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ant force obtained by formulas in
which the slope is greater than one-
fourth is incorrect, in direction at
least, for its component parallel to
the back of the wall would be sufficient
to cause rupture along the plane, A B.

Further illustration might be made by resorting to the mechanics
involved in Fig. 30. Suppose a block, B, is being pushed by a force,
P, against another block, A, resting on the floor, as shown. The force,
P, may be decomposed into a horizontal force, P^, and a vertical force,
P^. Then

p^ = F, + n (1)

and P, = Fft + P\ (2)

P„ = Pft X (coefficient of friction + cohesion), and no
If F^ is not sufficient to equalize P^, then P'„ must
Equation (1) holds,
coefficient of friction



more,
increase until
As F^ depends on the normal force and the
and cohesion, and F„ is equal in magnitude



and opposite in sense to the active vertical component of P, then
the writer believes that the most direct method of obtaining the
vertical component of P is by that outlined above.

L. D. Cornish,* M. Am. See. C. E. (by letter). — Mr. Cain corrects
the writer's Sections 15 (Cain) and 23, by stating that, for these cases,
where the inner face of the wall lies below his (Cain's) limiting plane,
the Rankine method alone applies. Such corrections are justified by
his own publications, but the sections as given are correctly computed
from the equations derived from the Cain theories, by Mr. Ketchum,
who, like the writer, probably was unfamiliar with the Cain theory of
the "limiting plane".

Mr. Cain discusses briefly the Eankine sections of Figs. 11 and 12,
and states that for years he had pointed out the inaccuracy of the
Rankine method when applied to walls with vertical backs, the earth
being level at the top. He extends this criticism further (E. P. p. 19)
by stating his conclusion drawn from experiments "that the direction
of the thrust, as given by Rankine, is never experienced in walls at
the limit of stability, except where the surface slopes at the angle of
repose."



• Cincinnati, Ohio.



DISCUSSION ON EARTH PRESSURES 221

Though the writer's Figs. 11, 12, and 13, Rankine, and Curves 1, Mr.
2, 2a, and 2h, of Fig. 24, do not in any way verify Mr. Cain's conclu- ^°''°'^^-
sions, they certainly indicate the inconsistency and unreliability of
the Rankine theory and formulas when applied to walls with vertical
backs. For walls with stepped or battered backs, such as Figs. 15
and 23, with large angles of surcharge, the Cain analysis, as shown
by its author, is inapplicable, and the Rankine method must be used.

Mr. Cain also states that the writer is unwarranted in his assump-
tion that the variation of p, in Figs. 2 to 8, offers any criterion
for judging of what the variation should be for Figs. 9 to 15, and,
to substantiate his statement, offers certain arguments based apparently
in part on the assumption that conclusions relative to walls 10 ft.
high should not be based on the experimental data of Leygue for
retaining boards 8 in. high. If such was his intention, it is due to
a misunderstanding of the writer's criticism, as it is plainly evident
that the variation in p is entirely independent of the height of the
walls. The writer criticized the Cain formulas in only two particulars :
one was with reference to Figs. 14 and 15 (Cain), being but slightly
larger than Figs 7 and 8, which is explained by the limiting plane
theory, which necessitates the use of the Rankine theory for Fig. 15.
The other criticism was that the Cain formula produced a section
(Fig. 11, Cain) larger than Fig. 10 (Cain), whereas a smaller section
might reasonably be expected because the experimental section, Fig.
4, is smaller than the section shown by Fig. 3. It is not apparent
how cohesion can account for such a variation.

The experiments of Dr. Miiller-Breslau, cited by Mr. Braune, are
extremely interesting, and indicate quite conclusively that the slope
of the surface has little or no influence on the slope of the resultant
earth pressure. It is to be hoped that Mr. Braune's proposed experi-
ments will develop some valuable data on the vexatious question of
the direction of the resultant pressure.

The writer trusts that the paper and discussions have been of some
material benefit in emphasizing the necessity for systematic experi-
mentation until sufficient data are obtained to permit the development
of working formulas on which all members of the Engineering Pro-
fession can agree; and he herewith tenders his thanks to the gentlemen
who have so kindly co-oi)erated with him by engaging in the discussion.



AMERICAN SOCIETY OF CIVIL ENGINEERS

INSTITUTED 1852



TRANSACTIONS



This Society is not responsible for any statement made or opinion expressed
in its publications.



Paper No. 1385

A COMPLETE METHOD FOR THE CLASSIFICATION
OF IRRIGABLE LANDS*

By F. H. Peters, Assoc. M. Am. Soc. C. E.



