + ~ t ( 3) ~ m l n = 9 0 ° - a - 4 , t (4 )

H q l q l

m m ~ - t a n ( a - - 4 ,1 ) ( 5 ) H m a x = ~ - t a n ( a + ~ 1 ) ( 6 )

Note: Th e ang le of inclination a is in bo th cases the sam e.

I n T a b l e 2 f fl d e s ig n a t es t h e a n g l e o f f r ic t i o n o f t h e c o a r s e m a t e r i a l a l o n g t h e w a l l o f t h e

d i s c h a r g e h o p p e r . I n f o r m a t i v e v a lu e s o f ff l h a v e b e e n c o m p i l e d in T a b l e 3 . M o r e e x a c t

v a l u e s h a v e t o b e d e t e r m i n e d o n t h e b a s is o f p r a c t ic a l te s ts .

T h e s p a n l o f th e a r c h a c r o ss t h e o u t l e t o p e n i n g e q u a l s t h e d i st a n c e m a r k e d i n F i g . 8 o n

t h e x - a x i s b y A B . T h e f e e t o f th e m e d i a n l in e o f th e a r c h , i . e. t h e p o i n t s A a n d B , h a v e a

d i s t a n c e f r o m t h e e d g e o f t h e i n c li n e d w a l l o f t h e o u t l e t o p e n i n g o f a t l e a s t h a l f th e d i a m e t e r

o f t h e p i e c e s i .e . D/2 a s c a n b e s e e n f r o m F i g . 8. F i g u r e 8 i n d i c at e s t h a t t h e s p a n l o f a n a r c h

o f c o a rs e m a t e r i a l c a n b e d e t e r m i n e d f r o m

l = a + D c o s a . 7 )

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R U D O L F K V A P I L

F i g u r e 8 a l s o s h o w s t h a t t h e a p e x S o f th e p a r a b o l i c m e d i a n l i n e o f t h e a r c h l ie s h a l f w a y

a l o n g t h e s e c t io n C E o f t h e a x i s o f t h e p a r a b o l a . P o i n t C is g iv e n a lo n g t h e a x i s o f t h e p a r a -

b o l a b y t h e i n te r s e c ti o n w i t h t h e t a n g e n t w h i c h t o u c h e s t h e p a r a b o l i c m e d i a n l in e o f t h e

a r c h a t t h e p o i n t s A a n d B .

TABLE 3. INFORMATIVE VALUES OF ANGLES OF FRICTION ~ ALONG THE WALL OF THE

DISCH ARGE HOPPER FOR VARIOUS COARSE MATERIALS

T y p e o f

c o a r se m a t e r i a l

F r i c t i o n o f c o a r se C o r r e sp o n d i n g a n g l e C o e f f i c i e n t o f

m a t e r i a l a g a i n s t a f r i c t i o n a l o n g w a l l f r i c t i o n a l o n g w a l l

w a l l c o m p o se d o f 6 1 f l

D o l o m i t e , l i m e s t o n e , S t e e l

M a r b l e C o n c r e t e

W o o d

G r a n i t e ,

G r a y w a c k e ,

M a g n e s i t e

I r o n o r e

( c o m p a c t a n d

v e r y c o m p a c t )

R o c k s a l t

G y p su m

S a n d s t o n e

S o l i d sh a l e

C o a l

C o k e

30 ° 40 ° 0-58 - 0 84

33 ° - 43 '~ 0' 65 - 0'9 3

37 ° 0 75

Ste el 31 o _ 42 c, 0. 60 - 0. 90

Conc re t e 35 ° - 42 ° 0 .70 - 0 ' 90

Steel 33 ° - 42 ° 0.67 - 0.9 0

Con cre te 36 ° - 43 ° 0.72 - 0.93

Wood 40 ° 0 -84

Ste el 25 ° - 41 ~ 0-47 - 0' 87

Con cre te 30 ° - 42 ° 0-58 - 0 '9 0

Ste el 31 ~' - 38 ° 0.61 - 0' 78

Con cre te 32 ° - 41 ° 0,62 - 0.87

Steel 32 ° - 42 ~ 0.62 - 0.9 0

Con cre te 34 ° - 42 °

0.67 - 0 90J

Stee l 28 ° - 40: ' 0 .53 =0.84 I

Con cre te 29 ° - 42 ° 0.55 - 0.9 0

Steel 20 ° - 402 0 36 - 0.84

Ste el 24 '~ - 37 ° 0.4 5 - 0.7 5

h

FIG. 8

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T h e e q u a ti o n s 3 ) a n d 4 ) i n d ic a t e t h e m a x i m u m a n d m i n i m u m a n g l e s /3 a n d t h e a n g l e

w h i c h i s i n c l u d e d b e t w e e n t h e t a n g e n t t a n d t h e a x is o f t h e p a r a b o l a i s g i v e n b y

~, = 90 ° -- ft .

I f th e s p a n I a n d t h e a n g l e f l a r e k n o w n , t h e h e i g h t h o f t h e a r c h c a n b e c a l c u l a t e d w i t h

d u e r e g a r d t o t h e e f fe c t o f th e i n c l i n a ti o n o f t h e w a l ls o f t h e d i s c h a r g e h o p p e r .

T h e a r c h o f c o a r s e m a t e r i a l h a s c e r t a in li m i ti n g b o u n d a r i e s w i t h in w h i c h t h e e q u i l i b r i u m

c o n d i t i o n s a r e fu l fi ll ed . T h e b o u n d a r i e s a r e g i v e n b y a c e r t a i n m a x i m u m a n d m i n i m u m

h e i g h t o f t h e a r c h .

T h e m a x i m u m h e ig h t o f a rc h f o r m e d o f c oa r se m a t e r ia l i s

½ co t 90 ° - - f lmax)

hln x

2

a n d t h e m i n i m u m h e i g h t o f a r c h is

½ co t 90 ° - - f lmln)

hmi n ~-- 2

8 )

9 )

T h e h o r i z o n t a l f o r c e e x e r t e d b y th e a r c h o n t h e w a l ls o f th e d i s c h a r g e h o p p e r c a n b e

c a l c u l a t e d f r o m t h e e q u a t i o n s

q 12

Hmln = 8 hmax 10)

q 12

/ m a x - - 8 l l )

T h e d i a g r a m s o f F i g . 9 a ) a n d 9 b ) in d i c a t e th e h o r i z o n t a l f o r c e a s a f u n c t i o n o f th e h e i g h t

o f t h e a r c h .

I

1o1

~ t I I I 1

i c ,

FIG. 9

I t s h o u l d b e n o t e d t h a t t h e a r c h a b o v e t h e o u t l e t o p e n i n g is f o r m e d b y t h e lo w e s t li n e o f

p i ec e s o f ro c k . T h i s l a y e r o f r o c k w h i c h f o r m s t h e a r c h i s s h o w n i n F i g . 1 0 h a t c h e d f o r t h e

s a k e o f t h e i l lu s t r a ti o n . T h e f e e t o f t h e a r c h a r e m a r k e d A a n d B . F i g u r e 11 s h o w s t h e

d e v e l o p m e n t a n d d i s t r ib u t i o n o f t h e s tr es s es i n t h e a r c h o f F i g . 1 0 , a s s h o w n i n a p h o t o -

e l a s ti c st r es s m o d e l o f t h e a r c h o f t h e l a t t e r.

