HYDRAULICS BRANCH OFFICIAL FILE COPY

EROSION OF COHESIVE SEDIMENTS

A report prepared by the

BUREAU OF RECLAMATION HYDRAULIC LABORATORY

OFFICE FILE COPY

WHEN BORROWED RETURN PROMPTLY

Task Committee on Erosion of Cohesive Materials Committee on Sedimentation

June, 1967

American Society of Civil Engineers

Frank D. Masch, Chairman Ernest T. Smerdon Phil "F" Enger

..

TABLE OF CONTENTS

Introduction .

Laboratory Research on Eros ion Resistance

Field Observations in Natural Channels .

Sediment Load . Shapes of Natural Channels Effects of Structures . Climate and Temperature Effects Predicting Erosion or Deposition

Design of Non-Eroding Channels

Observations and Tests . Design Information Available

Problems of Agricultural Lands and Channels

Land Erosion . Erosion Loss Equation Soil Erodibility .

Scour in Agricultural Changes . Design of Farm Drain Ditches and Terrace Design of Farm Irrigation Systems

Conclusions and Needed Research .

Bibliography .

1

2

5

20

20 24 28 30

. 32

.35

35 .37

.47

. 48 49 .53

. 54 Channels . 55

. 56

. 60

.64

\,

INTRODUCTION

The Task Committee on Erosion of Cohesive Materials was

forrrted by the Sedimentation Committee of the Hydraulics Divis ion

of ASCE to review the literature and to establish what has been done

and what the research needs are relative to:

a. the fundamental understanding of principles and pro­cesses of erosion of cohesive sediments, and

b. the planning, design, construction and maintenance of channels in cohesive materials.

The need to define the fundamental principles involved in the

erosion process and to develop criteria and guides applicable to

field problems is indeed great. This has been clearly demonstrated

by the numerous river, irrigation and drainage, and channel stability

problems encountered when dealing with soils displaying varying

degrees of cohesiveness.

From an abstracted bibliography prepared by the Task

* Committee [ 1] , sever al trends of res ear ch on cohesive sediments

can be noted. Most of the work on cohesive sediments has been

carried on by hydraulic engineers, agricultural engineers and soil

scientists. In general, research by each of these groups has been

directed toward solutions of the problems most often encountered

'~ Numbers in brackets correspond to similarly numbered entries

in the bibliography, pages 64- 70.

2

..

'f

by the particular group. For example, hydraulic research efforts have

been directed toward determination of tractive force , channel stability

criteria and othe r da t a relate d t o c hanne l d e sign. Many of these

studies have involved either field observations, flume tests, or shear

tests in specially designe d apparatus. Usually , some measure of

resistance to eros i on or rate of e rosion has be e n r e lated to mechani -

cal properties of the cohes iv e sediment s , such as vane shear strength,

compressive strength, Atterburg limits , <l i spers ion ratio , etc.

Agricultural e ngineers have been more c oncerned with ero ­

sion control in irrigation channels and furrows and with ra indrop

erosion. In the agricultural discipline , rates of erosion hav e been

related to furrow size and slope , time of irrigation, extent of vege -

tation and soil type. Research by soil scientists has proceeded

along lines in whif h special study has been given to the chemical,

mineralogical , a n d physical properties of the soil.

Estuarine sedimentation is another area in which eng ineers

are concerned with cohesive sediment s. In estuaries , sediment

particles are mostly in the fine silt and clay - size range. In estuaries ,

however, the sed iment problem is fu r ther complicated by the unsteady

nature of the fl ow and by flo c culation problems caused by reactions

between sea wate r a n d claye y s e diments. The problems of e stuarine

3

sedimentation were beyond the scope of the activities of this Task

Committee, and are not discussed in this report.

Even from a cursory glance through the literature on cohesive

sediments, one is struck immediately with the interdisciplinary nature

of the erosion problem. As contrasted to noncohesive sediments in

which the weight and size of the particles are the principle sediment

factors controlling erosion, the resistance of c ohesive sediments to

erosion is related to the electrochemical bond between individual

particles. Thi s bond in turn depends on the ionic charge on the parti­

cles, the presence of electrolytes, the mineralogy, temperature, pH,

ion exchange and absorption. These factors are usually not thought

of in the realm of Civil Engineering, but rather are left to the soil

chemists, mineralogists, and physicists. Still from an engineering

standpoint, it is desirable to have simple and readily measurable

properties to characterize the erosion resistance of cohesive sediments.

When considering the erosion of cohesive sediments, exclusive

of the estuarine problem, four broad catagories of study are particu­

larly significant. These are:

1. laboratory research on erosion resistance.

2. field observat ions in natural channels.

3. design of non-eroding channels.

4. problems of agr icultural land and channels.

4

The following sections of this report are concerned primari­

ly with each of these catagories, Much of the literature currently

available is reviewed briefly and recommendations are mad e for

practical application and for further res ear ch.

LABORATORY RESEARCH ON EROSION RESISTANCE

Much of the resear c h undertaken in the laboratory has been

directed toward determining relationships between a critical boundary

shear stress or a tractive force above which scour of a cohesive

material begins and pertinent soil prope rties and flow conditions.

Studies in specially designed apparatus and laboratory flumes have

attempted to define the mechanical soil properties which best charac-

terize the erosion resistance of var ious cohesive soils.

When concerned with stable c hannel design or localized scour

in beds of cohesive sediments, either a c r itical tractive forc e or a

safe permissible velocity is selected so that no undesirable erosion

occurs. These methods involve choosing the hydraulic variables

such that certain critical tractive forces or velocities are not ex-

ceeded. While it is generally understood that the scour resistance

of a cohesive sediment will depend in some fashion on the properties

5

of the sediment, the complete significance of such parameters as

density, moisture content, percent clay, vane shear strength, etc.

is not fully known at this time.

In work on the Klaralve'n, Sundborg [2] proposed that the

force resisting entrainment was proportional to the shear strength

of the sediment. In a similar manner , Dunn [3] related critical

tractive force at which erosion of a cohesive sediment was con-

sidered to have started to the vane shear strength of the soil. Dunn

tested samples of cohesive soils taken from channels in Colorado,

N ebraska and Wyoming. He subjected the samples to the erosive

action of a submerged jet and measured the magnitude of the boundary

shear stress causing scour by replacing the soil sample with a

shear plate coated with soil particles. Dunn's equation for the criti­

cal tractive fo:itce, Tc' is given by

Tc ::: 0. 02 + Sv tan 8

1000

+ O. 18 tan 8

in which S'V is the vane shear strength and 8 is the inclination with

the horizontal of the linear relation between critical tractive force

and vane strength. Dunn then relates 8 to the percent of soil finer

than O. 06 mm, plasticity index, and to various statistical repre­

sentations of the particle size distribution.

6

(1)

To help develop design criteria for unlined reaches of irri­

gation canals, Carlson and Enger [ 4] performed field and laboratory

studies with various cohesive soils. Critical t ractive forces were

obtained from a test in which the soil samples were set into a well

flush with the bottom of a circular tank and water circulated over

the sample with a rotating impeller. Among the various properties

measured were liquid limit, plasticity index, soil density, percent

of maximum Proctor density, shrinkage limits, soil gradation, and

vane shear strength values. Several correlations between the vari­

ables were obtained and recommendations for general use were

made for soils displaying properties similar to those tested. Ex­

amples were also presented illustrating the use of the results in the

design of unlined canals in cohesive soils.

Enger [5] also reports on studies made in a boundary shear

flume. In these studies samples of cohesive sediments were tested

by gradually increasing the boundary shear stress acting on a sample

until the shear became critical and the sample began to erode. For

the soils tested, the boundary shear required to produce erosion was

found to be a function of the moisture content at which the soil was

compacted.

Moore and Mas ch [ 6] made a series of tests using a vertical

7

submerged jet to determine the relative scour resistance of various

kinds of sediments. In these tests , the c haracteristi cs of the scour

surface were observed on remolded and natural sediments , and the

rates of scour were measured by the weight loss from the sample.

Results from these tests indicated that the mean depth of erosion

was proportional to the logarithm of the t ime -dur ing which scour

occurred. This is a result similar to that found in experiments on

noncohesive sediments.

A number of flume tests also have been performed to deter -

mine the relationship between critical tractive force and various

soil properties . Among the most notable are those by Smerdon and

Beasley [7] and more recently by Abdel-Rahman [8]. In the Smerdon

and Beasley studies, data from hydraulic and physical tests on soils

were analyzed statistically to determine the apparent correlation

between critical tractive force and pertinent soil properties. For

the soils tested, the critical tractive for c es computed from the

energy slope and channel properti es were found to correlate with

plasticity index, dispersion ratio , mean particle size and percent

clay. These correlations are illustrated in Figures 1 through 4.

