FLUVIATILE MORPHOGENESIS OF ROUNDNESS: THE HACKING RIVER, NEW SOUTH WALES,

AUSTRALIA

D r . Joseph P . B . M . O U M A *

Lecturer in Geography, Makerere University College, Kampala, Uganda

ABSTRACT

This paper is a summary of part of an intensive lithological, mechanical and morphological investigation into the sediments of the Hacking River, New South Wales, Australia. Only the major observations on roundness parameters, are sum­marized; sphericity is not discussed here.

Roundness increases as calibre decreases; but in sub-granule grades roundness declines as size decreases. Unweighted mean roundness does not approach 1.0 asympto­tically downstream: it flrst increases to a maximum, whence it declines downstream. It evolves downstream at a medium rate in above-cobble grades, fastest in cobble-granule range, and slowest in the sub-granule grades. Mean roundness evoives down­stream faster than calibre decreases (and calibre declines faster than mean sphericity evolves).

Roundness in the Hacking does not change at confluences, because of small tri­butaries and pétrographie unformity of the catchment. While roundness dispersion and roundness skewness evolve downstream along wave-like curves, in long sandy rivers roundness decreases downstream; unweighted mean roundness has been attained ; and roundness is positive-appro aching +1.0 asymptotically downstream.

RÉSUMÉ

Cette communication est un résumé d'une partie d'une recherche lithologique, mécanique et morphologique des sédiments de la rivière Hacking, Nouvelles Galles du Sud en Australie. Seules les observations principales relatives aux paramètres de l'arrondissement sont résumées, la sphéricité n'est pas discutée ici.

L'arrondissement des matériaux augmente quand leur calibre diminue, mais dans les dimensions inférieures aux granules, l'arrondissement diminue avec la dimension. L'arrondissement moyen non pondéré n'approche pas 1,0 asymptotiquement vers l'aval : il augmente d'abord jusqu'à un maximum, et puis décline vers l'aval. 11 évolue vers l'aval à un taux moyen dans les dimensions supérieures au galet, reste constant dans les dimensions entre le galet et le granule, diminue dans les dimensions inférieures au granule. L'arrondissement moyen évolue plus rapidement vers l'aval que la dimension diminue (et le calibre diminue plus rapidement que n'évolue la sphéricité moyenne).

L'arrondissement ne change pas aux confluents sur la rivière Hacking, à cause de la petitesse des tributaires et de l'uniformité pétrographique du bassin. Alors que la dispersion et l'asymétrie de l'arrondissement évoluent vers l'aval suivant des courbes ondulées, dans les longues rivières sablonneuses, l'arrondissement décroît vers l'aval.

INTRODUCTFON

This paper is a summary report of part of a fluvio-sedimentological research that investigated into lithology, calibre, roundness and sphericity of sediments in the Hacking River, New South Wales, Australia. Reported here are findings on evolution of roundness of sandstone, quartz, shale and coal.

* Dr. Joseph P. B. M. Ouma is lecturer in the Department Geography, of Makerere University College, University of East Africa, Kampala, Uganda.

319

o

00

r.SS

Î

o.

h->

K-

!" A

" */ïV^

(

ik vfinx X

„ ,

^N

r î

The Hacking River calchmenc, 64.38 square miles in area, occupies the southern portion of the Sydney Basin, in a centra! position on the Pacific coast both of Australia and of New South Wales (fig. 1.1). The portion of the river investigated drains 38.78 square miles (60.30% of the catchment).

With a perimeter of 30.8 miles, the catchment above the Audley Causeway is almost a rectangle 12 by 4 miles in extent, with a circularity of 0.71. The Hacking catchment is a rugged dissected plateau. Altitude ranges from 5 feet on the bed of the Hacking at the Audley Causeway to 1,125 feet at the headwaters of Kelly's Creek —giving a relief ratio of 65.6 feet/mile for the catchment, and 96.7 feet/mile for the Upper catchment. The catchment slopes gently northward, the eastern catchment being generally lower than its western counterpart.

Part of the Sydney Basin, the catchment has two fresh-water Triassic formations: the Narrabeen Group (largely shaly) and the Hawkesbury Sandstones. The Narrabeen Group outcrops between Kelly-Gill's Falls and the Lady Carrington Bower—i.e., in 7,08 square miles or 18,5% of the Catchment area. Lady Carrington Bower is about 14 miles downstream of the source of the Hacking, about 4 miles above the Audley Causeway (fig. 1,1). From slag heaps of the Helensburgh Coal Mine (opened in 18S8) in Upper Catchment, coal is washed into the Hacking River at the 5.8th mile below the source of the river.

With steep slopes, all the soils of the catchment are apt to erode rapidly; and the catchment experiences sub-tropical conditions and maritime influence. Rainfall is distributed evenly throughout the year, with a maximum in the late Autumn and early winter months of April, May and June.

METHODOLOGY

Subsequent to sieve analysis of a sample, each size grade coarser than 1 mm was divided into lithological separates, from each of which a microsplit was obtained for morphological analysis. A combination of the procedures of Wentworth (1919, pp. 507-521) and Wadell (1934, pp. 187-220) was modified to obtain data on roundness. The formula is

where P = roundness of a particle;

r i = radius of curvature of the sharpest edge or corner of the particle;

and R = ^(a + b + c), where a, b, and c are the principal axes of the particle. Inclusion of corners in the roundness analysis in this study is a departure from Went­worth. Altogether more than 35,000 particles and fragments were analysed from 120 samples of bed material from the Hacking River and its major tributaries. In all cor­relations with calibre under Roundness, the phi-scale was adopted.

A. MEAN ROUNDNESS, P.

1. Influence of Lilhology on Mean Roundness

The apparent values of mean roundness of sandstone, quartz, shale and coal were tested for significance. On the basis of 98 samples compared, there were significant

322

interseparate differences, at ihe 0.01 level of probability. These differences imply that, because lithological composition of the bed material of tlie Hacking River changes downstream (Ouma, 1966, pp. 37-57), the mean roundness of the aggregate bed material, likewise, changes downstream—at a rate partly controlled by the rate of change in lithological composition of the bed material. Secondly, any inferences from studies of mean roundness of aggregate bed material without corresponding studies in the separates should be drawn in the light of lithological composition of the bed material in the size grade or grades analyzed.

2. Influence of Calibre on Mean Roundness

The roundness values of all samples were averaged for each separate, grade by grade. A very high correlation exists between mean roundness and calibre in all four separates (table 1.1); and all regression coefficients are significantly different from zero, at the 0.001 level or better. However, separates both from the Hacking River and from its major tributaries show a marked break in the regression line (fig. 1.2) at sizes between — 1.5 and — 2.5 0 . This significant break can be explained.

Published works are available on roundness-calibre correlation on either side of the — 1.5 to —2.5 0 size range, but the writer has not located any work in which a cobble-io-silt size range was studied. The apparent lack, or at least the paucity, of such works makes it difficult to compare the results of the present investigation with those of other studies. For convenience, the two regression lines on either side of the break or inflection point in each separate (fig. i .2) will be considered as relating to the coarse and the fine limbs.

