1. GROUNDWATER
Freeze and Cherry: Groundwater
and
Fetter: Applied Hydrogeology
are the old and new testament of groundwater hydrology
Dingman has a good groundwater section (Chapter 8), which you will be responsible for by the end of the term

2. n = (Va + Vw)/V = Vv/V Properties of Aquifers
Aquifer - Geologic unit that can store enough water and transmit it at a rate fast enough to be significant
recall:
Porosity is
-can be measured as 1 minus the ratio of the bulk density to the particle density of the material
n = (Va + Vw)/V = Vv/V

3. Effective porosity is the fraction of the porosity that is available for transporting water (excludes fraction of pores too small to hold water, or those that are not inter-connected
- can be measured in the lab directly by saturating a dried sample of known volume and measuring water uptake in a sealed chamber over time
- for unconsolidated coarse-grained sediments there is no significant difference

4. Uniformity coefficient - measure of sorting
On a grain-size vs %finer plot:
d60 is the grain size diameter that corresponds to 60% finer by weight
d10 is the grain size diameter that corresponds to 10% finer by weight
(i.e. d60 is coarser than d10)
- Cu less than 4 is well sorted, more than 6 is poorly sorted

5. Porosity of Sedimentary Rocks
- sedimentary rocks usually have lower porosity than unconsolidated sediment because of compaction, and infilling of cementing material (e.g. calcite, dolomite, silica), although dissolution can reverse the latter effect
Ground water can be associated with both:
Primary Porosity - porosity between grains

6. Secondary pores (fractures) can be enlarged through dissolution by the ground water flow
- sedimentary rock may have primary porosity from deposition and secondary porosity from fractures along bedding planes
- secondary porosity also possible in cohesive sediments through wetting/drying, tectonic activity, etc.
- limestones, dolomites, gypsum can all have deposition reversed
- when in groundwater zone dissolution can occur
- flow starts initially through limited pore spaces, fractures, and bedding planes, and porosity enlarges over time

7. Porosity of Plutonic and Metamorphic Rocks
- primary porosity extremely low, but often not zero
- porosity increased over time by weathering and fracturing
- fracturing increases porosity of crystalline rocks 2 to 5%
- chemical and physical weathering increases with porosity
- highly weathered plutonic and metamorphic rocks can have posities between 30 to 60%
- sheet-like structures of weathering minerals such as micas can have very high porosities
Porosity of Volcanic Rocks
- lava cools rapidly at surface, traps degassing products
- holes in rock (vesicular) may or may not be interconnected
- cracks form during cooling
- volcanic rocks vary in porosity but can be very high
- basalt has lower gas content with porosity between 1 and 12%
- pumice (very high gas content) can have porosity approaching 90% (but effective porosity if not this high)
- weathering of volcanic deposits will also increase porosity

8. Specific Storage (Ss) :
Storativity or Storage Coefficient (S):
where b is the saturated thickness of the aquifer
Specific Yield (Sy)
- volume of water that drains from a saturated rock by gravity to volume of rock
- in an unconfined aquifer, S=Sy

9. Specific Retention (Sr)
volume of water held behind by capillary forces to volume of rock
(this water is also referred to as “pendular” water)
- essentially identical to the concept of field capacity
- specific yield can be determined in the lab using soil column methods
- soil in column is saturated from below and allowed to drain without evaporation going on
- allowed to drain for months before equilibrium is reached
- volume of water drained to the volume of column is Sy
- above difficult to do with rock
- can also be measured in the field with pump tests (discussed later)

10. Hydraulic Conductivity of saturated media and Darcy’s Law
- ability of the rock to transmit and hold water are most important hydrologic properties
- as pointed out only effective porosity important with regards to groundwater flow (e.g. vesivcular basalt - lack of interconnectivity, Clays and shales - pores too small)

11. Darcy’s experiment
Reality
For educational purposes only

12. Darcy’s experiment
Henry Darcy in 1856 was playing around with movement of water through sand filtration columns for the City of Dijon, France.
Darcy found that the flow of water through a bed of “a given nature” is:
- proportional to the difference in the height of the two ends,
- inversely proportional to the length of the flow path
- proportional to the x-sectional area of the pipe
- flow is further related to a coefficient dependant on the nature of the media
is Darcy’s Law for saturated flow through a pipe,
Where: ha and hb are heads at two ends of pipe
L is length pf flow path
K is hydraulic conductivity
A is the cross-sectional area of the pipe
Q is discharge

13. or:
negative sign is for flow in direction of decreasing head
dh/dl is the hydraulic gradient
recall Darcy’s Law for unsaturated flow from text is:
- we are not substituting Vx here, Q is discharge (remove A from above equation and we will have a velocity of flow)(see below).
- the term d(z+p/(w) is now combined into one term dh

14. Darcy’s Law
Ohm’s Law (rearranged)
Where: i = current
K = electrical conductivity
K = 1/ ρ where ρ = resistivity
V = voltage
L = distance
A = area

15. Form of Darcy’s law we will use most often calculates specific discharge
v is not a true velocity
v is also known as the “Darcian Velocity”
K is also known as “Darcy’s proportionality constant” or “coefficient of permeability”
- whereas in unsaturated flow K is a function of soil moisture, soil and fluid properties, in saturated flow it a function of soil and fluid properties only

16. - discharge is proportional to the specific weight ( of the fluid
- Q% 1/: (dynamic viscosity of the fluid - resistance of fluid to shearing)
- Q%d2 (square of the diameter of pores)
Darcy’s law can be re-expressed as:
where C is a shape factor (because x-sectional area of a pore is also related to it’s shape)

17. - intrinsic permeability (Ki) is representative of the character of the porous medium alone
- basically a function of the size of the openings through which the fluid moves
- larger the square of the pore diameter, the lower the resistance to flow
- Ki is essentially the “openess” of the flow path (in e.g. cm2)
- can also expressed in units called “darcys”
1 darcy=9.87x10-9 cm2
No fluid properties

19. By convention, if we always refer to K as the hydraulic conductivity, we can refer to Ki the permeability
(Note: Freeze and Cherry use k for permeability which is much more common)
- during the formation of clastic sedimentary rock, cementation and compaction can restrict throats between pores
- therefore, even though porosity may be reduced only slightly, permeability can be greatly reduced
- crystalline rocks have low permeability, although volcanics can have high permeability if connectiviy is good
- secondary permeability (like secondary porosity), through fracturing, weathering

20. Estimation of K
Hazen Method
- approximation
- for sandy sediments with d10 is betweem 0.1 and 3.0 mm
- developed on the basis of sand filtering for drinking water
- durable empirical equation
K is in cm/s
d10 is in cm
C is unitless coefficient which ranges from 40 in v. fine sand to 150 in coarse sand

21. Koseny-Carmen Equation
-for more non-uniform soils
- explicitly incorporates fluid properties and porosity
where n is porosity

22. Fair-Hatch Equation
- uses first two terms in the Koseny-Carmen equation and replaces the third with:
where: m is a packing factor (usually ~5)
C is the shape factor (6 for spheres, 7.7. for angular)
P is % of material held between adjacent seives
dm in this case is taken as the geometric mean of the rated sizes of adjacent seives

23. Permeameters
- tube filled with sample
- can be actual tube used to collect sample so minimal disturbance
2-types of permeameter:
1. Constant-head
- used for non-cohesive sediments (sands)
- best for samples with K>0.01cm/min
- rearranging Darcy’s law we can obtain:
where V is the volume of water discharging in time t
L is the length of sample
A is the x-sectional areah is the hydraulic head
K is the hydraulic conductivity
- dh/dl should mimic field
-h should never be greater than 0.5L (don’t want v to get too high. Why?)

25. 2. Falling-head permeameter
- used for cohesive seds with lower K
- initial water level in a falling head tube is measured as h0
- after a period t (several hours), level is measured again as h
(See Fetter for derivation of these equations)
where At is x-sectional area of falling head tube
Ac is the x-sectional area of the sample tube
For both constant-head and falling-head:
- make sure sample is fully saturated
- use dearied water if possible
Question: How would we arrive at Ki given a value for K above?

26. The Water Table
Question: How is the water table defined?
The following generalizations are valid:
1. In the absence of flow the water table will be flat
2. A sloping water table indicates flow
3. Ground-water discharge occurs in low zones
4. The water table has the same general shape as the surface topography (but less relief change)
5. Ground water generally flows from topographic highs to lows

27. Aquifers
- near the Earth’s surface there are few materials that are absolutely impermeable
-Ki for aquifers is generally >10-2 darcy
Confining layer
- layer having low or no peremeability
- whether a layer is considered “confining” or not will depend on main aquifer material
- usually confining layers have some permeability, just very low
types of confining layers:
Aquiclude - layer of low permeability that can store and transmit groundwater slowly between aquifers (now more commonly referred to as “leaky confining layer”)
Aquifuge - absolutely impermeable and contains no water

28. Unconfined aquifer (water table aquifer) - layer where highly permeable material extends to the water table
- recharge can be from any direction
Confined aquifer (artesian aquifer) - aquifers overlain by confining layer
- recharge from recharge areas where strata tips up, or leakage through confining layer
- artesian wells are drilled into confined aquifers
- water from an artesian well can rise above surface
- potentiometric surface is the level to which water will rise in a cased well
Perched Aquifer - aquifer in the vadose zone because of a lens of impermeable material
- common in glacial outwash (clay from ponds), volcanic deposits (weathered ash deposits with low K sandwiched between high K basalt)

30. Water Table and Potentiometric Surface Maps
Question: What is the difference between the water table and the potentiometric surface?
- surfaces measured in wells open only to the aquifers of interest
- measurements should be made within a brief period of time
- each well needs to be tied into a common datum (e.g. sea level)
- datum should be same for surface topography (esp. ponds, springs, etc.)
- measurements in pumping wells should be made with no pumping and after enough time for rebound
- map should include location of lakes and streams
- potentiometric levels are not influenced by surface topography
- very important to know whether your well is measuring confined or unconfined aquifer
- also important if measuring potentiometric surface to know you are in same confined aquifer