For the soils te ,sted, the critical tractive forces, Tc ' were found to

be best correlated with plasticity index and dispersion ratio , the

8

N --........ en

.D

Q)

0 ... 0 LL

a:, > -0 0 ... t-

0.100

0.050

0.020

0 u 0.010 +­... (.)

0.005

~

3 5

9

/, ·-

/1 ~ I )

0 V o7

0/

vo 0

V

T = 0.0034(PI) 0.8 4 C

10 20 ~ 0 100 2 00

Plasticity Index

FIG. I CRITICAL TRACTIVE FORCE DETERMINED .FROM ENERGY SLOPE VS. PLASTICITY INDEX. (ofter Smerdon and Beoseley [ 7J)

0.100

N --........ en ~ 0.050

-0 C ... t-

0.020

8 0.010 -... u

0.005 3

~ ......

"'

5

~D Tc= 0.213(Dr)-0·63

I~ ~o

0~ ~

~

"""' ~ "

10 20 50 100 200

Dispersion Ratio

FIG. 2 CRITICAL TRACTIVE FORCE DETERMINED FROM ENERGY SLOPE VS.

DISPERSION RATIO. (after Smerdon and Beoseley [7])

(\J ..... -' II)

..Q

~

Cl) (.) ... Q ~

Cl)

> -(.) IC ... t-

0.100

0.050

0 .020

~ 0.010 -... u

0.005 3 5

10

~,

0 /i / )

0

o/o V

0 /o ~/ D 0

/0 'c = 0.0022(Pl)O.S2

10 20 50 100 200

Plasticity Index

FIG . 3 CRITICAL TRACTIVE FORCE DETERMINED FROM VELOCITY PROFILE VS. PLASTICITY INDEX. (after Smerdon and Beaseley [7J)

0.10 n

C\I --' II)

..Q 0.05 Q)

0 ... 0

0 Tc= O.IIO(Drf

0·57

-"""Ii

~ ') C

LL

Q),

> 0.02 -0

IC ... ~

IC 0.01 0 -...

0 ~o 0

0 "' "' 00

0 ' ~ u

0.00 I:;

3 5 10 20 50 ICO 2 00

Dispersion Ratio

FIG. 4 CRITICAL TRACTIVE FORCE DETERMINED FROM VELOCITY PROFILE VS. DISPERSION RATIO. ( after Smerdon and Beaseley C 7J)

'

relations being given by:

O. 0034 { PI) O. 84 ( 2)

and

O. 213 ( Dr ) -O. 63 ( 3)

Calculating the tractive fo ·rce fr om the velocity profile , the relations

are :

Tc = o. 0022 { PI) o. 8 2 ( 4)

and

( 5)

in which PI is the Plasticity Index and Dr is the dispersion ratio.

Smerdon and Beasley consider equations (2) and (3) more reliable

than equations (4) and (5) because of a ccuracy of measurements.

A less significant correlation was also found to exist between criti­

cal tractive force and the phi mean particle size •

. Abdel-Rahman [8] made laboratory flume measurements of

the soil properties of clay beds , the velocity distribution, the erosion

depth as a function of time and the suspended load in the water.

Based on his test , an equilibrium state or termination of erosion was

11

found to occur. Empirical equations were determined for beds of

Opalinuston clay that g ive information on the mean depth of erosion,

tm'.at ste ady state cond i tions a n d on the be d roughn e ss , Em· The s e

equations ar e:

and

:::: 0 . 83 X 10 - 4 + 2. 90 X 10 - 6

in which R is the hydraulic radius; Se the energy slope ; pa pressure

dependent on viscosity of flow and mineralogy of the soil; Sv the vane

shear strength of the bed material after the flow of water; p ithe densi­

ty of water ; Yw the specific weight of water ; u* the friction velocity;

II

y s the submerged volume w e ight of the bed mate rial ; S0

the bed

slope ; µ the visco sity; and b1

is a constant. Abdel - Rahman 1 s tests

on mean erosion depth versus t ime show s imilar characteristics to

those determined b y Moore and Mas c h [6) in tests with the submerg e d

jet. Flume test w i th salt wa te r and e stuar ine s e d iments have also

12

(6)

(7)

been reported by Partheniades [9] who, contrary to the work of others,

reports that shear strength is not a factor in determining the resistance

of cohesive sediments.

It is not entirely clear whether tractive force measurements

made on soil samples set into a section of a smooth-bottom flume or

tank are totally representative of the boundary shear stress which

could cause erosion of a cohesive bed. As the flow over the bottom

suddenly encounters the soil sample , there is abrupt change in the

bed roughness which in turn can affect the velocity distribution. This

is particularly true when the surface of the soil sample is eroding.

Under these conditions, the average tractive force is not uniformly

distributed over the sample , and determinations of critical tractive

force from average channel and flow properties are not necessarily

representative of the boundary shear on the sample.

If the relationships between critical tractive force and vari­

ous properties of cohesive soils are to be investigated, there is a

necessity to measure a mean shear stress or tractive force that is

nearly constant over the entire surface of the sample tested. With

this in mind, Moore and Masch [6] developed a small rotating cylin­

der apparatu.s , Figure 5, which is useful in determining factors that

control the erosion resistance of cohesive sediments. In this appa -

13

14

Torsion Rod

Fluid

Upper End Piece

Soil Sample

----- Rotating Transparent Cylinder

Supporting Torque Tube

Lower End Piece

1-4------ Variable Speed Drive

.FIG. 5 DIAGRAM OF MODIFIED ROTATING CYLINDER TEST APPARATUS. (after Moore and Masc~ C6J)

ratus, a cylindrical sample of cohesive soil is placed concentrically

into another cylindrical container. Water fills the annular space

betwe en the sample and the outer cylinder. The outer cylinde r is

then rotated at a uniform speed and the torque transmitted to the

soil sample is measured to determine the shear stress on the s u r-

face of the sample. The quantity of erosion may also b e determined

in the apparatus by weighing the sample at fixed intervals of time.

Detail studies on the apparatus and its use have been reported by

Espey [ 10 ], R ektorik and Smerdon [ 11 ], and by Mas ch, Espey, and

Moore [12]. Figure 6 illustrates relations between vane shear

strength and critical tractive force as measured by the rotating

cylinder apparatus for several different clay materials, some pro­

perties of which are tabulated in Table 1. Because of the inter­

relation ship between various physical soil properties, tests were

run also to determine the affect of moisture content on critical

tractive force. Results from the Espey and Rekto r ik and Smerdon

tests are shown in F igure 7. With the exception of the San Saba

Clay, these data all illustrate the same general trends with the

critical tractive force decreasing with increasing m oi s ture content,

as also reported by Enger, and increasing with increasing vane

shear strength. Data obtained for San Saba clay displayed a great

15

S oil Name and Number

Texture

Liqui d L im it

Plastic Limit

Plasticity Index

Percent Clay

Mean Particle S i ze, mm

TABLE 1. PHYSICAL PROPERTI ES OF SOME CLAY- TYPE SEDIMENTS (after ESPEY [ 10] AND REKTORIK AND SMERDON [11])

Lake Char le s Lufkin Houston Houston Hous ton K319 K116 K177 K177A K1 77 B

Clay o r Clay or Clay or Clay or Clay or S ilty Clay C lay Loam Silty Clay Silty Clay Silty Clay

56. 4 4 9. 4 43.7 44. 7 48 . 7

22. 0 15. 9 20. 5 17 0 7 18.0

34.4 33. 5 23. 2 27.0 30. 7

46. 2 40. 3 55. 5 55. 5 55. 5

0 . 0019 0 . 0084 0.0033 0 . 0033 0.0033

San Taylor Saba Marl

Silty Clay

47.7 47

22.0 21

25. 7 26

44. 7 50

0.0020 0.0048

17

100 ..... ---------------------------------,

600

500 ~ot\ ~\O(

N ~o --' (/)

~

~

..c 400 -g' .. ~ -en ~

C

~ Q)

300 ..c en I\.. - ~ Q) ,le' C

I ~ C >

200

,.... t:: ~

100

San Saba

0 2 3 4

Critical Shear Stress, lbs/ft2

FIG. 6 VANE SHEAR STRENGTH VS. CRITICAL SHEAR STRESS.

60

~ ',gc,

0 '?cs I c,~ -- ~ .,,

55 • I-... Cl) -.... <( -- 5 C • -C 0

(.)

• ... ::::, - 45 .,, 0 ~

40

2.0 3.0

Critical Shear Stress, lbs/ft2

FIG. 7 CRITICAL SHEAR STRESS VS. MOISTURE CONTENT.

amount of s catter and w hen fitted with a least squares regression, the

resulting relation showed an opposite trend to those found for the other

soils, No explanation has been offered for the reverse behavior of this

particular so i l.

