1. Ground Water Hydrology Introduction - 2005
Philip B. Bedient
Civil & Environmental Engineering
Rice University

2. 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
Well mechanics- pumping for water supply, hydraulic control, or injection of wastes

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

4. Trends in Ground Water Use

5. 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

6. Regional Aquifer Issues

7. Typical Hydrocarbon Spill

8. Aquifer Characteristics
Matrix type
Porosity (n)
Confined or unconfined
Vertical distribution (stratigraphy or layering)
Hydraulic conductivity (K)
Intrinsic permeability (k)
Transmissivity (T)
Storage coefficient or Storativity (S)

9. Vertical Distribution of Ground Water

10. 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

11. Typical Soil-Moisture Relationship

12. 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

13. 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

14. 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

15. Porosity
Water

16. 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%

17. Rhombohedral packing of spheres with a theoretical porosity of 25.95%

18. Soil Classification Based on Particle Size (after Morris and Johnson)
Material
Particle Size, mm
Clay
<0.004
Silt
Very fine sand
Fine sand
Medium sand
Coarse sand

19. Soil Classification…cont.
Material
Particle Size, mm
Very coarse sand
Very fine gravel
Fine gravel
Medium gravel
Coarse gravel
Very coarse gravel

20. Particle Size Distribution Graph

21. 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

22. Cross Section of Unconfined and Confined Aquifers

23. 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

24. 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

25. 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

26. Ground Water Flow Darcy’s Law Continuity Equation Dupuit Equation

27. 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
V  1/∆L

28. V= - K dh/dl
Q = - KA dh/dl
Darcy’s Law

29. 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.
The average thickness of the aquifer is 30 m,
The average width of flow is 5 km.

30. 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

31. 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) / ( x 104 m2) = 0.25m/day

32. Therefore:
Seepage Velocity: Vs = V/n = 0.25 / 0.2 = m/day (about 4.1 ft/day)
Time to travel 4 km downstream: T = 4(1000m) / (1.25m/day) = days or 8.77 years
This example shows that water moves very slowly underground.

33. 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
10-7 to 10-9 cm/sec for Clays

34. 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

35. 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

36. Storage Coefficient S = Vol/ (AsH)
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 to 0.005
For unconfined aquifers, S values range between 0.07 and 0.25, roughly equal to the specific yield

37. Regional Aquifer Flows are Affected by Pump Centers
Streamlines and Equipotential lines

38. Derivation of the Dupuit Equation - Unconfined Flow

39. 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

40. 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,
d2h2/dx2 = 0

41. 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 Darcy’s law,
hdh/dx = -q/K

42. 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.

43. Cross Section of Flow q

44. Adding Recharge W - Causes a Mound to Form
Divide

45. 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.

46. Example L = 1000 m 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 = x 10-4 m/day

47. 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

48. 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 = m2/day into River 2
By setting q = 0 at the divide and solving for xd, the
water divide is located m from the edge of
River 1 and is 20.9 m high

49. Flow Nets - Graphical Flow Tool
Q = KmH / n
n = # head drops
m= # streamtubes
K = hyd cond
H = total head drop

50. Flow Net in Isotropic Soil
Portion of a flow net is shown below Y
Stream tube F
Curvilinear Squares

51. Flow Net Theory Streamlines Y and Equip. lines  are .
Streamlines Y are parallel to no flow boundaries.
Grids are curvilinear squares, where diagonals cross at right angles.
Each stream tube carries the same flow.

52. Seepage Flow under a Dam