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- Title: Lecture 12
- Type: Notes
- School: Penn State
- Course: C E 361
- Term: Spring
Water Resources EngineeringE i i Prepared by T. Wagener & P. Reed Penn State University Lecture 12 1 Hydrologic Processes 2 Content 1. 1 Infiltration 1. Unsaturated Flow 2. 2 Infiltration Methods (7 4 2 & 7 4 3) (7.4.2 7.4.3) 3 Soil Moisture Profile Figure 7.4.3 (p. 237) 4 Moisture zones during infiltration (from Chow et al. (1988)). What value would i have if the soil had been saturated, but has now completely drained through gravity forces? Soil Moisture Profile Figure 7.4.4 (p. 237) 5 Moisture profile as a function of time for water added to the soil surface. Infiltration Terminology The infiltration rate f is the rate at which water enters the soil surface [in/hr or cm/hr] The potential infiltration rate is the rate of infiltration h i fil i when water i ponded on the soil is d d h il surface (no ponding means the infiltration rate is less than potential) The cumulative infiltration F is the accumulated depth of infiltrated water F (t ) = f ( )d 0 6 t and dF (t ) f (t ) = dt Ponding Time tp 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. 7 Changing Infiltration Rate with Time f eventually becomes constant. Its value is close to the saturated hydraulic conductivity. F t Figure 7.4.5 (p. 238) 8 t+t defined in Chapter 8 as that rainfall that is neither retained on the land surface nor infiltrated into the soil. 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 + t is Ft + t or F(t + t) is computed using equation 7.4.15. The increase in cumulative infiltration from time t to t + t is Ft + t Ft or F(t + t) F(t) as shown in the figure. Rainfall excess is Green-Ampt Overview Green and Ampt (1911) modeled infiltration using the conceptual model shown Fig. 7.4.6 Key Details 1. Sharp idealized wetting front that divides soil moisture content i below from saturated soil with moisture content above the front 2. The f t h infiltrated to depth 2 Th front has i filt t d t a d th L in time t since the initial time period 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)). p 3. The land surface has water ponded with a small depth ho 9 Green Ampt Green-Ampt Method Derivation Consider the vertical soil column The control volume surrounds the wet soil G Given a soil with initial moisture content i, moisture content can increase to a maximum of (i.e., the soil porosity when all of the voids are filled with water) We can define the cumulative depth of water infiltrated p using the following relationship: F (t ) = L( - i ) = L The Darcy flux q through the soil column is equal to the infiltration rate f (i.e., this means q = -f since q is positive upward and f is positive downward). The change in soil moisture content effective saturation se and effective porosity e: = (1 - se ) e 10 Green Ampt Green-Ampt Method Derivation Formally, we can write the Darcy flux in terms of infiltration as shown Where f = infiltration rate [cm/hr] K = hydraulic conductivity [cm/hr] h1 = hydraulic head at the surface (h0 shown on the prior page) [cm] h2 = hydraulic head in the d y so be o the wetting front [c ] yd au c ead e dry soil below e e g o [cm] z1-z2 = L is the elevation change in the soil column h1 - h2 h q = -K yielding f = K z z1 - z2 We know for unsaturated soil we can write h2 = ( - - L ) [note suction head is negative because a vacuum exists in unsaturated soils] 11 Green Ampt Green-Ampt Method Derivation We can also assume that h0 is negligibly small (since ponded water will runoff) Also we can write L=F ( why ?) We can re-write our expression for infiltration using the above p g relationships and assumptions as follows: + F f =K F We can express the above equation as a differential equation since f = dF dt dF + F =K dt F 12 Green-Ampt Method Derivation The Green-Ampt equation for cumulative infiltration is derived by solving the differential equation: F + F dF = Kdt + F + F - + F dF = Kdt F (t ) 0 1 - + F dF = Kdt 0 t Yielding the Green-Ampt equation for cumulative infiltration [cm]: F (t ) F (t ) - l 1 + ln = Kt We can also obtain the infiltration rate f [cm/hr]: 13 f =K + 1 F (t ) Green Ampt Green-Ampt Method Parameters from Table Table 7.4.1 (p. 241) Green-Ampt Infiltration Parameters for Various Soil Classes 14 Green-Ampt Example Use the Green-Ampt method to evaluate the infiltration rate and cumulative infiltration depth for a silty clay soil at 0.2 hr. The initial effective saturation is 20 percent and you can assume ponding (Hint try initial ponding. guess F = 0.43) 15 Green-Ampt Solution Table 7.4.1 provides key parameters for a silty clay soil e = 0.423, = 29.22cm, K = 0.05cm / hr We can compute the change in soil moisture: = (1 - se ) e = (1 - 0.20)0.423 = 0.338 = 29 22 0.338 = 9.89cm 29.22 0 338 9 89 We can develop an iteration version of the cumulative infiltration function: You can see that our guess of F = 0.43 yields F = 0.43 so we have the answer. Normally, this requires an iterative solution solution. We can now compute f: F F F = Kt + ln 1 + = 0.05t + 9.89 ln 1 + 9.89 9.89 f =K + 1 = 0 05(1 + 0.05(1 ) = 1.2cm / hr 12 F F (t ) 16 Index -Index Method This is the simplest approach to account for infiltration since it assumes a constant rate of abstraction (in/h or cm/h). Figure 7.4.9 (p. 244) 17 Horton Method Figure 7.4.9 (p. 244) 18 SCS Method Later in this class we will spend some time on the SCS method, which is widely used within the U S to calculate infiltration U.S. infiltration. 19 Measuring Infiltration Rates Often done using a Double Ring Infiltrometer: http://www.upgmbh.com/produkte/pdf/10740.pdf 20 http://www.rickly.com/MI/Infiltrometer.htm 21
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