Hydrogeology

Learning Objectives

  • Describe groundwater recharge, flow, and discharge in the hydrologic cycle.
  • Distinguish aquifers, aquitards, and confined or unconfined conditions.
  • Estimate drainable storage and interpret a bounded recharge and pumping budget.
  • Apply Darcy’s law, hydraulic head, and transmissivity within their assumptions.
  • Interpret flow nets and pumping-related drawdown conceptually.
  • Identify contaminant pathways and the evidence needed for a groundwater assessment.

Groundwater and the Hydrologic Cycle

Hydrogeology

The study of groundwater occurrence, movement, and interaction with geologic materials and surface-water systems.

Groundwater in Engineering

Groundwater conditions affect effective stress, excavation inflow, seepage, settlement, slope behavior, water supply, and contaminant transport. Engineers represent a site with a conceptual model of geology, hydraulic heads, sources, boundaries, pathways, and receptors. The model is revised when field evidence changes the interpretation.

Recharge and Discharge

Precipitation may infiltrate through the unsaturated zone and recharge saturated material; groundwater then moves along gradients and may discharge to springs, streams, wetlands, coastal water, or wells. Surface-water exchange, evapotranspiration, and subsurface boundaries vary by site.

Groundwater in the Hydrologic Cycle

This conceptual section connects recharge and discharge; the illustrated paths are not a site-specific groundwater map.

Precipitation infiltrates to an aquifer and groundwater flows toward a stream discharge area

Aquifers and Storage

Aquifer

A geologic unit or system that is sufficiently saturated and permeable to transmit groundwater and yield usable quantities to wells or springs under the relevant conditions.

Aquifer Boundaries

  • Unconfined aquifer: its upper saturated boundary is the water table, where pore-water pressure is atmospheric.
  • Confined aquifer: it is bounded above and below by lower-permeability units and is pressurized relative to atmospheric pressure. Water in a well rises toward the potentiometric surface.
  • Aquitard: a unit that retards flow but can transmit water over time.
  • Aquiclude: a conventional term for a unit with negligible transmission for a stated problem; natural materials are not assumed to be perfectly impermeable.
Unconfined and Confined Aquifers

The section distinguishes the water table from the potentiometric surface and shows lower-permeability confining units schematically.

An unconfined aquifer has a water-table upper boundary while a confined aquifer has a potentiometric surface

Specific yield

The volume of water that drains by gravity from a saturated material, divided by its total volume, under stated drainage conditions.

Specific retention

The volume of water retained in a saturated material after gravity drainage, divided by its total volume, under stated drainage conditions.

Porosity and Drainable Storage

Under the conventional drainage definition, porosity is divided into specific yield and specific retention.

n=Sy+Srn = S_y + S_r

Variables

SymbolDescriptionUnit
nnPorosity: void volume divided by total material volumedimensionless
SyS_ySpecific yield under stated drainage conditionsdimensionless
SrS_rSpecific retention under stated drainage conditionsdimensionless

Storage Is Not the Same as Yield

Fine-grained material can have high porosity while retaining much of its water against gravity. Porosity alone therefore does not predict a well’s yield; hydraulic conductivity, aquifer geometry, boundaries, and pumping conditions also matter.

Drainable Unconfined Storage

For uniform specific yield and a representative water-table decline after gravity drainage, estimate release from the drained bulk interval.

Vd=SyApΔzV_d = S_y A_p\Delta z

Variables

SymbolDescriptionUnit
VdV_dWater volume released by gravity drainagem³
ApA_pPlan area of the affected aquiferm²
Δz\Delta zPositive magnitude of water-table declinem

Water Budget and Storage Change

Conservation requires change in groundwater storage to equal inflows minus outflows over the same interval. A deliberately simplified unconfined control volume receiving only recharge rcApr_c A_p and losing only pumping QpQ_p has storage-change rate rcAp−Qpr_c A_p-Q_p. Here rcr_c is recharge depth per time, ApA_p plan area and QpQ_p pumping volume per time. If specific yield is uniform and gravity drainage is representative, its average water-table change rate is (rcAp−Qp)/(SyAp)(r_c A_p-Q_p)/(S_y A_p). Positive means rising, negative means falling. Real budgets may also require lateral exchange, stream interaction, evapotranspiration, delayed drainage and other stresses; this lumped balance cannot predict a spatial drawdown cone or sustainable yield by itself.

