The Archaeology of Irrigation Canals

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The Archaeology of Irrigation Canals, with Special Reference to PeruAuthor(s): I. S. Farrington

Source: World Archaeology, Vol. 11, No. 3, Water Management (Feb., 1980), pp. 287-305Published by: Taylor & Francis, Ltd.Stable URL: http://www.jstor.org/stable/124251Accessed: 10-06-2015 18:18 UTC

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2/20

The

archaeology

f

irrigation

anals,

with

special

reference

o Peru

I.

S.

Farrington

An

irrigation

canal is

a delicate

artefact,

designed

with

engineering

precision

to

transport

a required amount of water from source to field in order to maintain an adequate soil

moisture environment

in the latter.

Its

construction must be

exact,

because

lack

of

aware-

ness

of,

or inattention

to,

the

principles

of

open

channel

hydraulics by

either

builders or

operators may

result in

severe

erosional

or

depositional problems.

In

order to

achieve the

required

irrigation

amounts for

any given system,

the

specific

crop

requirements,

as well

as

conveyance

and

field

losses must

be

understood. Water

losses from

an

irrigation

system generally

occur

during

transport

(conveyance)

and

during

immediate

application

(field).

Conveyance

losses

comprise

both surface

evaporation

and

seepage through

the

canal banks

and

bed. These

may

be as

high

as

40

per

cent for

earthen

canals,

although

they

will

vary according

to

the

material of

the

bed

and

banks,

and

the local

climate.

Field losses comprise surface run-off, evaporation and percolation through the soil

profile.

Hence

these,

too,

will

vary

according

to

local

soil,

slope

and

microclimatic

condition.

Each

irrigation

system

therefore

has its own

specific hydrology

or water

balance. The

problem

of

defining

the

delicate

balance

between

velocity

and

discharge

must be

solved

at the

construction

stage,

or must

be

sufficiently

understood to

allow

a

canal to

stabilize

its bed and

banks

within

the

broad

limits of

a constructional

trough.

Thus the

construc-

tion,

shape,

form

and

gradient

of

an

archaeological

canal

provide

a valuable record of its

engineering

qualities

and

of the

hydrology

of

the

irrigation-agricultural

system.

Such

qualities

may

be

measured

by

using

the

formulae of

open

channel

hydraulics, although

in prehistoric times this knowledge must have been gained by trial and error. It is the

object

of

this

paper

to

suggest

field

techniques

and methods of

hydraulic analysis

for

an

evaluation of

prehistoric

irrigation

systems,

and

to

illustrate these

with

reference to

my

own field

researches

in

Peru.

Archaeology

and

irrigation

studies

Irrigation

canals

have

intrigued

archaeologists

for

many years

because

of

two

alleged

socio-political

and

economic

implications

of

irrigation

agriculture.

World

Archaeology

Volume

i

No.

3

Water

management

?

R.K.P.

I980

0043-8243/1103-0287 $1.50/1


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3/20

288

I. S.

Farrington

First,

the existence

of an

irrigation system

is

believed

to

imply

a

certain amount

of

labour

organization,

and

hence a certain

type

of

society.

This

is the

Wittfogel

hypothesis,

which has both evolutionary and functional implications for the organization of society

(Steward 1955;

Wittfogel 1957).

However,

in recent

years

this

hypothesis

has come

under

a

great

deal of

scrutiny,

both

by anthropologists

and

field

archaeologists,

so that it can

no

longer

be

considered

valid for

all

cases

(Adams

i96o, 1966;

Earle

I978; Farrington

I977;

Leach

I959;

Millon

1962).

The

second

implication

is that

irrigation

must

be

linked

with

an

intensive form of

agriculture,

on the

grounds

of

high

technological

and labour

inputs,

and because multi-

cropping

is

often assumed

to have been the

general

practice.

This stems from

the urban-

centric

view that

regards irrigation

as

a

major

technical innovation

to

improve

the

efficiency

of local

agricultural systems.

The

argument

generally

runs

that,

since

systems

are often spatially extensive and since irrigation requires much effort in construction,

maintenance and

operation,

then

inputs,

and

ultimately productivity,

must be

high

(Price

1971;

Myers

I974).

This

is

often

supported by

the belief that

irrigation

allows

year-round

cultivation.

This

kind

of

logic

is

nonsense.

Of

course,

there have

been

labour

inputs

which result in a

feature

in the

agrarian landscape

which

needs

to

be

maintained

periodically

in

order that

it

may

operate efficiently.

Yet,

at the

local

level,

are

these

inputs

any

greater

than

those

expended

in the

preparation

(and

tillage)

of

swidden

horticultural

plots? My

own

field

work

in

the Cusichaca

Valley,

Peru,

reveals

extremely

low

inputs

in

the

maintenance and

operation

of

an

irrigation

system.

The labour

expended

in

canal

cleaning

and

maintenance

during the dry season in the Cusichaca area is approximately i man

day

per kilometre.

The construction

of

diversion weirs

in the main

canal,

and the

opening

of

secondary

canals

for

irrigation,

is

only

a

five-minute task.

The

most

time-consuming

task

is

the

construction of the field distribution

network

during

the

preparation

of the field before

planting.

These

related

tasks involve an

ox-plough

and at least

two

men for a maximum

of one

day per

hectare.

The

supervision

of water distribution

in the fields

during irriga-

tion

has not been

measured,

but

is of the same order of labour

input.

This

seems

to be

borne

out

by

researches

elsewhere.

Furthermore,

the

occurrence of

canals

in

a

non-

agricultural

context in

aboriginal

California

does not

imply

intensification,

but

merely

land

management (Steward i930).

Even on

a

larger

scale,

irrigation

systems

are

really

only

extensive

in a

spatial

sense,

and the level of labour

input

by

a

community

is

not

necessarily any greater

than

those

in

a

small scale

system.

With

regard

to

multicropping,

this too

appears

to have

been

practised only

sparingly

in

the

prehistoric

world.

Crop

varieties which enable

a

traditional

farmer to

produce

more than one

crop per

annum have

only

recently

been

developed.

The

exceptions

to the

rule are

probably

sawah

rice in some areas of South-east Asia

and the

production

of wet

taro in South-east

Asia

and Oceania.

