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Scope

NATIONAL ENGINEERING HANDBOOKSECTION 16

DRAINAGE OF AGRICULTURAL LAM)

CHAPTER 1. PRINCIPLES OF DRAINAGEContents

Page

Elements of Drainage DesignClassification of drainage methodsDevelopment of drainage-design criteria

Types of Drainage ProblemsSurface-drainage problemsSubsurface-drainage problems

Basin-type free-water tableWater table over an artesian aquiferPerched-water tableLateral ground-water flow problems

Differences in Drainage in Humid and Arid AreasCrop Requirements

Effects of excess water on cropsDrainage requirements determined by cropsCrop growth and the water table

Surface-Drainage PrinciplesSubsurf ce-Drainage Principles

Forms of soil waterGravity waterCapillary waterHygroscopic water

The water table and the capillary fringePrinciples of flow in the saturated zoneHydraulic headHydraulic gradientPaths of flow (streamlines)Flow nets and boundary conditionsPermeability and hydraulic conductivityRate of flowSink formation in subsurface drainage

Theories of Buried Drain and Open Ditch Subsurface DrainageClassification of drainage theories by basic assumptions

Horizontal flow theoriesRadial flow theoriesCombined horizontal and radial flow theoriesVan Deemter's hodograph analysisTransient flow concept

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Te c hn ique s f o r a pp ly ing d r a ina ge the o r i e sM a the m a t i c a l a na lys i sRe lax a t io n methodE l e c t r i c a l a na lo gModels

D r a i n a g e c o e f f i c i e n t sD ra in ag e c o e f f i c i e n t s f o r s u r f a c e d r a in a g eD r ai n ag e c o e f f i c i e n t s f o r s u b s u r f a c e d r a i n a g eDr a ina ge c o e f f i c i e n t s f o r pumping p la n t sD r ai n ag e c o e f f i c i e n t s f o r w a te rs h ed p r o t e c t i o nS p e c i a l r eq u ir em e nt s f o r f l a t l a n d

D ep th t o w at e r t a b l e

Cl as se s of pumped wel lsWa te r - t a b le we l l sC o nf in e d- aq u if er o r a r t e s i a n w e l l s

The or ies of f low in t o pumped we l l sWa te r - t a b le we l l sC o nf in e d- aq u if er o r a r t e s i a n w e l l sBas i s f o r des ign of pumped-drainage we l l s

Advantages of pumped-well dr ai na ge

F i g u r e s1-1 I l l u s t r a t i o n of h y d r a u l i c h ea d

r e 1-2 I l l u s t r a t i o n of h y d ra u l ic g r ad i e n t1 -3 E q u i p o t e n t i a l s u r f a c e s

r e 1-4 Di f f e r e nc e betwe en hyd r a u l i c g r a d ie n t a nds l o p e of t h e w a t er t a b l ee 1-5 Flow d i r e c t i o n i n i s o t r o p i c s o i l

1-6 Flow d i r e c t i o n i n a n i s o t r o p i c s o i lr e 1-7 S t r e a m l ine s a nd e qu ipo te n t i a l s

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NATIONAL ENGINEERING HANDBOOKSECTION 16

DRAINAGE OF AGRICULTURAL LAND

CHAPTER 1. PRINCIPLES OF DRAINAGEScope

T h i s c h a p t e r p r e s e n t s b a s i c p r i n c i p l e s a nd t h e o r i e s c o nc e rn in g t h e r em ov al o fe x c e s s w a t e r fro m a g r i c u l t u r a l l a n d . I n v a r i o u s br an c he s o f s c i e n c e , c e r t a i nlaws of f lo w have been dis cov ere d th a t ap ply t o t h e movement of wate r on thel an d s u r f ac e , w i th in ch an n e l s , and t hr o ug h th e s o i l . A l s o, much emp i r i ca li n f o r m at i o n p r ov i di n g a b a s i s f o r th e empi r ica l methods of d ra ina ge des ig n hasaccumulated over the yea r s . Rev iew of the se fundamenta l s a s they app ly tod r a i n a g e s ho u l d b e h e l p f u l t o t h e e n g in e e r i n c o r r e c t l y a p p r a i s i n g d r a i n a g ep ro bl em s i n t h e e a r l y s t a g e s of t h e i r i n v e s t i g a t i o n a nd working o u t t h e i rp r a c t i c a l s o l u t i o n . A k now le dge of d r a i n a g e p r i n c i p l e s i s n eces s a r y i n d eve lop -i n g l o c a l s t a n d a r d s f o r d r a i n a g e d e s i g n . E x i s t i n g d r a i n s n ee d t o b e e v a l u a t e d .Where l o c a l i n f or m a ti o n f o r d e s i g n c r i t e r i a i s l ack i n g , ex p e r i ence f ro m o th e rp l a ces may need t o b e ad ap ted f o r l o c a l u s e .Although t he fundamenta l equa t ion f o r f low i n sa t u r a t ed so i l s - -Da rcy ls Law (I)*--has been known f o r many y e a rs , i t s ap p l i c a t i o n t o mos t d r a in ag e p ro b lems i scomplex. Sev era l approximate methods fo r so lv in g th es e subsurface-f low problemshave been developed. The b as i c a s s ump t io n s i n t h es e me th od s a r e p r e s en t edb r i e f l y i n t h i s c h ap te r. T h ei r l i m i t a t i o n s i n p r a c t i c a l a p p l i c at i o n t o f i e l ds i t u a t i o n s a r e a l s o d i sc u ss e d.

Elements of Drain age DesignG e n er a ll y , t h e i n s t a l l a t i o n of a d ra i n ag e s ys te m, l i k e any s i m i l a r a p p l i c a t i o nof t h e s c i e n c e s , i n c l u d e s a d e s i r e d g o a l , a s u r v ey of e x i s t i n g c o n d i t i o n s ,p r ev io u s ex p e r i en ce w i th s im i l a r co n d i t i o n s , and p r ep a r a t i o n of d e s ig n s and p l an s .I n S o i l C o ns e rv a t io n S e r v i c e o p e r a t i o n s , t h e p r i n c i p a l e l e m e nt s of d r a i n a g ed e s ig n a r e c ro p r eq u ir em e nt s, s i t e i n v e s t i g a t i o n s , d e s ig n c r i t e r i a , and p la n sand s p ec i f i c a t i o n s . Each of t h e s e e l emen t s w i l l be t r e a te d i n d e t a i l i n t h i sand. i n o th er ch ap t er s o f t h i s Se ct i on o f the Na t iona l Engineering Handbook .A t s e v e r a l p o i n t s i n t h e d e s i g n p ro c ed ur e, i t may be ne ces sar y t o cho ose betweena l t e r n a t e l o c a t i o n s , m eth ods, o r m a t e r i a l s . The c ho ic e depends on t h e managementan d econ omic a s p ec t s of t h e f ar m o r r an ch a s w e l l a s o n t h e p h y s i ca l r eq u i r emen t so f t h e s i t e . The d es ig n e r may n eed t o p r e s en t t o t h e land ow ner a l t e r n a t e metho dso r i n t e n s i t i e s of d r a in ag e , s o t h a t t h e owner may make t h e f i n a l ch o i ce .T h e same t ec h n i ca l d es ig n e l emen t s f o r i n d i v id u a l f ar m sy s tems a r e p r e s en t f o rl a r g e g r ou p -d r a in ag e s y s tems , b u t p u b l i c o r co mmun ity- ty pe f a c t o r s a l s o a r ei n vo l v ed . T he se f a c t o r s i n c l u d e t h e d r a i n a ge o r g a n i z a t i o n ( d r a i n a g e e n t e r p r i s e ) ,l e g a l r eq u i r emen t s f o r r ig ht s- of -w ay and w a te r d i s p o s a l o r u s e , f i n a n c i a la r ra n g em e n t s, and c o s t a l l o c a t i o n . Such p r o j e c t s r e q u i r e c om p le te , d e t a i l e ddocumenta tion of t he surve ys , p la ns , and cons t ruc t io n .

*Numbers i n p a r e n th e s e s r e f e r t o r e f e r e n c e s l i s t e d a t end o f e a ch c h a p t e r .

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as s i f i c a t i o n o f d r a i n ag e meth od she methods used f o r l and d ra ina ge may be c la ss i f i e d i n two b road ca tegor ies - -

r f ac e d ra inage and subsu r fac e d ra inage- -depend ing on t he way t he water i s

1. I n s u r f a c e d r a i n a ge , l an d s u r f a c e s a r e re s ha p ed a s n e c e s s a r y t oe l i m i n a t e po nd in g and e s t a b l i s h s l o p e s s u f f i c i e n t t o i n d uc e g r a v i t a -t i o n a l f l ow o v e rl and and t hro u gh ch an n e l s t o an o u t l e t . Su r f acedr ai na ge may be d ' ivided in t o works whicha. remove wate r d i r e c t l y from land by land smoothing, land gradi ng,

bedd ing , and d i t ch i ngb . d i v e r t an d ex c lu d e w a t e r from l an d by d i v e r s i o n d i t ch e s , d i k e s ,

and floodways.2 . I n s u b su r f ac e d ra i na g e , d i t c h e s and b u r i e d d r a i n s a r e i n s t a l l e d w i t h i n

t h e s o i l p r o f i l e t o c o l l e c t a nd c on vey e x c es s gr ou nd wa t e r t o a g r a v i t yo r pumped o u t l e t . The d ro p i n p r e s s u re r e s u l t i n g from d i s ch a rg e i n d u cest h e f lo w o f e x c e s s grou nd w a te r t hr o ug h t h e s o i l i n t o t h e d r a i n s .a . In t e r c ep t o r d r a i n s a r e us ed t o p r ev en t en t r y upon t h e l an d when

ground water moves l a t e r a l l y . D ra i n s a r e o r i en t ed . app ro xi ma te l ya t r i g h t a n g l e s t o t h e d i r e c t i o n o f g ro un d- wa te r f lo w.

b . R e l i e f d r a i n s a r e u se d when l a n d s u r f a c e s a r e n e a r l y f l a t , f l owv e l o c i t i e s l ow , o r i n t e r c e p t i o n of g ro und wa t e r i n e f f e c t i v e .Dra ins a r e commonly (bu t no t ne ce ss ar i l y a lways) o r i en t ed approx i-ma t e l y p a ra l l e l w i t h t h e d i r ec t i o n of g rou nd -w at er f lo w .

velopment of drainage-design c r i t e r i as ig n c r i t e r i a a r e d ev el op ed i n two gen era l ways: (a ) f rom emp i r i ca l da t al l ec te d through eva lua t io n of ex i s t in g d ra inage sys tems , and (b ) f rom aeo re t i ca l ana ly s i s o f t he p rob lem, app ly ing known phy s ic a l l aws and t e s t in ge t h eo ry t h ro u g h .ev a l u a t i o n o f ex i s t i n g d ra i n ag e s y s t ems .

n exa mple of e m p i r i c a l c r i t e r i a a r e t h e d r a i n a g e c o e f f i c i e n t s u se d i n d e si g nd r a i n s i n humid a r e a s . Such c o e f f i c i e n t s a r e t h e r em ov al r a t e s f o r e x ce s s

r , found by expe r ienc e wi th many in s t a l l e d d ra inag e systems , to p rov ide ar t a i n d e g r ee of c r o p p r o t e c t i o n . Su ch p ro t e c t i o n h as been a s s e s s ed ca r e fu l l ya i ns t observed c rop response and p r oduc t ion , measurements o f f low from dra inag e

prov id ing good d ra inage , and measured he ig h t s o f water t ab le . S incei ri ca l c r i t e r i a a r e ba sed s u b s t a n t i a l l y on ex p e r i en ce an d a s s e ss men t s of

umerous i n t e r r e l a t i n g f a c t o r s , c a r e m us t be t a k e n i n t r a n s p os i n g t h e i r u s e f rome l o c a l i t y t o a n o th e r .

o re t i c a l an a l ys i s ap p l i e s proved p r i nc ip le s o r l aws to p rob lems hav ing knownmi t i n g co n d i t i o n s . The r e s u l t i n g ma t hema ti ca l ex p re s s i o n ex p l a i n s t h e o b se rv edt i o n of ex i s t i n g d ra i n ag e s y st ems and p e rmi t s t h e r a t i o n a l d e s i g n of new

U su al ly s e v e r a l v a r i a b l e s i t e f a c t o r s e n t e r t h e e x pr e ss io n. An exam plee t h e o r e t i c a l a n a l y s i s i s t h e e l l i p s e e q u at i on f o r s pa c in g s u b s ur f a ce d r a i n s

n i r r i g a t e d l a n d, w he re known s i t e c h a r a c t e r i s t i c s a r e a cc ou nt ed f o r i n t h eI n o n e form of t h e e l l i p s e e q u a t i o n , t h e v a r i a b l e s a r e h y d r a u l i c con-

i v i t y o f t h e s o i l , d e pt h t o im pe rm ea ble l a y e r , d e pt h t o t h e w at er t a b l e a t

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m i d po i nt b e tw ee n t h e d r a i n s , a nd r a t e w a t e r i s t o be r em oved . By s u bs t i t u t i ngknown o r e s t i m a t e d v a l u e s f o r t h e s e f a c t o r s , t h e e q u a t i o n may b e a p p l i e d t o av a r i e t y of s i t e s , a s lo ng a s t h e s i t e c o n d i ti o n s a r e w i t h in t h e l i m i t s f o r w hi cht h e e q u a t i o n was d e r i v e d . T h i s l a s t r eq u ir e me n t i s a l l i m po rt an t i n us in g t h i sk i nd of t h e o r e t i c a l a p pr oa ch .Whichever method i s u se d t o e s t a b l i s h d ra in ag e- de si gn c r i t e r i a , i t i s e v i d e n tt h a t i t s v a l u e de pe nd s n o t o n l y o n so un d a n a l y s i s o f t h e d r a in a g e s i t u a t i o n b u ta l s o on e v a l u a t i o n of i n s t a l l e d d r a i n s t o c he ck t h e i r p er fo rm an ce .

