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Water losses from irrigation canals
Journal of Hydrology, 92 (1987) 27~288 Elsevier Science Publishers B.V., Amsterdam
275 Printed in The Netherlands
15]
W A T E R L O S S E S FROM IRRIGATION C A N A L S
E. WACHYAN and K.R. RUSHTON
Department of Civil Engineering, University of Birmingham, P.O. Box 363, Birmingham B15 2TT (U.K.) (Received December 3, 1986; accepted for publication January 11, 1987)
ABSTRACT Wachyan, E. and Rushton, K.R., 1987. Water losses from irrigation canals. J. Hydrol., 92:275 288. This paper investigates the water losses from a canal to an aquifer. From field measurements, large losses from canals have been identified, even when the canal is lined. The reasons for these losses are investigated by performing numerical model solutions for a series of examples with different conditions at the lower boundary of the aquifer, at lateral boundaries and at the water table within the aquifer. Partial lining of a canal is shown to have little effect on the magnitude of the losses and total lining which contains defects is also ineffective. The paper emphasises the need for detailed field work into the conditions within aquifers in the vicinity of canals.
INTRODUCTION
Canals are widely used in irrigation schemes to convey water from a reservoir to the fields. Frequently the actual amount of water available for use by a crop is significantly less than the quantity of water released from the reservoir (Bos and Nugteren, 1978) and one of the most significant causes of these water losses is leakage from canals. An understanding of the nature of the losses to the aquifer can lead to improved management of the water resources. The problem of canal losses has been recognised for a long time. In 1883, soon after the construction of canals in the Punjab, measurements were made which indicated significant losses. These and other instances of losses from canals are reported by Ahmad (1974). Even though Ahmad recognised that the nature and conditions within the aquifer have some influence on the magnitude of the losses, he suggested that the losses should be calculated from the wetted perimeter multiplied by a factor which depends primarily on whether the canal is a main canal or a distributary. This assumption that the canal loss depends primarily on the wetted perimeter is commonly used. However, Bouwer (1969) demonstrated that the losses also depend on the hydraulic conductivity and the hydraulic conditions within the aquifer. Bouwer also prepared graphs from which losses can be estimated. The two limiting conditions used by Bouwer are concerned with an aquifer having an underlying layer of a very high hydraulic conductivity or an aquifer with an impermeable base having a lateral boundary at which the 0022-1694/87/$03.50
~ 1987 Elsevier Science Publishers B.V.
276 groundwater head remains at a constant value. A closer examination of these two conditions indicates that they relate to aquifer situations which rarely occur in practice. Additional conditions are described in this paper which relate more closely to practical situations. These include an underlying layer of lower hydraulic conductivity and a loss of water from the vicinity of the water table due to evaporation or water taken into storage. Consideration is also given to the influence of the size of the canal and the effectiveness of various forms of lining. A final section presents three alternative situations which carl apply at different stages during a typical year. FIELD EVIDENCE The occurrence of losses from canals has received detailed attention for many years. About 100 years ago estimates were made of losses f~om canals in the Indus Basin. Kennedy (Ahmad, 1974) estimated losses from main canals to be 0.25md 1 and water-course losses to be about 0.2md 1. From the earliest reported work, losses were expressed in units of length/time thereby inferring that the losses are a function of the wetted perimeter of the canal. Ahmad (1974) reviews a large number of measurements of canal losses in the Indus Basin; for main canals he quotes results ranging from 0.06 to 1.25 m d- i. He recognises that the losses are a function of the hydraulic conductivity of the aquifer but suggests that they are independent of the water table position within the aquifer. He concludes by suggesting that for design purposes the losses from main canals are 0.2m d -1 and the losses from water courses lie in the range 0.05 0.1 m d 1. These losses are large compared with evaporation rates from the canal water surface which are unlikely to exceed 0.01m d 1. A recent report concerned with waterlogging problems in the Indus Basin (O'Mara, 1986) suggests that the actual canal losses are about four times the wtlues adopted during the initial planning of the water control projects. Detailed reviews of losses from canals in Idaho, U.S.A., are presented by Worstell (1976). Typical losses which depend on the nature of the soil are as follows: (1) medium clay loam 0.15-0.45md i; (2) pervious soils 0.45~).60md 1; and (3) gravels 0.75-1.00md 1. Reference is made to the possible effect of the position of the water table but no evidence was available. F u r t h e r important information is presented concerning losses averaging 0.07rod 1 from lined canals which have weathered and aged for several years. Studies of conditions in the Ismailia Canal, Egypt (Pontin et al., 1979) indicate that significant losses occur. Direct losses determined using seepage meters ranged from 0.6 to 2.4md 1 whilst results from flow gauging indicated losses in the range 0.15-1.52 m d 1. A theoretical study into the change in losses that would result from an increase in the dimensions of the canal predicted that for a 60% increase in width and a 50% increase in depth, the total losses would only increase by 20%. Field studies of losses from canals in the Kadulla irrigation scheme, Sri Lanka, are reported by Holmes et al. (1981). From ponding tests in an unlined
277 c a n a l for an aquifer of r e l a t i v e l y low p e r m e a b i l i t y , losses were found to be 0.13 m d 1. W h e n a section of lined c a n a l was tested in a similar w a y the losses were e q u i v a l e n t to 0.12 m d 1. A careful i n s p e c t i o n of the c a n a l s h o w e d t h a t t h e r e were m a n y c r a c k s and joints filled w i t h silt. W h e n t h e s e w e r e m a d e good, the losses were r e d u c e d to 0.07 m d 1. Detailed m e a s u r e m e n t s h a v e been m a d e r e c e n t l y in the P e r i y a r Vaigai Project, M a d u r i , S o u t h I n d i a to i n v e s t i g a t e the effectiveness of lining canals. The e x t e n s i v e r e s u l t s for c a n a l losses c a n be s u m m a r i s e d as follows:
Main canals Large distributaries Medium distributaries Small d i s t r i b u t a r i e s
unlined 0.37md 0.18md 0.09 m d 0.06 m d
~ ~ 1 1
lined 0.11md 0.08md 0.06 m d 0.045 m d
All the a b o v e field results confirm t h a t s u b s t a n t i a l losses do o c c u r from c a n a l s but the f a c t o r s influencing these losses are not discussed in detail. DIFFERING BOUNDARY CONDITIONS W h e n s t u d y i n g the n a t u r e of losses from i r r i g a t i o n c a n a l s u s i n g m a t h e m a t i cal techniques, g r e a t care is needed in selecting the a p p r o p r i a t e conditions on the b o u n d a r i e s of the a r e a to be studied. T h r e e a l t e r n a t i v e sets of b o u n d a r y c o n d i t i o n s are discussed below; the first two were c o n s i d e r e d by B o u w e r (1969), the t h i r d is i n t r o d u c e d for the first time in this paper. In this section the t h r e e p r o b l e m s are i n t r o d u c e d and r e p r e s e n t a t i v e r e s u l t s quoted. The p r a c t i c a l significance of the different cases is considered in m o r e detail in a s u b s e q u e n t section. Case A refers to the loss from a c a n a l t h r o u g h a n aquifer of h y d r a u l i c conductivity k to an u n d e r l y i n g h i g h l y p e r m e a b l e aquifer ku. If the u n d e r l y i n g a q u i f e r is at a d e p t h Da below the c a n a l w a t e r level, Fig. la, the g r o u n d w a t e r h e a d at the i n t e r f a c e w i t h the u n d e r l y i n g aquifer will be h Da. It is possible to c a l c u l a t e the loss from the c a n a l u s i n g an a n a l y t i c a l solution due to K o z e n y and V e d e r n i k o v (Bouwer, 1969). F o r an infinitely deep aquifer, the loss from a t r o c h o i d a l c h a n n e l of width W = 4 m is 6.0 k m3d 1 per m e t r e length of c h a n n e l w h e r e k is the h y d r a u l i c c o n d u c t i v i t y of the aquifer. If the c h a n n e l is of t r a p e z o i d a l s h a p e the loss a p p r o a c h e s k 6.8 m 3 d 1m 1. As an a l t e r n a t i v e to the a n a l y t i c a l a p p r o a c h , n u m e r i c a l solutions c a n be o b t a i n e d u s i n g finite-difference t e c h n i q u e s with specified g r o u n d w a t e r h e a d s a l o n g the p e r i m e t e r of the c a n a l and at the base of the aquifer; c o n d i t i o n s on the free s u r f a c e s are t h a t the p r e s s u r e is a t m o s p h e r i c and t h a t the flow perpend i c u l a r to the b o u n d a r y is zero. Solutions to the finite-difference e q u a t i o n s can be o b t a i n e d u s i n g e i t h e r digital or a n a l o g u e c o m p u t e r t e c h n i q u e s ( R u s h t o n and Redshaw, 1979).
278 W
~Free
W= 4m b = 2m d = ~m
surface
D,
,.
\
k
,~ : >> k \
I ~
t .
.
..oo.
r= i
W b
....
RESULT' O=6 80k m3/d/rn
Ls~
. . . . . ku
_ _
.
h=
o
, : : -D a
"1 ]
~'~/~
Ls= 340m
.
W= 4rn, Ow=6m
~
"
b= 2rn, S=5m
d=lm,
L=lO2m, Da=l~m RESULTS O = 0 93k rn~/d/m
ah
0
,
"
L .. Wb
W=4rn T= Zm,
"-]
~
/
Ground surface
z,,, ~ 7 ~ / ~
Irnperrneabte base "~" ~ / / " / "/~ "/G
,.