Groundwater Movement

Hydraulic Head and Darcy’s Law

Total Hydraulic Head

For ordinary groundwater problems, total head combines elevation head and pressure head. Water moves from higher total head toward lower total head; elevation by itself does not determine the flow direction.

Hydraulic Head and Flow Direction

The piezometers share a datum and screen the same conceptual aquifer; actual measurement depends on screen placement and site conditions.

Two piezometers with different water elevations define a head gradient and flow from higher head to lower head

Darcy’s Law for One-Dimensional Flow

Specific discharge is proportional to the hydraulic-head gradient for laminar flow through a saturated porous medium.

q=QA=−Kdhdlq = \frac{Q}{A} = -K \frac{dh}{dl}

Variables

SymbolDescriptionUnit
qqSpecific discharge, based on total cross-sectional aream/s
QQVolumetric dischargem³/s
AAArea perpendicular to the chosen flow directionm²
KKHydraulic conductivity of the porous medium and fluidm/s
hhTotal hydraulic headm
llDistance along the flow directionm

Darcy’s Law Assumptions

The minus sign indicates flow toward decreasing head. Hydraulic conductivity is not intrinsic permeability: conductivity also depends on fluid properties. Darcy’s linear relation is appropriate for laminar porous-media flow; the transition criterion depends on the chosen pore-scale Reynolds-number definition and material. Coarse open conduits or high-velocity flow may require a non-Darcy model.

Explore Signed Discharge

Start with the worked-example heads, reverse them, then make them equal. Change one parameter at a time and compare discharge with the gradient and section area.

Darcy flow and hydraulic head

Concept and model scope

Reverse the heads, make them equal, and vary conductivity or section area. Compare flow direction with the head gradient.

Model and limits: Steady one-dimensional laminar flow through a saturated homogeneous porous medium. Positive discharge is left to right. Conductivity is K, not intrinsic permeability. The head profile is a graph, not a water-table prediction.

Controls
45.2 m

Left total head

Elevation plus pressure head at the left section, measured from the same datum as the right head.

Range: 0–80 m. Step: 0.1 m.

43.7 m

Right total head

Increasing this head past the left head reverses the discharge. Equal heads produce zero flow.

Range: 0–80 m. Step: 0.1 m.

2.5 ×10⁻⁴ m/s

Hydraulic conductivity

The displayed multiplier converts to m/s. Doubling K doubles discharge when other inputs are fixed.

Range: 0–10 ×10⁻⁴ m/s. Step: 0.1 ×10⁻⁴ m/s.

150 m

Flow length

Distance between the two head measurement sections. Increasing it reduces the gradient at a fixed head difference.

Range: 50–250 m. Step: 1 m.

6000 m²

Cross-sectional area

Total saturated area normal to flow, including grains and pores. The square inset shows an equivalent section; the head graph is independent of section shape.

Range: 1000–10000 m². Step: 100 m².

Hydraulic head versus distanceBoth heads use a common datum; the line and arrow update from the calculated signed discharge.Head (m)Distance (m)h₁ = 45.2 mh₂ = 43.7 m0150
Equivalent cross sectionA = 6000 m²Side 77.5 m

Discharge Q: 1.500e-2 m³/s

Specific discharge q: 2.500e-6 m/s

Signed head-loss gradient: 0.01000

Direction: Left → right

Effective porosity

The fraction of bulk material volume occupied by interconnected pores that contribute to the flow system represented by the model.

Average Advective Velocity and Travel Time

For uniform steady one-dimensional advection of a conservative tracer, divide specific discharge by effective porosity. This is a pore-volume average, not the path or speed of an individual molecule.

va=q/ne,t=L/∣va∣v_a = q/n_e, \qquad t = L/|v_a|

Variables

SymbolDescriptionUnit
vav_aSigned average linear advective velocitym/s
nen_eEffective porosity contributing to flowdimensionless
ttIdeal advective travel time over distance Ls

A Travel Time Is Not a Contamination Forecast

At zero discharge there is no finite advective arrival time over a nonzero distance. Dispersion, diffusion, sorption, degradation, fracture connectivity and transient flow can change concentration and arrival. Total porosity is not automatically effective porosity.

