GWH.ppt

Ground Water Hydrology

GW Resources - Quantity

• Aquifer system parameters

• Rate and direction of GW flow

• Darcy’s Law - governing flow relation • Dupuit Eqn for unconfined flow

• Recharge and discharge zones

GW Resources - Quality

• Contamination sources

Ground Water: A Valuable

Resource

• Ground water supplies 95% of the drinking

water needs in rural areas.

• 75% of public water systems rely on

groundwater.

• In the United States, ground water provides

drinking water to approximately 140

million people.

Aquifer Characteristics

1. Matrix type 2. Porosity (n)

3. Confined or unconfined

4. Vertical distribution (stratigraphy or layering) 5. Hydraulic conductivity (K)

6. Intrinsic permeability (k) 7. Transmissivity (T)

Vertical Zones of Subsurface

Water

• Soil water zone: extends from the ground surface down through the major root zone, varies with soil type and vegetation but is usually a few feet in

thickness

• Vadose zone (unsaturated zone): extends from the surface to the water table through the root zone, intermediate zone, and the capillary zone

Soil-Moisture Relationship

• The amount of moisture in the vadose zone

generally decreases with vertical distance

above the water table

Vertical Zones of Subsurface

Water Continued

• Water table: the level to which water will rise in a well drilled into the saturated zone

Porosity

– Porosity averages about 25% to 35% for most aquifer systems

– Expressed as the ratio of the volume of voids V_v to the total volume V:

n = V_v/V = 1- _b/_m

where:

_b is the bulk density, and

Porosity

Arrangement of Particles in a

Subsurface Matrix

Porosity depends on:

• particle size

• particle packing

Soil Classification Based on

Particle Size

(after Morris and Johnson)

Material Particle Size, mm Clay <0.004

Soil Classification…cont.

Material Particle Size, mm Very coarse sand 1.0 - 2.0

Particle Size Distribution

and Uniformity

• The uniformity

coefficient U indicates the relative sorting of the material and is

defined as D₆₀/D₁₀

Unconfined Aquifer Systems

• Unconfined aquifer:

an aquifer where the

water table exists under atmospheric

pressure as defined by levels in shallow

wells

Confined Aquifer Systems

• Confined aquifer:

an aquifer that is overlain

by a relatively impermeable unit such that

the aquifer is under pressure and the water

level rises above the confined unit

• Potentiometric surface:

in a confined

Special Aquifer Systems

• Leaky confined aquifer: represents a stratum that allows water to flow from above through a leaky confining zone into the underlying aquifer

Ground Water Flow

Darcy’s Law

Darcy’s Law

• Darcy investigated the flow of water through beds of permeable sand and found that the flow rate through porous media is proportional to the head loss and

inversely proportional to the length of the flow path • Darcy derived equation of governing ground water

flow and defined hydraulic conductivity K:

V = Q/A where:

A is the cross-sectional area V  -∆h, and

Example of Darcy

’

s Law

• A confined aquifer has a source of recharge.

• K for the aquifer is 50 m/day, and n is 0.2.

• The piezometric head in two wells 1000 m apart is 55 m and 50 m respectively, from a common

datum.

Calculate:

• the Darcy and seepage velocity in the aquifer

• the average time of travel from the head of the aquifer to a point 4 km downstream

The solution

• Cross-Sectional area 30(5)(1000) = 15 x 104 m2

• Hydraulic gradient (55-50)/1000 = 5 x 10 -3

• Rate of Flow through aquifer Q = (50 m/day) (75 x 101 m2_{) =}

37,500 m3_/day

• Darcy Velocity: V = Q/A = (37,500m3/day) / (15 x 104 m2) =

Therefore:

• Seepage Velocity:

V_s = V/n = 0.25 / 0.2 = 1.25 m/day (about 4.1 ft/day)

• Time to travel 4 km downstream:

T = 4(1000m) / (1.25m/day) = 3200 days or 8.77 years

Ground Water Hydraulics

• Hydraulic conductivity, K, is an indication

of an aquifer’s ability to transmit water

– Typical values:

