4.1 Code Verification
4.2 Characterization of Sediment for Vadose Zone Column Studies
.....4.2.1 Mineral Composition of Ottawa Quartz Sand
.....4.2.2 Grain Size Analyses
.....4.2.3 Capillary Fringe Measurement
.....4.2.4 Porosity Measurements
.....4.2.5 Permeability Measurement
.....4.2.6 Comparison of Hydraulic Conductivity Estimation
.....4.2.7 Measurements of Specific Yield and Retention
4.3 Experimental Setup for Column Study
4.4 Lab Measurements of Column Studies
.....4.4.1 Homogeneous Soil Column Test
.....4.4.2 Heterogeneous Soil Column Test
4.5 Sensitivity Analysis in VG Model
4.6 VG Model Simulations
.....4.6.1 Simulation for Homogeneous Column Studies
.....4.6.2 Simulation for Heterogeneous Column Study
4.7 Comparison of Lab Measurements and Model Simulations
.....4.7.1 Homogeneous Study
.....4.7.2 Heterogeneous Study



4.1 Code Verification

In the first two parts sub-models of the VG model, the vadose zone leaching and saturated zone mixing sub-models (VLEACHSM 2.0), the governing equation (Equation 3.1) and computer code have been developed primarily in response to the needs of USEPA research program, and from suggestions of Dynamac Co. The code is the computer program (Appendix A) that contains the Thomas algorithm (Appendix E) to solve the mathematical model numerically. Both the governing equation and the code should be verified. Verification of the governing equation demonstrates that it accurately describes the physical processes occurring in porous media. Code verification of the VG model was identified to demonstrate in the Sections 3.4 and 3.5. Verification of the governing equation is the more difficult than the code verification. By the way, it is possible to establish some confidence in the governing equation by comparisons with results of laboratory column experiments.



4.2 Characterization of Sediment for Vadose Zone Column Studies

To understand the physical mechanisms responsible for the movement of water and chemicals through sediments in the vadose zone for purposes of computer model validation, this study utilized soil column tests. The soil samples chosen for the tests was the commercial Ottawa quartz sand with grain size 0.725 ± 0.125 mm, 0.337 ± 0.087 mm, and 0.627 ± 0.552 mm. These sand sample sizes were evaluated to determine porosity, capillarity, hydraulic conductivity, specific yield, and specific retention. These important physical properties are used in the verification of the VG model.



4.2.1 Mineral Composition of Ottawa Quartz Sand

Sands are the most common and loosely packed minerals on the earth's surface. Smaller than gravel and larger than silt and clay, sand particles mostly range from 0.02 mm to 2.00 mm in diameter. Sands are naturally produced materials resulting from the mechanical and chemical breakdown of rocks. Sand accumulates in areas where sediments are transported and deposited, such as in desert, beach, and river environments. Dry sand is blown by the wind, and rocks, stumps, or shrubs will stop some of it, forming little mounds. In time the mounds may grow into sand dunes. Unless they become covered by vegetation, dunes usually migrate. Their movement is caused by the slow shifting of sand from the windward to the leeward side of the dune. Sand also occurs in alluvial fans, which are fan-shaped, sedimentary deposits at the mouths of mountain canyons. 

Sand is found in nearly every geological environment and has at least a component of a lot of rock types. Especially applicable to this study is the commercially available Ottawa sand. The Ottawa sand consists of a single mineral quartz. It is a naturally occurring very homogeneous, inorganic material formed as a result of geological processes. This sediment has a definite chemical composition (SiO2) and an ordered atomic arrangement in its mineral. It is obtained from the St. Peter Sandstone which is a sedimentary rock built of grains of sand held together by a natural cement. It is found in a massive formation from 140 ft to 275 ft in thickness, that outcrops along the Fox rivers near Ottawa, in Illinois (Steila, 1976). The Ottawa sand was chosen by the American Society for Testing Materials as the standard sand to be used in testing cement and the strength of concrete.


Characteristics of Quartz Sand

The most common component of sand is quartz. This is because quartz is abundant, hard, nearly insoluble in water, and resistant to chemical decay. Other sands are made of silicates such as feldspar. The quartz sands usually contain a small quantity of feldspar and white mica. Yellow, brown, and red sands contain iron compounds. Red desert sands are usually made of quartz coated with iron oxides. Green sand deposits, found for the most part on the ocean floor, owe their color to glauconite, a potash-bearing mineral. Mixed with certain shore and river sands are grains of gold, platinum, and uranium and gemstones. The best field indicators of quartz are crystal system, hardness, fracture, color, luster, etc (Sinkankas, 1966).

