Assessment of Hydraulic Conductivity of Soil

Assessment of Hydraulic Conductivity of Soil Hydraulic Conductivity Soil Chapter 1 Introduction Hydraulic conductivity or permeability of a soil is one important soil properties used in geotechnical engineering. It can be seen from the difficulty in measuring accurate and reliable values of hydraulic conductivity. Hydraulic conductivity of soil is basically the capacity of water to let water to pass through the pores or voids in the soil. There are many methods developed in order to measure the hydraulic conductivity of soil; both laboratory and in-situ field methods. Some of the common laboratory methods are the constant-head test and falling head test. On the other hand, the common in-situ field methods are pumping well test, borehole tests (e.g. slug test, variable head test), infiltrometer tests and using porous probes (BAT permeameter). All these in-situ field test methods were used to measure the hydraulic conductivity of subsoil for both saturated and unsaturated media. One other in-situ field measurement method that has been introduced is the Two-Stage Borehole (TSB) test, also known as the Boutwell permeameter test. This testing method is commonly used to test a low hydraulic conductivity soil such as compacted clay liner used in landfill barrier system or covers used at waste disposal facilities, for canal and reservoir liners, for seepage blankets, and for amended soil liners. The advantage of using this method is that it can be used to measure both the vertical and horizontal hydraulic conductivity values of soil, kv and kh respectively. One other advantages of using this method is that it can be used to measure the rate of infiltration of water or other fluid into a large mass of soil which can represent the tested site. However, the application of the TSB/Boutwell permeameter test for natural soil or other soils having a higher permeability value has been limited. This report will discuss the theory behind the TSB/Boutwell permeameter test and the application of this method on natural soil. The methodology of this test will also be included in this report. In addition to the standard TSB setup, this report will also discuss the modification made to the standard TSB test which can be easily and quickly installed in shallow boreholes for subsequent testing. The methodology and results from the modified setup will also be included. The results from both the standard and modified setup will then be compared. Objectives The objectives of this project is summarised into four stages. In the first stage, the objective is to measure the hydraulic conductivity of the soil using the standard TSB/Boutwell permeameter setup. The second stage involves the modification of the standard TSB/Boutwell Permeameter setup. The aim is to obtain a simple installation setup which can be easily and quickly installed in shallow boreholes for subsequent testing. In the third stage, the objective is to test the modified TSB/Boutwell Permeameter test in the field. This is done by carrying out a series of tests in varied subsurface media at the assigned site location. The results from both the standard and modified TSB/Boutwell Permeameter test will be compared. The last stage of the project consists of particle size analysis of the soil obtained from site. The results from the two setups will again be compared to the hydraulic conductivity values obtained from the derivation of the Particle Size Distribution curves. The tasks that are done in this project include: The review of TSB/Boutwell Permeameter methodology Developing the modify TSB/Boutwell Permeameter Completion of field tests using the TSB/Boutwell Permeameter Collection of soil samples and subsequent particle size analysis Chapter 2 Literature Review 2.1 Soil Water Soils are consists of separate solid particles. The pore spaces between the solid particles are all interconnected which mean that water is free to flow through these interconnected pore spaces (Whitlow, 2001). The water will flow from a higher pore pressure point to a lower pore pressure point. The pressure of the pore water is measure relatively to the atmospheric pressure. The level in which the pressure is zero (i.e. atmospheric) is defined as the water table (Craig, 2004). The soil above the water table is assumed to be unsaturated and the soil below the water table is assumed to be fully saturated. The level of water table changes in relation with climate conditions and can also be affected by any constructional operations (Craig, 2004). It is usual to express a pressure as a pressure head or head which is measured in metres of water when considering water flow problems. According to Bernoullis equation, the total head at a point in flowing water can be given by the sum of three head components; pressure head (u/ÃŽ ³w), velocity head (v2/2g) and elevation head (Z). This relationship is illustrated in the equation below: (Equation 1) where; h = total head u = pressure v = velocity g = acceleration due to gravity ÃŽ ³w = unit weight of water Z = elevation head However, since the seepage velocities in the soil are so small due to the high resistance to flow offered by the granular structure of the soil, the velocity head is often omitted from the equation (Whitlow, 2001). The total head at any point is then can be adequately represented by: (Equation 2) In saturated conditions, the one-dimensional water flow in soil is governed by the Darcys Law, which states that the velocity of the groundwater flow is proportional to the hydraulic gradient: (Equation 3) where; v = velocity of groundwater flow = flow/area (q/A) k = coefficient of permeability or hydraulic conductivity (constant) i = hydraulic gradient = head/length (h/L) The empirical validity of Darcys Law depends heavily on the hydraulic conductivity, k, which must be carefully determined so that it can represent the soil mass (Azizi, 2000). The different practical methods that can be used to measure the hydraulic conductivity will be discussed in Section 2.3. It is important to study the flow of water through porous media in soil mechanics. This is necessary for the estimation of underground seepage under various conditions, for investigation of problems involving the pumping of water for underground constructions, and for making stability analyses of retaining structures that are subjected to seepage forces (Das, 2006). Hydraulic Conductivity (Coefficient of Permeability) Hydraulic conductivity, k, of a soil is the capacity of the soil to allow water to pass through it. The value of hydraulic conductivity is often used to measure the resistance of a soil to water flow. Hydraulic conductivity has units of length divided by time. The most common unit used of measurement is meter per second (m/s). Although hydraulic conductivity has the same unit as those to describe velocity, it is not a measure of velocity (Coduto, 1999). Importance of Hydraulic Conductivity Hydraulic conductivity is a very important parameter in geotechnical engineering or in determining the widespread of contamination. This can be seen in the difficulties in measuring it. This is because hydraulic conductivity can varies from one point in a soil to another, even with small changes in the soil characteristics. It is also, as mentioned in the previous section, influenced by the viscosity and unit weight of the fluid flowing through the soil. Hydraulic conductivity is also dependent to the direction of flow which means