effects of soil properties on overland flow and infiltration

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EFFECTS OF SOIL PROPERTIES ONOVERLAND FLOW AND INFILTRATIONProfessor Ben Chie Yen a & Professor Ali Osman Akan ba University of Illinois at Urbana-Champaign , Urbana, Illinois,61801, USAb Department of Civil Engineering , Old Dominion University ,Norfork, Virginia, 23508, USAPublished online: 21 Jan 2010.

To cite this article: Professor Ben Chie Yen & Professor Ali Osman Akan (1983) EFFECTS OF SOILPROPERTIES ON OVERLAND FLOW AND INFILTRATION, Journal of Hydraulic Research, 21:2, 153-173,DOI: 10.1080/00221688309499442

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EFFECTS OF SOIL PROPERTIES ON OVERLAND FLOW AND INFILTRATION

EFFETS DES PROPRIETES DU SOL SUR LE RUISSELLEMENT ET SUR L'INFILTRATION

Professor BEN CHIE YEN Professor of Civil Engineering, University of Illinois a t Urbana-Champaign Urbana, Illinois 61801, USA

Professor ALI OSMAN AKAN Associate Professor, Depar tment of Civil Engineering, Old Dominion University, Norfork, Virginia 23508, USA

Soil properties have profound effects on overland flows over porous media. These effects are investigated by using a surface-subsurface flow conjunctive simulation model which solves the Saint-Venant equations for the overland flow and Richards' equation for the two-dimensional unsaturated and saturated porous medium flow. Guided by a dimensional analysis, four soil properties are studied, namely, porosity, vertical and horizontal saturated hydraulic conductivities, and unsaturated soil hydraulic characteristics which is expressed in two pairs of parameters describing the relationships between the degree of saturation and suction pressure, and between the relative conductivity and suction pressure, respectively. The results confirm the common belief that overland flow increases for decreasing soil porosity or saturated conductivity while the infiltration into the soil decreases. The effect of the ratio between horizontal and vertical saturated conductivity is insignificant, indicating the soil anisotropic effect is unimportant. Moreover, the overland flow decreases and infiltration increases for soils having small suction pressure head in the saturation and relative conductivity vs. suction pressure relationships, corresponding to, e.g., increasing soil particle sizes, than for soils having large suction pressure head.

Résumé Les propriétés du sol ont des effets profonds sur Ie ruissellement au-dessus d'un milieu poreux. Ces effets sont étudiés au moyen d'un modèle de simulation conjointe de l'écoulement superficiel-souterrain, qui résoud les equations de Saint-Venant pour Ie ruissellement et l'équation de Richards pour l'écoulement bi-dimensionnel en milieu poreux saturé et non saturé. A partir d'une analyse dimensionnelle, on étudie quatre propriétés du sol: sa porosité, sa conductivité hydraulique saturée, verticale et horizontale, et ses earactéristiques hydrauliques non saturées que l'on exprime au moyen de deux jeux de paramètres décrivant respeciivement la relation entre Ie degré de saturation et la pression d'aspiration, et la conductivité relative et la pression d'aspriration. Les résultats confirment la croyance tres répandue selon laquelle Ie ruissellement augniente lorsque la porosité du sol ou sa conductivité saturée diminue alors que l'infiltration dans Ie sol diminue. L'effet du rapport entre la valeur horizontale et la valeur verticale de la conductivité saturée n'est pas significatif, ee qui indique que l'effet anisotrope n'est pas important. En outre, Ie ruissellement diminue et l'infiltration augmente dans Ie cas de sols pour lesquels la valeur de la pression d'aspiration dans les rapports saturation/pression d'aspiration et conductivité relative/pression d'aspiration est faible, ce qui correspond par exemple a un accroissement de la granulométrie; Ie phénomène est différent dans Ie cas de sols ayant une pression d'aspiration élevée.

Received October 18, 1982. Open for discussion till October 1, 1983

Summary

Journal of Hydraulic Research 21 (1983) no. 2 153

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1. Introduction Infiltration is an important component in reliable mathematical modeling of free surface flow over porous media. Yet unsteady open-channel flow routing rarely takes into account directly the effect of infiltration. Traditionally, the concept of infiltration was treated as a hydrology problem and was developed empirically. In the physically-based approaches utilized during the past two decades, infiltration was treated as an unsaturated subsurface flow process. Early analytical solutions to the infiltration problem were reported by Philip [14] and Young [21]. In more recent studies, Childs [7], Brutskern and Morel-Seytoux [6], and Parlange [11] developed integral equations to describe infiltration. Noblanc and Morel-Seytoux [10] and Babu [5] adopted perturbation techniques for the analysis of infiltration.

In a different category of theoretical treatments, infiltration was evaluated based on numerical solutions of the unsaturated subsurface flow equations. The pioneering works in this category were summarized by Freeze [8]. Among the more recent studies, Whisler and Watson [19], Ahuja [1], Jeppson [9], Whisler et al. [20], and Reeder et al. [15] reported further developments in the numerical treatment of the infiltration problem. These numerical models are slightly more versatile than the analytical approaches in that they allow the consideration of certain complexities of real soils. However, their capability of truely representing the infiltrability (i.e. infiltration capacity) is open to discussion because they treat the subsurface flow as an individual component independent of the surface runoff.

Smith and Woolhiser [16] were probably the first to report in the literature a conjunctive surface-subsurface flow model concerning infiltration using kinematic wave approximation to describe the surface flow and a one-dimensional equation to represent the unsaturated subsurface flow. Recently, Akan and Yen [4] reported the development and verification of a high-accuracy surface-subsurface flow conjunctive model which accounts for the dynamic equilibrium between the two components. This model is adopted in this study and the part relevant to this paper will be briefly described later.

A number of researchers including Philip [13], Parlange [12], Akan and Yen [3], and Reeder et al. [15], investigated the effect of the ponding depth and surface water supply rate on infiltration. Whisler and Klute [18] and Talsma [17] studied the influence of the hydraulic properties of the soil on subsurface flow. In all these studies, the infiltration and/or subsurface flow was treated as an individual component disregarding the overland flow. To the knowledge of the authors no previous studies were published on the effects of the soil properties on a conjunctive surface-subsurface flow system. The objective of this paper is to illustrate, by using a hydraulic-based mathematical model, the effects of the basic soil properties on infiltration, subsurface flow, and overland flow.

2. Summary of conjunctive model utilized The details (including assumptions involved) and the verification of the hydraulic based mathematical surface-subsurface conjunctive model employed in this study have been reported elsewhere [2, 4]. Therefore, only a summary of the part of the model relevant to this paper is briefly described as follows.

In this model surface runoff is represented by the Saint-Venant equations simplified for wide channels

(1)

Sf) = 0 (2)

^ + U- i + f = 0 dx dt

3(vy) + 3(v2y) ( 3 t 3 x g y (b°

_ay 3x

154 Journal de Recherches Hydrauliques 21 (1983) No. 2

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in which v is the cross-sectional average velocity of the flow; x is the horizontal distance; y is the flow depth measured normal to x; t is time; i is the time rate of lateral inflow, or surface water supply; f is the time rate of infiltration; g is gravitational acceleration; S0 is the bottom slope; and Sf is the friction slope which is computed by using the Darcy-Weisbach formula

Sf = fd 4 (3)

The frictional resistance coefficient f̂ is evaluated from an approximate form of the Moody diagram, being equal to 24/IR, 0.223/IR0-25, and [2 log (2y/k) + 1.74]-2 for laminar, transitional, and turbulent flows, respectively, where IR is the Reynolds number equal to vy divided by the kinematic viscosity, v, and k is a measure of surface roughness. With a proper set of initial and boundary conditions, Eqs. 2 and 3 are solved by means of a four-point implicit finite difference scheme in conjunction with a generalized Newton iteration technique.

The subsurface flow is modeled as two-dimensional motion of a single-phase incompressible fluid in a nondeformable porous medium and it is represented by the equation

| <*sx Kr JS) + g | (KSZ Kr | § = n 3 J $ (4)

in which H is the piezometric head; and the soil properties include the soil porosity n; the saturated hydraulic conductivities (coefficients of permeability), Ksz and Ksx, in the z and x directions, respectively; the relative hydraulic conductivity, Kr (assumed isotropic); the capillary pressure head, P; and the degree of saturation, S. Equation 4 is applied to saturated groundwater flow as well as unsaturated soil water flow. In the zone of saturation P is the positive pressure head and Kr is unity. By neglecting the entrapped gases in the soil, for saturated soil S is also set equal to unity and 9S/3P = 0. Hydraulic relationships among P, S and Kr for the soils are needed for applying Eq. 4 to the zone of aeration. The present model partly accounts for the hysteresis property by allowing two different P-S-Kr relationships: one for each of the wetting and drying processes. An implicit finite difference scheme based on the successive-line over-relaxation method is employed for the solution of the subsurface flow equation allowing a variety of initial and boundary conditions.

The surface and subsurface flow components are interrelated by a common pressure head and an exchange of water at the ground surface. In the mathematical sense, the top boundary condition for the subsurface flow equation (Eq. 4) is determined by the surface flow condition. Conversely, infiltration, a lateral outflow term in Eq. 1, is controlled by the soil water conditions. Therefore, the solutions must be obtained by coupling the surface and subsurface flow equations at each time step. In the model a quasi-implicit coupling procedure is adopted.

Infiltration is defined here as the passage of water through the overland surface into the soil. As the instantaneous distribution of the piezometric head in the soil is determined from the numerical solution of Eq. 4, the rate of infiltration at each time step of computation is evaluated as

f = KsN " r FN

where N indicates the direction normal to the ground surface.

(5) round surface


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3. Dimensional analysis and soil conditions considered 3.1 Dimensional analysis The parameters that would affect the subsurface and surface flows over a porous medium can be grouped as the overland properties, soil properties, and fluid properties in addition to the initial and boundary condition parameters. For a one-dimensional overland surface which has no lateral variations, the overland parameters are the surface length L, slope S0, and surface roughness k. The soil parameters are the porosity n, saturated hydraulic conductivities K sx and K s z in the horizontal (x) and vertical (z) directions, respectively, and the unsaturated soil moisture movement property represented by a nondimensional symbol a . The fluid properties include the fluid density p, specific weight V. surface tension a, and kinematic viscosity v. For a given uniform surface water supply rate (e.g., rainfall intensity) i over a duration t,j and specified boundary and initial conditions, and noting t h a t y / P = g, the discharge per unit width, q, and depth, y, of the overland flow and the infiltration rate f at a given section x and time t are functions of the influential parameters, i.e.,

q, y, f = Fx, 2, 3 &> x> i> lo> P» CT' v> S> L> so> k> n> Ksx' Ksz> o) (6)

where Fj represents a function.