However,

a

great

deal

depends

on

the

reliability

of the water

supply,

and

the

traditional

technique

of

continual

cropping

during

a

single growing

season was

perhaps

much

more

prevalent,

both

in an

edaphic

and

hydraulic

systems

context.

Continual

cropping

is

a

widespread

traditional

farming practice.

Stated

simply,

it is

the

planting

at

different

times of a

variety

of

specially

adapted crops,

so that the

planting

season

may

extend

over

several

months.

As

a

consequence,

harvesting

will be

at different times. The

availability




4/20

The

archaeology

of

irrigation

canals,

with

special

reference

to Peru

289

of

irrigation

water

during

the

dry

season

in

Highland

Peru enables the

cropping

season

to

begin

earlier

in the

year (Farrington

1979).

Much of the archaeological literature on irrigation canals merely notes their presence

at

a certain

period(s)

and records

their association

with

sites.

It

may

describe or

even

classify

the

main features

of an

irrigation system

(Kus 1972;

Riley

1975;

Woodbury

1960;

Woodbury

and

Neely

1972)

but does

not

fully

elucidate the

technology,

hydraulics

or

hydrology

of the

canals.

Even where

excavations

into

canals have been

carried

out,

the

researchers have

not

used their

data to its

full

potential (Haury

I945;

Kus

1972;

Myers

1974;

Riley

I975).

Canal excavation

On

the basis of their

construction,

two

types

of

canal can be

distinguished:

lined and

unlined. In

many

respects

they present

similar

problems

to the

excavator. Stone and

cobble lined channels are

perhaps

the easiest

with

which to

deal.

Cobble

lining

is,

in

general,

applied

only

to canal

banks,

whereas

stone

slabs often form

a

complete bed/bank

lining.

It is

quite straightforward

to take out and record

carefully

all the

deposits

which

have infilled the

channel,

but

the critical area for

hydraulic

analysis

is

the

actual

lined

channel

itself.

It

is

unlikely

that such a channel would

have

been allowed

to silt

up

greatly during operation,

and hence

the stone-lined channel itself

should reveal

the

hydraulic

characters of that

particular

reach.

It

is

also

important

to

trench

the

banks

and excavate below the

lining

in case there are

vestiges

of former

stone-lined or

earthen channels.

Bank

deposits

may

reveal

silt

lenses from the

periodic

cleaning

of

the canal.

In the excavation of

unlined

or earthen

canals,

the

whole area

of

cultural

disturbance

must

be

trenched

and

recorded.

The

bed and

banks of such

canals are

subject

to

normal

fluvial

processes

to a

greater

extent than

for

lined

canals,

and hence the

profile

of

the

channel or channels needs to be

carefully

recorded.

A

reduction in

discharge

may

result

in a

composite

canal form characterized

by

berms

(Blench

1957; Farrington

and Park

1978).

Meandering

may

produce

an

asymmetrical

cross-section which

is

deeper

on the

outside

of the

bend,

or

a series

of berm

deposits

on

the other

(Farrington

and

Park

1978,

fig. 2e).

Silt

deposited by

a

relatively

efficiently

flowing

canal will

be thin

(o-I-Io cm.),

and

periodic cleaning

will often

reduce

this to a

minimum.

However,

a

period

of

disuse

may

result

in

the

filling

of

the canal

trough by

aeolian

material.

Subsequently,

a

new

canal

may

be cut into

the

aeolian

deposit,

and

this

composite history

of

operation

and

re-use

may

be

recorded

in

a

series of

thin

channel

perimeter

silts

separated

by

several

centimetres

of

sand

(Farrington

and Park

I978,

figs.

2d;

2e).

In certain

cases,

deflation

and

trampling

may

remove all surface

vestige

of a channel. In this instance

it is

necessary

to remove the

topsoil

and

progressively

excavate each channel

from

the truncated silt

lines,

working

outwards from the centre

(Farrington

1972).

The excavation of a single trench across a canal is inadequate. Groups of trenches must

be

dug

no

more

than

Ioo

m.

apart,

in order

that the

relationship

between

the

various

channels can be

understood

and the

gradient

of the channel floor

measured.




5/20

290

I. S.

Farrington

Technology,

hydraulics

and

hydrology

The constructional

details of coastal

Peruvian

irrigation

devices

have

been

reviewed

else-

where

(Farrington

1974)

and need not be discussed

within the

context of this

paper.

Suffice

it to

say

that Peruvian

irrigation

systems

were of the

continuously

flowing

type,

and

were

regulated

only

at

the

field intake.

The

transfer

of water from river to

field

by

means of a

continuously

flowing

canal net-

work

involves an intricate balance

of

supply,

demand

and

constructional

ability.

The

construction

technology

of canals and

other

irrigation

devices is

therefore critical to the

efficient

operation

of a

system,

for

a

canal must

be built

precisely

to

carry

a

set amount of

water

at

permissible

velocities with

little or no

damage

to itself.

However,

in some

cases,

a

canal

may

be

required

to

carry

less than it could

theoretically

accommodate at

maximum

flow. Then, through normal fluvial processes of sedimentation, it would tend to form a

new

stable

bermed

channel

within

the

original,

which would

carry

the

required discharge

more

efficiently.

In some

cases,

erosion

of a new

channel

appears

to

have

taken

place

within

the overall

trough

as the canal seeks

to stabilize at a new

discharge

capacity

(Farrington

and Park

1978).

Thus,

very

accurate

surveying

is

essential in

any hydraulic

analysis.

Each

silt

layer

of

a

cross-section

must be

surveyed

at intervals of not more than

20

cm.

across

the

channel,

and at

every

break

of

slope,

in

order that its

precise configura-

tion

can

be determined. The

gradient

between

corresponding

levels

in

adjacent

excava-

tions

can

then be calculated. For

stone-lined

canals in the Andes it

is

possible,

with

very

little

cleaning

out,

to

survey

cross-sections

every

50

m. or so

to

achieve

a

complete profile

of the changing hydraulic parameters along the length. It is important that attention be

paid

to

detail,

particularly

with

regard

to minor breaks

of

slope

which

may

represent

a

depositional

or erosional

berm,

because

these

may

be critical

in the

analysis

of

the

opera-

tional

history

of that

particular

section.

The

hydraulic

variables,

velocity

and

discharge,

can

then be calculated

for

each cross-section

and

for each channel indicated within

it.