T h e r e l a t i o n s h i p s d e r i v e d a b o v e a r e r i g i d l y v a l i d f o r a r c h e s f o r m e d a b o v e t h e c e n t r a l

p a r t o f a n o u t l et o p e n i n g i n t h e f o r m o f a l o n g s lo t b e c a u se o n l y th e n c a n w e r e g a r d t h e

a r c h o f c o a r s e m a t e r i a l a s b e i n g i n a b i a x i a l s ta t e o f s t re s s in a v e r t i c a l p l a n e . T h e o u t l e t

o p e n i n g s h a v e u s u a l l y t h e f o r m o f a s q u a r e , a c i r c le , o r a r e c t a n g l e , s o t h a t w e h a v e t o d e a l

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286

R U D O L F K V A P 1 L

w i t h t h e s t re s s s t a t e s o f a t h r e e - d i m e n s i o n a l a r c h w h i c h c o m p l i c a t e s m a t t e r s . T h e i n v e s t ig a -

t i o n s s h o w , h o w e v e r , t h a t t h e e a r l ie r s t a t e m e n t s a r e s u b s t a n t i a l l y v a l i d f o r t h e s e c a se s . T h e

d i s c r e p a n c ie s a p p e a r t o l i e b e t w e e n p r a c t i c a l l y p e r m i s s i b l e l im i t s .

W e c a n s u m m a r i z e th e f o r m a t i o n o f a r c h es o f c o a rs e m a t e r i a l a b o v e t h e o u t l et o p e n i n g

as fo l l ow s :

1. T h e r e s t r i c t i o n o f t h e g r a v i t y fl o w o f c o a r s e m a t e r i a l in t h e o u t l e t o p e n i n g i s t h e m a i n

r e a s o n f o r th e f o r m a t i o n o f a r ch e s . ( C o a r s e m a t e r i a l c a n n o t f o r m a n a r c h i f

e / d : I .

see Pa r t I , F ig . 29 . )

2 . T h e a r c h o f c o a r s e m a t e r i a l is f o r m e d b y t h e l o w e s t l a y e r o f b l o c k s c l u s te r e d a b o v e

t h e o u t l e t o p e n i n g o f t h e d i s c h a r g e h o p p e r ( se e F i g . 1 0).

FIG 10

% ° ~ N

FIG . 11

3 . T h e m e d i a n l i ne o f a n a r c h o f c o a r s e m a t e r i a l is p a r a b o l i c i n f o rm .

4 . T h e h e i g h t o f a n a r c h o f c o a rs e m a t e r i a l d e p e n d s

i n t e r a l i a

o n t h e i n c l i n a t i o n o f t h e

w a l l s o f t h e d i s c h a r g e h o p p e r . T h e a r c h h e i g h t b e c o m e s le s s i f t h e w a l ls a re s t e e p e r.

5 . A d e c r e a s i n g h e i g h t o f a r c h o f c o a r s e m a t e r i a l i n c r e a s es t h e s t re s s o n t h e s t r u c t u r e

o f th e d i s c h a r g e h o p p e r , i t s ol id i fi e s t h e a r c h a n d m a k e s i t m o r e d i ff ic u lt t o r e m o v e .

6 . D i s c h a r g e h o p p e r s w i t h e x c e s s iv e l y s t e e p w a i l s a re d a n g e r o u s i n o p e r a t i o n . T h e

i n c l i n a t io n o f t h e h o p p e r w a l ls c a n b e r e g a r d e d a s e x c e ss i v e i f a ~ 6 0 °. I t is n o r m a l l y

a d e q u a t e i f a ~ ¢ 1 × s w h e r e ~ 1 i s t h e a n g l e o f f r i c ti o n o n t h e w a l l o f t h e d i s c h a r g e

h o p p e r a n d s i s t h e f a c t o r o f s a fe t y , v a r y i n g f r o m s = 1 .0 5 ( f o r s m o o t h s u r f a c e s ) t o

s = 1 -15 ( fo r r o ug h su r f ace s ) .

7 . T h e a r c h f o r m s m o r e e a s i ly if t h e m o b i l i t y o f t h e m i x t u r e o f c o a r s e m a t e r i a l i s

s m a l l e r ( s ee T a b l e 1 , g r o u p 4 o f m a t e r i a l s ).

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287

8. Flat arches can be formed more easily if the particles are more irregular and stronger.

Sticky constituents assist in the formation of arches.

9. Arches o f coarse material form more easily if the individual blocks of rock are larger,

i.e. if a lesser number is required to form the arch. This results in the following:

10. A smaller area of outlet opening facilitates arching and an enlargement of the area

reduces it.

11. The practical elimination of arching during self-acting discharge through a horizontal

outlet opening depends on the application of the so-called minimum area required

for the outlet opening.

The minimum areas required for horizontal outlet openings for coarse material can be

calculated from the same equations as were quoted in Part I of this article for bulk material.

These equations are listed for ease of reference in the following Table 4.

TABLE 4 FORMULA FOR THE DETERMINATION OF THE MINIMUM DIMENSIONS REQUIRED OF

OUTLET OPENINGS FOR COARSE MATERIAL

AREA OF OUTLET OPENING

Square opening F. Circular opening F~

F . = (5 X D) ~ x k F~ = 0 85 (5 x D) 2 x k or

= 0-85 x Fa

WIDTH OF OUTLET OPENING

Length of one side of square opening Diameter of ci rcular opening

a = x / 5 x D ) 2 x k o r d = ~ / 0 - 8 5 . 5 0 . 7 8 5D ) e × k

a= V Fa d=

or

The following symbols have been used in the equations of Table 4:

D = average diameter of lumps of rock

k = coefficient derived from the nomogram shown in Fig. 12.

The coarse material is a mixture of various particle sizes. Extremely different and variegated

combinations may be produced and their detailed assessment would be very complicated.

To simplify matters the nomogram contains only the major fractions which constitute the

coarse material. The lumps, and their percentage from 25 to 100 , are marked as I, and

their characteristic shape (rounded, angular, sharp-edged) is indicated along the various

functional lines. The designation II represents medium size particles (coarse pebbles), III

the finer fractions (gravel, sand etc.) and IV the sticky constituents (moist alumina, loam,

etc.). The key to the nomogram is marked in its proper sequence by arrows. The value of

the coefficient varies from 0.6 to 1.4. The nomogram indicates that, for example, coarse

material with a content of sticky constituents (IV) of over 10 is unsuitable for self-acting

flow through the outlet opening.

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RUDOLF KVAPIL

I t i s p o s s i b l e t o c o m p i l e m o r e a c c u r a t e f o r m u l a e t h a n t h o s e g i v e n a b o v e f o r t h e d e t e r -

m i n a t i o n o f t h e s i ze o f t h e o u t l e t o p e n i n g s f o r c o a r s e m a t e r i a l. S u c h f o r m u l a e w o u l d ,

h o w e v e r , i n c l u d e a n u m b e r o f c o m p l i c a t e d t e r m s . I t i s p o s s i b le t h a t f o r p r a c ti c a l p u r p o s e s

i t is b e t t e r t o u s e s i m p l e e q u a t i o n s w h i c h m a y i n c lu d e a c e r t a i n a m o u n t o f e r r o r , y e t p r o d u c e

f a i r l y s a f e p r e d i c t i o n s .

1 i

~

5 0 / ,

FiG 12

U n i l a t e r a l d i sc h a r g e h o p p e r s a r e o f t e n f o u n d i n p r a c t ic e . A r c h e s o f c o a r s e m a t e r i a l c a n

a l s o b e p r o d u c e d i n t h e se .

F i g u r e 1 3 s h o w s d i a g r a m m a t i c a l l y t h e f o r m a t i o n o f a r c h i n g i n a u n i la t e r a l d is c h a r g e

h o p p e r . T h e a r c h i s f o r m e d b y t h e l o w e s t l a y e r o f t h e b l o c k s, s h o w n s h a d e d . A p h o t o -

e l a st ic s t re s s m o d e l o f th e a r c h o f F i g. 1 3 is s h o w n i n F i g . 1 4. T h e f o r m o f th e i s o c h r o m a t i c

l in e s c l e a r l y re v e a l s t h e a r c h i n g o f th e l o w e s t l a y e r o f b l o c k s .