(b)
" ~J
b=2rn d = l m , L = 102, O=13m, Oa= llrn kc=OOO21k RESULTS g=l 91k m3/d/m
"~"~'~'~'~--~
Ground surlace F. . . . ~ - - ~
/c)
iDw : 594 " ~i
~k i
IS 5 06
Fig. 1. Three arrangements of boundary conditions. (a) Case A with highly permeable base; (b) case B with impermeable base and fixed head at lateral boundary; and (c) case C with flow through zone of low-conductivity. A n i l l u s t r a t i v e e x a m p l e is p r e s e n t e d i n Fig. la; for t h e p a r t i c u l a r d i m e n s i o n s q u o t e d t h e l o s s d e t e r m i n e d from t h e n u m e r i c a l s o l u t i o n is: Q
=
6 . 8 0 k m 3 d 1 per m e t r e l e n g t h o f c a n a l
279
This result is the same as the a n a l y t i c a l values for a trapezoidal c h a n n e l in an infinitely deep aquifer. A n o t h e r i m p o r t a n t r e s u l t from the n u m e r i c a l solution is t h a t the width of the s a t u r a t e d c o l u m n at the i n t e r f a c e with the high-conductivity l a y e r is 2L s = 6.80 m. This width was d e t e r m i n e d using a finite-difference mesh with a h o r i z o n t a l spacing of 0.05 m in the region where the w a t e r table intersects the highly permeable base. It corresponds exactly with the value expected for parallel d o w n w a r d flow u n d e r a gradient minus one. Case B refers to losses from a canal into an aquifer with an impermeable base (Fig. lb). This problem was considered in great detail by B o u w e r (1969); extensive graphs are p r e s e n t e d based on electrical a n a l o g u e solutions for a r a n g e of geometries. C e r t a i n of Bouwer's results have been r e p r o d u c e d using both digital and a n a l o g u e g r o u n d w a t e r models using t e c h n i q u e s for free surface problems as described by R u s h t o n and Redshaw (1979). P a r a m e t e r values for a typical problem are listed in Fig. lb. W a t e r is assumed to flow from the canal to distant lateral b o u n d a r i e s on which the g r o u n d w a t e r head is specified at h = - 6.0 m. T a k i n g the distance to the o u t e r fixed head b o u n d a r i e s as 102 m and with the o t h e r dimensions as listed in Fig. lb, the total loss from the canal to the two lateral b o u n d a r i e s is: Q _
0.93km3d 1m 1
Case C differs from cases A and B in t h a t the aquifer is assumed to be u n d e r l a i n by a thin layer of lower h y d r a u l i c c o n d u c t i v i t y of thickness T and h y d r a u l i c c o n d u c t i v i t y kc, Fig. lc. Provided t h a t t h e r e is a more permeable p a r t i a l l y s a t u r a t e d l a y e r b e n e a t h this low-conductivity layer, the pressure at the base of the low-conductivity layer a p p r o a c h e s atmospheric, hence the g r o u n d w a t e r head equals the depth below the canal w a t e r level:
h
=
-D
This canal is assumed to be one of the series of similar canals spaced a distance 2L apart; c o n s e q u e n t l y t h e r e is an axis of s y m m e t r y at a distance L from the canal c e n t r e l i n e at which the h o r i z o n t a l flow is zero: ~h/~x
=
0
F r o m a n u m e r i c a l solution to this problem using the dimensions and par a m e t e r values listed on Fig. lc, the total loss from the canal is found to be: Q =
1.91km~d 1m 1
For this example the v a l u e chosen for the h y d r a u l i c c o n d u c t i v i t y of the lower l a y e r is: k~ =
0.0021k
The r e a s o n for choosing this p a r t i c u l a r value is t h a t it results in a depth of the free w a t e r surface below the canal level at the mid point b e t w e e n the canals of 5.94m; this elevation is similar to the depth below canal level at the o u t e r b o u n d a r y of 6.0 m for case B.
280 DETAILED COMPARISONS Detailed c o m p a r i s o n s of the three cases help to identify w h i c h c o n d i t i o n s r e p r e s e n t typical field situations. Case A relates to a zone of high permeability at some depth below the canal. A l t h o u g h such a c o n d i t i o n c a n occur, it is n o t common. Case A is in fact a limiting c o n d i t i o n of the u n d e r l y i n g zone of case C. The i m p o r t a n t issue c o n c e r n i n g case B is the influence of the o u t e r fixed head b o u n d a r y . B o u w e r (1969) suggested t h a t the distance to this b o u n d a r y should be at least ten times the width of the c a n a l bed. To i n v e s t i g a t e the influence of the position of this lateral b o u n d a r y , a series of solutions were obtained with a g r a d u a l l y i n c r e a s i n g distance to the o u t e r b o u n d a r y (Table 1). As the distance to the o u t e r b o u n d a r y increases, the loss from the canal becomes smaller and tends to zero as the distance to the o u t e r b o u n d a r y becomes very large. This o c c u r s because each increase in the distance to the o u t e r b o u n d a r y leads to a decrease in the head gradients resulting in a decrease in the loss from the canal. The flow p a t t e r n s for this p a r t i c u l a r set of b o u n d a r y conditions, c o n s t r u c t e d from a n u m e r i c a l solution in which L - 102 m, are plotted in Fig. 2. These plots indicate t h a t at a s h o r t distance from the canal the flow becomes predominantly horizontal. Figure 2b presents the detailed shape of the equipotentials in the vicinity of the canal. It is i m p o r t a n t to consider the physical significance of the lateral b o u n d a r y in case B. For the dimensions of Fig. 2, this lateral b o u n d a r y c o r r e s p o n d s to a d r a i n a g e c h a n n e l which fully p e n e t r a t e s the aquifer in w h i c h the w a t e r level is 6 m below canal level at a distance of only 100m from the canal. Such a s i t u a t i o n is unlikely to o c c u r in practice because d r a i n a g e channels, if provided, do not fully p e n e t r a t e the aquifer and are c e r t a i n l y far less t h a n 6 m below the level of a c a n a l which is only 100m distant. C o n s e q u e n t l y the c o n d i t i o n s of case B do not represent most practical s i t u a t i o n s and therefore a t h o r o u g h e x a m i n a t i o n of case C is required to determine w h e t h e r it represents more realistic conditions. The first stage in the i n v e s t i g a t i o n of case C is to consider the effect of i n c r e a s i n g distances to the o u t e r b o u n d a r y . Table 2 c o n t a i n s results for a l o w - c o n d u c t i v i t y layer 11 m below the w a t e r level in the c a n a l with a h y d r a u l i c TABLE 1 Case B; effect on canal losses of increasing the distance to outer boundary. Depth of impermeable baseD ~ llm; depth to water tableD w = 6m; canal dimensions: W 4m, b = 2m, d ~ lm Distance to outer boundary L (m)
Loss from canal Q (m:~d 1m ~)
12 30 66 102
4.57k 2.70 k 1.33k 0.93 k
281 F r e e woter surfoce
h:
6m
11rn (a)
Distence L =102 m
b
h=0 i
/ F r e e w o t e r surfQce
/
~ ~
~
~
,
,'~., ~/A
I
i'?~''''
De= 11m
I_ ~
(b)
0
~ . . . . . . . . . . . . . . . . . . . . . . .
I
o
7---+
.....
5 Distonce, m
I_
t
' o
/
!
......
,
"~
J~ .
.
.
.
.
.
............
,, . . . .
.....
10
.
.
.
.
.
.
.
.
.
.
.
.........
20
m31dlm
.
l ~......... ..... ! ......... 15
Q =0.465k
,
I
,
25
Fig. 2. E q u i p o t e n t i a l a n d flow l i n e s for a q u i f e r u n d e r l a i n by i m p e r m e a b l e ba s e w i t h fixed h e a d of 6.0m at 102m from t h e c a n a l c e n t r e l i n e . O t h e r d i m e n s i o n s : / 9 , = 11 m, W = 4 m, b = 2 m a n d d lm.
c o n d u c t i v i t y of 0.2% of the o v e r l y i n g s t r a t a . T h e s e r e s u l t s i n d i c a t e t h a t as the d i s t a n c e b e t w e e n c a n a l s increases, the q u a n t i t y of w a t e r lost from the c a n a l also increases. A second c o n s e q u e n c e of i n c r e a s e d d i s t a n c e s b e t w e e n c a n a l s is a d e c r e a s e in the s a t u r a t e d d e p t h at the o u t e r b o u n d a r y from s = 10.31 m w h e n the d i s t a n c e to the o u t e r b o u n d a r y is 3 0 m to s = 0.10m w h e n L -- 150m. E q u i p o t e n t i a l s and flowlines are s k e t c h e d in Fig. 3 for the case w h e r e L - 102 m and kc = 0.0021 k. This figure shows that, a l t h o u g h w a t e r flows from the c a n a l in a s i m i l a r m a n n e r to case B, it m o v e s t o w a r d s the l o w - c o n d u c t i v i t y l a y e r and passes t h r o u g h to the u n d e r l y i n g m o r e p e r m e a b l e layer. T h e loss from the c a n a l to the l o w - c o n d u c t i v i t y l a y e r is 1.91km3d l m 1 c o m p a r e d to the v a l u e for case B of 0.93 k m 3d l m 1 w h i c h was o b t a i n e d for the s i t u a t i o n w h e r e the w a t e r level in the d r a i n a g e c h a n n e l is 6 m below c a n a l level. A c o m p a r i s o n of the e q u i p o t e n t i a l s in the v i c i n i t y of the c a n a l shows s t e e p e r g r a d i e n t s w h e n the w a t e r is m o v i n g t o w a r d s the l o w - c o n d u c t i v i t y layer. The m a g n i t u d e of the v e r t i c a l flows t h r o u g h the l o w - c o n d u c t i v i t y l a y e r for the four s p a c i n g s b e t w e e n c a n a l s is i l l u s t r a t e d in Fig. 4. W h a t e v e r the d i s t a n c e to the o u t e r b o u n d a r y , the m a g n i t u d e of the flow i m m e d i a t e l y b e n e a t h the c a n a l is similar. H o w e v e r , at g r e a t e r d i s t a n c e s from the c a n a l t h e r e are c l e a r differences in the d i s t r i b u t i o n of the v e r t i c a l flows t h r o u g h the low-conductivity l a y e r due to s m a l l e r h e a d differences across it. T h e l a r g e s t v a l u e of L in T a b l e 2 (and Fig. 4) is 150 m c o r r e s p o n d i n g to a d i s t a n c e b e t w e e n c a n a l s of 300m. A l t h o u g h l a r g e r s p a c i n g s c a n be used, the s a t u r a t e d d e p t h d e c r e a s e s and t h e r e f o r e t h e r e is a d i s t a n c e at w h i c h the
282 TABLE 2 Case C; effect on c a n a l losses of i n c r e a s i n g t h e d i s t a n c e to t h e o u t e r b o u n d a r y . D e p t h to lowc o n d u c t i v i t y l a y e r D = l l m ; t h i c k n e s s a n d h y d r a u l i c c o n d u c t i v i t y of l o w . c o n d u c t i v i t y l a y e r T ~ 2 m a n d k~ = 0.002k; c a n a l d i m e n s i o n s : W = 4 m , b = 2m, d = l m D i s t a n c e to o u t e r b o u n d a r y L (m)
Loss from c a n a l Q (m3d l m ~) D e p t h to w a t e r table D w(m)
30 48 102 150
0.75 k 1.14 k 1.86 k 1.99k
?--
~
._C..ana,! w_a_t_er_L_e..v~. . . . . . . . ,
tO_= 1
- •
1
( a )
2.0
-2.5
Free w a t e r surface
3'0
4
~
-5.0
~
T=2m
0.64 1.61 5.62 10.90
--
10Zrn
~Dw 5 9"* m
"I
T/, z, z~, / , /" . / / / // If/-///~.'// O / / / , / /
k - 0.0021 k
)" "
Fig. 3. E q u i p o t e n t i a l a n d flow lines for a q u i f e r u n d e r l a i n by l o w - c o n d u c t i v i t y l a y e r w i t h k~ = 0.0021k. C a n a l d i m e n s i o n s : W = 4 m, b = 2 m a n d d = 1 m. --="
Distance
from the canal
50
axis( L )
100
150
1° Vert i cat flow (retold)
3
Q = 1 984 k m3/d/m
6 8
O = 1-882k
10
=48m Q= 1.134 k m3/d/m
12 \ L=30m Q= 0-750 k
rn31dlm
m31dlm
Fig. 4. D i s t r i b u t i o n of vertical flow t h r o u g h l o w - c o n d u c t i v i t y l a y e r for k,. = 0.002 k w i t h different v a l u e s of L.
