Infiltration--Part 1

ENV 2110 Hydrology home

  1. General Considerations
    1. infiltration is one of the two major compartments that precipitation can fill (the other is runoff)
    2. this is very important because
      1. infiltration rate, f (typically in/hr), is affected by many factors
  2. Infiltration vs Runoff
  3. Effects of soil

    1. subsurface conditions
        1. surface conditions

    Effects of vegetation

            1. factors influencing infiltration are illustrated in Fig 3.11 on p 64
  4. Soil Properties and Soil Moisture
    1. if we assume that the soil is homogeneous and that rainfall is constant and uniform, we can make certain general statements about the infiltration process

    qv = Vw/Vt

      • note that qv, like h , ranges from 0 to 1; both are often expressed as percent (in which case you multiply by 100)
      • qv can be seen as the product of the porosity and the degree of saturation (S)
        • the degree of saturation also varies between 0 and 1

    qv = S*h

      • the degree of saturation is the proportion of void spaces that are filled with water (Vw/(Vw+Va)
      • note that when the soil is fully saturated, S = 1, therefore: qs = h
      • if we multiply the porosity times the volume of soil, we get the maximum volume of water that will fit into that soil
        • this will be Vw under saturated conditions
      • qv usually ranges between some initial unsaturated value, q0, to the value for soil saturated with water, qs
        • the difference between the initial qvalue and the final value is called Dq or IMD
        • the difference between qs and the present qof the soil gives the amount of additional water that can be stored in the soil
      • the easiest way to measure water content of soil is gravimetrically
      • take a fresh weight on a sample then dry it and get the dry weight
        • the difference represents the mass of the water which had been present the fresh sample
        • I define the gravimetric water content as:

    qg = mw/mT (Note: Ward and Elliot define qg = mw/mS but no one else I know does)

      • this is also called the percent moisture
      • soil density
        • the behavior of a portion of soil sometimes depends on the density
        • density is symbolized rand is defined in general as mass per volume; for soil a few different densities are defined:
          • the bulk density is the overall fresh mass of a chunk of soil (spaces, water and all), divided by the total volume of that chunk:

    rb = mt/Vt

      • the dry bulk density excludes the mass of any moisture from the bulk density:

    rdry = ms/Vt

      • the particle density is the density of the actual substance from which the particles were formed (eg, it is the particle density of silica sand is the density of the silica)

    rp = ms/Vs

    = (rdry*Vt)/[Vt*(1-h )]

    rdry = rp (1-h )

      • NOTE: densities are often given in terms of specific gravity (sg or Gs); for a substance q, density is related to the density of water by:

    rq = sg*rw

      • the density of water is 1000 kg/m3 or 62.4 lb/ft3
      • for soil, dry bulk density ranges from about 95 to 135 lb/ft3, particle density is about 165 lb/ft3
      • a few other relationships:

    qg = mw/mT = (Vw*rw)/(Vt*rb)

    = (

    or qV = (rb/rW)qg


    rb = mt/Vt = (mw+ms)/Vt =

    = ---------------- =
    qv*rw + rdry


    rb = (rb/rW)qg*rw + rdry


    rdry = rb(1-qg)

                1. infiltration of water is driven by two forces: gravity and capillary action
      • when soil is unsaturated, there is a driving force (called capillary suction) which pulls water into the soil
        • the number for this is y or S, units are ft, in, cm etc (this value is -1 times the capillary head, which is negative)
          • the term head is used for the potential energy represented by water at some elevation
          • water at elevation will tend to move downward until the energy is dissipated
          • likewise, water under capillary suction or tension will move upward until energy is dissipated
        • water rises under capillary action because the surface tension acts to reduce surface area; in soil pores this tension has an upward vertical component which acts opposite the force of gravity
          • water will rise until the force of gravity is equal to the force due to surface tension
          • note that the term for surface tension, t , is in units of N/m; this is the force required to add surface area by stretching in one direction (the force is a function of how long the side is)
            • a meniscus hangs down off the vertical by angle a , the vertical component of the surface tension is given by cos a

    gravitational force = force due to surface tension

    mass*acceleration = surface tension * circumference * angle

    p r2hrwg = 2p rt cos a (equation 3.12)

    solving for h:

        1   2t  cos a
    h = - * --------

    in other words: the smaller r is, the bigger h can be

      • therefore, small pores fill first and drain last (this leads to the difference between qvs h curves for wetting and drying)
      • nonetheless, the less water soil contains, the thirstier it is (and vice versa)
      • if we apply water to soil which is at some water content q0, less than saturated, to start with water will soak in at some high rate since the dry soil has a high suction
        • the rate will decrease as the water takes up more water and the capillary suction decreases
          • if we continue to add water, water will continue to be taken up, theoretically until the soil is saturated
          • in practice, the soil will become about 80 to 90% saturated
        • if we stop applying water, the soil will drain down to some point where the capillary suction is balanced by gravity
          • the volume of water still held by soil at this point is called the field capacity of the soil
          • these are seen at the inflection points on Fig 3.7 on p 60
            • in Fig 3.7, you can see that for the first few days after a rain, water content decreases rapidly up to the inflection point; after that, the water content decreases more slowly
      • these relationships are important in determining the amount of water available to plants (qpaw)
        • the wilting point for a soil is the point where the suction force exerted by plant roots equals the suction force required to take more water out of the soil (this is approx -10 to -30 bars)
        • the following a rain, the soil will quickly drain to field capacity; however, not all of that water is available for plants
          • only that water which can be drawn out before the wilting point is reached is actually usable by plants
          • hence we write:

    qpaw = qfc - qwp

      • Figure 3.8 on p 61 gives qfc, qwp, & qpaw for a range of soil types; Figure 3.9 on p 62 summarizes the relationship between water content & plant growth and gives some terms
        • hydroscopic water: the water tightly bound (hydrogen-bonds etc) to soil grains (plants donít have the suction to get this water off, but oven drying will get it)
        • capillary water: water available to plants that remains after the soil has drained; this water is held by capillary forces
        • percolation or gravity water: this is water in excess of the field capacity; it drains under the influence of gravity (itís not bound); too much of this will actually drown plant roots
        • donít agonize over the stuff between the bottom of p 57 and the middle of p 62
  5. Soil Water Balance
  6. this is a special case of the general hydrological equation that we derived in the first week of class:
  7. D SM = P + IR - Q - G - ET

      • typical values are shown in Table 3.1 on p 71
      • you can see from Figure 3.18 that the seasonal changes in water content of soil determines what types of soil water we have at different times of year

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