With Discussion by Messrs. T. Kennard Thomson and G. N.

Houston.



Synopsis.
This paper deals with the classification by the Dominion Govern-
ment of a very large area of irrigable land developed by the Canadian
Pacific Railway Company in the Province of Alberta. The reason
for undertaking the work is stated. The climatic, soil, and crop con-
ditions of the area under discussion are described, and, as governed
by these, the basis of the classification is stated. Then the actual
manner in which the classification of the land was made is described
in detail.



The Reason for Government Classification. — The development of
the Western Section irrigation block was carried out by the Canadian
Pacific Railway Company. Construction was started in 1903, and the
project was practically completed in 1910. The development covers
a gross area of about 1 037 000 acres, of which more than 223 000 acres
are irrigable. There are 17 miles of main canal, 254 miles of secondary
canals, and 1 300 miles of distributaries. The total cost of construc-
tion has been $4 325 000, and it is estimated that a further expenditure

* Presented at the meeting of November 1st, 1916.



CLASSIFICATION OF IRKIGABLE LANDS 223

of $1 500 000 will be necessary to replace wooden structures with con-
crete. About 66% of the irrigable lands have been sold.

The law in force in Alberta, and tmder the provisions of which the
project was constructed, is the Dominion statute entitled the Irriga-
tion Act.

This Act contains a clause to the effect that, before a water license
is granted to any person or corporation, a certificate must be issued,
by the Chief Engineer appointed under the Act, certifying "that the
works as constructed are capable of carrying and utilizing a stated
quantity of water". It is necessary to certify to the carrying capacity
of the works because this has a fixed ratio to the irrigable area, based
on the legal duty of water, which is fixed. The Minister of the In-
terior, who is created by the Act the high executive officer of the
Crown, decided that in the case in question the fullest intent of the
quotation above should be carried out, and ruled that ''utilization"
should be held to mean "beneficial utilization".

This decision made it necessary to make a complete classification
of all the irrigable land, and this had to be based on a rigid definition
of the words "beneficial use" in terms of dollars and cents.

Determination of the Basis for Classification. — It was admittedly
a difficult problem to assign a cash value to the term "beneficial use",
which made necessary a balancing of the added returns of irrigation
against the added cost of irrigation — both in comparison with dry
farming.

The so-called "dry farming" method of agriculture was generally
practiced in the Province, and the value of the returns from this
method of agriculture were known. The value of returns from irriga-
tion agriculture in the district was not known, because there had
been very little actual irrigation. It was necessary to make a con-
servative estimate of the added returns over dry farming due to
irrigation.

The added cost of irrigation was considered to be made up of four
items: the additional first cost of the irrigable land over non-irrigable
land; the annual charge for water; the ordinary cost of smoothing
and leveling the land to allow of an even spreading of the water; and
the concentrated cost of reaching, from the head-gate, certain areas
of land which, being cut off by a depression, required embankment or
flume construction, or, being in a depression, required drainage. The



224 CLASSIFICATION OF IRRIGABLE LANDS

first two items were known, and the average cost of smoothing and
leveling was estimated.

The governing element in the basis of the classification, which
will be described in detail later, was the item of concentrated cost.

In making an estimate of the added returns of irrigation, it was
necessary, because of the lack of actual data for the district, to make
a very broad study of all the essential features, and these are dealt with
under the headings of "Climate", "Topography and Soil", and "Crops".

Climate. — The tract lies approximately 120 miles north of the In-
ternational Boimdary and 50 miles east of the foot-hills of the Rocky
Moiintains, and has a general slope from west to east. The elevation
of the western boundary is about 3 300 ft. above sea level and that of
the eastern end is about 2 900 ft.

The climatic conditions are very similar to those in Northern
Montana and the higher valleys of Colorado, where irrigation has
been practiced successfully for years. The average growing season
between spring and fall killing frosts (32° Fahr.) is about 101 days.

Tables 1 and 2 show the temperature and precipitation for Calgary
and Gleichen, which are nearly at the west and east ends of the tract,
respectively. The irrigation season extends from May 1st to Sep-
tember 30th.

Topography and Soil. — The topography is generally rolling, with
rather steep slopes which locally run up to 10 or 15 ft. in 100 ft. There
are many cross-drainage lines, and, in order to avoid expensive cross-
ings, the locators were forced to drop the elevation of the canals, thus
losing command of some of the higher and better lands. The topo-
graphy is somewhat smoother in the eastern than in the western por-
tion of the tract.