Types of Dr ain age ProblemsS uc c e s s f u l d r a i na ge of a w e t a r e a de pe nds on a c o r r e c t d i a g nos i s o f t h e p robl em .A t some s i t e s , a b r i e f f i e l d s t u d y and c om pa ris on w i t h p r ev i ou s i n s t a l l a t i o n sunde r s i m i l a r c ond i t i ons may be a s u f f i c i e n t b a s i s f o r d e s i g n . More com plexd r a i na ge p rob le m s r e qu i r e m or e de t a i l e d r e c onn a i s s a nc e a nd p r e l i m i na r y s u r ve yst o de t e r m i ne t h e s ou r c e o f dam ag ing w a t e r , how w a t e r r e a c he s t h e w et a r e a , a ndw hat de s i gn c r i t e r i a a pp l y . T he d r a i na ge sys t em may be de s i gne d , howe ve r, on l ya f t e r t h e n a t u r e o f t h e pro ble m h a s be en i d e n t i f i e d .T he f o l l ow i n g t y p i c a l d r a i na ge p r ob le m s ha ve be e n d i v i de d i n t o s u r f a c e a nd sub-s u r f a c e p r obl e ms f o r conve n i enc e . A c t ua l l y , w e t l a nd may i nvo l ve bo t h s u r f a c eand s u b s u r f a c e w a t e r , an d t h e d r a i n a g e d e s i g n sh o u l d c o n s i d e r t h e i r i n t e r -dependence.Sur face -dra inage problemsF l a t and n e a r l y f l a t a r e a s o f l a n d a r e s u b j e c ~ o ponded w a te r c au se d by :

1. Uneven l a n d s u r f a c e w i t h p o c k e ts o r r i d g e s wh ic h p r e v e n t o r r e t a r dn a t u r a l r u n o f f . S lo wl y p er m ea bl e s o i l s m ag ni fy t h e p ro bl em .

2. Low-capac i ty-d i sposa l chann e l s wi th in t h e a r ea which remove wa t e r sos l o w ly t h a t t h e h i g h w a t e r l e v e l i n t h e c h a n n el s c a u se s po nd in g o n t h el a nd f o r dam ag ing pe f i ods .

3 . O u t l e t c o n d i t i o n s w hi ch h o l d t h e w a t e r s u r f a c e ab ov e gr ou nd l e v e l , s u cha s h i g h l a k e o r pond s t a g e s , o r t i d e w a t e r e l e v a t i o n s .

S ou rc es of s u r f a c e w a te r a r e r a i n f a l l o r s nowmelt on t h e a r e a i t s e l f , i r r i g a t i o n -s u r f a c e w a st e , r u n o f f o r s e ep a ge f r om a d j o i n i n g h i g h e r l a n d , o r o v e r f l o w fr oms t r e a m c ha nne l s .S u r f a c e - d r a i na ge m e t hods, s uc h a s l a n d g r a d i ng o r sm oot hi ng a nd f i e l d d i t c he s ,a r e us ed o n f i e l d s t o c o l l e c t and c onvey s u r f a c e w a t e r t o n a t u r a l c h a n n e l s o rc o n s t r u c t e d d i s p o s a l s y s t e m s . Inadeq ua te o u t l e t s may re qu i r e downs tream-channeli mprove me nt , l e ve e s w i t h c u l v e r t s a nd f l a p ga t e s , o r d r a i na ge pumps. D i ve r s i ons ys te m s a r e e f f i c i e n t i n p r ev e n t in g o r r e du c in g t h e p on din g of s u r f a c e w a te rw he re t h e s o u r c e i s o u t s i d e t h e a r e a t o b e p r o t e c t e d . T he se and o t h e r f e a t u r e sof s u r f a ce - d r a in a g e s ys te ms w i l l b e d e s c r i b ed more f u l l y i n o t h e r c h a p t e r s .Subsurface-drainage problemsS ubs u rf a c e -d r a i nage p r ob le m s a r i s e fr om many c a us e s. F l a t l a n d t e nds t o be poo r l yd r a i ne d , p a r t i c u l a r l y wh er e t h e s u b s o i l p er m e a b il i t y i s low. The re a r e many weta r ea s , however, where th e r e i s no e v i de n t c onne c t i on be tw ee n t h e a r e a o f s e e page ,o r a h i g h w a t e r t a b l e , and t h e t op og ra ph y of t h e s i t e . High w a t e r t a b l e s may

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o c c ur w he re t h e s o i l i s e i t h e r s l o wl y o r r a p i d l y p e rm e ab l e, w he re t h e c l i m a t e i se i th e r h umid o r a r i d , and w here t h e l an d i s e i t h e r s l op in g o r f l a t .Fo r t h ese r easo n s , i t i s co n v en ient t o c l a s s i f y su b su r f ace - d ra in ag e p ro blems byth e so urce o f exce ss g round water and t he way i t moves i n t o and through th ep ro blem a r e a . T h i s meth od o f i d e n t i f y i n g su b su r f ace co n d i t i o n s i s e s p e c i a l l yus ef u l fo r th e more complex dra in age prob lems because i t a l s o i n d i c a t e s t h e ki ndof d ra i nag e sys tem needed . The reco nnai ssanc e and pre l i mina ry surveys a r e car -r i ed o u t t o o b t a in t h e n eed ed in f o r m a t io n on g ro un d- wa te r o ccu r r en ce and o th e rs i t e c o n d i t i o ns . D e t a i l e d i n fo rm a ti o n i s i n C ha pt er 2 , D r a i n a g e I n v e s t i g a t i o n s .A s ex p e r i en ce w i th su b su r face - d r a in age p ro b lems accu mu la t e s f o r a g iv en a r ea ,the amount of p r e l i m i n a ry i n f o r m a t io n ne ed ed t o i d e n t i f y c e r t a i n pro bl em t y p e su s u a l l y i s reduced. New are as o r new k in ds o f d ra i nag e prob lems re qu i r e g r ea te re m ph as is a t t h e p r e l i m i n a r y s t a g e o f p l a nn i n g.The fo l low ing examples i l l u s t r a t e some of th e more impor tan t t ypes o f subsur face -d r a i n ag e p ro b lems. Pa r t i c u l a r emp hasi s i s g i v e n t o t h e s o u r c e and d i r e c t i o n o fground-water f low. Deta i led des ign of d ra in age sys tems fo r subsu r face d ra in agei s d i scu s sed i n Ch ap te r 4 , Su b sur f ace D r a in ag e . Re f e r t o t h e f i g u r e s i n Chap-t e r 4 f o r i l l u s t r a t i o n of most o f th e d ra ina ge problems desc r ibed be low.Bas in- type f r ee-water tab leI n v a l l ey b o ttoms and o n w id e b en ch land s , t h e f r e e g ro un d w a te r s a t u r a t e s t h es e di m en t s down t o t h e f i r s t im p er vi o us b a r r i e r . T y p i c a l l y , t h e w a t e r t a b l es l op es ge n t ly downval ley . Th is la rg e , ver y s lowly moving body of g round wateri s f e d by s p r i n g s , s u r f a c e s t r e a m s , o r s u b s u r f a c e p e r c o l a t i o n a ro un d t h e p e r i -m et er of t h e v a l l e y ; and by i n f i l t r a t i n g r a i n f a l l , i r r i g a t i o n l o s s e s , o r s u r f a c er u no ff o n t h e v a l l e y f l o o r i t s e l f . E v e nt u a ll y , t h e gro un d w a t er d i s c h a r g e se f f l u e n t s e e p ag e a t s t re am ba nk s o r a t t h e g ro un d s u r f a c e i n low areas, o r e x c e p tf o r ground water used by p l an ts o r t h a t pumped f rom we l l s , i t escapes th rougha q u i f e r s a t t h e l ow e r end o f t h e v a l l e y o r b e nc h la n d. H e ig h t of t h e w a t e r t a b l ef l u c t u a t e s w i t h t h e s e a s o n a l v a r i a t i o n o f a c c r e t i o n s t o t h e gr ou nd -w at er b a s i n .The g e n e ra l s l o p e of t h e wa t er t a b l e v a r i e s o n l y s l i g h t l y i n re s po n se t o t h e s ech an g es i n in f lo w . Where s a l t s a r e p r e sen t i n t h e so i l , t h ey t en d to move upwardt o t h e s u r f a c e a s c a p i l l a r y r i s e r e p l e n i s h e s t h e e v a p o ra t i on from t h e g ro un d.Phrea tophyte s g row where th e wate r t a b l e i s c l o se t o o r a t t h e s u rf a ce .R e l i e f d r a i n s may b e us ed t o l ow er t h e w a t e r t a b l e i n s uc h a r e a s , u n l e s s s o i lp e r m e a b i l i t y i s too low. The ground-water s lo p e i s t oo n e a r l y f l a t and t h ep e r vi o u s se di me nt s a r e t o o de ep f o r e f f i c i e n t i n t e r c e p t i o n ( e x ce p t , p e rh a ps , a tt h e s i d e s o f v a l l e y s n e a r t h e b a s e of t h e h i l l s o r t h e a l l u v i a l c on es ). Whereeconomical ly f e as ib le , pumped-dra inage we l l s a r e somet imes used to lower theb a s in - ty p e w a t e r t a b l e .W ate r t a b l e o v er a n a r t e s i a n a q u i f e rGround w a t e r may b e c o n f in e d i n a n a q u i f e r s o t h a t i t s p r e s s u r e s u r f a c e ( e l ev a -t i o n t o wh ic h i; would r i s e i n a w e l i t a p p i n g t h e a q u i f e r ) i s h i g h e r t h a n t h ead j a cen t f r ee- w a te r t a b l e . The p r e s su r e su r f a ce may o r may n o t b e h ig h e r t h ant h e g round sur fa ce . Such ground wate r i s te rm ed a r t e s i a n . P r e s s u r e i n t h ea q u i f e r i s f rom the weigh t of a con t in uous body of water ex tend ing t o a sou rceh i g h e r t h a n t h e p r e s s u r e s u r f a c e . L ea ks a t h o l e s o r weak p o i n t s i n t h e c on f i n i n gl a y e r abo ve th e aq u i f e r c r e a t e an upward f l o w , w i th h y d r au l i c h ead d ec r eas in g i nth e upward d i r ec t i o n . The g ro un d w a te r moves i n r e sp o n se t o t h i s h y d r au l i cg r a d i e n t an d e scap es as seepag e a t t h e g ro un d su r f ac e ab o ve , o r i t e s c a p e sl a t e r a l l y t hr ou gh o t h e r a q u i f e r s a bove t h e c o n fi n i ng l a y e r .

