6 Groundwater

KNS 3143 Engineering HydrologyHydrological Cycle

KNS 3143 Engineering Hydrology

KNS 3143 Engineering HydrologyGroundwater

Chapter 6


KNS 3143 Engineering HydrologyOccurrence of GroundwaterRainfall where does it go?Overland flowAbsorbed by surface layer of soilWater infiltrates into soil may:EvaporatesFlow close to surface as throughflowPercolate under gravity as groundwater


KNS 3143 Engineering HydrologyWhat is groundwater?Water in the saturated zone, below the water tableVertical Zones of Subsurface Water


KNS 3143 Engineering HydrologyGround zones4 main zones:1. Soil zone unsaturated except during heavy period of infiltration2. Intermediate zone between soil & capillary zone, connects/links btw a near-ground surface region and the near-water-table region through which infiltrating fluids must pass.3. Capillary zone almost all the pores are full of water4. Saturated zone

Why is groundwater important?in some areas, it is the only source of waterIt represents a major proportion of the earths usable water resources: freshwater


KNS 3143 Engineering HydrologyAquiferSaturated permeable geologic unit which can transmit significant quantity of water under ordinary hydraulic gradients Most common aquifer materials: unconsolidated sands and gravelsoccur in alluvial valleys, old stream beds covered by fine deposits (buried valleys) and coastal plains.other materials:sandstones and cavernous limestonesThe study of water flow in aquifers and the characterization of aquifers is hydrogeology



Schematic cross section illustrating unconfined and confined aquifers (Bedient, 2002)


KNS 3143 Engineering HydrologyTypes of AquifersUnconfined AquiferAlso called free, phreatic or water-table aquifersUpper surface of the zone of saturation is under atmospheric pressure and is constituted by the water table Water level does not rise above the water table

Confined AquiferGroundwater is confined under pressure greater than atmospheric by overlying impervious or semipervious strataA confined aquifer is sandwiched between two layers of much less pervious material, called the aquicludes and aquitardsAquicludes are saturated impermeable geologic unit which is incapable of transmitting significant quantity of water under ordinary hydraulic gradients Aquitards are semi permeable confining layer; other terms: confining layer


Specific storage (Ss), storativity (S), specific yield (Sy) and specific capacity are material physical properties that characterize the capacity of an aquifer to release groundwater from storage in response to a decline in hydraulic head; sometimes referred to as "storage propertiesIn the field of hydrogeology, these properties are often determined using some combination of field hydraulic tests (e.g., aquifer tests) and laboratory tests on aquifer material samples6 basic physical properties of fluid and porous media to describe the hydraulic aspects of saturated groundwater flowfluid: density, ; viscosity, ; compressibility, media: porosity, n or void ratio, e; permeability, k; compressibility, KNS 3143 Engineering HydrologyPhysical Properties of Aquifers


KNS 3143 Engineering HydrologyPhysical Properties of AquifersSpecific storage, Ssthe amount of water that a portion of an aquifer releases from storage, per unit mass or volume of aquifer, per unit change in hydraulic head, while remaining fully saturatedSs = g( + n)

Storage coefficient or Storativity, SDefined as the volume of water yielded per unit horizontal area and per unit drop of water table (for unconfined aquifers) or piezometric surface (for confined aquifers) S = Ssb = gb( + n)The S value of confined aquifers are relatively small and often in the range of 0.01 to 0.00005


Specific yield, Sy the drainable porosity, is a ratio, less than or equal to the effective porosity, indicating the volumetric fraction of the bulk aquifer volume that a given aquifer will yield when all the water is allowed to drain out of it under the forces of gravity:

where Vwd is the volume of water drained VT is the total rock or material volumeprimarily used for unconfined aquifers, since the elastic storage component, Ss, is relatively small and usually has an insignificant contributionSy of unconfined aquifers may yield from a few percent for fractured rock to as much as 30% for unconsolidated materials of uniform particle sizeKNS 3143 Engineering HydrologyPhysical Properties of Aquifers


KNS 3143 Engineering HydrologyHydraulic conductivity, KDepends on a variety of physical factors and is an indication of an aquifers ability to transmit watere.g. sand aquifers have K values many orders of magnitude larger than clay unit Table 1 indicates representative values of K for a variety of materialsVelocities and flow rates also vary over the same range, as expressed by Darcys Law v = Ki or Q = AKiThe permeability of a porous medium is the ease with which fluid can flow through the medium (also referred to as intrinsic permeability). It is dependent only on the physical properties of the porous medium.