The

principles

of

open

channel

hydraulics,

as outlined

by

Chow

(i959),

indicate

that

the

velocity

and

discharge

of canals

may

be

conveniently expressed

by using

the formulae

of uniform

flow. Most

prehistoric

canals were

relatively simple

constructions and avoided

very

steep

slopes,

weirs,

etc.

In

an

archaeological

context canals have

been

analysed

in

this

way by

Jones,

Blakey

and MacPherson

(1960);

Garbrecht

and

Fahlbusch

(I975);

Busch, Raab and Busch (1976); and Farrington and Park (1978).

Velocity

In this

case,

velocity

(v)

is

the mean

speed

of

water

(m. sec.-')

flowing past

a

given

point

in

a

canal.

Within the

concept

of

uniform

flow

it

is

believed to be constant

along

any

particular

reach of

constant

slope.

Velocity

is a critical

measurement

because

it

indicates

whether

the canal

is

prone

to erosion

or

deposition

at that

point.

It

may

be

calculated

by

using

one

of

a number of

formulae,

of

which

two are

most

commonly

employed.

The

Chezy

Formula

was the first

developed

in uniform

flow

hydraulics

in

1769

and

is expressed as follows:

V= ___*r.s

\/3

28




6/20

The

archaeology

of irrigation

canals,

with

special reference

to Peru

291

where

V

is the mean

velocity (m.

sec.-1);

r

is

the

hydraulic

radius,

which is calculated

by

dividing

the channel cross-sectional area

(A) by

its wetted

perimeter (WP),

i.e. the cross-

sectional perimeter of bed and banks in contact with the flow, so that r =Al WP; s is the

gradient,

normally

of the

water

surface

along

the

canal,

but

for excavated canals

the

bed

slope

is

acceptable;

and C

is

the

Chezy

factor of flow resistance.

C

has to be calculated

by

using

one of a number of

formulae,

of which the

one

by

Bazin

has

been used

archaeologi-

cally by

Jones,

MacPherson and

Blakey

in their examination of

the

flow

chracteristics of

the Dolaucothi

Roman

aqueduct

in

Wales

(1960).

All of the

formulae for the calculation

of

C

contain

a

coefficient

of surface

roughness

which has been

derived

experimentally.

The

two

stage

calculation

of

velocity

using

the

Chezy

formula is

unwieldy

and

it is

perhaps

more beneficial to utilize

the

single

formula derived

by

Manning

(I891)

from

the

Chezy

equation,

using

a

range

of

values for

n

determined

from Bazin's

experimental

data and his own verifications

(Chow

1959: 99;

Barnes

1967).

For metric measurements

the

Manning

formula

may

be

stated thus:

I

2 1

V=

-rls-

n

where n

is the

coefficient

of

surface

roughness,

which

serves

to

retard

flow.

In

general

canals

whose bed and banks are of

fine

grained

sand or

silt

have a

low value of

n,

in

contrast

to those of coarser material such as

gravel

or

cobbles. Values of n have

been

experimentally

established

for a whole

range

of artificial and

natural channels

(table

I;

TABLE I

Selected

values

of

the

roughness

coefficient

n.

(After

Chow

1959,

pp.

111-13;

Barnes

1967)

Type

of

channel

bed and banks n

Gravel

bottom

with

sides of

random

stone

00o23

Gravel

bottom

with

sides of

dry

rubble

oo033

Cemented rubble

o0025

Dry rubble 0.032

Dressed

ashlar

o.OI5

Earth/gravel

anal

-

straight

and uniform

0'025

Earth/gravel anal-straight

and

uniform

with

vegetation

0-027

Earth/gravel

winding

0'025

Earth/gravel winding

with rubble sides

0-030

Rock

cuts

-

smooth

0-035

Chow

1959;

Barnes

1967).

Naturally,

the value

of n

will

be

altered

during

deposition

or

erosion,

and

also

by

the

growth

of

vegetation.

The

angle

of bends

within

a

canal will

also

affect the value. Perhaps

the most

important aspect

of

surface roughness is that, if the

channel

flow

is

relatively

shallow,

then the

roughness

of

the

channel

bed is

emphasized

within

the

moving

water

and serves to retard

it. The

value

of n

in

these

instances is

thus

greater.

The

Manning

formula

has

been

used

quite

successfully

in

the

analysis

of canals




7/20

292

I.

S.

Farrington

in the Moche

Valley

(Farrington

and Park

I978).

A

sample

calculation

is

given

in

the

Appendix.

The velocity calculated by applying Manning's formula may then be compared with

experimentally

derived values

of

permissible

velocity.

The

maximum

permissible

velo-

city

of a canal

is

the

highest

speed

of

flow

possible

without

large

scale

scour,

and it is

a

function

of

the nature of the

bed

and

banks

and the

sediment load

of the

canal.

Fortier

and

Scobey

(1926)

have

published

tables of

maximum

permissible

velocities for

various

types

of

canal

carrying

different sediment

loads and

flowing

less

than

O-9I

m.

deep

(table

2).

Above this

velocity,

canals

will be

subject

to scour and

erosion;

however

these authors

TABLE

2

Permissiblecanal

velocities.

(After

Fortier and

Scobey

1926,

p.

955)

v

(m.

sec.-)

-for

water

carrying

Original

material

excavated

for

canal colloidal silts

Fine sand

(non-colloidal)

o076

Sandy

loam

(non-colloidal)

o076

Silt loam

(non-colloidal)

o-91

Alluvial silts

when

non-colloidal i

.o6

Ordinary

irm

loam i

o6

Volcanic ash

I

o6

Fine

gravel

1532

Stiff

clay (very

colloidal)

1-52

Graded,

loam

to

cobbles,

when

non-colloidal

1-52

Alluvial

silts

when

colloidal

1'52

Graded,

silt to

cobbles,

when colloidal

ir68

Coarse

gravel

(non-colloidal)

x-83

Cobbles and

shingles

i.68

Shales and hard

pans

1.83

Hard

rock

4.0o6

state that an old established canal can tolerate

slightly greater

velocities than a

newly

dug

one.

Naturally,

earthen canals

will erode

at

lower velocities than those which

are

lined,

although

cobbles

are

more

prone

to

erosion than

granite

slabs. For modern

earthen

canals

on the north

Peruvian

coast,

Perisutti

has

estimated that o-8

m. sec.-1

is the maximum

permissible

velocity, although

for

canals

dug

in the coarse

gravels

of

Quaternary

outwash

plains

a

maximum in

the order of

1-5

-

1.8

m.

sec.-1

seems more

appropriate

(Farrington

and Park

1978).

