3/7/ Basic Types of Rocks. A Brief Review of Physics

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1 A Brief Review of Physics Energy is the capacity to do work. Work is equal to the product of the net force applied to a fluid and the distance through which the force moves: W = F l W is work [M 2 T -2 ] F is force [MT -2 ] l is distance [] Force acting on a body is equal to the product of mass of the body and its acceleration: F = m a m is mass [M] a is acceleration [T -2 ] Weight of a body is the gravitational force exerted on it by the earth: w = m g w is weight [MT -2 ] g is acceleration of gravity [T -2 ] Mass density of a fluid or a solid is its mass per unit volume: m V is density [M -3 ] V is volume [ 3 ] Weight density (specific weight) of a substance is its weight per unit volume: w V g is specific weight [M -2 T -2 ] Pressure is the force applied to a unit area perpendicular to the direction of the force: P F A P is pressure [M -1 T -2 ] A is area [ 2 ] BASIC MECHANICA PROPERTIES Property Symbol Definition SI Unit Dimension of Unit Derived Basic Mass m kilogram kg ength l meter m Time t second s Velocity v v=l/t m/s Acceleration a a=l/t 2 m/s 2 Force F F=ma Newton N kgm/s 2 Weight w w=mg Newton N kgm/s 2 Pressure p p=f/a Pascal N/m 2 kg/(ms 2 ) Work W W=Fl Joule Nm kgm 2 /s 2 Energy E work done Joule Nm kgm 2 /s 2 Mass Density =M/l 3 kg/m 3 Weight Density =w/l 3 N/m 3 kg/(m 2 s 2 ) 3 Basic Types of Rocks Igneous rocks: crystalline solids which form directly from the cooling of magma. Example: granite. Sedimentary rocks: formed from material deposited as sediment by water, wind, or ice and then consolidated by pressure. Example: sandstone. Metamorphic rocks: these are made up of igneous and sedimentary rocks of all ages which have been subjected to intense pressure and/or high heat. Example: marble. 1

2 Porosity of Earth Materials Porosity - the percentage of void space compared to the total volume of soil or rock Vv n 100 V V v is the volume of void space in a sample V is the total volume of the sample Alternative expression: V Vd V d n V V w d b w b d b is the bulk density of the sample d is the particle density of the sample Calculation of Porosity aboratory Determination of Porosity (Heath, 1983) 1. Known volume of material is dried at 105 C until it reaches a constant weight. This removes any moisture from the sample 2. Dried sample is then submerged in a known volume of water and allowed to remain in a sealed chamber until it is saturated 3. The sample is then removed and the volume of water in the chamber is measured 4. The volume of void space (V v ) is equal to the difference between the original water volume and the final volume 2

3 Porosity Ranges for Sediments Well-sorted sand or gravel 25 50% Sand and gravel mixed 20 35% Glacial till 10 20% Silt 35 50% Clay 33 60% Mobile vs. Immobile Porosity Effective porosity is also referred to as porosity of mobile water (percentage of pore space filled with mobile water) Porosity of mobile water plus porosity of immobile water is equal to total porosity Effective vs. Total Porosity Effective Porosity porosity that is available to fluid flow Total Porosity - total porosity in a material Sand: effective porosity close to total porosity Clay: effective porosity may be a lot smaller than total porosity Porosity Type Primary porosity porosity that developed as sediment or rock was deposited or formed. Controlling factors: grain size sorting grain shape packing geometry Cubic packing n=47.65% Secondary porosity porosity that developed subsequent to deposition or formation of sediment or rock. Resulting from dissolution of original materials fracturing Rhombohedral packing n=25.95% 3

4 Grain-size Distribution Specific Yield, and Specific Retention d 60 Specific yield (S y ) is the ratio of the volume of water that drains from a saturated rock or soil due to gravity to the total volume of the rock. d 10 Specific retention (S r ) is the ratio of the volume of water a rock or soil can retain against gravity drainage to the total volume of the rock. C d d u C u (uniform coefficient) C u < 4: well sorted C u > 6: poorly sorted n S y S r Usually S y n in gravel and sand (small S r ) S y << n in clay and silt (large S r ) Retention Processes Darcy s experiment and hydraulic conductivity h1 h2 Q KA h2 h1 or Q KA datum Q h 1 h 2 Q: volumetric flow rate [ 3 T -1 ] h 1 : hydraulic head upstream [] A h 2 : hydraulic head downstream [] K: HYDRAUIC CONDUCTIVITY A: cross sectional area normal to flow direction [ 2 ] : distance between locations where h1 and h2 are measured [] 4

5 Darcy s aw h2 h1 Q KA Alternatively Q q K A dh dl KA dh dl It is much better to use symbol q for specific discharge q is called specific discharge, also Darcy velocity. However, q is not true flow velocity! The true flow velocity, v, also referred to as seepage velocity or pore water velocity is defined as v Q na K dh n dl q n Bulk area is A Area for flow is (n A) K: hydraulic conductivity [T -1 ] (m/day, ft/day, cm/s, ) K is a property of both fluid and porous matrix K kg fluid density [M -3] dynamic viscosity [M -1 T -1 ] g acceleration of gravity [T -2 ] k [intrinsic] permeability [ 2 ] property of porous matrix only commonly used when dealing with multiphase fluids. Note that the notation K i for intrinsic permeability as used in Fetter is more commonly written elsewhere as lower case k. Darcy is a special unit for intrinsic permeability 1darcy cm 2 Hydraulic conductivity of selected rocks (from Heath, 1981) MADE Site Monitoring Network 5

6 Poorly sorted mixture Hydraulic conductivity is of gravel, sand and silt the most critical factor controlling groundwater Well-sorted coarse flow and contaminant sand transport in groundwater Clay Photo and data from Columbus Air Force Base Columbus, Mississippi 6