The Ottawa quartz sand consists of rounded grains of clear colorless quartz, which have diamond-like hardness, and are pure silica (Silicon Dioxide, SiO2) uncontaminated by clay, loam, iron compounds, or other foreign substances (Kraus, 1959). The origins of the name are uncertain, possibly from the German word "quarz," hard, itself of uncertain derivation. The quartz is widespread amongst the different environments.


Samples for Soil Column Tests

Ottawa quartz sand was used as sediment samples for lab column tests in order to obtain soil property values for the VG model simulation. These uniform sands can be described in terms of porosity, permeability, bulk density, specific yield, and specific retention, and capillarity. These soil properties control the velocity and extent of chemical contaminant migration in the vadose zone.



4.2.2 Grain Size Analyses

Grain size analysis, which is among the oldest of soil tests, is widely used in engineering classifications of soils. The purpose of this portion of the study is to determine the variations in grain size distributions for the commercial Ottawa sand samples used in the column studies. Since particle diameters typically span many orders of magnitude for natural sediments, this study should employ a way to conveniently describe these samples. The base two logarithmic f scale is one useful and commonly used way to represent grain size distribution information for a sediment (Masch and Denny, 1966). A tabular classification of grain sizes in terms of f units, mm, and other commonly used measurement scales is included for comparison in Figure 4.1

Figure 4.1 Grain Size Distribution of Ottawa Sand Samples a, b, and c.

Logarithmic f values (in base 2) are defined from measured particle diameter as follows:

f =  -log2=  -(log10d / log102)                    (4.1) 

where f is particle size in f units, and d is diameter of particle in mm. Note that the negative sign is affixed so that commonly encountered sand sized sediments can be described in positive f values as d is smaller than 1. 

A grain size distribution analysis is a tedious and time-consuming task. Although the initial sieving is simply collecting the uniform sand between sieve number 20 and 30 (0.600 and 0.840 mm), 40 and 60 (0.250 and 0.425 mm), 16 and 200 (0.075 and 1.180 mm), for this soil column test, this study was performed to obtain an actual grain size distribution of these samples. Depicted in the Figures 4.1 and 4.2 are percent frequency of particle size occurrence, plot of grain size distribution called cumulative weight percent curves, and a logarithmic plot of grain size distribution for these samples. The curves are cumulative percent frequency distribution curves that represented the cumulative weight percent by particle size of the samples. In the cumulative weight percent passed curve and cumulative weight percent-retained curve, these samples were shown to be categorized as coarse, medium, fine, well sorted, and clean sand according to the lab manuals (ASTM, 1976; BS 1377, 1975, 1975; AASHTO, 1974).

Figure 4.2 Logarithmic Grain Size Distribution Curve of Ottawa Sand Samples a, b, and c (U.S. Standard Sieve Sizes).

The following five descriptive parameters are geometric mean (GMe), median, standard deviation (sf), coefficient of uniformity (Cu), and coefficient of concavity (Cc), have been calculated from the cumulative percent curves. In the first three formulas below, the subscript in the ({fx) terms refers to the grain size at which x percent of the sample is coarser than that size, or the size at which x percent of the sample is passed through that particular sieve size and any coarser screened sieves above that particular sieve.

The best graphic measure for determining overall size is the geometric graphic mean (GMe). It corresponds very closely to the mean as computed by the method of moments, yet is much easier to find. It is much superior to the median because it is based on three points and gives a better overall picture (Figures 4.1 and 4.2).

GMe = (f16+f 50+f84)/3                     (4.2)

Median is defined as that value at which half of the particles by weight are coarser than the median, and half are finer. It is the diameter corresponding to the 50 percent mark on the cumulative frequency curve and may be expressed either in f or in mm. The advantage is that it is by far the most commonly used measure and the easiest to determine. The disadvantage is that it is not affected by the extremes of the curve, therefore does not reflect the overall size distribution of sediments (especially skewed ones) well. For bimodal sediments it is almost worthless and its use is not recommended through this study

Median (graphic) = f50                  (4.3)

The inclusive graphic standard deviation (sf) formula includes 90 percent of the distribution and is the best overall measure of sorting. Measurement of sorting values for a large number of sediments has suggested the verbal classification for sorting for each value of inclusive graphic standard deviation.

sf = (f84 - f 16)/4 + (f95 - f 5)/6.6         (4.4)

The coefficient of uniformity (Cu) is a nonstatistical measure of the spread of the curve (Figure 4.2). It is similar to the standard deviation, but is used for samples that does not follow a normal curve. This parameter is defined in different ways by different people.