Mar tin [13 ] , Griss inger [ 14], and others have repor ted on the

effects of chemical and physical properties on erosion resistance.

Ma rtin discuss es the effect of clay type and electrolyte on compress ive

s t rength a nd notes that a change in k inemati c v i scosity results as clay

ma terial goes into s us pension during eros ion and tha t this in turn i s a

fa ctor which may affect the tra c t ive fo rce. Data are presented by

Gris singe:t; _ and Asmussen [ 15 J on the effects o f the quantity o f water .··,I'

within the ,soil and the length of time the soi l sample has been at a

given wate.r content before testing. The results show tha t the rate

of erosion .decreases with wet age at the time o f he test, b ut increases

w ith the time after erosion beg ins. Bergt_ager and Ladd [16) conclude

that previous investigator s had not adeq ua tely controlled the engi-

neering pr operties of the clays be ing eroded and tha t relative soil

properties were not measured. They discus s drawbacks regardin g

the concept of the c r itical tractive for c e and stress the importance of

clay fabr ic a n d inner particle forces.

19

FIELD OBS ERV A TIO NS IN NATURAL CHANNELS

Generally, e rosion or depos iHon o c curring in a natural water

channel depends on the local f o r c es exe r t ed by the flowing water, the

geology a n d properties o f the mate:dal over which the water flows , and

on the sediment l oad being transpor ted. Seasonal changes may occur,

and lo c al s cour o r depos i tion may res ult d u e to man - made o r natural

structures.

Sediment Load

The impo rtanc e of sed iment l oa d in influencin g the c haracter­

istics of natural streams has been re c ogni zed by most researchers.

Cons i derable stu dy has b een conduc t e d to establ i sh sed iment erodibility

and predict sediment loads. Anders on [ 17 , 18] obtaine d da ta from 14

watersheds on the west s i de of the C oas t Ran ge in S outhe r n California.

From regress ion a n aly s i s he found tha t the sed iment y ields of water ­

sheds depend on the wat ershed c h a racte r i s tic s , lan d u s e a n d c ondition,

and the nature of storms and streamflow. Results o f A n derson's

analysis were pr e sen ted b y fiv e equ a tio:ns , which are summarized in

Table 2. Correlati on co effici e n ts f o r th ese equ ati on s v ary from

about O. 85 to O. 89.

20

TABLE 2

EQUATIONS RELATING PHYSI CAL CHARACTERIS TICS OF SOI L AND COVER DENSIT Y TO EROSI ON

{after ANDERSON [ 17 ])

Equation

Log Eg == 3. 07 3 - 2. 430 log C + 3. 427 log Dr

Log Eg = 4. 786 - 2. 486 log C + 2. 47 3 log ER

Log E 8 = 11. 461 - 2. 524 iog C + 2. 189 log S - 3. 288 log ( s i + cl ) .

Log Eg = 2. 1 27 - 2. 341 log C + 3. 861 log Dr + 1. 3 53 log Coll

ME

Log Es :: 10. 279 - L 78 8 l og C + 1. 151 log S - 3 . 164 l o g C o ll

C o rrelation c oefficient

. 888

. 878

. 849

• 890

. 854

ln Table 2 , Eg i s t he a v erage suspended sediment c ontent o f stream flow

in ppm; C, the average cover d ensity on wa tershed in per cent; Dr , the

d i spers i on ratio; ER, th e e r o s ion ratio; S , the s u spens ion; ( s i + cl}, the

u ltimate silt plus cla y; C oll , the c olloid , a n d ME, the m o i sture equivalent.

Z e rni al and Laur s en [ 19 ] u sed an e mpirical for m ula to p re d ict

the sed im ent load from five western str eams for compar ison w i th field

m easurement data collected fr om the streams by the U. S. G eologic al

Survey. The f o rmula u s ed for the pr ediction was:

21

7/6

( I

T Q

T C

. in which c is the mean sed iment concent r ation, in percentage by weight;

Pa is the fraction of the bed ma te r ial having a mean particle s ize d in

I

feet ; y O is the d e pth of fl ow in feet. TO

des cribe s that part of the total

tractive force asso ciated w ith the sediment particle s ; T refers t o the C

c ritical tractive fo rce , in pounds p er square foot , a n d i s evaluated for

each fraction , Pd• as equal to 4 d; TO

i s the tractive force acting on the

bed , i n pounds per s quare foot , a n d i s evaluated as equal to Yw y 0 S

where Sis taken as the s lop e of the water s u rface ass u m ing uniform

flow; Y w is the spe cifi c we ight of wate r ; p i s the density of water ; and

w denotes the fa ll v eloci ty, in feet per second of a quar tz s phe re of

d iame ter d.

Some of the pr edic ted and meas u red values were in good ag ree-

ment, in Figu re 8 , b u t several c ases ind icated s o m e va riation, F igure

9. The var iability o f the load - dis charge c ha r a cteristic s was assessed ,

and the effects of cha nges in channel instab ility, temperature a n d bed -

mater ial fo r the five s tr earns were pr e s ented. Table s 3, 4 and 5

22

(8)

... Cl C

LL

GI C'I

" -C Cl u ... Cl a..

100

80

J

I 60

40

30 -10

d(min v-., - ,/

~ ~ t:,,,

V V d(min / ,, /

I / V ~! I I I

/ / if d(max) id(max)

I I ~ . I

I I J I -- -Measured Ii' I --Predicted

I

I (a) Section C2 ( b) Se c t ion C I I I

I -10 Mean Particle Diameter, mm

FIG. 8. PREDICTED AND MEASURED COMPOSITION OF SUSPENDED LOAD ON MIDDLE LOUP RIVER. (after Zernial and LaursenCl9J)

100 d(mln) ~~ d(m~ r ., -

/. ....

/

I/ ,1 ;,,. /

~

) ff d(max} I I ,

'/ d(max)

... 80 Cl C

iZ

/ ~ t/ Cl Cl

" 60 - ---Measured C ., ' -Predicted u ...

I Cl Q.

40 (a) Sho1hon i { b) Riverton

I I I

-10 -10 30

Mean Particle Diameter, mm

FIG. 9. PREDICTED AND MEASURED COMPOSITION OF SUSPENDED LOAD ON FIVEMILE CREEK. ( after Zernial and Laursen Cl9J)

23

s h ow these effects. It was concluded that the sediment load is a unique

function of the flow, fluid, and bed material characteristics and that

the watershed and stream characte r istics can be used to evaluate the

sediment yield.

Shapes of Natural Channels

Schumm [20, 21, 22] collected data at over 40 cross sections

located near Geological Survey gag ing stati ons throughout the Western

United States. The channel s were considered stable and info rmation

collected included: channel width (b), maximum channel depth (y}, mean

annual dis charge (Q), mean annual flood or the total dis charge with a /

recurrenc-e interval of 2. 33 years (Qb), and percent silt-clay in the

bed (Sc) and the banks (Sb). Fro m thi s information, a width - depth ratio

(F) and the' percent silt-clay in the per imeter of the channel (M) was

calculated. M was calculated as:

M = (Sc) (b) + (Sb) (2y)

b + 2y

{9)

Streams from which the data were collected varied in width-

depth ratio from about 2. 5 to '138, in per cent per imeter silt-clay

from about 1. 4 to 89 , and in m ean annual dis charge from about 5. 8

to 5,200 cfs.

24

TABLE 3. EFFECTS OF CHANNEL INSTABILITY

(after ZERNIAL AND LAURSEN [9 ]) I

I Approximate effects on Os, in percentage

-

( ) 7/6 I (VT: Change d -2.lL Loca t ion - 1 £

in Yo Yo C

I Middle Loup,

+10 -1 0 -25 +12 Section C

Middle Loup, +24

Section c 2 -22 -55 +22

Fivemile-+55 -40 -70 +55

Shoshoni

Fivemile-Riverton

+27 -24 -55 +29

Rio Grande-+20

Bernalillo -19 -34 +21

PJ Total

effects

-23

- 57

- 7 2

-56

-35

.-

N lJ1

'

I I I

TABLE 4. EFFECTS OF TEMPERATURE CHANGES

(after ZERNIAL AND LAURSEN [9 ])

Change in percentage

f ( Location

Change in Change -) To/ e temperature in w w

M i ddle Loup, - 54 -42 +236

Section C

Middle Loup, Section c 2

-54 -38 +190

Fivemile--59

-43a +230 Shoshoni -50b +110

Fivemile --58

-46a +294 Riverton _55b +135

Rio Grande--24

-17a + 51 Bernalillo _25b + 88

aMaximum probable size of bed material. bMinimum probable size of bed material.