T h e s a m e b a s ic c o n s i d e r a t i o n s a s f o r s y m m e t r ic a l d is c h a r g e h o p p e r s a p p l y t o a r c h f o r m a -

t i o n i n u n i l a t e ra l d i s c h a r g e h o p p e r s .

I n t h e c a s e o f u n i l a t e ra l d i s ch a r g e h o p p e r s t h e r e i s a n e x c e ll e n t w a y o f d e s t r o y i n g b y

m e c h a n i c a l m e a n s a n y r a n d o m a rc h e s.

T h e m e c h a n i c a l d e s t r u c t i o n o f t h e a r c h o f c o a r s e m a t e r i a l is b a s e d i n p r in c i p l e o n a

r e l ax a t io n o f th e a b u t m e n t u n d e r n e a t h t h e f o o t o f t he a r c h .

I t s h o u l d b e e m p h a s i z e d t h a t a r e la t iv e l y s li g h t r e l a x a t io n o f t h e a b u t m e n t , p r a c t ic a l l y

le ss t h a n a f e w c e n t i m e t e rs , is a d e q u a t e t o d e s t r o y a n a r c h o f c o a r se m a t e r i a l .

F i g u r e 1 5 i n d i c a t e s t h e a r c h i n g i n a u n i l a t e r a l d i s c h a r g e h o p p e r .

T h e r e l a x a t i o n o f t h e a r c h a b u t m e n t h a s b e e n a c h i e v e d i n F i g . 1 6 a) b y l if ti n g th e p l a t e

2 in t h e d i r e c t i o n o f t h e a r r o w .

Th e s am e e f f ec t c an be ach i eve d i f , i n s t ea d o f l if t i ng , t he p l a t e 2 is de f l ec t ed [s ee F i g . 16 b )]

o r s h i f t e d in a h o r i z o n t a l p l a n e [ se e F i g . 1 6 c )]. V a r i o u s d e s i g n s a r e p o s s ib l e f o r t h e e l e m e n t

2 i tself .

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FIG. 13

FIG. 14

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290 R U D O L F K V A P I L

FK~ 15

/ I

a)

i ~ Z1 . . . f - ~ - [ t I

b)

c )

FIG 16

C a r e m u s t , h o w e v e r , b e t a k e n t o s ee th a t t h e h o r i z o n t a l e x t e n s i o n o f t h e z o n e i n w h i c h

t h e r e l a x a t io n o f t h e a r c h a b u t m e n t i s t o b e p r o d u c e d b y th e p l a t e 2 is a d e q u a t e t o d e s t r o y

b o t h a r c h e s o f s m a l l a n d t h o s e o f g r e a t h e ig h t .

3. D I S C H A R G E H O P P E R S A N D B IN S F O R C O A R S E M A T E R I A L

T h e p r o b l e m s c o n c e r n i n g d i s c h a rg e h o p p e r s b e f o r e c r u s h e rs a n d b i n s f o r c o a r s e m a t e r i a l

a r e s o m a n i f o l d t h a t w e c a n d e a l i n t h is a r t i c le o n l y w i t h a f e w s e l e c te d c a s e s.

I t i s d e s i r a b l e i n p r a c t i c e t h a t t h e r e s h o u l d b e n o a r c h i n g a t a l l i n a d i s c h a r g e h o p p e r

b e f o r e a c r u s h e r o r , i f a n a r c h is f o r m e d , i t s h o u l d b e d e s t r o y e d r a p i d l y a n d s u re l y .

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T h e r u le s f o r a p r o p e r d i s c h a rg e h o p p e r b e f o r e a c ru s h e r c a n b e s u m m a r i z e d i n t h e f o ll o w -

i n g m a i n p o i n t s .

1. T h e s h a p e o f t h e d i s c h a r g e h o p p e r b e f o r e a c r u s h e r s h o u l d s u i t th e f l o w c h a r a c te r is t ic s

o f t h e m o v i n g m a t e r i a l a s f a r a s p o s s i b le , i .e . t h e k i n e t i c fl o w o f t h e c o a r s e m a t e r i a l

s h o u l d c o n t r a c t a s l i t t l e a s p o s s i b l e .

2 . T h e o u t l e t o p e n i n g o f t h e d i s c h a rg e h o p p e r s h o u l d b e f i tt e d w i t h a m e c h a n i c a l d e v ic e

t h a t i s c a p a b l e o f r e m o v i n g a n y a r c h e s q u i c k l y a n d s a fe ly .

3 . T h e c o a r s e m a t e r i a l s h o u l d b e t i p p e d i n s u c h a w a y t h a t t h e d i s c h a r g e h o p p e r i s

s t r e s s e d d y n a m i c a l l y a s li tt l e a s p o s s i b l e b y t h e i m p a c t o f t h e c o a r s e m a t e r i a l . I t is

a d v i s a b l e t o le a v e a p r o t e c t i v e c u s h i o n o f c o a r s e m a t e r i a l i n t h e d i s c h a r g e h o p p e r .

( s e e F i g . 1 7 , w h e r e t h e p r o t e c t i v e c u s h i o n i s m a r k e d a s 2 ) .

4 . T i p p i n g s h o u l d b e c a r r i e d o u t i n a d i r e c t io n s u c h t h a t t h e d r a w - o f f d e v i ce (e .g . a

v i b r a t in g e x t r a c t o r ) is n o t s t re s s ed d y n a m i c a l l y b y i m p a c t o f a n y c o a r s e m a t e r ia l .

F i g u r e 1 7 s h o w s a s h a p e s u i t a b l e f o r a d i s c h a r g e h o p p e r b e f o r e a c r u s h e r .

L.~.I

F I G . 1 7

T h e k e y t o F i g . 1 7 i s a s fo l l o w s : 1 = d i r e c t i o n o f t i p p i n g , 2 : p r o t e c t i v e c u s h i o n o f

c o a r s e m a t e r ia l , 3 : a d j u s t a b le c l o s u r e b y c h a i n s c r e en ( a n y a r c h e s c a n b e d e s t r o y e d b y

d e f l e i n g t h e c lo s u r e ) , 4 ---- s h o r t c h u t e , 5 : v i b r a t i n g e x t r a c t o r , 6 = m o t i o n o f m a t e r i a l

a t S , 7 : c h u t e , 8 = c r u s h e r , 9 : p a s s a g e o f f i n e r r a n g e s , 1 0 = d a m p i n g c u s h i o n , 1 1 :

d i r e ct io n o f m o t i o n o f c r u s h e d m a t e ri a l.

I n c e r t a i n c a s es i t m a y b e n e c e s s a r y t o b u i l d s p e c i a l b i n s f o r c o a r s e m a t e r i a l.

I f a r c h i n g o v e r t h e o u t l e t o p e n i n g is t o b e p r e v e n t e d , t h e d i m e n s i o n s o f t h e o u t l e t o p e n i n g

( in t h e c a s e o f s y m m e t r i c a l b i n s ) m u s t a t l e a s t m e e t t h e c o n d i t io n s o f t h e m i n i m u m a r e a

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292 RUDOLF KVAPIL

n e c e s s a r y f o r a n o u t l e t o r , in t h e c a s e o f u n i l a t e r a l b i n s , th e o u t l e t o p e n i n g s h o u l d b e d e s i g n e d

i n s u c h a w a y t h a t a c c i d e n t a l a r c h e s c a n b e d e s t r o y e d b y m e c h a n i c a l m e a n s [s ee F i g . 1 6 ( a - c) ] .