The soil conditions over such a large area, of course, have a wide
variation. Extreme conditions, varying from almost pure sand to
very hea^'y clay, may be found, but, speaking generally, the soil is the
usual clay loam commonly found on the prairies of the Northwest. As a
whole, the area is overlaid with a surface soil containing a good pro-
portion of humus, which proves very fertile. In general, the subsoil
is a heavy clay, making it imperative to apply the irrigation water
with care, in order to avoid water-logging the land. Local conditions
where the soil is heavily impregnated with white alkali are fotmd, but
black alkali is rare. As will be indicated later, great care was taken



CLASSIFICATION OF IKRIGABLE LANDS



225



TABLE 1. — Table of Precipitation and Temperature at Calgary,

Alberta.





Precipitation, in Inches.


Mean Temperature, in Degrees,
Fahrenheit.


Year.










Total for year.


Total for irriga-
tion season.


For year.


For irrigation
season.


1885


13.91


9.33


37.05


53.6


1886


11.32


5.98


38.04


56.2


1887


13.69


9.13


33.86


54.1


1888


17.51


11.39


35.15


54.6


1889


11.59


6.41


39.54


54.7


1890


14.94


10.86


35.68


54.5


1891


10.44


8.74


37.71


55.0


1892


7.91


5.13


36.13


53.6


1893


11.05


7.17


31.76


53.9


1894


11.71


8.02


37.17


55.3


1895


15.12


10.99


36.66


53.1


1896


16.05


8.12


36. (X)


55 6


1897


20.58


15.02


37.10


57.8


1898


15.. 58


11.84


37.80


56.6


1899


26.15


31.46


34.70


53.0


1900


17.57


13.18


38.60


54.1


1901


22.31


16.47


39.20


53.3


1903


34.57


30.75


37.00


52.7


1903


22.77


19.91


37.50


.52.6


1904


11.89


8.71


36.90


54.2


1905


14.12


10.03


39.00


54.6


1906


16.24


13.50


39.30


55.6


1907


14.96


11.48


30.70


52.66


1908


18.35


15.68


40.69


56.02


1909


16.03


11.98


35.97


55.78


1910


11.79


8.53


37.88


54.98


1911


19.38


15.08


35.67


52.68


1913


81.38


16.54


39.45


54.14


1913


17.08


12.85


39.94


57.08


1914


17.71


8.97


40.52


58.02


Mean for period..


16.43


12.07


37.29


54.67



TABLE 2.-



-Table OF Precipitation and Temperature at
Gleichen, Alberta.





Precipitation, in
Inches.


Mean Temperature, in
Degrees Fahrenheit.




Year.


Total for year.


Total for

irrigation

season.


For year.


For irrigation
season.


Remarljs.


1903
1904
1905
1906
1907
1908
1909
1910
1911
1912
1913
1914


15.83
10.22
11.94
17.73

"solsi

■"9.96


13.41
7.09
9.61

13.36

""i3".83
17.13

6.91
10.88

6.20
10.18

5.55


3

37.09
37.96
38.08

"34!62
40.18


'.55! 08
55.03
55.90

'54 .'90
55.82 r
57.08
53.56
55.06


Records not
complete.


Mean for
period....


14.36


10.38


37.59


55.30





326 CLASSIFICATION OF lERIGABLE LANDS

in the classification to exclude as non-irrigable any areas in which the
soil analysis showed this great enemy to irrigation to exist in dan-
gerous quantity.

Crops. — The leading crops in the Province are hard wheat, oats,
and barley. The hardier strains of alfalfa grow excellently under ir-
rigation, and small fields throughout the tract produce from 3 to 4
tons per acre in two or three cuttings. Experimental plot work
has indicated that a heavy yield of sugar beets, with a high
saccharine content, can be raised under irrigation. The irrigation
tract under consideration is so yoTing in development as yet that no
good general crop reports can be obtained. In the Lethbridge District,
about 100 miles to the south, however, there are about 15 000 acres
under the alfalfa crop which produce about 4 tons per acre under
irrigation.

For purposes of comparison, the following points are noted with
reference to this tract. The general elevation is about 2 850 ft. ; the
soil conditions are more favorable as regards texture and absence of
alkali; the annual precipitation is about 2 in. less; and the annual
mean temperature is about 4J° Fahr. higher.

The Dominion Government Experimental Farm at Lethbridge has
kept records of the returns from irrigated and non-irrigated crops
since 1908, and Table 3 has been compiled by using these actual returns
and inserting the prices which were obtained each year, f. o. b. cars,
at Lethbridge. This table must be accepted as showing results from
plots on the experimental farm, which are no doubt higher than those
obtained by the average farmer, but it is considered that the table
shows truly the relative increase due to irrigation. To be indicative
of the crops commonly raised im.der irrigation in the district, the
table should include alfalfa and timothy hay.