Deteriorating roundness with diminishing calibre has been observed for the fine limb by several workers—e.g., Russell and Taylor, in the Mississippi River (1937, p. 251); Wadell, in St. Peter Sandstone (1935); and Pettijohn and Lundahl, 1943 (Pettijohn, 1957, p . 63). As well as later workers with comparable results, they studied mostly size grades finer than 1 mm. Studies ofthecoarselimb include those of Plumley in the 34-64 and 16-32 mm grades (1948). But his conclusions are not unequivocal, because he used only two size grades. Wentworth, however, perceived the existence of the inflection points (fig. 1.2) when he said :

" In most sands the roundest grains are neither the largest nor the smallest, but belong to grades just short of the coarsest which are abundant in the deposit " (Twenhofel, 1961, p. 222).

In each separate there is an optimum size at which maximum roundness occurs, e.g., in the granule-to-small pebble range, — 1.5 to —2.5 0 in the Hacking. This obser­vation confirms Ziegler's predicition, 1911, that "there is probably... an optimum size at perhaps the smaller pebble grade where rounding, under the influence of these opposing factors is at a maximum" (Twenhofel, 1961, p. 222). Among the most influ­ential lithological properties on morphogenesis is relative density, which, beside the influence of turbulence, largely controls the size at which sedimentary particles begin to saltate more than they travel by traction. The relative densities of sandstone, quartz, shale and coal in the Hacking are 2.066-2.55, 2.65, 2.94-3.05, 1.74-1.80. Since coal has the lowest density among the four separates, it has the coarsest particle at which hydraulic diameter permits saltation. Because rounding is encouraged by gentle abrasion, rather than by saltation, the onset of saltation marks the beginning of deteriorating roundness. It is emphasized that saltation encourages chipping, spliting, and other processes which are inhihitive to progressive rounding. Size reduction in particles smaller than 2 mm is very slow (Ouma, 1966). Concomitant changes in round­ness, are, similarly, slow. Probably in subgranule size grades particles are increasingly composed of chips knocked off coarse pieces; and the cushioning effect of water prevents significant rounding of these chips. The finer the calibre on the fine limb,

323

o

<

^

^ S

œ

s -

b

%

"À

*Sl

a -o ~

o

a;

i

,i|i

00 O

i'i ^

!

« u

5W

— <n

•a- r-

X

X

X

X

X

X

o c-r

CJ

^ co

^t

•«r o

c^i r—

o b

o o

o d

o •*

<N

•£>

WTi

m

O

O

q o

u-i

<-i

fi

i^'

rj

o q o

o iTk

O

U-]

<n

o o o o ?

c

e

rr

o o

o

u-i

r-

H

CA

•fl-

o

o o o

•o

•«

*

ri

in

o o d

o q —

>n

r^

s o o o

Q

q wi in

•fl-

\&

o o o o

in r*

•*

CO

H»

rN

O

O

o d

•c

•o

•o

r^

O

b s o

CC

•

*

-r M

O

(n

O

O

d

o o d m

M

F-l

O

S

d

w~i

O

•Û

»

d <n

<"1

•O

C

*l O

f

ï O

O

Q

O

S

o d

d

—

o -H

IO

o r-

r-- to —

d

—•

in n

s a o .=

O

U.

S «

o .=

OH

, a£

U

U.

g ¥ —

•

—

ai. «

OS

0

0 C

=

F

—

n_

•M

J<

U

O

n

B

£m

? g

«;2 oo

bo c

c -*

-M

fj O

B

rt

a K

ï 1

.»- ._ tftf on

oo c

c •

—

• —

•a

M

u o

d n

ïï

s g

,_ ,—

ai

oi

un e

» c

c -

_ •

—

M

-a

o u

13 «

J

ÏI

ta

a B

•a

o O

X

X

X

X

X

X

-H r-

o o

o o

o o

d d

d d

—

cû

O

O

O

O

o o

d d

28

CO

M

-

5 S

o o

o S

d

d

o .b U

H,

o .5 O

U,

OU

O

O

ii îi

3

a

s.s o u,

o o

H

H

a •a

X

X

•t

^r

co ^o

S S

o

o o

o d

d

\o

o r*i o d + >/-* f-i ^ o d I

o f-i o d + o f-i

<o

o d 1

__ •

o

o d + o \o r-J O

d j

^ r-) == O

+ r-

co

O

d 1

co

•o

o d ~r

o <n

r-N

O

d i

O

•a-

rJ

o d _L

CO

<

n r

j

o d [

_ CJ O

d -f

o r~

t*^

O

d 1

o\ c

o

o o d -ï-

•fl

o d i

U

oo

II

a 324

i 3-

4 'Z Lt

4i «•

« ï t 1

u

-"i

il-t-

:+

:'

••

??

—::T

•"

'""

"''"

.-"

.'- :::

::: -

."

:..

:Ï_

T

: .t

" .

. :

: ; J. .. .~.~z

xx ...

.: x

: x

x

T

- - - -. -

1 M

,4 ..L

-i-ul.

. .;

. J.

xx

L

UJ

XJ

J..L

L à

it?i

%..

,7:. . ...

.,t..

. ^

:.

':

::

' l:i±

ji .ij

; :

„.

..

..

. :

r ••-••••..

--j-- - --

• • 3

3;

"3- U

.

1 • ,

... -

. nlo

: - * . ' t

i «

œ 13

-! H

-.,. *s2r

-, • •'

t.-.h ï

. i-r. L J_,..._,_ -iiiiS

r-jrcXL

ifaJîlJjJJ--.

. |_, jj,

.j. .-,-

1. „

T

.-,^-

^.

wj

^.

^.

j Q

_jj^

_|-|-^

.

„ J

1

j - T.

' • -

...:..::::: : : !

: at

ï *t

1

u

HI -H

H-I+

-ff it

! 1

'i

J "

x

: :

? g

,

J 1

J

4

IX

3

L

1

T1

' 1

t

' !

ï 1'

_ _

1

—

H "•

1 ;l

W

J ,. -

j J

11

'

1

t '

..

X

- ? '-i-c

il

x s t

J '

-, x

: :

,-,.3 J

*f

Xg

-H

t-

-l ^

--

-~-

-1---

hi

." '

1

> iïï I--

.1 1

l- i.H

,1

l«

3

L

1 1

I 1?

, 'y

?

S lr

' , O

, 1

' S

fi

l?

t K

5,

,, s

t i

::

..

..

:;

K

-° M

t,

1

, 1

.

xx

. :

::

::

::

te

7 l

1*1

1

1

y S

1 u

j| 1 1

11

! |

| 1

~

Î .i

-•- 11 1

1 1

! 1

*-M

* i

!i

' j

' ,

11 i 1

-

..

.:

:.

::

1 ,_

j

11

r

i ,1

_

x .

:„

::

::

..

.:

^ 0

îr —

' .

: 1

J r

t ' "

'1

1 B

a1, •* *

1

^ '

r r,

1 1 !

..

1 1

H

-

1 1 '

. 1 ».

1 ' „ '

*i ' l

m

1*

' '

t X

' -1

- - -« -

1 ^

. ^

1 .

..

. n ^

j. +

•

1 '

' '

II

- '

! (

' -

J.

. . !_

1

1

i_

1

H ,_

. 1

1

1

L

' J

ii 4-

-i

-.

-.

..

1 ,

, 1

' r '

j •-

n

, 1

1

- .

r • -•

1—

1

' '

,1

1

J '

j t

-X

J j

1

X

j -

--

--

-i

t -

r-J

•* .