The

minimum

permissible

velocity

is

just

as

critical

to

the efficient

operation

of a

canal

system.

In

general,

it is

difficult to calculate

the

velocity

below which a canal

will

start

silting,

encouraging

the

growth

of

vegetation.

Chow

(1959:

I58)

has estimated

this

to be

between

o'6I-o.9I m.

sec.-1,

whereas

Perisutti

(pers.

comm.

1977)

has

suggested

that

0-45

m.

sec.-l would

be more

appropriate

for the

earthen canals

of

the north

Peruvian

coast.




8/20

The

archaeology

of

irrigation

canals,

with

special reference

to Peru

293

Thus,

by

careful measurement

of

the

cross-sectional

area of

each

significant

berm

within the

canal,

and the canal

bed

slope,

it is

possible

to estimate the

velocity

of

that

channel and to make statements concerning the stability and efficiency of its hydraulic

section.

The

importance

of this

cannot

be stressed too

heavily,

for

it

provides

the

archaeologist

with

a measure of the

awareness

that

ancient

farmers

and

engineers

had

of

the

principles

of

hydraulics.

Discharge

The

velocity

of the water

within

the canal is

intimately

related

to

the

depth

of

water

transported,

and hence

to

discharge,

Q. Discharge

is the

amount

of

water

passing

through

a

given

cross-section

at a

given

time and

is

measured in

m.3

sec.-l.

It

can be calculated

from the relationship: Q= A. V.

The

discharge

of a canal can be

thought

of

as

equalling

the

product

of

the water

requirements

of

the

crop

or

crops

and

the

field

area,

plus

conveyance

and field

losses

through

seepage

and

evaporation.

Thus

it is a

fairly

sensitive

measure

of

a

farmer's

perception

of the

hydrology

of

his

agriculture.

The

study

of the Vichansao

canal and

of

irrigation requirements

in

the Moche

valley

has demonstrated

quite

clearly

the

sophistic-

ation

with which the

hydraulic

and

hydrological principles

in the

operation

of that

system

were

understood

(Farrington

and Park

1978).

As

discharge

is

increased to

satisfy

increased

demand,

the canal constructor

is

faced

with two

engineering

possibilities.

Either

he

can

construct a new

larger

canal

which

will

be capable of carrying the new discharge at permissible velocities, or he can try to

increase

discharge

within

the

same canal.

In

the

latter case he will increase the

depth,

and

thus

velocity

will tend

to be increased.

This

may

take the

canal

velocity

over the

permis-

sible

limits

and

hence

scouring

may

occur.

This

may

result in either lateral

erosion of

the

banks or

scouring

of the

bed,

or

both.

The

various

berms

noted

in an excavated

cross-

section

may

assist

in

the elucidation

of such

a canal

history.

If

the maximum

permissible

velocity

is not

reached,

then a

new

stable

hydraulic

section

may

be

formed

by

deposition.

Similarly,

when

the

amount of

required discharge

is

reduced,

or

is

smaller

than that

capable

of

being transported

by

the

channel,

then

sedimentation

may

occur

and berms

may

be

deposited

(Blench

I957).

Thus it

is

possible

to

elucidate

through

the

analysis

of

a

series of cross-sections the

operational history

of a canal, and to obtain through calcula-

tions

of the

discharge

a

measure of the

downstream

requirement

for

irrigation.

In

the

absence of

modern

studies,

this

may

be

the

only

measure available.

The

concept

of

critical flow

The

formulae

of uniform

flow are

only

useful for

the

analysis

of

canals

of

fairly

uniform

shape, gentle

and

regular

slope,

and which run

straight

or in

wide,

gentle

curves. Not all

canals

possess

the criteria

which

render

them

totally

amenable

to

this

type

of

analysis.

Changes

in canal

shape,

gradient

and

layout

occur

frequently,

and have a

profound

impact

upon

the

hydraulic

parameters

thus

far

identified. Flow

becomes

unsteady

and

gravity

waves

are

produced,

which

may

be

propagated

either

upstream

or downstream




9/20

294

I. S.

Farrington

according

to

the state

of

flow of the canal.

Thus,

it

is

important

to introduce

the

concept

of

critical

flow,

which describes the effect of

gravity

on the

state of

flow.

It

may

be

represented

by

the

ratio between

inertial

and

gravity

forces

and is

recognized

by

the

Froude number, which is usually given by the following formula:

F-g.

Vg.D

where

g

is the

acceleration due

to

gravity

and

D is

the

hydraulic depth,

i.e.

the cross-

sectional

area

of a

channel divided

by

its width at the

free

surface

(W),

so that

D

=A/

WV

For

rectangular

channels,

the

depth

(y)

of flow

is

normally

used in

place

of

hydraulic

depth.

When the Froude number

is

equal

to

I,

the flow

is

said

to

be

in

a critical state.

This

means

that the

specific energy

within

the

channel

is at

a minimum for a

given

discharge,

and the discharge is at a maximum for a given specific energy; the velocity head* is

equal

to

half

the

hydraulic depth

in a

gently sloping

channel

(Chow

I959: 63).

Thus a

canal

at the critical state

will have a

uniform

depth

at a

given

discharge (i.e.

critical

depth),

and

the

slope

of the channel

which maintains

this

state of flow

is

known

as the

critical

slope.

At or near the critical

state,

flow

is

unstable,

which means

that

any

change

in

specific energy,

i.e.

change

in

slope

or direction of

canal,

will cause

major

depth

changes.

Thus

a canal

flowing

at or near

the

critical

state must flow in a

straight

channel

at a constant

(i.e.

critical)

slope,

in

order

to

carry discharges approaching

bankfull.

When the Froude number

is

less

than

i,

the flow

is

regarded

as

sub-critical.

Velocity

is

lower

than in

the critical

state and the

depth

is

greater.

In this state

gravity

forces

are

dominant.

Gravity

waves are

always propagated

upstream

since their

celerity

is

greater

than the

velocity

of

flow.

Supercritical

flow

is

indicated

when the Froude

number

is

greater

than

i and the

forces

of

inertia are

dominant.