In porous medium flows the unsaturated soil moisture movement parameter a can be described by the soil hydraulic relationships of the pressure head, P, vs. the unsaturated soil relative conductivity, Kr, and vs. the degree of saturation, S. In other words, nondimensionally,

a = F4 [(S, P V S ), (Kr, PV&S )] (7)

It is conceivable that a can be expressed alternatively by relevant soil structural characteristics such as the size spectra and packing distribution of the soil particles, a measure of the water content of the soil, together with representative flow resistance coefficient which depends on the Reynolds and Weber numbers of the porous medium. However, Eq. 7 is adopted in this study because of its practicality. The S-P and Kr-P relations can be measured in the field or laboratory and they are used by many soil scientists.

Applying dimensional analysis to Eq. 6, and neglecting the Weber number effect on the overland flow, one has

q y f _ „ ,t x lt;d v2 c k K s z K s x > ,_.

h V T - F s ' 6> 7 <£ ' L' TT• ~[3' S ° ' XT' n' — K ^ ' a) (8)

3.2 Hydraulic process of overland and porous medium flows Physically, under an initially dry overland surface, the soil moisture is in static equilibrium, especially if a sufficiently long time has passed since the occurence of last water supply. The static piezometric head is governed by the elevation of the water table. The moisture content varies with depth in accordance with the S-P relationship of the soil. However, if the water table is sufficiently low and the soil is considerably dry, the nature of the S-P relationship may cause a nearly uniform moisture content, approximately equal to the hygroscopic water content of the soil, near the ground surface. Having a high infiltrability (infiltration capacity), a dry soil can absorb almost the entire surface water supply applied. However, a thin ground layer of the soil becomes saturated soon, and the wetting front of the percolating water in the porous medium starts to propagate in the soil. The deepening of the wetted zone reduces the infiltrability

156 Journal de Recherches Hydrauliqu.es 21 (1983) No. 2

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http://Hydrauliqu.es

of the soil. At the same time, if the infiltration rate is less than the surface water supply rate (e.g., from rainfall and upstream inflow), overland flow is initiated in the direction of the ground surface slope.

As the top layers of the soil gradually become saturated, the hydraulic gradient available for the percolating flow decreases. Consequently, both the infiltration rate and the speed of wetting front propagation decrease with time. Meanwhile, with decreasing infiltration more water becomes available for overland flow if the surface water supply remains constant, resulting in continuous build-up of the overland flow with increasing depth and discharge. Obviously, for otherwise identical conditions, infiltration rate is higher for soil with high porosity or conductivity, and consequently less water is available for the overland flow.

If initially the ground surface is not dry or an initially surface overland flow already exists, the initial soil moisture conditions is adjusted according to the S-P relationship. Otherwise the physical processes of the infiltration and overland flow are the same as described in the preceding paragraph.

3.3 Soil conditions considered In order to investigate the effects of the soil characteristics on infiltration and overland flow, the surface-subsurface conjunctive model mentioned in the preceding section is applied to a hypothetical drainage basin, which is shown in Fig. 1. The geometry of the basin is selected such that the effects of the soil properties can be individually, thoroughly, and clearly studied without losing generality. The length of the basin, L, is 100 m. The overland slope, S0, is 0.0001 and the overland surface roughness, k, is 0.001 m. The thickness of the homogeneous (but could be anisotropic) porous medium is 10 m and the initial groundwater table is horizontal at 3 m below the ground surface, both measured at the upstream end of the aquifer. These two depths are selected such that they are sufficiently large to have insignificant direct effects of the aquifer bottom and groundwater table on the infiltration and overland flow.

r- i

Uniform Surface Supply i , td

\ \ 1 I 1 I \ I SQ= O.OOOI

Ground Surface - '

L = 100m

Initial Water Table "\ Fig. 1

Description of hypothetical basin

Description du bassin hypothétique

The aquifer is bounded by a vertical impervious formation at its upstream side. A constant piezometric head equal to the elevation of the initial water table is maintained at the downstream boundary of the aquifer. However, the direct effects of these boundary conditions on the flows investigated are small because the initial water table is relatively low and the infiltration into the homogeneous soil is essentially vertical.

Moreover, the overland surface water supply is at a temporally and areally uniform rate of 0.020 mm/s (72 mm/h) over a 60-minute duration. Thus, itd/L = 0.72 x 10 ■>, v2/gL3= 0.2 x 10"18 , S0 = 0.0001, and k/L = 10 - 5 . For these conditions of the hypothetical basin, Eq. 8 can be simplified as


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iL ' i t ( j ' i f - T7 | t

- F 8 , 9, 10^ t d ' L' ^ s z ^sx >

n, -r—, r7—, a) (9)

in which a is defined by the relationships of K r and S with p / p g / o as indicated in Eq.

In this paper the effects of soil propert ies are investigated for four different porosities, n, ranging from 0.20 to 0.60, four different values of K s z / i , ranging from 0.00625 to 0.25, three values of K s z / K s x (0.1, 1, 10), and three different types of the relationships for S vs. P / p g / a and for K r vs. P/pg/o , respectively, which are shown in Fig. 2 and will be further discussed at the beginning of Section 6.