)

TABLE 5. EFFECTS OF BED- MATERIAL VARIATIONS

(after ZERNIAL AND LAURSEN [9 ])

Approximate effects on Qs , in percentage

( y: )716 I 1(9 Location

Change Change ...2:.._Q_ - 1 in d in w T

C

M i ddle Loup, - 13 - 24

Se c tion C +13 -13 + 84

Middle Loup, I I -49 -68 +59 -30 +1160

Section c 2 I

Fivemile-- 49 - 71 +59 -29 +1400

Shoshoni

F ivemile--33 - 52

R iverton +39 -23 + 415

Rio Grande-- 49 -65

Bernalillo +59 -24 + 490

Total effec ts

+ 84

+1300

+1600

+ 450

+ 610

I

!

N --.J

Analyses of the data indicated that the mean annual flood and

the weighted mean percent silt-clay are most significantly related to

the width and a multiple correlation analysis yielde_d the equation,

b = Qb o. 45

5.76 ____ _ ( 10}

MO. 36

for the channel width.

Neither mean annual d i scharge nor the mean annual flood was

found to significantly affect the width-depth ratio. A regress ion line

was determined graphically for the data in Figure 10, resulting in the

equation:

F = 255M-1.0S ( 11}

for the wid,,th - depth ratio.

Effects of Structures

Frequently the upsetting of natural conditions by man causes

a cohesive channel to change its shape, erode, or deg r ad e. Often

comprehensive plans and manmade struc tures are necessary to alleviate

this problem, Miller and Borland [23] reported on a study and stabi ­

lization program on Fivemile and Muddy Creeks in central Wyoming.

Due to manmade changes, the d i scharge had increased from less than

5 ,000 acre -fee t to over 90 , 000 acre - feet on Fivemile Cre e k and over

28

•

600.0

100.0

LL

0 -0 a:: .s;;; -0. Cl)

C) I

.s;;; -,:, j

10.0

1.0 0.1

"" ' "'

~

'

" ", "\ • •

" ' . . , " J\..

'~ • • • • • '""' • • '

"' . • • ~ • • • ~, • • •• • . • " . ...

~ • • . V

. ' .. .. ' I\. • •

. " ~

~

1.0 10.0

Weiohted Mean Percent Silt-Clay (M)

F1G.IO WIDTH-DEPTH RATIO VS. MEAN PERCENT SILT-CLAY. (after Schumm C22J)

29

"I

~~ I'

100

20,000 acre-feet on Muddy Creek in a period of about 25 years. Due to

the increase in flow, erosion had greatly accelerated, and the streams

were contributing over 50 percent of the sediment being deposited in

Boysen Reservoir. A detailed field investigation was undertaken to

collect geologic, hydrologic and hydraulic data. Using the data collected,

control measures, including wooden and concrete jacks, groins and

jetties and vegetation, were designed. These measures proved successful

and resulted in a stabilized channel and a ninety percent reduction of

sediment inflow into Boysen Reservoir.

Woolheiser and Miller [24] present the results of a study of

channel eras ion above and below gully control structures, This study

was intended to do c ument present and past conditions a n d experiences

at several gully control structures in order to provide data which

would aid in the design of these structures. The study concentrated

primarily on the scour hole development at the principle spillway

outlet and changes in the channel bed profile downstream from the

structure along the line of maximum depth of flow in the stream,

Climate and Temperature Effec ts

Wallis and Willen [25] obtained O to 6-inch samples of soil from

2 58 locations in northern California ' s mountain lands. A part of their

30

analyses included relating clima tic parameters to textural and erodibility

measures of the soil. Although correlation was not highly significant,

they found from regression analysis that for the soils, a pr e d icition of

total clay (clayce> could be made , bas ed on the climate, from the equation:

clay ce = O. 343 + 0. 06201 (P) + O. 4213 (Kw)

0. 05764 (KwP ) - 0. 0003761 (P )2 ( 12)

O. 0002589 ( Kw )2 + 0. 0001781 (KwP) 2

in which P is the m ean annual precip itation in inches and Kw is the d is -

sociation constant of water summed for 12 m onths by using the mean

monthly temperature s calcula ted for each site.

I t was found that for the m ountain soils the surface aggregation

ratio (S/ A ), which expresses the amount of surface area of the particles

greater than sand size relative to the amount of aggregated s ilt and clay

that i s availabl e for aggrega te formation, was an effe ctive m easure of

the soil erodibility. Predictions o f the surface aggregation ra tio were

made from the c limate variables as :

S/ A = 322. 6 - 6. 39 (P) - 7. 52 (Kw ) + 2. 42 (KwP) +

0. 0404 {P) 2 + 0, 0553 (Kw)2

- O. 00693 (KwP )2 ( 13)

Wolman [26] found sev ere erosion in winter months when bankfull

31

flow attacked channel banks that were previously wet. He also noted

significant erosion from combinations of cold per i ods, wet banks,

frost action, and rises in stage, and that crystallization of ice and fre­

quent thawing without a change of stage also produced some erosion.

Predicting Eros ion or Deposition

In a study on channel deter i oration of natural and artificial

drainageways 'in Nebraska and Iowa, Schroeder [27 J classified 121

test reaches as being (1) stable, {2) fairly stable or questionable,

and (3) deteriorating channels. Using the mean annual peak discharge

and stage-discharge relationships, the depth was obtained and tractive

forces were computed from:

{ 14)

where k is a variable dependent on the bed-depth ratio and the side

slope of the c hannel, y w the specific weight of water, y 0 the depth of

water in the channel, and S is the slope of water surface or c anal bed.

The percent densi ty of vegetative cover was re co rded for the channels ,

and soil tests of the channel material were conducted.

Curves were developed , Figures 11 and 12, showing limiting

tractive forces for the bed and banks of the c hannels. Curves of

tractive force versus plastic index are shown for no yegetal cover

32

I. ... Percent Range

Doubtful - of Vegetative Stable Stable =tion Cover Scour Chamel Channel - 0-25 0- t ~ t -25-50 6 ~ -0

,... 6- 50-75 --0 -0 ---<> -r:'.

75-100 C/ 9 ~ 4 5= I.

-~ 0-

0-- Recommended Limit

I. C\I --........ en

., For 100% Vegetation - I 0 . -- ·- >-- - . ~

V -

' -0-

.0 ~

~ • 0 I. ~

0 LL

~ r----r-- 0-0 r-- 9

0-r-- f-Q=.. ~ q - -• >

0- --r-- Transition Zone r-- ,_ --0 ~ )-

,_ ' -0

0 ~

I-

~ r-- -0 ~-~--- ---- _'1.__ - ~ , ( ;----7 J ,._ ,;--- " Recommenaec Limit 9

-0

... _ -;- For No Vegetation -- -

0-9 <) ( >- 0 ~ -.. i- - : ~ · i9 i-

h A-~ ... -...... ....... ,'

<>- Depositional Lint ·t ------ ;, _ ....

tr --z ... ~--6 >-4

1-0 ... ~ Allowable Limit Wet - ; )- 0-

-1'l ,.. -Channel Desian 0- <>-' -c ,-

I I - - I 9 ... - -.:'. I 0-~ - ... - ,,.....1 i-o- 0 - ,J,. - 0-

/ '/ / 0 i7~ K.; '"" Recommended Wtt 0-

/ ~ 77 -:, -, )- Channel DeslQn ~ .I -, / , , , , , , ,

"4 38 32 26 20 · 14 8 2 0 .03 • D .20 .3 0 Plastic Index Mean Grain Size, mm

N-0n Plastic FIG.I I LIMITING BED TRACTIVE FORCES FOR EPHEMERAL CHANNELS

(after Schroeder (27J)

1.9

1.7

N \,3 --' tn _g

~ ., u ... 0

LL .9 -~· -u C ... ~

.5

., 5

Percent Ran9e 0-

of Ve9etativ1 ~r~ Cover Sccu t

0-25 r 0- t t 25-50 6 50-75 ~ -0 --<> -a:\

75-100 ? ? ? 'r J.