This

state

has

higher

velocities

and lower

depths

than the

critical. In this case

any

disturbance

within the channel

slope, shape

or direction

will

produce

gravity

waves

which will increase the

depth

of water and be

propagated

down-

stream

quicker

than the

velocity

of flow. Such

a disturbance

will also

produce

a

hydraulic

jump

in the

channel which serves

to

dissipate

energy,

reduce

velocity

and increase

the

flow

depth

downstream

(i.e.

the

sequent

depth).

Thus

at

a

Froude

number

of

2,

the

sequent depth

is

I.6

times

greater

than the initial

depth.

Thus a

canal

in a

supercritical

state cannot flow at bankfull in the

uniform flow sense

of the

term.

Discharge

will be

adjusted

to ensure that

there

is

no overbank

spillage.

The level of

agreement

between

the

computed

hydraulic

variables

and

the

hydrology

of

irrigation agriculture

within the Moche

valley suggests

that the state

of

flow

in the

Moche canals excavated was subcritical

(Farrington

and Park

I978).

The

importance

of

the

concept

of critical flow to

prehistoric

irrigation

canal

research is best illustrated

when

the

question

of

moving

water down

steep

slopes

is

considered.

*

Velocity

head at a

cross-section

is

equal

to

the

square

of the mean

velocity

divided

by

twice

the acceleration due to

gravity.

It is

important

in

calculating energy

loss and

also in cases

where

velocity is non-uniform and supercritical.




10/20

The

archaeology of

irrigation

canals,

with

special reference

to Peru

295

The

problem

of

moving

water

down

steep

slopes:

two case studies

from

Peru

The

relationship

between

required discharge

and

permissible

velocity

is

most

graphically

seen when solutions to the

problem

of

transporting

water down

slopes

are

considered.

Prehistoric

canals

in

many parts

of the

world

are

constructed to flow down

gradients

rarely

greater

than

2

per

cent. The

prehistoric

engineer

went to

great lengths

to

construct

tall

aqueducts

against

hillsides or

across

valleys

in

order to maintain

a

gentle

gradient.

If the

slope

is

steepened,

the

whole

range

of

hydraulic

properties

at

a

given

discharge

is

altered

to such

an extent

that local

erosion

and

scouring

may

occur

and/or

the flow

becomes

supercritical,

and

there

is

spillage

as well. This

must have been

recog-

nized

by

prehistoric

engineers,

albeit

empirically,

in

order for

them to

adapt

their

constructions to accommodate

the

problems

introduced

by

the

slope.

Various solutions

to

problems

of

slope

can be illustrated

by

reference to

the author's

work

in

both the

Moche

and

Cusichaca

valleys.

These

studies

reveal an

acute

awareness

by

the

prehistoric

engineer

of the

velocity/discharge

relationship

and

of the

overriding importance

of

the

nature of

the

material

forming

the

bed and

banks.

In

the Moche

valley,

excavations

in

three

types

of

location

demonstrate

quite

clearly

the

variety

of solutions and

the

difficulties

encountered with

them. These locations

are:

main

supply

canals

within

field

areas;

major

conveyance

canals;

and

terrace distribution

systems

(fig.

I).

Figure

I

Location

of

excavations

and

principal

canals

in

the

Moche

Valley

The

analysis

of

excavations

within

the main

supply

canals of

two

field

systems,

Esperanza

and

Pampa

de Huanchaco

(fig.

2a),

reveals an

ingenious, yet reasonably

well




11/20

296

I.

S.

Farrington

understood,

method of

transporting

discharges

down

relatively steep slopes (I-2

per

cent).

In

both

cases the canal

trough

was

dug

into the

pampa

soils

of sand and

gravel-

sized material, slightly wider and deeper than necessary. The original channel could have

carried a

discharge

of

between

1-3-I-6

m.3

sec.-1

but

at

a

velocity capable

of severe

erosion,

2

m. sec.-1. In

each case the

discharge

required

was

about

045

m.3

sec.-l

but

a.

Huanchaco

HVT8

0 I

0

l

m

b. VC

0

_

m

b. IVC

E

Figure

2

Selected

cross-sections

of Moche

Valley

excavations

the

velocity

of the excavated

canal

still

approached

that

capable

of

erosion

(I'6-ix8

m.

sec.- ).

It

appears

that the canal was

permitted

to downcut a channel with a

slightly

larger

discharge

before

the

required

amount was sent down

in,

what was for

it,

a

relatively

stable

hydraulic

section.

However,

the Froude

number for these canals is in the

range

o075-Iz*.

Hence

any

obstruction

within the

channel

would have

produced

surface

waves

and

overflow

along

the

berm.

For the most

part

these

canals are

straight,

although

the

effect

of

bridges (i.e.

Inca road

walls)

on

the

Pampa

de

Huanchaco could have had severe

effects

lower

down

the

system.

It

is believed

that

channel

widening

or

ponding

immedi-

ately

before

the

bridges

reduced the

flow

to a

subcritical state and hence an

overspill

wave

was

not

produced

as the canal

passed through

the

channel

constriction.

It

is understood

that the

now

sand-filled,

2 m.

wide,

stone-rimmed

trough

carrying

the

Vichansao

down

a

1-93

per

cent

slope

to

the

Pampa

de

Huanchaco

was constructed to

allow

the

canal

to

self-adjust

its channel in order

to

carry

the

0-5

m.3

sec.-l

required

discharge efficiently.




12/20

The

archaeology

of

irrigation

canals,

with

special

reference

to

Peru

297

Exactly

the same solution

appears

to have

been

attempted

in

the construction

of

the

Intervalley

conveyance

canal from Chicama to Moche.

The location

5

excavations

(Kus

1972) were trenched across a gently curving (and hence in hydraulic terms straight), and

steep

(I'43 per

cent)

length.

A

canal

trough 7

m.

wide and

2-4

m.

deep

was

initially

constructed

for an estimated

discharge

of

only

2'2

m.3

sec.-l

(fig. 2b).

However,

a

channel

of

this

size would

have allowed a

velocity

of

2-68

m.

sec.-l

for this

discharge,

and

hence

it

would

have been scoured.

Farrington

and

Park

(I978)

have

analysed

this

cross-

section

and

suggest

that the

lower channel

(FB)

was

the result of an

initial

attempt

to

achieve the

correct

discharge.