B i n s o f 'c l a s si c a l' f o r m u s u a l l y h a v e l a r g e o u t l e t o p e n i n g s a n d l a r g e c l o s u r e d e v i c es . T h e

g r e a t e st b a s ic d i s a d v a n t a g e o f b i n s o f t h i s t y p e is t h a t t h e d i s c h a rg e h o p p e r a n d t h e o u t le t

o p e n i n g r e s t r i c t t h e k i n e t i c f lo w o f c o a r s e m a t e r i a l . T h e p r i m e r e q u i s i t e f o r t r o u b l e - f r e e

o p e r a t i o n o f c o a r s e m a t e r i a l b in s is th e p r i m a r y m o t i o n o f t h e m a t e r i a l w h i ch m e a n s t h a t

t h e g r a v i t y f l o w o f t h e m a t e r i a l s h o u l d n o t b e r e s t r i c t e d b y t h e b i n s t r u c t u r e .

Th i s cond i t i on i s f u l f il l ed by a spec i a l b i n w i t h a d i s cha r g e t r o ug h [ 2, 4 , 6 ]. F i gu r e 16

s h o w s s u c h a b i n i n s c h e m a t ic f o r m .

T h e k e y t o F i g . 1 8 is a s f o l l o w s : 1 ~ b i n , 2 ~ d i s c h a r g e t r o u g h , 3 - - s l o t a l o n g t h e

w h o l e h e i g h t o f t h e b i n .

A s t h e f r ic t i o n o f th e c o a r s e m a t e r i a l a l o n g t h e w a l l o f th e d i s c h a rg e t r o u g h is m u c h l es s

t h a n t h e f r i c t io n w i t h i n t h e c o a r s e m a t e r i a l , o n l y t h a t p a r t o f t h e m a t e r i a l w i l l r o l l i n t o t h e

1 . . . . .

FtG 18 FIG 19

d i s c h a r g e t r o u g h w h i c h l ie s a l o n g t h e s u r f a c e s lo p e o f t h e b i n c o n t e n t s . T h i s is s h o w n

d i a g r a m m a t i c a l l y in F i g . 1 9 w h e r e 1 ---- b i n , 2 ~ d i s c h a r g e t r o u g h , B A ~ - b i n d r a w - o f f ,

t, = h e i g h t o f d i s c h a r g e o p e n i n g . P i n d i c a t e s t h e r e m a i n i n g m o t i o n l e s s b i n c o n t e n t s . I t is

a n a d v a n t a g e i f th e d i s c h a r g e t r o u g h is w i d e n e d i n t h e d i r e c t io n o f t h e f lo w o f th e m a t e r i a l

a l s o i f t h e d i a m e t e r o f t h e d i s c h a r g e r o l l e r i s g r e a t e r t h a n t h e w i d t h o f t h e s l o ts .

T h e d i s c h a r g e t r o u g h e l i m i n a t es a r c h i n g a n d c a n b e a p p l i e d t o b i n s in v a r i o u s w a y s .

T h e f lo w o f m a t e r i a l f r o m a b i n t h r o u g h t h e d i s ch a r g e t r o u g h i s i l lu s t r a te d i n i ts s e p a r a t e

phase s i n F i g . 20 .

T h e i n s t a l la t io n o f b in s w i t h d is c h a r g e t ro u g h s i s r e c o m m e n d e d f o r a l l c o a r s e m a t e r i al

w h i c h c o n t a i n s n o s t i c k y c o n s t i t u e n t s .

S u c h a p p l i c a t i o n s a r e b e n e f i c ia l a l s o in c a s e s w h e r e s e l f - c o m m i n u t i o n o f t h e m a t e r i a l

( l u m p c o a l , l u m p o r e , e t c .) o r th e d e v e l o p m e n t o f d u s t m u s t b e k e p t t o a m i n i m u m .

T h e e f fe c t o f th e d i s c h a r g e t r o u g h i s s o i m p o r t a n t t h a t t h i s e q u i p m e n t c a n a l so b e u s e d ,

f o r e x a m p l e , f o r th e s t o r a g e o f c o b b l e s to n e s a n d o t h e r l a r g e- s iz e d m a t e r i a l w h i c h w o u l d

no t f l ow ou t o f ' c l a s s i ca l' b i n s a t a l l .

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f c ing p ge

292

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i

Fro 32

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FIG 34

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GRAVITY FLOW OF GRANULAR MATERIALS IN HOPPERS AND BINS IN MI NE S II 29 3

The minimum width b of the slots and the minimum diameter d of the circular profile o f the

discharge trough, both of which are increasingly larger in a downward direction, can be

approximately determined by Fig. 21 as a function of the maximum size of the lumps D.

For the sake of completion, figures for the minimum height v of the outlet opening are also

quoted.

B A

12

°° / /

~ oB o

40

20 ~ ~.-

5

Z-

lO0 150 200 250 300 cm

d b v

FIG. 21

a )

FIG 22

In certain cases bins with the discharge trough may also be used for a certain degree of

homogenization of the bin contents. This possible application is illustrated in principle

by Fig. 22. The bin is filled in such a way [see Fig. 22 a)] that the individual layers of the

materials are blended when discharge takes place through the trough [see Fig. 22 b)].

In conclusion we can say that the bin with discharge trough has the following advantages:

i) The coarse material has a primary motion in the discharge trough so that arching

cannot occur.

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294 R U D O L F K V A P I L

ii) T h e o u t l e t o p e n i n g m a y b e r e l a ti v e l y s m a l l i n si ze s o t h a t s i m p l e a n d e a s i ly c o n t r o l l e d

d i s c h a r g e d e v i ce s c a n b e a p p l i e d .

i ii ) T h e s p e c ia l d r a w - o f f d e v i c e r e d u c e s th e r i s k o f s e lf - c o m m i n u t i o n a n d o f d u s t c o n -

c e n t r a t io n i n t h e d r a w n - o f f m a t e ri a l.

i v) I n c e r t a i n c a s e s t h e b i n w i t h d i s c h a r g e t r o u g h m a y a l s o b e u s e d f o r p a r t i a l h o m o -

g e n i z a t i o n .

4 . C H U T E S F O R C O A R S E M A T E R I A L

I n p r a c t ic a l q u a r r y a n d m e t a ll i fe r o u s o p e n p i t o p e r a ti o n s a ls o i n u n d e r g r o u n d m i n in g )

t h e g r a v i t y f lo w o f c o a r s e m a t e r i a l c a n b e u t i l i z e d v e r y w i d e l y a n d s u c ce s sf u l ly . T h e c o a r s e

ma te r i a l in such ca se s moves a long chu te s o r o re pa s se s [4 , 5 ] .

O

/

/

/

/

90

F I G . 2 3

\

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G R V I T Y F L O W O F G R N U L R M T E R I L S I N H O P P E R S N D B I N S I N MINES--II 295

F i g u r e 2 3 p r o v i d e s a s u r v e y o f th e s c o p e f o r t h e g r a v i t y f lo w o f c o a rs e m a t e r ia l .

T h e k e y is as fo l l o w s : G F = s c o p e f o r g r a v i ty f lo w o f c o a r s e m a t e r ia l , A = c h u t e s,

A I = o p e n c h u t e s , A I I ---- c o v e r e d c h u t e s , B = o r e p a s se s , B I = i n c l i n e d o r e p a s s e s,

B I I = v e r t i c a l o r e p a s s e s, fl = i n c l i n a t i o n o f c h u t e o r o r e p a s s .

I f t h e o p e r a t i o n i s to b e t r o u b l e - fr e e , t h e r a t i o b e t w e e n t h e c o a r s e m a t e r i a l a n d t h e

i n c l i n a t io n f l i s th e m a i n f a c t o r t o b e w a t c h e d .