Transmissivity

Aquifer Transmissivity

For a laterally uniform aquifer of saturated thickness bb and hydraulic conductivity KK, transmissivity represents the ability of the full saturated thickness to transmit water under a hydraulic gradient. Layering or anisotropy may require a more detailed representation.

Transmissivity for a Uniform Layer

Relates hydraulic conductivity to saturated aquifer thickness for a uniform layer.

T=KbT = Kb

Variables

SymbolDescriptionUnit
TTTransmissivitym²/s
KKHydraulic conductivitym/s
bbSaturated aquifer thicknessm

Flow Nets

Flow-Net Interpretation

A two-dimensional flow net combines flow lines with equipotential lines. In a homogeneous isotropic region, the two families intersect approximately at right angles and are drawn to form curvilinear squares. A flow net can estimate seepage and head distribution only when its boundary conditions and material assumptions represent the problem.

Two-Dimensional Flow-Net Discharge

For a homogeneous isotropic section, seepage per unit width is proportional to the head loss per potential drop and the number of flow channels.

qw=KHNfNdq_{\mathrm{w}} = K H \frac{N_f}{N_d}

Variables

SymbolDescriptionUnit
qwq_{\mathrm{w}}Seepage discharge per unit width, distinct from specific discharge qm²/s
KKHydraulic conductivitym/s
HHTotal head difference across the sectionm
NfN_fNumber of flow channelsdimensionless
NdN_dNumber of equipotential dropsdimensionless
Orthogonal Radial Flow Net

This analytical idealization is a plan of an isotropic annulus: equal logarithmic radial intervals produce the equipotential circles. It is not a cutoff-wall section or a site-specific flow solution.

Radial flow lines approach a well and meet concentric circular equipotentials at right angles in an isotropic annulus

Groundwater Testing and Well Response

Hydraulic Conductivity Testing

Constant-head laboratory tests are commonly suited to more permeable specimens; falling-head methods are commonly used for less permeable specimens. Field pumping or slug tests sample a larger volume but require interpretation with assumptions about aquifer geometry, well construction, boundaries, and transient response. Select and interpret the method for the site question.

Constant-Head Permeameter

For a saturated specimen with steady laminar flow, express K from a collected volume over an elapsed time.

K=VLAΔh tcK = \frac{VL}{A\Delta h\,t_c}

Variables

SymbolDescriptionUnit
VVCollected water volumem³
LLSpecimen length along flowm
AASpecimen cross-sectional aream²
Δh\Delta hMaintained head loss across specimenm
tct_cCollection intervals

Pumping and Drawdown

Cone of Depression

Pumping changes hydraulic head around a well. In an unconfined aquifer, the water table may form a drawdown surface; in a confined aquifer, the potentiometric surface declines. The response varies with time and distance and is affected by transmissivity, storage, recharge, boundaries, and neighboring stresses.

Pumping-Induced Drawdown

The unconfined-aquifer section is qualitative; it does not predict drawdown magnitude or radius of influence.

Pumping lowers the water table near a well and produces distance-dependent drawdown

Steady and Transient Response

Steady-state models assume head no longer changes with time at the analyzed locations. Transient models represent head changes during pumping or recovery. Theis-type solutions and steady radial-flow solutions rely on different assumptions; select a model only after checking whether its aquifer, well, boundary, and timing assumptions are reasonable.

Steady Confined Radial Drawdown

The Thiem relation for a fully penetrating well in a homogeneous isotropic confined aquifer with constant transmissivity and a specified fixed-head outer boundary.

s(r)=Q2πTln⁡(R/r),0<rw≤r≤Rs(r) = \frac{Q}{2\pi T}\ln(R/r), \qquad 0 < r_w \le r \le R

Variables

SymbolDescriptionUnit
ssReduction of potentiometric head from its undisturbed valuem
rrRadial distance from well centrem
rwr_wFinite well radiusm
RRSpecified fixed-head boundary radiusm

Transmissivity From Two Observation Wells

For the same steady confined model and two radii r1<r2r_1 < r_2, subtract the drawdowns: s1−s2=Qln⁡(r2/r1)/(2πT)s_1-s_2 = Q\ln(r_2/r_1)/(2\pi T). The common outer reference cancels. Solve this relation for transmissivity only if the observations and pumping rate are consistent with the model assumptions; well spacing r2−r1r_2-r_1 is not a substitute for the radius ratio.