Physical Properties of Aquifers


KNS 3143 Engineering HydrologyHydraulic Conductivity, kIntrinsic permeability, k can be related to hydraulic conductivity, K by

where = dynamic viscosity [L2 T-1] = fluid density [M L-3]g = gravitational constant [L T-2]

Table 1 Representative Values of Hydraulic Conductivity (K)

Unconsolidated SedimentsHydraulic Conductivity K (cm s-1)Well-sorted gravelWell-sorted sands and glacial outwashSilty sands, fine sandsSilt, sandy silt, clayey sands, tillClay1 to 10-210-1 to 10-310-3 to 10-510-4 to 10-610-6 to 10-9Note on units: 1 m s-1 = 1 x 102 cm s-1 = 3.28 ft s-1 = 2.12 x 106 gal d-1 ft-2


KNS 3143 Engineering HydrologyTransmissivity, TOften used in ground water hydraulics (confined aquifers) Rate at which water is transmitted through its unit width under a unit hydraulic gradientDefined as the product of K and the thickness of aquifer, b Unit of T is m2 d-1 (or ft2 d-1) Physical Properties of Aquifers


KNS 3143 Engineering HydrologyDarcys LawGroundwater moves in horizontal or lateral directions at velocities generally range from 1 to 500 m yr-1 Analyzing subsurface movement of water, actual paths of water molecules as they flow through the pores, cracks and crevices of other aquifer material are taken as smooth paths as if the water molecules moved right through the solid particles.


KNS 3143 Engineering HydrologyThe Darcy velocity is expressed as:

where= Darcy velocity (m d-1) K= Hydraulic conductivity of the aquifer material (m d-1)= Hydraulic gradient (change of hydraulic head along the length of the flow path

Darcys Law (contd)


KNS 3143 Engineering HydrologyVertical cross section of groundwater flow with linear, parallel streamlines

, p0 set to 0

hi = head pressureL = distancezi = elevation

Darcys Law (contd)Piezometer


KNS 3143 Engineering HydrologyUniform flow does not change with distance (notice the straight and parallel streamlines) Nonuniform flow changes with distance and streamlines may curve, diverge or converge 1-D flow is assumed to be steady. If the flow changes with time, the flow is called unsteady or transient.Darcys Law (contd)


KNS 3143 Engineering HydrologyIf piezometers are placed at two points on a streamline (points 1 and 2), the velocity of the groundwater can be calculated with the equation:

v= Darcy velocity of waterh1= Pressure head at point 1 z1= Elevation head at point 1h2= Pressure head at point 2z2= Elevation head at point 2L= distance of flow between points 1 and 2 as measured along streamline lengthK= hydraulic conductivity of soil or aquifer materialDarcys Law (contd)


KNS 3143 Engineering HydrologyThe groundwater flow, Q, is given by:

where Q= flow rate (m3 d-1)A= area normal to flow direction (m2)v= Darcy velocity (m d-1)K= hydraulic conductivity (m d-1)i = hydraulic gradient Darcys Law (contd)


KNS 3143 Engineering HydrologyValidity of Darcys LawValid only for laminar flow velocities are small and water molecules travel in smooth paths more or less parallel to the solid boundaries of the pores

Not valid water flows through extremely fine-grained materials (e.g. colloidal clays)where the medium is not fully saturated


KNS 3143 Engineering HydrologyGroundwater PotentialThe potential yield of groundwater at any given location depends to a large extend, on the types of geologic formation in the area and thus on the physical properties of the formation (aquifer).2 conditions:Steady Flow ConditionTransient Condition


KNS 3143 Engineering HydrologySteady Flow ConditionConfined AquiferFlow system around a pumped or flowing well in a confined aquifer can be analyzed with the Dupuit-Forchheimer assumption of horizontal flowAt steady state, the flow in the aquifer comes from infinitely far away, so that the flow across and imaginary cylindrical surface in the aquifer at radius r from the pumped well is the same as the flow Q from the well. Thus,

whereQ = flow from well (m3 d-1)K = hydraulic conductivity of aquifer (m d-1)r = radial distance from well center (m)b = thickness of aquifer (m)dh/dr = hydraulic gradient (slope of piezometric head h at distance r from the pumped well) (2rb: surface area of cylinder)