31. Extrapolating Well Measurements
- often we want to map the direction of water flow in a confined or unconfined aquifer, but do not have enough wells
- graphical solution for 3 or 4-points
1. Map scale drawing showing location of wells
2. Note water level at each well
3. Measure map distance and elevation change between each well
4. Find map distance for unit change in head between each pair
5. Mark even increments of head change along each line
6. Make lines of equal head

32. Piezometer and Piezometer Nests
- basic device for measuring head is a tube or pipe through which the water level can be measured
- open to water flow at bottom and open to atmosphere at top
- intake usually slotted pipe or commercially available well point
- must allow for intake of water, but not clastic material
- water levels measured by pressure transducers or with manual soundings
- nests are groups of peizometers at one location, but with well points going to different depths to obtain vertical hydraulic gradient

33. Steady-State flow vs Transient flow
Steady-state flow - when at any point in a flow field, magnitude and direction of flow are constant with time
- flow velocity may vary from point to point in the field, but the pattern is constant through time
Transient flow (unsteady flow, nonsteady flow)

34. Compressibility and Effective Stress
- at any point in an aquifer, the weight of overlying material applies downward stress on the aquifer material. This is Total stress
- upward stress on the aquifer material caused by fluid pressure counteracts total stress to a degree
- difference is the effective stress (i.e. the stress actually applied to the aquifer skeleton)
and of course
In confined aquifers P can change with little change in saturated thickness of aquifer. In these cases σT will remain essentially constant so that σe is what changes:
Question: What will happen to the effective stress acting on the aquifer skeleton if we pump water out of a confined aquifer?

35. Compressibility of water is constant at 4.4x10-10 Pa-1
Need a estimation of compressibility of the solid matrix
-assume that the matrix acts as a elastic body:
- subject the matrix to a change in effective stress and it will deform
Aquifer compressibility is defined as:
where: α is aquifer compressibility
db is the change in aquifer thickness
b is the original aquifer thickness

36. There are 2 ways an aquifer can compress:
1. By compression of individual rock grains and crystals 2.
The first is negligible to non-existent in most cases
If necessary, compressibility can be determined in the lab using loading cells
- aquifer compressibility will also depend on loading history of aquifer
- compressibility of water close to least-compressible rock
- must be realized that stress field at depth is 3-D, but changes in the horizontal stress field can be considered negligable
- i.e. large changes in stress only occur in the vertical direction
Summary of compaction:
when fluid pressure (head) is reduced in a confined aquifer, the following will occur:
1. Effective stress will increase
2. Aquifer material now bears an additional portion of the overburden load
3. Aquifer compacts a bit releasing water from storage
4. Reduction in water pressure also causes water to expand slightly releasing additional water
- if compaction is propagated to the surface, land subsidence can occur

41. Near Las Vegas
Earth Fissures

42. Approximate maximum subsidence amounts as of 1997 for selected locations in the Southwest
Arizona
Nevada
California
Texas
Eloy
15 ft
Las Vegas
6 ft
Lancaster
El Paso
1 ft
West of Phoenix
18 ft
New Mexico
Southwest of Mendota
29 ft
Houston
9 ft
Tucson
<1 ft
Albuquerque
Davis
4 ft
Mimbres Basin
2 ft
Santa Clara Valley
12ft
Ventura

44. Now we can use interferometric processing of Synthetic Aperture Radar (SAR) data.

45. Homogeneity and Isotropy
Homogeneous units
- values of Storativity and K similar throughout for sandstones: similar grain size, porosity, cemetation, thickness for plutonics and metamorphics: similar fracturing, strike and dip, etc.
- definition is usually arbitrary, but one common one is that the distribution of K must be monomodal
Heterogeneous units
- hydraulic properties change spatially
- can be changes in thickness, bedding of different hydraulic properties, etc.
- interlayered clay and sand deposits can create extreme layered heterogeneity
- limestones often heterogeneous because solution pathways form along bedding planes
discontinuous heterogeneity - occurs at faults or large-scale stratigraphic features

47. trending heterogeneity - usually in units where deltas, alluvial fans, etc have formed
- trending heterogeneity in large sedimentary formations can cover 2 to 3 orders of magnitude in Ki
If a porous medium has equal intrinsic permeability in all directions it is said to be isotropic
If the pattern of voids allows for a path of least resistance (i.e. direction in which Ki is higher) the unit is said to be anisotropic
- fractured rocks, basalts often highly anisotropic
- sedimentary rocks may have many homogenous units
- directions of maximum and minimum anisotropy are the principal directions of anisotropy
If an xyz coordinate system is setup along the principal directions:
Kx=Ky=Kz is an isotropic situation
Kx…Ky…Kz is an anisotropic situation
Kx=Ky…Kz is a transversley isotropic situation (common in layered deposits