T h e r u l e is t h a t t h e i n c l i n a t io n f l m u s t b e i n c r e a s e d i f t h e c o a r s e m a t e r i a l is o f m o r e

c o m p l e x n a t u r e . W e h a v e p l o t t e d i n F i g . 2 3 th e m i n i m u m i n c l in a t i o n s fl r e q u i r e d f o r t h e

i n d i v i d u a l g r o u p s o f m a t e r i a l 1 - 4 s e e a l s o T a b l e 1 ).

T h e r e l a t i o n s h i p b e t w e e n t h e g r o u p o f m a t e r i a l 1 - 4 ) a n d t h e a n g l e o f i n c l in a t i o n is o f

g r e a t i m p o r t a n c e a l s o f o r t h e o p e r a t i o n o f d e e p d i sc h a r g e h o p p e r s a h e a d o f c r u s h er s . I n

l a r g e d i s c h a r g e h o p p e r s t h e r e i s s o m e s e g r e g a t i o n o f t h e m a t e r i a l a l o n g t h e s u r f a c e s l o p e [ 1 0].

T h i s s e g r e g a t i o n m a y c a u s e g r e a t o p e r a t i o n a l d if f ic u l ti e s i n t h a t , a s s h o w n o n F i g . 2 4 a ) ,

t h e f in e c o n s t it u e n t s a d h e r e t o t h e i n c li n e d h o p p e r w a ll . T h e i n c l i n a t io n o f t h e h o p p e r w a ll

is i n a d e q u a t e f o r th e m o v e m e n t o f fi ne a n d p a r t l y d a m p c o n s t i tu e n t s a n d i s r e s p o n s ib l e

f o r a p a s s i v e z o n e P . T h i s p a s si v e z o n e P a l s o g r e a t l y d i m i n i s h e s t h e v o l u m e o f th e d i s c h a r g e

h o p p e r .

FIG. 24

T h e s e d i f f ic u l ti e s c a n b e e a s i l y r e m o v e d i f t h e d i r e c t i o n o f se g r e g a t i o n i s r e v e r s e d a s s h o w n

i n F i g . 2 4 b ) . [ T h e c a p t i o n N T i n F i g . 2 4 b ) r e p r e s e n t s t h e l e v e l t e s te r . ] T h e f i n e c o n s t i t u e n t s

e x i s t i n t h i s c a s e a l o n g t h e v e r t i c a l w a l l a n d t h e c o a r s e p i e c e s a l o n g t h e i n c l i n e d h o p p e r w a l l.

T h e m a t e r i a l f l o w c o r r e s p o n d s i n t h i s c a s e b a s i c a l l y t o t h e s e n s e o f F i g . 2 3.

S~

FIG. 25

I n o r e o r s t o n e q u a r r i e s t h e c h u t e c a n b e a r r a n g e d d i r e c tl y o n t h e s lo p e o f t h e f a c e a s

s h o w n i n F i g . 2 5. T h e m a t e r i a l i s t i p p e d i n t o t h e c h u t e a t t h e u p p e r e d g e M a n d t h e c o a r s e

m a t e r i a l i s e x t r a c t e d a t t h e l o w e r e d g e N . T h e l e n g t h o f th e c h u t e i s m a r k e d b y L a n d i t s

a n g l e o f i n c l i n a t i o n b y 3 .

R.M. U

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296 RUDOLF KV PIL

I t m u s t b e e m p h a s i z e d t h a t n o t a l l c o a r s e m a t e r i a l is s u it a b l e f o r c h u t e t r a n s p o r t . W e c a n

d i s ti n g u is h t w o p r i n c i p a l g r o u p s :

a ) c o a r s e m a t e r i a l w h i c h i s s u i t a b l e ,

b ) c o a r s e m a t e r i a l w h i c h is u n s u i t a b l e f o r c h u t e tr a n s p o r t .

C o a r s e m a t e r i a l w h i c h i s s u i ta b l e f o r c h u t e t r a n s p o r t i s c h a r a c t e r i z e d b y b e i n g c o m p o s e d

o f n o t h i n g b u t l a rg e p i ec e s o v e r 8 in . d i a m e t e r a n d b y th e a b s e n c e o f f in e a n d l o a m y c o n s ti t u e n ts

s o t h a t n o s t ic k i n g o r f r e e z i n g c a n o c c u r . B a s e d o n t h e d i s t ri b u t i o n o f T a b l e 1 w e f in d t h a t

t h e c o a r s e m a t e r i a l o f g r o u p 1 a n d 2 i s s u i t a b l e f o r c h u t e t r a n s p o r t s e e T a b l e 1 a n d F i g . 23 ) .

T h e r e a s o n i s t h a t t h e c o a r s e m a t e r i a l o f g r o u p 1 a n d 2 m o v e s i n t h e c h u t e a t a n i n -

c l i n a t i o n / 3 s e e F i g . 2 3 ) w h i c h is sm a l l e r t h a n t h e n a t u r a l a n g l e o f f r i c t io n ~ . T h i s m e a n s

t h a t s u i t a b l e c o a r s e m a t e r i a l f u lf il s t h e c o n d i t i o n

3 < : ~ . t2)

I f t h i s c o n d i t i o n i s m e t th e c h u t e m a y r e m a i n o p e n z o n e A I i n F i g . 23 ) . T h e e x a c t i n c l i n a t i o n

o f t h e c h u t e s h o u l d b e e s t a b l is h e d b y p r a c t i c a l t e st s. F o r p r e l i m i n a r y d e s i g n s w e c a n u s e t h e

f o l lo w i n g a p p r o x i m a t e f o r m u l a f o r t h e in c l i n a t io n o f t h e c h u t e :

t an f i

:

f l )< n 13)

w h e r e f i = i n c l i n a t i o n o f c h u t e , f t - c o e f f ic i e n t o f f r i c t i o n a l o n g th e c h u t e w a l l s e e T a b l e 3 )

a n d n = s a f e t y f a c t o r w h i c h i s a t l e a s t n -~ 1 .1 f o r s u i t a b l e c o a r s e m a t e r i a l g r o u p 1 a n d 2

Tab l e 1 ) .

T h e i n c l i n a t i o n f l o f t h e c h u t e m u s t b e i n c r e a s e d a s s o o n a s t h e p e r c e n t a g e o f f in e , m o i s t ,

c o n s t i t u e n t s r is e s. T h i s a p p l i e s t o c o a r s e m a t e r i a l o f g r o u p 3 s e e T a b l e 1 ). T h e d e s i g n o f t h e

i n c l i n e d c h u t e s f o r s u c h m a t e r i a l s m u s t t a k e i n t o a c c o u n t t h e r e l a t i o n s h i p

S a f e t y c o n s i d e r a t i o n s m a k e i t a d v is a b le t o c o v e r t h e c h u t e . F o r m u l a 1 3 ) c a n b e u s e d in

m o s t c a s e s f o r t h e c a lc u l a t io n o f th e i n c l in a t i o n o f a c o v e r e d c h u t e z o n e A I I i n F ig . 2 3) .

T h e f a c t o r n m u s t , h o w e v e r , b e t a k e n s o m e w h a t l a r g e r . I n m o s t c a s e s a f a c t o r o f n . . .. 1 -4 5

p r o v i d e s a d e q u a t e s a fe t y .

T h e c h a r a c t e r i s t i c f e a t u r e o f c o a r s e m a t e r i a l w h i c h is u n s u i t a b l e f o r c h u t e t r a n s p o r t is it s

c o n s i d e r a b l e p r o p o r t i o n o f f in e , e a r t h y a n d l o a m y c o n s t it u e n t s a n d a ls o a c e r t a in m o i s t u r e

c o n t e n t . T h e s e a r e c o n t a i n e d i n g r o u p 4 o f T a b l e 1. T h e s e d e t r i m e n t a l p r o p e r t i e s r e n d e r

s u c h m a t e ri a ls u n s u i t a b le f o r c h u t e t r a n s p o r t .

