Groundwater Hydrology

Groundwater Hydrology

Understanding the principles of groundwater flow, including Aquifers, Darcy's Law, and Well Hydraulics.

Introduction

Groundwater

Water found underground in the cracks and spaces in soil, sand, and rock. It is stored in and moves slowly through geologic formations of soil, sand, and rocks called aquifers.

Types of Aquifers

Unconfined Aquifer (Water Table Aquifer)

The upper water surface (water table) is at atmospheric pressure. It is free to rise and fall. Recharge usually comes directly from overhead infiltration.

Confined Aquifer (Artesian)

Sandwiched between two impermeable layers (aquicludes). The water is under pressure greater than atmospheric. If a well penetrates it, water rises above the top of the aquifer.

Leaky Aquifer (Semi-confined)

Bounded by semi-permeable layers (aquitards) that allow some slow leakage of water into or out of the aquifer.

Geologic Formations

Aquiclude

A formation that contains water (high porosity) but cannot transmit it rapidly enough to furnish a significant supply to a well or spring (e.g., clay).

Aquitard

A formation that only retards but does not completely stop the flow of water to or from an adjacent aquifer. It does not yield water freely to wells, but may store groundwater (e.g., sandy clay).

Aquifuge

A formation that neither contains nor transmits water (e.g., solid granite without fractures).

Darcy's Law

Henry Darcy (1856) formulated the fundamental law governing groundwater flow in porous media.

Aquifer Properties

Porosity ( $n$ )

The ratio of the volume of voids to the total volume of the rock or soil. It indicates how much water the geologic material can hold.

Specific Yield ( $S_y$ )

The volume of water that an unconfined aquifer releases from storage by gravity drainage per unit surface area per unit decline in the water table.

Specific Retention ( $S_r$ )

The volume of water retained against gravity drainage by molecular attraction and surface tension.

Note

n = S_y + S_r

. This means that not all water stored in the voids (porosity) can be extracted; a portion is always retained.

Darcy's Law

Q = K i A

Variables

$Q$ : Discharge ( $m^3/s$ )
$K$ : Hydraulic Conductivity (m/day or m/s). A property of both the porous medium and the fluid.
$i$ : Hydraulic Gradient ( $dh/dl$ ). The drop in hydraulic head per unit length of flow.
$A$ : Cross-sectional area perpendicular to flow ( $m^2$ ).

Darcy's Law Groundwater Flow Simulator

Adjust aquifer parameters to see the hydraulic head profile and calculate the steady-state discharge $Q$ .

Conductivity K (m/d): 10

Upstream Head h₁ (m): 50

Downstream h₂ (m): 45

Length L (m): 100

Area A (m²): 100

Hydraulic Gradient (i)

0.0500

Discharge (Q)

50.00 m³/day

Loading chart...

Note

Transmissivity ( $T$ ): For a confined aquifer of thickness

b

, Transmissivity is defined as

T = K \cdot b

. It represents the rate at which water is transmitted through a unit width of the aquifer under a unit hydraulic gradient. Units:

m^2/day

S

For confined aquifers, the Storativity ( $S$ ) is the volume of water released from storage per unit surface area of the aquifer per unit decline in the piezometric head. Unlike specific yield in unconfined aquifers (where pores actually drain), water released in confined aquifers comes solely from the expansion of the water and the compaction of the aquifer matrix due to pressure reduction. It is a dimensionless value, typically very small (

10^{-5}

10^{-3}

Steady Flow to Wells

When a well is pumped, water is removed from the aquifer, lowering the head near the well. This creates a Cone of Depression.

Cone of Depression (Thiem Equation)

Loading chart...

Pumping Rate (Q)1000 m³/day

Transmissivity (T)500 m²/day

Radius of Influence (R)1000 m

Initial Head (h₀)50 m

Simulates steady-state flow to a well in a confined aquifer.
Notice how increasing Q deepens the cone, while increasing T makes the cone shallower (easier flow).