The soil moisture is assumed initially in s ta t ic equilibrium under uniform piezometric head determined by the groundwater table. In other words, the initial pressure head changes linearly from zero at the water table to -3.0 m near the soil surface. According to the P-S-K r relationships given in Fig. 2, the degree of saturat ion is nearly constant when the pressure head is lower than -2.75 m. Hence, the uniform piezometric head distribution adopted as the initial condition represents also a near uniform moisture content with S = 0.10 (hygroscopic water) at the upper layers of the soil. Hysteresis is not considered here since this paper concerns mainly with soil wetting process. A summary of the conditions investigated is given in Table 1.

4. Effect of soil porosity The effect of soil porosity on the conjunctive overland and porous medium flows and infiltration are investigated through the resul ts of Runs 1 , 2 , 3 and 4 listed in Table 1. The soil propert ies and other hydraulic propert ies for these runs are identical except for the soil porosity which ranges from 0.20 to 0.60 and the results are shown in Figs. 3 to 6. In real i ty , such a change in porosity without changing the saturated permeability can

300 - 1 —

- 4 0 0

Saturation S Relative Conductivity K,

Example unsaturated soil hydraulic properties considered

-1.5 -2.0 Pressure (m)

Fig. 2

- 3 0 -3.5

Exemple de propriétés hydrauliques d'un sol non saturé


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Table 1. Summary of Soil Characteristics Analyzed TEST

RUN

n K sz 10 mm/s

K sz i

K sx K sz K i

TYPE

vs P

OF

' a S

TYPE

vs P

OF

' a

0.4 1.25 0.0625

2 3 4

5 6 7 8 9 10 11

12 13 14 15 16 17

0.2 0.5 0.6

0.4 0.4 0.4 0.6 0.2 0.4 0.4

0.4 0.4 0.4 0.4 0.4 0.4

1.25 1.25 1.25

0.125 2.50 5.00 0.125 2.50 1.25 1.25

1.25 1.25 1.25 1.25 1.25 1.25

0.0625 0.0625 0.0625

0.00625 0.125 0.250 0.00625 0.125 0.0625 0.0625

0.0625 0.0625 0.0625 0.0625 0.0625 0.0625

1 1 1

1 1 1 1 1 0.1 10

1 1 1 1 1 1

B B B

B B B B B B B

A C B B A C

0.75

0.50

025

Effect of soil porosity on overland flow Fig. 3 discharge

Effet de la porosité du sol sur Ie debit de ruissellement

be achieved, e.g., by a proper combination of changes in soil porosity and liquid viscosity. In accordance with the hydraulic process discussed in Section 3.2, the higher the porosity, the more the water will infiltrate into the soil and the smaller the overland flow. As shown in Fig. 3 for discharges at x/L = 1.0 and x/L = 0.6 and in Fig. 4 for the depth profiles at t/t^ = 0.75, (rising limb of hydrograph), 1.0 (peak flow), and 1.25 (recession), respectively, the effect of porosity is pronounced and significant. The overland flow starts at a delayed time after the commencement of the surface water supply. Since the


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25

20

x/L

0.2 0.4 0.6 0.8 10

10

^

„ -

1 1

t / t d =

0 . 7 5 ^ -

l.25""~

1

1

_, l .0"*~"

. ^ 0 . 7 5 "

—1.25

1

1 1

"~~^_____

"~~~~~

1

.1.0 —

0.75-

.1.25-

1

. 1.0

0.75

1.25

n — 0.20 — 0.40

— 0.60 1

= 0.30

0.25

0.20

_^0 . I5

: 0 I 0

0 0 5

20 40 60 80 100 ie (m)

Effect of soil porosity on overland flow Fig. 4 Effet de la porosité du sol sur la pro-depth fondeur de ruissellement

duration of water supply is limited, both the discharge and depth of the overland flow attain their respective maxima at the cessation of the surface water supply, t/t<j'= 1.0, at values lower than their asymptotic values. During the flow recession after the cessation of the surface water supply, both the discharge and depth of the overland flow decrease and reach zero a short while later. This attainment of zero overland flow for a pervious surface is clearly different from the asymptotic nature of the flow for the case of an impervious overland surface.

The corresponding area-averaged infiltration graphs and the soil saturation profiles computed for these example runs are shown in Figs. 5 and 6. The case of n = 0.50 is not included in Fig. 6 for the sake of clarity. Intuitively, the infiltration should be higher in the downstream portion because of the greater flow depth of the former. However, as pointed out previously by Akan and Yen [3], within the range of overland flow depths considered, the effect of spatial variation of the depth on the rate of infiltration into the homogeneous soil is only secondary. Consequently, for a given run the infiltration graphs computed at various overland sections are nearly identical and they can be represented by an area-averaged infiltration graph as shown in Fig. 5.

As expected, after the initial saturation of the top layer soil, the infiltration rate decreases with time as shown in Fig. 5. Under a constant initial rate of infiltration equal to the supply, soil of low porosity becomes saturated sooner at the surface than for soil of high porosity because smaller amount of water is needed for the former to fill the pores entirely. The surface layer saturation is reached at t / t d = 0.117 (t = 7 min) for n = 0.20 and at t / t d = 0.483 (t = 29 min) for n = 0.60. Consequently, the decline in the infiltration rate with time occurs earlier in soil of lower porosity as shown in Fig. 5.