Basis of Classification Adopted. — The basis of classification adopted
was as follows: Land shall be classified as irrigable:

(1)- — If it lies at a lower elevation than the point of delivery,
after allowing a reasonable grade for a farm lateral.

The point of delivery shall be deemed to be a point 3 in. below the
crest of the measuring weir at or within the farm boundary. Where
this measuring weir is not at or within the farm boimdary, the point
of delivery shall be the elevation of full supply level in the lateral
supplying the field outlet, and all measuring weirs shall be built in



CLASSIFICATION OF IRRIGABLE LANDS 227

accordance with the plan of farm weirs filed with the Commissioner of
Irrigation and dated November Ist, 1908.

The grade of farm laterals, when a factor in land classification,
will be considered reasonable:

(a) Where the natural slope of the ground is less than 0.10 ft. in
100 ft. at a rate not less than 0.05 ft. in 100 ft. ;

(h) Where the natural slope of the ground is greater than 0.10 ft.
in 100 ft. at a rate of not less than 0.10 ft. in 100 ft. ;

(c) Where the slope of the ground is at or near the critical slope
of 0.10 ft. in 100 ft. at either of the grades mentioned in
clauses (a) and (&), such as good and reasonable practice
demands.

Extremely flat country may be irrigated by checks and flooding,
and the grade of the farm lateral need not be considered in such cases,
it being understood that the Minister of the Interior, or officers ap-
pointed by him, shall be the final judges of what constitutes "ex-
tremely flat country".

(2). — If such land can be reached by an estimated concentrated
expenditure at one or more points, for embankments, flumes, etc., not
in excess of $8 per acre for the land to be served and benefited through
them.

(3). — If such land can be served by a second or other delivery at
a cost not in excess of $8 per acre for the land to be served and ben-
efited through them.

(4). — When lying in a depression, if it can be drained at a cost
not exceeding $8 per acre, and is suitable, arable land which would be
benefited by irrigation.

(5). — The prices 'to be made use of in estimating the cost of em-
bankments, flumes, or other structures, shall be, unless otherwise
ordered by the Minister of the Interior :

Earth fill or excavation 12 cents per cu. yd.

Lumber in place on any structure $40 per 1 000 ft. b. m.

Rock rip-rap 50 cents per superficial yard.

(6). — In all unusual or exceptional cases, which are not covered by
the preceding paragraphs, the classification will be made by officers of
the Department, under the direction of the Minister of the Interior, in



228



CLASSIFICATION OF lERIGABLE LANDS



TABLE 3. — Records of Eeturns from Irrigated and Non-Irri-

AT Lethbridge, Alta.,



1908.


1909.


1910.


1911.




•d


>>9




•d


>-.5




•d


>»s




_■


>> =


>,


be





>>


I


j=.2


>.


S

M
i


^.2


>>


.1




Q


a a

■3.S?
0_^








•5.£f




a s

6?



Wheat,



Bushels, 34



0.00



27.55



35.15



12.81



29 I 14



24.76! 11.95



Hailed.





















Oats,


Bushels, 80


88


8


56


77


21


21


68


47


Hailed.


$28.00


30.80


2.80


18.34


25.22


6.88


5.67


18.36


12.69



Barley,



Bushels, 55



22.20



B.60 5.64



19.74



30



14.10



Hailed.



Potatoes,


Bushels, 92


235


143


159


605


446


103


521


418


356


560


204


$41.40


105.75


64.35


71.55


272.25


200.70


46.35


234.45


188.10


160.20


252.00


91.80



a fair and reasonable manner, and will be based on the beneficial use
of water.

Much attention was given to the question of the maximum slope
permissible for land to be classified as irrigable, but this was not in-
cluded in the official basis. The engineer in charge, in approving the
classification, was gmded by the rule that generally a maximum slope
of 10 ft. in 100 ft. was permissible, and where very small areas only
were concerned a maximum slope of 12 ft. in 100 ft.

As indicated under the heading, "Determination of the Basis for
Classification", the classification was based on a cost of $8 per acre,



CLASSIFICATION OF IKKIGABLE LANDS



239



GATED Crops at the Dominion Government Experimental Farm
Canada, from 1908 to 1914.



1913.


1913.


1914.


Averages.


>>

Q


1








^1

•5.SP


Q


•a




>>

a




^1

a c«




u


ot




b


25^




k<


Ol




t'


C5fc






^




'"'






"






"^





Ked Fife."