Cu = d60/d10                                       (4.5)

The coefficient of concavity (Cc) is a measure of the shape of the curve between the grain sizes d60 and d10 (Figure 4.2), and is defined as:

Cc = d302/(d10·d60)                               (4.6)

Some of the properties obtained above will be used to estimate hydraulic conductivity in Section 4.2.6.



4.2.3 Capillary Fringe Measurement

Capillarity is a phenomenon in which the groundwater surface is elevated or depressed when it comes in contact with a soil in vadose zone (Figure 2.1). The result depends on the outcome of two opposing forces, adhesion and gravity (cohesion). Adhesion, which is the attraction of water molecules onto the solid surfaces, causes the water to rise up the vadose zone until this force is balanced by gravity, which is the attraction of molecules to each other, acting to minimize the adhesive surface.

The objective of this part of the study was to determine if capillary action in the test sand in the vadose zone is significant and necessary to consider in the VG model. The experiment apparatus consisted of a cylindrical clean plastic pipe and a water dish as shown in Figure 4.3. This pipe has 4.8 cm of inter diameter and is 40 cm long. After standing the pipe on the dish, the pipe was filled with the Ottawa sand sample of mean grain size of 0.720 mm. Then the dish was filled with tap water as soon as possible and the capillary fringe was measured after 20 minutes of wetting the sand. This procedure was repeated 10 times and mean capillary fringe in lab was determined to be 2.13 cm. In this method, the phenomena of capillarity was detected visually. The length of soil column will be 100 cm for the soil column test. Therefore, the capillary fringe effect will occupy only 2.13 percent of the whole column height. The capillary fringe is small enough to be neglected both in soil column test and the VG model calculation.

Note: A Capillary Barrier

Flow of fluids through unsaturated media often results in counterintuitive behavior. One very important example is that flow through coarse material is impeded relative to flow through fine material under unsaturated conditions. That is, under unsaturated conditions, water flows more readily through clayey soil than through gravel! The key to understanding how gravel layers can be capillary barriers to flow of water in the unsaturated zone is appreciating that gravel has almost all "large" pores, similar to the macropores described in the previous section. Under negative capillary-pressure heads, these large pores fill with air and essentially stop the transport of water. (Water actually does move by vapor diffusion, but this is an exceedingly slow process.) Clays, on the other hand, have almost all "small" pores. Thus, under anything but extreme negative capillary-pressure heads, many of the pores will be filled with water and will conduct water, albeit at slow rates (relative to saturated gravel, but at very fast rates relative to vapor diffusion). The situation can be appreciated by looking at the hydraulic conductivity curves for gravel versus a clayey material. At saturation, Kgravel >> Kclay, but at moisture contents not too far below saturation, Kclay >> Kgravel. That is, flows are impeded in the gravel relative to the clay at intermediate to low values of the moisture content.

Figure 4.3 iagram of Setting Capillary Fringe Lab with Coarse Size (0.720 mm) Ottawa Quartz Sand Samples.


4.2.4 Porosity Measurements

Porosity is one of the most important physical input parameters of vadose materials in hydrologic or contaminant transport studies. Soils contain particles of different types and sizes. Space between particles, called pore space, determines the amount of water that a given volume of soil can hold. Porosity is the measure of how much water a soil can contain if saturated, or in other words, the ratio of pore space to the total volume. Porosity is also the total porosity which is the sum of the aeration and water-filled porosity of soil.

Depending on the method of actually measuring porosity, porosity can be defined on a volumetric (nV), areal (nA), lineal (nL), and a statistical point count basis (nN) (Singh, 1981):

nV = Vv/VT ,     where   VT = Vv + Vm         (4.7)

nA = Av/AT ,     where   AT = Av + Am         (4.8) 

nL = Lv/LT ,      where   LT = Lv + Lm         (4.9)

nN = Nv/NT ,     where   NT = Nv + Nm      (4.10) 

where, V, A, L, and N are volume, area, length, and point counts, respectively. The subscript "v" indicates the subset corresponding to the voids, "m" the subset of solid matrix or mineral material, and "T" the total set.

Direct Method (Porosity from Volumetric Estimation, nV)

Porosity is defined as the volume of the voids divided by the total volume of the porous sample. Volumetric porosity can be determined in the following procedure: first, an unconsolidated dry sample is weighed and its weight recorded. A density of the solid phase material is assumed to be 2.65 g/cm3, the density of quartz as previously mentioned in section 4.2.1. The sample weight is divided by the density to calculate the volume of the sediment grains only, Vm. The sample is then placed in a cylinder and tapped gently until it settles no more. The volume (VT) that the sample occupies in the cylinder is measured and recorded. The volume of the voids (Vv) can be determined from:

Vv = VT - Vm                        (4.11)

where, Vv is the volume of void, VT is the total volume, and Vm is the volume of sediment grains.

