Hydrology Notes

INFILTRATION

  • Infiltration is the process of water penetrating into the soil.

Factors Affecting Infiltration Rate

  1. Condition of the soil surface

  2. Vegetative cover

  3. Soil properties

    • Porosity

    • Hydraulic conductivity

    • Moisture content

Unsaturated and Saturated Flow

  • Unsaturated flow: Flow through a porous medium when some voids are occupied by air.

  • Saturated flow: Occurs when voids are filled with water.

Water Table

  • Interface between saturated and unsaturated flow.

  • Atmospheric pressure prevails at the water table.

  • Saturated flow occurs below the water table, and unsaturated flow occurs above it.

Control Volume Analysis

  • Consider a control volume with sides of lengthsdx, dy, and dz, having a volume of dxdydz.

  • The volume of water contained is \theta dxdydz. Where \theta is not defined in the document.

Darcy Flux

  • Darcy flux - Flowthrough the control volume

  • Defined as q = \frac{Q}{A}where Q is the volumetric flow rate and A is the soil area.

Darcy's Law

  • Relates Darcy flux (q) to the rate of head loss per unit length of medium.

  • For vertical flow, the head loss per unit length is the change in total head (\delta h) over a distance (\delta z), i.e., \frac{\delta h}{\delta z}.

  • Expressed as q = -K \frac{\delta h}{\delta z}, where K is hydraulic conductivity.

Unsaturated Flow Characteristics

  • Void spaces are partially filled with water.

  • Water is attracted to particle surfaces through electrostatic forces.

  • Suction head (\psi) - is the energy due to soil suction forces. (use average)

  • Total head (h) - is the sum of suction and gravity heads: h = \psi + z.

  • Darcy's law for unsaturated flow:

    q = -K \frac{\partial(\psi + z)}{\partial z}.

Green Ampt Method

  • Describes soil moisture distribution during downward movement.

Moisture Zones

Infiltration Rate

  • f: Rate at which water enters the soil surface (in/hr or cm/hr).

  • Potential infiltration rate: Rate when water is ponded; actual rate is less if no ponding.

Cumulative Infiltration

  • F: Accumulated depth of water infiltrated.

  • Expressed as F(t) = \int_{0}^{t} f(x) dx.

  • Infiltration rate: f\left(t\right)=\frac{dF\left(t\right)}{dt} .

Rainfall Hyetograph

  • Illustrates rainfall pattern as a function of time.

  • Increase in cumulative infiltration from time t to t + \Delta t is F(t + \Delta t) - F(t).

  • Rainfall excess: Rainfall that is neither retained nor infiltrated.

Green and Ampt Model

  • Simplified infiltration model.

  • Wetting front: Sharp boundary dividing soil with moisture content \theta_i below and saturated soil with porosity n above.

  • Wetting front has penetrated to depth L in time t.

  • Water is ponded to a small depth h_0 on the surface.

Vertical Column of Soil

  • Consider a unit horizontal cross-sectional area.

  • Moisture content increases from \theta_i to n as the wetting front passes.

  • Increase in water stored: L(n - \thetai) = L\Delta\theta = F, where \Delta\theta = n - \thetai.

  • Cumulative infiltration: F(t) = L(n - \theta_i) = L\Delta\theta (Equation 7.4.17).

Darcy's Law Application

  • Expressed as q = -K \frac{\Delta h}{\Delta z} (Equation 7.4.18).

  • q = -f because q is positive upward and f is positive downward.

Boundary Conditions

  • Point 1 at the surface: h1 = h0.

  • Point 2 at the wetting front: h_2 = -\psi - L.

  • Darcy's law: f = K \frac{h_0 - (-\psi - L)}{L} (Equation 7.4.20a).

  • Assuming h_0 is negligible: f = K \frac{\psi + L}{L} (Equation 7.4.20b).

Wetting Front Depth

  • From Equation 7.4.17: L = \frac{F}{\Delta\theta}.

  • Substituting into Equation 7.4.20: f = K \frac{\psi \Delta\theta + F}{F} (Equation 7.4.21).

Differential Equation

  • Since f = \frac{dF}{dt}, Equation 7.4.21 becomes: \frac{dF}{dt} = K \frac{\psi \Delta\theta + F}{F}.

Solving for F

  • \frac{F}{\psi \Delta\theta + F} dF = K dt.

