Week7 - Groundwater Flow Groundwater Flow • Aquifers and...

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Unformatted text preview: Groundwater Flow Groundwater Flow • Aquifers and aquifer properties • Darcy’s equation • Well drawdown drawdown Aquifers Aquifers • Portion of geologic porous material that is able to store able to store and transmit water transmit Aquifer properties Aquifer properties • Porosity (n): fraction of porous material volume (n): fraction of porous material volume that is void (%) • Permeability (k): measure of typical pore size (units of L2) • Hydraulic conductivity (K): ability of the media to transmit water (units of LT-1) • Storage coefficient (S): capacity of porous media to store water, expressed as volume of water stored per unit media volume (dimensionless) 579 porosity remains independent of the support scale until the averaging volume becomes so large that it encompasses portions of the porous medium that have significantly different characteristics; under these circumstances, the porosity again becomes dependent on the size of the support scale. The range within which the porosity is independent of the support scale is given by the interval between the scales L0 and L1 shown in Figure 6.4. Therefore, as long as the support scale is between L0 and L1 , the porosity need not be associated with any particular support scale. The sample volume associated with the support scale L0 is commonly referred to as the representative elementary volume (REV). For sandy soils, an averaging volume with a radius on the order of 10 to 20 grain diameters appears to be adequate for obtaining a stable average (Charbeneau, 2000). The relationship between the porosity and support scale is typical of the relationship between many other hydrogeologic parameters and support scales, although the REV of other parameters may be different. In general, there is no guarantee that a REV exists for any hydrogeologic parameter, and in the absence of a REV the value of the parameter must be associated with a support scale. All earth materials are collectively known as rocks ; and the three main categories of rocks are igneous, sedimentary, and metamorphic rocks. Igneous rocks, such as basalt and granite, are formed from molten or partially molten rock (magma) formed deep within the earth; sedimentary rocks, such as sand, gravel, sandstone, and limestone, are formed by the erosion of previously existing rocks and/or the deposition of marine sediment; and metamorphic rocks, such as schist and shale, are formed through the alteration of igneous or sedimentary rock by extreme heat or pressure or both. Typically, igneous and metamorphic rocks have less pore space and fewer passageways for water than sedimentary deposits. Rocks are further classified as either consolidated or unconsolidated. Solid masses of rock are referred to as consolidated, while rocks consisting of loose granular material are termed unconsolidated. In consolidated formations, original porosity or primary porosity is associated with pore spaces created during the formation of the rock, while secondary porosity is associated with pore spaces created after rock formation. Examples of secondary porosity in consolidated formations include fractures, and solution cavities in limestone. Representative values of porosity in consolidated formations are given in Table 6.1. Table 6.1: Representative Hydrologic Properties in Consolidated Formations Hydraulic conductivity Material Porosity Specific yield (m/d) Sandstone 0.05–0.50 0.01–0.41 10−5 –4 Limestone 0–0.56 0–0.36 10−4 –2000 Schist 0.01–0.50 0.20–0.35 10−4 –0.2 Siltstone 0.20–0.48 0.01–0.35 10−6 –0.001 Claystone 0.41–0.45 — — Shale 0–0.10 0.01–0.05 10−8 –0.04 Till 0.22–0.45 0.01–0.34 10−5 –30 Basalt 0.01–0.50 — 10−6 –2000 Pumice 0.80–0.90 — — Tuff 0.10–0.55 0.01–0.47 — Between 60% and 90% of all developed aquifers consist of granular unconsolidated rocks (Lehr et al., 1988; Todd, 1980), where the porosities are associated with the intergranular spaces deter- 580 mined by the particle-size distribution. In general, granular material is classified by particle size distribution, and many different organizations have established classification standards for use in various disciplines. The United States Department of Agriculture (USDA) soil classification system is one of the most widely used in water-resources engineering and is given in Table 6.2, along with corresponding values of porosity. The porosities of granular materials tend to decrease with Table 6.2: USDA Classification and