-1

-r •-

:;

1 ^- -

•• ,

~

Lr-

ïL-;:&

f? JL

l_r

-J ' _

J

T Sï::i

:l:::î M

'

L

. - "* ^

.L

- i . • , ™

1

t

i '

i •-.

ir

' 4

ÏÏ i :

^ —

. '

' i

—a

J^Ll.

L>at,jtfd i--L ?

^g

Tj_

i

1

1 Jr

>:~

t:

"-V

Î:ix; 11

, =

" r- 1'! F

t 5*^kl

^if

l L;

n

--L. 1

W

iiL-W 1

l*

r x.

' "

T '

Kv

- --

-(

--

- .

||

..

:>

. t

..

P

• r-v

. K

1

k

i"

• !

::

::

;i

j 1

'

* T H

?

•*

•'

• " ^ —

i —

x

- :

—

S"

.. j

: J~

l ;

T4t_" T

f ^j~

- ,

- -h

, - 3-

+-

rn-r—

i.J

rf-i ±

r—-:

: M

s::

-

:- $

--ja

r :

_ +.1s.te

.+..„„..:

33:2

-s- • •

lu lu 'M -1 s

f •H

^

^s fa

._

_

:.

:_

.:

._

::

::

:_

: ±

. J n

w-

--

- —

f"

_"S

"^s

~F

iii "

":

: •".""

""

__

fi !l ï-i"i

ii—-

Jrî _

, O

i -'

--

-.

_

^._

^_

_ •S

r,

i •

1j.

2

: :

::

::

: s

_ 4

-.- - j-

-- jt.

;!

-T

r -1

:

:r

--

--

--

-"

* 1

1 i" '

\ • rrj

. ^T

TT

^^"^ r ^

T^

-__

i_--*-

---f-- _

.*,-_.-*-.*

p r- - j i

-; "t ~ 1

r:' T

::":'::zz: .".T

.". :::_. x ::

_g. .

_

^ ,| + •

| z\z„

:::+:.::..::

ri

; •

M

• • x

s i

j-- _

. .

J ._

.. -.

. ..T

»

---,--• ,

i;

, •

- — -

-; —

;;

;-

T

;;

; •;

vi

-

!—

' H

S.

ii

r T

- :

;;

j:

: ^

—:

j_ -1

.... ,.ft- ..n

(T

. ... T.

- -

ato

xrT

xrà

cr.T

--• -i-'-rr.n

TT

rr'rTT

i.mi

• T

I-LID

...

- - -l-l~ -U.^.

JJ

^ . ,-,.*

_.,

- ~ . , . . - .y.. .(_]_ .

x i

--

--

-; rt •

..

..

..

1 a

, a

i-rh T

J^

-o'^

-hh

-H-f+

i-H

i-f-HJi-1

i ^ft

H

' a

i 3» x

x j

1«

^ • "K

ir

^

4

s f

| x

::: "JES

E

::

::

:x

::

: u

. PW

J X

XE

SK

X;

----

4 m

w

•

33

-X ;

±

, 3

j . •

ï s. .... ^ s

• —

J

—

: • • : : •. .

..

..

..

4—

.

x:::::::::.::::

;i :x

::x:x

::x:

Kr-

St

•J Vf

lis.

K

K

UW

H

l'H

•

•*

r ; :.. : X

EL

. :

: :

: : :

r OVJ

r :

i:

._

x:

x:

^ T

..

.X

.X

.:

. •-'

; --;- -

::~J:::::::: .... z

i :.

: :

. r

h L

0

II

EX

et

ex

st

xi

&!

^j- ----- -

^ JJ.

:;--•;

_. _

_. _ _ x

. - 4

- •• - - -•-. - -L

^:. - il-. -

r

TT

" • • "

^ • "^

^ • " T

• " " .

" "

1

r "

.;-.„

.. .

..

..

i •

-'

&•

••

:_

::

:

fi I a.*^ 1

T

rP

hr : ::

:.... :

. |

! ....::::::

::..:::: :

. :. x : : : : : :

Pr­ît k il ' 4. r

•]• i M

. Bj

i 1

-H

...

...--. . : . .

. "

, H

, 1

M

IT'W

i

rP

^ ^

H J

L ^

^ ''i

J_I_L ,JiL

LiJ

.. . $feLL JHyy-LLL 4- 4_i. -L JJJ

•n-r

i1-ff=

rrf T

«J

^rrH-*>

7S

rl- +

-p

- -| h

tl

U f

'nk»i n

1*

M

n

™

1*

î ;.... ,:±

:. ;...:.:.

r- Y

IL

-.-,-.,;£---

"n

--

-................

...... .........

... .

..

..

X_

_

..

. .

..

..

_

. ^

T.

..

..

..

..... .._

:,...... >

.

......_.

..

. E

J1L

—[JijlL

L!lT

iTtrJi,h

A-..lj..U

325

the less the effect of rounding processes. Consequently, on the fine limb, the finer the calibre of a particle, the poorer its roundness, irrespective of its lithology. But on the coarse limb, roundness increases with decreasing calibre: if size grades transported by traction are reduced by comminution, the finest size grades so transported should have undergone the longest period of rounding. This view is tenable, because commi­nution also includes abrasion and wet sand-blasting, which are very effective in rounding.

One further inference may now be drawn. If all size grades of bed material are analyzed for roundness in the downcurrent direction, until the limiting maximum roundness is attained in the roundest grade, there is a progressive reduction downstream in the coarseness of the size at which maximum roundness occurs. But size decreases systematically donwstream. Below a particular aggregate size in the granule-pebble range, roundness deteriorates downcurrent. In all separates, however, the relative efficiency of comminutional processes that effect active rounding on the coarse limb can be compared with that of viscosity, turbulence... which inhibit progressive rounding on increasingly finer grades on the fine limb.

The amount of improvement in mean roundness which separates acquire as they travel from creeks into the Hacking is indicated by the difference between the value of maximum roundness attained by each separate in the Hacking and the corresponding value in (he creeks. Also, if it were necessary or desirable to use only one size grade to trace the development of roundness downcurrent, probably reliable results would be obtained by studying the optimum size grade only. However, in a long river the opti­mum size gets progressively finer downcurrent until the size grade of inflection brackets the median calibre.

3. Influence of Distance of Transport un Mean Roundness

The roundness-calibre curve {fig. 1.2) summarizes the probable evolutionary path for roundness downstream. Roundness-sphericity correlation is significant and mostly positive (Ounia, 1966, p. 158). This relationship suggests that, by virtue of their superior sphericity, certain size grades coarser than the calibre of inflection outrun those of low sphericity. These fast-rolling particles induce correspondingly high values of roundness downstream, without having been necessarily rounded significantly as they rolled. Size grades on the fine limb, however, show diminishing sphericity with increased fineness (Ouma, 1966, p. 22/ ; Pettijohn and Lundahl, 1943, p.73;MacCarthy, 1933, pp. 205-224; Wadell, 1935, p . 250 ff.; and Lamar, 1927, pp. 148-151|. Roundness on the fine limb, therefore, deteriorates downstream.