283
saturated depth in the upper aquifer zone becomes zero. For the aquifer dimensions and hydraulic conductivities used in Table 2, that distance is about 160 m.
Different hydraulic conductivities of the lower layer The examples for case C quoted in Table 2 all relate to a hydraulic conductivity for the lower layer of kc = 0.002 k. Table 3 contains a set of results with differing values of kc. In all the examples the difference in groundwater head between the water surface in the canal and the bottom of the lower layer is 1am. Example 7 corresponds to the third line of Table 2. Smaller values of k,: result in smaller losses from the canal because the effective overall hydraulic conductivity between the upper and lower constant head boundaries is decreased thereby reducing the flow of water and increasing the elevation of the water table. Indeed, as the hydraulic conductivity of the lower layer tends to zero, the water table approaches the horizontal since there is no outlet for the water. Larger values of the hydraulic conductivity of the lower layer lead to increasing losses from the canal. For values of kc greater than 0.005k, the saturated section does not extend to the outer boundaries at 102m. For instance, with kc = 0.01 k the saturated region extends 60 m on either side of the canal centreline. The limiting case of the hydraulic conductivity of the two layers being the same corresponds to case A; the loss from the canal then equals the value quoted earlier of 6.80kmad lm 1. TABLE 3 Losses from canal for case C; Fig. lc for different hydraulic conductivity of the lower layer. Canal dimensions: W = 4m, b = 2m, d = l m , total depth D = 13m, depth to the layer D, = l l m , thickness of lower layer T = 2 m. Distance to outer no flow b o u n d a r y L = 102 m Example
Hydraulic conductivity ratio kjk
Loss from unit length of canal Q/k (m 2)
Width of flow t h r o u g h lower layer 2L (m)
Max. depth to w a t e r table Dw
(m) 1 2 3 4 5 6 7 8 9 10 11 12 13
0.0 0,0001 0.0002 0.0004 0.0008 0.001 0.002 0.0021 0.004 0.01 0.02 0.04 1.0
0.0 0.13 0.26 0.49 0.92 1.11 1.86 1.91 2.70 3.79 5.12 6.26 6.80
204 204 204 204 204 204 204 204 204 120 95 60 6.80
0.0 0.36 0.68 1.28 2.42 2.99 5.55 5.94 9.88 11.0 11.0 11.0 11.0
284
This detailed i n v e s t i g a t i o n of case C suggests t h a t losses from c a n a l s t h r o u g h u n d e r l y i n g l o w - c o n d u c t i v i t y l a y e r s r e p r e s e n t the c o n d i t i o n s w h i c h often o c c u r in practice. In the field, it is u n l i k e l y t h a t t h e r e will be a single c o n t i n u o u s l o w - c o n d u c t i v i t y l a y e r of c o n s t a n t t h i c k n e s s but m o r e v a r i a b l e zones of low h y d r a u l i c c o n d u c t i v i t y h a v e a similar effect. WATER WITHDRAWN IN THE VICINITY OF THE WATER TABLE
In all the s i t u a t i o n s discussed a b o v e it has been a s s u m e d t h a t the w a t e r t a b l e acts as a zero flow b o u n d a r y . In p r a c t i c e t h e r e are a n u m b e r of r e a s o n s why w a t e r m a y be effectively w i t h d r a w n from the aquifer in the v i c i n i t y of the w a t e r table. (1) The w a t e r table i n t e r s e c t s the g r o u n d s u r f a c e c a u s i n g s e e p a g e faces or w a t e r l o g g i n g . This is especially c o m m o n w h e n the c a n a l lies on an e m b a n k m e n t . (2) E v a p o t r a n s p i r a t i o n o c c u r s from the w a t e r t a b l e due to r o o t s of plants or trees e x t e n d i n g into the s a t u r a t e d zone. (3) T h e w a t e r table rises and w a t e r is t a k e n into storage. E a c h of these e x a m p l e s c o r r e s p o n d s to an a l t e r n a t i v e m e a n s by w h i c h w a t e r is effectively w i t h d r a w n from the aquifer u n d e r l y i n g the canal; this c a n lead to a c h a n g e in the c a n a l losses. To i l l u s t r a t e the effect of this w i t h d r a w a l of water, it will be a s s u m e d t h a t t h e r e is an u p w a r d v e l o c i t y w h i c h d e c r e a s e s u n i f o r m l y from 6.00 k m m d ~a d j a c e n t to the c a n a l to 3.00 k m m d 1, at 100m on e i t h e r side of the canal; this is e q u i v a l e n t to a t o t a l u p w a r d flow of 0.90 k m :3d ~m 1. If this is s u p e r i m p o s e d on the aquifer and b o u n d a r y c o n d i t i o n s for case C, e x a m p l e 6 of 'Fable 3, the t o t a l loss from the c a n a l b e c o m e s 1.82k c o m p a r e d to 1.11 km:~d ~m ~ w h e n no flow crosses the w a t e r table. A n o t h e r c o n s e q u e n c e of the flow from the v i c i n i t y of the w a t e r t a b l e is t h a t the d e p t h to w a t e r t a b l e i n c r e a s e s from 2.99 m to 6.01m. The effect of w a t e r w i t h d r a w n from the w a t e r t a b l e h a s b e e n explored for the s i t u a t i o n w h e r e v e r t i c a l flow o c c u r s t h r o u g h the u n d e r l y i n g l o w - c o n d u c t i v i t y layer. Results could equally well be o b t a i n e d for the s i t u a t i o n w h e r e the u n d e r l y i n g l a y e r is i m p e r m e a b l e . SIZE AND I,INING OF CANALS
Only one size of c a n a l has been considered thus far and the n e x t step is to consider the effect of the size of the canal. S u b s e q u e n t l y the effect of p a r t i a l or c o m p l e t e lining on the c a n a l losses will be considered. T a b l e 4 records the losses with t h r e e different c a n a l sizes for the e x a m p l e of an u n d e r l y i n g l o w - c o n d u c t i v i t y l a y e r w i t h kc = 0.002 k. F o r the s m a l l e s t c a n a l with a w e t t e d p e r i m e t e r of 3.83 m the loss is 1.80 m 3d 1m 1whilst for the l a r g e s t c a n a l w i t h a wetted p e r i m e t e r of 9.66m the loss is only slightly h i g h e r at 1.95m3d l m 1. T h e s e results d e m o n s t r a t e t h a t the s t a n d a r d p r o c e d u r e of ass u m i n g t h a t the loss is p r o p o r t i o n a l to the w e t t e d p e r i m e t e r c a n be v e r y misleading. A second set of results, T a b l e 5, shows the effect of different types of lining. The c a n a l d i m e n s i o n s are those used in m a j o r i t y of the s o l u t i o n s described
285 TABLE 4 Effect of canal dimensions on losses. Total aquifer depth D 13 m; depth of aquifer D, thickness and hydraulic conductivity of lower layer T 2m, k,. - 0.002k
b
d
Loss from unit length of canal Q/k (m-')
3
1
1
1.80
4 s
2 4
1 2
1.86 1.95
Dimension of unlined canal (m) W
11 m,
Maximum depth to water table D~.(m) 6.0 5.55 5.22
a b o v e a n d t h e l o w e r l a y e r h a s a h y d r a u l i c c o n d u c t i v i t y of 0.002 k. T h e first r e s u l t is for a n u n l i n e d c a n a l , w h i l s t t h e s e c o n d r e f e r s to t h e c a s e of t h e sides lined, b u t t h e bed u n l i n e d . The r e d u c t i o n in t h e loss from 1.86k to 1.83 k m 3d 1m l is e q u i v a l e n t to a d e c r e a s e of o n l y 2%. In a n o t h e r s i m u l a t i o n , t h e bed is c o m p l e t e l y l i n e d a n d t h e sides left u n l i n e d ; t h e loss b e c o m e s 1.79m3d 1m 1 w h i c h is e q u i v a l e n t to a r e d u c t i o n from t h e u n l i n e d losses of a l m o s t 4%. T h i s i n d i c a t e s t h a t t h e d e p o s i t i o n of s i l t on t h e bed of t h e c a n a l m a y h a v e l i t t l e effect on t h e t o t a l losses. P e r f e c t l i n i n g of a c a n a l w o u l d p r e v e n t all losses, b u t an e x a m i n a t i o n of a c t u a l c a n a l s i n d i c a t e s t h a t even w i t h t h e g r e a t e s t c a r e t h e l i n i n g does n o t r e m a i n perfect. A w e l l - m a i n t a i n e d c a n a l m i g h t a c h i e v e t h e c o n d i t i o n t h a t t h e l i n i n g is 99% perfect. If t h e t h i c k n e s s of t h e l i n i n g is 10 cm, t h e n t h e effective h y d r a u l i c c o n d u c t i v i t y of t h i s 10cm l a y e r is 0.01k. W h e n t h i s c o n d i t i o n is i n c o r p o r a t e d in t h e n u m e r i c a l model, t h e losses a r e as r e c o r d e d in t h e final line of T a b l e 5. The t o t a l loss from t h e c a n a l b e c o m e s 1.34km:~d l m 1 w h i c h is 71% of t h e losses w h e n no l i n i n g is p r e s e n t . T h e 10cm t h i c k n e s s of h y d r a u l i c c o n d u c t i v i t y 0.01 k is e q u i v a l e n t to an a d d i t i o n a l l e n g t h of t h e flow p a t h of 10 m w i t h t h e s t a n d a r d h y d r a u l i c c o n d u c t i v i t y k. The l e n g t h e n i n g of t h e effective flow p a t h by 10m does n o t l e a d to a m a j o r r e d u c t i o n in t h e losses. TABLE5 Effect of lining of canal on losses for the aquifer properties as in Table 4. Canal dimensions: W::4m,