Representative Hydrologic Properties in Unconsolidated Formations Particle Hydraulic size* Specific conductivity Material* (mm) Porosity yield (m/d) Very coarse gravel 32.0–64.0 — — – Coarse gravel 16.0–32.0 0.24–0.40 0.10–0.26 860–8,600 Medium gravel 8.0–16.0 0.24–0.44 0.13–0.45 20–1,000 Fine gravel 4.0–8.0 0.25–0.40 0.15–0.40 — Very fine gravel 2.0–4.0 — — — Very coarse sand 1.0–2.0 — — — Coarse sand 0.5–1.0 0.20–0.50 0.15–0.45 0.08–860 Medium sand 0.25–0.5 0.29–0.49 0.15–0.46 0.08–50 Fine sand 0.10–0.25 0.25–0.55 0.01–0.46 0.01–40 Very fine sand 0.05–0.125 — — — Silt 0.002–0.05 0.34–0.70 0.01–0.40 10−5 –2 Clay < 0.002 0.33–0.70 0–0.20 < 10−2 *USDA Soil Classification System, gravel classification given by Morris and Johnson (1967). increasing particle size, however, this does not mean that water flows with more resistance through aquifers composed of larger particle sizes. In fact, the opposite is true. Porosities are considered small when n < 0.05, medium when 0.05 ≤ n ≤ 0.20, and large when n > 0.20 (Kashef, 1986). The most common aquifer materials are unconsolidated sands and gravels, which occur in alluvial valleys, coastal plains, dunes, and glacial deposits (Bouwer, 1978). Consolidated formations that make good aquifers are sandstones, limestones with solution channels, and heavily fractured volcanic and crystalline rocks. Clays, shales, and dense crystalline rocks are the most common materials found in aquitards. Aquifers range in thickness from less than 1 m to several hundred meters, and may be long and narrow as in small alluvial valleys, or they may extend over millions of square kilometers and underlie major portions of states (Bouwer, 1984). The depth from the ground surface to the top of the saturated zone of an aquifer may range from 1 m to more than several hundred meters. Geologic Perspective. Geologic characterization of the subsurface environment is regarded as an essential component of most ground-water studies (Stone, 1999). Although geologic characterizations are typically performed by professional geologists, engineers are expected to have sufficient understanding of geologic principles and nomenclature to collaborate with geologists and understand the relationship between the geology and hydrology in the subsurface environment. The science of this relationship is called hydrogeology. The most fundamental aspect of the geologic setting in a subsurface environment is the stratigraphy, which describes the geologic units present and their relationship to each other. The description of each geologic unit (also called stratigraphic kg About and About k and K K = ν Darcy Equation Darcy’s Equation Δh Q = KA L • K: hydraulic conductivity hydraulic conductivity • A: cross sectional area (perpendicular to flow); flow); • Δh/L = hydraulic gradient (head change per unit length of flow) per unit length of flow) • Notice that flow occurs from higher to lower head (basic hydraulics) lower head (basic hydraulics) “Piezometric” Head (h) Head (h) P h= +z ρg • For unconfined aquifers, h is the elevation of the water table (P=0). • For confined aquifers, h is the elevation of the “potentiometric surface”. Components of Head Components of Head • Pressure Head (P/ρg): It’s used to Head It used to represent the pressure at any point within the distribution system. • Elevation Head (z): It’s the physical elevation at any point within the distribution system; it is referred to a datum. Groundwater drawdown near well Groundwater drawdown near a well • Pumping at a well creates a localized at well creates localized depression in the groundwater level (water table) table) • This depression diminishes with distance from the pumping location (r) from the pumping location (r). • Drawdown (s) is defined as the head diff difference between the before and after th pumping. Two piezometers are installed in a confined aquifer with an estimated hydraulic conductivity of 10 m/d and a porosity of 0.2. The reference piezometer is located at point A, and the second piezometer is located at point B, 1 km from point A at an angle of 45◦ clockwise from true north. The water level at B is 10 cm below A. Calculate the seepage velocity along line AB. Explain why this is not the actual seepage velocity in the aquifer. A third piezometer is located in the aquifer at point C, 0.5 km from A at an angle of 140◦ clockwise from true north, and the water level at C is 8 cm below A. Calculate the seepage velocity and Darcy velocity (= specific discharge) in the aquifer. ...
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