It is neither feasible nor fitting in this paper to give a detailed account of particulate morphogenesis of each separate downstream. Instead, only the evolution of roundness in sandstone is given, as an example. Roundness evolution in the other three separates is only briefly summarized, with the aid of figures 1.6, 1.7, and 1.8,

The unweighted mean roundness of each sample was computed for each separate, and each set of means is plotted against the distance of transport. Figure 1.3 gives the fitted regression lines for log of roundness versus distance. The influence of the Nar-rabeen-Hawkesbury Transition Zone (fig, 1.4) near the Bower is in evidence. Near the Bower (13.74 to 14.20 miles below source) there is a significant departure, at the 0.00Î level, from the trend of roundness established in the first 14 miles of stream transpor­tation. Table 1,2 summarizes the results of tests of significance oT roundness-distance correlations in all four separates. Above the Bower the unweighted mean roundness of sandstone increases exponentially downstream; but below that location mean round­ness rapidly deteriorates, also exponentially. Both coefficients of regression are signi­ficantly different from zero, at the 0.001 level or better. The dispersion diagram and the fitted mean curve of rise or decline in mean roundness (fig. 1.4) complement the scatter of points and the regression lines in figure 1.3. Used together, the two figures

326

fi 6 o 13 * D I S T A N C E I N I - i l L É S D O W N S T R E A M

Fig. 1.3.

help to visualize the significance of the trends they show. Figure 1.4 gives the trend of roundness in each size grade as well as the fitted line of regression of mean roundness.

Several works exist which show a rise in roundness downcurrent. The list includes the findings of Plumey in the Black Hills (1948), Krumbein in Arroyo Seco (1942), and Grogan on the beaches of Lake Superior (1945). Plumey studied the 16-32 and 32-64 mm, grades, Krumbein, the 16-32 mm size range; and Grogan worked on pebbles. Roundness of the grades in the Hacking was found to increase rapidly at first, but the rate of increase soon decreased downcurrent. Beyond a certain distance roundness was maintained approximately constant. The results from the present investigation

327

FIG ' • ' ROUNQNESS DISPERSION D I A G R A M AND F ITTED MEAN CURVE OF REGRESSION IN SANDSTONE

9 10 12 DISTANCE IN MILES DO'.VNSTflEAM

328

Fig. 1.4

above the Bower are similar to the previous ones for individual size grades. However, the type of roundness increase for unweighted mean roundness is very different from those types shown in previous works. Figure 1.4 shows the curve for unweighted mean roundness of sandstone. This mean increases downstream at an increasing rate, down to the Bower. And this trend is explained in the framework of a roundness-evolution theory to be explained and tested later.

In figure 1,4 the coarsest and finest grades have the slowest rates of roundness increase downstream. Above the calibre of inflection (fig, 1,2) the finer the size, the rounder the particle. But calibre decreases downstream; and the unweighted mean roundness is computed by giving equal weight to all contributary size grades, irre­spective of what mechanical proportion of the separate each constitutes. Therefore, at first, the farther downstream the bed material is carried, the higher the proportion of above-granule size grades each of which contributes a high roundness value to the unweighted mean roundness. Consequently, the farther downstream the bed material is transported, the higher its unweighted mean roundness, until the calibre of inflection is within the mean size grade. It is noteworthy that, as long as the number of size grades with high roundness values continue to increase donwstream, the rate of increase in roundness increases. This is represented in Phase ! of figure 1.5. Figure 1.5 is the conceptual scheme of the postulate within whose framework evolution of roundness downstream is explained in the present investigation. But after Phase I a distance is covered downstream of which the number of high-roundness grades progressively diminishes. The influence of low roundness values of sub-granule grades on unweighted mean roundness begins to increase. Consequently, the rate of increase of unweighted mean roundness downstream begins to fall. This occurs in Phase II (fig. 1.5). Beyond Phase II a distance is travelled over which unweighted mean roundness is nearly constant—Phase III. As more of the coarse grades are eliminated, unweighted mean roundness starts to fall below its maximum value already attained. This fall indicates the predominant influence of the low-roundness sub-granule grades. The point of inflection has been passed. No size grade in the bed material now improves significantly in roundness downstream; and unweighted mean roundness decreases rapidly down­stream. This is Phase IV. The influence of saltation and selective sorting become especially significant. Low sphericity and, so, low roundness result.

Down to the Bower (fig. 1.4) the development of unweighted mean roundness is still in Phase I of figure 1.5. Probably Phase II is just beginning. However, due to the cessation oftheNarrabeen Group within the transition zone, and due to the low durabi­lity index of sandstone (Ouma, 1966, p . 69), Phases II, III, and IV are, perhaps, all

' " 'il'rhfcS .ÎBnWtfiikci!

p l i •'••?' :RikfepH(>'i£ WFJI

F ig . 1.5

329

rJ

m

-J m

<

i-

> ?

-*Z

*&

a 1 •S

s&

I

«c ^

a bio

ffl

33

•" S

ri

O

o CTN

i-,

^ _

• E

L,

—

o o °1

Z

=

V

^

"I

in

=•5

^ i I' +

o a>

« j-

i

p

a "5 *

j

'M

o 'o J=

" J s &

"£ C

J

£ i>

-» 5t

>-« c O)

m

x x

o o

ss g

g

1

X X

o

T

o f

j

o o

o

o

d d

rO

—

fl

O

x x

_ o C

\

C*

r*n

O

O

C

CO

C

O

C*

^

"*

O

-* o

r-

o

b/1 O

f-

<2

a •*

o —

o o

o

o

o o

*3-

rj —

a\ o

o

o c

d c

CC

Ch

f~

0\

*—

CO

o o

o

o

d d

!

q d + H

b-X X

z z s * o ° ca .D

O

d +

SG S

Z

Z

above below

o d + above below

q ?

Il below Confli

O

o U

o N

3

CO

M S

a X

z Z

330

compressed within a few hundred yards. The dashed line in figure 1.4 is an estimate of the probable curve over the reach of inflection. The rapid destruction of grades at the coarse end of the fine limb leads to an initially high rate of decrease of unweighted mean roundness below the Bower. Buc after the coarse grades within the fine limb are eliminated through comminution, the proportion of fine grades within the fine limb is also increased by selective sorting and saltation. The rate of decrease of unweighted mean roundness, therefore, falls progressively downstream. In Phases 1 and V the mean changes exponentially, rising at a rising rate in the former, and falling at a falling rate in the latter.

Several inferences can be drawn from the foregoing discussions. First, if the deduc­tions in the preceding discussions show that the postulates in figure 1.5 are tenable, the following conclusion is warranted! in fluvial transportation the unweighted mean roundness of a lithological separate does not approach 1.0 asymptotically downstream. Rather, it increases downcurrent until it reaches a maximum value, the magnitude of which is peculiar to each separate through lithology and mechanical composition. Further transportation downstream leads to diminishing values of unweighted mean roundness. It was also found under Calibre in this investigation that size decreases downstream exponentially and approaches zero asymptotically; and in the roundness-calibre curve (fig. 1.2), in size grades finer than the calibre of inflection, there is a signi­ficant positive correlation between mean roundness and calibre. It is, therefore, con­cluded that, downstream of the reach within which mechanical composition induces the occurrence of inflection in the roundness-distance curve, unweighted mean round­ness decreases exponentially downstream, and approaches zero asymptotically.