Explore Confined Drawdown

Set pumping to zero, increase it, and compare observations near and far from the well. The boundary radius is an input; the simulator does not predict a radius of influence.

Confined aquifer drawdown

Concept and model scope

Explore steady radial drawdown. Compare the well and an observation point while changing pumping rate, transmissivity and the fixed-head boundary.

Model and limits: Thiem equation s = Q ln(R/r)/(2πT), with a fully penetrating well in a homogeneous, isotropic confined aquifer of constant transmissivity. R is an imposed constant-head boundary, not a predicted radius of influence. Storativity and time do not enter this steady model. The curve is potentiometric head reduction, not a moving water table. Well loss and dewatering are excluded.

Controls
50 m³/day

Pumping rate

Prescribed extraction Q. At zero pumping, drawdown is zero everywhere.

Range: 0–200 m³/day. Step: 1 m³/day.

100 m²/day

Transmissivity

Hydraulic conductivity times confined saturated thickness. Increasing T reduces drawdown at fixed Q, r and R.

Range: 10–500 m²/day. Step: 1 m²/day.

500 m

Fixed-head boundary radius

Assumed outer radius R at which drawdown is zero. It is specified here, not inferred from pumping.

Range: 200–1000 m. Step: 10 m.

10 m

Observation distance

Radial distance r from the well centre. The well radius is fixed at 0.5 m; observations are outside it and inside R.

Range: 1–150 m. Step: 1 m.

Steady confined drawdown versus radial distanceSeparate labelled graph axes show distance horizontally and drawdown positive downward. The curve ends at the finite well radius without clipping its calculated depth.Drawdown (m), downward +02Observation r = 10 m−500 mWell+500 mSigned distance from well centre

At observation: 0.311 m

At well radius 0.5 m: 0.550 m

Illustrative steady model. A computed head below the aquifer roof would violate the confined assumption; aquifer elevation and site-specific evidence are needed to assess that condition.

Confined Well Model Limits

Use consistent time units for discharge and transmissivity. This steady model omits well losses, leakage and storage; it does not use storativity to predict a transient response. Head must remain above the aquifer roof for the fully confined assumption. An unconfined water table needs a model that accounts for changing saturated thickness.

Groundwater Quality and Contaminant Pathways

Source, Pathway, and Receptor

Potential sources include industrial releases, agricultural chemicals, leaking wastewater systems, and saline water. A source can affect a receptor only through a transport pathway; advection, dispersion, diffusion, sorption, degradation, fractures, and density contrasts influence that pathway. Geophysics or a map alone does not establish contaminant identity or concentration.

Groundwater Source–Pathway–Receptor

The plume and receptors are illustrative; contaminant transport requires site-specific hydrogeologic and chemical evidence.

A surface source infiltrates to an aquifer and a conceptual plume follows groundwater flow toward receptors

Engineering Assessment of Groundwater Effects

Excavation Uplift and Water Management

Artesian pressure beneath a low-permeability excavation base can exceed the available resisting weight. For an illustrative unit-area plug with drained upper surface, let hph_p be pressure head at its underside, tpt_p its thickness, γ\gamma its total unit weight and γw\gamma_w water unit weight. Compare underside pressure u=γwhpu = \gamma_w h_p with total plug weight per area γtp\gamma t_p. A weight-only screening ratio is γtp/u\gamma t_p/u; it excludes side shear, structural restraint, seepage gradients and other failure modes and is not a design acceptance check. Distinguish hydraulic uplift or blow-in from undrained shear heave in clay.

Pressure relief, cutoffs, structural resistance or staged excavation may be considered after investigation. Select measures for the site and check settlement, discharge treatment, neighboring wells, redundancy and monitoring. Pumping does not by itself prove that risk is eliminated. Coastal over-pumping can induce salinization; recovery and mitigation depend on the aquifer and cannot be declared universally irreversible.

Groundwater Impact Assessment

Build and update a site-specific groundwater conceptual model before assessing excavation inflow, dewatering, seepage, drawdown, or contaminant transport. Do not infer adequacy from a generic threshold.