b = 2m, d=
lm
Form of lining
Loss from unit length of canal Q / k (m2)
Maximum depth to water table Dw(m)
Unlined Sides lined, bed unlined Bed lined, sides unlined Hydraulic conductivity within 10cm of canal reduced to 1% of normal values
1.86 1.83 1.79
5.55 6.08 6.01
1.34
8.45
286
CONDITIONS AT DIFFERENT TIMES OF THE YEAR
All the examples quoted above assume that some form of dynamic equilibrium is applicable with the inflows balancing the outflows. In practice conditions will vary during the year but the actual changes depend on site-specific details such as the ability of deeper aquifers to move water away laterally. Since the time variant behaviour is so site specific, detailed time variant studies will not be included. Instead, three possible conditions, which are likely to occur in many situations, will be studied. These three conditions are illustrated in Fig. 5. Condition 1 represents the situation when flow occurs through the lowconductivity layer to an underlying more permeable zone. Consider the case when the water table in the underlying zone is at 16.0 m below canal level (i.e. 3 m below the base of the low-conductivity zone). At the base of the low-conductivity zone, the pressure is approximately atmospheric; therefore conditions for case C apply. For a distance between canals of 204 m, the results can be taken from example 6 of Table 2. Consequently the total loss is 1.11km:~d lm 1 which, when divided by a width of 204 m, is equivalent to an average vertical Condition 1 .02m phreatlc
Surface
98m :;
2~,~¢ = o . o o l , : / / / / / / ~ / / > : / . ~ h=-13 Om
..~.>%< (Q= 1.11k m31d/m) initia[
m
~: :/%~. ,
~.Om 30m
w a t e r table
L=lO2m Condition 2
I h=-70m
48m 52rn
( Q =0.61 k3rn/d/m)
Condition 3 k" m3/d'm ~ ~ O'Z"50
[i
t 23"84 7 m
16rn 2 2~ ~
k¢ : o. oo 1 k> ~ / X / / ' X , ~ / , : I Y / . ~ 1 7 / 7 / : 9 H / / / ~ d
h= -7.Ore
" ( Q=O .458 k m3/d/m )
v!
J_z. o m
Fig. 5. Typical aquifer conditions during a year. (a) Start of canal operation; (b) region below low-conductivity layer fully saturated; and (c) as (b) but with flows from the water table.
287 flow from the b a s e of the l o w - c o n d u c t i v i t y zone of 0.0054 k m d 1. F o r a specific yield of Sy, the rise in g r o u n d w a t e r h e a d in the u n d e r l y i n g a q u i f e r would be: O.O054k/Sy m d 1
T a k i n g t y p i c a l v a l u e s o f k = 1.0rod 1 a n d Sy = 0.12, the a v e r a g e rise e a c h d a y would be 0.045 m, t h u s it would t a k e a b o u t 67 d a y s for the w a t e r table to rise 3 m to the b a s e of the l o w - c o n d u c t i v i t y layer. This a s s u m e s t h a t no w a t e r c a n m o v e a w a y l a t e r a l l y in the deeper aquifer. In p r a c t i c e some l a t e r a l outflow is likely to o c c u r r e s u l t i n g in a longer time for the rise in w a t e r table. C o n d i t i o n 2 r e p r e s e n t s the s i t u a t i o n w h e r e the aquifer u n d e r l y i n g the lowc o n d u c t i v i t y l a y e r is fully s a t u r a t e d . F o r example, if the p i e z o m e t r i c head in this u n d e r l y i n g a q u i f e r is 6.0 m a b o v e the base of the l o w - c o n d u c t i v i t y zone, the g r o u n d w a t e r h e a d at the b a s e is - 7.0 m r e l a t i v e to the c a n a l w a t e r level. W i t h these c o n d i t i o n s included in the n u m e r i c a l model, the flow from the c a n a l is r e d u c e d to 0.61km3d l m 1 and the d e p t h from the c a n a l level to the w a t e r t a b l e m i d w a y b e t w e e n the c a n a l s is 1.47 m c o m p a r e d to 3.02 m w h e n the w a t e r t a b l e is w i t h i n the lower aquifer. With such a s h a l l o w w a t e r table, it is likely t h a t significant e v a p o r a t i v e losses will o c c u r from the v i c i n i t y of the w a t e r table; this leads to the t h i r d condition. C o n d i t i o n 3 is s i m i l a r to condition 2 in t h a t the g r o u n d w a t e r h e a d in the u n d e r l y i n g aquifer is - 7.0 m, but t h e r e is also a loss from the v i c i n i t y of the w a t e r table. T h e s e losses are t a k e n to be the s a m e as t h o s e of the p r e v i o u s section w i t h 0 . 0 0 6 k m d 1 in the v i c i n i t y of the c a n a l falling to 0 . 0 0 3 k m d m i d w a y b e t w e e n the canals. With t h e s e conditions, the t o t a l loss b e c o m e s 1.36 k m 3d 1m ~1 from the c a n a l with a m a x i m u m d e p t h to w a t e r table of 3.84 m below c a n a l level. E a c h of t h e s e c o n d i t i o n s could o c c u r in a p r a c t i c a l situation. F o r c o n d i t i o n 1 the loss is at its m a x i m u m at 1.11m3d l m 1 but following a rise in the g r o u n d w a t e r h e a d in the deeper aquifer, the loss is reduced until, as the w a t e r t a b l e rises and e v a p o r a t i o n from the w a t e r t a b l e occurs, the loss from the c a n a l m a y i n c r e a s e to a b o u t 1.36 k m 3d- xm 1. CONCLUSIONS Field m e a s u r e m e n t s d e m o n s t r a t e t h a t significant losses do o c c u r from c a n a l s w h e t h e r t h e y are lined or unlined. This p a p e r h a s e x p l o r e d the likely flow m e c h a n i s m s w h i c h explain these losses. The existing m e t h o d s of a n a l y s i s h a v e been e x t e n d e d to i n c l u d i n g the effects of layers w i t h a low h y d r a u l i c c o n d u c t i v i t y at some d i s t a n c e b e n e a t h the c a n a l and losses f r o m the v i c i n i t y of the w a t e r table. F o r e a c h of t h e s e conditions, the c a n a l losses are; g e n e r a l l y h i g h e r t h a n the v a l u e s based on the e x i s t i n g a p p r o a c h e s . A s t u d y of the effect of lining i n d i c a t e s t h a t little is to be g a i n e d from lining e i t h e r the b a s e or the sides of the canal. P e r f e c t lining of the t o t a l c a n a l will p r e v e n t all losses but linings t h a t h a v e a n y i m p e r f e c t i o n s are s h o w n to r e s u l t in o n l y a small r e d u c t i o n in the losses.
288 F u r t h e r w o r k is r e q u i r e d o n t w o a s p e c t s c o n c e r n i n g c a n a l l o s s e s . T h e first r e q u i r e m e n t is for d e t a i l e d field w o r k w i t h c a r e f u l s t u d i e s o f t h e u n d e r l y i n g s t r a t a u s i n g n u m e r o u s p i e z o m e t e r s to m o n i t o r t h e g r o u n d w a t e r h e a d s b e n e a t h a n d to t h e s i d e s o f t h e c a n a l s . S e c o n d l y , f u r t h e r d e t a i l e d m o d e l l i n g w o r k is a d v i s a b l e to i n v e s t i g a t e t h e p r o b a b l e l o s s e s f r o m a q u i f e r s w i t h a g r e a t e r h e t e r o g e n e i t y t h a n c o n s i d e r e d in t h e p r e s e n t s t u d y .
REFERENCES Ahmad, N., 1974. Groundwater Resources of Pakistan. Ripon Printing Press, Lahore, 295 pp. Bos, M.G. and Nugteren, J., 1978. On Irrigation Efficiencies. Int. Inst. Land Reclam. Improv., Neth., 138 pp. Bouwer, H., 1969. Theory of seepage from open channel. In: Ven Te Chow (Editor), Advances in Hydroscience, 5. Academic Press, New York, N.Y., pp. 121-172. Holmes, D.W., Wooldridge, R., Weller, J.A., Gunston, H. and Batchelor, C.H., 1981. Water Management study at Kaudulla Irrigation Scheme, Sri Lanka. Rep. No. O.D. 38, Hydraul. Res. Stat., Wallingford. O'Mara, G., 1986. Conjunctive Water Use. Proc. Budapest Symp., IAHS Publ. No. 156. Pontin, J.M.A., Laila Abed and Weller, J.A., 1979. Prediction of seepage loss from the enlarged Ismalia Canal. Rep. No. O.D.28, Hydraul. Res. Stat., Wallingford. Rushton, K.R. and Redshaw, S.C., 1979. Seepage and Groundwater Flow. Wiley. New York, N.Y., 332 pp. Worstell, V., 1976. Estimating seepage losses from canal systems. J. Irrig. Drain. Div. Am. Soc. Civ. Eng., 102, IRI, pp. 137 147.