At

bankfull

it

appears

to have

had a

capacity

of

2-05

m.3

sec.-1,

but

with a

velocity

still

above the maximum

permissible

for a

channel

cut into the

outwash

sands and

gravels

of

the Rio

Seco.

Thus,

a third bermed channel

(B)

appears

to

have been

scoured,

which became

hydraulically

stable,

having

a

velocity

of

I-5

m.

sec.-l,

i.e. 39 per cent of the requirement.

Artificial

terracing

is

a

common

feature

of the

prehistoric

landscape

of both

Highland

and

Coastal

Peru.

Narrow

bench

terraces

with

dry

stone walls

are characteristic

not

only

of the

Inca

period,

but

were

almost

certainly

built to a

small extent over

2,000

years

earlier.

Many

of these

systems

are

irrigated

from

either a

supply

canal

or

spring.

The

technology

of

transferring

water to the first

terrace,

and from terrace to

terrace,

is

relatively straightforward,

but

again

involves

a

delicate

balance between field

require-

ments and

discharge.

In

1972

I

excavated

a

number of trenches to establish the

operational history

of

canals

and associated terraces

on Cerro

Orejas,

a

steep

mountain

about

25

km.

from

the

Pacific

coast in the Moche valley. These excavations were mainly in the supply canal and sur-

viving

offtake

structures

which

diverted water to the terraces.

These

revealed a

very

sophisticated

technology

for the

transference

of

very

small

discharges

as free

overfall onto

the

terraced

fields. The main

canal flowed at a

fairly gentle grade

above

the

fields

carrying

a

discharge

of

c.

o0

I-0o2

m.3

sec.-1,

and

at distances which

varied

from

30

to

40

m.

along

it

there

were

narrow,

straight,

stone-lined

offtake

channels

which

took a small

amount of

the

discharge through

the canal bank and to

the

edge

of the wall above

the first

terrace

(fig.

3).

The

offtakes are

in

general

20-30

cm. wide and would have diverted

a

discharge

in

the

order of

oo003

m.3

sec.-1 which

was

probably

never more

than

3-5

cm.

deep.

At the

edge

of the

terrace the

water

was

allowed

to

spill

over

as

a free

nappe

and was

probably

collected in a trough or canal in front of the base of the wall. There it was distributed to

the field

or

sent down to

the

next

terrace. There

is,

on

Orejas,

no

surviving

evidence

of

such a

structure

because of the amount of

destruction

of the

system.

The

height

dropped

over

each terrace was never more than

2

m.

on

Cerro

Orejas,

although

in

the

Cusichaca

valley

an

Inca

terraced

system

still in

use

has an offtake canal which

drops

water

approxi-

mately

4

m. from one terrace to the

one

below.

Although

free

falling

water will

accelerate

due

to

gravity

and

may

cause scour at the

collection

point,

the

use of

granite

for the

canal

and

trough lining,

plus

the

small

discharge

requirement,

would

reduce the amount of

erosion

considerably.

Cook

(I916)

has described three Inca methods

of

taking

water

onto

terraced

systems

in

the

vicinity

of

Ollantaytambo:

by

narrow vertical channel down the face; over

upright

stones

and

into

basins;

and

between a double row

of

stones.

The

first

would be

suitable

for

very

small

discharges

indeed,

perhaps

in

the

order

of

o.i

to

0.5

1.

per

second

(i.e.




13/20

298

I.

S.

Farrington

ooooI

to

00ooo005

.3

sec.-l);

the

second is that

described

for

Orejas;

and the

third

appears

to be the

description

of

drainage

channels

common

on

such

terraces

in the

Andes.

Highland systems

of

irrigation

are

on a much smaller scale than those of the coast for

two reasons.

First,

the

rugged

terrain offers

little

extensive,

gently

sloping

land

suitable

for

irrigation

agriculture.

Secondly,

there is

a

marked

wet

season which obviates the

need

Figure

3

Cerro

Orejas

canal

and

spillway

to terraces:

(a)

cross-section;

(b)

plan

for

much

irrigation.

Hence,

irrigation

offers a

valuable

supplement

to rainfall

during

the

growing

season and

in

places

does serve to extend

the cultivation

year by enabling

certain

crops

to be

planted

earlier.

Thus,

the amounts of water

needed are small.

However,

in

contrast

with the

major systems

of

the

coast,

the

technology

of

moving

water

down

slopes

is far more sophisticated. Suitable and reliable water sources are often located several

kilometres

in

distance and several hundred metres

in altitude

from

the field

area.

High-

land

technology

may

be illustrated with reference

to

ongoing

research undertaken as

a

member

of

the

Cusichaca

Project

in the Cusichaca

valley,

Provincia

Cuzco.

The

Quishuarpata

canal

is a

small,

granite-lined

channel,

never

more

than

80

cm.

wide

and

30

cm.

deep. Fairly

flat,

well

cut,

but

irregularly

shaped granite

blocks

have been

fitted

together

to form the canal floor

and others

placed

upright

as the

channel

sides,

thus

forming

a

good

rectangular

to

trapezoidal hydraulic

section. The

complete

bank

structure

comprises

a double faced

granite

wall infilled

with

gravel

and small

stones. The

canal

itself

is derived

from

the

Rio

Hualancay

at

an altitude

of

c.

3,500

m.

and

its main

task was

to

supply

a

relatively

small

discharge

to two small field systems at Quishuarpata (c.

2,900

m.)

and

Hawa

Huillca

Raccay

(c.

2,700 m.)

and to a

number

of

Pre-Inca and Inca

archaeological

sites

including

the fort at

Huillca

Raccay

(fig.

4).

The canal also

received




14/20

The

archaeology of

irrigation

canals,

with

special

reference

to Peru

Figure

4

Location

of excavations

and

chutes

on

the

Quishuarpata

anal,

Cusichaca,

and cross-

sectionof Trench TQx

supplementary

water

from

three

small mountain streams

through

which

it

was con-

structed.

The total

length

of

the canal to

the

head

of

the Huillca

Raccay

fields

is

approxi-

mately

6 km.

This

is

a net

gradient

of

about

13

per

cent.

For

the most

part

the

canal

maintains

a

gradient

of between

5-15

per

cent,

but

there

are,

at the

approach

to

both

field

systems,

two

short,

but

very steep

chutes with

gradients

in

excess of

40

per

cent.

