Infiltration Part 1

General Considerations

infiltration is one of the two major compartments that precipitation can fill (the other is runoff)
this is very important because

it replenishes soil moisture, used by plants
it replenishes groundwater which is the reservoir that feeds the base flow of rivers
water which infiltrates does not runoff:

runoff carries away topsoil or silt thereby damaging cropland or waterways
runoff can cause flooding

the rate of infiltration can also modulate the rate of overland flow

infiltration rate, f (typically in/hr), is affected by many factors

vegetation
soil texture
soil structure
temperature
rainfall duration & intensity
moisture status of the soil

Infiltration vs Runoff

Effects of soil

subsurface conditions

predictions of subsurface water movement are often based on the assumption that we have a homogeneous, isotropic medium (which we don’t)

homogeneous means that the soil is the same from place to place
isotropic means that the soil (especially the hydraulic conductivity of the soil) is the same in every direction, ie vertical and horizontal

soil characteristics greatly affect the degree of runoff versus infiltration

clay content reduces infiltration, especially after the ground is saturated with water (which swells the clay)

sandy soil or friable loams, both of which have low clay content, have higher rates of infiltration

more densely compacted soils have lower rates of infiltration

note: rainfall can actually compact soil
rainfalling directly on soil also tends to plug the opening in the ground with fines from near the surface (like espresso grind coffee in a melitta filter)

waterlogged soil has a lower rate of infiltration than dry soil (Fig 3.17, p 69)

saturated soil takes up less water (so it is like the blotter over the sponge in Fig 3.15 on p 68)
prolonged or heavy rains reduce infiltration

temperature can have an effect

colder water has a higher viscosity, hence it infiltrates more slowly
frozen soil may have no infiltration--it may actually be coated with ice if it was saturated when it froze (concrete frost); alternatively, dry soils retain pores on freezing (lattice frost)

thus the timing and dynamics of a storm event can have a great influence on the proportion of runoff

generally speaking, longer or repeated rains result in more runoff

surface conditions

human development of an area usually has a dramatic effect on increasing runoff

paving and roofs have essentially no infiltration
one of the engineering calculations that must be done when planning a development is the excess flood flow--this must be taken into account
diverted stormwater may have substantially poorer quality than native runoff (metals and oils etc from the streets and yards)

commercial and industrial establishments that discharge stormwater at a point are now subject to the restrictions of categorical wastewater discharge permit

Effects of vegetation

vegetation can greatly increase the rate of infiltration

intercepts precipitation and buffers the release of water to the soil surface
shield the soil surface from some of the effects of compaction by rainfall

clear cutting a forest can increase runoff and erosion disastrously, as can overgrazing and improper cropping

proper management reduces the effects
in fact, well conducted forestry (including some clear cutting) can increase the amount of snowmelt which is available for human use without dangerously increasing erosion
plowing along hillside contours tends to slowdown runoff and thus decrease erosion and increase infiltration

factors influencing infiltration are illustrated in Fig 3.11 on p 64

Soil Properties and Soil Moisture

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

some major factors affecting infiltration rate in this case are soil/water relationships

soil type or texture

the principle divisions are clay, silt and sand

mixtures of these are called loams
one classic loam classification scheme is the USDA soil triangle (fig 3.2 on p 52)

the soil type and texture tells us the size and number of voids or pores, interconnected spaces in the soil

numerical values associated with this include

the hydraulic conductivity, K (in/hr etc)

porosity, h (dimensionless, but may be given as ft/ft)

equation 3.3 defines h = 1 - V_s/V_t

note that the total volume of soil consists of the volume occupied by the soil grains, the volume filled with water and the volume filled with air

for a given porosity, the more water a soil contains, the less air

soil moisture

can be given on a mass per mass, mass per volume (unusual) or volume per volume basis

infiltration problems are usually looking at the volume of water per volume of soil:

q_v = V_w/V_t

note that q_v, like h , ranges from 0 to 1; both are often expressed as percent (in which case you multiply by 100)

q_v 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

q_v = S*h

the degree of saturation is the proportion of void spaces that are filled with water (V_w/(V_w+V_a)

note that when the soil is fully saturated, S = 1, therefore: q_s = 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 V_w under saturated conditions

q_v usually ranges between some initial unsaturated value, q₀, to the value for soil saturated with water, q_s

the difference between the initial qvalue and the final value is called Dq or IMD

the difference between q_s 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:

q_g = m_w/m_T (Note: Ward and Elliot define q_g = m_w/m_S 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:

r_b = m_t/V_t

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

r_dry = m_s/V_t

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)

r_p = m_s/V_s

= (r_dry*V_t)/[V_t*(1-h )]

r_dry = r_p (1-h )

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

r_q = sg*r_w

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:

q_g = m_w/m_T = (V_w*r_w)/(V_t*r_b)

= (r_W/r_b)q_v

or q_V = (r_b/r_W)q_g

and

r_b = m_t/V_t = (m_w+m_s)/V_t =

q_v*V_t*r_w+r_dry*V_t
= ---------------- = q_v*r_w + r_dry
V_t

so:

r_b = (r_b/r_W)q_g*r_w + r_dry

therefore:

r_dry = r_b(1-q_g)

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 r²hr_wg = 2p rt cos a (equation 3.12)

solving for h:

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

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 (q_paw)

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:

q_paw = q_fc - q_wp

Figure 3.8 on p 61 gives q_fc, q_wp, & q_paw 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 don’t 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 (it’s not bound); too much of this will actually drown plant roots

don’t agonize over the stuff between the bottom of p 57 and the middle of p 62

Soil Water Balance

this is a special case of the general hydrological equation that we derived in the first week of class:

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

Infiltration--Part 1