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t / t d

20

E E 10

) 0.25 ]

1

0.50 0.75

dl \ \ V "• ^ x / ^ 0 . 5 0 ^ ^ " ^ ^

^^~-0.20

i i I

1.00 1

1 1 1

1.25 1

20 40 60 t (min)

.00

0.75

0.50 i

= 0.25

80

Effect of soil porosity on infiltration Fig. 5 Effet de la porosité du sol sur l'infil-tration

o.i

0 2

0 3 -

-

_

1/,d= ^^ ^ ''tffï

/ 0.68 ^S^'' / / '

( S S^' // 1 ~

- / / / O /■

'If / 1 y ■ y

1/ - /

n 0.20

0.60

1 , , . , . , .

2000

- 6 0 0 0

0.2 0 6 0.8

Fig. 6

Effect of soil porosity on wetting front propagation

Effet de la porosité du sol sur la propagation du front liquide

However, propagation of the wetting front in a soil with low porosity is faster than that of high porosity as shown in Fig. 6, despite that the volume of water entering the low porosity soil is smaller. For low porosity little void space is available in the soil for the water to fill. Hence, even a small rate of surface infiltration could cause a high degree of saturation of the soil as in the case of n = 0.20. This causes a high relative


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1.00

0.75

0.50

0.25

Effect of soil saturated conductivity on infiltration

Fig. 7 Effet de la conductivity saturée du sol sur l'infiltration

2000

4000

6000

Effect of soil saturated conductivity on Fig. 8 wetting front propagation

Effet de la conductivité saturée du sol sur la propagation du front liquide

conductivity which consequently results in a fast movement of the wetting front. A deep wetted zone, in turn, reduces the hydraulic gradient available for the surface water to enter the soil. Hence, as shown in Fig. 5, the infiltration rate is continuously smaller for a low-porosity soil than for a high porosity soil. The wetting front propagation shown in

Fig. 6 is for x/L = 0.5, which is essentially the same as those for x/L = 0 and 1.


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f/t<j -O 0.25 0.50 0.75 . _ 1.00 1.25

15

1 co

E 1.0 ro O er

0.5

0 20 40 60 80 t (min)

Effect of soil saturated conductivity on Fig. 9 Effet de la conductivité saturée du sol overland flow discharge sur le debit de ruissellement

5. Effect of saturated soil conductivity The saturated hydraulic conductivity of a soil is one of the major factors expected to influence the infiltration and the overland flow rates. In order to illustrate the effect of the vertical saturated conductivity on the flow process, four runs having different values of Kz s/i , ranging from 0.00625 to 0.25 (identified as Runs 1, 5, 6 and 7 in Table 1) are analyzed and the results are plotted in Figs. 7 to 9. In addition, the effect of the horizontal saturated conductivity, Ksx, relative to the vertical saturated conductivity, Ksz, is studied from the results of Runs, 1, 10 and 11 listed in Table 1. The conditions of these runs are identical except the ratio Ksx/Kg which are 0.1, 1 and 10, respectively. The results indicate that for infiltration into sufficiently deep unsaturated soil and for the range of K s x /K s z studied, the effect of this parameter, K s x /K s z , on the overland flow and infiltration is insignificant and hence the results of Runs 10 and 11 are not shown here.

Theoretically, for a given soil the conductivity can be changed by changing the fluid viscosity (e.g., change in temperature) without changing the porosity. The effects of the vertical saturated conductivity on the surface and subsurface flows and infiltration are similar to those of porosity. As expected, a low soil conductivity implies an inhibition of water to infiltrate and percolate down the soil. Accordingly, for otherwise identical conditions, the area-averaged infiltration, f, is lower for small K s z than for large K s z as illustrated in Fig. 7. Furthermore, low soil conductivity represents high resistance to moisture flow in the soil. Therefore, in low conductivity soils the surface saturation occurs sooner under a constant initial rate of infiltration since a major portion of the infiltrated water remains near the surface and fills the pores. Accordingly, the decline in the infiltration rate occurs earlier in low-conductivity soil than in high-conductivity soil as shown in Fig. 7. In the case of K s z/i = 0.00625, the rate of infiltration is reduced sharply to a nearly constant value of f/i = 0.07 (f = 1.6 x 10"3 mm/s), whereas for higher Ksz/i the decrease of f with respect to time is relatively gradual.

Conversely, the high-conductivity soil with K sz/i = 0.25 allows a large amount of infiltration. With relatively little resistance to the flow, the infiltrated water can easily percolate through the soil causing a rapid propagation of the wetting front, allowing almost the entire available surface water to infiltrate. Consequently this soil does not


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Variation of overland peak discharge with Fig. 10 Variation du debit de ruissellement de saturated conductivity and porosity pointe en fonction de la porosité et de la

conductivité non saturée

0.005 0.01 0.02 0.05 0.1 0.2

Fig. 11 Variation of infiltration with saturated conductivity and porosity Variation de l'infiltration en fonction de la porosité et de la conductivité saturée

produce any overland flow. Furthermore, for this run at t/t<j = 1.1 the water on the overland surface is completely depleted. Without water supply available on the ground surface, the infiltration ceases abruptly as shown in Fig. 7. Yet, because of high conductivity, the moisture continues to percolate down the soil, causing the drying of the top soil layers as shown in the saturation profile for t/t<j = 1.17 (t = 70 min) in Fig. 8. This is clearly in constrast to the low conductivity case (e.g., the case of K s z/i = 0.00625) where for a long time only a thin top layer of soil is wetted by a small volume of infiltrated water as shown in Fig. 8.

