Figure 7.4.2 (p. 235) (a) Cross-section through an unsaturated porous medium; (b) Control volume for...
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Transcript of Figure 7.4.2 (p. 235) (a) Cross-section through an unsaturated porous medium; (b) Control volume for...
![Page 1: Figure 7.4.2 (p. 235) (a) Cross-section through an unsaturated porous medium; (b) Control volume for development of the continuity equation in an unsaturated.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649edd5503460f94bee1a1/html5/thumbnails/1.jpg)
![Page 2: Figure 7.4.2 (p. 235) (a) Cross-section through an unsaturated porous medium; (b) Control volume for development of the continuity equation in an unsaturated.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649edd5503460f94bee1a1/html5/thumbnails/2.jpg)
Figure 7.4.2 (p. 235)(a) Cross-section through an unsaturated porous medium; (b) Control volume for development of the continuity equation in an unsaturated porous medium (from Chow et al. (1988)).
![Page 3: Figure 7.4.2 (p. 235) (a) Cross-section through an unsaturated porous medium; (b) Control volume for development of the continuity equation in an unsaturated.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649edd5503460f94bee1a1/html5/thumbnails/3.jpg)
Porous media definitions
[Note: Many are analogous to snow properties.]
Soil matrix properties:
particle density
bulk density
porosity
ρm =mass of mineral grains
volume of mineral grains=
M m
Vm
; typically ρm ≈ 2650 kg m-3
ρb =mass of mineral grains
volume of soil=
M m
Vs
φ =n = θ s =volume of voids
volume of soil=
Vvoid
Vs
→ φ = 1 −ρb
ρm
Water content variables: (only relevant for unsaturated zone)
volumetric water content
relative saturation
θ =volume of water
volume of soil=
Vw
Vs
; 0 ≤ θ ≤ θ s
s =θθs
; 0 ≤s≤1
![Page 4: Figure 7.4.2 (p. 235) (a) Cross-section through an unsaturated porous medium; (b) Control volume for development of the continuity equation in an unsaturated.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649edd5503460f94bee1a1/html5/thumbnails/4.jpg)
[Note: Soil type/texture is used to identify soil hydraulic properties via tabulated relationships.]
![Page 5: Figure 7.4.2 (p. 235) (a) Cross-section through an unsaturated porous medium; (b) Control volume for development of the continuity equation in an unsaturated.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649edd5503460f94bee1a1/html5/thumbnails/5.jpg)
porosity
Sat. hydraulic
conductivity (Ks)
Sat. matric head (|ψs|)
“Brooks-Corey” or “Clapp-Hornberger” Soil Hydraulic Parameters (based on soil type)
![Page 6: Figure 7.4.2 (p. 235) (a) Cross-section through an unsaturated porous medium; (b) Control volume for development of the continuity equation in an unsaturated.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649edd5503460f94bee1a1/html5/thumbnails/6.jpg)
Table 7.4.1 (p. 241)Green-Ampt Infiltration Parameters for Various Soil Classes
![Page 7: Figure 7.4.2 (p. 235) (a) Cross-section through an unsaturated porous medium; (b) Control volume for development of the continuity equation in an unsaturated.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649edd5503460f94bee1a1/html5/thumbnails/7.jpg)
Figure 7.4.3 (p. 237)Moisture zones during infiltration (from Chow et al. (1988)).
![Page 8: Figure 7.4.2 (p. 235) (a) Cross-section through an unsaturated porous medium; (b) Control volume for development of the continuity equation in an unsaturated.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649edd5503460f94bee1a1/html5/thumbnails/8.jpg)
Figure 7.4.4 (p. 237)Moisture profile as a function of time for water added to the soil surface.
![Page 9: Figure 7.4.2 (p. 235) (a) Cross-section through an unsaturated porous medium; (b) Control volume for development of the continuity equation in an unsaturated.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649edd5503460f94bee1a1/html5/thumbnails/9.jpg)
Figure 7.4.5 (p. 238)Rainfall infiltration rate and cumulative infiltration. The rainfall hyetograph illustrates the rainfall pattern as a function of time. The cumulative infiltration at time t is Ft or F(t) and at time t + Δt is Ft + Δt or F(t + Δt) is computed using equation 7.4.15. The increase in cumulative infiltration from time t to t + Δt is Ft + Δt – Ft or F(t + Δt) – F(t) as shown
in the figure. Rainfall excess is defined in Chapter 8 as that rainfall that is neither retained on the land surface nor infiltrated into the soil.
![Page 10: Figure 7.4.2 (p. 235) (a) Cross-section through an unsaturated porous medium; (b) Control volume for development of the continuity equation in an unsaturated.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649edd5503460f94bee1a1/html5/thumbnails/10.jpg)
Figure 7.4.6 (p. 238)Variables in the Green-Ampt infiltration model. The vertical axis is the distance from the soil surface, the horizontal axis is the moisture content of the soil (from Chow et al. (1988)).
![Page 11: Figure 7.4.2 (p. 235) (a) Cross-section through an unsaturated porous medium; (b) Control volume for development of the continuity equation in an unsaturated.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649edd5503460f94bee1a1/html5/thumbnails/11.jpg)
Figure 7.4.8 (p. 243)Ponding time. This figure illustrates the concept of ponding time for a constant intensity rainfall. Ponding time is the elapsed time between the time rainfall begins and the time water begins to pond on the soil surface.
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f (t) =P , t0 < t≤tp
fc(t−tc) , tp ≤t≤tr
⎧⎨⎪
⎩⎪
Modeling Actual Infiltration using the time-compression approximation (TCA)
Actual infiltration model:
![Page 13: Figure 7.4.2 (p. 235) (a) Cross-section through an unsaturated porous medium; (b) Control volume for development of the continuity equation in an unsaturated.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649edd5503460f94bee1a1/html5/thumbnails/13.jpg)
TCA condition #1:
![Page 14: Figure 7.4.2 (p. 235) (a) Cross-section through an unsaturated porous medium; (b) Control volume for development of the continuity equation in an unsaturated.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649edd5503460f94bee1a1/html5/thumbnails/14.jpg)
TCA condition #2:
fc (t)dt =P ⋅tp0
tp−tc
∫
![Page 15: Figure 7.4.2 (p. 235) (a) Cross-section through an unsaturated porous medium; (b) Control volume for development of the continuity equation in an unsaturated.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649edd5503460f94bee1a1/html5/thumbnails/15.jpg)
Depending on the particular infiltration capacity model chosen (Philip or Green-Ampt), the two TCA conditions (equations) can be solved explicitly for the two unknowns (time to ponding and compression time) to get an explicit expression for the actual infiltration: f(t).
See supplementary TCA notes for more details…
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F = f(t)0
tr
∫ dt= P0
tp
∫ dt + fc(t−tc) dttp
tr
∫
Q = P− f(t)0
tr
∫ dt= P− fc(t−tc) dttp
tr
∫ =Ptr −F
From actual infiltration model, can compute cumulative infiltration and/or infiltration excess runoff: