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 insitu field methods. Some of the common laboratory methods are the constanthead test and falling head test. On the other hand, the common insitu 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 insitu field test methods were used to measure the hydraulic conductivity of subsoil for both saturated and unsaturated media.
One other insitu field measurement method that has been introduced is the TwoStage 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, k_{v} and k_{h} 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 Bernoulli’s equation, the total head at a point in flowing water can be given by the sum of three head components; pressure head (u/γ_{w}), velocity head (v^{2}/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
γ_{w} = 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 onedimensional water flow in soil is governed by the Darcy’s 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 Darcy’s 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 (K_{v}) of a soil is usually higher than the horizontal hydraulic conductivity (K_{h}) 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)

Clean gravels  Very good drainage 

Fissured and weathered clays 


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; γ_{w}= unit weight of water
η = viscosity of water
K = absolute coefficient (units m^{2}). 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 insitu 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 Darcy’s Law (Equation 3). The soil sample is contained in a cylinder of crosssectional 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 (m^{3}/s)
L = the length of the sample (m)
A = crosssection of the sample (m^{2})
h = hydraulic head (m)
The above diagram shows a simple setup of the constanthead 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; Darcy’s 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 corecutter 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 deaired 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 Darcy’s 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 = crosssectional area of the standpipe
A = crosssectional 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 poresize 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 laserdiffraction 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).
Hazen’s equation:
(Equation 8)
KozenyCarman’s equation:
(Equation 9)
Breyer’s equation:
(Equation 10)
Slitcher’s equation:
(Equation 11)
Where; g = acceleration due to gravity
v = kinematic viscosity
n = porosity of the soil
d_{10} = 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
Ρ = 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 d_{60}and d_{10} can be obtained from the particle size distribution. d_{60}and d_{10} represent the grain size for which 60% and 10% of the sample respectively is finer than.
Insitu 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 macrostructural 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 Darcy’s 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 freedraining 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 insitu borehole tests are as follow:
Slug test
Twostage borehole test/ Boutwell Permeameter
Variable head test
Insitu constant head test
Slug test is one of the cheapest insitu 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:
Hvorslev’s time lag analysis
(Equation 19)
Gibson’s roottime method
(Equation 20)
where; A