Characterize sources, aquifers and confining units, hydraulic boundaries, heads, receptors, and uncertainty. Select field tests and monitoring to answer the project question. Keep unresolved data and criteria on hold until a qualified project review resolves them.

Groundwater Impact AssessmentBuild and update a site-specific groundwater conceptual model before assessing excavation inflow, dewatering, seepage, drawdown, or contaminant transport. Do not infer adequacy from a generic threshold.. Characterize sources, aquifers and confining units, hydraulic boundaries, heads, receptors, and uncertainty. Select field tests and monitoring to answer the project question. Keep unresolved data and criteria on hold until a qualified project review resolves them.. Start → Define project question, receptors, and zone of influence; Define project question, receptors, and zone of influence → Build conceptual model: geology, heads, boundaries, pathways; Build conceptual model: geology, heads, boundaries, pathways → Hydraulic data and uncertainty adequate?; Hydraulic data and uncertainty adequate? — Yes → Evaluate flow, drawdown, inflow, seepage, or transport; Hydraulic data and uncertainty adequate? — No → Plan targeted mapping, tests, sampling, or monitoring; Plan targeted mapping, tests, sampling, or monitoring → Update model from verified observations; Update model from verified observations → Build conceptual model: geology, heads, boundaries, pathways; Evaluate flow, drawdown, inflow, seepage, or transport → Applicable project criteria resolved?; Applicable project criteria resolved? — Yes → Predicted effects conflict with those criteria?; Applicable project criteria resolved? — No → Hold: resolve criteria and decision authority; Hold: resolve criteria and decision authority → End; Predicted effects conflict with those criteria? — Yes → Compare feasible controls; revise and reassess; Predicted effects conflict with those criteria? — No → Document assumptions and verify with monitoring; Document assumptions and verify with monitoring → End; Compare feasible controls; revise and reassess → Build conceptual model: geology, heads, boundaries, pathways

Start → Define project question, receptors, and zone of influence; Define project question, receptors, and zone of influence → Build conceptual model: geology, heads, boundaries, pathways; Build conceptual model: geology, heads, boundaries, pathways → Hydraulic data and uncertainty adequate?; Hydraulic data and uncertainty adequate? — Yes → Evaluate flow, drawdown, inflow, seepage, or transport; Hydraulic data and uncertainty adequate? — No → Plan targeted mapping, tests, sampling, or monitoring; Plan targeted mapping, tests, sampling, or monitoring → Update model from verified observations; Update model from verified observations → Build conceptual model: geology, heads, boundaries, pathways; Evaluate flow, drawdown, inflow, seepage, or transport → Applicable project criteria resolved?; Applicable project criteria resolved? — Yes → Predicted effects conflict with those criteria?; Applicable project criteria resolved? — No → Hold: resolve criteria and decision authority; Hold: resolve criteria and decision authority → End; Predicted effects conflict with those criteria? — Yes → Compare feasible controls; revise and reassess; Predicted effects conflict with those criteria? — No → Document assumptions and verify with monitoring; Document assumptions and verify with monitoring → End; Compare feasible controls; revise and reassess → Build conceptual model: geology, heads, boundaries, pathways

  • Start: terminator
  • Define project question, receptors, and zone of influence: process
  • Build conceptual model: geology, heads, boundaries, pathways: process
  • Hydraulic data and uncertainty adequate?: decision
  • Plan targeted mapping, tests, sampling, or monitoring: process
  • Update model from verified observations: process
  • Evaluate flow, drawdown, inflow, seepage, or transport: process
  • Applicable project criteria resolved?: decision
  • Hold: resolve criteria and decision authority: process
  • Predicted effects conflict with those criteria?: decision
  • Document assumptions and verify with monitoring: process
  • Compare feasible controls; revise and reassess: process
  • End: terminator
Key Takeaways
  • Aquifers transmit water; aquitards retard it, and confined conditions are expressed through a potentiometric surface.
  • Specific yield differs from porosity because some water remains after gravity drainage.
  • Darcy’s law relates discharge to conductivity and hydraulic gradient within its porous-media flow assumptions.
  • Flow nets and pumping models depend on their geometry, boundary conditions, and material assumptions.
  • Groundwater decisions should preserve uncertainty, use project-specific criteria, and verify predicted responses with suitable observations.

References