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A w a t er t a b l e s u p p or t ed by a r t e s i a n p r e s s u r e u s u a l l y i s more d i f f i c u l t t o l ow erand m ai n t ai n a t t h e d e s i r e d h e i g h t t ha n a w at e r t a b l e n o t s u b j e c t t o s u chp r e s s u r e . T h i s i s because water i s co n t in u o u s ly r ep l en i sh ed f ro m th e h ig h e rsource and because i t i s d i f f i c u l t t o remove o r c o n t r o l wa t e r a t t h e s o u rc e .Wet a r e a s o v e r l y i n g w a t er u n de r a r t e s i a n p r e s s u r e r e q u i r e r e l a t i v e l y d ee p andc l o s e l y s pa ce d d r a i n s , r e l i e f w e l l s , or pumped-dra inage we l l s th a t t ap t hea q u i f e r . S uch a r e a s may b e i m p r a c t i c a l t o d r a i n .The dra inage sys tem requ i red t o c on t r o l a r t es ia n f low may depend on th e k ind ofu n d er l yi n g m a t e r i a l . The upward f lo w from t h e s our ce aq ui fe r may rea ch t hew a t er t a b l e t hr ou g h a s t r a t u m o f f a i r l y u ni fo rm m a t e r i a l , o r i t may pass throughf r a c t u r e s o r o t h e r na rr ow o pe n in g s i n s a n ds t on e , c l a y , l a v a , l i m e s t o ne , o r o t h e rm a t e r i a l s t h a t i n th em se lv es a r e p r a c t i c a l l y impermeable. Sur fac e see ps i n somep l a c e s a r e c a us ed by a r t e s i a n f l o w t h a t w e l l s up t h ro ug h r e l a t i v e l y s m a l l o p en in gsi n t h e co n f in in g ma te r i a l , cau s in g g ro un d- wa te r mounds o r su r f ac e s eep s . T h i sk i nd of s e e p u s u a l l y may b e d r a in e d by p l a c i ng a r e l i e f d r a i n a s d e ep a s p r a c t i -cab l e t h ro u gh th e s eep ag e zo ne . A d d i t i o n a l i n t e r c ep t in g d r a i n s may b e need ed t op i c k up f lo w t h a t e s c a p e s l a t e r a l l y ab ov e t h e c o n f i n i n g l a y e r .

Perched-water tab leI n s t r a t i f i e d s o i l , a su b su r face - d r a in ag e p ro blem may b e cau sed wh er e ex cessw a te r i n t h e n or ma l r o o t zon e i s h e ld u p b y a l a y e r of low p e r meab i l i t y so t h a tt h e p e r ch ed w a te r i s disco nnec ted f rom th e main body of ground wat er . This mayo ccur when su r f a ce so u r ces b u i l d u p a l o ca l w a te r t a b l e o v e r t h e s lo w ly p er meab lel a y e r . L a t e r a l p e r c o l a ti o n i s too s low t o d r a i n t h e pe rc he d w a te r n a t u r a l l y .D ra in a ge s y st e ms f o r p er ch ed -w at er t a b l e s a r e ba s ed o n t h e p a r t i c u l a r s i t e con-d i t i o n s . U s u al l y t h ey c o n s i s t of r e l i e f d r a i n s , b u t a n i n t e r c e p t i o n d r a i n mayb e e f f e c t i v e i n c u t t i n g o ff l a t e r a l se ep ag e i n t o t h e wet a r e a . T h e o r e t i ca l l y ,p e rch ed w a te r co u ld b e d r a in ed downward by d r i l l i n g v e r t i c a l d r a in s ( w e l l s )t hro ug h t h e r e s t r i c t i v e l a y e r . A co l lec t io n-d ra i n system probably would ben e c e s s a r y, h ow ev er, a nd t h e v e r t i c a l d r a i n s m ig ht b e i m p r a c t i c a l o u t l e t s f o reco no mic o r o t h e r r easo n s . Pe rch ed -w a te r t a b l e s i n i r r i g a t e d a r e as may b e su b-j e c t t o c o n t r o l by r e d uc i n g s ee p ag e fro m c a n a l s , by i mp ro vi ng i r r i g a t i o n p r a c t i -ce s , o r by p ro v id in g ad eq u a t e su r f ac e d r a in ag e .La te ra l ground-water f low problemsThi s group of subsu rface -drain age problems i s ch a r ac t e r i zed b y mo r e o r l e s sho r i zo n t a l g round-water pe rc o l a t io n wi t h in o r toward th e crop- roo t zone. Thef l o w p a t t e r n i s s t r o n gl y i nf lu e nc e d by s o i l s t r a t i f i c a t i o n and o t h e r n a t u r a lb a r r i e r s t o f lo w.A dj ac en t s o i l l a y e r s o f t e n h av e p e r m e a b i l i t i e s t h a t d i f f e r a h und re d o r a thou-s an d f o l d . A cc or di ng t o D a rc y 's law o f f l o w , t h e e f f e c t i v e v e l o c i t y un de r ag i ve n g r a d i e n t v a r i e s d i r e c t l y w i t h t h e p e rm e a b i l i ty . Flow o f g ro un d w a t er i sd is c us se d f u r t h e r i n t h e s e c t i o n on " S u b s u r f a c e - ~ r a i n a ~ er i n c i p l e s . " A l ls i g n i f i c an t f l o w may b e l im i t ed t o t h e more p er meab le l ay e r s . The d ep th ,o r i e n t a t i o n , and i n c l i n a t i o n o f t h e s t r a t a d e t er m i ne t h e d r a i n a g e m ethod andl o c a t i o n . For example, h i l l s i d e seepa ge may appea r where ground wa ter movesl a t e r a l l y o v e r be dr oc k o r o v e r a l a y e r of f i n e s e d i m e nt s t o a p o i n t w he re i temerg es a t t h e su r f ac e . One o r mor e i n t e r c ep t in g d r a in s may b e us ed t o c u t o f ft h e f l ow w hich o th e r w i se w ou ld r eac h th e r o o t zone.A l l u v i a l f an s and v a l l ey b o tto ms commonly co n ta i n san d o r g r av e l d ep o s i t s . T heseo ccur i n a v a r i e t y of w ays , a s i n de ep e x t e n s i v e l a y e r s , n ar ro w " s t r i n g e r s "( ol d s tre am be d l o c a t i o n s ) , l e n s e s , o r i n h i gh l y s t r a t i f i e d s o i l p r o f i l e s . Such

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pi dl y permeable de po si ts may ser ve a s channel s fo r ground-water movement i nme p l a c e s a t h i g h r a t e s o f f lo w . A s o i l l a y e r of low p e r m e a b il i t y o v e r l y i n g

e r may c r e a t e a de g r e e of c onfine me n t , which i n tu r n de ve lops a nward h y d r a u l i c g r a d i e n t , p a r t i c u l a r l y i f t h e l ow er en d o f t h e a q u i f e r i s c lose d

d pe r m e a b i l i ty . I n t e r c e p t i o n d r a i n s a r e e f f e c t i v e w here t h e a q u i f e rc l o s e e nough t o t h e s u r f a c e s o t h a t i t i s f e a s i b l e t o c u t o f f t h e fl ow .ie f we l l s o r pumping may be used where in te rc ep t i on i s n o t p r a c t i c a l .

c e s o i l m asses o f low pe r m e a b i l i ty , suc h a s c l a y l e n s e s a nd o f f s h o r ey ba r s f or me d i n t h e g e o l o gi c p a s t , a r e l o c a l b a r r i e r s t o gro und -w ater f lo w.

ey may c a use the wa te r t a b le t o be he ld t o a h igh l e ve l and th e f low to e sc a peo un d o r o v e r t h e b a r r i e r . P er me ab le l a y e r s t h a t become t h i n n e r o r g r a d u a l l y

n p e r m e a b i l i t y i n a dow nstream d i r e c t i o n h av e a s i m i l a r e f f e c t o n t h eD r ai n s p l ac ed j u s t u p sl o pe from t h e r e s t r i c t i o n u s u a l l y a r e e f fe c -

v e i n t h es e s i t u a t i o n s . I r r i g a t i o n c a n a l s ee pa ge c r e a t e s a no th e r k in d oft e r a l g round- wa te r f low p roblem . An in t e r c e p t ing d r a in a t t he toe of a c a n a l

o r r i v e r l e v e e may c u t o f f much of th e f low th a t wou ld r e a c h t he we t a r e aa h o r i z o n t a l b a r r i e r f orm s a c o n ve n ie nt " f l o o r " f o r i n t e r c e p t i o n . However,e d e s i g n e r must c o n s i d e r t h e s t e e p e r h y d r a u l i c g r a d i e n t s u ch a d r a i n c a u se si t s e f f e c t on t h e ca n al -s ee p ag e l o s s and o n t h e s t a b i l i t y o f t h ebankment aga in s t s lou ghin g o r p ip ing . River seepage through or under levee sa t e s s i m i l a r p r ob le ms .

e se ex amp les i l l u s t r a t e t h e u n l im i t ed v a r i e t y of subsur face-dra inage problems.e p r in c i p l e s o f in t e r c e p t io n , r e l i e f , o r pumped-well d r a in a ge may be a pp l i e d

c h a c c o r d ing t o th e pa t t e r n of subsu r f a c e f low. The pa t t e r n o f f low becom esown from a f i e l d i n v e s t i g a t i o n o f s o i l s t r a t i f i c a t i o n , w a t e r so u r ce , and w a t e r

or p r e s s u r e d a t a .Di f fe r enc es i n Dra inage i n Humid and Ar id Areas

na ge i n humid a r e a s ha s to do l a r g e l y wi th e xc e ss wa te r r e su l t in g fr om p r e-t a t i o n ; i n a r i d and s e m ia ri d a r e a s , t h e need f o r d r a i n ag e a r i s e s p r i n c i p a l l yom i r r i g a t i o n , w i t h f o r e i g n gro un d w a te r a n i m p or t an t s o u r c e i n some a r e a s .

ce-dra inage systems may be req uir ed i n e i t h e r humid o r i n i r r i g a t e d a r e a s .ia u s u a l l y a n i n t e g r a l p a r t o f i r r i g a t i o n s ys te ms on sl o wl y

rm eabl e s o i l s o r i n a r e a s of h i gh p r e c i p i t a t i o n r a t e s .e pu r pose o f subs u r f a c e d r a ina ge i s t o l o we r t h e wa t er t a b l e t o a p o i n t w he rew i l l no t i n t e r f e r e wi t h p la nt growth and development . The minimum depth a t

i ch t h e w a t er l e v e l s h ou l d b e m a i nt a in e d v a r i e s a c c o r di n g t o b o t h t h e c r opi r em e n t and t h e s o i l . One o f t h e p r i n c i p a l f a c t o r s i n t h e h e i g h t o f t h e

t er t a b l e i n a r i d a r e a s i s c o n tr o l of s a l i n i t y and a l k a l i n i t y i n t h e s o i l andnd water . Th is i s a ma jo r r e a so n f o r t h e a d i f f e r e n c e i n t h e s u b su r fa c e

ai na ge of humid and o f a r i d c l i m at e s .e de p th of d r a ins i n humid c l im a te s i s g e n e r a l l y 3 t o 5 f e e t . W a t e r i sa t i v e l y p u re , t h e r e us u a l l y i s a n a t u r a l e x c e s s of w a t e r o v e r p l a n t r e q u i r e-

th er e i s a n e t downward movement o f ground wa te r.s i n s em i ar id o r a r i d c l i m a te s r e q u i r e s ub s ur fa ce d r a i n s a t l e a s t 5 t o 7 f e e t

Most of t h e wa te r needed by t h e crop i s ad ded b y i r r i g a t i o n . U s u al l yi s somewhat s a l i n e b e ca u se of s a l t s i n t h e s o i l , t h e i r r i g a t i o n wa-

o r b o t h. A w a t e r t a b l e a s h ig h a s 24-30 i n c he s b elo w t h e s u r f a c e , s u i t a b l e many humid a r e a s , w ould c r e a t e a h a rm f ul s a l t c o n c e n t r a t i o n i n t h e r o o t z on e

n a r i d a re a s.