Familiar works were cited earlier which show increase downstream of roundness of certain gravel or pebble grades. But, for instance, Russell and Taylor showed that in the Mississippi River the mean roundness of sand decreases downstream. They computed unweighted mean roundness. From a Lake Erie beach, Pettijohn and Lundahl (1943, p . 74) who analyzed five size grades bracketting 0.70 and 0.088 mm obtained similar results to those of Russell and Taylor. These two works furnish results which were subsequently used to examine the roundness of quartz in the Hacking River. But both in the Mississippi and on the beach of Lake Erie the size grades ana­lyzed were finer than the size grades within which inflection occurs in the Hacking sediments.

Below the reach where inflection occurs in the roundness-distance curve, the mechanical composition of bed material only permits a downcurernt decrease in unweighted mean roundness. Specific gravity of a separate, turbulence of the stream.., determine the size at which suspension replaces saltation. It was noted that, because of their small weight in the water, fine particles rarely overcome viscosity and surface tension to make direct impact on one another. Abrasion is at a minimum. Fine chips of low sphericity also come off coarse grades farther upstream. The negative roundness-distance correlation in sandy rivers is subject to a very complex suiteof influences.

Some comparison is now made between observed rates of size reduction and of change in unweighted mean roundness. Calculations in this investigation (Ouma, 1966, p. 176) show that, over the first 12.2 miles, calibre decreases by 36.4% from 21.380 to 13.583 mm. Over this distance unweighted mean roundness increases by 62%. Above the Bower, therefore, the rate of increase in roundness of sandstone is about twice as fast as the rate of size reduction. But below that location a size reduction of 30.7% between the 14th and 16th mile is accompanied by only a 40% decrease in unweighted mean roundness. From this observation and from similar ones in the other three separates, it is deduced that, while a given size reduction is accompanied by a numerically bigger percentage of change in unweighted mean roundness, the percentual rates of size reduction and change in unweighted mean roundness are closer together downstream than upstream of the reach of inflection. That is to say,

331

•fc b * H i

DISTANCE IN MIE,ES OOWN STREAM

332

Fig. 1.6.

Jflâjl .7 '.~^ycsûU-fc/cjïîl-iÇif—M.EilIf;—HO(tifHFTETSS" qF^;5 HJTi EJ ftOWJil'STBfAM'"^ ' . r "'."!" . r-:^f "r i- ~ -H ~-:d ! - - ^ ^ i - r ;

; 1 ^ ^ ^ l ^ t ^ -H' - [ 1,^-^^r! ; ; ;--.--:- ;-- i-:..- r:/ - ÊiîMZS -flu*' — ^- — - ^J-ofl ftim-

l -C . i s ^ a u „

B-1B ri ti d^H mm S 4 mm

C "i — ~ i - 2 mm

J

, E

I IlotC . orig.n oT *na<e i - * mites heiow Soirco-

1" \

* - ^

M 1+ '1

rt •

J "r*!*1!

,5V f\\ ' i tt

X ?\ * V \mWp'

' I f b ^

<***—+—"T" i ; * " i ^ ' M/ M ' c/ r

DISTANCE IN MILES DCWNSÎBE4M

Fig. 1.7.

333

in a separate of low durability index, trail sportational and other factors are about equally influential upon calibre and upon unweighted mean roundness below the reach where inflection occurs.

The downstream evolution of roundness in quartz, shale and coal is very similar to that in sandstone. The first three separates are not discussed here individually: the similarity is obvious from figures 1.4, 1.6, 1.7, and 1.8.

It can now be suggested that cleavages and cleats of coal and the fissility of shale partly determine the maximum mean roundness attainable. They affect the magnitude

a a io BPSTANCË IN M ! l £ S DOWN TEVJJ

Fig. 1.8.

334

of this maximum value more than they influence the rate at which it is approached during rounding; and, over the phase of declining roundness (fig. 1.2), the structure and durability index of a laminated and inherently weak separate, e.g., shale, work in the same direction.

4. Adverse Influence of Channel Erosion and Selective Sorting upon Evolution of Mean Roudnness Downstream

In a detailed study of pothole sediments and bed material, it was statistically proved that channel degradation and bank erosion lower the roundness of grades on the coarse side of the calibre of inflection. Selective sorting on the fine side of the calibre of inflection also lowers roundness. But in as far as they are reflected in the unweighted means of roundness of each separate, the flow and other characteristics of pools are not significantly different from those of riffles. Similarly, the affluents into the Hacking, because of their small size and because they drain sub-catchments of pétrographie identity to the Hacking's, effect little change in roundness of Hacking sediments at confluences.

B. ROUNDNESS DISPERSION, Vp

Time and space do not allow a detailed discussion here of evolution of roundness dispersion. Only a summary of findings in the Hacking is given.

1. Influence of Calibre, Mean Roundness and Distance, respectively, on Roundness Dispersion

Roundness dispersion is positively correlated with calibre down to the size where inflection occurs in the curve of dispersion versus calibre (fig. 1.9). But in size grades finer than the calibre of inflection the correlation is negative. There is only a remote chance, at less than the 0.001 level, that both the positive and negative correlations are not statistically significant. A correlation of percentual coefficients of variation of roundness with calibre showed very similar trends to figure 1.9(a), and were significant, at the 0.001 level or better.

Similarly, regressions of roundness dispersion upon mean roundness (fig. 1.9(b)) are significant, at least at the 0.01 level.

At this point reference may now be made to the complete theoretical scheme of evolution of roundness parameters in figure 1.10. The trend of mean roundness dispersion downstream is explained in the framework of the theory postulated in the conceptual scheme of figure 1.10. This scheme is subdivided into phases of evolution of physical parameters of roundness, including roundness dispersion. The working of the scheme will now be briefly explained, with reference to roundness dispersion.

Near the source of a river, bed material is largely angular. On the basis of roundness, the fragments and particles of a separate are grouped close to zero. The roundness frequency distribution is well sorted, i.e., values of roundness dispersion are low. As they are transported downstream, some particles and some fragments of a separate are rounded faster than others. Therefore, because of intralitho logical differences, and because only a little wear is necessary to round corners and edges to increase the round­ness of some particles significantly, the following occurrences are conceivable: particles in a given size grade, which have travelled the same distance in a river, may have signi­ficantly diffsrent degrees of roundness. The mean dispersion of roundness at a lower location is, therefore, greater than that upstream. Mean roundness dispersion is also increased by the supply of angular material freshly eroded from the channel and bank. After some distance downstream there is bound to occur a symmetrical roundness frequency distribution of particles in a size grade. At that location, theround-

335

V p F I © ;[ j.O>(a) CORRELATION OF VARIABILITY OF ROUhl ONE5S WITH C A U B R E

.D:'"OT. :i±i~L:h;:;xi'

HE

'x£ m 3-bii

IW-iic:

i . L j J

H-fr [ M-:-!-l h xprgi: _t:

m-1-r. *a

':-k n tïTfe

EISSÏ Jit TF

^

-ioS frx* 4 « '

m g

T.

S £f ^ r

& ; BSE r

:SSÏ ffiS=S

w+- a.. J+f :xt : S M

+ . 1* S •M

& if ±n € -I-1- — ^m^i

ni -/-

Hi­st IHfcflf

COj ÛCS D-10 MEAN ROUWENEÎS

336

Fig. 1.9(a) and 1.9(b).