)-

-~ - t--. Recommended Llmlt i-- 0 t-- t--. For 100 °/. Vet eta ion -~

~

I'-.. ~ ,-

r-,...__ -..._

r--,..... Reconvnended L1m1t 1,.. F'~r I o ''eg,1tn Inn -0

............ \ 0 'I' r--,......._ I - ) ') I I 0-

i"-l 0- 6 I r--,.....- "" I>-

~ ........... -?9 (~ i .. ~~~i!~~"--~ f~! 0:' ~ r---,..... -0 :>

I 9 r--... ... ,.., I - 0~

~- Sand bed I'? ()-~ ' 9 "\.. - 9 I)-<> 6~ 1\...-0 " I~

" " 1'·· Sand bed A lowoble L1m1t For y -n ~ ,)-¢-' ' Wet Channel Desian -~ ' - ... _ 9 .,~ tr - : µ-

'P - t-- ; 0 - -

/ i~ v/ ~ ~ ~ t7, ... ) ... ) 9 1 9 P- "" ' Rtcommendet wet

/ I'°/ 17" ;' .._ .... \ ~ Channel DHian , , , , , , , , ,

0 46 42 38 34 30 26 22 18 14 10 6 2 0.03 .06 .15 Plastic Index

FIG.12 Limitino Bank Tractive ForcH For Ephemeral Channels (after Schroeder C 27J}

Mean Grain Size, mm Non Plastic

0-0-

J"\ -s

.3 0

and 100 percent vegetal cover. Although there is a wide scatter of

points, these curves may be used as a guide for predicting conditions

of eras ion or d e position. Whe r e banks are flatter than a 5 to 1 slope

they should be consider e d essentially the same as a bed condition,

and where channels ar e quite sinuous , vegetation should not be con-

sidered a limiting factor. Th e wet channel design limits shown on ,t'

Figures 11 and 12 were obtained from limited data and, therefore ,

were not advocated for use in des ign.

Hjulstrom [28] has pres e nted a curve relating grain size and

erosion velocity from stu dies of the River Fyr i s. Much of the infor-

mation available for designed channels is also of considerable benefit

in predicting erosion conditions of a natural stream.

DESIGN OF NON - ERODING CHANNELS

Observations and Tests

Observations, tes ts, and data c olle ction have been conducted

on sever al canal syste ms with the objectives of developing satisfac tory

design methods. The U. S. Bureau of Reclama tion observed and tested

46 channel test reaches located throughout the Western United States

[ 4 , 29 , 30 , 31 , 32]. The cana l s and laterals had been in operation for

35

a number of years a n d discharges varied from 2 to 3,000 cfs. F i eld

data were obtained on both the hydraulic s and soils , and several soil

samples were obta ine d from each tes t site. Both s oil s and hydraulic

tests were conducted on the samples obta ined from the test reaches.

An electronic dig i tal compu ter was use d to inve stigate ab out 40 da t a

correlations from the reaches. These correlations were reported by

Carlson and Enger [ 4]. Correla ti on coefficients for the data corre ­

lations varied from "imaginary" to greater than O. 9. Thomas and

Enger [32] reported a c orrelation from this da t a which gave sati sfactory

results within certain limits . Their equation i s presented as equation ( 18)

in the following se ction, Design Information Ava i labl e.

Simon s and Alberts on [ 33] have u sed info rmation c ollected fr om

field observations to develop design crite r i a. The d e s ign information

developed also i s repor te d in the se ction, Des ign Info rmation A v a ilable.

Flaxman [3 4 ] conduc ted field ob s ervations along exi sting channels ,

and obtaine d soil samples from the c hannels for laboratory analysis. He

concluded that the un c onfined compress ive strength of soils i s a good

ind ica tor of erosion p o tentia l , and 11 that s oils of low strength are easily

susceptible to erosion in c han n el flow while those of h igh strength resist

hydraulic stresses of cons iderable magnitude. "

36

Des ign Information A vailable

In 1926 , Fortier and S cob ey [ 3 5] pr e sente d the final report of

the Special Committee on Irrig ation Hydraulics on Permi ss ible Canal

Velocities. The Special Commi ttee had submitted q uestionnar ie s to

a number of engineers who se exper i enc e qualified them to make esti-

mates of the maximum m ean velocities allowable in c a nal s o f various

materials. Constructive replies a n d suggestions were received from

10 engineers. From this a n d oth er available mater ial, the values in

Table 6 wer e re commend ed as maxim u m p erm is s ible mean ve l ocities.

In an attempt to more adeq uately p re d ict channel behavior , two

other des ign the o r ies, the regime theory and the tractive - force the o ry,

have b een studied. S imons and Albe rts on [33] have presented con­

siderable information on des ign by the reg ime theory. Thi s theory

has evolved from the empirical equation of R. Go Kennedy:

V C m y

where C a n d m were thought of as c onstants, V represen t s the critical

mean veloci ty in feet per second for whic h no sil ting or s c ouring o f

the channel occurs, a n d y is the d epth in feet. The orig inal value

suggested for C was O. 84 , a nd for m, O. 640 Other values have been

37

TABLE 6

PERMISSIBLE CANAL VELO CITIES (after FORTIER AND SCOBEY [35))

Velocity in feet per se cond, after aging , of c anals c arrying:

Original material exc avated for c anal

Water transporting . Clear water ,

no detritus

( 1)

F ine sand (non-colloidal) ,, ..............• :

Sandy l oam (non -c olloidal} ............. . .. :

Silt l o am (non - colloidal) ......... . ........ :

Alluvial silts when non - colloidal ....... . .. .

O rdinary f i rm loam . , . , .. , ..... , , . . . . . . • . .

Volcanic ash .......•.......•..... • .......

Fine gravel. . , ........•••................

Stiff clay (very colloi dal ) •• • ............•..

Graded loam to cobbles , when non - colloidal •

A lluvial silts when colloidal. • ....••......•.

G rade d silt to cobbles , when colloidal. .... .

Coarse gravel (non-c olloidal ) .............. :

Cobbles and shingles ...................... :

Shales and hard - p ans •....•....•.......... :

(2 )

1. 50

1. 7 5

2. 00

2. 00

2. 50

2. 50

2. 50

3. 7 5

3.75

3. 7 5

4. 00

4. 00

5. 00

6. 00

Water trans - non -colloidal silts , porting

,colloidal silts (3 )

2. 50

2. 50

3.00

3. 50

3. 50

3. 50

5. 00

5. 00

5. 00

5. 00

5. 50

6. 00

5. 50

6. 00

sands , gravels , or rock fragments

(4 )

1. 50

2.00

2. 00

2. 00

2, 25

2. 00

3. 7 5

3. 00

5, 00

3. 00

5. 00

6. 50

6. 50

5. 00

suggested for these constants.

Using data obtained from canals in India and the Western

United States , Simons and Albertson [ 33] presented several plots

to aid in the design of canals. Reproductions of several of these

plots are presented i n Figures 13 through 19.

The curves shown in Figure 13 provide a means of estimating

the wetted perimeter for a given dis charge. After the wetted per -

imeter has been found , the average channel width may be determined

from Figure 14, and the top w i dth from Figure 15. For the given

/

disch~rge, , the hydraulic radius may be found directly from the curves

of Figure 16, and as the hydraulic radius and depth are closely related,

the aver~'.ge depth may be determined from Figure 17.

The required cross - sectional area may be determined from the

curves in Figure 18 , and knowing the d i scharge and area , an average

velocity 'may be determined, Us ing the average velocity, a value of

R 2S may' be estimated from the curves of Figur e 19, and utilizing the

hydraulic· radius found from 'F igure 16, the slope may be evaluated.

Utiliz ing this method , Simons and Albertson stated that canals

in the four following groups c ould be designed :

1. Canals formed in coarse non - cohes ive mater ial (charge < 500 ppm)

39

100

10

250

200

150

100

50

0 0

40

A Sand bed and banks

B Sand bed and p = 2.51 Q Q.512 -~ ~~ cohesive banks I,,

-,_ .;,,,, - C Cohesive bed - ~· .v .. and banks ~ fj ... ~E

~

D Coarse non- / • . ........ - cohesive material • ... E - ,,._ -E Imperial Doto r.. .... ~ _., --~ c/ - 10 )~ • like B

Q. Okd": L~ ~ y ".: -::Joi~ A~ ,,; ........ ., !a,:>1P• I

~ • 8~ L.....-rl' 8 I I I --• 12,i. ~/ 3t _. ' L..,,,L, L, o Simon 8 Bender

l) ~ ...... r'1).

0 Punjab

~ 6 i...rl Canals

<t Sind Canals A .... • U.S.B.R. Canals . -

...... • Imperial Canals ..

--.. .c 'C 3t

• 0 g ~ • > Cl

JT'(n . -

,o FIG.13

Al RO

.... 1Q

DischarQe, ch

100 1000 10000

VARIATION OF WETTED PERIMETER WITH DISCHARGE AND TYPE OF CHANNEL. (after Simons and Albertson C 37J)

~

....... ~.,

L

----.:;,, / ,_

/ -I/

~ ........ -

V 1W'

- V Simons a Bender o r

Sind Canals c, ... v ~"" - Imperial Canals 0 ....... .... ,.

/

.L A -

- V,

Dfa K, ;Qj "(.)

Wetted Perimeter. ft

50 100 150 200 250 300

FIG.14 VARIATION OF AVERAGE WIDTH WITH WETTED PERIMETER. (after Simons and Albertson C37J)

240

200

160

120

80

40

0

20

10

1.0 0.8

0.6

0.4

0.2

--.. .t:: .. ,, ·-~

• 0 C ... ., > ct

~

I. ,<

_rin . 20

A B -- C ..