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Crop RequirementsEf f e c t s o f e xc e ss wa te r on c r opsThe g rowth o f m os t a g r i c u l t u r a l c r ops i s s h a r p l y a f f e c t e d b y c o n ti n u ed s a t u r a t i o no f a n y s u b s t a n t i a l p a r t o f t h e r o o t z on e o r b y ponded w a te r o n t h e s u r f a c e .P o o rl y d r a i n e d s o i l s d e p r e s s c r op p r o d uc t io n i n s e v e r a l ways:

1. E v a po r a ti o n , w hi ch t a k e s h e a t from t h e s o i l , l o w er s s o i l t e m p e ra t ur e .A lso , we t s o i l r e q u i r e s more he a t t o warm up tha n doe s d r y so i l , duet o t h e h i g h s p e c i f i c h e a t o f w a t e r a s compared t o t h a t o f s o i l . T hu s,the growing season i s shor t e ne d .

2 . S a t u r a t io n o r s u r f a c e ponding s t o p s a i r c i r c u l a t i o n i n t h e s o i l a nd p re-v e n ts b a c t e r i a l a c t i v i t y .

3 . C e r t a i n p l a n t d i s e a s e s a nd p a r a s i t e s a r e e n co ur ag ed .4 . H ig h w a t e r t a b l e l i m i t s r o o t p e n e t r a t i o n .5. S o i l s t r u c t u r e i s a d v e r s e l y a f f e c t e d .6 . S a l t s and a l k a l i , i f p r e se n t i n t h e s o i l o r ground w a t er , t en d t o b e

c o nc en tr at e d i n t h e r o o t zo ne o r a t t h e s o i l s u r fa c e.7 . Wet s p o t s i n t h e f i e l d d e l a y f a rm o p e r a t i o n s o r p r e v e n t u ni fo r m

t r e a t m e n t .Dra inage requirements de te rmined by c ropsD i f f e r e n t c r o p s ha v e w i d el y d i f f e r i n g t o l e r a n c e s f o r e x ce s s w a t e r , b o t h a s t oamount and t im e . Whi le wa te r i t s e l f may no t be in ju r i ou s to p l a n t r oo t s ,s a tu r a t i on o f th e r oo t z one r e s u l t s i n a n oxygen de f i c i e nc y a nd a c cum ula t ion oft o x i c g a s e s . A sh or t t e rm of oxyge n de f i c i e nc y c a n r e duc e wa te r up ta ke , nu t r i e n tu p t ak e , and r o o t r e s p i r a t i o n and b u i l d u p t o x i n s w hich l e a d s t o d e a t h of c e l l sand r o o t s , a nd , i f e x te nde d , th e de a th o f the p l a n t i t s e l f . However, c om ple tesa tu ra t i on of r oo ts over an extended per io d may cause no se r i ou s damage i f i toccu rs dur ing dormant per iod s of p l an t growth o r f low f rom dra in age i s s u f f i c i e n tto su pply some oxygen and remove to x ic gase s. The de si gn er of a drain age systemr e co g n iz e s t h e s e d i f f e r e n c e s i n c ro p r eq u i re m en t s b y s e l e c t i n g a n a p p r o p r i a t ed e g re e o r i n t e n s i t y of d r a i n a g e ( o f t e n t er me d t h e d r a i n a g e re q u ir e m en t ) f o r t h es i t e . The d r a i n a g e r e q ui r em e n t i s based on (a ) t h e maximum d u ra t io n and freq uencyof s ur fa ce ponding, (b) th e maximum he ig ht of t he wat er t ab l e , o r ( c) th e minimumr a t e a t w hi ch t h e w a t er t a b l e m ust b e lo we re d. The l o c a l d r a i n a g e g u id e i n d i c a t e st h e d r a i n a g e c r i t e r i a r e q u i r e d f o r v a r i o u s c r o p - s o il c om b in at i on s . F u r t h e r i n f o r -mat ion and guidance can b e o b t a i n e d f ro m r e p o r t s o f c o n t i n u i ng r e s e a r c h on e f f e c t sof f l o od i n g, w a t e r t a b l e d ep t h s and s o i l g a se s on a g r i c u l t u r a l c r op s ( 2 ) .Crop growth and the water t a b l eThe wa te r t a b le may be de f ine d a s th e upper s u r f a c e o f the s a tu r a t e d z one o f f r e e ,unconfined ground wat er . (A more accu ra t e de f i n i t i on has been made i n te rms ofw a t e r p r e s s u r e s and f i l m t e n s i o n s . ) The s o i l - m o i s tu r e c o n t e n t f o r a s i g n i f i c a n the ig h t a bove a wa te r t a b le i s s u b s t a n t i a l l y g r e a t e r t h an f i e l d c a pa c i ty . For t h i sreaso n, p lant - root growth i s a f f e c t e d by a wa te r t a b le much more tha n th e he igh tof w a t er t a b l e a l o n e i n d i c a t e s .

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t he r imp o r t an t f ea tu r e of w a te r t ab l e s i s t h e i r f l u c t u a t i o n , b o t h s e a so n a ld sh o r t - p e r io d . Water t a b l e s a r e s eldo m s t a t i c . They r e spo n d t o ad d i t i o n sd d e p l e t i o n s o f gro un d w a t er from n a t u r a l o r a r t i f i c i a l c a u s e s . S o ur c es s u c h

s d i s t a n t - i n f l u e n t s e ep a ge fro m p r e c i p i t a t i o n and s t re a mf lo w a r e s e a s o n a l , ande i r e f f e c t s on t h e w et a r e a may b e d e lay ed f o r mo nths o r ev en y ea r s . D i r e c tec ip i t a t i o n and i r r i g a t i o n - p e r c o l a t i o n w as t e s , o f co u r se , may chang e th e

mping f rom deep we l l s may cause a g ra dua l lower ing of th e water ta b l e a s waters t aken from a l a rg e bas in of f r e e g round wate r . I n o t he r a re as , pumping mayake s i g n i f i c an t immed ia te ch ang es i n t h e h e ig h t o f w a te r t a b l e d ue t o p r e s s u re

ges i n conf ined wate r which " suppor ts" th e water t ab le .e f i e l d o f d ra in a ge , i t i s i m po rt a nt t o t h i n k o f t h e t r u e r e l a t i o n of t h e

a b l e t o ro o t development and crop product ion . The te rm "water t ab l e" i smet imes mi s l ead in g . Ca p i l l a r y f o r c es and f l u c tu a t i n g g ro un d- wa te r f l ow s r e s u l t

n s o il - m o i s tu r e c o n d i t i o n s t h a t a r e d i f f e r e n t f rom t h e e r r on e o us c on c ep t o f aeak f ro m sa tu r a t i o n t o a much lo wer mo i s tu r e co n ten t such a s f i e l d

A co ns id er ab le amount of ground wate r i s pr es en t and moves throughs a t u r a t e d a nd n e a r l y s a t u r a t e d s o i l i mm ed ia te ly a b ov e t h e w a t er t a b l e .

Su r f ace - D r a in ag e P r in c ip l e si s accompl ished i n two gen era l ways: ( a ) e xcess water i s

o ll ec te d and removed f rom th e ground s u r f a c e w i t h i n t h e a r e a a f f e c t e d ; o r ,y means of co n s t r u c t i o n o u t s id e t h e a r ea , w a te r i s diver ted away f rom theb e p r o t e c t e d. I n e i t h e r c a s e , t h e s ys te m i s c o n v e n i e nt l y d i v id e d i n t o

f u n c t i o n a l 'p a r t s :1. C o l l e c t i o n sy st em . B ed di ng , f i e l d d i t c h e s , row d i t c h e s , o r d i v e r s i o n

d i t c h e s a r e p a r t o f t h e s ys te m t h a t f i r s t p i c k s up w a t er f rom t h e l a n d.2 . D isp o sa l sy s tem. T h i s i s t h e p a r t o f t h e s ys te m t h a t r e c e i v e s w a t erf rom the c o l le c t io n sys tem and conveys i t , u s u a l l y i n a n open d i t c h ,

t o t h e o u t l e t .3 . O u t l e t . T h i s i s th e end po in t o f th e d ra in age sys tem under cons ide ra-

t i o n .n da me nt al ly , s u r f a c e d ra i n a g e u s e s t h e p o t e n t i a l e n e rg y t h a t e x i s t s du e t o

a t i o n t o p r o v i d e a h y d r a u l i c g r a d i e n t . The s u rf a c e- d ra i n ag e s ys te m c r e a t e se r - su rf ace s lo p e t o move w a te r f ro m th e l an d t o an o u t l e t a t a lower

a t i o n . The d e s i g n of c o l l e c t i o n s y st e m s, s u ch a s b ed di ng o r f i e l d d i t c h e sn f l a t l a n d i s b as ed mo s tl y on e m p i r i c a l c r i t e r i a ; i . e . , t h e de s i gn i s based oni e l d o b se r v a t io n s o f d ra in ag e - sy s tem p e r fo r man ce . The r a t e a t w hich su r f a ce

ter must be removed from th e la nd i s a fun ct i on of th e crop requ i rement andr ce of ex ces s w a te r .he w a te r - su r f ace p r o f i l e i s t h e s t a r t i n g p o i n t i n t h e d e s i g n o f t h e d is p o sa l -s te m d i t c h e s . I n o pe n d i t c h e s , t h e h y d r a u l i c g r a d e l i n e i s t h e w a te r - su r f ace

f i l e . U s u al l y, t h e su rv e y of t h e s u rf a c e- d ra i n ag e o u t l e t e s t a b l i s h e s t h ew er h y d r au l i c - co n t r o l p o in t f o r t h e d es ig n o f t h e d i sp o sa l sys tem. O th e r co n-o l p o i nt s a r e t h e l an d e le v a t i o n s a r c r i t i c a l low ar e a s and r e s t r i c t i o n s i n

c h , s uc h a s c u l v e r t s , b r i d g e s , and w e i r s . The d e s i g n of a d i s p o s a l sy st emv es , t h e r e f o r e , t h e co mp u ta ti o n o f a w a te r - su r f ace p r o f i l e t hr o ug h th e co n-

o l p o i n t s , f o r known o r t r i a l d i t c h c r o s s s e c t i o n s .

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B e r n o u l l i ' s t h e o r e m i s use d t o c om pu te t h e hyd r a u l i c g r a d e l i ne f o r s t e ady - f lowc o n d i t i o n s . L os s e s o f hea d due t o f r i c t i o n a r e c om pu ted by a n ope n- cha nnelf o rm u l a, u s u a l l y M an ni ng 's . Head l o s s e s a t c o n s t r i c t i o n s c au s i n g n on un if or mf lo w , s uc h a s a t b r id g e s o r c u l v e r t s , a r e compute d by f o r m u l a u s i ng a pp r op r i a t el o s s c o e f f i c i e n t s . The f i e l d s ur v ey m ust i n c l u d e s u f f i c i e n t i n fo r m a t io n f o re v a l u a t i o n of t h e r ou g hn e ss an d c r o s s - s e c t i o n f a c t o r s , i n c l u d i n g h ea d l o s s t h ro u g ho b s t r u c t i o n s .I n d r a i n a g e d e s i g n , n o n st e ad y f l o w may o cc u r a s i n d i s c h a r g e i n t o t i d a l s t r ea m s .Such problems may sometimes be so lved by d iv i d i ng t ime in to conve nien t inc rem entsw i t h i n e a c h o f w h ic h t he va r y i ng f l ow may be t a ke n a s a c o ns t a n t , m ea n- flow r a t e .