10-2 to 10-3 cm/sec for Sands

10-4 to 10-5 cm/sec for Silts

Ground Water Hydraulics

Transmissivity (T) of Confined Aquifer

-

The product of K and the saturated

thickness of the aquifer T = Kb

- Expressed in m

/day or ft

/day

- Major parameter of concern

Ground Water Hydraulics

Intrinsic permeability (k)

Property of the medium only, independent of fluid

properties

Can be related to K by:

K = k(



g/µ)

where: µ = dynamic viscosity



= fluid density

Storage Coefficient

Relates to the water-yielding capacity of an aquifer

S = Vol/ (A



H)

– It is defined as the volume of water that an aquifer releases from or takes into storage per unit surface area per unit change in piezometric head - used

extensively in pump tests.

• For confined aquifers, S values range between 0.00005 to 0.005

• For unconfined aquifers, S values range

Regional Aquifer Flows are

Affected by Pump Centers

Dupuit Assumptions

For unconfined ground water flow Dupuit

developed a theory that allows for a simple solution based off the following assumptions:

1) The water table or free surface is only slightly inclined

2) Streamlines may be considered horizontal and equipotential lines, vertical

Derivation of the Dupuit

Equation

Darcy’s law gives one-dimensional flow per unit width as:

q = -Kh dh/dx

At steady state, the rate of change of q with distance is zero, or

d/dx(-Kh dh/dx) = 0

OR (-K/2) d2h2/dx2 = 0

Which implies that,

Dupuit Equation

Integration of d2h2/dx2 = 0 yields

h2 = ax + b

Where a and b are constants. Setting the boundary condition h = h_o at x = 0, we can solve for b

b = h_o2

Differentiation of h2 = ax + b allows us to solve for a,

a = 2h dh/dx

And from Darcy’s law,

Dupuit Equation

So, by substitution

h2 = h

02 – 2qx/K

Setting h = h_L2 = h

02 – 2qL/K Rearrangement gives

q = K/2L (h₀2- h

L2) Dupuit Equation

Then the general equation for the shape of the parabola is

h2 = h

02 – x/L(h02- hL2) Dupuit Parabola

Cross Section of Flow

Adding Recharge W -

Causes a Mound to Form

Dupuit Example

Example:

2 rivers 1000 m apart K is 0.5 m/day

average rainfall is 15 cm/yr evaporation is 10 cm/yr

water elevation in river 1 is 20 m water elevation in river 2 is 18 m

Example

Dupuit equation with recharge becomes

h2 = h

02 + (hL2 - h02) + W(x - L/2)

If W = 0, this equation will reduce to the parabolic Equation found in the previous example, and

q = K/2L (h₀2- h

L2) + W(x-L/2) Given:

L = 1000 m K = 0.5 m/day h₀ = 20 m

h_L= 28 m

Example

For discharge into River 1, set x = 0 m

q = K/2L (h₀2- h

L2) + W(0-L/2)

= [(0.5 m/day)/(2)(1000 m)] (202 _m2 _{– 18 m}2 _{) +}

(1.369 x 10-4 m/day)(-1000 m / 2)

q = – 0.05 m2 /day

The negative sign indicates that flow is in the opposite direction From the x direction. Therefore,

Example

For discharge into River 2, set x = L = 1000 m: q = K/2L (h₀2- h

L2) + W(L-L/2)

= [(0.5 m/day)/(2)(1000 m)] (202 _m2 _{– 18 m}2 _{) +}

(1.369 x 10-4 m/day)(1000 m –(1000 m / 2))

q = 0.087 m2/day into River 2

Flow Nets - Graphical Flow Tool

Q = KmH / n

n = # head drops m= # streamtubes K = hyd cond

Flow Net in Isotropic Soil

Portion of a flow net is shown below

 

Stream tube

Flow Net Theory

1. Streamlines  and Equip. lines  are .

2. Streamlines  are parallel to no flow

boundaries.

3. Grids are curvilinear squares, where diagonals cross at right angles.