Confined Aquifer (Thiem Equation)

Assumptions of Thiem's Equation

Radial flow toward the well. Homogeneous, isotropic aquifer of infinite areal extent. Steady-state flow (equilibrium reached). Full penetration of the well.

Thiem Equation (Confined)

Q = \frac{2 \pi T (h_2 - h_1)}{\ln(r_2/r_1)}

Note

Where

h_1, h_2

are piezometric heads at radii

r_1, r_2

from the well center.

Unconfined Aquifer (Dupuit Equation)

Modeling flow in unconfined aquifers is mathematically complex because the upper boundary (the water table) is not fixed; its elevation changes as water flows. To simplify this, Jules Dupuit and Philipp Forchheimer introduced key assumptions.

Dupuit-Forchheimer Assumptions

Groundwater flow is strictly horizontal.
The hydraulic gradient is equal to the slope of the free water table and is constant with depth ( $dh/dl \approx \tan \theta$ ). These assumptions allow the 3D groundwater flow equations to be reduced to 2D, forming the basis of the Dupuit equation for steady flow to a well in an unconfined aquifer.

Dupuit Equation (Unconfined)

Q = \frac{\pi K (h_2^2 - h_1^2)}{\ln(r_2/r_1)}

Specific Capacity of a Well

Specific Capacity

The ratio of the discharge (

Q

) to the drawdown (

s

) in the pumped well:

Q/s

. It is a measure of the productivity of a well and typically decreases as the pumping rate or pumping time increases.

Well Losses and Specific Capacity

Components of Drawdown

The total drawdown in a pumping well consists of aquifer losses (head loss due to flow through the porous media, proportional to

Q

) and well losses (head loss due to turbulent flow through the well screen and gravel pack, proportional to

Q^2

Total Drawdown Equation

s_w = BQ + CQ^2

Variables

$s_w$ : Total drawdown in the well
$B$ : Aquifer loss coefficient
$C$ : Well loss coefficient
$Q$ : Pumping rate

Step-Drawdown Test

A test conducted by pumping the well at successively higher constant rates. It is used to determine the aquifer and well loss coefficients (

B

and

C

) and evaluate the efficiency of the well.

Unsteady Flow (Theis Equation)

In reality, steady state is rarely reached immediately. The Theis Equation describes the drawdown (

s

) as a function of time (

t

) and distance (

r

Theis Equation

s = \frac{Q}{4 \pi T} W(u)

Note

Where

W(u)

is the Well Function (exponential integral) and

u = \frac{r^2 S_c}{4 T t}

, with

S_c

being the Storage Coefficient.

Cooper-Jacob Approximation

For small values of

u

(specifically

u \le 0.01

), which occurs at large times (

t

) or small distances (

r

), the Theis Well Function

W(u)

can be truncated to a simpler logarithmic expression. This is known as the Cooper-Jacob approximation.

Cooper-Jacob Equation

s = \frac{Q}{4 \pi T} \ln\left(\frac{2.25 T t}{r^2 S_c}\right)

This method allows engineers to plot drawdown (

s

) against the logarithm of time (

\log t

) on semi-logarithmic paper. The resulting straight line makes it very easy to calculate Transmissivity (

T

) and Storage Coefficient (

S_c

) from pumping test data.

Groundwater Management

Sustainable management of aquifers is essential to prevent depletion, land subsidence, and water quality degradation.

Safe Yield

The maximum quantity of water that can be continuously withdrawn from a groundwater basin without adverse impacts (e.g., permanent lowering of the water table, intrusion of poor-quality water). Withdrawing more than the safe yield is termed overdraft.

Artificial Recharge

The process of increasing groundwater replenishment beyond natural rates. Techniques include spreading basins (allowing surface water to infiltrate over large areas) and injection wells (pumping water directly into the aquifer). This is used to combat overdraft and restore depleted aquifers.

Saltwater Intrusion

In coastal aquifers, freshwater floats on denser saline ocean water. Overpumping lowers the freshwater head, causing the saltwater wedge to migrate inland, contaminating drinking water wells. This is modeled using the Ghyben-Herzberg relation, which states that for every 1 meter the water table is lowered above sea level, the saltwater interface rises 40 meters below sea level.