275 Printed in The Netherlands
15]
W A T E R L O S S E S FROM IRRIGATION C A N A L S
E. WACHYAN and K.R. RUSHTON
Department of Civil Engineering, University of Birmingham, P.O. Box 363, Birmingham B15 2TT (U.K.) (Received December 3, 1986; accepted for publication January 11, 1987)
ABSTRACT Wachyan, E. and Rushton, K.R., 1987. Water losses from irrigation canals. J. Hydrol., 92:275 288. This paper investigates the water losses from a canal to an aquifer. From field measurements, large losses from canals have been identified, even when the canal is lined. The reasons for these losses are investigated by performing numerical model solutions for a series of examples with different conditions at the lower boundary of the aquifer, at lateral boundaries and at the water table within the aquifer. Partial lining of a canal is shown to have little effect on the magnitude of the losses and total lining which contains defects is also ineffective. The paper emphasises the need for detailed field work into the conditions within aquifers in the vicinity of canals.
INTRODUCTION
Canals are widely used in irrigation schemes to convey water from a reservoir to the fields. Frequently the actual amount of water available for use by a crop is significantly less than the quantity of water released from the reservoir (Bos and Nugteren, 1978) and one of the most significant causes of these water losses is leakage from canals. An understanding of the nature of the losses to the aquifer can lead to improved management of the water resources. The problem of canal losses has been recognised for a long time. In 1883, soon after the construction of canals in the Punjab, measurements were made which indicated significant losses. These and other instances of losses from canals are reported by Ahmad (1974). Even though Ahmad recognised that the nature and conditions within the aquifer have some influence on the magnitude of the losses, he suggested that the losses should be calculated from the wetted perimeter multiplied by a factor which depends primarily on whether the canal is a main canal or a distributary. This assumption that the canal loss depends primarily on the wetted perimeter is commonly used. However, Bouwer (1969) demonstrated that the losses also depend on the hydraulic conductivity and the hydraulic conditions within the aquifer. Bouwer also prepared graphs from which losses can be estimated. The two limiting conditions used by Bouwer are concerned with an aquifer having an underlying layer of a very high hydraulic conductivity or an aquifer with an impermeable base having a lateral boundary at which the 0022-1694/87/$03.50
~ 1987 Elsevier Science Publishers B.V.
276 groundwater head remains at a constant value. A closer examination of these two conditions indicates that they relate to aquifer situations which rarely occur in practice. Additional conditions are described in this paper which relate more closely to practical situations. These include an underlying layer of lower hydraulic conductivity and a loss of water from the vicinity of the water table due to evaporation or water taken into storage. Consideration is also given to the influence of the size of the canal and the effectiveness of various forms of lining. A final section presents three alternative situations which carl apply at different stages during a typical year. FIELD EVIDENCE The occurrence of losses from canals has received detailed attention for many years. About 100 years ago estimates were made of losses f~om canals in the Indus Basin. Kennedy (Ahmad, 1974) estimated losses from main canals to be 0.25md 1 and water-course losses to be about 0.2md 1. From the earliest reported work, losses were expressed in units of length/time thereby inferring that the losses are a function of the wetted perimeter of the canal. Ahmad (1974) reviews a large number of measurements of canal losses in the Indus Basin; for main canals he quotes results ranging from 0.06 to 1.25 m d- i. He recognises that the losses are a function of the hydraulic conductivity of the aquifer but suggests that they are independent of the water table position within the aquifer. He concludes by suggesting that for design purposes the losses from main canals are 0.2m d -1 and the losses from water courses lie in the range 0.05 0.1 m d 1. These losses are large compared with evaporation rates from the canal water surface which are unlikely to exceed 0.01m d 1. A recent report concerned with waterlogging problems in the Indus Basin (O'Mara, 1986) suggests that the actual canal losses are about four times the wtlues adopted during the initial planning of the water control projects. Detailed reviews of losses from canals in Idaho, U.S.A., are presented by Worstell (1976). Typical losses which depend on the nature of the soil are as follows: (1) medium clay loam 0.15-0.45md i; (2) pervious soils 0.45~).60md 1; and (3) gravels 0.75-1.00md 1. Reference is made to the possible effect of the position of the water table but no evidence was available. F u r t h e r important information is presented concerning losses averaging 0.07rod 1 from lined canals which have weathered and aged for several years. Studies of conditions in the Ismailia Canal, Egypt (Pontin et al., 1979) indicate that significant losses occur. Direct losses determined using seepage meters ranged from 0.6 to 2.4md 1 whilst results from flow gauging indicated losses in the range 0.15-1.52 m d 1. A theoretical study into the change in losses that would result from an increase in the dimensions of the canal predicted that for a 60% increase in width and a 50% increase in depth, the total losses would only increase by 20%. Field studies of losses from canals in the Kadulla irrigation scheme, Sri Lanka, are reported by Holmes et al. (1981). From ponding tests in an unlined
277 c a n a l for an aquifer of r e l a t i v e l y low p e r m e a b i l i t y , losses were found to be 0.13 m d 1. W h e n a section of lined c a n a l was tested in a similar w a y the losses were e q u i v a l e n t to 0.12 m d 1. A careful i n s p e c t i o n of the c a n a l s h o w e d t h a t t h e r e were m a n y c r a c k s and joints filled w i t h silt. W h e n t h e s e w e r e m a d e good, the losses were r e d u c e d to 0.07 m d 1. Detailed m e a s u r e m e n t s h a v e been m a d e r e c e n t l y in the P e r i y a r Vaigai Project, M a d u r i , S o u t h I n d i a to i n v e s t i g a t e the effectiveness of lining canals. The e x t e n s i v e r e s u l t s for c a n a l losses c a n be s u m m a r i s e d as follows:
Main canals Large distributaries Medium distributaries Small d i s t r i b u t a r i e s
unlined 0.37md 0.18md 0.09 m d 0.06 m d
~ ~ 1 1
lined 0.11md 0.08md 0.06 m d 0.045 m d
All the a b o v e field results confirm t h a t s u b s t a n t i a l losses do o c c u r from c a n a l s but the f a c t o r s influencing these losses are not discussed in detail. DIFFERING BOUNDARY CONDITIONS W h e n s t u d y i n g the n a t u r e of losses from i r r i g a t i o n c a n a l s u s i n g m a t h e m a t i cal techniques, g r e a t care is needed in selecting the a p p r o p r i a t e conditions on the b o u n d a r i e s of the a r e a to be studied. T h r e e a l t e r n a t i v e sets of b o u n d a r y c o n d i t i o n s are discussed below; the first two were c o n s i d e r e d by B o u w e r (1969), the t h i r d is i n t r o d u c e d for the first time in this paper. In this section the t h r e e p r o b l e m s are i n t r o d u c e d and r e p r e s e n t a t i v e r e s u l t s quoted. The p r a c t i c a l significance of the different cases is considered in m o r e detail in a s u b s e q u e n t section. Case A refers to the loss from a c a n a l t h r o u g h a n aquifer of h y d r a u l i c conductivity k to an u n d e r l y i n g h i g h l y p e r m e a b l e aquifer ku. If the u n d e r l y i n g a q u i f e r is at a d e p t h Da below the c a n a l w a t e r level, Fig. la, the g r o u n d w a t e r h e a d at the i n t e r f a c e w i t h the u n d e r l y i n g aquifer will be h Da. It is possible to c a l c u l a t e the loss from the c a n a l u s i n g an a n a l y t i c a l solution due to K o z e n y and V e d e r n i k o v (Bouwer, 1969). F o r an infinitely deep aquifer, the loss from a t r o c h o i d a l c h a n n e l of width W = 4 m is 6.0 k m3d 1 per m e t r e length of c h a n n e l w h e r e k is the h y d r a u l i c c o n d u c t i v i t y of the aquifer. If the c h a n n e l is of t r a p e z o i d a l s h a p e the loss a p p r o a c h e s k 6.8 m 3 d 1m 1. As an a l t e r n a t i v e to the a n a l y t i c a l a p p r o a c h , n u m e r i c a l solutions c a n be o b t a i n e d u s i n g finite-difference t e c h n i q u e s with specified g r o u n d w a t e r h e a d s a l o n g the p e r i m e t e r of the c a n a l and at the base of the aquifer; c o n d i t i o n s on the free s u r f a c e s are t h a t the p r e s s u r e is a t m o s p h e r i c and t h a t the flow perpend i c u l a r to the b o u n d a r y is zero. Solutions to the finite-difference e q u a t i o n s can be o b t a i n e d u s i n g e i t h e r digital or a n a l o g u e c o m p u t e r t e c h n i q u e s ( R u s h t o n and Redshaw, 1979).
278 W
~Free
W= 4m b = 2m d = ~m
surface
D,
,.
\
k
,~ : >> k \
I ~
t .
.
..oo.
r= i
W b
....
RESULT' O=6 80k m3/d/rn
Ls~
. . . . . ku
_ _
.
h=
o
, : : -D a
"1 ]
~'~/~
Ls= 340m
.
W= 4rn, Ow=6m
~
"
b= 2rn, S=5m
d=lm,
L=lO2m, Da=l~m RESULTS O = 0 93k rn~/d/m
ah
0
,
"
L .. Wb
W=4rn T= Zm,
"-]
~
/
Ground surface
z,,, ~ 7 ~ / ~
Irnperrneabte base "~" ~ / / " / "/~ "/G
,.