Obviously, for a low-conductivity soil with small infiltration, a major portion of the surface water supply becomes surface runoff whereas for high conductivity the overland

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Variation du rapport debit de ruisselle-ment/infiltration en fonction de la poro-sité du sol

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Fig. 13 Volume of overland flow relative to infiltration for different soil porosities and saturated conductivities Volume de ruissellement par rapport a l'infiltration pour différentes valeur de la porosité du sol et de la conductivité saturée

runoff is relatively reduced. This effect of soil conductivity on overland flow is clearly illustrated in Fig. 9 for the discharge hydrographs computed at the downstream end of the overland flow plane (i.e., x/L = 1.0) and at x/L = 0.60. For the high conductivity case of Run 7 with Ksz/i = 0.25 no surface runoff is produced. The variation of the overland flow with time is similar to that discussed in Section 4 for the effect of soil porosity and hence the water surface profiles are not shown here.

The profound effects of the saturated conductivity of the soil on the surface and subsurface flows can further be demonstrated clearly in Figs. 10 and 11 using the results of Runs 1, 2, 4, 5, 6, 8 and 9 (Table 1). Figure 10 shows that the peak overland discharge decreases with increasing soil vertical saturated conductivity, and this decrease is more pronounced for larger porosity. Figure 11 shows the area-averaged infiltration rate at the time of termination of the surface water supply (t/t^ = 1.0), it increases with increasing saturated conductivity and this effect is also more pronounced for larger porosity.


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An interesting feature of overland flow on a porous medium is the relative amount of the surface water supply that produces surface runoff as compared to the infiltrated water. This information is shown graphically in Figs. 12 and 13 using the results of Runs 1 to 6, 8 and 9. Figure 12 shows the time variation of the ratio of the overland flow at x/L = 1.0, q x n = i to the time rate of infiltration over the entire overland surface, fL, for different values of soil porosity n for K s z/i = 0.0625. Similar plot of the time variation °f 9x/L = l/fL f° r constant n and different K sz/i can be obtained from Figs. 7 and 9. Figure 13 shows the variation of the ratio of the cumulative surface runoff volume at x/L = 1.0, Vs, to the cumulative infiltrated water volume Vf =ƒ fL dt, over the duration of the surface water supply, i.e., from t = 0 to t = t<j. For the conditions investigated log Vs/Vf varies linearly with K s z / i . A similar graph can be plotted for the same volume ratio for the entire period of surface supply and surface runoff including the recession part. The figures again show the significant effects of the soil porosity and vertical saturated conductivity on the surface and subsurface flows. As expected, for small n or K sz/i, the amount of infiltration is small and hence the values of q/fL or Vs/Vf are comparatively large. It should be noted that in Fig. 12 at early time q and Vs are zero but f and Vf are nonzero.

6. Effect of unsaturated soil hydraulic characteristics As mentioned in Section 3.1, among the different alternatives to describe the hydraulic characteristics of an unsaturated soil, a pair of relations between the degree of saturation, S, and soil moisture pressure, P, and between the relative conductivity, Kr, and soil pressure are adopted in this study because of their practicality. Three different types of S-P relationship (A, B and C) and also of Kr - P relationship (1, 2, 3) are tested as shown in Fig. 2. For a given soil the degree of saturation, S, is a measure of the volume of the pores being filled with water, corresponding to which through the combination of the interacting forces between the soil particles and the water and air in the pores, the hydraulic pressure, P, is determined. When the degree of saturation of the soil is low, relatively small portion of the space in the pores is filled with water and, in a simplified view, the surface tension action is active and the suction pressure is comparatively high. Moreover, with the relatively small water space in the pores available for the water movement, the hydraulic resistance of the water flow is high; in other words, the relative conductivity, Kr, is low. Conversely, when the degree of saturation is high, only a few pores are still not filled with water, the surface tension action is weak and the suction pressure is low, and with most of the pore space filled and available for the water movement, the flow resistance is low and the relative conductivity is high. The general S-P and Kr - P variation characteristics are shown in Fig. 2 as a typical example.

In reality, normally a change in the S-P relation is expected to be accompanied by a change in the Kr - P relation. However, theoretically and experimentally, it is possible to vary one of these relationships to a certain extent while keeping the other one unchanged. In the laboratory conditions, this can be achieved by a proper combination of different types of fluids at different temperatures. Therefore, for the sake of clarity, in the present study, the effects of each one of these relationships on conjunctive surface-subsurface flows are investigated separately.

6.1 Effect of saturation - pressure relation The effect of the degree of saturation - pressure relation on the conjunctive surface and subsurface flows are explored through the results of Runs 1, 12 and 13 listed in Table 1. The pressure is expressed in terms of suction head. In these three runs the controlled conditions are identical except the S-P relationships which are types A, B and C, respectively, shown in Fig. 2. For a given degree of saturation, Type A soil offers the smallest suction head, corresponding to, e.g., larger soil particle sizes than Types B or C which have the same porosity as Type A.


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Fig. 14 Effect of soil saturation - pressure head relation on propagation of wetting front for Type 2 soil

Effet de la relation saturation du sol/-pression sur la propagation du front liquide pour un sol du type 2.