The porosity (0.338, 0.398, and 0.299) can then be determined from equation (4.7) above. Note that this method does not take sample moisture weight into consideration.


Indirect Method (Porosity by Saturation)

In principle, the porosity would be easily measured by using a sample of known total volume, VT. However, accurately determining the total volume of the sample is not a trivial matter, and all methods contain a degree of uncertainty. According to the procedure described in the lab manuals (ASTM, 1976; BS 1377, 1975; AASHTO, 1974), the samples are first oven dried, 105oC being the standard temperature, until it reaches a constant weight. In this procedure, each samples were air-dried and oven-dried which had the almost same porosities (differences of mean porosity values are 1.60, 0.24, and 1.42 %). De-aired water, such as boiled water, is used in this procedure for avoiding air bubbles in the sample. The sample is then placed in a cylinder and tapped gently until it settles no more. The volume (VT ) that the dry sample occupies in the cylinder is measured and recorded. The sample is then placed in a known volume of water in a sealed volumetric chamber, and left undisturbed to absorb water. Upon saturation, the volume of voids, Vv, in the sample is simply the volumetric difference between the water in the chamber before and after saturation. The porosity, nsat, is then determined by:

nsat  = Vv/VT                       (4.12)

where, nsat is the porosity by the saturation, Vv is the volume of void, and VT is the total volume.

In this practice, it was quite difficult to exactly and completely saturate a sample of given volume. There is always some pore space that does not become filled with water, decreasing the measured porosity value as seen in our cases. Therefore, the result of this procedure was not used in this study.


Comparison Between Porosity Values by Volumetric and Saturation Method

The effective porosity (ne) is the volume of pore space through which fluid flow can effectively take place divided by the total volume of the sediment or rock. The effective porosity is commonly used because some of the pores within a porous media may be isolated or "dead-end" space which will not contribute to the ability of the medium to transmit water or other fluids. The relationship between effective porosity and total porosity depends on the sizes and shapes of the grains within the porous media, and on the packing arrangement or fabric of the sediment. In this practice, we will assume that the effective porosity is equal to the porosity determined by volumetric method, that is:

ne = nvol                           (4.13) 

where ne is the effective porosity and nvol is the volumetric porosity.


Direct Method (nv)

Indirect Method (nsat)

Sample a b c a b c
Mean 0.338 0.398 0.299 0.320 0.333 0.208
Bulk Density, g/cm3 1.755 1.595 1.859 - - -
Standard Deviation 0.008 0.006 0.004 0.003 0.004 0.008
Sand Sample a mean grain size 0.725 ± 0.125 mm
Sand Sample b mean grain size 0.337 ± 0.087 mm
Sand Sample c mean grain size 0.627 ± 0.552 mm
Table 4.1 Comparison of Porosities by Two Different Methods


The porosities for sand samples have been calculated using two different methods namely estimation by volumetric and by saturation. As shown in Table 4.1, the mean porosities are 0.338, 0.398, 0.299, 0.320, 0.333, and 0.208, respectively. These values indicate the porosity from the volumetric estimation (direct method) is best suited to serve as the effective porosity for soil column tests.


4.2.5 Permeability Measurement

Permeability refers to the propensity of a material to allow fluid to move through its pores or interstices. Permeability is an important soil parameter for any project where flow of water through soil is a matter of concern. There are several factors that influence the permeability of a soil: the viscosity of its water which is a function of temperature, size and shape of the soil particles, degree of saturation, and void ratio. The void ratio is the ratio of volume of voids to volume of solids. For a given soil, permeability is inversely proportional to soil density. The more tightly particles are packed, the tendency for the material to allow water to flow through it is reduced.

Typical lab methods used to determine the permeability of soil samples are: (1) Falling-Head Laboratory test, and (2) Constant Head laboratory test. In this exercise the permeability of the Ottawa sand samples is determined by a Falling-Head laboratory measurement technique. The fundamental description of permeability is based on the equation:

v·A                           (4.14)

where, the variable q is the discharge [V/T], v is the apparent velocity, and A is the cross sectional area of the flow. Now, Darcy's Law describes the factors important in determining the value of v, which is

v  =  k·i                        (4.15)

where k is a constant for the material and is called the coefficient of permeability, and i is the hydraulic gradient which is related to the water pressure.

Apparatus and supplies for this practice are permeability device, standpipe, specimen holder, overflow container, tubing and de-aired water container, meter tape, thermometer, stopwatch, 1000 cc graduated cylinder, etc.