(b)
" ~J
b=2rn d = l m , L = 102, O=13m, Oa= llrn kc=OOO21k RESULTS g=l 91k m3/d/m
"~"~'~'~'~--~
Ground surlace F. . . . ~ - - ~
/c)
iDw : 594 " ~i
~k i
IS 5 06
Fig. 1. Three arrangements of boundary conditions. (a) Case A with highly permeable base; (b) case B with impermeable base and fixed head at lateral boundary; and (c) case C with flow through zone of low-conductivity. A n i l l u s t r a t i v e e x a m p l e is p r e s e n t e d i n Fig. la; for t h e p a r t i c u l a r d i m e n s i o n s q u o t e d t h e l o s s d e t e r m i n e d from t h e n u m e r i c a l s o l u t i o n is: Q
=
6 . 8 0 k m 3 d 1 per m e t r e l e n g t h o f c a n a l
279
This result is the same as the a n a l y t i c a l values for a trapezoidal c h a n n e l in an infinitely deep aquifer. A n o t h e r i m p o r t a n t r e s u l t from the n u m e r i c a l solution is t h a t the width of the s a t u r a t e d c o l u m n at the i n t e r f a c e with the high-conductivity l a y e r is 2L s = 6.80 m. This width was d e t e r m i n e d using a finite-difference mesh with a h o r i z o n t a l spacing of 0.05 m in the region where the w a t e r table intersects the highly permeable base. It corresponds exactly with the value expected for parallel d o w n w a r d flow u n d e r a gradient minus one. Case B refers to losses from a canal into an aquifer with an impermeable base (Fig. lb). This problem was considered in great detail by B o u w e r (1969); extensive graphs are p r e s e n t e d based on electrical a n a l o g u e solutions for a r a n g e of geometries. C e r t a i n of Bouwer's results have been r e p r o d u c e d using both digital and a n a l o g u e g r o u n d w a t e r models using t e c h n i q u e s for free surface problems as described by R u s h t o n and Redshaw (1979). P a r a m e t e r values for a typical problem are listed in Fig. lb. W a t e r is assumed to flow from the canal to distant lateral b o u n d a r i e s on which the g r o u n d w a t e r head is specified at h = - 6.0 m. T a k i n g the distance to the o u t e r fixed head b o u n d a r i e s as 102 m and with the o t h e r dimensions as listed in Fig. lb, the total loss from the canal to the two lateral b o u n d a r i e s is: Q _
0.93km3d 1m 1
Case C differs from cases A and B in t h a t the aquifer is assumed to be u n d e r l a i n by a thin layer of lower h y d r a u l i c c o n d u c t i v i t y of thickness T and h y d r a u l i c c o n d u c t i v i t y kc, Fig. lc. Provided t h a t t h e r e is a more permeable p a r t i a l l y s a t u r a t e d l a y e r b e n e a t h this low-conductivity layer, the pressure at the base of the low-conductivity layer a p p r o a c h e s atmospheric, hence the g r o u n d w a t e r head equals the depth below the canal w a t e r level:
h
=
-D
This canal is assumed to be one of the series of similar canals spaced a distance 2L apart; c o n s e q u e n t l y t h e r e is an axis of s y m m e t r y at a distance L from the canal c e n t r e l i n e at which the h o r i z o n t a l flow is zero: ~h/~x
=
0
F r o m a n u m e r i c a l solution to this problem using the dimensions and par a m e t e r values listed on Fig. lc, the total loss from the canal is found to be: Q =
1.91km~d 1m 1
For this example the v a l u e chosen for the h y d r a u l i c c o n d u c t i v i t y of the lower l a y e r is: k~ =
0.0021k
The r e a s o n for choosing this p a r t i c u l a r value is t h a t it results in a depth of the free w a t e r surface below the canal level at the mid point b e t w e e n the canals of 5.94m; this elevation is similar to the depth below canal level at the o u t e r b o u n d a r y of 6.0 m for case B.
280 DETAILED COMPARISONS Detailed c o m p a r i s o n s of the three cases help to identify w h i c h c o n d i t i o n s r e p r e s e n t typical field situations. Case A relates to a zone of high permeability at some depth below the canal. A l t h o u g h such a c o n d i t i o n c a n occur, it is n o t common. Case A is in fact a limiting c o n d i t i o n of the u n d e r l y i n g zone of case C. The i m p o r t a n t issue c o n c e r n i n g case B is the influence of the o u t e r fixed head b o u n d a r y . B o u w e r (1969) suggested t h a t the distance to this b o u n d a r y should be at least ten times the width of the c a n a l bed. To i n v e s t i g a t e the influence of the position of this lateral b o u n d a r y , a series of solutions were obtained with a g r a d u a l l y i n c r e a s i n g distance to the o u t e r b o u n d a r y (Table 1). As the distance to the o u t e r b o u n d a r y increases, the loss from the canal becomes smaller and tends to zero as the distance to the o u t e r b o u n d a r y becomes very large. This o c c u r s because each increase in the distance to the o u t e r b o u n d a r y leads to a decrease in the head gradients resulting in a decrease in the loss from the canal. The flow p a t t e r n s for this p a r t i c u l a r set of b o u n d a r y conditions, c o n s t r u c t e d from a n u m e r i c a l solution in which L - 102 m, are plotted in Fig. 2. These plots indicate t h a t at a s h o r t distance from the canal the flow becomes predominantly horizontal. Figure 2b presents the detailed shape of the equipotentials in the vicinity of the canal. It is i m p o r t a n t to consider the physical significance of the lateral b o u n d a r y in case B. For the dimensions of Fig. 2, this lateral b o u n d a r y c o r r e s p o n d s to a d r a i n a g e c h a n n e l which fully p e n e t r a t e s the aquifer in w h i c h the w a t e r level is 6 m below canal level at a distance of only 100m from the canal. Such a s i t u a t i o n is unlikely to o c c u r in practice because d r a i n a g e channels, if provided, do not fully p e n e t r a t e the aquifer and are c e r t a i n l y far less t h a n 6 m below the level of a c a n a l which is only 100m distant. C o n s e q u e n t l y the c o n d i t i o n s of case B do not represent most practical s i t u a t i o n s and therefore a t h o r o u g h e x a m i n a t i o n of case C is required to determine w h e t h e r it represents more realistic conditions. The first stage in the i n v e s t i g a t i o n of case C is to consider the effect of i n c r e a s i n g distances to the o u t e r b o u n d a r y . Table 2 c o n t a i n s results for a l o w - c o n d u c t i v i t y layer 11 m below the w a t e r level in the c a n a l with a h y d r a u l i c TABLE 1 Case B; effect on canal losses of increasing the distance to outer boundary. Depth of impermeable baseD ~ llm; depth to water tableD w = 6m; canal dimensions: W 4m, b = 2m, d ~ lm Distance to outer boundary L (m)
Loss from canal Q (m:~d 1m ~)
12 30 66 102
4.57k 2.70 k 1.33k 0.93 k
281 F r e e woter surfoce
h:
6m
11rn (a)
Distence L =102 m
b
h=0 i
/ F r e e w o t e r surfQce
/
~ ~
~
~
,
,'~., ~/A
I
i'?~''''
De= 11m
I_ ~
(b)
0
~ . . . . . . . . . . . . . . . . . . . . . . .
I
o
7---+
.....
5 Distonce, m
I_
t
' o
/
!
......
,
"~
J~ .
.
.
.
.
.
............
,, . . . .
.....
10
.
.
.
.
.
.
.
.
.
.
.
.........
20
m31dlm
.
l ~......... ..... ! ......... 15
Q =0.465k
,
I
,
25
Fig. 2. E q u i p o t e n t i a l a n d flow l i n e s for a q u i f e r u n d e r l a i n by i m p e r m e a b l e ba s e w i t h fixed h e a d of 6.0m at 102m from t h e c a n a l c e n t r e l i n e . O t h e r d i m e n s i o n s : / 9 , = 11 m, W = 4 m, b = 2 m a n d d lm.
c o n d u c t i v i t y of 0.2% of the o v e r l y i n g s t r a t a . T h e s e r e s u l t s i n d i c a t e t h a t as the d i s t a n c e b e t w e e n c a n a l s increases, the q u a n t i t y of w a t e r lost from the c a n a l also increases. A second c o n s e q u e n c e of i n c r e a s e d d i s t a n c e s b e t w e e n c a n a l s is a d e c r e a s e in the s a t u r a t e d d e p t h at the o u t e r b o u n d a r y from s = 10.31 m w h e n the d i s t a n c e to the o u t e r b o u n d a r y is 3 0 m to s = 0.10m w h e n L -- 150m. E q u i p o t e n t i a l s and flowlines are s k e t c h e d in Fig. 3 for the case w h e r e L - 102 m and kc = 0.0021 k. This figure shows that, a l t h o u g h w a t e r flows from the c a n a l in a s i m i l a r m a n n e r to case B, it m o v e s t o w a r d s the l o w - c o n d u c t i v i t y l a y e r and passes t h r o u g h to the u n d e r l y i n g m o r e p e r m e a b l e layer. T h e loss from the c a n a l to the l o w - c o n d u c t i v i t y l a y e r is 1.91km3d l m 1 c o m p a r e d to the v a l u e for case B of 0.93 k m 3d l m 1 w h i c h was o b t a i n e d for the s i t u a t i o n w h e r e the w a t e r level in the d r a i n a g e c h a n n e l is 6 m below c a n a l level. A c o m p a r i s o n of the e q u i p o t e n t i a l s in the v i c i n i t y of the c a n a l shows s t e e p e r g r a d i e n t s w h e n the w a t e r is m o v i n g t o w a r d s the l o w - c o n d u c t i v i t y layer. The m a g n i t u d e of the v e r t i c a l flows t h r o u g h the l o w - c o n d u c t i v i t y l a y e r for the four s p a c i n g s b e t w e e n c a n a l s is i l l u s t r a t e d in Fig. 4. W h a t e v e r the d i s t a n c e to the o u t e r b o u n d a r y , the m a g n i t u d e of the flow i m m e d i a t e l y b e n e a t h the c a n a l is similar. H o w e v e r , at g r e a t e r d i s t a n c e s from the c a n a l t h e r e are c l e a r differences in the d i s t r i b u t i o n of the v e r t i c a l flows t h r o u g h the low-conductivity l a y e r due to s m a l l e r h e a d differences across it. T h e l a r g e s t v a l u e of L in T a b l e 2 (and Fig. 4) is 150 m c o r r e s p o n d i n g to a d i s t a n c e b e t w e e n c a n a l s of 300m. A l t h o u g h l a r g e r s p a c i n g s c a n be used, the s a t u r a t e d d e p t h d e c r e a s e s and t h e r e f o r e t h e r e is a d i s t a n c e at w h i c h the
282 TABLE 2 Case C; effect on c a n a l losses of i n c r e a s i n g t h e d i s t a n c e to t h e o u t e r b o u n d a r y . D e p t h to lowc o n d u c t i v i t y l a y e r D = l l m ; t h i c k n e s s a n d h y d r a u l i c c o n d u c t i v i t y of l o w . c o n d u c t i v i t y l a y e r T ~ 2 m a n d k~ = 0.002k; c a n a l d i m e n s i o n s : W = 4 m , b = 2m, d = l m D i s t a n c e to o u t e r b o u n d a r y L (m)
Loss from c a n a l Q (m3d l m ~) D e p t h to w a t e r table D w(m)
30 48 102 150
0.75 k 1.14 k 1.86 k 1.99k
?--
~
._C..ana,! w_a_t_er_L_e..v~. . . . . . . . ,
tO_= 1
- •
1
( a )
2.0
-2.5
Free w a t e r surface
3'0
4
~
-5.0
~
T=2m
0.64 1.61 5.62 10.90
--
10Zrn
~Dw 5 9"* m
"I
T/, z, z~, / , /" . / / / // If/-///~.'// O / / / , / /
k - 0.0021 k
)" "
Fig. 3. E q u i p o t e n t i a l a n d flow lines for a q u i f e r u n d e r l a i n by l o w - c o n d u c t i v i t y l a y e r w i t h k~ = 0.0021k. C a n a l d i m e n s i o n s : W = 4 m, b = 2 m a n d d = 1 m. --="
Distance
from the canal
50
axis( L )
100
150
1° Vert i cat flow (retold)
3
Q = 1 984 k m3/d/m
6 8
O = 1-882k
10
=48m Q= 1.134 k m3/d/m
12 \ L=30m Q= 0-750 k
rn31dlm
m31dlm
Fig. 4. D i s t r i b u t i o n of vertical flow t h r o u g h l o w - c o n d u c t i v i t y l a y e r for k,. = 0.002 k w i t h different v a l u e s of L.
