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<br />754
<br />
<br />HYDRAULIC ENGINEERING '94
<br />
<br />However, the runoff production on large slope hillsides has different characteris-
<br />tics. When precipitation intensity is large enough runoff can be produced before soil
<br />moisture beiDg less tban soil absorption capacity. i.e.,
<br />\R' =l-F-E ;fl-E>F
<br />R =0 ifl-E<F
<br />
<br />R:=f-(W,-W,) ifW,>W.
<br />R1 -O,W2 -F+ WI if W1 < Will
<br />R=Rl+Rl
<br />The seepage rate, F. can be presented in Horton Equation:
<br />-..
<br />F-F,+(F,-F,le
<br />in which, Fo is tbe maximum seepage rate, Fe is the stable seepage rate, k is a
<br />parameter representing soil feature, t is the time intenal.
<br />
<br />(5)
<br />
<br />(6)
<br />
<br />The calculation of conOuent
<br />
<br />Flow on hiUsides and in rills arc non-steady, according to the characteristics of
<br />flow in large slope channels. tben
<br />0(2 .,4
<br />~+~=~n m
<br />
<br />S ~S or Q=k,4' (8)
<br />f , '
<br />in which, Q is the water discharge; A is the hydraulic section area; r(x,t)" is the lateral
<br />inflow. i.e., tbe out now at the hill foot; S~s the friction slope; Sois the hillside or rill
<br />
<br />slope; k.is a friction parameter. II is a exponent. For now on hillsides. k. ==; s!. n is
<br />
<br />Manning roughness. The connuent equation on hillside or in rill can expressed by:
<br />.Q -'I '-'0(2
<br />_ +K' -Q' - =r(x,/) (9)
<br />::iiX' . a ::ii'
<br />
<br />The sediment yield model
<br />
<br />The processes of soil erosion, sediment movement and deposition, sediment
<br />discharge per unit of widtb on both hillside surfaces and rills may be expressed by a
<br />similar form of Meyer-Peter equation:
<br />q.=k,(t'o-f)'"
<br />now stress t'o-yhSo' the parameter m-3/2. parameter kl""
<br />
<br />(10)
<br />
<br />in wbich. the
<br />
<br />8 ( 1, )
<br />.rp 1, -1
<br />In consideration of soil cohesion, the soil erosion incipient shear stress can be
<br />written as:
<br />
<br /><, =O,046C.(l, -1 )D (II)
<br />in which, CEis a parameter representing soil cohesion, it is generally greater than 1.0, D
<br />is the average diameter of lased soil.
<br />
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<br />
<br />tt5
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<br />
<br />MODEL-SEDIMENT YIELD
<br />
<br />The continuity equation at soil loss can be presented as:
<br />dq,
<br />fiX = P, (12)
<br />
<br />in which, P, is the soil erosion rate per unit area, x is tbe distance originating from
<br />hiUtop.
<br />Accoding to the experiment results conducted by Li Riming. at. al (Li, 1973). the
<br />soil erosion rate in unit area can be written as:
<br />P =k (t -< )" (13)
<br />, 3 0 ,
<br />in which, both k2 and k] arc parameters.
<br />Tben, combining Eq,(IO) and Eq,(I2) tb. following .xpression can b. nbtained:
<br />",d'fo
<br />P,-k,(m-IX<,-<,l dx (14)
<br />
<br />Comparing Eq,(l3) witb Eq,(l4), w. bav.
<br />k, =m (15)
<br />d<,
<br />k,=k,(m-IJ-;t;- (16)
<br />
<br />According to tbe research conducted by Xie Shunan at. al ( Xie, 1992)
<br />S, -1.25S f
<br />
<br />dh =!S-~R x-~
<br />dx 2 0 I
<br />I !_!
<br />The., K=-lk(m-l)S'Rx' (17)
<br />1 2.S I 0 I
<br />Sediment yield in unit area and unit time interval can be derived as:
<br />ISL 1m-I jlOLS, .
<br />E,-I ,P,dX-1.25Lk'm+ll( -glR,-<.l -<;)
<br />
<br />jlOLSo ))
<br />=O,0651( -lR -< ). -<'I (18)
<br />fir 'c c
<br />Each of tbe sub-watershed should be divided into two parts: tbe area without soil
<br />loss Agand the area of soil loss (A-Aa). In the well vesetalCd. residential and pavement
<br />places, it can be considered there is no soil loss. But in bad vegetated places soil ero.
<br />!ion occurs. Then the average soil yield per unit area iD unit time interval may be ob.
<br />tained:
<br />~OLSo 3) 3 J
<br />E ~O,065C,1 -lh-O,046C (1 -l)DI' -OOIC'(l -l)'D'1 (19)
<br />. fir & , . 6.
<br />m which, C" :;z (A-AD) / A, A is tbe watershed area, Aais the area without soi11oss.
<br />
<br />~.~plication of the watersbed model
<br />
<br />The watershed model is used to tbe small watershed of Xiang shuitan, which is 10'
<br />cated at the upstream ofTuojaDI River in southwest ofChiDa. The area of the water.
<br />shed is 44.7 km:Z, the length of the watershed is 13.38 km, aDd its hillside slopes range
<br />from 1/10101/3,
<br />The aonuual precipitation in the watershed is 965.8 mm. The maximum precipita.
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