S ubs u r f a c e - D r a i na ge P r i nc i p l e sForm s o f s o i l w a t e rG r a v i t y w a t e rWate r tha t i s f r e e t o move downward t h ro u g h t h e s o i l b y t h e f o r c e o f g r a v i t y i sc a l l e d g r a v i t y w a t e r. A t s a t u ra t i o n , a l l po re s a r e f i l l e d and t h e s o i l h ol dst h e maximum am ount o f w a t e r t h a t c a n be a bso r be d w i t hou t d i l a t i o n . ( D i l a t i o ni s t h e bu lk in g o r f l o t a t i o n of s o i l g r a i n s . )C a p i l l a r y w a t erC a p i l l a r y w a t e r i s h el d i n t h e s o i l a g a i n s t g r a v i ty . I t i n c l u d e s t h e f i l m ofw a te r l e f t a ro un d t h e s o i l g r a i n s and t h e w at er f i l l i n g t h e s m al l er p o re s a f t e rg r a v i t y w at e r h a s d ra i n e d o f f .I f g r a v i t y w a te r i s a ll ow ed t o d r a i n from a s a t u r a t e d s o i l ( n o t i n f lu e n c e d bya w a te r t a b l e ) , t h e q u a n t i t y o f c a p i l l a r y w a te r h el d i s c a l l e d f i e l d c a p a c it y .C l os e t o t h e w at e r t a b l e , t h e q u a n t i t y of c a p i l l a r y wa te r h el d i n a g r a n u l a rm a t e r i a l i s g r e a t e r t h a n f i e l d c a p a c i t y . The amount of w a t er h e ld a t a g i v e npo i n t de pe nds on t h e d i s t a n c e ab ove t h e w a te r t a b l e , a s w e l l a s o n t h e s o i l po res i z e s an d s h a p e s. T h i s f or m o f c a p i l l a r y w a t e r i s s om et im es c a l l e d f r i n g e w a te r .J u s t ab ov e t h e w a te r t a b l e , f r i n g e w a te r c om p le te ly f i l l s t h e c a p i l l a r y p o r e s ,and i n t h i s r e l a t i v e l y n ar ro w zo ne , s a t u r a t i o n o c cu r s a t s l i g h t n e g a t i v e p r e s s u r e( t e n s i o n ) . O penin gs s o l a r g e t h a t c a p i l l a r y r i s e i n them i s n e g l i g i b l e a r ec a l l e d s u p e r c a p i l l a r y o p e ni n gs . E xam ple s of m a t e r i a l s c o n t a i n i n g s u p e r c a p i l l a r yo p e ni n gs a r e g r a v e l , b o u l d e r s , some f or ms o f l a v a , s t r u c t u r a l l y f r a c t u r e d r oc ko r c l a y , s o l u t i o n o pe ni ng s i n r o c k , a nd s o i l c o n t a in i n g r o o t h o l e s .Hygroscopic wa te rWhen a g r a n u l a r m a t e r i a l i s c o m pl e te l y d r i e d by h e a t i n g , t h e n ex po se d t o t h e a i r ,i t a b s o r b s a t m o s ph e r i c m o i s t u r e . T h i s w a t e r , w hen i n e q u i li b r i u m w i t h t h ea t m os phe r i c m o i s t u r e , i s c a l l e d h y g r o s c o p i c w a t e r .The w at er t a b l e and t h e c a p i l l a r y f r i n g eThe w a t e r t a b l e i s t h e up pe r s u r f a c e of t h e s a t u r a t e d z o ne of f r e e g ro un d w a t e r .F ree ground wa te r i s d e f i n ed a s w a t e r n e i t h e r c o n fi n ed by a r t e s i a n c o n d i t i o n sn o r s u b j e c t t o t h e f o r c e s of s u r f a c e t e n si o n . A t t h e w a t e r t a b l e , w a t e r p r e s s u r ei s a t a t m o s ph e r i c p r e s s u r e . Thu s t h e w a t e r t a b l e i s t he i m a g i na r y s u r f a c e s epa -r a t i n g c a p i l l a r y w a t e r ( un d er t e n s i o n ) fr om t h e f r e e g ro un d w a t e r be lo w.The w a te r t a b l e i n g r a n u l a r m a t e r i a l i s n o t a n o b s e r v a b l e , p h y s i c a l s u r f a c e b e-c a us e c a p i l l a r y w a te r s a t u r a t e s t h e m a t e r i a l j u s t a bo ve t h e w a te r t a b l e anddec rea ses i n amount gr ad ua l ly upward . An exc ept i on i s w at er i n s u p e r c a p i l l a r y

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i n w hich t h e w a te r i s i n eq u i l i b r i u m w i th t h e a tmo sp h er e . Auger h o l e sd p i e z o m et e rs a r e s u p e r c a p i l l a r y i n s i z e a nd o pe n t o t h e a tm o sp h er e, a nd s o

he y f i l l t o t h e t r u e w a t er - ta b l e l e v e l when b or ed o r d r i v e n j u s t i n t o t h e w a t e ra b l e .

i s b or ed t o l o c a t e t h e w a t e r t a b l e i n a f i n e o r mediurn-u r e d s o i l , t h e o bs e rv e r f i n d s i t d i f f i c u l t t o re c og ni z e t h e to p of t h e

u r a t e d z one b e c a us e of t h e g r a du a l c ha ng e from m o i s t t o s a t u r a t e d s o i l . A l so ,t may t a k e ho u rs o r e ve n d ay s f o r a n au ge r h o l e t o r e g i s t e r t h e w at e r t a b l e i np ermeab le s o i l s . Smal l w e l l s o r p i ezomete r s r e ac t more q u i ck ly t h a n l a r g e

s be c au se l e s s w a t e r ne ed f l ow t hr o ug h t h e s o i l t o f i l l t h e s m a l l e r o p en i ng s .ter i n t h e c a p i l l a r y f r i n g e may b e a s i g n i f i c a n t p r o p o r t i o n of g ro un d w a t e rving toward su bs ur fa ce drain s--as much a s 20 per cen t o r more under some

n au g e r h o l e o r p ip e sh ou ld p en e t r a t e t h e s a t u r a t ed zo ne o n ly a s h o r t way i f t h ei s t o b e measu red acc u r a t e ly . T h i s i s p a r t i c u l a r l y i m p o r -

t a n t where upward f low o r conf ined f low would be tapped by a deeper ho le. Anug er h o l e t h a t p e n e t r a t e s two o r more a q u i f e r s i n a s t r a t i f i e d s o i l c o n ta i ni ngo n f in ed w a te r wo uld r e g i s t e r t h e h i g h e s t h y d r au l i c h ead mo d if i ed by l eak ag e

fr om th e aq u i f e r s o f h ig h e r h y d r a u l i c h ead t o t h o se of l ow er h ead .e se c h a r a c t e r i s t i c s of t h e w a t er t a b l e h av e a s i g n i f i c a n t b ea r i ng o n t h e ki n df i e l d measur emen ts t o b e made, o n t h e d ev i ce s u sed t o make th e o b se r v a t io n s ,

and o n t h e i n t e r p r e t a t i o n s o f d a t a f o r d ra i n- sy s te m d e s i g n .i p l e s of f lo w i n t h e s a t u r a t e d z on e

Flow of w a te r i n t h e s a t u r a t ed zon e i n v o lv e s mech anica l, ch emica l , and th e r ma le n e rg y , a nd m o l e cu l a r a t t r a c t i o n . A f u l l d i s cu s s io n o f so i l - w a te r movement i si n num erous p u b l i c a t i o n s on s o i l p h y s i c s and s o i l p e r m e a b i l i ty . H ere on l y t h e

n i cal f o r ce s t en d in g t o move w a te r t h ro u g h so i l s w i l l b e co n s id e r ed .ydrau l ic head

I n s a t u r a t e d f lo w th ro u gh s o i l s , a s i n op en c ha n n el f lo w , t h e t o t a l e n er gy con-t e n t (E ) of w a t e r i s t h e sum o f t h e k i n e t i c , p r e s su r e , an d g r av i t y compo nent s.A s e x p re s s ed i n B e r n o u l l i ' s e q u at i o n:

E = k i n e t i c e n e r g y -I- r e s su r e p o t e n t i a l + e l e v a t i o n p o t e n t i a l .e l o c i t i e s i n ground-water f low a r e almo st always low, making th e ve lo ci ty

( k i n e t i c ) t erm n e g l i g i b l e . E s s e n t i a l l y , t h e n , t h e e ne rg y c a us in g f lo w i s t h esum of th e two po te n t i a l energy i t e m s , p r e s s u r e and e l e v a t i o n . T h i s p o t e n t i a lf o r f l o w i s ca l l ed " h y d r au l i c h ead . "I n t h e E n g l is h s y st e m o f u n i t s , e n er gy i s expr esse d foot-pounds. Hydra ul ic headi s co n v en ien tly ex p r es sed a s t h e en e r g y co n ten t p e r u n i t w e igh t o f w a te r , o rfoot-pounds pe r pound, which i s f e e t , d i m e n s i o n a l ly . T hu s, t h e h y d r a u l i c h ea d( f i g . 1 - l ) , a t a gi ve n p o i nt i s :

where H = h y d r a u l i c h e ad , f t . ; P = p r e s s u r e a t t h e p o i nt r e f e r r e d t o t h e a tmos-p h er e , l b / f t 2 ; W = s p e c i f i c w ei gh t of t h e w a t e r, l b / f t 3 ; a nd Z = e l e v a t i o n o fth e p o in t ab ov e a da tu m, f t .

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--Figure 1-1, Illustration of hydraulic head

P r e s s u r e H e a da t P o i n t " P " =

E l e v a t i o n H e a d

H y d r a u l i c G r a d i e n t = H I - HzLFigure 1-2, Illustration of hydraulic gradient

D A T U M

a t P o i n t " P " =7 r Y

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e z om e te r s c on v e r t p r e ss u r e a t a p o i n t t o a p h y s i c a l p r e s s u r e h ea d t h e h e i g h tth e wa te r co lumn i n t h e p i ez o me t er . T h i s h e i g h t i s n o t h y d r a u l i c h e ad , s i n c e

t i s o n l y t h e t er m P/W i n t h e e q u a ti o n . To f i n d t h e h y d r a u l i c h ea d a t t h e p o i n t( l ow e r en d o f t h e p i e zo m e t e r) t h e e l e v a t i o n (Z ) of th e po in t above th e da tum must

d de d t o t h e p r e s s u r e h e ad . The e l e v a t i o n o f t h e w a t e r s u r f a c e i n t h e piezom-r e f e r r e d t o t h e d atum, i s P/W + Z , and so i s n u m e r ic a l ly e q u a l t o t h e

r a u l i c hea d a t t he l ow e r e nd of t h e p i e z om e t e r.u l i c g r a d i e n t

ound- wa te r f l ow r e s u l t s f rom t h e f o r c e " a va i l a b l e " t o move w a t e r t h r ough t h eo i l du e t o d i f f e r e n c e s i n e ner gy c o n t en t ; i . e . , d i f f e r e n c e s i n h y d r a u l i c h ea d.

i s a n al a go u s t o t h e f l ow of h e a t o r e l e c t r i c i t y , w he re f lo w i s due t on t em p er at ur e ( h ea t p o t e n t i a l ) o r d i f f e r e n c e s i n v o l t ag e ( e l e c t r i c a l

n t i a l ) . H y dr a ul ic g r a d i e n t i s t h e d i f f e r e n c e i n h y d r a u l i c h ea d a t two p o i n t s ,he d i s t a nc e bet we en t he po i n t s m e as ur ed a l ong t h e path of flow--f i g . 1 -2 ). I n t h i s f i g u r e , t h e p l a n e o f t h e p a pe r i s a v e r t i c a l s u r f a c e t hr ou gh

t h e p a t h o f f l ow .H1 - H2H ydr a u l i c G r a d i e n t =

where L = d i s t a nc e m ea su re d a l ong t he pa t h of f l ow , f t .S u b s c r i p t s 1 and 2 r e f e r t o t h e p o i n t s o f t h e hi g h e r and l ow er h y d r a u l i ch ea d, r e s p e c t i v e l y ; o t h e r u n i t s a r e de f i n ed i n t h e pr e ce d in g p ar a gr a ph s .

n a g i v e n f l ow s y s te m ( f i g . 1-3) e a c h " pa r t i c l e " o f w a t e r i n t h e s y s te m ha s i t sA l l p a r t i c l e s o r p o i n ts , of a g i v e n h y d r a u l i c h e adl i e i n t h e c o r r es p on d in g e q u i p o t e n t i a l s u r f a c e ( H I ) . A l l p o i n t s of h y d r a u l i cad H2 l i e i n t h e e q u i p o t en t i a l s u r f ac e H z , and so on . The fo rc e t ending t o pro-c e fl ow a c t s i n t h e d i r e c t i o n o f g r e a t e s t d e cr e as e i n hy d r a u li c h ea d; i . e . ,r ma l t o t h e e q u i p o t e n t i a l s u r f a c e , a s F a t p oi nt P , o r F ' a t p oi nt P ' . Theg ni tu de of t h i s f o r c e i s p r o p o rt i o n al t o t h e h y d r a ul i c g r ad i e n t a t t h e p o i n t .