283
saturated depth in the upper aquifer zone becomes zero. For the aquifer dimensions and hydraulic conductivities used in Table 2, that distance is about 160 m.
Different hydraulic conductivities of the lower layer The examples for case C quoted in Table 2 all relate to a hydraulic conductivity for the lower layer of kc = 0.002 k. Table 3 contains a set of results with differing values of kc. In all the examples the difference in groundwater head between the water surface in the canal and the bottom of the lower layer is 1am. Example 7 corresponds to the third line of Table 2. Smaller values of k,: result in smaller losses from the canal because the effective overall hydraulic conductivity between the upper and lower constant head boundaries is decreased thereby reducing the flow of water and increasing the elevation of the water table. Indeed, as the hydraulic conductivity of the lower layer tends to zero, the water table approaches the horizontal since there is no outlet for the water. Larger values of the hydraulic conductivity of the lower layer lead to increasing losses from the canal. For values of kc greater than 0.005k, the saturated section does not extend to the outer boundaries at 102m. For instance, with kc = 0.01 k the saturated region extends 60 m on either side of the canal centreline. The limiting case of the hydraulic conductivity of the two layers being the same corresponds to case A; the loss from the canal then equals the value quoted earlier of 6.80kmad lm 1. TABLE 3 Losses from canal for case C; Fig. lc for different hydraulic conductivity of the lower layer. Canal dimensions: W = 4m, b = 2m, d = l m , total depth D = 13m, depth to the layer D, = l l m , thickness of lower layer T = 2 m. Distance to outer no flow b o u n d a r y L = 102 m Example
Hydraulic conductivity ratio kjk
Loss from unit length of canal Q/k (m 2)
Width of flow t h r o u g h lower layer 2L (m)
Max. depth to w a t e r table Dw
(m) 1 2 3 4 5 6 7 8 9 10 11 12 13
0.0 0,0001 0.0002 0.0004 0.0008 0.001 0.002 0.0021 0.004 0.01 0.02 0.04 1.0
0.0 0.13 0.26 0.49 0.92 1.11 1.86 1.91 2.70 3.79 5.12 6.26 6.80
204 204 204 204 204 204 204 204 204 120 95 60 6.80
0.0 0.36 0.68 1.28 2.42 2.99 5.55 5.94 9.88 11.0 11.0 11.0 11.0
284
This detailed i n v e s t i g a t i o n of case C suggests t h a t losses from c a n a l s t h r o u g h u n d e r l y i n g l o w - c o n d u c t i v i t y l a y e r s r e p r e s e n t the c o n d i t i o n s w h i c h often o c c u r in practice. In the field, it is u n l i k e l y t h a t t h e r e will be a single c o n t i n u o u s l o w - c o n d u c t i v i t y l a y e r of c o n s t a n t t h i c k n e s s but m o r e v a r i a b l e zones of low h y d r a u l i c c o n d u c t i v i t y h a v e a similar effect. WATER WITHDRAWN IN THE VICINITY OF THE WATER TABLE
In all the s i t u a t i o n s discussed a b o v e it has been a s s u m e d t h a t the w a t e r t a b l e acts as a zero flow b o u n d a r y . In p r a c t i c e t h e r e are a n u m b e r of r e a s o n s why w a t e r m a y be effectively w i t h d r a w n from the aquifer in the v i c i n i t y of the w a t e r table. (1) The w a t e r table i n t e r s e c t s the g r o u n d s u r f a c e c a u s i n g s e e p a g e faces or w a t e r l o g g i n g . This is especially c o m m o n w h e n the c a n a l lies on an e m b a n k m e n t . (2) E v a p o t r a n s p i r a t i o n o c c u r s from the w a t e r t a b l e due to r o o t s of plants or trees e x t e n d i n g into the s a t u r a t e d zone. (3) T h e w a t e r table rises and w a t e r is t a k e n into storage. E a c h of these e x a m p l e s c o r r e s p o n d s to an a l t e r n a t i v e m e a n s by w h i c h w a t e r is effectively w i t h d r a w n from the aquifer u n d e r l y i n g the canal; this c a n lead to a c h a n g e in the c a n a l losses. To i l l u s t r a t e the effect of this w i t h d r a w a l of water, it will be a s s u m e d t h a t t h e r e is an u p w a r d v e l o c i t y w h i c h d e c r e a s e s u n i f o r m l y from 6.00 k m m d ~a d j a c e n t to the c a n a l to 3.00 k m m d 1, at 100m on e i t h e r side of the canal; this is e q u i v a l e n t to a t o t a l u p w a r d flow of 0.90 k m :3d ~m 1. If this is s u p e r i m p o s e d on the aquifer and b o u n d a r y c o n d i t i o n s for case C, e x a m p l e 6 of 'Fable 3, the t o t a l loss from the c a n a l b e c o m e s 1.82k c o m p a r e d to 1.11 km:~d ~m ~ w h e n no flow crosses the w a t e r table. A n o t h e r c o n s e q u e n c e of the flow from the v i c i n i t y of the w a t e r t a b l e is t h a t the d e p t h to w a t e r t a b l e i n c r e a s e s from 2.99 m to 6.01m. The effect of w a t e r w i t h d r a w n from the w a t e r t a b l e h a s b e e n explored for the s i t u a t i o n w h e r e v e r t i c a l flow o c c u r s t h r o u g h the u n d e r l y i n g l o w - c o n d u c t i v i t y layer. Results could equally well be o b t a i n e d for the s i t u a t i o n w h e r e the u n d e r l y i n g l a y e r is i m p e r m e a b l e . SIZE AND I,INING OF CANALS
Only one size of c a n a l has been considered thus far and the n e x t step is to consider the effect of the size of the canal. S u b s e q u e n t l y the effect of p a r t i a l or c o m p l e t e lining on the c a n a l losses will be considered. T a b l e 4 records the losses with t h r e e different c a n a l sizes for the e x a m p l e of an u n d e r l y i n g l o w - c o n d u c t i v i t y l a y e r w i t h kc = 0.002 k. F o r the s m a l l e s t c a n a l with a w e t t e d p e r i m e t e r of 3.83 m the loss is 1.80 m 3d 1m 1whilst for the l a r g e s t c a n a l w i t h a wetted p e r i m e t e r of 9.66m the loss is only slightly h i g h e r at 1.95m3d l m 1. T h e s e results d e m o n s t r a t e t h a t the s t a n d a r d p r o c e d u r e of ass u m i n g t h a t the loss is p r o p o r t i o n a l to the w e t t e d p e r i m e t e r c a n be v e r y misleading. A second set of results, T a b l e 5, shows the effect of different types of lining. The c a n a l d i m e n s i o n s are those used in m a j o r i t y of the s o l u t i o n s described
285 TABLE 4 Effect of canal dimensions on losses. Total aquifer depth D 13 m; depth of aquifer D, thickness and hydraulic conductivity of lower layer T 2m, k,. - 0.002k
b
d
Loss from unit length of canal Q/k (m-')
3
1
1
1.80
4 s
2 4
1 2
1.86 1.95
Dimension of unlined canal (m) W
11 m,
Maximum depth to water table D~.(m) 6.0 5.55 5.22
a b o v e a n d t h e l o w e r l a y e r h a s a h y d r a u l i c c o n d u c t i v i t y of 0.002 k. T h e first r e s u l t is for a n u n l i n e d c a n a l , w h i l s t t h e s e c o n d r e f e r s to t h e c a s e of t h e sides lined, b u t t h e bed u n l i n e d . The r e d u c t i o n in t h e loss from 1.86k to 1.83 k m 3d 1m l is e q u i v a l e n t to a d e c r e a s e of o n l y 2%. In a n o t h e r s i m u l a t i o n , t h e bed is c o m p l e t e l y l i n e d a n d t h e sides left u n l i n e d ; t h e loss b e c o m e s 1.79m3d 1m 1 w h i c h is e q u i v a l e n t to a r e d u c t i o n from t h e u n l i n e d losses of a l m o s t 4%. T h i s i n d i c a t e s t h a t t h e d e p o s i t i o n of s i l t on t h e bed of t h e c a n a l m a y h a v e l i t t l e effect on t h e t o t a l losses. P e r f e c t l i n i n g of a c a n a l w o u l d p r e v e n t all losses, b u t an e x a m i n a t i o n of a c t u a l c a n a l s i n d i c a t e s t h a t even w i t h t h e g r e a t e s t c a r e t h e l i n i n g does n o t r e m a i n perfect. A w e l l - m a i n t a i n e d c a n a l m i g h t a c h i e v e t h e c o n d i t i o n t h a t t h e l i n i n g is 99% perfect. If t h e t h i c k n e s s of t h e l i n i n g is 10 cm, t h e n t h e effective h y d r a u l i c c o n d u c t i v i t y of t h i s 10cm l a y e r is 0.01k. W h e n t h i s c o n d i t i o n is i n c o r p o r a t e d in t h e n u m e r i c a l model, t h e losses a r e as r e c o r d e d in t h e final line of T a b l e 5. The t o t a l loss from t h e c a n a l b e c o m e s 1.34km:~d l m 1 w h i c h is 71% of t h e losses w h e n no l i n i n g is p r e s e n t . T h e 10cm t h i c k n e s s of h y d r a u l i c c o n d u c t i v i t y 0.01 k is e q u i v a l e n t to an a d d i t i o n a l l e n g t h of t h e flow p a t h of 10 m w i t h t h e s t a n d a r d h y d r a u l i c c o n d u c t i v i t y k. The l e n g t h e n i n g of t h e effective flow p a t h by 10m does n o t l e a d to a m a j o r r e d u c t i o n in t h e losses. TABLE5 Effect of lining of canal on losses for the aquifer properties as in Table 4. Canal dimensions: W::4m,