• D ~

E " C a:: (.)

-~

C ... ,, >,

::c

41

(l I,"

.,,, .... ./

./

/

W=0.92Wt-2.0 / I/

V

- l,11" Ve>

V ....... oSimons a Bender ......

., .... e Punjab Canals

./

/ '-

/ V

/ /

,,cJ

..cl.Al _. .,..., ~ " ~·

Top Width, ft

60 100 140 180 · 220 260

FIG.15 VARIATION OF AVERAGE WIDTH WITH TOP WIDTH.

(ofter Simons and Albertson C 37])

Cohesive bed and banks R=0.4 30o.361 Sand bed and cohHive banks

Sand bed and banks ·-non-cohesive materials

n Coarse ·~ Imperial Data Like B - -- E -

l'l'O ~ ..

.... ~ ,__...-- - --1>' Ill~ 11.J - ....-- ... --~~ 7 .,:. $~

....... __........... -- -... ic.. "I)()~ i.,..--. & -.r. ... R= 0.247Q0.:36 I l...-4 ~~ ~ ' ,.., C -~ '8 ::; ( b -.--. r-1,..,,-"'i 8

300

It .. L,..,

~ ~ """'~ LJ ~ o Simons Bender

~ ~

e> Punjab Canals - - • -- <» Sind Cana Is ~

• U.S.B. R . Canals • ~ Imperial Canals

Discharge, c fs

4 10 100 1000 lOOOO

FIG.16 VARIATION OF HYDRAULIC RADIUS WITH DISCHARGE AND TYPE OF CHANNEL, ALL DATA·. (after Simons and Albertson C37J)

12

10

--8 .. "' .:! ~ 0 a::

6 u -:, 0 ... ~ >.

4 J:

2

N -1000 -~ 8 ·--u Cl)

en en "' . o ... u

100 ... CD -0 3 -0

0 CD ... <t

10

42

/ 'f /

(I.J ,,/ I (J

, ov

II. /

i.,,/'iP /

p ("\/

j5JJ u, Simons a Bender o lo~ 0 -8 /

// Sind Canals<»

Imperial Canalse

r/~

V :> e

)P 0

-~ oS 0

/ v"" CD p

Average Bed Depth, ft

2 4 6 8 10 12 14 FIG. 17 VARIATION OF HYDRAULIC RADIUS WITH DEPTH.

(after Simons and Albertson C37J )

I I ~ ~

I I I I I I I J

lJ lf A= l.076Q0,873 < i.,"" .... I

, Sand or cohesive bed -· ,

"'

15

and cohesive banks Coarse non-cohesive - --/

/ ~"' (t(~

~ ;wi

, Sand bed and banks ' "' ~" lA = 0.45Q0.873 ~14 r«. / -,.,

I I

~ " , -., .. o Simons a Bender u •/

/

-~ ..... o Punjab Canals ~.)

J ,_ ~/

<J$ind Canals let' v"'

~ • Cana ls / •U.S. B.R. /

I i.,,

/ ®Imperial Cana ls

• 'II" , / ,, Discharge, cfs I

10 100 IOOO 10000

FIG. 18 VARIATION OF AREA OF WATER CROSS-SECTION WITH DI SCHARGE AND TYPE OF CHANNEL. { after Simons and Albertson C 37J)

10

8

6

4

2

I

(.) Q> en

' --.;. -(.)

0 "ii > Q> O'I 0 ... Q> > ct

0.0001

43

Coarse non-cohesive / '

./ V

v = 1s.ocR2s> V3 1 ,Y •

/

.,,,..,,. ~-"., Like B I .SI /, . ~

• If'.. • I / 0

( t" ~)""_1' 1/o l/ /. ~g~

~ oSimons a Bender

V = 17.9(R2s)0.286 ~I

I

~e°j4: c Punjab Canals

- 0 V= l~.86{~)V3 c, Sind Canals - .,. /o~Of Sand beds and I:> Sand beds and banks • U.S.B.R. Canals

cohesive banks,

ic~

0 ),

I) ~>. ~·' Gt Imperial Canals

... vt,di~ C) ,,.

0 0

()~ R2S ,,,.

0.001 0.01 0.1

FIG.19 VARIATION OF AVERAGE VELOCITY WITH R2S AND TYPE OF CHANNEL.

(after Simons and Albertson C 37])

2. Canals formed in sandy material with sand beds and banks (charge < 500 ppm)

3. Canals possessing sand beds and slightly cohesive to cohesive banks (good results when charge < 500 ppm, qualitative results when charge > 500 ppm)

4. Canals having cohesive beds and banks (charge < 500 ppm).

A method of design by the tractive-force theory has been pre­

sented by Doubt [36]. The method involves three phases: (1) a channel

is first designed to meet the capacity (maximum discharge) requiremenit,

(2) the channel is checked to determine if it meets the requirements for

stability, and (3) the economical proportions of the channel and its as -

s ociated structures are checked. When necessary, the original design

1s altered, thus resulting in a trial s elution.

The average unit frictional forces on the wetted perimeter

(which are equal to the average unit tractive forces but are oppositely

directed) are computed from;

( 16)

where f is the average unit frictional force in pounds per square foot,

'{ w the specific weight of water in pounds per cubic foot, R the actual

hydraulic radius in feet, and St is the rate of energy loss at the inter­

face of the earth material and the flowing body of water, foot-pounds

per pound of water per foot of channel.

The value of St is computed from:

44

(1. 486) 2 A 2 R 4 / 3

where Q is the actual discharge in cubic feet per second; A the actual

flow area in square feet; and nt is the Manning's roughness - coefficient

for the earth material in the wetted perimeter (not to be confused with

Manning's coefficient n, which is usually larger than nt). Lane [37]

suggested the relationn = D75 1 / 6 /36, in which D75 is the size of

earth material in the wetted perimeter of which 7 5 percent is smaller

expressed in inches.

As the tractive forces are not distributed evenly around the

wetted perimeter of a channel, the maximum actual tractive force

is usually obtained from experimental data such as that also presented

by Lane [37], Figure 20.

Several methods have been suggested to determine the allowa -

ble tractive force, or the maximum tractive force that the channel

materials can safely withstand before erosion o c curs. Thomas and

Enger [32] found that, within given limits , the follow ing equation

provided satisfactory results for critical tractive force.

45

( 17)

I Tc = 0, 00124 + 0, 00081 PI + 0. 00030 Do/o + 0. 00022 Mcp o-;pkcp (18)

46

I. -....

Trapezoids SS = 2:1 a US:1-" I - I

""'

/ l.,...,--"'

/b

I /

.8 I

I I 0

<A >->,.. 0 ... ., u ... if • > :;:: o. u

I I

.6 J f-- Rectan9IH

4 I C ... ~

J

2 I I

o.

I

2 4 6 8 10

B/y Ratio

FIG. 20 MAXIMUM TRACTIVE FORCES IN TERMS OF yyS. ON BOTTOM OF CHANNELS. ( Lane C37J)

,,

where Tc is the critical tractive force in pounds per square foot, PI

the plasticity index, D% the in-place percent maximum soil density,

I and M<po-<pk<p is a description of soil gradation. The limits of equation

(18) are:

0 < PI < 22

65 < D % < 100

-12 < Mcpo-cj:,k' cp < 40

13 < LL < 42

in which LL is the liquid limit.

Dunn [3 ], Smerdon and Beasley [7] and Schroeder [27] have

also found the plasticity index to be a measure of the allowable tractive

force. However, to date, only empirical relations are a v ailable for

determining the allowable tractive force.

PROBLEMS OF AGRICULTURAL LAND AND CHANNELS

The problem of erosion of cohesive mater ials as related to agri -

cultural land can be d ivided into two general c atagories : The first per ;:.

tains to land erosion from rainfall and has historically be en viewed

from the point of view of the damage that erosion does to the produc-

tivity and value of agricultural la:p.d. Much less conce rn has been

47

focused on the ultimate disposal of the eroded sedimentso The second

eras ion category is related to design, operation and maintenance of

earthen water conveyance structures in agricultureo These include

field ditches and channels s ,uch as drainage ditches , farm irrigation

channels, terrace and diversion channels and i rrigation furrowso

Land Erosion

Erosion is generally thought of as a slow pro ce ss , but figures

representing the annual loss of soil are staggering. It is estimated

that, the annual rate of-soil loss for the Mississippi R iver Basin is

about 400 tons per square mile [38 ]. An annual rate as high as 97,740

tons per square mile was measured from a small watershed in western

Iowa. Each year one billion tons of suspended sediment are estimated

to be transported to the oceans from the United States. In addition,

vast qua1;1tities of eroded soil never reach the o c ean, but are depos ited

in the flood plains, in river c han nels, and in reservoi rs.