31


63


32


27


45


18


20


67 47


26


46


20


26.63


54.10


27.48


20.05


33.41


13.86


14.78


49.50


34.73


22.13


37.98


15.85



" Banner."



77


145


68


73


115


42


49


113


64


59


101


43


26.08


49.12


33.04


19.71


31.05


11.34


14.64


33.76


19.12


18.74


31.38


12.64



" Claude."



29


81


52


40


94


54


30 97


67


34.5


73.0


38.5


10.37


28.96


18.59


13.40


29.14


16.74


11.10


35.89


34.79


13.53


26.64


14.11



" Irish Cobbler."



133.20



501



225.45



205



92.25



229



528



237.60



299



134.55



400



180.00



232.75



95



43.75



234



105.10



492



258



221.46 116.36



but as this is a very crucial point, many details are given in order to
explain just what the figure means.

Under the conditions of its land sale contract and water agree-
ment, the Company delivers the water to at least one point on each
parcel of land, usually of 160 acres, and the cost figure was applicable
only to the added expenditure necessary for the farmer to distribute
the water over the land. The figure was not a general one applied to
the total irrigable area in each parcel, and including the ordinary
costs of leveling and smoothing the land, but was the concentrated cost
of reaching certain areas of land which, being cut off by a depression,



230



CLASSIFICATION" OF IREIGABLE LANDS



required embankment or flume construction, or, being in a depression,
required drainage.

The following study, which was made by the writer in examining
the cost data before the basis of classification was adopted, will make
the point quite clear.

Referring to Fig. 1, the area, A-D-E, can be easily irrigated with-
out any high expenditures for flumes, embankments, etc., and the $8
figure does not recognize any expenditure necessary for this area.
The area, R-J-K-L, is separated from the field outlet by a wide de-
pression, and it required a costly raised ditch and flume to carry water
from B ix> C. The basis of classification means that if the cost of
the raised ditch and flume from £ to C is less than a concentrated ex-

-Field outlet Elev.100.0




F^G. 1.

penditure of $8 per acre on the area, H-J-K-L, then H-J-E-L shall be
classed as irrigable. Again, the $8 figure does not recognize the
ordinary costs of preparation necessary for the irrigation of H-J-K-L
after the water has been conducted to C. Now, in truth, it would
require a certain expenditure per acre in smoothing the land, building
field laterals, distributaries, etc., to irrigate A-D-E, and similarly a
certain expenditure per acre would be required to irrigate H-J-K-L
after water had been conducted to C.

• In considering how much may be profitably spent in preparing land
for irrigation, it is usual to compute it at so much per acre for the
whole parcel of land, this figure including all flumes, embankments.



PLATE III.

TRANS. AM. SOC. CIV. ENGRS.

VOL. LXXXI, No. 1385.

PETERS ON

CLASSIFICATION OF IRRIGABLE LANDS.




13 UJ ill L



12i 'il



r T




■-e



CLASSIFICATION OF IRKIGABLE LANDS



331



ditches, etc., and also the smoothing of the land to allow of proper
irrigation.

The writer will now endeavor to show what the concentrated cost of
•$8 per acre means for diilerent cases, and for the average case, couched
in the usual terms, as explained in the foregoing paragraph.

If it is assumed that the average piece of land will require an ex-
penditure of $4 per acre for smoothing, ditches, etc. (there being no
clearing of any kind necessary in this district), and if this is com-
bined with the concentrated cost of $8 per acre, it is seen immediately
that the actual total cost of preparing any land which requires the
"concentrated" expenditure is really $8 plus $4, or $12 per acre. It
must be realized that in every parcel of land, considered as a imit,
there will be a varying proportion which can be prepared for irrigation
with an expenditure of only $4 per acre, and of other land which will
require in addition to this the "concentrated cost" expenditure of $8
per acre.

TABLE 4. — Cost per Acre for Structures and Preparation
OF Land for Irrigation.



to -a


£




eof
ring
ted
re.


"S


6
u
o




rt .


■3




6 w


1


o
o

o


Hxsarr


1"


01

ft
2


8

o


o ©

c3 a


18
2


9)

II


^•s


o
o


H


S|8S


'Z


o
O


Eh


C5





<


(!)


(2)


(3)


(4)


(5)


(6)


(7)


(8)


(9)


(10)


100


f4


$400








813





100


$400


$4.00


90


4


360


10


10


13


$120


100


480


4.80


80


4


820


20


20


12


240


100


560


5.60


70


4


380


30


30


12



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