Chapter 2 Mathematical Model of Groundwater Flow
§2.1 Basic Concepts
1.Underground water
All water beneath the land surface is referred to as underground water（or subsurface water）.The equivalent term for water on the land surface is surface water.Underground water occurs in two different zones.One zone，which occurs immediately below the land surface in most areas，contains both water and air and is referred to as the unsaturated zone.The unsaturated zone is almost invariably underlain by a zone in which all interconnected openings are full of water.This zone is referred to as the saturated zone.
Water in the saturated zone is the only underground water that is available to supply wells and springs and is the only water used reasonably.Recharge of the saturated zone occurs by percolation of water from the land surface through the unsaturated zone.The unsaturated zone is，therefore，of great importance to groundwater hydrology.This zone may be divided usefully into three parts：the soil zone，the intermediate zone，and the upper part of the capillary fringe.
The soil zone extends from the land surface to a maximum depth of a meter or two and is the zone that supports plant growth.It is crisscrossed by living roots，by voids left by decayed roots of earlier vegetation，and by animal and worm burrows.The porosity and permeability of this zone tend to be higher than those of the underlying material.The soil zone is underlain by the intermediate zone（Figure 2.1），which differs in thickness from place to place depending on the thickness of the soil zone and the depth to the capillary fringe.
The lowest part of the unsaturated zone is occupied by the capillary fringe，the sub zone between the unsaturated and saturated zones.The capillary fringe results from the attraction between water and rocks.As a result of this attraction，water clings as a film on the surface of rock particles and rises in small-diameter pores against the pull of gravity.Water in the capillary fringe and in the overlying part of the unsaturated zone is under a negative hydraulic pressure-that is，it is under a pressure less than the atmospheric（barometric）pressure.The water level is the level in the saturated zone at which the hydraulic pressure is equal to atmospheric pressure and is represented by the water level in unused wells.Below the water level，the hydraulic pressure increases with increasing depth.
Figure 2.1 Underground water
2.Confining bed and aquifer
From the standpoint of underground water occurrence，all rocks（includes unconsolidated sediments）that underlie the Earth's surface can be classified either as aquifers or as confining beds（Figure 2.2）.
Figure 2.2 Unconfined aquifer and confined aquifer
A confining bed is a rock unit having very low hydraulic conductivity that restricts the movement of ground water either into or out of adjacent aquifers.
Aquifer is a geologic unit that stores and transmits water，that is，an aquifer is a rock unit that will yield water in a usable quantity to a well or spring.Groundwater occurs in aquifers under two different conditions.Where water only partly fills an aquifer，the upper surface of the saturated zone is free to rise and decline.The water in such aquifers is said to be unconfined，and the aquifers are referred to as unconfined aquifers.Unconfined aquifers are also widely referred to as water-table aquifers.Where water completely fills an aquifer that is overlain by a confining bed，the water in the aquifer is said to be confined.Such aquifers are referred to as confined aquifers or as artesian aquifers.
Unconfined aquifer—Water is in contact with atmospheric pressure—Drill and well hit the water level.Although unconfined aquifers are used for water supply，they are often contaminated by wastes and chemicals at the surface.
Confined aquifer—Recharge up-gradient forces water to flow down and get trapped under an aquiclude.Water is under pressure due to the weight of the up-gradient water and the confinement of the water between“impermeable”layers.Water flows to surface under artesian pressure in an Artesian Well.Confined aquifers are less likely to be contaminated and thereby provide supplies of good quality.
3.Porosity
Porosity is the percentage volume occupied by voids and independent of scale，the ratio of openings（voids）to the total volume of a soil or rock is referred to as its porosity.Porosity is expressed either as a decimal fraction or as a percentage.Thus
Where：n is porosity as a decimal fraction；Vv is the volume of openings（voids）；Vt is the total volume of a soil or rock sample；Vs is the volume of solids in the sample.
Porosity of unconsolidated deposits depends on the range in grain size（sorting）and on the shape of the rock particles but not on their size.Fine-grained materials tend to be better sorted and，thus，tend to have the largest porosities.For example，a pile of marbles and a pile of beach balls have spherical shape and differing sizes；the porosities are identical due to the similar shaping.
4.Permeability
Permeability measures the transmission property of the media and the interconnection of the pores.It is related to hydraulic conductivity and transmissivity.If the pore spaces between individual particles are connected，the water is capable of movement，both laterally and under gravity.Thus，although sandstone and mudstone are both quite porous，sandstone is permeable while mudstone is impermeable.
Good aquifer=High porosity+High permeability.For example，sand and gravel，sandstone，limestone，fractured rock，basalt.
Aqiuiclude，confining bed，aquitard—“Impermeable”unit forming a barrier to groundwater flow.For example，granite，shale，clay.
5.Specific yield and specific retention
Porosity tells us the maximum amount of water that a rock can contain when it is saturated.However，it is equally important to know that only a part of this water is available to supply a well or a spring.Hydrologists divide water in storage in the ground into the part that will drain under the influence of gravity（called specific yield）and the part that is retained as a film on rock surfaces and in very small openings（called specific retention）.The physical forces that control specific retention are the same forces involved in the thickness and moisture content of the capillary fringe.
Specific yield tells how much water is available for man's use，and specific retention tells how much water remains in the rock after it is drained by gravity.Thus
Where：n is porosity；Sy is specific yield；Sr is specific retention；Vd is the volume of water that drains from a total volume of Vt；Vr is the volume of water retained in a total volume of Vt；and Vt is total volume of a soil or rock sample.
In coarse sand the specific retention is low and the specific yield high.Fine clay has a high retention rate and a low specific yield，even though its porosity is quite high.