W e s h a l l n o w l is t a f e w i m p o r t a n t s t r u c t u r a l a n d t e c h n o l o g i c a l c o n d i t i o n s w h i c h h a v e t o

b e o b s e r v e d i n t h e p r a c t i c a l o p e r a t i o n o f c h u te s .

S h o u l d i t b e c o m e n e c e s sa r y , fo r r e a s o n s o f u n h i n d e r e d t ip p i n g , t o w i d en t h e c h u t e a t t h e

u p p e r e d g e M s e e F i g . 2 5 ) f r o m b t o d , i t i s p r e f e r a b l e n o t t o u s e t h e s y m m e t r i c a l s p r e a d

s h o w n i n f r o n t e l e v a t io n i n F i g . 2 6 a ). T h e e n l a r g e d p o r t i o n f o r t h e f il li ng s h o u l d h a v e a n

a s y m m e t r i c a l f o r m r e la t iv e t o t h e c h u t e c e n t r e l i ne b e c a u s e t h is p r e v e n t s m o s t o f t h e a r c h i n g .

T h e c o r r e c t e n l a r g e m e n t i s s h o w n s c h e m a t i c a ll y i n F i g . 2 6 b ) .

A v e r y i m p o r t a n t f a c t o r f o r c h u t e t r a n s p o r t is th e t y p e o f d r a w - o f f o f th e m a t e ri a l. I f

o n l y th e f r o n t p a r t t h e s h a d e d t r i a n g le 1 - 2 - 3 i n F i g. 2 7 ) is d r a w n o f f a t t h e e n d o f t h e c h u t e ,

o n l y t h e c o a r s e m a t e r i a l in s id e t h e a c t i v e z o n e A is s e t i n t o m o t i o n , T h e o t h e r m a t e ri a l

r e m a i n s s t a t i o n a r y i n t h e p a s s iv e z o n e P , t h e f o r m a t i o n o f w h i c h i s u n d e s i r ab l e .

T o m o v e t h e c o m p l e t e fi ll in g o f a c h u t e , t h e m a t e r i a l m u s t b e e x t r a c t e d o v e r th e w h o l e

c r o s s - s e c t i o n a l a r e a l in e j o i n i n g p o i n t 1 a n d 4 i n F i g . 2 7 ). T h i s c a n b e a c h i e v e d b y a s u i t a b le

d i s c h a r g e d e v i c e a t t h e e n d o f th e c h u t e .

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G R A V I T Y F L O W O F G R A N U L A R M A T E R I AL S IN H O P P E R S A N D B IN S 1N M I N E S - - I I

297

Figure 28 shows a chute diagrammatically . The key is: 1 = tipping 2 = inflow

por tion of chute 3 = chute 4 = discharge device 5 = lateral guide walls 6 ---- cover of

chute to safeguard against projected lumps of rock and 7 = front protective wall.

Unsuitable coarse material need not be excluded from chute transport. It can be used

providedthe harmful constituents are separated from this material.

b

F I G . 2 6

4

F I G . 2 7

O

( 6 ~ l t )

F I G . 2 8

2

7

F I G . 2 9

Figure 29 shows the possible solution in principle.

The key s: 1 = tipping 2 = discharge hopper 3 ---- separa tion device for coarse and

fine sizes 4 = chute 5 = discharge from chute 6 = ore pass for fines 7 = draw-off for

ore pass. The separation device 3 also separates the fine sizes so that only coarse material

passes to the chute.

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298

RUDOLF KVAPIL

T h e c h u t e s m a y h a v e v a r i o u s c o n s t r u c t i o n a l f e a tu r e s . A c i r c u la r p r o fi le o f th e b a s e o f t h e

c h u t e i s m o s t b e n e f ic i a l. T h e s i d e w a ll s o f t h e c h u t e s h o u l d b e v e r t i c al . A h e i g h t v o f th e s e

s i de w a l l s o f v = d / 4 t o r, ----d / 2 is a d e q u a t e . T h e m i n i m u m d i a m e t e r o f t h e c h u t e w it h

c i r cu l a r b o t t o m c a n b e d e t e r m i n e d b y t h e g r a p h i n F i g . 3 0 as a f u n c t io n o f t h e d im e n s i o n

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T h e f o l l o w i n g r u le s c a n b e l a i d d o w n f o r t ro u b l e - f r e e o p e r a t i o n o f c h u t es :

1 . C o a r s e m a t e r i a l o f g r o u p 1 a n d 2 s ee T a b l e I ) is v e r y s u i ta b l e f o r c h u t e t r a n s p o r t .

O t h e r m a t e r i a l s u c h a s g r o u p 3 r e q u i r e e i t h e r s t e e p e r i n c l i n a t i o n s / 3 s e e F i g . 2 3 ) o r a

d e g r e e o f p r e p a r a t i o n s u c h a s se p a r a t in g o u t t h e h a r m f u l c o n s t i t u e n t s s e e F i g . 29 ).

2 . T h e i n c l in a t i o n o f t h e c h u t e / 3 m u s t b e s u b o r d i n a t e d t o t h e p r o p e r t ie s o f t h e c o a r s e

m a t e r i a l s ee F i g . 23 ) .

3 . T h e c o a r s e m a t e r i a l s h o u l d b e e x t ra c t e d o v e r t h e w h o l e c r o s s -s e c t io n a l a r e a p o i n t

1 - 4 i n F i g , 2 7 ) a t t h e e n d o f th e c h u t e .

4 . T i p p i n g a t t h e u p p e r e d g e o f t h e c h u t e s h o u l d b e d i r e c te d a g a i n s t t h e s l o p e s o a s t o

d a m p e n t h e i m p a c t e n e r g y o f t h e c o a r se m a t e r i a l s ee F ig s . 28 a n d 2 9 ).

5 . I t i s a d v i s a b l e t o p r o t e c t th e s u r f a c e o f th e c h u t e s t r u c t u r e b y w e a r - r e s is t i n g m a t e r i a l

s u c h a s p l a t e s o f f u s e d b a s a l t .

5. O R E P A S S E S F O R C O A R S E M A T E R I A L

O r e p a s s e s a r e w i d e l y u s e d i n m i n i n g f o r t h e v e r t i c a l t r a n s p o r t o f c o a r s e m a t e r i a l [1 ],

T h e y m a y b e d i v i d e d in t o t w o g r o u p s s ee F i g . 23 ). G r o u p B I i n c lu d e s in c l i n e d o re p a ss e s

w i t h a g r a d i e n t b e t w e e n 7 0 ° a n d 8 5 ° a n d g r o u p B I I c o n t a i n s v e r t i c a l o r e p a s s es f r o m 8 5 °

t o 9 0 °. W e s h o u l d l i k e t o a d d t h a t o r e p a s s e s w i t h g r a d i e n t s o f l es s t h a n 7 0 ° m a y a l s o b e u s e d

i n p r a c ti c e . T h e s e c a n , h o w e v e r , o n l y b e u s e d f o r th e t r a n s p o r t o f c o a r s e m a t e r ia l o f g r o u p

1 o r a t b e s t o f g r o u p 2 s e e T a b l e 1 a n d F i g . 2 3 ).