t t h e w a te r t a b l e , t h e pr es su re component of energy (P/W) i s z er o r e l a t i v e t op h e r ic p r e s s u r e . T h e r ef o r e , t h e h y d r a u l i c h ea d H of a p o i n t a t t h e w at eri s Z , t h e e l e v a t i o n of t h e p o i n t a b o ve t h e d at um .

e r -t a bl e s l o p e r e p r e s e n t s t h e h y d r a u l i c g r a d i e n t o f f l o w o n l y un de r c e r t a i nH y d r a ul i c g r a d i e n t may d i f f e r g r e a t l y f ro m t h e w a t e r - ta b l e s l o p e

i s s i g n i f i ca n t upward o r downward component of f low such as i n t heof pumping w e l l s o r s u b s u r f a c e d r a i n s , i n f lo w fr om a r t e s i a n a q u i f e r s ,

d i n uns a t u r a t e d s e e pa ge f rom c a n a l s . As shown i n f i gu r e 1 -4 , s l o pe o f t hee r t a b l e i s H1 - H2 ( o r t a n ge n t of t h e a n g l e ) by d e f i n i t i o n . S i s t h e h o r i -S

t a l p r o j e c t i o n of t h e p a t h of f l ow L . But t h e h y d r a u l ic g r a d i e n t i s H1 - H2Le of t h e a n g l e ) . On f l a t g r a d i e n t s and w i t h p a r a l l e l f l ow , t h e w at er -

e i s e s s e n t i a l l y t h e h y d r a u l i c g r a d i e n t be ca us e S = L n e a r l y ( t a n g e n ts n e a r l y t h e same a s t h e s i n e f o r s m a l l a n g l e s ) . I t s h ou l d b e n ot e d t h a t t h e

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Fi gur e 1-3, E q u i p o t e n r i a l s u r fa c e s

-- H y d r a u l i c G r a d i e n t a t W a te r T a b l e = H I - H 2-- ,.. LH I - Hz1. S l o p e o f W a t e r T a b l e .--1 SF ig u re 1 - 4 , D i f f e r e n c e b e t w e e n h y d r a u l i c g r a d i e n t

and s l o p e of t h e w a te r t a b l e

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a t e r t a b l e i s no t i nv ar ia bl y a pat h of f low; w ate r may be f lowing down from orup i n t o t h e u n s a t u r a t e d z on e, t h u s c r o s s i n g t h e w a te r t a b l e .P a t h s of f l o w ( s t r e a m l i n e s )The f o r c e d ue t o h y d r a u l i c g r a d i e n t t e n d s t o move w a t er a l o ng t h e l i n e of f o r c en orma l t o t h e eq u i p o t e n t i a l s u r f aces . W he th er t h e f l ow moves ac t u a l l y i n t h esame d i r e c t i o n a s t h e l i n e of fo r ce d ep end s o n wh et he r t h e s o i l h a s t h e s ameh y d ra u l ic c o n du c t iv i ty i n a l l d i r e c t i o n s . I f t h e s o i l i s " i s o t r op i c , " i . e . , i fi t s h y d r a u l i c c o n d u c t i v i t y i s t h e same i n a l l d i r e c t i o n s , t h e p a th of f lo w w i l lb e a lo n g t h e l i n e s o f f o r c e and p er p e n d i c ul a r t o t h e e q u i p o t e n t i a l s u r f a c e s .I f t h e s o i l h as a h i g h e r h y d r au l ic c o n d u c ti v i t y i n one d i r e c t i o n t ha n i n a n ot h erd i r e c t i o n , t h e p a th o f f l ow w i l l n o t b e p e r p e n d ic u l a r t o t h e e q u i p o t e n t i a l s u r -f a c e . Such a s o i l i s s a i d t o b e " a n i s o t r o p i c . " W a te r -l a id s o i l s o f t e n h av eb ed di ng p l a n es o r p a r t i c l e o r i e n t a t i o n c a u si n g them t o b e a n i s o t r o p i c . Thep a t h s o f f lo w i n a n i s ot r o p i c s o i l s w i l l b e p e r p e n d ic u l a r t o t h e e q u i p o t e n t i a ls u r f a c e s a t p o i n t s wh ere t h e l i n e s of f o r c e a r e e x a c t l y p a r a l l e l t o o r no rm alt o t h e b ed di ng p l an e . A s o i l w i t h m i c r o s t r a t i f i c a t i o n ( t h i n l a y e r s w it h wi de lyd i f f e r e n t h y d r a u l ic c o n d u c t i v i t i e s ) w i l l c a u s e w a te r t o f l ow i n a way s i m i l a rt o t h e f l ow i n an a n i s o tr o p i c s o i l .Many f lo w systems common i n s o i l dra in ag e may be s t ud ie d i n two dimensions r a t h e rt h a n t h r e e , b e c a u se of u n i f o r m i ty i n t h e t h i r d d im en si on . E q u i p o t e n t i a l l i n e st h e n r e p r e s e n t t h e i n t e r s e c t i o n of t h e p l a n e of t h e pa p er w i t h t h e e q u i p o t e n t i a ls u r f ac es . An examp le o f t h i s r ep re s en t a t i o n i s t h e f l ow i n t o a s ys te m of p a r a l l e ld r a i n s , w he re t h e f l o w i s a t r i g h t a ng le s t o t h e d ra i ns .A two-dimensional syste m on th e X-Y p l an e i s i l l u s t r a t e d i n f i g ur e 1-5. The s o i li s i s o t r o p i c ( h y d r a u li c c o nd u c t i v it y i s u nif or m i n a l l d i r e c t i o n s ) i n f i g u r e 1-5.F i g u r e 1-6 shows a n ot h e r s o i l , w i t h a l i n e of f o r c e n or ma l t o t h e e q u i p o t e n t i a ll i n e a nd a t a n a ng l e b t o t h e v e r t i c a l a x i s Y . But i n t h i s s o i l , w hich i sa n i s o t r o p i c , t h e h o r i z o n t a l h y d r a u l i c c o n d u c ti v i t y Kh e xc e ed s t h e v e r t i c a l h y dr au -l i c c on d uc t i v i ty Kv . The d i r e c t i o n of f l o w i s n o t a lo ng t h e l i n e o f f o r c e , b u ta lo ng a l i n e c l o s e r t o t h e h o r i z on t a l a x i s . It may be shown t h a t t h e an g l e t h ep a t h of f l o w makes w i t h t h e h o r i zo n t a l i s

Ka = tan-' Kh zanThus, th e f low pa t t e r n may be computed and d rawn fo r an a n i so t r op ic system i ft h e e q u i p o t e n t i a l l i n e s a r e known, and i f t h e r e l a t i v e h y dr a u l i c c o n d u c t i v i t i e sKv and Kh a r e known.I n a n a l y z i n g t h e d i r e c t i o n of f l ow o f g ro un d w a te r , t h e i n v e s t i g a t o r s h ou ld b ea wa re of t h e e f f e c t o f a n i s o t r o p i c s o i l s o n t h e f l ow p a t t e r n .F low ne ts and boundary cond i t ionsFlow i n t h e s a t u r a t e d zone o f ten i s s t u d i e d b y means of g rap h i c r ep r e s e n t a t i o n sof hydr au l ic head and pa t hs of f low. Cross se c t io ns a r e t aken through th e p roblema r e a , u s u a l l y i n v e r t i c a l p l an e s . L i n e s c o n ne c t in g p o i n t s o f e q u a l h y d r a u l i c he ad

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F i g u r e 1-5, Flow d i r e c t i o n i n i s o t r o p i c soil

X -AX I S

Y-AX I S

F i g u r e 1-6 , Flow d i r e c t i o n i n a n i s o t r o p i c soil

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on s uc h p l an e s a r e c a l l e d e q u i p o t e n t i a l l i n e s , o r " e q ui p o t e n ti a l s . " L in e si n d i c a t i n g t h e p a t h s of f lo w a r e c a l l e d " s t r e a m l i n e s . " A graph showing equipo-t e n t i a l s and s t r e a m l i n e s f o r a f lo w sy st em o r p a r t of a f low system i s c a l l e da "flow net ."The f low net i s t h e r e s u l t of th e ope ra t ion o f Darcy ' s Law i n a sys tem wheret h e r e a r e c e r t a i n s o ur c e s of w a t er and c e r t a i n c o n s t r a i n t s t o f l ow . T he sec o n d i t i o n s t h a t g ov er n t h e p a t t e r n of f low i n a ground-water system, when tak ent o g e t h e r , a r e ca l l e d "bo un da ry co n d i t i o n s . " T op og raph y, l o ca t i o n and q u a n t i t yo f w a t e r s o u r c e , s t r a t i g r a p h y , and d r a i n l o c a t i o n s a r e t h e p r i n c i p a l i t e ms makingup t he boundary cond i t io ns . A f i e l d s u rv e y of t h e s e e l e m en t s i s a b a s i s f o r( a ) i s o l a t i n g t h e f l o w s ys te m t o b e s t u d i e d , and ( b) d e s i g n i n g t h e d r a i na g esystem.F i g u r e 1-7 i l l u s t r a t e s two fl ow n e t s i n s a t u r a t e d s o i l s . Each i s t a k en i n av e r t i c a l p la ne a t r i g h t a n gl es t o a d r a i n , w it h t h e s o i l s a t u r at e d t o t h e s ur f a ceand an im pe rm eabl e l a y e r a t t w i ce t h e d r a i n d ep t h . The d r a i n i s o ne o f s ev e r a lequ al l y spaced d r a i ns . The upper f low ne t i s f o r a n i s o t r o p i c s o i l . The l ow erf l ow n e t i s f o r t h e same b ou nd ar y c o n d i t i o n s e x ce p t t h a t t h e s o i l h a s a h o r i z o n t a lp e rm eab i l i t y 1 6 t i m es i t s v e r t i c a l p e rm eab i l i t y ( an i s o t ro p i c ) . Numbers on eachs t r e a m l i n e i n d i c a t e t h e p e r c en t of t h e t o t a l f l ow w hich o c c ur s t o t h e l e f t oft h a t s t r e a m l i n e . N ot e t h a t 50 p e rcen t o f t h e f lo w reach i n g the d r a i n t h ro ug h t h ei s o t r o p i c s o i l o r i g i n a t e s i n a s t r i p ov e r t h e d r a i n and c o v er in g a bo ut o n e- f ou rt hof t h e s ou r c e a r e a . F or t h e s o i l w i t h h o r i z o n t a l p e r m e a b il i t y 1 6 t im e s g r e a t e rt ha n th e v e r t i c a l , 50 p e r c e n t of t h e f l o w o r i g i n a t e s i n a much w i d er s t r i p ,co v e r i n g n ea r l y on e-h al f o f t h e s o u rce a re a .I f t h e w at e r s o u r ce w er e c u t o f f a t t h e s o i l s u r f a c e , t h e w a te r t a b l e would d ro pi n bo t h ca ses , bu t th e d rop would be much more un ifo rm i n th e second case . Th iss am e e f f ec t i s o bs er v ed i n l a ye r e d s o i l s , e x c e pt t h a t t h e f l ow n e t , w h i l e ha v i ngt h e s am e g en e ra l s h ap e , would s how s h a rp b reak s i n d i r e c t i o n wh ere t h e l i n e sc ro s s ed f ro m o n e s t r a t u m t o an o t h e r .Flow ne ts may b e p lo t t ed f rom ac tu a l f i e l d measurements of hyd rau l ic head i np iezometers . A dra inage p rob lem i s sometimes rep roduced i n a l abo ra t o ry tankmodel, f rom which f low da ta may be taken more re ad i l y . E l e c t r ic a l ana logs p rov id ead d i t i o n a l u s e fu l t o o l s fo r s e t t i n g up some d ra i n ag e p ro bl ems . Plow n e t s a r er e a d i l y p l o t t e d f rom e l e c t r i c a l a na l og d a t a . T h er e a r e a l s o me thods o f c om pu ti nga r i t h m e t i c a l l y t h e h y d r a u l i c h ea d t h ro ug ho ut a c t u a l o r i d e a l i z e d f l ow s ys te m s.However, num eric al methods a r e te di ou s f o r complex problems.Flow n e t s a r e us ed t o s t u d y s u ch s p e c i a l p ro bl ems a s t h e d ep t h and s p ac i n g o fd r a i n s , t h e b e s t l o c a t i o n f o r a d r a i n c o n d ui t d e s ig ne d t o i n t e r c e p t f l ow o ve ra n impe rm eable l a y e r , t h e e f f e c t o f p e r vi o us b a c k f i l l i n l e s s p er me ab le s o i l ,t h e q u an t i t y of f l o w en t e r i n g t h e bo tt om h a l f o f a b u r i ed d ra i n , and can a l s eep -ag e . Such s p ec i a l co n d i t i o n s may j u s t i f y f lo w-n e t an a l y s i s fo r an i n d i v i d u a ld r a i n de s ig n , b u t t h i s t e ch ni qu e i s m ore o f t en employed i n r e s e a rch o r ev a l u a t i o nwork.Pe rm eab i l i t y an d h y d rau l i c co n d u c t i v i t y"Permeab i l i ty" o f a porous medium such as s o i l i s i t s c a p a c i t y t o t r a ns m i t f l u i d s .I t i s u se d a s a q u a l i t a t i v e t er m; i . e . , i t i s u se d a s a t e r m f o r t h i s p r o p er t yo f s o i l . The t erm i s a l s o m o di fi ed t o d e s c r i b e t h e r e l a t i v e e a s e of t r a n s m i ss i o n ,a s " rap id l y permeab le , " o r "slowly permeab le ."