that the vertical hydraulic conductivity would not be the same as the horizontal hydraulic conductivity. This condition of the soil is said to be anisotropic. Studies that have been made indicate that the value of vertical hydraulic conductivity (Kv) of a soil is usually higher than the horizontal hydraulic conductivity (Kh) in one or two order of magnitude (Chen, 2000). Some applications in which information on hydraulic conductivity is very important are in modelling the groundwater flow and transportation of contaminants in the soil. Hydraulic conductivity data of a soil is also important for designing drainage of an area and in the construction of earth dam and levee. In addition, it is very important in tackling most of the geotechnical problems such as seepage losses, settlement calculations, and stability analyses (Odong, 2007). Factors Affecting Hydraulic Conductivity The hydraulic conductivity of a soil depends on many factors. The main factor that affecting the value of hydraulic conductivity is the average size of the pores between particles in the soil, which in turn is related to the distribution of particle sizes, particle shape and roughness, pore continuity, and soil structure (Craig,2004). In general; the bigger the average size of the pores, the higher the value of hydraulic conductivity is. The value of hydraulic conductivity of a soil that has a presence of small percentages of fines will be significantly lower than the same soil without fines. In the other hand, the presence of fissures in clay will result in a much higher value of hydraulic conductivity compared to that of unfissured clay (Craig, 2004). The range of the hydraulic conductivity value is very large. Table 1 below illustrates the range of hydraulic conductivity which differs from one soil type to another which is mainly due to the different average size of the pores between the soil particles. Table 1 Range of hydraulic conductivity values (m/s) with different soil type (Whitlow, 2001) 102 101 1 10-1 Clean gravels Very good drainage 10-2 10-3 10-4 Clean sands Gravel-sand mixtures 10-5 10-6 Very fine sands Silts and silty sands Fissured and weathered clays Good drainage Poor drainage 10-7 10-8 10-9 Clay silts (>20% clay) Unfissured clays Practically impervious The hydraulic conductivity is also dependent to viscosity and density of water in which both are affected by temperature. It is therefore conclude that the value of hydraulic conductivity will then be affected by changes in temperature. Theoretically, it can be shown that for laminar flow and saturated soil condition the relationship between temperature and hydraulic conductivity: (Equation 4) Where; ÃŽ ³w= unit weight of water ÃŽ · = viscosity of water K = absolute coefficient (units m2). This value is dependent on the characteristic of the soil skeleton. Since most of the laboratory graduations were standardised at 20C, the value of hydraulic conductivity at this temperature is taken as 100% (Craig, 2004). Other value of hydraulic conductivity at 10C and 0C are 77% and 56% respectively (Craig, 2004). Hydraulic Conductivity Tests Most of the tests for measuring hydraulic conductivity measured one average value of hydraulic conductivity. However, some tests measured both the vertical and horizontal hydraulic conductivity values to obtained more accurate estimation. There are numbers of experiments and test that can be done to measure the hydraulic conductivity of a soil. These tests to measure the hydraulic conductivity can be done both in the laboratory and in the field. The following sections will briefly discussed the most common laboratory and in-situ tests practiced today to measure the hydraulic conductivity of a soil. Although with all the various tests developed to measured the hydraulic conductivity, there are uncertainties arise on how the soils that being tested represent the whole soil condition at the site of interest. It is therefore a good practice to perform different tests and comparing the results obtained. Laboratory Permeability Tests One problem with laboratory tests is that the samples collected do not adequately represent the detailed conditions of the soil, e.g. fissures, joints or other characteristics in the site of interest. Even with carefully conducted tests and good sampling techniques, it is impossible to obtain a very accurate result. The results typically have a precision of about 50% or more (Coduto, 1999). It is therefore important to take this into consideration if any construction activities or contamination remediation operations to be perform at the site of interest. Constant Head Permeability Test The constant head test is used to measure the hydraulic conductivity of more permeable soils such as gravels and sands which have a hydraulic conductivity value of 10-4 m/s (Whitlow, 2001). The equipments used for this test is called a constant head permeameter. A schematic illustration of this equipment is shown in Figure 2.1. The constant head permeameter was developed base on the basic idea of Darcys Law (Equation 3). The soil sample is contained in a cylinder of cross-sectional area A. Continuous water supply is let to flow from a tank to the sample to maintain a constant head. The water that flow through the sample is collected in a collection jar or container and the discharge through the sample is measured by calculating the volume of the water in the collection container over a period of time t. h Figure 2.1 Schematic diagram of Constant Head Permeameter (www.geology.sdsu.edu) The hydraulic conductivity, k of the tested soil is then calculated by: From equation 3: (Equation 5) Where; Q = the discharge through the sample (m3/s) L = the length of the sample (m) A = cross-section of the sample (m2) h = hydraulic head (m) The above diagram shows a simple setup of the constant-head permeameter. Other setup is also available which make use a pair of standpipes to measure the pore pressure and potential at two points. This is illustrated in Figure 2.2 below. Although both the setups are different, it makes used of the same concepts; Darcys Law. Figure 2.2 Alternative setup of Constant Head Permeameter (Whitlow, 2001) Falling Head Permeability Test The falling head test is used to measure the hydraulic conductivity of less permeable soils such as fine sands, silt and clay. The water flow resistance in these types of soil are very high which unable to measure accurate measurements of hydraulic conductivity if used with constant head permeameter. Undisturbed samples are required to perform laboratory test to measure the hydraulic conductivity of a soil. However, a small degree of disturbance of the sample is accepted as it is very hard to obtain a perfect undisturbed sample. An undisturbed sample can be obtained usually using a U100 sample tube or a core-cutter tube (Whitlow, 2001).The schematic illustration of the falling head test setup is shown in Figure 2.3. Figure 2.3 Laboratory setup of falling head test (Whitlow, 2001) The sample is place in a cylinder container with a wire mesh and gravel filter at both end of the cylinder. The base of the cylinder is left to stand in a water reservoir fitted with a constant level overflow. At the other end, which is the top of the cylinder, it is connected to a glass standpipe of known diameter (Whitlow, 2001). These standpipes are then filled with de-aired water and it is allow to flow through the soil sample. The height of the water in the standpipe is measured at several time intervals. The test is then repeated using standpipes of different diameters. It is a good practice to take note of the initial and final unit weight and water content of the sample to get additional information about the properties of the sample (Whitlow, 2001). The hydraulic conductivity of the sample is then calculated from the results obtained from the tests. The Darcys Law concept is still used in determining the hydraulic conductivity. The derivation of the hydraulic conductivity for the falling head test is done as follow (Whitlow, 2001). Deriving from Equation 3: With reference to Figure 2.3, if the level of the water in the standpipe fall dh in a time of dt the flow, q will be and the hydraulic gradient, i Therefore; (Equation 6) Where; a = cross-sectional area of the standpipe A = cross-sectional area of the sample When equation 6 is rearranged and integrated, the final equation to calculate the hydraulic conductivity is given as (Equation 7) Particle Size Analysis Particle size analysis is commonly used to classify the physical properties of the soil being tested. This testing method is used for both soil science and engineering purposes (Keller and Gee, 2006). In context of engineering purposes, it is commonly used to define the particle size distributions of the soil. The data obtained from the particle size distributions can then be used to estimate the pore-size classes needed in calculating the hydraulic properties of the soil such as hydraulic conductivity (Keller and Gee, 2006). There are various methods of measuring particle size analysis. Traditional methods include sieving, hydrometer and pipette. Other new techniques are also been developed; one example is laser-diffraction techniques (Eshel et al, 2004). However, particle size analysis is dependent on the technique used for defining the particle size distribution. It is therefore a common practice to do more than one method to define the particle size distribution (Keller and Gee, 2006). The results from all the different methods can then be compared to obtain more representative result. For the traditional particle size analysis methods, two separate procedures are used in order to obtain wider range of particles sizes (Head, 1980). The two procedures are sieving and sedimentation procedures (hydrometer or pipette method). Sieving is used to categorise large particle such as gravel and coarse sand. The particles can be separated into different size ranges using a series of standard sieves. For the finer particles such as silt and clay, sedimentation procedure is used (Head, 1980). Once the particle size distribution is defined from the particle size analysis, the hydraulic conductivity of the tested soil can then be estimated using a number of established empirical equations. However, the applicability of the above equations depends on the type of soil that is being tested. The following paragraphs summarised several empirical equations from previous studies (Odong, 2007). Hazens equation: (Equation 8) Kozeny-Carmans equation: (Equation 9) Breyers equation: (Equation 10) Slitchers equation: (Equation 11) Where; g = acceleration due to gravity v = kinematic viscosity n = porosity of the soil d10 = grain size in which 10% the sample is finer than The estimation of the hydraulic conductivity from these equations required information on the kinematic viscosity v and porosity n of the soil. The kinematic viscosity can be calculated by: (Equation 12) Where; = dynamic viscosity ÃŽ ¡ = density of water The porosity n can be calculated using the empirical relationship below: (Equation 13) Where U is the coefficient of grain uniformity and is given by: (Equation 14) The values of d60and d10 can be obtained from the particle size distribution. d60and d10 represent the grain size for which 60% and 10% of the sample respectively is finer than. In-situ Field Permeability Tests Due to the problems associated with reliability and laboratory tests, as mention in Section 2.3.1, field methods of measuring the hydraulic conductivity should be used to obtain more accurate and reliable measurements. In the field test, the soil disturbances is kept to a minimum level and they usually involves the testing of larger, more representative samples. Although, in term of cost and time, field measurement method is more expensive, it will as well provide more reliable measurement of hydraulic conductivity when dealing with a wide range of soil macro-structural characteristics. Other more economic option of field measurement can also be done. Such example is by performing borehole test, provided the pumping observation sequences are carefully planned and controlled (Whitlow, 2001). Well Pumping Tests This method is more suitable if used to measure hydraulic conductivity in homogenous coarse soil strata (Craig, 2004). The procedure involves the measurement of water that is being pumped out of a well at a constant rate, then observing the effect of these pumping activities to the drawdown of the groundwater level at other wells. The diameter of the well is normally at least 300mm and penetrates to the bottom of the stratum under test (Craig, 2004). The pumping rate and the groundwater levels in two or more monitoring wells are then recorded. The analysis of the results depends whether the aquifer is confined or unconfined. Well pumping test in a confined aquifer In confined aquifer the permeable stratum is squeezed in between two impermeable layers. This is illustrated in Figure 2.4 below. To perform the test, the pumping rate must not be too high to reduce the level in the pumping well below the top of the aquifer. The interface between the top aquifer and the overlying impermeable stratum therefore forms the top stream line (Whitlow, 2001). Figure 2.4 Pumping test in confined aquifer (Azizi, 2000) Figure 2.4 illustrates the arrangement of the pumping well and two other monitoring wells. Two assumptions were made at this point; the piezometric surface is above the upper surface of the aquifer and the hydraulic gradient is constant at a given radius (Whitlow, 2001). In steady state condition, the hydraulic gradient through an elemental cylinder with radius r from the well centres estimated as follow: where; dr = thickness h = height The area in which the water flow, A: where; D = the thickness of the aquifer Substituting the area A into the Darcys Law (Equation 4) will give; Hence: And therefore the hydraulic conductivity is: (Equation 15) In the case that the piezometric level is above ground level, where the water level inside the well inserted into the confined aquifer rises above the ground level, this scenario is called Artesian conditions (Azizi, 2000). This is illustrated in Figure 2.5. Figure 2.5 Artesian conditions (Azizi, 2000) Well pumping test in unconfined aquifer An unconfined aquifer is a free-draining surface layer that allows water to flow through the surface. The permeable stratum is not overlain by an impermeable layer. The piezometric surface is therefore in the same level of the water table. This is illustrated in Figure 2.6 below. The surface layer permeability is very high, thus allowing the water table to fluctuate up and down easily. Figure 2.6 Pumping test in an unconfined aquifer (Whitlow, 2001) Under steady state pumping conditions, the hydraulic gradient i at a given radius is assumed to be constant in a homogenous media. Homogenous unit is where the properties at any location are the same. For instance, sandstone has grain size