A c i r c u l a r s e c t i o n i s b e s t f o r t h e g r a v i t y f l o w o f c o a r s e m a t e r i a l i n a n o r e p a s s b e c a u s e i t

h a s , a s i l l u s t r a t e d i n F ig . 3 1, t h e o p t i m u m h y d r a u l i c r a d i u s R . T h e c i r c u l a r c r o s s - s e c t io n

o f a n o r e p a s s is al so m o s t a d v a n t a g e o u s f o r s t a b il it y o f t h e s t r u c tu r e . F o r t h e s a k e o f c l a ri ty

t w o d i f fe r e n t s e c ti o n s u n d e r t h e s a m e l o a d i n g c o n d i t io n s ) a r e c o m p a r e d in F i g . 32 . T h e

u p p e r p a r t o f F i g . 3 2 sh o w s t h e n a t u r e o f th e l o a d i n g s c h e m a t ic a l ly . T h e s tr e ss d i s t r ib u t i o n is

r e p r e s e n t e d b y i s o c h r o m a t i c l in e s in t h e m i d d l e p a r t o f th e i ll u s tr a ti o n . T h e c i r c u la r

s e c t io n o f a n o r e p a s s h a s t h e o p t i m u m s tr e ss d i s t r i b u t io n , t h e i s o c h r o m a t i c li n es d e s c ri b -

i ng concen t r i c c i r c l e s .

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T h e d i s c h a r g e o f t h e m a t e r i a l f r o m a n o r e p a s s c a n b e e f f ec t e d i n v a r i o u s w a y s d e p e n d i n g

o n t h e p r a c t i c a l c ir c u m s t a n c e s . F i g u r e 3 3 i l lu s t r a t e s th e m a t e r i a l f l o w i n i ts i n d i v i d u a l p h a s e s

f o r a l a t e r a l e x t r a c t i o n o f t h e c o a r s e m a t e r i a l . T h e r e a r e s t a t i o n a r y p a s s i v e z o n e s n o t i c e a b l e

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I f t h e c o a r s e m a t e r i a l is e x t r a c t e d in t h e c e n t r a l p a r t o f t h e o r e p a s s s e e F i g . 3 4 ) , t h e r e a r e

s t a t i o n a r y p a s s iv e z o n e s , b o t h o n t h e f r o n t a n d o n t h e r e a r w a l l. T h e h e i g h t o f a p a ss i v e

z o n e d e p e n d s t h e m a t e r i a l a n d t h e c r o s s -s e c t io n b e i n g t h e s a m e ) m a i n l y o n t h e l o c a t i o n

o f t h e o u t l e t o p e n i n g .

A d e t a i l e d in v e s t i g a t i o n o f t h e g r a v i t y fl o w i n t h e o r e p a s s a c c o r d i n g t o F i g . 3 4 ) e n a b l e s

t h e d i s t r i b u t i o n o f t h e r a t e o f f lo w o f t h e m a t e r i a l i n t h e s e p a r a t e h o r i z o n t a l s e c t io n s to b e

e s t a b l i s h e d . T h i s i s s h o w n i n F i g . 3 5 a , b ) . T h e r a t e s o f f lo w in t h e s e s e c t i o n s a n d i n t h e

p l a n e s C 1, O 1 a n d C 2 a re i n d i c a t e d i n F i g . 3 5 b ) as h o r i z o n t a l c o l u m n s p l o t t e d f r o m C 1,

O 1 a n d C 2. T h e r a te s o f fl o w d i ff e r a l o n g a d i a m e t e r o f a n o r e p a s s , b u t t h e y b e c o m e m o r e

u n i f o r m a s t h e d i s ta n c e f r o m t h e d i s c h a rg e e n d i n c r e as e s .

A f t e r a d e t a i l e d a n a l y si s o f t h e g r a v i t y f lo w w e c a n d i s ti n g u i sh t h r e e z o n e s o f m o t i o n i n

an o r e pa s s [ s ee F i g . 35 c ) ] :

I D i s c h a r g e z o n e .

I I T r a n s i t i o n z o n e .

I I I Z o n e o f u n i f o r m s u b s id e n c e o f f il li ng .

Z o n e I , t h e d i s c h a r g e z o n e , m a k e s c o n t a c t w i t h t h e s i d e w a l l s a t t h e p o i n t s m a r k e d i n

F i g . 3 5 c ) b y i i a n d i2 . T h e a c t i v e z o n e I i s w i d e e n o u g h a t t h e s e p o i n t s t o t o u c h t h e s i d e

w a l ls . I f t h e o u t l e t is e x a c t l y a t t h e c e n t r e o f t h e o r e p a s s , t h e p o i n t s i t a n d i s l ie a t t h e s a m e

l e v e l. I f t h e o u t l e t li es , h o w e v e r , n e a r e r t o o n e o f t h e s i d e w a l l s , t h e p o i n t o f c o n t a c t is

s h i f t e d a t t h a t w a l l t o a l o w e r l e v e l. I n F i g . 3 5 c ) t h e o u t l e t o p e n i n g l ie s n e a r e r t o t h e r e a r

w a l l s o t h a t m l i s g r e a t e r t h a n m ~. Z o n e I t h e d is c h a r g e z o n e ) t h e r e f o r e t o u c h e s t h e r e a r

w a l l a t p o i n t / 2 w h i c h is a t a lo w e r l e ve l a b o v e t h e o u t l e t o p e n i n g t h a n p o i n t i l. T h e m o t i o n

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3

RUDOLF KVAPIL

o f t h e m a t e r i a l a lo n g a p l a n e t h r o u g h a d i a m e t e r is m o s t u n i f o r m i n t h e d i sc h a r g e z o n e o f

t he o r e pa s s .

Z o n e I I i n t h e c e n t r a l p a r t o f t h e o r e p a s s i s c a l le d th e t r a n s i t i o n z o n e b e c a u s e i n th i s z o n e

t h e r e is a c o n t i n u o u s d e c l in e in t h e n o n - u n i f o r m i t y o f m o t i o n .

FIG 35

T h i s n o n - u n i f o r m i t y o f m o t i o n d i s a p p e a r s c o m p l e t e l y i n Z o n e I I I, i n w h i c h t h e c o a rs e

m a t e r i a l s u b s id e s e v e n l y a c r o s s t h e w h o l e c r o s s - s ec t io n . T h e u n i f o r m i t y o f t h e m o t i o n c a n

b e s e e n v e r y c l e a r l y i n F i g . 3 4 w h e r e t h e s t r ip s o f t h e f il li n g , o r i g i n a l l y h o r i z o n t a l , d o n o t

b e c o m e d e f o r m e d , b u t m e r e l y s u b si d e. T h e s u b s i d e n c e is m a r k e d i n F i g , 3 4 b y a t h i c k a r r o w .

E a c h o f th e Z o n e s I , I I a n d I I I h a s i ts o w n c h a r a c t e ri s ti c . Z o n e I d e s e r v e s s p e c ia l a t t e n t io n .

I n t h e c a s e o f g r a v i t y fl o w o f c o a r se m a t e r ia l i t is t h e d i s c h a r g e z o n e w h i c h c a n c a u s e t r o u b l e

i n th e o r e p a s s w i t h a r c h i n g ) . T h e t r a n s i t i o n Z o n e I I c a u s e s v e r y li tt l e d i ff ic u l ti e s. I n t h e

Z o n e I I I w h e r e t h e s u b s i d e n c e i s u n i f o r m , d i f fi c u lt ie s a r e p r a c t i c a l l y n o n - e x i s t e n t b e c a u s e

t h is z o n e m e e t s t h e c o n d i t io n s f o r a n o p t i m u m g r a v i t y f l o w o f c o a r se m a t e r i a l b y p r i m a r y

m o t i o n ) .