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I-eD r a i n

I S O T R O P I C S O I L

I impervious L a y e rM i d p o i n tB e t w ee n D i a i n s

d l m p e r v i o u s L a y e rM i d p o i n tD r a i n B e t w e e n D r a i n s

Figure 1-7, Streamlines and equipotentials

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d r au l ic co n d u c t iv i t y " o f a s o i l i s a n u mer i ca l v a lu e f o r p e r meab i l i t y . I ts e qu a l t o t h e p r o p o rt i o n a l it y f a c t o r K i n th e Darcy equa t ion . The Darcy

i s a n ex p r e s si o n of e f f e c t i v e v e l o c i t y of f lo w a s a f u n c t i o n of h y d r a u l i cn t a nd t h e t r a n s m i s s i o n p r o p e r t i e s o f t h e s o i l and w a te r . I t was found that

v e l o c i ty i s p r o p o rt i o n a l t o h y d r a ul i c g r a d i e n t , a l l o t h e r t h i n g s b e in g:

L= e f f e c t i v e fl ow v e l o c i t y , d im e ns io ns -T

( E f f e c t i v e f l o w v e l o c i t y i s t h e v e l o c i t y w i th r e s p e c t t o t h e t o t a l a r e aof th e porous medium--not th e void a re a alo ne. I t may be def i ned a st h e q u a n t i t y of f lo w p e r u n i t o f t i m e d i v i d e d b y t h e t o t a l a r e a of t h eporous medium producing t h a t q ua nt i t y of f low.)

LK = a f ac t o r , d imen s io n s -Ti = h y d r a u l i c g r a d i e n t , d i me n s io n le s s

u s, h y d r au l i c co n d u c t i v i t y i s t h e e f f ec t i v e v e l o c i ty o f f l ow when th e h y d r au l i ci s u n i t y . I n d r a i n a ge d e s i g n , i t i s co n v en ien t t o ex p r es s v an d K i n

inc hes per hour . Darcy 's Law i s v a l i d f o r f l ow v e l o c i t i e s i n al mo st a ny n a t u r a ln a g e s i t u a t i o n .

i c co n d u c t iv i t y d ep en ds on p r o p e r t i e s b o th of t h e s o i l and of t h e t r an s -A h i g h v a l u e i s a s s o c i a t e d w i t h h i g h p o r o s i t y , c o a r s e ope n t e x t u r e ,

and h ig h ly d eve lo p ed s t r u c t u r e . S o i l s d o n o t v a ry g r e a t l y i n p o ro s i t y , b u t afew l a r g e p o re s a r e more e f f e c t i v e i n c o n t r i b u t i n g t o h i gh c o n d u c ti v i t y t h an

any sma l l pores . F ine- tex tured so i l s -m ay depend a lmos t e n t i r e l y on t h e s t r u c -t u r a l p o re s f o r t h e i r c o n d u c t iv i t y . The q u a l i t y o f t h e w a te r t ra n s m i t t ed , p a r t i -c u l a r l y t h e s a l i n i t y and a l k a l i n i t y , may ha ve a marked e f f e c t o n h y d r a u l i cc o n d u c t i v i t y .So i l w i t h in a d r a in ag e -p r ob lem a r ea s eldo m h as u n if or m p e r mea b i l i t y . T h i s v a r i a -t i o n i s ex h ib i t ed i n two imp o r t an t ch a r ac t e r i s t i c s : t h e s o i l may b e nonhomogeneousdue t o s t r a t i f i c a t i o n , b a r r i e r s , o r o t h e r d i s t i n c t masse s; o r i t may have a hi gh erp e r me ab i l i t y i n o n e d i r e c t i o n t h an an o th e r , even th ou gh homog eneou s. So i l s w i t ht h i s l a t t e r q u a l i t y a r e c a l l e d "a ni so tr op ic " ( s ee s ec t i o n on " Path s of Flowt').Rate of f lowThe r a t e o f f l o w ( Q ) p a ss i ng a g iv e n c r os s - s e c ti o n a l a r e a of s a t u r a t e d s o i l (A)i s t h e p r o du c t of t h e a r e a and t h e e f f e c t i v e v e l o c i t y o f f lo w t hr ou gh t h e s ec -t i o n (v) :

Combining t h i s e xpre ssi on wit h t he Darcy Law

we have th e expre ss ion

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T h i s e q u a t i o n may b e u se d t o e s t i m a t e t h e q u a n t i t y o f f lo w i n s i m p l e d r a i n a g ep ro bl em s, s u c h a s m ig ht b e fo un d i n h i l l s i d e i n t e r c e p t i o n o v e r a s l o p i n g , imper-meable l ay e r . I n more complex f l o w p ro b lems, b o th t h e h y d r a u l i c g r ad i e n t andt h e h y d r a u l i c c o n d u c t i v i t y v a r y t h r o ug h o u t t h e f l o w r e g i o n and a n a l y s i s i s mored i f f i c u l t . A l s o , t h e b o u n da r i e s o f f l ow may b e d i f f i c u l t t o d e t e rm i n e . F orth ese p r o b lems , i t u s u a l l y i s i m p r a c t i c a l t o d e f i n e c o m p le t el y t h e a r e a , p-ermea-b i l i t y , a nd h y d r a u l i c g r a d i e n t , s o l e s s d i r e c t me th od s of e s t i m a t i n g f lo w a r eemp lo yed. T h ese a r e d i s cu s sed i n Ch ap te r 4 , Subsur face Drainage .S i n k f o r m at i o n i n s u b s u r f a c e d r a i n a g eSu b su r f ace d r a in ag e i s a cc om pl is he d b y p l a c i n g be lo w t h e w a t e r t a b l e a n a r t i f i c i a lc h a n n el i n wh ic h t h e h y d r a u l i c h ea d i s l e s s t h an i t i s i n t h e s o i l t o b e dr ai ne d.T hus a h y d r a u l i c g r a d i en t t o w ar d t h e ch an n e l i s induced , and a "s ink" i s c r e a t k d .The s ink i s m a i n t a i n e d , of c o u r s e , b y re mo vi ng w a t e r fro m t h e a r t i f i c i a l c h a n ne lby gr av i t y o r by pumping.Two f a c t o r s d e t e r min e t h e r a t e a t wh ich w a te r moves t ow ar d t h e s in k a t an y p o in t :The h y d r a u l i c g r a d i e n t a nd t h e h y d r a u l i c c o n d u c t i v i t y . T h i s i s i n a c co r d w it hD a rc y 's Law. T o t a l fl o w t o t h e s i n k i n v o l v e s h y d r a u l i c c o n d u c t i v i t y th r o ug h o u tth e wh ole s o i l mass t h r ou g h w hich w a te r moves t o t h e s in k . The f l o w n e t d e l i n -e a t e s t h e e x t e n t and p a t t e r n o f f lo w th r ou g ho u t t h i s s o i l m as s, a s d i s c u s s e d o nth e p r eced in g p ag es .The d e s i r e d c o n t r o l of t h e w a t e r t a b l e i s acco mpl i sh ed ( a ) b y l o c a t i n g t h e s in kv e r t i c a l l y a nd h o r i z o n t a l l y s o a s t o t a k e a dv an ta ge o f t h e more p erm ea bl e s o i lm a s se s , a nd ( b ) by c o n t r o l l i n g t h e h y d r a u l i c g r a d i e n t . H y d r au l i c g r a d i e n t mayb e c o n t r o l l e d t h r ou g h d e p t h o f t h e s i n k , s p a c in g of t h e s i n k s , and ( i n m eth od sof d r a i n a ge ) t h e p r e s s u r e a t t h e s i n k . I n E qu at io n 1-1

P P(++zl) - ($ + z,)H y d r a u l i c g r a d i e n t = Lt h e s e t h r e e c o n t r o l s a f f e c t Z2, L and P 2 , r e s p e c t i v e l y .D ra in ag e d e v i c e s t h a t a r e u s e d ' t o form s i n k s a r e b u r i e d d r a i n s , d i t c he s , r e l i e fwe l l s (upward f low) , ve r t i c a l d ra in s (downward f lo w) , and pumped we l l s . Theh y d r a u l i c he ad i n b u r i e d d r a i n s a nd i n d i t c h e s d ep en ds on t h e w a t er - su r f ac e e l e -v a t i o n b e ca u se t h e w a t e r i s a t a tm o sp he ri c p r e s su r e . R e li e f w e l l s , a t t h e i rl o wer en ds wh er e t h e s in k u su a l ly i s f or med , o p e r a t e un d er a p r e s su r e d epen den to n t h e e l e v a t i o n of t h e i r ou t l e ts - -o r of t h e w a t e r s u r f a c e i n t h e d r a i n i n t owhich they d isc ha rge , i f submerged. Pumped we l l s c r ea te s in ks which may bee i t h e r a t a t m o s p h e ri c p r e s s u r e o r a b ov e a t m o s ph e r i c p r e s s u r e , d ep en di ng o n t h es o i l s t r a t i f i c a t i o n and wh eth er t h e s i n k i n q u e st i o n i s above or be low th e waterl e v e l i n t h e pumping w e l l .

T h e o r i e s of Buried Drai n and Open Dit ch Sub surfa ce DrainageWater movement i n t he s at ur a te d zone may be analyze d by appl ying Dar cy ' s Law t ot h e p a r t i c u l a r s e t of b o un da ry c o n d i t i o n s a t t h e d r ai na ge -p ro bl em s i t e . I f i tw er e p o s s i b l e by f i e l d s u r v ey s t o d e t e rm i n e t h e e x a c t l o c a t i o n o f i mp er me ab lel a y e r s , t h e l o c a t i o n and h y d r a u l i c h ea d of a l l i n f l o w t o and o u tf l o w fro m t h esy s tem, p e r mea b i l i t y i n a l l p a r t s o f t h e sys t em, t ime an d r a t e of ch an ges i n f l o w ,symmetry o f t h e sys t em-- a l l t h e f a c t o r s w hich a f f e c t t h e amount an d p a t t e r n o ff low-- then th e prob lem would be comple te ly def ine d and sub je c t t o d i r e c t ande x a c t s o l u t i o n .