  • \int \frac{F + \psi \Delta\theta - \psi \Delta\theta}{\psi \Delta\theta + F} dF = \int K dt.

  • F(t) - \psi \Delta\theta { \ln[F(t) + \psi \Delta\theta] - \ln(\psi \Delta\theta) } = Kt (Equation 7.4.22a).

  • F(t) - \psi \Delta\theta \ln \left( 1 + \frac{F(t)}{\psi \Delta\theta} \right) = Kt (Equation 7.4.22b).

Green-Ampt Equation

  • Equation 7.4.22: Cumulative infiltration.

  • Infiltration rate: f = K \left[ \frac{\psi \Delta\theta}{F(t)} + 1 \right] (Equation 7.4.23).

  • If h0 is not negligible, substitute \psi + h0 for \psi in Equations 7.4.22 and 7.4.23.

Successive Substitution

  • Rearranging Equation 7.4.22: F(t) = Kt + \psi \Delta\theta \ln \left( 1 + \frac{F(t)}{\psi \Delta\theta} \right) (Equation 7.4.24).

Green-Ampt Parameters

  • n: Porosity

  • \theta_e: Effective porosity

  • \psi: Wetting front soil suction head (cm)

  • K: Hydraulic conductivity (cm/h)

  • \Delta\theta = (1 - S_e)n.

  • S_e: Effective saturation

  • \Delta\theta in terms of initial saturation Si: \Delta\theta = n - \thetai = (1 - S_i)n (Equation 7.4.26).

Sample Problem: Green-Ampt Method

  • Silty clay soil.

  • Time increments: 0.1 hr up to 6 hr.

  • Initial effective saturation: 20%.

  • Continuous ponding.

Ponding Time

  • Elapsed time between rainfall start and ponding.

  • Using Green-Ampt equation with constant rainfall intensity i.

  • Substituting F = it_p into Equation 7.4.23: i = K \left( \frac{\psi \Delta\theta}{F} + 1 \right).

  • Solving for tp: tp = \frac{K \psi \Delta\theta}{i(i - K)}.

Other Infiltration Methods

Ф-index Method

  • Constant abstraction rate.

Horton's Equation

  • Empirical relation: f = fc + (f0 - f_c)e^{-kt} (Equation 7.4.28).

  • Cumulative infiltration: Ft = fc t + \frac{(f0 - fc)}{k} (1 - e^{-kt}) (Equation 7.4.29).

Richard's Equation

  • Solved by Philip (1957, 1969).

  • Cumulative infiltration: F = St^{1/2} + Kt (Equation 7.4.30).

  • Infiltration rate: f(t) = \frac{1}{2}St^{-1/2} (Equation 7.4.31).

  • S: Sorptivity.

  • As t \to \infty, f(t) \to K.

SUBSURFACE FLOW

Groundwater

  • Rocks below a certain depth are saturated.

  • Water flows towards lower elevation at equal pressure.

  • Water flows towards lower pressure at equal elevation.

  • Flow varies with material; larger holes mean faster flow.

Advantages of Groundwater

  • Less seasonal variation than surface water.

  • High biological purity due to slow movement.

  • Constant temperature.

  • Available virtually everywhere if deep enough.

Groundwater Properties

  • All water beneath the surface.

  • Occupies pores.

  • Porous media contains numerous small pores.

  • Pores contain fluids (water and air).

  • Pores act as fluid conduits.

  • Rock types and pore arrangement affect storage and flow.

Important Processes

  • Infiltration creates soil moisture.

  • Subsurface flow through soil.

  • Groundwater flow.

Soil Zones

  • Zone of aeration: Pores contain water & air.

    • Soil water zone: Water moves down (up) during infiltration (evaporation).

    • Vadose zone: Water held by capillary forces; near field capacity.

    • Capillary zone: Saturated at base, near field capacity at top; water pulled up from the water table.

Energy of Water in Soil

  • Cohesion: Water molecules attract each other.

  • Adhesion: Attraction between soil particles and water.

  • Meniscus: Curved air-water interface as water drains.

  • Determined by:

    • Pressure potential.

    • Gravity potential.

    • Osmotic potential: Water moves from low to high solute concentration.

Factors Affecting Water Movement

  • Soil texture (particle size).

  • Pore space.

  • Soil moisture content.

  • Slope of soil/rock layer.

Rates of Flow

  • Typical groundwater flow: 0.01 m/yr to 100 m/yr.