It is estimated that 380 million cub ic y ards of sediment are

dredged each year from the nation's harbors and waterways to keep

them clean [39]. The annual cost for this dredg ing is about $125

million. Reservoir capacity lost each year as a result of sedimentation

is difficult to determine accurately, but conservative estimates place

48

this loss at 1. 5 billion cubic yards. This amounts to an annual loss of

nearly one million acre-feet of reservo ir storage due to sedimentation- -

much of which i s ero ded soils from agricultural and forest lands.

In 1966 , Smith [40] reported that uncontrolled erosion in the

United States produced nearly 4 billi on tons of sediment e a c h year.

Considering the 19 55 estimate of one b i ll i on tons reaching the sea ,

then approximately 3 b i lli on tons of eroded material is deposited at

some point between the p oi nt where eros ion occurs a n d the sea, Smith

also reports that there is evidence that the pr inciple means of water

pollution from agricultural chemicals may be from erosion of cohesive

soils with the c h emicals adsorbed on the clay and organic fraction of

the soil.

The importance of erosion of c ohesive soil s from agr icultural

land i s obvious. Miuch rese,arc h has been a cc omplished b ut m uc h re­

ma ins to be done if the erosion and res u ltant pollution fr o m ero ded

sediments are to be con trolled. Smith summarizes researc h on

eros ion of agricultural l and and sugg e?ts some pro m ising a pproaches

to erosion c::ontrol.

Erosion Loss Equati on. In 1961 , the Agr icultural Researc h

Service of .the USDA published a spe cial repor t entitled 11A Un iversal

Equ ation for Predicting Rainfall - Eros ion Losses 11 [41]. Thi s report

49

presented an empirical equation to predic t soil losses by erosion from

agricultural land derived from statisti c al analysis of erosion measure -

ments in the fie ld and under natural and simulated rainfall conditions.

The equation i s:

A ::: (RF ) (K) (LS ) ( C) ( PF} (19)

in which A is the average annual soil loss in tons per acre predicted

by the equation, RF the rainfall factor, K the soil erodibili ty factor,

LS the length and steepness of slope fac to r , C the c ropping and manage -,,

ment factor , and PF is the supporting c onservation practice factor

(te rracing , strip- crapping, contouring}.

'Phe rainfall factor, RF , in equation (19) was found to be de-

p endent dn two meas u rable rainfall characteristic s. One was the rain ­

fall energy which c ould be expressed in terms such as foot - tons per

acre-inch. Another index was rainfall intens i ty. The product of the

rainfall e:nergy times its maximum 30 minute intens i ty was found to

represent the rainfall in the erosion equation. This pr o duct was

called the rainfall erosion index. The rainfall erosion indic es have been

calculated for 181 l ocations in the Unite d States a n d were found to vary

as follows: Southeastern Sta tes, 142 to 779; Northeastern States, 62 to

220; and North Central States , 64 to 261.

50

The soil erodibility factor , K , is of primary importance in the

erosion of cohesive soils by rainfall. The factor was said to depend

on many soil chara c teristi cs. Values of this soil erodibil i ty fa c tor ,

which measures the relative erodibility o f soils, are being determined

for so-called "benchmark" soils where erosion losses have been mea -

sured. Wischmeier and Smith [ 42] have indicated that values of tp.e soil

erodibility factor range from O. 50 for soil high in silt content with a

weakly-formed and unstable struc ture , to 0. 10 or less for soils with a

high sand content and nearly permanent structural stabil i ty. Soil

erodibility factors average about O. 33 for silty loams and about O. 25 for

sandy loams. The higher soil erodibility factor ind icates a more

erosive soil.

The length and steepness of the slope fa c tor, LS , increases as

slope length increases or steepne ss of slope increases , but not at

uniform rat es. Increases in slope length of the fiel ds i s much m ore

critical where the s lope is great. The fa cto r , LS, can be estimated

by the empirical equation:

LS = O. 0177 (0. 4 3 + 0. 30S + O. 04 3S 2f'{£- (20)

in which f is the slope length in feet and S i s the predo m inent field

s lope expressed as percent [43 ].

51

The cropping management fa c to r, C , depends on s uc h man ageme nt

practices as crop rotations and the k inds of crops grown. S om e c rops

provide mor e p r otection against erosion than o thers. Fac t or s such as

seasonal d is tr ibuti'on of ra instorms , dates of plowing, se e d ing and

harvesting , residue managem ent pra c tice s , seedin g m ethods and tillage

procedures all m u st be known to c a lculate C .

The conservation practic es factor , PF , d e p ends on the conserva ­

t ion practice s us e d in fa r m ing. Such practice s as c ontou r farming and

str ip c r opping reduce the fa ctor , PF. Values of PF range from 0. 9 0

for contouring on steep slopes to 25 for contour str ip cropping on gentle

slopes [ 42], Terrace s , wh ile be ing a cons e rvation prac ti ce, are a ccounted

for by reducing the slope l e ng th fr om th at of the entire field to the hor i -

zontal d i stance between terraces.

The ·equation for es timating soil loss i s a valuabl e tool to d e­

termine conservation p r a c t ices needed to con trol eros ion. Con serva tion

and manag e m ent p ractice s may be des ig n ed whic h will keep erosion to

a tolerable level , perhaps 1 to 5 ton s per a cr e per y ear. The e q uation

may also be us e d to estima te sed iment y i e ld although the a c tual sed imen t

yields from the fie ld may be m uch less than the calculated eros i on be ­

cause of depo sition in terra ce channels or at the b ottom of slop es.

The equati on for estimating s oil lo sses is constantly be ing re -

52

vised as additional erosion data are availa ble. But the method is quite

easily used and the procedure i s outlined and c urves and tables for the

various factors are presented in m o st Soil Conservation Service Hand ­

books and in a recent text by S chwa b, et, al. [ 4 3 ].

Soil Erodibility, In the 1930 1 s , researchers attempted to relate

soil erodibility to measurable physical characteristics of the soil.

Middleton [ 44] , in 19 30, found the <lispers ion ratio (a measure of the

stability of aggregates of cohe s iv e soils in water ) and what he called

the erosion ratio to be the mos t significant soil characteristic s influ ­

encing soil erodibility. His erosion ratio was the dispersion ratio

divided by the rati o of the total weight of silt and clay sized aggregates

in the nondispersed sample to the total we ight of silt a nd clay in the

dispersed sample. Middleton a l so s uggested that organic matter , the

silica -se squioxide rati o , and the total exc hangeable bases influ enced

the erodibility of soi ls. M i ddleton et, al. [45 , 46] group e d soil s fr o m

the ten or ig inal USDA er o sion sta tions a ccording to the above c riteria,

Lutz [4 7] in 1934, Yoder [ 48] in 193 6 , Peele [49 ] in 1937 , and

Peele et, al. [ 50 J in 1945, als o investigated aggregate stabil ity and

other soil properties including th e cla y in the so il and found them to

be related to s oil eros i on,

In more recent i nvestigations , Anderson [ 17 , 51] found M i ddleton's

53

..

dispersion ratio to be statistically signifi c ant in soil eros i on. Ander-

son [ 51] and Andre and Anders on [ 52] also defined the surface-aggre­

gation ratio as a nothe r useful erosion index, Wallis a n d Stevan [53]

have shown these erosion indexes to be related to the c ation e·xchange

capacity of the soil and found calcium and magnesiu m to be particular­

ly important.

In flumes or other special apparatus t o s imulate eros ion for c es

where cohesive soils wer e used, investigators have d e t e rmined that

many s oil properties are statistic ally correlated w i th erosion re ­

sistance of cohesive soils [11 , 7, 14 , 54, 55, 56]. Yet these tests have

all been run with disturbed soils and do not give information which can

readily be used in design. Thi s is exemplifie d by the fact that no de -

sign procedures for water c onveya nce structures c onsider all the indi ­

vidual soil properties whic h have been suggested from pas t research.

Most often the designs c onsider only the soil t exture o r a single mea ­

sure of the strength of c ohe s ive for c es suc h as the p lasticity ind ex

or the dispe rsion rati o. The se meas u res do , however , ass i st in making

estimates of the relative er od ibility of soils .

Scour in Agr icu ltural Channels

Most often the flow in agricultural c hannels 1s inte rmittent and

54

'

relatively shallow. The channel bed may have a vegetative covering

or may be tilled leaving the physical condition of the bed in different

states of erodibility at the time of a potential erosion producing event.

Stable channel design is qui te critical in these channels , but

the defin ition of channels s t ab l e aga inst scour may be slightly different

for an intermittently flowing channel than for one flowing continuously.