Among the three S-P relationships investigated, Type C allows the highest saturation for a given suction pressure head, and hence causing the soil to reach full saturation near the surface at the earliest time as shown in Fig. 14. However, the surface saturation is followed by a decline in infiltration rate as shown in Fig. 15. This is due, e.g., for otherwise identical conditions, to the relatively small flow passages between the small soil particles for the Type C soil, and hence high water movement resistance of the soil. With the reduction in infiltated water volume, a smaller depth of soil is wetted at the later stages of the process as shown in Fig. 14. The same reasoning explains also the high infiltration rates and deep wetted portions of the Type A soil.

Figures 16 and 17 illustrate respectively the influence of the S-P relationship on the surface runoff discharge and flow depth. The trends in Figs. 16 and 17 are consistent with those in Figs. 14 and 15. For example, with the largest volume of infiltration in comparison to Types A and B, the overland flow discharge and depth are expected to be smallest for Type C soil.

6.2 Effect of relative conductivity - pressure relation The effect of relative conductivity - pressure head relation on the conjunctive surface-subsurface flow is investigated through Runs 1, 14 and 15 listed in Table 1 for soil Types 1, 2 and 3, respectively. These three runs are identical in every respect except for different Kr - P relations as shown in Fig. 2. For a given suction pressure Type 1 offers the lowest relative conductivity corresponding to, e.g., a soil with small soil particle sizes, and hence it tends to hold the infiltrated water near the surface; whereas Type 3 with high relative conductivity allows easy percolation of the soil water. This mechanism is revealed in Fig. 18 which shows that near the ground surface Type 1 soil consistently has higher degree of saturation than Types 2 and 3. Conversely, at the lower layers, Type 3 has higher degree of saturation than Types 1 and 2 because of easy percolation.

Journal of Hydraulic Research 21 (1983) no. 2

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t / t d

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0,75

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Effect of soil saturation - pressure head relation on overland flow discharge for Type 2 soil

Fig. 16 Effet de la relation saturation du sol/-pression sur le debit de ruissellement pour un sol de type 2

Accordingly, the soil surface of Type 1 becomes saturated soon, and an early decline of the infiltration r a t e occurs. However, since only a shallow soil depth is wetted in Type 1 through the process, the hydraulic gradient acting on the infiltrating water remains high, and the infiltration r a t e is grea ter than in soil Types 2 and 3 at la ter stages of the process.

In accordance with the principle of continuity, the overland flow discharge and depth increase with decreasing infiltration loss. Hence from Fig. 19, over most of the overland runoff period type 1 soil gives lower overland flow discharge and depth than Types 2 and 3 a t corresponding location and t ime. As far as the overland flow is concerned, the effect of Type 1 soil relat ive to types 2 and 3 is similar to Type A to Types B and C, in that order. Thus, the overland flow hydrographs for Types 1, 2 and 3 are very similar to those shown in Fig. 16, with the peak discharges q/iL equal to 0.46, 0.50 (shown in Fig. 16), and 0.59, respect ively. The overland flow depth profiles for soil types 1, 2, and 3 are also similar to those shown in Fig. 17 for soil Types A, B and C, respectively.


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Effect of soil relative conductivity -pressure head relationship on propagation of wetting front for Type B soil

Fig. 18 Effet de la relation conductivite relative du sol/pression sur la propagation du front liquide pour un sol du type B


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6.3 Combined ef fect of S-P and Kr - P relationships Since in natural soils usually both S-P and K r - P relat ions change with soils, it would be helpful to confirm that the conclusions of Sections 6.1 and 6.2 apply to the case of combined effects . This confirmation is obtained by using the results of Runs 1, 16 and 17 listed in Table 1. These three runs have different pairs of S-P and K r - P relationships, namely, Type 2 K r - P with Type B S-P, Type 1 K r - P with Type A S-P, and Type 3 K r - P with Type C S-P, respectively. For simplicity only the results of area-averaged infiltration and overland discharge at x/L = 1.0 are shown in Figs. 20 and 21, respectively.

These figures show the same general trend of the effects of S-P and K r - P relations.


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t / 1 d

.0 0.25 0.50 0.75 1.00 1.25

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Overland discharge for soils with differ- Fig. 21 Niveau de ruissellement pour des sols ent unsaturated hydraulic properties présentant des propriétés hydrauliques

non saturées différentes

7. Conclusions By using a hydraulic based conjunctive surface-subsurface flow simulation model and guided by dimensional analysis, the effects of soil properties on the overland surface runoff and infiltration have been systematically investigated. The results confirm the common belief that soil properties are major factors influencing the overland surface runoff and infiltration into the porous medium. Thus, for a specified surface water supply to a given drainage surface, the overland flow depends on the hydraulic conditions of the porous medium. Specifically, the following results have been observed. a) Soil porosity and saturated hydraulic conductivity are two major factors imposing similar effects on the overland runoff and infiltration of surface flow over an unsaturated soil. The effect of the variation of the horizontal saturated conductivity relative to the vertical saturated conductivity is insignificant provided the groundwater table is low and the soil is homogeneous. b) The effects of the unsaturated soil hydraulic property, expressed in terms of degree of saturation - pressure and relative conductivity - pressure relationships, on infiltration and overland flow are also significant, although they are not as predominant as compared to the effects of soil porosity and saturated conductivity. c) For a given surface water supply to a given porous drainage basin, the overland surface runoff increases with decreasing soil porosity or saturated conductivity. It also increases for soils with increasing suction pressure (e.g., with increasingly fine particles) for a given degree of saturation or relative conductivity. d) For a given surface water supply to a given porous surface, the infiltration decreases with decreasing soil porosity or saturated conductivity, and with increasing suction pressure for given relative conductivity or degree of saturation. e) The wetting front tends to form earlier and propogate faster with decreasing porosity, whereas it tends to form earlier but propogate more slowly with decreasing saturated conductivity of the soil.