*\ i°

«s

a o

.° J

; .-

<fl +

o o 1

ness dispersion in that grade reaches its maximum value— i.e., sorlring of roundness dis­t r ibut ions at its worst. This value of maximum dispersion marks the approximate end of Phase I and the start of Phase II (fig. 1.10). In Phase II the particles in any grade become increasingly better rounded than they are in Phase I. The poorly-roimded "tail" of the roundness frequency distribution shrinks, and roundness dispersion steadily decreases. The decrease continues until the mean roundness for all grades is close to unity or to the maximum value possible for the separate. At this point roundness frequency dis­tribution in a size grade is at its best sorted, i.e., roundness dispersion is at its lowest numerical value. This low-dispersion point marks the end of Phase II and the start of Phase Hi . Phase III represents a period, size grade, or distance, where there is an approximately constant roundness in a grade. Not all the grades of a separate develop in phase with respect to roundness parameters- But it is conceivable that unweighted means of roundness pass through evolutionary phases parallel to those of individual grades with respect to any physical parameters of roundness.

It was observed in a previous section that, as postulated in figure 1.5, unweighted mean roundness begins to deteriorate after Phase III. Consequently, for some time, within a certain size range, or over a certain distance, there is an increasing admixture of poorly- and well-rounded particles. The admixture raises the numerical value of roundness dispersion, because it causes an increasingly broad-based roundness fre­quency distribution of particles. Also (fig. 1.2), on the fine limb, the finer the calibre, the poorer the roundness. The finest material at a location near the mouth of a long river is uniformly poorly-rounded. Consequently, roundness dispersion is small, i.e., sorting is good.

Evolution of roundness dispersion is persistently discussed in terms of changes in mean roundness of a grade of the separate as a whole. The evolution of mean roundness has also been usually discussed hitherto mainly with respect to distance of transport. But calibre decreases downstream. The effect of size reduction on roundness dispersion is hereby implied.

To summarize: as calibre decreases exponentially from boulders and from blocks to fine mature sand, roundness dispersion evolves, regardless of lithology, along a rather complex curvilinear route, as shown in the scheme, figure 1.10. No comparisons are here made between observations on roundness dispersion in the Hacking River and findings in previous works, because no previous work on roundness dispersion has been located.

2. Influence of Dislance of Transporta I ion upon Mean Roundness Dispersion

From the preceding discussions and from the correlations of mean roundness dis­persion with calibre, influence of distance can be inferred. Also, it has already been stated that, because of cessation of the Narrabeen Group in the Hacking, Phases II, III, and IV are all crammed into a few hundred yards. Therefore, figures 1.11 and 1.12, understandably, support the theory just put forward.

If the theory of roundness evolution so far put forward is tenable, different litho-logical separates pass through any one phase at different reaches in a river. Furthermore, if the unweighted means of any roundness parameter in all separates in a sample are averaged into a grand mean, and if a grand mean is computed at all sampled locations in a river, then only Phases 1 and V (fig. 1.10) may be faintly discernible. No roundness parameter is likely to show a systematic evolution downstream, if only one average value is computed for all grades of all separates in the bed material at a location. And if the distance of a sample below the mountain course is estimated, together with the median diameter of the bed material from which the separate is sub-sampled, the phase of morphogenetic evolution of the separate sub-sample may be esti­mated.

338

, - ' • i ! i i • i i i . . i . i r . i . i i i i i s ii h i 1 £ | J S „ l i l t ^CO jBEI-j1" - i û " - ! l Fl. l . i ia.l-OE. VAS JL6 J. I t 1LQ1 - J K U l i I E t t l £ : 4 . U U X l - O L - t l WOEU) W N St B A S H . U - J I W - l -H 1CKIMS- .

y -I.,- T . r | . .-J_ . . . . . . . . . . r | _ .;„„.,. -....s.., - T . . r + T . Ï B <4-L-l ! ! _ ' . ! t jJJ • ' ! ! ! L _ I _ J „ . I - . . . . ' ' f | 1 . P i • ' ! • V > 1 . 0 , 1 | , . (J -, .<ju | 1 1 ' ; 1 ! 7 ^ ™ -T- p - I p : " I ,

' ' ' ! • ' i ' ' r : ' i ^ i

L :-i-4-J-| • „ ! - ) _ : . . ' ! : . : | | . ,! J J - rA.;. -loX! ._L^J_4_|_L_|_1_|„ J—s-,-i i . . ; . „ • „ , , a . ^4 . - i . . ... ;..;_.... ' i . . ? J.V L 1 — ; T i a — •: - J—r~ s • •• -i-™ r v - - - • " • ; • • ( -l ! • 1 . 1 - 7 , , • . . ? I l l .

; - . j iX) ! T ^

M * . 1 . . s H i - 1 ; 1. ^ . .

. , __ . ; . . J. j . 1 „„ . ' _ . i i .1 . . .

T~_~"" i " - i t T~ [.."^tn. " ^ i ^ - r : ^ =çi?l ^- - - •-•- - - -|- i j - i - - - - 1- -1- -

I I . 1 ! . . ! . . i 131 . : • ! W i I t U C M ' 1 - f -m i u , v j A — , | ' , , i ; ' i u i 1 . • , i T ioLi • J -

. . . i , i ft. Ll m > 1 I 1 I - u i - *•! r r-r~ , . . . . . . . . . . g .-[•, -). s j^^^^je 3_ ; J . - ; [ ; = •

• . ' . . , i . B J. ' ...iy .. 1J4J • - — • f T 1 . ! • , . . ; ! i.„UJ rt.'Jnr.oiOiiy'JIUVi^'n tJ > I l • ' ' • -'- - " • ' E » — ^ i • ! - "

1 - - . . _ - — . q 1 ,.' , . J i . . . . 1 "1 I 1 ' 1 ! i B . : * i • ' i 1 . 7,

, , ;. _ . à. J ;*.,. .:. .' ' . -L& . j . : . j . . . . . . . A . - - 1--n-U~4„ 1.U .XL . ; l - u . „ . .. j.t- J. L ......-»-\-l. • I-JX4 - -iâ-U-_ [ _ ) „ « . ^ . ^ . r „ , -g-t, . „ . „ l J. r T . . . . . - I - , J. l ^ l ^ - ^ ^ J . ^ i_ fe_l_l_

| - , t ; . ,. . .. .; • i - d - . - r . - - | - - -f-!-,.-! - ! - ] - " : " i - 1 - I . . - H - - -1 4-L. L >. .l_.„Ua—il i-u-- :•- . . . . . . ' . „ , I" . .

, „ , , 1 , ) . 1 i , • , .1 . -, ) I •- , B 1 I I !1 . . ' , . . . . , , I

- . . , , ! • 1 . . : I i i • , . i i . | . ' s ; i i . i

j • I . ! . , ! • 1 i : !