KNS 3143 Engineering HydrologyConfined AquiferGeometry and symbols for pumped well in confined aquifer


KNS 3143 Engineering HydrologyConfined AquiferThe piezometric head h is expressed with respect to the bottom of the aquifer. Rearangging and integrating the two points at different distances from the well yields: or [Thiem equation]

where T is the transmissivity of the aquifer

h0 is the background hydraulic headh-h0 is the drawdown at the radial distance r from the pumping well Q is the discharge rate of the pumping well (at the origin)R is the radius of influence, or the distance at which the head is still h0


KNS 3143 Engineering HydrologyUnconfined AquiferComponent b is replaced by the height h of the water table above the lower boundary of the aquifer yielding:

Separating variables and integrating between r2, h2 and r1, h1 then gives


KNS 3143 Engineering HydrologyUnconfined AquiferGeometry and symbols for pumped well in unconfined aquifer


KNS 3143 Engineering Hydrologyb. Transient FlowEquations developed for transient well flow normally show how the drawdown s of the piezometric surface or water table (s = H-h) is related to time of pumping the well. The equations also contain the storage coefficient (or specific yield) S of the aquifer and time of pumping.


KNS 3143 Engineering HydrologyConfined AquifersTheis equation describes transient (non-equilibrium) groundwater flow towards a fully penetrating well in the confined aquifer the basis for practically all methods of pumping test analysis Using the equation, transmissivity T, and storage coefficient S, can be determined from the drawdown measurements without having to wait for the stabilization of pumping water levels as in the case of steady state methods Theis equation gives drawdown s or h0 - h at any time after beginning of pumping:

where Q = pumping rate kept constant during the testW(u) is called the well function of uu is a dimensionless parameter given by:

wheret = time since beginning of pumpingwhilst, W(u) values for various values of parameter u are usually presented in table forms (Table 2)


Class ExerciseGiven k = 14.9m/day storavity = 0.0051 thickness = 20.1m Q = 2725m3/dayWhat is h0-h at r = 7m after 1 day?



Class ExerciseWhat if the transmissivity is 600 m2 d-1 ? (Ans: h0-h = 3.11 m)

What if the transmissivity is 300 m2 d-1 and storativity is 0.01? (Ans: h0-h = 5.24 m)KNS 3143 Engineering Hydrology


KNS 3143 Engineering HydrologySimplified SolutionA simplified solution to the Theis equation was developed by Cooper and Jacob (1946) which is applicable for small u (u < 0.01)

The equation enables direct calculation of s in relation to r and t for given values of Q, T, and S.


KNS 3143 Engineering HydrologyUnconfined AquifersExact solution of transient flow equation for unconfined aquifers is difficult because T changes with t and r as the water table declines during pumpingHowever, if s is small compared to H, the Theis and Cooper and Jacob solutions can be used to determine hydrological properties of unconfined aquifers


KNS 3143 Engineering HydrologySafe YieldThe rate at which the groundwater can be withdrawn without causing a long-term decline of the water table or piezometric surface. Equals to average replenishment (recharge) rate of the aquifer.Excessive groundwater pumping occurs so often, however, that the definition of safe yield has been stretched beyond the true hydrologic meaning of the term.In areas of limited water resources, safe yield is defined as the economic safe yield, which is the rate at which groundwater can be withdrawn without danger of the wells drying up before an adequate tax base for the more expensive water supplies has been established.Another interpretation of safe yield could be the legal safe yield, which is the rate at which a well owner can pump groundwater without getting involved in legal action.In its broadest sense, safe yield can be considered as the rate at which groundwater can be withdrawn without producing undesirable effects.


KNS 3143 Engineering HydrologyUndesirable EffectsSubsidence of the land surfaceIf the water table is permanently lowered, the intergranular pressure at any given depth would be increased to cause the void ratio of the porous medium (soil) to decrease sufficiently, and thus resulting in the subsidence of the land surface. This may lead to some detrimental effects on life and property.

Saltwater intrusionIn coastal aquifers, the interface between heavier saltwater and lighter freshwater may migrate inland due to excessive pumping, thus affecting the quality of the well water.


Thank YouKNS 3143 Engineering Hydrology


6 Groundwater

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