distribution, porosity and thickness variation within a very small limit (Fetter, 2001). With reference to the arrangement of pumping well and two monitoring wells in Figure 2.6 above, the hydraulic conductivity can be determine by: Deriving from Equation 3: where; Hydraulic gradient i is And area through which the water flow, Then, Thus, hydraulic conductivity for an unconfined aquifer (after integrating the above equation) is (Equation 16) Borehole Permeameter Tests There are many borehole tests developed to determine the hydraulic conductivity of a soil. The most common in-situ borehole tests are as follow: Slug test Two-stage borehole test/ Boutwell Permeameter Variable head test In-situ constant head test Slug test is one of the cheapest in-situ field methods to determine the hydraulic conductivity of a soil. The procedure of this test involves the rapid adding or removing a slug or water into a monitoring well. The slug can be of anything that can displace the volume of the water in the well, e.g. water, plastic tubing capped at both ends, and other material of known volume and can fit into the monitoring well. The rate of rise and fall of the groundwater level is then observed until it reaches an equilibrium state. In a variable head test, a slug is introduced into the monitoring well by either adding in a measured volume of water into the well or other materials mentioned earlier. The rate of water level fall is then measured in time. This is called falling head test. The water can also be removed out from the well by using a bailer or a pump. The rate of water level rise is then measured with time. This is called a rising head test. Depending on the properties of the aquifer and the soil, and the size of the slug used the water can either returns to its original water level before the test quickly or very slowly. For instance, if the porosity of the soil is high then the water level will returns very quickly to its original water level before the test is done. There is also the constant head test. In this test the water level or head is maintained throughout the test at a given level. This is done by adjusting and measuring the flow rate of the water at intervals from start to the end of the test (Whitlow, 2001). The constant head test is said to give more accurate results, provided the water pressure is controlled so that it would not cause fracturing or other disturbance to the soil (Whitlow, 2001). There are several assumptions made for this test: The soil is homogenous, isotropic, uniformly soaked Infinite boundaries Soil does not swell when wetted The expressions use to calculate the hydraulic conductivity for the above tests depend on whether the stratum is unconfined or unconfined, the position of the bottom of the casing within the stratum and details of the drainage face in the soil (Craig, 2004). The horizontal hydraulic conductivity is tend to be measured if the soil is anisotropic with respect to permeability and if the borehole extends below the bottom of the casing. On the other hand, the vertical hydraulic conductivity is often measured if the casing penetrates below soil level in the bottom of the borehole (Craig, 2004). The following expressions are all recommended in BS 5930 to calculate the hydraulic conductivity (Whitlow, 2001). For variable head test: (Equation 17) Or, (Equation 18) For constant head test: Hvorslevs time lag analysis (Equation 19) Gibsons root-time method (Equation 20) where; A20% clay) Unfissured clays Practically impervious The hydraulic conductivity is also dependent to viscosity and density of water in which both are affected by temperature. It is therefore conclude that the value of hydraulic conductivity will then be affected by changes in temperature. Theoretically, it can be shown that for laminar flow and saturated soil condition the relationship between temperature and hydraulic conductivity: (Equation 4) Where; ÃŽ ³w= unit weight of water ÃŽ · = viscosity of water K = absolute coefficient (units m2). This value is dependent on the characteristic of the soil skeleton. Since most of the laboratory graduations were standardised at 20C, the value of hydraulic conductivity at this temperature is taken as 100% (Craig, 2004). Other value of hydraulic conductivity at 10C and 0C are 77% and 56% respectively (Craig, 2004). Hydraulic Conductivity Tests Most of the tests for measuring hydraulic conductivity measured one average value of hydraulic conductivity. However, some tests measured both the vertical and horizontal hydraulic conductivity values to obtained more accurate estimation. There are numbers of experiments and test that can be done to measure the hydraulic conductivity of a soil. These tests to measure the hydraulic conductivity can be done both in the laboratory and in the field. The following sections will briefly discussed the most common laboratory and in-situ tests practiced today to measure the hydraulic conductivity of a soil. Although with all the various tests developed to measured the hydraulic conductivity, there are uncertainties arise on how the soils that being tested represent the whole soil condition at the site of interest. It is therefore a good practice to perform different tests and comparing the results obtained. Laboratory Permeability Tests One problem with laboratory tests is that the samples collected do not adequately represent the detailed conditions of the soil, e.g. fissures, joints or other characteristics in the site of interest. Even with carefully conducted tests and good sampling techniques, it is impossible to obtain a very accurate result. The results typically have a precision of about 50% or more (Coduto, 1999). It is therefore important to take this into consideration if any construction activities or contamination remediation operations to be perform at the site of interest. Constant Head Permeability Test The constant head test is used to measure the hydraulic conductivity of more permeable soils such as gravels and sands which have a hydraulic conductivity value of 10-4 m/s (Whitlow, 2001). The equipments used for this test is called a constant head permeameter. A schematic illustration of this equipment is shown in Figure 2.1. The constant head permeameter was developed base on the basic idea of Darcys Law (Equation 3). The soil sample is contained in a cylinder of cross-sectional area A. Continuous water supply is let to flow from a tank to the sample to maintain a constant head. The water that flow through the sample is collected in a collection jar or container and the discharge through the sample is measured by calculating the volume of the water in the collection container over a period of time t. h Figure 2.1 Schematic diagram of Constant Head Permeameter (www.geology.sdsu.edu) The hydraulic conductivity, k of the tested soil is then calculated by: From equation 3: (Equation 5) Where; Q = the discharge through the sample (m3/s) L = the length of the sample (m) A = cross-section of the sample (m2) h = hydraulic head (m) The above diagram shows a simple setup of the constant-head permeameter. Other setup is also available which make use a pair of standpipes to measure the pore pressure and potential at two points. This is illustrated in Figure 2.2 below. Although both the setups are different, it makes used of the same concepts; Darcys Law. Figure 2.2 Alternative setup of Constant Head Permeameter (Whitlow, 2001) Falling Head Permeability Test The falling head test is used to measure