  • Permeability varies greatly; clean sandstone may have K = 0.1 m/s, while clay can have K = 1E-10 m/s.

Aquifers and Aquitards

  • Aquifer: Yields sufficient water.

  • Aquitard: Does not yield enough water.

  • Unconfined aquifer.

  • Confined aquifer.

Water Table

  • Intersects the land surface at lakes, ponds, and streams.

  • Streams can gain water from or lose water to the groundwater system.

  • Water table is closest to the surface at streams.

  • Perched water table.

Groundwater Use

  • Drawdown: Depression of piezometric surface due to pumping.

  • Cone of depression: Lowering of piezometric surface around a well.

  • Shape depends on hydraulic conductivity, storativity, and layer thickness.

Geologic Action by Groundwater

  • Weathering and cementation.

  • Karst: Erosion by groundwater, forms caves and sinkholes that collapses.

Types of Aquifers

  • Aquifer: Stores and transmits water.

    • Unconsolidated deposits: sand and gravel, sandstones etc.

  • Aquiclude: impermeable boundaries of aquifers; stores, doesn't transmit.

    • Clays and less shale

  • Aquitard: transmit don't store.

    • Shales and less clay

    • Leaky confining layers of aquifers

  • Confined aquifer: Bounded by impervious layers.

  • Unconfined aquifer:Bounded by a water table.

Groundwater Contamination

  • Plumes: Created when contaminants enter the aquifer.

  • Processes affecting plume movement:

    • Advection

    • Dispersion

    • Retardation

    • Chemical precipitation

    • Biotransformation

Plume Movement Processes

  • Advection: water carries substance

  • Dispersion: Spreading caused by advection

  • Retardation: Contaminants held to aquifer solids temporarily

  • Chemical Precipitation: heavy metals react with soils to precipitate in solid form.

  • Biotransformation: Chemicals change form or are destroyed

RUNOFF AND STREAMFLOW

Surface Runoff

  • Water that travels over the ground surface to a channel.

Peak Runoff Estimation by Rational Method

  • Q_p = CIA

    • C is runoff coefficient, i is rainfall intensity (m/s), A is watershed area (m²) and Q_p is peak runoff (cms)

  • Important for sizing storm water conveyance structures.

Limitations of Rational Method

  • Runoff coefficient isn't dependent Rainfall rate and antecedent moisture conditions

  • Rainfall is not uniform over the catchment area; Limit application to areas smaller than 80 has. (ASCE)

  • Higher coefficients should be used for less frequent storms as smaller percentage of rainfall abstraction

Streamflow

  • Measure of water volume transported by a stream.

Stream Parameters

  • A stream begins at its headwaters, often in the mountains, fed by an underground spring or the runoff from rain and snow melt

  • Measured by determining the cubic feet per second or gallons per hour.

Factors Influencing Flow Velocity

  • Depth of stream channel

  • Width of stream channel

  • Roughness of stream bottom

  • Slope or incline of surrounding terrain

Factors Influencing Stream Volume

  • Weather or climate

  • Seasonal changes

  • Merging tributaries

  • Human impact

Measurement

  • Discharge: volume of water that flows past a point during a specific time, Usually reported as the number of cubic feet of water passing a point each second (cfs)

  • Stillings wells are used to measure a streamflow

Watershed

  • Area of draining to a stream

  • Streamflow generated by water entering surface channels

  • Affected by Physical, vegetative, and climatic features and Geologic considerations

  • Annual Hydrographs and Storm Hydrographs

Baseflow Separation Techniques

  • Straight line method

  • Fixed base method

  • Variable slope method

DIRECT RUNOFF AND EXCESS RAINFALL

  • Excess (effective) rainfall

  • Rainfall that is not retained or infiltrated

  • Becomes direct runoff

  • Excess rainfall hyetograph(excess rainfall vs time)

Abstraction (losses)

  • Phi Index

  • Difference between total and excess rainfall hyetographs

  • Constant rate of abstraction yielding excess rainfall hyetograph with depth equal to depth of direct runoff

  • a = \sum{m=1}^{M} (Rm - A_t)

Water Runoff Coefficients

  • Ratio of the peak rate of direct runoff to the average intensity of rainfall in a storm

  • Ratio of runoff to rainfall over a given time period

  • \frac{\sum Rd}{\sum Rm}