Sometimes low rates of scour during short periods of peak flow may

have the effect of cleaning sediments depos i ted in the channel during

low flow per i ods, Nonetheless , reasonable design criteria are needed

and some suggested procedures from the literature are given.

Design of Farm Drain Ditches and Terrace Channels I

Most farm drain ditches are designed on the basis of limiting

velocity. Typical suggested values are [ 57]:

Stiff clay s o ils - 4 feet per se c ond

Sandy loam soi ls 2. 5 feet per secon d

F ine sandy soils 1. 5 feet per se c ond

Published data on allowable tra c tive for c es in cohesive soil have

not been used to any extent in the design o f farm drains. However, the

use of tractive force data (or depth- slope produc t ) for the design of

dra in d i t c hes which are stable again st s cour has been suggested [58].

55

The suggested procedure considers that some shallow farm drain ditches

are cultivated, and this leaves the soil in a more erodible state. The

suggested des ign curves are shown in Figure 21. The product of depth

of flow and slope of the ditch should not exceed the values giv en. These

results can be converted to critical tra c tive force values by multiplying

the (y) (S) values by the specific weight of water.

Channel type terrace design i s generally based on limiting

velocities with values being about 1. 5 feet per second for erosive soils

and 2. 0 feet per second for most soils and 2. 5 feet per second for soils

with high organic content [59]. Using tractive forc e data, McCool and

Beasley [60] have presented a method for the design of channel type

terraces considering the spatially varied flow in the channel. The left

curve in Figure 21 , where the c hannel bot tom i s cultivated, could like­

ly be used for the design of chann e l type terrac es .

. Design of Farm Irrigation Sy stems

Most surface irr igation systems are des igne d on the bas i s of

experience with similar soils as far as e ros ion is c once rned. In 1946 ,

data were presented by Gardne r , et. a l. [61] on c r i tic al fu rrow stream

56

40

30

,c ., 20 "'O

C

>, -u +-.,, C

n: 10

8

6

Relative Erosiveness of Soil

Erosion Resistant ·+ Moderately

Erosion Resistant

+ Erosive

+ Very Erosive

0.001 0.002 0.003

DX S, ft

0.006 0.01

FIG.21 DEPTH X SLOPE OF DITCH VS. PLASTICITY INDEX.

0.015

u-, --.J

sizes for different furrow slopes, The curves do not take into account

the relative erodibility of the soil. A rule - of - thumb suggested to de-

termine the maximum n onerosive furrow stream discharge in gallons

per minute i s 0. 10 divided by the furrow slope in feet/ feet [ 62 ]. For

border strips the maximum allowable noneros ive stream is suggested

as Q = 0, 0019 s - O, 7 5 where Q i s in cubic feet per second per foot of

border width and S is border strip slope in feet/ feet [ 6 3 ], Again, vari-

ations in soil e rodibility are not considered in the se gui delines.

Assuming Chezy' s equation c an be used to determine the rate

of flow in a furrow , then Q = CA V RS. If the channel is broad and

shallow, the hydraulic radius , R, is approximately equal to the depth

of flow, y. Therefore , the stream size, Q , is proportional to y 3 / 2 s1 / 2 .

The Soil Conservation Service rule-of- thumb for maximum furrow

stream s i ze converted from gallons per m inute to c ub i c feet per second

is:

0. 10 = 0 , 00023/S 449S

Us ing the Chezy equation for w i de shallow channel s

( 21 )

(22 )

in whi c h K1 is a c onstant representing the produc t of the Chezy C and

58

59

A / D, Equating equations (21) and (22) to determine the relationshi p of

y and S for the maximum noneros ive str e am in i rrigation furrows gives :

0. 0002 3/S = K1 y 3 / 2 s 112 (23)

or

Y3/ 2 8 3 / 2 = 0.00023 = K2 ( 24)

and

yS = (K2)2/3 = K3 ( 2 5)

in whi ch K2 and K3 are also c onstan ts. Therefore, the maximum non -

erosive stream occurs for some c onstant valu e of the pro d u ct y and S,

In other words , the r e is a maxi mum valu e of tra c t iv e f o r c e for non -

erosive irr i gat i on fu rrow streams s inc e t rac tive for ce i s proportional

to the produc t o f y a n d S. Thi s w ould c orr e spond t o t h e c ritical tractive

force.

At this t ime no fina lized values of lim iting tractlv e fo rce c an be

g iven for small agr icultural c hann els in c o h esive soil s. The v alues of

limiting t ractive for c e whic h c a n be used for the c hannels whi ch flow

intermittently will be greater than c a n safe ly be used in continuously

flowing larger c hannels. The reason for this is possibly because slow

rates of scour are not objectionable for the short p er i ods of time when

peak flow oc c urs in these channels.

C ONCL USIONS AND NEEDED RESEARCH

A great deal of resear ch has been conducte d into the basic

aspects of scour resistanc e of cohes ive sediments. Still the properties

which control erosion resistance of cohesive sediments have not b een

conclusively defined. The Task Committee considers that a major

research effort must be undertaken to d efine those propertie s whether

chemical, physical or environm ental that d ete rmin e the res i stance of

a cohesive sed iment to flowing water. The p orp erties of th ese sed im ents

which influenc e th eir ability to resist eros i on need to be better und er­

stood. The m ineralogy of the clay fraction a nd the role of d ifferent

cations associated with the clays needs investigating. Also , the influ ­

ence of suspended sediment and its effe c t on the vis co sity of th e water

produ cing erosion needs to be better understood.

M uch prog ress has been made on appara t us to s imulate the

e rosion forces on c ohesive soils. Problems in transla ting the re ­

s u lts to design crite r ia are still e ssentially unsolved and more s tudy

60

is needed, Simple laboratory devices which permit soil conditions to be

easily controlled or undisturbed samples to be used need to be further

developed.

Cohesive soils have bonds which are related to the soil mineralogy

and chemistry. Consequently, water qual i ty can play an important role in

changing these bonds by chemical action. This is also important in

estuarine erosion where some research has been conducted, but still more

work is needed.

The immediate necessity of stable channel design does not allow

the designer to wait for the development of a complete method of analysis.

For practical purposes, though, design methods should be complete enough

to allow economical and useful designs to be made. The methods should

be sufficiently logical and simple to be readily understood and used and

should not require so much work as to make their use impra c t ical. For

very light sediment loads, sufficient design informa tion to meet these

requirements is probably available, However, thi s information should be

assembled and presented in a simple and logical manner , with design

examples.

Additional research whi ch may be of benefit for des ign purposes

is studies on stable channel shapes and the influenc e of heavy sediment

loads. Also , research into the stability of mixtures , such as cohes ive

61

sediments and gravels , may prove valu able.

More basic research, which may eventually provide informa ­

tion to improve des ign c riteria , should b e c onducted on the effect of

the mineralogical characteristics of very fine par ticles on c ohesion.

The remarkable variety of properties exhibited by the very fine

fractions may be the clue to the many varieties of results obtained

from past tests on cohesive so il s.

A great deal of research has also been c onducted on the erosion

of agricultural soils. Efforts to correlate the erodibility of soils to

soil properties have been attempted but the results are still not readi -

ly useable in routine design of water conveyance structures in farm

operations. Often the structures are shallow and re latively flat

bottomed and are tilled as a part of agricultural operations. This

changes the structure and resistanc e of the so il to e ros ion. The soil

is often no t saturate d when the flow event occurs s o s oil m oisture be ­

comes an important variabl e. Flow i s seldom uniform, b ut has lateral

inflow (as in channel type terrace s or drainage d itche s ) or lateral out ­

fl ow (as in infiltration from i r rigation furrows }, so flow is spati ally

varied and m or e complex to a nalyze , The flow i s shallow and ra infall

on the s u rfa c e of the flow may affe ct the res ulta n t channel erosion in

unexpe c ted ways.

62

From these and other factors, some critical areas of research

needed in agriculturally related problems include study of effects of

prior physical disturbances and research o:n shallow flow hydraulics.

The effect of physical activity on a soil prior to a potential erosion

producing event needs study. Among these effects are physical com­

pacting forces such as traffic, tillage operations, freezing and thawing,

or effect of soil moisture variations and stress. Also , most agricultural

erosion occurs as a result of splash erosion or channel erosion with

relatively shallow flow. The importance of rain energy has not been

sufficiently considered in shallow channel flow and needs study.

Finally, the design of on-farm water conveyance structures 1s

based on empirical relationships and experienc e. Research is needed

to develop useful design procedures for these chann els taking into

account variability in soil conditions and vegetative cov er.

ACKNOWLEDGEMENTS

The committee wishes to express its appreciation to the Bureau

of Engineering Research at The University of Texas for their assistance

m the preparation of this manuscript.

63

[1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

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