the hydraulic conductivity of less permeable soils such as fine sands, silt and clay. The water flow resistance in these types of soil are very high which unable to measure accurate measurements of hydraulic conductivity if used with constant head permeameter. Undisturbed samples are required to perform laboratory test to measure the hydraulic conductivity of a soil. However, a small degree of disturbance of the sample is accepted as it is very hard to obtain a perfect undisturbed sample. An undisturbed sample can be obtained usually using a U100 sample tube or a core-cutter tube (Whitlow, 2001).The schematic illustration of the falling head test setup is shown in Figure 2.3. Figure 2.3 Laboratory setup of falling head test (Whitlow, 2001) The sample is place in a cylinder container with a wire mesh and gravel filter at both end of the cylinder. The base of the cylinder is left to stand in a water reservoir fitted with a constant level overflow. At the other end, which is the top of the cylinder, it is connected to a glass standpipe of known diameter (Whitlow, 2001). These standpipes are then filled with de-aired water and it is allow to flow through the soil sample. The height of the water in the standpipe is measured at several time intervals. The test is then repeated using standpipes of different diameters. It is a good practice to take note of the initial and final unit weight and water content of the sample to get additional information about the properties of the sample (Whitlow, 2001). The hydraulic conductivity of the sample is then calculated from the results obtained from the tests. The Darcys Law concept is still used in determining the hydraulic conductivity. The derivation of the hydraulic conductivity for the falling head test is done as follow (Whitlow, 2001). Deriving from Equation 3: With reference to Figure 2.3, if the level of the water in the standpipe fall dh in a time of dt the flow, q will be and the hydraulic gradient, i Therefore; (Equation 6) Where; a = cross-sectional area of the standpipe A = cross-sectional area of the sample When equation 6 is rearranged and integrated, the final equation to calculate the hydraulic conductivity is given as (Equation 7) Particle Size Analysis Particle size analysis is commonly used to classify the physical properties of the soil being tested. This testing method is used for both soil science and engineering purposes (Keller and Gee, 2006). In context of engineering purposes, it is commonly used to define the particle size distributions of the soil. The data obtained from the particle size distributions can then be used to estimate the pore-size classes needed in calculating the hydraulic properties of the soil such as hydraulic conductivity (Keller and Gee, 2006). There are various methods of measuring particle size analysis. Traditional methods include sieving, hydrometer and pipette. Other new techniques are also been developed; one example is laser-diffraction techniques (Eshel et al, 2004). However, particle size analysis is dependent on the technique used for defining the particle size distribution. It is therefore a common practice to do more than one method to define the particle size distribution (Keller and Gee, 2006). The results from all the different methods can then be compared to obtain more representative result. For the traditional particle size analysis methods, two separate procedures are used in order to obtain wider range of particles sizes (Head, 1980). The two procedures are sieving and sedimentation procedures (hydrometer or pipette method). Sieving is used to categorise large particle such as gravel and coarse sand. The particles can be separated into different size ranges using a series of standard sieves. For the finer particles such as silt and clay, sedimentation procedure is used (Head, 1980). Once the particle size distribution is defined from the particle size analysis, the hydraulic conductivity of the tested soil can then be estimated using a number of established empirical equations. However, the applicability of the above equations depends on the type of soil that is being tested. The following paragraphs summarised several empirical equations from previous studies (Odong, 2007). Hazens equation: (Equation 8) Kozeny-Carmans equation: (Equation 9) Breyers equation: (Equation 10) Slitchers equation: (Equation 11) Where; g = acceleration due to gravity v = kinematic viscosity n = porosity of the soil d10 = grain size in which 10% the sample is finer than The estimation of the hydraulic conductivity from these equations required information on the kinematic viscosity v and porosity n of the soil. The kinematic viscosity can be calculated by: (Equation 12) Where; = dynamic viscosity ÃŽ ¡ = density of water The porosity n can be calculated using the empirical relationship below: (Equation 13) Where U is the coefficient of grain uniformity and is given by: (Equation 14) The values of d60and d10 can be obtained from the particle size distribution. d60and d10 represent the grain size for which 60% and 10% of the sample respectively is finer than. In-situ Field Permeability Tests Due to the problems associated with reliability and laboratory tests, as mention in Section 2.3.1, field methods of measuring the hydraulic conductivity should be used to obtain more accurate and reliable measurements. In the field test, the soil disturbances is kept to a minimum level and they usually involves the testing of larger, more representative samples. Although, in term of cost and time, field measurement method is more expensive, it will as well provide more reliable measurement of hydraulic conductivity when dealing with a wide range of soil macro-structural characteristics. Other more economic option of field measurement can also be done. Such example is by performing borehole test, provided the pumping observation sequences are carefully planned and controlled (Whitlow, 2001). Well Pumping Tests This method is more suitable if used to measure hydraulic conductivity in homogenous coarse soil strata (Craig, 2004). The procedure involves the measurement of water that is being pumped out of a well at a constant rate, then observing the effect of these pumping activities to the drawdown of the groundwater level at other wells. The diameter of the well is normally at least 300mm and penetrates to the bottom of the stratum under test (Craig, 2004). The pumping rate and the groundwater levels in two or more monitoring wells are then recorded. The analysis of the results depends whether the aquifer is confined or unconfined. Well pumping test in a confined aquifer In confined aquifer the permeable stratum is squeezed in between two impermeable layers. This is illustrated in Figure 2.4 below. To perform the test, the pumping rate must not be too high to reduce the level in the pumping well below the top of the aquifer. The interface between the top aquifer and the overlying impermeable stratum therefore forms the top stream line (Whitlow, 2001). Figure 2.4 Pumping test in confined aquifer (Azizi, 2000) Figure 2.4 illustrates the arrangement of the pumping well and two other monitoring wells. Two assumptions were made at this point; the piezometric surface is above the upper surface of the aquifer and the hydraulic gradient is constant at a given radius (Whitlow, 2001). In steady state condition, the hydraulic gradient through an elemental cylinder with radius r from the well centres estimated as follow: where; dr = thickness h = height The area in which the water flow, A: where; D = the thickness of the aquifer Substituting the area A into the Darcys Law (Equation 4) will give; Hence: And therefore the hydraulic conductivity is: (Equation 15) In the case that the piezometric level is above ground level, where the water level inside the well inserted into the confined aquifer rises above the ground level, this scenario is called Artesian conditions (Azizi, 2000). This is illustrated in Figure 2.5. Figure 2.5 Artesian conditions (Azizi, 2000) Well pumping test in unconfined aquifer An unconfined aquifer is a free-draining surface layer that allows water to flow through the surface. The permeable stratum is not overlain by an impermeable layer. The piezometric surface is therefore in the same level of the water table. This is illustrated in Figure 2.6 below. The surface layer permeability is very high, thus allowing the water table to fluctuate up and down easily. Figure 2.6 Pumping test in an unconfined aquifer (Whitlow, 2001) Under steady state pumping conditions, the hydraulic gradient i at a given radius is assumed to be constant in a homogenous media. Homogenous unit is where the properties at any location are the same. For instance, sandstone has grain size distribution, porosity and thickness variation within a very small limit (Fetter, 2001). With reference to the arrangement of pumping well and two monitoring wells in Figure 2.6 above, the hydraulic conductivity can be determine by: Deriving from Equation 3: where; Hydraulic gradient i is And area through which the water flow, Then, Thus, hydraulic conductivity for an unconfined aquifer (after integrating the above equation) is (Equation 16) Borehole Permeameter Tests There are many borehole tests developed to determine the hydraulic conductivity of a soil. The most common in-situ borehole tests are as follow: Slug test Two-stage borehole test/ Boutwell Permeameter Variable head test In-situ constant head test Slug test is one of the cheapest in-situ field methods to determine the hydraulic conductivity of a soil. The procedure of this test involves the rapid adding or removing a slug or water into a monitoring well. The slug can be of anything that can displace the volume of the water in the well, e.g. water, plastic tubing capped at both ends, and other material of known volume and can fit into the monitoring well. The rate of rise and fall of the groundwater level is then observed until it reaches an equilibrium state. In a variable head test, a slug is introduced into the monitoring well by either adding in a measured volume of water into the well or other materials mentioned earlier. The rate of water level fall is then measured in time. This is called falling head test. The water can also be removed out from the well by using a bailer or a pump. The rate of water level rise is then measured with time. This is called a rising head test. Depending on the properties of the aquifer and the soil, and the size of the slug used the water can either returns to its original water level before the test quickly or very slowly. For instance, if the porosity of the soil is high then the water level will returns very quickly to its original water level before the test is done. There is also the constant head test. In this test the water level or head is maintained throughout the test at a given level. This is done by adjusting and measuring the flow rate of the water at intervals from start to the end of the test (Whitlow, 2001). The constant head test is said to give more accurate results, provided the water pressure is controlled so that it would not cause fracturing or other disturbance to the soil (Whitlow, 2001). There are several assumptions made for this test: The soil is homogenous, isotropic, uniformly soaked Infinite boundaries Soil does not swell when wetted The expressions use to calculate the hydraulic conductivity for the above tests depend on whether the stratum is unconfined or unconfined, the position of the bottom of the casing within the stratum and details of the drainage face in the soil (Craig, 2004). The horizontal hydraulic conductivity is tend to be measured if the soil is anisotropic with respect to permeability and if the borehole extends below the bottom of the casing. On the other hand, the vertical hydraulic conductivity is often measured if the casing penetrates below soil level in the bottom of the borehole (Craig, 2004). The following expressions are all recommended in BS 5930 to calculate the hydraulic conductivity (Whitlow, 2001). For variable head test: (Equation 17) Or, (Equation 18) For constant head test: Hvorslevs time lag analysis (Equation 19) Gibsons root-time method (Equation 20) where; A

Being Tall

7/30/12 â€Å"Six, seven†. That’s what I would say about twice a day when asked how tall I was. I’ve always been tall so over time I had gotten used to and annoyed of this question and I would usually make these feelings evident in the tone of my response. However, it wasn’t the only response I was used to giving. â€Å"I don’t have it†. That’s what I would say about twice a day when asked where my homework was. †C†. That’s what I would say when my friends asked me how I did on the big test. I repeated the same answers over and over again but never really thought about them.Over the past year I began to question these responses and came to the conclusion that they were the wrong answers. I wasn’t lying about my height or my homework, or my grades or my studying habits, but ever since I started to think about these questions I’ve been able to change the answers. I haven’t gotten any shorter or mor e intelligent but by actually thinking about the question I’ve been able to give the correct answer. I started to realize that I was being asked the same questions over and over around sixth grade.I wasn’t even thinking about high school back then let alone college and beyond so I still had some time to figure out the right answers to these questions. â€Å"Wow do you play basketball? † Teachers would ask as they saw me struggle to fit through the doorway. â€Å"Uhh yeah† I would flatly reply. â€Å"Why didn’t you study, you knew you had a test†. â€Å"I don’t know,† I wasn’t even thinking about what those words meant but it was still just the practice round for the real thing so I still had time to find the right answers.I was explicitly warned when high school rolled around that â€Å"it counts now†. It was spelled out to me multiple times that high school was the real deal and even my Freshman grades would coun t towards college. I was also told that I wasn’t done growing yet and I would only be getting taller. I wasn’t thrilled about either of these facts, but instead of using my height to my advantage or taking school seriously I continued to wander through my life getting increasingly tired of the questions I was being asked. Do you even want to go to this school? † â€Å"Yeah, yeah of course† I would jadedly reply, solely to humor the asker. â€Å"How great is it to be that tall? † â€Å" Yeah its pretty great, ha-ha† I would say politely, but emptily none the less. As my high school career continued and the college clock kept ticking I failed time and time again to find the right answers to these questions. Around the middle of my junior year the college process had begun and I had decided to go visit a college over March vacation.As I got out of the car I immediately fell in love with the school, the campus was perfect and the students looked like