The

first chute

falls

vertically

for

2'5

m.

through

a

split

rock and then

descends a

further

51

m. for an

average gradient

of

43

per

cent

(fig. 5a).

This chute was remodelled

at

some

stage

in

prehistoric

times because

it had

initially

been

built within an

active

springhead.

The second

drops

a total of about

93

m. in two

stages (2A, 2B),

whose

average

gradients

are

64 per

cent

and

60

per

cent

respectively,

and these are

linked

by

a

short

I-5

m. cross

slope

channel

whose

slope

was

only 15 per

cent. A

detailed

survey

of

this

chute

has revealed

that

in

fact

the

gradient

actually changes

quite

markedly

within

very

short

distances.

On the

lower

part

of the

chute

(2B),

subtle

changes

can

be

noted in the

canal bed

slope

from

74

per

cent to

31

per

cent.

This

gives

the

impression

that the

canal

was

built as

a

flight

of

very

steep,

narrow

steps.

This

feature was also noted

in

part

of

chute I.

Surface

evidence

on the

slope

itself

reveals that the

lower

slopes

of both

chute locations

were

formerly

terraced

but

that these had

fallen into

disrepair,

probably

as a result

of

active

slope

processes

before

the canal

chutes were

constructed.

In

both chutes there is

no

evidence

of a

stilling pond

at the

toe and

there is no

apparent

fluvial erosion of

the bed or

banks.

At the

toe,

the

gentler gradient

would serve as a

hydraulic

jump

as

the canal

was

299




15/20

300

1. S.

Farrington

'2A

2E

A

m

0 10

20 30

,

I

m

cm

0

0C

20

30

b.

Cross-section

at

A

Figure 5 Quishuarpata canal Chute 2

turned

through

a

sharp

angle (90-115?).

The

question

is;

how

was this achieved with

such

efficiency?

The

first

step

in

unravelling

the

mystery

was

to calculate

the

main

hydraulic

parameters

of

the

canal

in the

reach between

its last intake

and

the head

of

chute

i.

A

series

of

three

trenches were

excavated

and

surveyed

along

the

length.

They

show

a

granite-lined

trapezoidal

channel

about

70

cm. wide

and

zo

cm.

deep,

perched

on a man-made

ledge

on

a

50

per

cent

slope.

Along

this

reach the

average gradient

was

quite

steep,

5

per

cent.

If it

is

assumed that the canal flowed at

bankfull,

then

the

estimated

velocity

would be

2'53

m.

sec.-l which is within the

permissible velocity

limits for

granite.

Bankfull

discharge

has

then been estimated to be

o0375

m.3 sec.-~.

The

Froude

number

for

the

length

is

273

and

thus the flow is

supercritical.

Hence

any

obstruction or curve

in

the canal

would

create a

wave

surge,

and

if

the

canal

were

flowing

at

bankfull,

there would be substantial

spillage

and

discharge

would be

adjusted accordingly.

This

particular

channel reach

is

quite

sinuous,

and

thus

waves would have been

created

in a

situation of

supercritical

flow.

It

is

possible

to calculate the

height

these

waves would have

attained

above normal

depth

by

using

the

following equation

(Woodward

and

Posey 194I:

II9):

V2 0D=- sin2 (--)

g

2

where

g

is

the

acceleration due to

gravity,

f

is

the wave

angle

and

0 is

the deviation

angle




16/20

The

archaeology of

irrigation

canals,

with

special

reference

to Peru

301

of the curve

and

represents

half the

wavelength

of the

disturbance. These

angles

can

be

readily

derived

from

simple

equations

(Woodward

and

Posey 1941;

Chow

1959:

45I-3; see Appendix). It is possible therefore to calculate D for each progressively

shallower

depth,

until

the

point

is

reached

at

which the increased

height

caused

by

the

wave

is

equal

to or less than the

height

of

the

banks.

Thus,

irrespective

of the

Froude

number,

the

discharge

will

stabilize at that

figure.

For this

particular

reach of canal the

radius

of

curvature

is

rarely

more than

30

m.

and

thus the stablized

discharge

is

esti-

mated to be

O'I2175

m.3

sec.-1.

The normal

depth

of the channel

is

9

cm.

and

the

wave

height

9-1

cm.,

giving

a combined

height equal

to

the

height

of the

right

hand

bank.

The

velocity

of

the canal is

2-5

m.

sec.-l

It must be

stressed that

this is

the

maximum

possible

flow

for

this

particular

reach

and

it

is

more than

likely

that the

canal

was maintained

at

this kind of

discharge

to

the head of the chutes.

The means by which water was diverted through a small intake channel to the head of

chute I

is

poorly

understood at

present.

It

is

believed

that some form of

hydraulic

jump

was

constructed

just

before

the inlet to

check

velocity

and

increase

depth

and

that

part

of

the flow would then

be

diverted

quite easily

into

a basin on

top

of the

split

rock.

The hole

in the

rock could

then act as a

metering

device to

control

the rate

of

flow down the chute.

Research

is

still

progressing

on the

hydraulics

of

this

feature.

In

the

hydraulic

analysis

of

chutes the

Manning

Formula

cannot be

applied

because it

was derived for uniform flow

in

relatively

gently sloping

channels.

Water

flowing

down

steep slopes

is

always

in a

supercritical

state

and is

best

calculated

by

using

a Bernoulli-

derived

equation.

The

U.S. Bureau of

Reclamation

(I955:

41-3)

recommend

the use of

the

following

formula to calculate

velocity

on such

slopes:

V=

2g(Z

-

o.5H)

where

Z

is the

height

of the total fall

and

H

the

depth

of the

approach

channel.

Such

an

equation theoretically

evaluates the acceleration due to

gravity

of

a

falling

body.

Water

as

it

enters a

chute

initially

accelerates but

ultimately

will achieve

a uniform

high

velocity

in

which

retarding

forces

are

equal

in

magnitude

and

opposite

in direction

to

the

driving

forces.

Such

an

equation

does not take account of

two

primary

features

of channel

hydraulics,

surface

roughness

and

slope,

and these will

act as

retarding

forces.

The floors of the

Quishuarpata

chutes are

fitted,

granite

slabs,

whose

edges

are

bevelled to

depths

of

between

i

and

3

cm. so as to

produce

a

slightly

roughened

surface.