1 j - • 1 , j . 1 , ! 1 ; ' 1 : • • • i . i i i

i ^ ° t ! ^ IJ ' • ' , I j 4 ( _ - ' ' s_ , L. -|__L. s * i . ' . Î ^ — • ; - -s ., : H i ï >: 5 T . - i "

1 4_'..-.r - „_^. .. _ ^ J - ^ , - - ^ — L - -f f-^- i - - V ^ T - - ! - ! 'TV"" i " r: ,|M " -rT-^-r - -! 1 : • : ' I ! . . . i ' i ! , , 1 ' : : i i • ! . . i ' , . f . , 1 , ' = „ - . - • - . - , - . - U . - . l - j . - — J _ . r - , — - • . - — -| ! — . - - _ _ - L - , . - - T - , - . - ^ ^ - j . 1 -Z ' O O "• ' ' - — ™ — * — — — * - — - i - ^ — -r - r ".' ' t - t -^-! -" '"- ' -—*-f ^ J - r ' T " - - " — - j 1 -

! . • • 1 1 • • , ' ! , . ' i 1 . • "1 ^ S T " \ r- " '. r T l T T T T n 1 ' '

1 ; ' ' ' , , ; *• ' ' _ ^ ~ „ . ^ . ™ L _ J . * i , i , , ; , * 1 —<--• , . . . . i . . , . , ! 1 !

. i j _ . . .1 . . . • '~L_ . J . i - . ] > _ : i.p . 'X. X 4- . . . jZ- . - -

. - « . . ^ . . J . ' . x _ ^ l i . -kiJJ- 4 s-^- - 4 L „_ 13.S0 »^» - - —^-p*. - — ^ - - i - i - ^ r1 : - 1 . r r r " T ^ ^ ^ ^ ^ ^ ? - - ^ ^ M — ,-]-1 ' ' . 1 • • s H s

1 J ' . _, . . . b j i i ^ . . „ i . _ ^ s J . i__ | I • ( ] , : , ! 1 1 "tr- _ : ^ - l - • - . ; : . .. . >: r t : j x ; : i ; ; ; r ± ? " : . : : : :

1 ! , • i t i 3'ED * "" ' - '— I I ' I • - 1—I L ' 1 1 ' -^ h--»- - T T ^ - -7- - - T - 1 - — - —- - ] — - T ~

r - - 1 - - - • i—'- - ~ • - ^ - ' - - . ; - ! - ; ' 1-^- ^ r ^ - - - - | - ^ - 5 - 1 - ' " . ' 3 '

" X T • - --i - . [ - - - . .. -2 ' C . 'J i 5 ; - ! - U jï- - . L t [ 1 S 1 ! 1 . 1 1 ' iT f 7 1 r

±±±3S±I--:ïS S""-, "ff" ttX " i t' s'*a ' W >n T i - - ; : K ; 1 \" B

p i i . ± T ; x : : ~- - v - : w T T < i bi r i - j * 1

11 i •IJ.'-I I T) 1- U , W i s ...

ft v l ' i J 1 MM ^ 1 . .j.... j , h , ; . . . j . . _> 4 . . . . - * - - ï i • • « £

" ^ 1 J • H -

LP ^ " 1 >

(_.. X i , u LL U-uU J Lia LLLIO. L U U J J -X _ „ . p _ _ _. x . _ _IJ ^ ^ ^ x 5 -,1 M : « ii

YV J

p - ^ _ _ r. ^ - . - _ L ^ . ^—_ . . , | - . _ _ ^ ,.*_ _ . ^ . . . 2 - ? 0

i4

c - . - j „........... — S n n

j . U_ „ . . „ . 5-BO

d

- X ^- —- - . , ; „ __ . i_ . _ _ __ A. . ' 1 ; . _ ___ 3 S r> r t r r r T "Br ' ' r l T I + H ' H - H " "h fe • • -H "H4 : ; : : : . : : . . : . ± : : : : x C T I > 4 I

-f- -1- - r

Fig. 1.11.

C. ROUNDNESS SKEWNESS, Skp

In summary, roundness skewness, in contrast to mean roundness and roundness dispersion, is negatively correlated with calibre in the coarse limb, and positively in the fine limb (fig. 1.13), both significantly at the 0.001 level or better.

These correlations can be explained briefly. At all points where frequency distri­bution of roundness is symmetrical, roundness skewness is zero. These zero-positions of roundness skewness are A, B and C (fig. 1.10). With progress of morphogenesis beyond A, the negative "tail" passively grows; and numerical values of roundness skewness increase until a distance is covered, or a size distribution is attained, where a balance exists between the population of poorly - and well-rounded particles. This is a turning point. Beyond that distance, or finer than the median diameter of that size dis­tribution, roundness frequency distributions show a shrinking "tail". Values of round­ness skewness, although still negative, progressively tend toward the zero-line and

339

• IÔ ' 1? jc^f

[03 vp

: 1 .- ' - - i - \ : ; - : ! ; < - - ' - L > - 1 - • - -, • 1 ? - '-'. < - • - ' - . - • • . - - -• ^ - , - ? - - ; - < .

a;

U.f

•Ht M-

i l

H " ;

'in ïh

• 1 . ;

!r;l:iii

M-:iVi'

! H J • !4T| f ;

-u;n.n

, . I ; i* -

1":

•L^i*4Aî±i/:

.. 1 ;

«s ; là U

- I (• ; - f , - I •

ffojivfij-i'i'WJ

>v if i-ji ;5pe7 ;.

-, :T. ' • ! \ ! :

4Â-

" T T '&:. ^t

. I ' m :

u.'; ."p-^J^nj^^iiriiTTp'jpJi.iS TççrT ijrc

U

,'.^f!(:S*.jlftf

: d - ,

yfOIT i ' ïdUi t i 1

:.qiq. î-ï I 'I • \

' I M

I—

!"H-

! | r-

-i ; )• .

s-»

!_;.!•: 051

ii-B

tël "L;"G:

iff; •H-r • r

r; , . T

- • • - M

5Lbd \?

±1; H ; h ;}•$_;

Fig. 1.12.

T?75.

positive values. When a high degree of mean roundness is attained, the roundness distri­bution is once again symmetrical, and B is fixed. It is only sufficient here to note that the curveof skewness evolutiondoes not go above thezero-lineatif. This is so, because as soon as roundness begins to fall below the maximum value, the negative "tail" again starts to grow. The "tail", as it were, retraces its previous course. When the C-point of symmetry is reached, the poorly-rounded particles are just on the verge of outnumbering the well-rounded ones. The positive "tail" is jusf about to start growing. Immediately beyond C, the values of roundness skewness are positive. Roundness skewness increases numeri­cally and approaches 1.0 asymptotically.

Figure 1.14 shows that roundness skewness decreases as mean roundness improves, at the O.OJ level or better. The conceptual scheme (fig. 1,10) explains why. Except between the A-B and B~C troughs, the sense of evolution of roundness skewness is opposite that of evolution of mean roundness. In the Hacking the A-B-C portion of the curve (fig. 1.10) is highly compressed. Consequently, the regression lines in figure 1.14 are ail negative. In a negative correlation of roundness skewness with mean roundness, if roundness skewness declines as mean roundness rises, the maximum value of mean roundness is yet to be attained; and comminution is stili more influential than selective sorting. But if, in this negative correlation, roundness skewness becomes increasingly positive as mean roundness falls, the maximum mean roundness is already attained, and selective sorting is predominant over comminution.

340

•ja:i - is

•O'J t-;-r

m :;s

p:x: tt

I a *£

sfccfï-

;=G:"

4 ; ^

3 *

*&g • < * * . ; s

i ?

tlœ

*£? m m m

** î j l t t

3* fEi-

is; W

PS

e i_i

^

X S ,

*KT

re H-J-i-U,-!