Aquifer Storage Parameters

Understanding how much water an aquifer can store and yield is crucial for groundwater development.

Specific Yield ( $S_y$ )

The ratio of the volume of water that drains from a saturated rock owing to the attraction of gravity to the total volume of the rock.

Specific Retention ( $S_r$ )

The ratio of the volume of water a rock can retain against gravity (due to surface tension) to the total volume of the rock.

Porosity Relationship

n = S_y + S_r

Storage Coefficient (S)

In confined aquifers, water is released not by gravity drainage, but by the decompression of the water and the elastic compaction of the aquifer matrix as pressure drops. The storage coefficient (

S

) is the volume of water released from storage per unit surface area of the aquifer per unit decline in the hydraulic head.

Key Takeaways

Groundwater is a critical component of the hydrologic cycle, stored in permeable geologic formations called aquifers.
Unconfined aquifers have a free water table, while confined aquifers are pressurized between impermeable layers.
Darcy's Law ( $Q = KiA$ ) states that groundwater discharge is proportional to the hydraulic gradient and the cross-sectional area.
Hydraulic Conductivity ( $K$ ) measures a material's ability to transmit water.
Porosity ( $n$ ) is the sum of Specific Yield (drainable water) and Specific Retention (retained water).
Transmissivity ( $T$ ) integrates hydraulic conductivity over the entire aquifer thickness ( $T = K \cdot b$ ).
Pumping a well creates a localized drop in the water table or piezometric surface, known as a Cone of Depression.
Steady-state flow assumes the cone of depression has stabilized and is no longer expanding.
The Thiem Equation models steady flow in confined aquifers, while the Dupuit Equation models unconfined aquifers.
In reality, steady state takes a long time to achieve. Unsteady flow modeling is required for most pumping tests.
The Theis Equation calculates dynamic drawdown, and the Cooper-Jacob approximation simplifies it for graphical analysis on semi-log plots.
Sustainable Groundwater Management requires pumping below the Safe Yield to prevent overdraft and land subsidence.
Artificial Recharge supplements natural infiltration to replenish aquifers, while overpumping near coasts risks Saltwater Intrusion.

PreviousFlood Routing - Examples & Applications

Quiz Me

NextGroundwater Hydrology - Examples & Applications

Introduction

Groundwater

Types of Aquifers

Unconfined Aquifer (Water Table Aquifer)

Confined Aquifer (Artesian)

Leaky Aquifer (Semi-confined)

Geologic Formations

Aquiclude

Aquitard

Aquifuge

Darcy's Law

Aquifer Properties

Porosity (nnn)

Specific Yield (SyS_ySy​)

Specific Retention (SrS_rSr​)

Note

Darcy's Law

Variables

Darcy's Law Groundwater Flow Simulator

Note

Storativity (Storage Coefficient, SSS)

Steady Flow to Wells

Cone of Depression (Thiem Equation)

Confined Aquifer (Thiem Equation)

Assumptions of Thiem's Equation

Thiem Equation (Confined)

Note

Unconfined Aquifer (Dupuit Equation)

Dupuit-Forchheimer Assumptions

Dupuit Equation (Unconfined)

Specific Capacity of a Well

Specific Capacity

Well Losses and Specific Capacity

Components of Drawdown

Total Drawdown Equation

Variables

Step-Drawdown Test

Unsteady Flow (Theis Equation)

Theis Equation

Note

Cooper-Jacob Approximation

Cooper-Jacob Equation

Groundwater Management

Safe Yield

Artificial Recharge

Saltwater Intrusion

Aquifer Storage Parameters

Specific Yield (SyS_ySy​)

Specific Retention (SrS_rSr​)

Porosity Relationship

Storage Coefficient (S)

Porosity ( $n$ )

Specific Yield ( $S_y$ )

Specific Retention ( $S_r$ )

Storativity (Storage Coefficient, $S$ )

Specific Yield ( $S_y$ )

Specific Retention ( $S_r$ )