they were straight out of a brochure. All the school’s features were amazing and while on the tour I began to grow increasingly excited about the school and the idea of college. As the tour came to a conclusion all the prospective students gathered in a room to hear a lecture about the application process from an admissions officer. As I stood amongst the other students I realized that I was the tallest one there.I was used to being to the tallest person at a given place but this was different. I realized that because of my height, I stood out, but in a good way; all the admissions officers and faculty noticed me before the other kids there. I saw my height for what it really was: and untapped advantage I had been given. I realized that when people were asking me how tall I was, it was because they were astounded, almost impressed at my height. As I happily chewed on this realization, I was slapped across the face by a second epiphany.As the speaker went more into the ap plication process, he began to talk about the school’s average GPA for high school students; my GPA wasn’t even remotely close to this average. â€Å"They just boost those numbers up for the presentation† I lied to myself â€Å"I’m sure everyone else here is just as shocked by those averages† I looked around and literally every other student nodded in agreeing upon hearing the numbers. My separation from the group continued as the other students began to ask questions like â€Å"Are 3 honors courses enough or are you looking for more in an applicant? and â€Å"I only have a 3. 5 GPA but I take six courses, is that taken into consideration? † I started to feel something I had never felt before, an impending sense of doom that came over me like a tidal wave as I started to mentally panic that I wasn’t going to end up here, that I had thrown away a golden opportunity that was given to me. The feeling was sharp and it stung. I felt sick to my stomach on the ride home as I wallowed over the idea of not ending up at college at all. As I continued to think this over at home I came to the onclusion that this could be a good thing, I should take this realization and use it to turn my grades around with the little time I had left. I thought about the questions I had always been asked and realized that the answers I grew accustomed to giving were not in fact the right ones. I remembered hearing an old proverb that now seemed to be directly speaking to me: â€Å"No matter how far you have traveled down the wrong road, turn back. † Turn Back. That night I decided to turn back, even though I had traveled so far down the wrong road.When I came back to school after the vacation I felt stronger than ever, I was so ready to attack school. The second day I was ready to hear those oh so familiar words: â€Å"Where is your homework? † It was a small homework assignment and the teacher undoubtedly expected me to have b lown it off. â€Å"Right here† I proudly retorted to the impressed teacher. Later that day a man at the gas station asked me if I was a basketball player. Again, I proudly said that I was and made a friendly joke about having a tough time with it because I’m so short.As the semester went on I continued to walk towards the right path, correctly answering life’s questions. Every night as soon as I got home I would sit down and complete every homework assignment with consciousness and pride as opposed to half-heartedly completing three or four out of five assignments. With the new found knowledge that people naturally notice and look up to me, I am setting a good example around the campus for others to follow, from cleaning up trash in the student center to starting a new club. A began to find myself on the right road, even though I was a little late.My hard schoolwork paid off when my grades landed me on the honor role for the first time. I also decided to put my size to good use by playing football in the fall of my senior year. With all this being said, I am the first one to admit that I was the definition of a late bloomer academically. Having already experienced low academic performance I can honestly say that I want to excel through college and beyond, not just with grades, but in all aspects of life. In the end the answers are what count, not the questions, and I’m ready to answer any question life gives me, correctly.

Nathaniel Hawthorne and His Religious Connotations in His...

Nathaniel Hawthorne and His Religious Connotations in His Works Nathaniel Hawthorne is noted for his religious connotations in his works. Young Goodman Brown, The Ministers Black Veil and The Birthmark is three exemplary stories. His writing technique uses ambiguity in that the reader is opened to many different ways of interpretation. In respect to religious methodology the main characters of these short stories all encounter some sort of revelation. In Young Goodman Brown the main character leaves his pure wife Faith adorned in pink ribbons symbolizing her innocent nature on a short but very intriguing journey. His walk begins in the woods adjacent to Salem Village, and with him he is accompanied by a devilish character. It†¦show more content†¦All that Brown can say to his acquaintance is That old woman taught me my catechism. (Hawthorne 313) Through his journey with the devil Goodman brown witnesses more and more hideous and unholy sights and sounds. The forest becomes a nightmare to the young man and he still proceeds on. He sees h is honorable minister and the good deacon traveling along the path speaking of a meeting in the forest. Brown doesnt understand knowing that a meeting was never held out there. He proceeds on and finally comes to this wretched place. The horrid sounds fill his ears and boggle his mind. The congregation of his beloved church is there before the altar of a flaming rock surrounded by flame engulfed trees. But one person is missing, Faith. A figure escorts a fair damsel to the altar. The devil makes a speech and tells the assembly that evil is the nature of mankind and the only thing that has importance. The young man is summoned to the altar and we see that the lady was Faith. They are the two whom have not gone to the dark side. His last words before Faith is baptized into darkness are look up to heaven, and resist the wicked one. But if Faith heard his cry or not he does not know because after uttering those words he finds himself in the calm woods. He staggers back to town and is disgusted at his community. He shuns his congregation and even his own wife makes him shudder. He lost his faith and doesnt have any belief inShow MoreRelatedEdgar Allan Poe And Nathaniel Hawthorne848 Words   |  4 Pagesis effectively expressed by Edgar Allan Poe and Nathaniel Hawthorne despite differences in their writing style through the stories of The Raven and The Scarlet Letter respectively. Although their writing style is different, both authors indicate that breaking free from intellectual traditions of the past is present in their writing. Both Poe and Hawthorne want to know why things happen rather than how things happen so they focus on how the mind works. As well as being gothic writers, they wantedRead MoreNathaniel Hawthornes The Scarlett Letter Essay1269 Words   |  6 Pagesunjust criticism in her society. At first glance an unruly or even wicked girl, Hester’s daughter reveals herself to be the personification of excellence in the eyes of her literary creator. Through the portrayal of The Scarlet Letter’s Pearl, Nathaniel Hawthorne argues for the importance of individuality, the supremacy of nature over civilization, and the wisdom of children. Together, these transcendentalist principles function together to make Pearl a fitting representation of Hawthorne’s themes andRead MoreThe Apologue Of Faith And Faith979 Words   |  4 Pages of Faith and faith Nathaniel Hawthorne’s Young Goodman Brown (1835), is a primary prototype of an allegory. There are populous references to Faith in the symbolic oriented composition, but there is an underlying connotation of Faith. Hawthorne introduces the reader to a newlywed couple, Young Goodman Brown and Faith, as the wife is aptly named. The significance of the wife’s name and the religious references to faith will be explicated accordingly. â€Å"Poor little Faith.