Ground Water Hydrology Introduction - 2005

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Ground Water HydrologyIntroduction - 2005

• Philip B. Bedient
• Civil Environmental Engineering
• Rice University

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GW Resources - Quantity

• Aquifer system parameters
• Rate and direction of GW flow
• Darcys Law - governing flow relation
• Dupuit Eqn for unconfined flow
• Recharge and discharge zones
• Well mechanics- pumping for water supply,
  hydraulic control, or injection of wastes

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GW Resources - Quality

• Contamination sources
• Contaminant transport mechanims
• Rate and direction of GW migration
• Fate processes-chemical, biological
• Remediation Systems for cleanup

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Trends in Ground Water Use
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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.
• Supplies about 40 of Houston area

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Regional Aquifer Issues
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Typical Hydrocarbon Spill
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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)
8. Storage coefficient or Storativity (S)

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Vertical Distribution of Ground Water
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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
• Capillary zone extends from the water table up
  to the limit of capillary rise, which varies
  inversely with the pore size of the soil and
  directly with the surface tension

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Typical Soil-Moisture Relationship
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Soil-Moisture Relationship

• The amount of moisture in the vadose zone
  generally decreases with vertical distance above
  the water table
• Soil moisture curves vary with soil type and with
  the wetting cycle

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Vertical Zones of Subsurface Water Continued

• Water table the level to which water will rise
  in a well drilled into the saturated zone
• Saturated zone occurs beneath the water table
  where porosity is a direct measure of the water
  contained per unit volume

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Porosity

• Porosity averages about 25 to 35 for most
  aquifer systems
• Expressed as the ratio of the volume of voids Vv
  to the total volume V
• n Vv/V 1- ?b/?m
• where
• ?b is the bulk density, and
• ?m is the density of grains

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Porosity

Water
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Arrangement of Particles in a Subsurface Matrix

• Porosity depends on
• particle size
• particle packing
• Cubic packing of spheres with a theoretical
  porosity of 47.65

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• Rhombohedral packing of spheres with a
  theoretical porosity of 25.95

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Soil Classification Based on Particle Size(after
Morris and Johnson)
Material Particle Size, mm
Clay lt0.004
Silt 0.004 - 0.062
Very fine sand 0.062 - 0.125
Fine sand 0.125 - 0.25
Medium sand 0.25 - 0.5
Coarse sand 0.5 - 1.0
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Soil Classificationcont.
Material Particle Size, mm
Very coarse sand 1.0 - 2.0
Very fine gravel 2.0 - 4.0
Fine gravel 4.0 - 8.0
Medium gravel 8.0 - 16.0
Coarse gravel 16.0 - 32.0
Very coarse gravel 32.0 - 64.0
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Particle Size Distribution Graph
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Particle Size Distribution and Uniformity

• The uniformity coefficient U indicates the
  relative sorting of the material and is defined
  as D60/D10
• U is a low value for fine sand compared to
  alluvium which is made up of a range of particle
  sizes

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Cross Section of Unconfined and Confined Aquifers
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Unconfined Aquifer Systems

• Unconfined aquifer an aquifer where the water
  table exists under atmospheric pressure as
  defined by levels in shallow wells
• Water table the level to which water will rise
  in a well drilled into the saturated zone

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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 aquifer,
  the hydrostatic pressure level of water in the
  aquifer, defined by the water level that occurs
  in a lined penetrating well

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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
• Perched aquifer occurs when an unconfined water
  zone sits on top of a clay lens, separated from
  the main aquifer below

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Ground Water Flow Darcys Law Continuity
Equation Dupuit Equation
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Darcys 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
• V ? 1/?L

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Darcys Law
V - K dh/dl Q - KA dh/dl
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Example of Darcys 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.
• The average thickness of the aquifer is 30 m,
• The average width of flow is 5 km.

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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
• assume no dispersion or diffusion

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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) 0.25m/day

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Therefore

• Seepage Velocity Vs
  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
• This example shows that water moves very slowly
  underground.

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Ground Water Hydraulics

• Hydraulic conductivity, K, is an indication of an
  aquifers ability to transmit water
• Typical values
• 10-2 to 10-3 cm/sec for Sands
• 10-4 to 10-5 cm/sec for Silts
• 10-7 to 10-9 cm/sec for Clays

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Ground Water Hydraulics

• Transmissivity (T) of Confined Aquifer
• -The product of K and the saturated
  thickness of the aquifer T Kb
• - Expressed in m2/day or ft2/day
• - Major parameter of concern
• - Measured thru a number of tests -
  pump, slug, tracer

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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
• g gravitational constant

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Storage Coefficient

• Relates to the water-yielding capacity of an
  aquifer
• S Vol/ (As?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 between
  0.07 and 0.25, roughly equal to the specific yield

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Regional Aquifer Flows are Affected by Pump
Centers
Streamlines and Equipotential lines
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Derivation of the Dupuit Equation - Unconfined
Flow
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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
• 3) Slopes of the free surface and hydraulic
• gradient are equal

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Derivation of the Dupuit Equation

• Darcys 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,
• d2h2/dx2 0

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Dupuit Equation

• Integration of d2h2/dx2 0 yields
• h2 ax b
• Where a and b are constants. Setting the boundary
  
•      condition h ho at x 0, we can solve for
  b
• b ho2
• Differentiation of h2 ax b allows us to solve
  for a,
• a 2h dh/dx
• And from Darcys law,
• hdh/dx -q/K

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Dupuit Equation

• So, by substitution
• h2 h02 2qx/K
• Setting h hL2 h02 2qL/K
• Rearrangement gives
• q K/2L (h02- hL2) Dupuit
  Equation
• Then the general equation for the shape of the
  parabola is
• h2 h02 x/L(h02- hL2) Dupuit Parabola
• However, this example does not consider recharge
  to the aquifer.

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Cross Section of Flow
q
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Adding Recharge W - Causes a Mound to Form
Divide
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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
• Determine the daily discharge per meter width
  into each
• River.

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Example

• Dupuit equation with recharge becomes
• h2 h02 (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- hL2) W(x-L/2)
• Given
• L 1000 m
• K 0.5 m/day
• h0 20 m
• hL 28 m
• W 5 cm/yr 1.369 x 10-4 m/day

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Example

• For discharge into River 1, set x 0 m
• q K/2L (h02- hL2) W(0-L/2)
• (0.5 m/day)/(2)(1000 m) (202 m2 18 m2
  )
• (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,
• q 0.05 m2 /day into river 1

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Example

• For discharge into River 2, set x L 1000 m
• q K/2L (h02- hL2) W(L-L/2)
• (0.5 m/day)/(2)(1000 m) (202 m2 18 m2
  )
• (1.369 x 10-4 m/day)(1000 m (1000 m /
  2))
• q 0.087 m2/day into River 2
• By setting q 0 at the divide and solving for
  xd, the
• water divide is located 361.2 m from the edge of
• River 1 and is 20.9 m high

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Flow Nets - Graphical Flow Tool
Q KmH / n n head drops m streamtubes K
hyd cond H total head drop
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Flow Net in Isotropic Soil

• Portion of a flow net is shown below

Y
Stream tube
F
Curvilinear Squares
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Flow Net Theory

1. Streamlines Y and Equip. lines ? are ?.
2. Streamlines Y are parallel to no flow
   boundaries.
3. Grids are curvilinear squares, where diagonals
   cross at right angles.
4. Each stream tube carries the same flow.

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Seepage Flow under a Dam