T h e p o s i ti o n a n d e x t e n t o f Z o n e s I , I I a n d I I I al s o d e p e n d o n t h e a r r a n g e m e n t o f t h e

o u t l e t o p e n i n g i n t h e c a s e o f a v e r t i c a l o r e p a s s. T h i s is s h o w n s c h e m a t i c a l l y f o r a f e w

e x a m p l e s i n F i g . 3 6 w h e r e P i n d i c a t e s t h e p a s s i v e z o n e .

T h e t y p e o f e x t r a c t i o n h a s g r e a t i n fl u e n c e o n t h e a c t iv i t y o f a n o r e p a s s . F i g . 3 7 , c a s e I

i n t h e c e n t r e o f th e p i c t u r e ) s h o w s a n o r e p a s s w i t h l a t e ra l e x t r a c t i o n a s a n e x a m p l e .

T h e a c t i v it y o f t h e o r e p a s s w i ll d e p e n d o n t h e l o c a t i o n o f p o i n t K i n r e l a t io n t o p o i n t s

O a n d M . I f w e s h i ft p o i n t K i n s p a c e b e t w e e n t h e a r r o w s m a r k e d i n b a s i c e as e I b y n , t h e

a c t i v i ty o f t h e o r e p a s s w i l l d i m i n i s h . T h e c a s e s d e n o t e d i n F i g . 3 7 b y 1 a n d 2 i n c i rc l e s )

r e p r e s e n t a d i m i n i s h e d a c t i v it y c o m p a r e d w i t h b a s i c c a s e I. T h e a n g l e o f in c l i n a t io n o f t h e

c h u t e i s s o m e w h a t s m a l l e r . C o m p a r e d w i t h t h e b a s i c c a s e I t h e c a s e s 3 a n d 4 i n F i g . 3 7

r e p r e s e n t a n i m p r o v e m e n t i n a c t iv i ty b e c a u s e t h e a n g l e o f g r a d i e n t o f th e c h u t e i s g r e a te r ,

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302 RUDOLF KVAPIL

t h u s i m p r o v i n g t h e e x t r a c t i o n r a te . T h e s h i f t in g o f p o i n t K i s, o f c o u r s e , a p o s i t iv e f e a t u r e

i n t h a t t h e d i s ta n c e K M b e c o m e s s h o r t e r a t th e s a m e a n g l e o f in c l i n a ti o n o f t h e c h u t e.

I f i t b e c o m e s l o n g e r , t h e r e s u l t s a r e d e t r i m e n t a l .

T h e a c t iv i ty o f a n o r e p a ss i m p r o v e s a s t h e p o s i ti v e p o s i ti o n m a r k e d i n F i g . 3 7 b y p )

o f t h e o v e r f l o w l ip o f th e c h u t e b e c o m e s b e t te r . T h e o p t i m u m w o u l d t h u s b e r e a c h e d i f t h e

o r e p a s s w e r e b o t t o m l e s s .

A n i n c r e a si n g in c l i n a t io n o f t h e o r e p a s s s ee F ig . 3 8 ) w i t h o u t r e g a r d f o r t h e p r o p e r t i e s

o f th e c o a r s e m a t e r ia l i n c re a s e s th e p a s s i v e z o n e P . T h e e n l a r g e m e n t o f t h e p a s s iv e z o n e P

w i ll b e s ti ll m o r e e v i d e n t i f t h e o r e p a s s h a s a r e l a t i v e l y l o n g c h u t e a s i n d i c a t e d s c h e m a t i c a ll y

i n t h e l o w e r p a r t o f F i g . 3 8 .

i

-i :

Ie; 38

A c e r t a in i m p r o v e m e n t c a n b e a c h i e v e d i f t h e e x t r a c t i o n o f t h e o r e p a ss i s c o m p o s e d a s

s h o w n i n F i g . 3 9 .

T r o u b l e - f r e e o p e r a t i o n o f o r e p a ss e s c a n , h o w e v e r , o n l y b e a c h i e v e d i f t h e i n c l i n a ti o n o f

t h e o r e p a s s / 3 i s c h o s e n t o s u it th e p r o p e r t i e s o f t h e c o a r s e m a t e r i a l a c c o r d i n g t o F i g . 2 3 ).

T h e n e c e s s a r y i n c l i n a t i o n d e p e n d s , o f c o u r s e , a ls o o n t h e f r i c t i o n a l o n g t h e s i de w a l ls .

F i g u r e 4 0 u p p e r p a r t ) s u m m a r i z e s th e i n c li n a t io n s f o r o r e p a ss e s w i t h s m o o t h w a l ls

d e p e n d i n g o n t h e g r o u p s o f m a t e r i a l 1 - 4 s ee T a b l e 1 ).

T h e l o w e r p a r t o f th i s il l u s tr a t io n s h o w s t h e m i n i m u m i n c l in a t i o n n e c e s s a r y f o r o r e p a s se s

d r i v e n i n s o l i d r o c k , i . e . w i t h a p p r e c i a b l e f r i c t i o n a l o n g t h e s i d e w a l l s .

T h e m a i n r e q u i r e m e n t s f o r t r o u b l e -f r e e o p e r a t i o n o f o r e p a ss e s a r e a s f o ll o w s :

I . T h e s a fe in c l i n a t i o n o f t h e o r e p a ss d e p e n d s o n t h e n a t u r e o f th e c o a r s e m a t e r i a l a n d

o n t h e f r i c t i o n a l o n g t h e s i d e w a l l s s e e T a b l e 1 a n d F i g . 23 ) . A m o r e c o m p l e x c o m p o s i -

t i o n o f t h e c o a r s e m a t e r ia l d e m a n d s a g r e a t e r a n g l e o f in c l in a t i o n .

2 . A c i r c u l a r c r o s s - s e c t io n o f t h e o r e - p a s s i s b e s t.

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3. Co arse material o f grou p 4 Table 1) can no t be transported in ore passes driven in

sol id rock.

4. W e can dis tinguish three zones in the kinetic f low of an ore pass:

I Discharge zone max. s econdary mo t ion)

II T ransit ion zon e trans it ion from secondary to primary motio n)

I II Zon e o f uni form subs idence pr imary mot ion) .

5 . A smaller discharge Z on e I imp roves the re liabi li ty of operation. T he s ize of Zo ne I

depends on the locat ion o f the out le t opening .

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6 . T h e m i n i m u m d i a m e t e r re q u i r e d f o r a n o r e p a s s i n s o l id r o c k c a n b e c a l c u l a t e d f r o m

t h e f o r m u l a

d = / 0 . 8 5 5 × D ) 2 k

0 . 7 8 5

w h e r e D - - s iz e o f t h e b i g g e s t l u m p s o f t h e m a t e r i a l a n d k : -- f a c t o r d e t e r m i n e d f r o m

t h e n o m o g r a m , F i g . 12 .

7 . T h e o u t l e t o p e n i n g a n d e x t r a c t i o n d e v i ce s h o u l d b e d e s i g n e d i n s u c h a w a y t h a t a n y

a r c h es w h i c h m a y a r is e c an b e r e m o v e d q u i c k l y a n d w i t h o u t h a z a r d .

R E F E R E N C E S

1. BENTHAUS F. D ie Ges tal tun g von Berge bunkerr t und deren Bede utung f i i r d ie Verbesserung des

Be t r i ebsab lau fes in s t e i l e r Lagerung , Gl i i c k au f 97 1061 1961).

2. KVAPILR . E n t l a d e t r i c h t e r u n d B u n k e r f i i r g r o b s t i i c k i g e s M a t e r i a l . Czech ed i t ion ) SN TL -Praha 1955).

3 . KVAPm R.

Theor ie toku sypk ych a balvani tych hm ot v zasobnic ich .

Czech ed i t i on ) SN TL -Praha 1955).

Theorie der Schii t tgutbewegung German edi t ion) . Ver lag-Technik-Ber l in 1959) .

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