† (Hawthorne 234), is more symbolicRead More How Young Goodman Brown Became Old Badman Brown Essay1596 Words   |  7 Pages Nathaniel Hawthorne was a nineteenth-century American writer of the Romantic Movement. Born in Salem, Massachusetts, in 1804, he was one of those rare writers who drew critical acclaim during his lifetime. Hawthorne used Salem as a setting for most of his stories, such as The Scarlet Letter, The Blithedale Romance, and â€Å"Young Goodman Brown†. Today, readers still appreciate Hawthornes work for its storytelling qualities and for the moral and theological questions it raises. Nathaniel HawthornesRead MoreHawthorne’s Use of Allegory1212 Words   |  5 PagesHawthorne’s Use of Allegory The Ministers Black Veil by Nathaniel Hawthorne is a short story that was first published in the 1836 edition of the Token and Atlantic Souvenir and reappeared over time in Twice-Told Tales, a collection of short stories by Nathaniel Hawthorne. The short story narrates the events following Reverend Mr. Hoopers decision to begin wearing a black veil that obscures his full face, except for his mouth and chin. Mr. Hooper simply arrives one day at the meeting house wearingRead MoreThe Birthmark By Nathaniel Hawthorne1707 Words   |  7 PagesMany of Nathaniel Hawthorne s stories are based off of morality and is heavily influenced by religious beliefs and women. Hawthorne published The Birthmark, a parable, dark romanticism, at a time when people praised the scientific method and were starting to think science could make anything possible. He set his story about sixty years earlier in the 160-year-long wake of the Newtonian Revolution, in the Age of Enlightenment, when science was gainin g recognition. His story argues that, despiteRead MoreHawthorne’s Use of Allegory1545 Words   |  7 PagesThe Ministers Black Veil by Nathaniel Hawthorne is a short story that was first published in the 1836 edition of the Token and Atlantic Souvenir and reappeared over time in Twice-Told Tales, a collection of short stories by Nathaniel Hawthorne. The short story narrates the events that follow Reverend Mr. Hoopers decision to start wearing a black veil that obscures his full face, except for his mouth and chin. Mr. Hooper simply arrives one day at the meeting house wearing the semi-transparentRead MoreYoung Goodman Brown Essay931 Words   |  4 PagesThroughout Young Goodman Brown and other works of Nathaniel Hawthorne, the themes of sin and guilt constantly reoccur. Like many authors, Hawthorne used events in his life as a basis for the stories that he wrote. Hawthorne felt that ones guilt does not die with him/her but is rather passed down through the generations. Hawt hornes great-great uncle was one of the judges during the Salem witchcraft trials. Hawthorne felt a great sense of guilt because of this. Hawthorne used a great deal of symbolism toRead MoreEarly American Literature Influenced by Religious Ideologies and Philosophies1769 Words   |  8 Pageswriters, which developed into Realism by the middle of 19th century. Throughout American Literature, religious ideologies and philosophies influenced the way that writers portrayed the time period, characters, feelings, and God. Through Puritan writers, literature is influenced by religious ideologies and philosophies. Puritans writers, beginning in about 1560, put most of their focus into making their work God centered. They believed in the â€Å"Elect† and that Jesus died only for these few people. WritersRead MoreReview Of Upon Returning From The Forest 1577 Words   |  7 PagesUpon returning from the forest, everything appears different to DImmesdale. Hester saddened and Pearl celebrating his departure, Dimmesdale encounters various people on his way back to his studies. Firstly, he encounters a church elder, whom Dimmesdale, â€Å"by the most careful self-control...could refrain from uttering certain blasphemous suggestions that rose into his mind, respecting the communion-supper.† (149) Second, Dimmesdale met an elderly widow, â€Å"poor...lonely, and with a heart as full of reminiscences

Tim OBriens, the Things They Carried Critical Essay on Ptsd

Dan Gaumer Gaumer 1 Prof Montgomery English 104 10/22/12 Hard Times of Norman Bowker Have you ever found yourself carrying something heavy for a long period of time? Do you remember feeling pain, or wanting to drop the object because it was too much to bear? Tim O’brien’s novel, The Things They Carried, is about men in the middle of the Vietnam War just trying to survive. These men, like all soldiers, carried many things ranging from the physical items of war to the emotional and mental weight that comes along with the horrors of war. â€Å"They carried all they could bear, and then some, including a silent awe for the terrible power of the things they†¦show more content†¦Already physically and emotionally defeated, they can’t seem to pick up their lives where they left off. Even in instances of supportive partners, the inevitable horrors of the war haunt them in sleep or come back to them in daydreaming. They all came back with multiple disorders, PTSD with the common symptoms. The war was over and there was no place in particular to go (131). Various examples of this disorder are found in a few chapters such as Speaking of Courage and The Man I Killed. For Vietnam veterans, nothing could replenish the zest for life they had before the war. According to OBriens text, upon their arrival home the veterans imagine, even hallucinate, what things would have been like if they had not suffered through the war. Examples of such occurrences exist in the stories Speaking of Courage and The Man I Killed. Norman Bowker in Speaking of Courage daydreams of talking to his ex-girlfriend, now married to another guy, and of his dead childhood friend, Max Arnold. He lives out over and over his unfulfilled dream of having his Sally beside him and of having manly conversations with Max. He cannot stop day dreaming and dwelling in the past. Gaumer 3 Unemployed and overwhelmed by inferiority and disappointment, Bowker lacks a motivating force for life. Emotionally stricken, he only finds satisfaction in driving slowly and repeatedly inShow MoreRelatedThe Things They Carried By Tim O Brien2000 Words   |  8 Pageschange for the American soldier, but also for the American citizens back home, fearing what could happen to their families and their country. In the novel, The Things They Carried, Tim O’Brien, a Vietnam war veteran himself, tells stories through a soldier’s eyes to describe the Vietnam war and to prove how war changes people. O’Brien’s stories in this novel are directly inspired by his real-life experiences in the Vietnam war. These stories go step by step telling the story of becoming and being