Fig. 1.13.

;3ût s u t

it'#

•^! |ss:^àTi7 ïsrtiriâaéif s s i s i f e j s

H IIJ^JÔ

S3" tt

tp=t tO-6

~T

"F

+ r ci: d Ssttf

ta 5 E

1 u ^ .

:Lhi:r ïS£

• t e

ifeié.

. j .

Î&SW SI; i± -a

£ts-£f

ï£p~-...i-&-

±-m ru il • - 4 . ^ . :

^^4q_n:

iT i - f

..'. J""|"hT-tl -

iff r-H-Lrl

- f i - > !" ! u • —I

B"±Tt: U T

P

Fig. 1.14.

341

&' :ïs-"BV5ct*rMj4-6f-ïbu s*fel*Ste£s!- •nitH- jiCV:

tli 'n rFlt1

NNCB . , .., , .LIJ.1.1- ; - I j - , , .

:! ixL-;:! slii^?i

\An IfTjT h-i H

' 3 f

i i^ i t Ufcf- L>Ct

S

•JSEJ-

I H - H «

-i-tr

^"|-;-H

saj^3i5Ïbna

ÎKP

M

*4% zS

- , r | . . J . . . . . . . . _

! J - '(» --' I ;

- i - -SJWP

" ' ! ;

r t l ...•.

-:L-H-

% i - -1

h

$

f.j--

r-v-M=:

i

SM T ^ S S K T

to

*k R?F

xifc

3& œ

! - - - Î - I -J.Î. -;.|.-

•a

i*hti

-l-^-J-i-i-Ï-^— U É^^vj.ri-i

_±1ï r H ma.

Fie. L i s .

10 12 DISTANCE fH MILES OOWN STREAM

Fig. 1.16.

342

Previous sections may be consulted for downstream evolution of roundness skewn-ness. The correlations in figures 1.15 and 1.16 are explicable in the framework of figure 1.10. It is inferred that, as long as roundness increases downstream, roundness skewness tends toward negative values. Secondly, except in a portion of Phase IV, after the maximum mean roundness is attained, roundness skewness tends toward positive values. But in the middle and lower courses of a long sandy river, e.g., the Mississippi, mean roundness invariably declines downstream; and the maximum mean roundness is attained above the middle course. In all sandy rivers, roundness skewness tends increasingly toward -I-1.0 in the downstream direction.

D. SUMMARY AND CONCLUSIONS ON EVOLUTION OF ROUNDNESS

(a) Roundness increases as calibre decreases. But in sub-granule grades, roundness declines as size decreases.

(6) Most important is the observation that unweighted mean roundness does not approach 1.0 asymptotically downstream. Rather, it first increases to a maximum, and then declines in the downstream direction.

<c) Also, roundness evolves downstream at a medium rate in grades coarser than cobbles, fastest in cobble-granule range, and slowest in the sub-granule grades.

(d) Furthermore, mean roundness evolves downstream faster than calibre decreases, and calibre declines downstream faster than sphericity evolves.

(e) Pétrographie uniformity of the Hacking River catchment and the small size of tributaries are partly responsible for lack of change in roundness at confluences.

(f) Roundness dispersion and roundness skewness also evolve downstream along wave-like curves.

(g) In iong sandy rivers, roundness decreases downstream, and the distance below the river source is already passed at which the maximum unweighted mean roundness is attained.

(li) Hence, long sandy rivers exhibit positive skewness, which approaches + 1 . 0 asymptotically in the downstream direction.

A SELECT BIBLIOGRAPHY

GROCAN, R.H. , 1945. Shape variations in some Lake Superior beach pebbles. Journ. Sed. Petrol 15, 3-10.

KRUMBECN, W.C. and PETTIJOHN, F.J., 1938. Manual of sedimentary petrography, New York, Appleton-Century-Crofts, Inc.

KRUMBEIN, W . C , 1942. Flood deposits of Arroyo Seco, Los Angeles County, California. Bull. Geo!. Soc. Amer., 53, 1355-1402.

LAMAR, J.E., 1927. Geology and economic resources of the St. Peter Sandstone of Illinois. ///. Geol. Survey, 53, 148-151.

MACCARTHY, G.R., 1933. The rounding of beach sands. Amer. Journ. Sci., 25,205-224. OUMA, J .P.B.M., 1966. The Hacking River sediments: calibre and morphogenesis.

Unpublished Ph.D. Thesis, Univ. of Sydney. PETTIJOHN, F.J. and LUNDAHL, A.C. , 1943, Shape and roundness of Lake Erie beach

sands. Journ. Sed. Petrol., 13, 69-78. PETTIJOHN, F. J., 1957. Sedimentary rocks. New York, Harper & Bros. PLUMLEY, W.J., 1948. Black Hiils terrace gravels: a study in sediment transport. Journ.

Ceo!., 56, 526-577. RUSSELL, R .D . and TAYLOR, R.E., 1937. Roundness and shape of Mississippi River

sands. Journ. Geol., 45, 225-267. TWENHOFEL, W. H., 1961. Treatise on sedimentation. New York, Dover Publications, Inc. WADBLL, H., 1934. Shape determination of large sedimental rock-fragments. Pan-

Amer. Geologist, 61, 187-220. WADELL, H., 1935. Volume, shape and roundness of quartz particles. Journ. Geol.,

43, 43, 250-280. WENTWORTH, C.K., 1919. A laboratory and field study of cobble abrasion—a prelimi­

nary report. Journ. Geo!., 27, 507-521.

343

DISCUSSION

Intervention of J. ZELLER

Question: What are the mineralogical and petrographical properties of the grains studied ? And especially what is the size of the single minerals ?

Answer: The mineralogical and petro graphical properties of the particles are very significant. Any study of roundness morphogenesis (or sphericity morphogenesis, which has been reported elsewhere) which takes no account of Hthology is, at best, useless. For instance the S.G. of the lithological separates investigated in the Gacking River (sandstone, quartz, shale and coal) was found to be significantly a co-determinant of the particular size grade where inflection takes place. Coal had the largest size, and shale the smallest,

Intervention of Mr. J. M. KENNEDY

Question: Is not the velocity of river How very important in considering the critical size of granules ? That is a shift in the critical inflection point should occur as a function of river velocity.

Answer: Yes, velocity is important. And ! believe that velocity, and, so, the turbu­lence, as well as S.G. and other lithological... properties are significant influences on the inflection size grade. That is why that inflection takes place over a size range - 1 . 5 0 to - 2 , 5 0 .

Intervention of Mr. J. BURZ

Questions

1. Which range of size in include your investigations ?

2. Have you any explication for the change of roundness in function of decreasing of grain size ?

3. Which is the critical size for the changing of roundness ?

Answers

1. I studied sizes ranging from blocks and boulders (over 1056 mm) to fine sand (less than 0,5 mm),

2. Yes, if roundness is result of comminution, the smaller the particle, the longer it has been rounded and, so, the higher the roundness. But once saltation replaces traction, the flatter, less rounded particles travel faster downstream than the better-rounded ones. Also saltation encourages chipping and, so reduction in roundness. When roundness decreases with decreasing size, i.e. at sizes less than —1.5 0 , saltation has replaced traction,

3. The critical size range is —2.5 0 to —1.5 0 or about 4 mm— I mm.

344