The

irregularity

in

fitting

produces

a

jigsaw-like

series of bevelled

indentations across

the

canal

bottom.

This would

inevitably

cause

turbulence

within

the

canal

flow

and hence

serve to

reduce

velocity.

Furthermore, given

the

predicted

low

discharges

in the

chutes,

the

depths

of

indentation were

probably

as

great,

if not

greater,

than the flow

depth.

This

would

have

further reduced the overall acceleration of

the

water.

Such

energy

dissipation

is

further

assisted

by

the

step-like

arrangement

of

the

channel

bed

over

the former

terrace

walls. The

slight changes

in

slope angle,

from

steep

to

slightly

less

so, would

produce

a

hydraulic jump

effect in

which

water would back

up

into a wave

at

approximately

the

change

in

angle.

Thus the actual

velocity

would be

substantially

less

than that

theoretically possible.

The division of chute

2

into two

sections,

although




17/20

302

I. S.

Farrington

engineered

for

topographical

reasons,

would have

the effect of

further

controlling

the

velocity

to

within

permissible

limits,

so much

that

this

chute could

be

regarded

as

two

separate ones,

A and B. The

sharp

curves at the

toe

of

each

chute

would

also

act

to

dissipate

energy by temporarily ponding

water

before

transferring

it

down-stream at a

lesser

velocity.

If chute zB

is

considered,

the estimated

depth

of

the

cross-slope approach

is

c.

5

cm.

As the water

is turned to

plunge

down the chute it will accelerate under

the

forces of

gravity.

At

io

m. loss

in

height,

the

theoretical

velocity

of

the canal would be

I4

m.

sec.-1,

which is over three times

greater

than

the

permissible

velocity

for

hard

rock

(U.S.

Water

Resources

Committee,

1938: io8).

The theoretical

depth

of water in

the

60 cm.

wide

channel would

have been

1-43

cm. The

roughness

caused

by bevelling

would

have

been almost

as

deep

as

the theoretical flow

depth,

and thus

would have

caused

massive dissipation of energy. One metre above the toe of chute 2B, the theoretical

velocity

is estimated to be

24

m.

sec.-l

and the

depth 0o85

cm.

Clearly,

the

means of con-

struction

of the canal served to

dissipate

sufficient

energy

to

restrain the

velocity

to

within

permissible

limits.

The

critical constructional

factors

are

the width of the

channel

which

served to

spread

the flow and the

degree

of

bevelling

in

the channel

floor.

The

former

terracing

may

have further assisted in

reducing

velocity.

Thus the

Cusichaca

engineers

were able

to

irrigate

successfully

the

35

ha. Hawa

Huillca

Raccay

and

enable

the

production

of

early

miska

maize,

the

local

delicacy (Farrington

1979).

Conclusions

The

archaeology

of

irrigation

canals

is in

its

infancy.

The

prehistoric

canal

is

not

simply

another

component

of

the

prehistoric

landscape

to

describe,

and about which to

make

inferences.

It is an artefact

designed

to do a

specific

job

and

serves as

testimony

to

the

empirical

understanding prehistoric

farmers had of

open

channel

hydraulics

and

the

hydrology

of their

farming

system.

The

methodology

to

elucidate

this

information

is

relatively

straight-forward

for

gentle

slopes

and

is

rooted in

careful excavation and

surveying,

but becomes more

complex

when the

question

of

moving

water down

steep

slopes

is

considered.

Acknowledgements

I

would

like

to

thank the

Directors

of the two

projects

with

which

I

have

worked,

Dr

M.

E.

Moseley (Moche-Chan

Chan

Project)

and

Dr

A

Kendall

(Cusichaca

Project)

and

their

respective

funding

bodies.

My

own

research in the Moche

valley

was funded

by

a

grant

from

the

Department

of

Education and

Science,

London.

I

would

also

like

to thank

P.

M.

Fleming

(CSIRO),

C. C.

Park

(SDUC,

Lampeter),

P. Bellwood and G.

Sheridan

(ANU) for their constructive comments on an earlier version of this paper.

6.vii.I979

Department

of Prehistory

and

Anthropology

Australian National

University




18/20

The

archaeology f irrigation

anals,

with

special

reference

o Peru

303

Appendix

The calculation of

velocity, using

the

Manning

equation,

can

be done

simply

by

measur-

ing

the

appropriate

cross-sectional variables and

gradient,

and

assuming

a suitable value

of

n and

substituting

these into the

equation

and

solving

it.

Discharge,

Froude

number

and

additional

depth

caused

by

supercritical

wave

surges

can then be calculated.

This

may

be illustrated with

reference to the

Quishuarpata

canal

excavation,

TQi

(fig. 4).

TQi

-

a

granite-lined,

trapezoidal

channel. From the

table of

the coefficient

of

surface

roughness (n),

dressed

ashlar

seems

the most

appropriate.

n

0I015.

At

bankfull:

A

A

w d

A

w

WP

rWP

n

s

0o68 o0I9

o-io62

0o17 o095

o-iiI8 0o15

0-053

V==353

m.

sec-1

Q=0-375

m.3

sec.-1

F

--=273

Vg.D

Thus at

bankfull

the

canal

is

flowing

supercritically

and is

prone

to

spillage

because

of

the

curving

nature of

the course.

Maximum

radius of

curvature,

R=30

m.

Assume canal

flowing

at

9

cm.

deep:

w d A D

WP

r

n

s

o062 oog9 0-0487 0-0785 0o738 o-o66 0-015 0-053

V=25

m.

sec-l

Q=o'i2I75

m.3

sec.-l

F=2-85 (i.e.

supercritical

flow)

To calculate additional

height

(y)

of

the

wave caused

by

obstruction

one

needs

to know

angles

/

and 0.

I

sin/

=-=o035I

F

S=20?35'

tan

0=

-

=o'o55

R.

tan

/3

0=30o0

V2

6

yV

sin2

(/+)

g

z

=oo09o695

m.

y=9'07

cm.

y+

d=

I8-07

cm.

Therefore the

depth

of flow

plus

the additional

height

of the wave

surge

is

I8o07

cm. and

the

total

depth

of

the

channel

is

I9

cm.

The

flow

is

still

supercritical

but can

be retained

within

the

existing

channel.




19/20

304

L S.

Farrington

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The Archaeology of Irrigation Canals

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