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Dra i nag e p ro bl em s a r e s el do m s o co m pl e t e ly d e f i n e d i n p r ac t i ce , h o weve r. Us u a l l yt h e y c o n s i s t o f a more o r l e s s complex combina t ion o f d i f f e r e n t p roblems . Thep ro ced u re i s t o d e t e rm i n e t h e b ou nd ar y c o n d i t i o n s , f i r s t a pp r o xi m a t el y , t h e n i na s much d e t a i l a s n eces s a ry b y m eans o f t h e r eco n n a i s s an ce an d p re l i m i n a ry s u rv ey s .C e r t ai n s i t u a t i o n s o r s e t s of b ou nd ary co n d i t i o n s a r e r eco g n ized a s p ro bl em t y p esf o r w hi ch ex p er i en c e o r a n a l y s i s h a s g i v en u s d e s i gn c r i t e r i a . A f t e r i d e n t i f i c a -t i o n o f t h e pr ob le m t y p e , t h e ne c e s sa r y f i e l d m ea su re me nt s a nd i n v e s t i g a t i o n s a r emade s o t h a t d e s i g n c r i t e r i a may b e ap p l i e d . For some d ra i n ag e p rob l em s , t h e r ea r e fe w n u m er i c a l c r i t e r i a , i f a n y, a nd t h e d e s i g n e r r e l i e s m o s tl y on good j ud g-m en t. B ut i n a l l d r a i n a g e p ro bl em s t h e b a s i c pr o c e du r e i s t h a t p r e v i o u s l yo u t l i n e d .D r a in a ge t h e o r i e s h a ve be e n d e ve l op e d t o d e s c r i b e o r t o a t t e m p t t o d e s c r i b e t h ea c t i o n o f a g i v e n s a t u r a t e d f l ow s ys te m. They a r e u s e f u l i n g e t t i n g a n a p pr o xi -m a t e s o l u t i o n t o a c t u a l f i e l d pr ob le ms. To us e them, t h e des ign er must comparet h e f i e l d s i t u a t i o n w i t h t h e u n d e rl y in g a ss um pt io ns o n w hi ch t h e d r a i n a g e t h e o r i e sa r e b a s ed . He t h en ap p l i e s s u ch o f them a s h i s ju dg ment i n d i c a t e s a r e m os ta p p l i c a b l e . B ot h s t e a d y s t a t e and no n st e ad y s t a t e p ro bl em s a r e e n co u nt e re d i nd ra i n ag e work. The fo l l owi n g ap p rox i m at e t h eo r i e s h av e b een ap p l i ed t o on e o rbo th type s of p rob lems .C l a s s i f i c a t i o n o f d r a i n a g e t h e o r i e s b y b a s i c a s su mp ti on sH o r i z o n t a l f l o w t h e o r i e sT h es e ap p rox i m at i o n t h e o r i e s a r e b a s ed on two a s s um p t i on s : ( a ) t h a t a l l s t ream-l i n e s i n a g r a v i t y f l ow sy st em a r e h o r i z o n t a l , and ( b ) t h a t t h e v e l o c i t y a l on gt h e s e s t r e a m l i n e s i s p r o p o r t i o n a l t o t h e s l o p e of t h e f r e e- w a te r s u r f a c e , b u tindependen t o f dep th .Although i t can b e shown t h a t t h e s e a r e e r ro n eo u s as s u mp t i on s , ( s e e "Hy drau l icG r a di e nt ' ' p ag e 1-12) t h e t he o r y of h o r i z o n t a l f l o w g i v e s s u f f i c i e n t l y a c c u r a t er e s u l t s i f i t s a p p l i c a t i o n i s r e s t r i c t e d t o s i t u a t i o n s where t h e f lo w i s l a r g e l yh o r i z o n t a l . T hr ee f i e l d c o n di t i o ns of t h i s k i nd a r e :

1. Open d i t c h e s t h a t a r e s h a l l o w com pared t o t h e i r s p ac i n g and t h a t p en e-t r a t e t o o r a r e c l o s e t o a n i mpermeable l a y e r .

2. Open d i t c h e s t h a t a r e ex ca va te d i n s t r a t i f i e d m a t e r i a l s .3 . B u ri e d d r a i n s u n de r c o n d i t i o n s 1 and 2 , p a r t i c u l a r l y i f t h e ba c kf i l l e d

t r e n c h i s m ore p e rm eab l e t h an t h e u n d i s t u rb ed m a t e r i a l .One ex p re s s i o n o f t h e h o r i z o n t a l f l o w t h eo ry i s t h e e l l i p s e e q u a ti o n , of w hic ht h e t i l e - spa c i ng fo rmula deve loped by Donnan ( 3 ) i s one form. Ap p l i ca t i o n o ft h e e l l i p s e e q ua t i on i s d i s cu s s ed i n C h apt e r 4 , Su b s u r face Dra i n ag e .Visser ( 4) i n a n o th e r a p p l i c a t i o n o f t h e e l l i p s e e q u a ti o n , e x t en de d i t t o a p p lyt o n o n st e ad y s t a t e p ro bl em s. H i s method was d ev e lo p ed f o r co n d i t i o n s i n t h eNe t h e r l an d s , b u t acco rd i n g t o Van Sc h i l f g aa r d e , K irkh am , an d F re v e r t ( 5 ) , t h emethod p o s s i bl y c ou ld b e a p p l ie d p r o f i t a b l y i n i r r i g a t e d a r e a s o f t h e a r i d r e g i o n s .R a d i a l f lo w t h e o r i e sA t i l e l i n e may b e t h o u g h t o f a s a h o r i z o n t a l w e l l , w i t h w a t e r a p pr o ac h in g t h et i l e a l o n g r a d i a l s t r e a m l i n e s . T h i s a n al o gy i s t h e b a s i s f o r t h e r a d i a l f lo wt h e o r i e s , wh ich a ss um e (a ) a homogeneous i s o t r o p i c s o i l o f i n f i n i t e d ep t h , and(b) a f l a t wa t e r t ab l e . 'T h i s m eth od can g i v e a go od ap p rox i m a ti o n of ac t u a l f l o w

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c o n d i t io n s i f t h e c u r v a tu r e of t h e wa t er t a b l e i s s m al l ( a s wi t h a l ow r a i n f a l lr a t e a nd r e l a t i v e l y h i g h p er m e a b i li t y ) , and i f b elow t h e d r a i n t h e r e i s no l a ye ro f g r e a t l y r e du c ed p e r m e a b i l i t y .Combined h o r i z o n t a l a n d r a d i a l f l o w t h e o r i e sHooghoudt ( 6 ) and Erns t ( 7 ) ha ve de vel ope d s o l u t i o ns o f t h e f l ow p rob le m byc om bi ni ng t h e r a d i a l an d h o r i z o n t a l f lo w h y p o t h es e s . T he se s o l u t i o n s c o r r e c tt h e m a j or s ho r tc om ing o f t h e e l l i p s e e qua t i on ( n e g l e c t o f c onver ge nc e o f f l own e a r t h e d r a i n ) . They a r e v a l u a b l e an d r e l i a b l e a p pr ox im a ti on s f o r t h e st e ad y -s t a t e p ro bl em o f r em ov in g s t e a d y r a i n o r e q u i v a l e n t a c c r e t i o n .Hooghoud t m od i f i e d t h e e l l i p s e e qua t i on by i n t r oduc i ng a n " e qu i va l e n t de p t h , "a nd h e p r e pa r ed e x t e n s i v e t a b l e s o f t h e e q u i v a l e n t d e p t h f o r s o l u t i o n o fs t e a d y - s t a t e p ro b le m s. V i s s e r ( 4 ) r e po r t s on a nomogr aphi c s o l u t i o n ba s e d onth e same ge ne ra l assumpt ions a s Hooghoudt's method, and Van Beers (8 ) has deve lopednom ogra phs f o r c a l c u l a t i o n o f d r a i n s pa c i ng a c c o r d i ng t o t he Hooghoudt a nd E r ns tf o r m u l a s .Van Deemter's ( 9 ) hodogr a ph a na l y s i sT h i s i s a ma th em at ic al a n a l y s i s i nv o l vi n g t h e s o l u t i o n of c e r t a i n d i f f e r e n t i a le q u a t i o n s s o a s t o s a t i s f y t h e b ou nd ar y c o n d i t i o n s . Van D eem ter u se d t h i sa n a l y s i s t o s t u d y t i l e d r a in a g e, b u t h i s r e s u l t s a p pl y o n ly t o t i l e r un ni ng f u l l .I n summary, t h e a pp r o xi m a te s o l u t i o n s o b t a i n e d by a p p l i c a t i o n of t h e s e t h e o r i e sa r e s i m p l e r t h a n e xa c t s o l u t i o ns wh ic h may be a va i l a b l e f o r some p r ob l em s , a ndt h e y p r o v i d e s o l u t i o n s t o o t h e r p r ob le ms f o r wh ic h no o t h e r me th od s a r e y e tknown. I t i s i m p o r t an t , h o we ve r, t h a t t h e f o l l o w i n g i n h e r e n t l i m i t a t i o n s b er e c ogn i z e d s o t h a t t h e m ethod w h ic h i s m ost ne a r l y a p p l i c a b l e may be a pp l i e d :

1. H o r i z o n t a l f l o w t h e o r y ( e l l i p s e eq u at io n ). -- Us e w he re t h e f l o w i sl a r g e l y h o r i z o n t a l , a s f o r d r a i n s s h a ll o w compared t o t h e i r s p a c in gw i t h a l l . i mp er me ab le l a y e r s a t o r c l o s e t o t h e b ot to m of t h e d r a i n .

2 . Radial f low theory. --Apply i t t o h om og eneou s i s o t r o p i c s o i l of g r e a td e pt h, w i t h a f l a t o r n e a r l y f l a t wa te r t a b l e .

3. Combined ho r i z on t a l a nd r a d i a l t he o r i e s ( a s H ooghoud tl s) .- -U se f o rs i t u a t i o n s wh er e t h e i mp er me ab le l a y e r i s e i t h e r s h al l ow o r d e ep , b yus i ng H ooghoudt 's e qu i va l e n t de p t h o r t h e nomograph p ub l i s he d byV i s s e r .

4 . Van ~ e e m t e r ' s o do gr ap h a n al ys is .- -A p pl y Van ~ e e m t e r ' s n a l y s i s o n l yt o t i l e d r a i n s r u n ni ng j u s t f u l l , o r t o p ro ble ms w he re t h e w a te rt a b l e s t a n d s i m me di at el y a bo ve t h e d r a i n s .

T r a n s i e n t f l o w c o n c e p tThe d r a i n a g e o f i r r i g a t e d l a n d p r e s e n t s p ro bl em s wh ic h a r e d i f f e r e n t f ro m th o s ei n humid a r e a s . The r i s e and f a l l of t h e w at er t a b l e i n i r r i g a t e d a r e a s ge n e r a ll yf o l l o w s a c y c l e w hi ch i s r e l a t e d t o t h e a p p l i c a t i o n of i r r i g a t i o n w at er d u ri n gt h e g ro wi ng s e as o n an d t h e t e r m i n a t i o n o f i r r i g a t i o n w a t e r u s e i n t h e o f f s e as o n.C o n t r a st e d w i t h t h e s t e a d y - s t a t e g ro un d- wa te r c o n d i t i o n s i n humid a r e a s t h es t o r a g e and d i s c h a r g e of g ro un d w a te r i n i r r i g a t e d a r e a s f o l l o w s a t r a n s i e n t o rnon s tea dy- s ta t e regimen. The Bureau of Recla mat ion ha s developed a method ford r a i n s p a c i n g b as ed o n t h e t r a n s i e n t - f l o w c o n ce p t w hi ch g i v e s c o n s i d e r a t i o n t ot h e w id e d i v e r s i t y of s o i l s an d g ro un d- wa te r c o n d i t i o n s p r e v a i l i n g i n We st er nU n i t e d S t a t e s . A t h e o r e t i c a l f o r m u l a, w hi ch i n c o r p o r a t e s mo st of t h e f a c t o r sinvolved, was developed by R . E . G l ove r , a nd p r oc e du r e s f o r u s e o f t h e fo r m ul a

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were developed by Lee D . Durn, bo th eng i nee r s fo r t he Bureau of Reclamat ion (1 0) .The t r ans ien t - f low concep t has been i n use by th e Bureau f o r s e v e r a l ye a r s , an dth r ou g h ex p e r i en ce w i th i t s use many ref i ne me nts have been made (11 ). Van Beers'(8 ) nomographs fo r c a l cu la t i on of d r a i n sp acin gs in c lu de one fo r t he Glover/Dummformula and i t s u se i s recommended when us in g me tr ic u n i t s .T ech n iq u es f o r ap p ly in g d r a in ag e t h eo r i e sThe f o re g o i ng a r e t h e p r i n c i p a l t h e o r i e s o f s a t u r a t e d fl o w to wa rd d r a i n s . Anumber o f techn ique s have be