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Journal of Hydraulic Research 21 (1983.) no. 2 171

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References Bibliographic

1. AHUJA, L.R., A numerical and similari ty analysis of flow into crusted soils, Water Resources Research, 9 (4): 987-993, August 1973.

2. AKAN, A.O., Unsteady shallow water flow on porous media, Ph.D. thesis, Dept. of Civil Eng., Univ. of Illinois a t Urbana-Champaign, Illinois, 1976.

3. AKAN, A.O. and B.C. YEN, Infiltration into initially dry porous media, Proc. of 18th IAHR Congress, 5: 127-134, September 1979.

4. AKAN, A.O. and B.C.YEN, Mathemat ical model of shallow water flow over porous media, J. Hyd. Div., ASCE, 107 (HY4): 479-494, 1981.

5. BABU, D.K., Infiltration analysis and per turbat ion methods, 1. Absorption with exponential diffusivity, Water Resources Research, 12 (1): 89-93, February 1976.

6. BRUTSKERN, R.L. and H.J. MOREL-SEYTOUX, Analytical t r e a tmen t of two-phase infiltration, J. Hyd. Div., ASCE, 96 (HY12): 2535-2548, 1970.

7. CHILDS, E.C., The u l t imate moisture profile during infiltration in a uniform soil, Soil Science, 97: 173-178, 1964.

8. FREEZE, R.A., The mechanism of natural groundwater recharge and discharge, 1, one-dimensional, ver t ica l , unsteady, unsaturated flow above a recharging or discharging groundwater flow system, Water Resources Research, 5 (1): 153-171, February 1969.

9. JEPPSON, R.W., Axisymmetric infiltration in soils — numerical techniques of solution, J. of Hydrology, 23: 111-130, 1974.

10. NOBLANC, A. and H.J. MOREL-SEYTOUX, Per turbat ion analysis of two-phase infiltration, J . Hyd. Div., ASCE, 98 (HY9): 1527-1541, 1972.

11. PARLANCE, J. , Theory of water movement in soils: 2, one-dimensional infiltration, Soil Science, 111: 170-174, 1971.

12. PARLANCE, J. , Theory of water movement in soils: 6, effect of water depth over soil, Soil Sc ience , 113: 308-312, 1972.

13. PHILIP, J .R. , The theory of infil tration: 6, effect of water depth over soil, Soil Science,85: 278-286, 1958.

14. PHILIP, J .R. , Theory of infi l trat ion, in Advances in Hydroscience, 5: 215-305, 1969. 15. REEDER, W.J., D.L. FREYBERG, J .B. FRANZINI and I. REMSON, Infiltration under rapidly

varying surface water depth, Water Resources Research, 16 (1): 97-104, February 1980. 16. SMITH, R.E. and D.A. WOOLHISER, Overland flow on an infi l trat ing surface, Water Resources

Research, 7 (3): 899-913, June 1971. 17. TALSMA, T., Soil water interchange process, Studies of the Australian Arid zone, Part 3: Water

in Rangeland, Ed. by K.M.W. Howe, CSIRO: 45-53, Melbourne, Australia, 1978. 18. WHISLER, F.D. and A. KLUTE, Analysis of infil tration into strat if ied soil columns, Proc. of

Symp. on the Water in the Unsaturated Zone, Wageningen, The Netherlands, IASH Publication 82: 451-470, June 1966.

19. WHISLER, F.D. and K.K. WATSON, One-dimensional gravi ty drainage of uniform columns of porous mater ia l s , J. of Hydrology, 6: 277-296, 1968.

20. WHISLER, F.D., A.A. CURTIS, A. NIKNAM and M.J.M. RÖMKENS, Modeling infiltration as affected by soil crust ing, Surface and Subsurface Hydrology, Proc. of the Fort Collins Third International Symp. on Theoret ical and Applied Hydrology, Colorado, S ta te University, July 1977, ed. by H.J. Morel-Seytoux, J .D. Salas, T.G. Sanders, and R.E. Smith, 400-409, Water Resources Publications, Li t t le ton, Colorado, 1979.

21 . YOUNGS, E.G., Moisture profiles during vert ical infil tration, Soil Science, 84: 283-290, 1957.


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Notations F function f infiltration rate f,j Weisbach resistance coefficient g gravitational acceleration H piezometric head i lateral inflow rate or surface water supply rate Kr relative conductivity of soil Ks saturated hydraulic conductivity of soil k surface roughness L basin length N direction normal n soil porosity P pressure head q overland flow discharge per unit width S degree of saturation of soil Sf friction slope S0 overland surface slope t time t(j duration of surface water supply Vf cumulative volume of infiltrated water Vs cumulat ive volume of surface runoff v surface flow velocity x horizontal direction y surface flow depth z vertical direction a unsaturated soil hydraulic parameter (Eq. 7) v kinematic viscosity of liquid p density of liquid o surface tension

Journal of Hydraulic Research 21 (1983) no. 2

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effects of soil properties on overland flow and infiltration

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