b = 2m, d=
lm
Form of lining
Loss from unit length of canal Q / k (m2)
Maximum depth to water table Dw(m)
Unlined Sides lined, bed unlined Bed lined, sides unlined Hydraulic conductivity within 10cm of canal reduced to 1% of normal values
1.86 1.83 1.79
5.55 6.08 6.01
1.34
8.45
286
CONDITIONS AT DIFFERENT TIMES OF THE YEAR
All the examples quoted above assume that some form of dynamic equilibrium is applicable with the inflows balancing the outflows. In practice conditions will vary during the year but the actual changes depend on site-specific details such as the ability of deeper aquifers to move water away laterally. Since the time variant behaviour is so site specific, detailed time variant studies will not be included. Instead, three possible conditions, which are likely to occur in many situations, will be studied. These three conditions are illustrated in Fig. 5. Condition 1 represents the situation when flow occurs through the lowconductivity layer to an underlying more permeable zone. Consider the case when the water table in the underlying zone is at 16.0 m below canal level (i.e. 3 m below the base of the low-conductivity zone). At the base of the low-conductivity zone, the pressure is approximately atmospheric; therefore conditions for case C apply. For a distance between canals of 204 m, the results can be taken from example 6 of Table 2. Consequently the total loss is 1.11km:~d lm 1 which, when divided by a width of 204 m, is equivalent to an average vertical Condition 1 .02m phreatlc
Surface
98m :;
2~,~¢ = o . o o l , : / / / / / / ~ / / > : / . ~ h=-13 Om
..~.>%< (Q= 1.11k m31d/m) initia[
m
~: :/%~. ,
~.Om 30m
w a t e r table
L=lO2m Condition 2
I h=-70m
48m 52rn
( Q =0.61 k3rn/d/m)
Condition 3 k" m3/d'm ~ ~ O'Z"50
[i
t 23"84 7 m
16rn 2 2~ ~
k¢ : o. oo 1 k> ~ / X / / ' X , ~ / , : I Y / . ~ 1 7 / 7 / : 9 H / / / ~ d
h= -7.Ore
" ( Q=O .458 k m3/d/m )
v!
J_z. o m
Fig. 5. Typical aquifer conditions during a year. (a) Start of canal operation; (b) region below low-conductivity layer fully saturated; and (c) as (b) but with flows from the water table.
287 flow from the b a s e of the l o w - c o n d u c t i v i t y zone of 0.0054 k m d 1. F o r a specific yield of Sy, the rise in g r o u n d w a t e r h e a d in the u n d e r l y i n g a q u i f e r would be: O.O054k/Sy m d 1
T a k i n g t y p i c a l v a l u e s o f k = 1.0rod 1 a n d Sy = 0.12, the a v e r a g e rise e a c h d a y would be 0.045 m, t h u s it would t a k e a b o u t 67 d a y s for the w a t e r table to rise 3 m to the b a s e of the l o w - c o n d u c t i v i t y layer. This a s s u m e s t h a t no w a t e r c a n m o v e a w a y l a t e r a l l y in the deeper aquifer. In p r a c t i c e some l a t e r a l outflow is likely to o c c u r r e s u l t i n g in a longer time for the rise in w a t e r table. C o n d i t i o n 2 r e p r e s e n t s the s i t u a t i o n w h e r e the aquifer u n d e r l y i n g the lowc o n d u c t i v i t y l a y e r is fully s a t u r a t e d . F o r example, if the p i e z o m e t r i c head in this u n d e r l y i n g a q u i f e r is 6.0 m a b o v e the base of the l o w - c o n d u c t i v i t y zone, the g r o u n d w a t e r h e a d at the b a s e is - 7.0 m r e l a t i v e to the c a n a l w a t e r level. W i t h these c o n d i t i o n s included in the n u m e r i c a l model, the flow from the c a n a l is r e d u c e d to 0.61km3d l m 1 and the d e p t h from the c a n a l level to the w a t e r t a b l e m i d w a y b e t w e e n the c a n a l s is 1.47 m c o m p a r e d to 3.02 m w h e n the w a t e r t a b l e is w i t h i n the lower aquifer. With such a s h a l l o w w a t e r table, it is likely t h a t significant e v a p o r a t i v e losses will o c c u r from the v i c i n i t y of the w a t e r table; this leads to the t h i r d condition. C o n d i t i o n 3 is s i m i l a r to condition 2 in t h a t the g r o u n d w a t e r h e a d in the u n d e r l y i n g aquifer is - 7.0 m, but t h e r e is also a loss from the v i c i n i t y of the w a t e r table. T h e s e losses are t a k e n to be the s a m e as t h o s e of the p r e v i o u s section w i t h 0 . 0 0 6 k m d 1 in the v i c i n i t y of the c a n a l falling to 0 . 0 0 3 k m d m i d w a y b e t w e e n the canals. With t h e s e conditions, the t o t a l loss b e c o m e s 1.36 k m 3d 1m ~1 from the c a n a l with a m a x i m u m d e p t h to w a t e r table of 3.84 m below c a n a l level. E a c h of t h e s e c o n d i t i o n s could o c c u r in a p r a c t i c a l situation. F o r c o n d i t i o n 1 the loss is at its m a x i m u m at 1.11m3d l m 1 but following a rise in the g r o u n d w a t e r h e a d in the deeper aquifer, the loss is reduced until, as the w a t e r t a b l e rises and e v a p o r a t i o n from the w a t e r t a b l e occurs, the loss from the c a n a l m a y i n c r e a s e to a b o u t 1.36 k m 3d- xm 1. CONCLUSIONS Field m e a s u r e m e n t s d e m o n s t r a t e t h a t significant losses do o c c u r from c a n a l s w h e t h e r t h e y are lined or unlined. This p a p e r h a s e x p l o r e d the likely flow m e c h a n i s m s w h i c h explain these losses. The existing m e t h o d s of a n a l y s i s h a v e been e x t e n d e d to i n c l u d i n g the effects of layers w i t h a low h y d r a u l i c c o n d u c t i v i t y at some d i s t a n c e b e n e a t h the c a n a l and losses f r o m the v i c i n i t y of the w a t e r table. F o r e a c h of t h e s e conditions, the c a n a l losses are; g e n e r a l l y h i g h e r t h a n the v a l u e s based on the e x i s t i n g a p p r o a c h e s . A s t u d y of the effect of lining i n d i c a t e s t h a t little is to be g a i n e d from lining e i t h e r the b a s e or the sides of the canal. P e r f e c t lining of the t o t a l c a n a l will p r e v e n t all losses but linings t h a t h a v e a n y i m p e r f e c t i o n s are s h o w n to r e s u l t in o n l y a small r e d u c t i o n in the losses.
288 F u r t h e r w o r k is r e q u i r e d o n t w o a s p e c t s c o n c e r n i n g c a n a l l o s s e s . T h e first r e q u i r e m e n t is for d e t a i l e d field w o r k w i t h c a r e f u l s t u d i e s o f t h e u n d e r l y i n g s t r a t a u s i n g n u m e r o u s p i e z o m e t e r s to m o n i t o r t h e g r o u n d w a t e r h e a d s b e n e a t h a n d to t h e s i d e s o f t h e c a n a l s . S e c o n d l y , f u r t h e r d e t a i l e d m o d e l l i n g w o r k is a d v i s a b l e to i n v e s t i g a t e t h e p r o b a b l e l o s s e s f r o m a q u i f e r s w i t h a g r e a t e r h e t e r o g e n e i t y t h a n c o n s i d e r e d in t h e p r e s e n t s t u d y .
REFERENCES Ahmad, N., 1974. Groundwater Resources of Pakistan. Ripon Printing Press, Lahore, 295 pp. Bos, M.G. and Nugteren, J., 1978. On Irrigation Efficiencies. Int. Inst. Land Reclam. Improv., Neth., 138 pp. Bouwer, H., 1969. Theory of seepage from open channel. In: Ven Te Chow (Editor), Advances in Hydroscience, 5. Academic Press, New York, N.Y., pp. 121-172. Holmes, D.W., Wooldridge, R., Weller, J.A., Gunston, H. and Batchelor, C.H., 1981. Water Management study at Kaudulla Irrigation Scheme, Sri Lanka. Rep. No. O.D. 38, Hydraul. Res. Stat., Wallingford. O'Mara, G., 1986. Conjunctive Water Use. Proc. Budapest Symp., IAHS Publ. No. 156. Pontin, J.M.A., Laila Abed and Weller, J.A., 1979. Prediction of seepage loss from the enlarged Ismalia Canal. Rep. No. O.D.28, Hydraul. Res. Stat., Wallingford. Rushton, K.R. and Redshaw, S.C., 1979. Seepage and Groundwater Flow. Wiley. New York, N.Y., 332 pp. Worstell, V., 1976. Estimating seepage losses from canal systems. J. Irrig. Drain. Div. Am. Soc. Civ. Eng., 102, IRI, pp. 137 147.