A falling head permeability setup is shown in Figure 4.4. The sand sample is divided to form three specimens with different weights. The dry density of each specimen is calculated by determining the difference in weight between the permeameter and the permeameter plus compacted sand. Also, each specimen's diameter and length are measured.

Figure 4.4 Falling Head Permeability Setup for Ottawa Sand Samples.

After obtaining these initial data, permeability tests can be performed. The soil specimen is first saturated with water under a vacuum. Water is then allowed to move through the specimen and the time required for a certain quantity of water to pass through the specimen is measured and recorded. Using these data together with others described previously, one can determine the hydraulic conductivity (K) from following equation (Todd, 1959):

where K is hydraulic conductivity [cm/sec], a is cross sectional area of standpipe [cm2], L is length of soil specimen [cm], A is cross sectional area of soil specimen [cm2], h1 and h2 are the elevations [cm] of the water level in the standpipe at different times (t1 and t2, [sec]), and Dt [sec] is the difference between times t1 and t2.

Permeability tests should be performed three times per sample, one for each test specimen with different dry weights. Each specimen's void ratio can be computed using the specific gravity of the sand and the corresponding dry density. As shown in Figure 4.5, a curve of hydraulic conductivity, K, versus void ratio e can then be plotted on semilogarithmic paper, with void ratio on the arithmetic scale and permeability on the logarithmic scale. The averages of these values (0.297, 0.076, and 0.031) are close to the value from Hazen's method from grain size analyses (0.312, 0.075, and 0.033).

Figure 4.5 Relationship between void ratio and hydraulic conductivity for Ottawa sand samples a, b, and c in falling-head permeability tests.


4.2.6 Comparison of Hydraulic Conductivity Estimation

The hydraulic conductivity (K) for these samples have been estimated in three different ways. First, it is calculated by applying the Hazen approximation (Fetter, 1994) to the result of the grain size analyses in section 4.2.2. The Hazen approximation of hydraulic conductivity is applicable when the effective particle size d10 is between 0.1 mm and 3.0 mm, and is calculated as follows:

C(d10)2                        (4.17)

where K is the hydraulic conductivity [cm/sec], d10 is the Hazen's effective grain size in [cm], than which 10 % of the sample is finer, and C is a coefficient which depends the sorting characteristics of the sediment. When sediment type is coarse sand, well sorted, or clean, C should be between 120 and 150 (Fetter, 1994). C values of samples a, b, and c are 120, 150, and 120, respectively.

The Krumbein and Monk equation is also used to estimate the permeability, k (in darcies) of sediment from a grain size analysis (Krumbein and Monk, 1943). This equation was developed empirically using very well sorted sediment samples ranging from -0.75 to 1.25 f in mean grain size, and with standard deviations ranging from 0.04 to 0.80 such as this Ottawa sand sample.

The Krumbein and Monk equations for each samples are: 

k   =   760 (GMe)2e-1.31 sf         (4.18)

where, k is intrinsic permeability in darcies, GMe is geometric mean grain diameter in mm, sf is standard deviation in f scale.

The Krumbein and Monk permeabilities (k) [in darcies] calculated in equation (4.18) above are converted into hydraulic conductivities (K) [cm/sec] using the relation:

K  =   (krg)/ m                                    (4.19)

where, K is the hydraulic conductivity [cm/sec], r is density of water, 0.9982 [g/cm3] at 20°C, g is acceleration of gravity, 980 [cm/sec2], m is dynamic viscosity of water, 0.01 [g/(cm·sec)] at 20°C, and k is permeability in [cm2]. Conversion factor to convert to k to K is 9.87·10-9 [cm2/darcy].

From a simple visual inspection of the cumulative frequency curves (Figures 4.1 and 4.2), the concentrated distribution of size classes shows that these samples are very well sorted sands (Inclusive Graphic Standard Deviation, sf, are 0.564, 0.408, and 0.783). According to Krumbein and Monk, permeability decreases as it's standard deviation increases. Standard deviation is a statistical concept which assumes that the sample for which the calculations is performed has a normal distribution (bell-shaped curve) about a mean value. These sediment samples fit in this model.

Comparison in Porosities and Hydraulic Conductivities

Ottawa Sand Samples Experimental Procedure
Falling-Head Permeability Test (cm/sec) Grain Size Analyses
Hazen's K Method (cm/sec) Krumbein and Monk (cm/sec)
Sand Sample a   n = 0.338 Lab 1st  0.308 0.312 0.262
Lab 2nd 0.294
Lab 3rd 0.289
Average K 0.297
Sand Sample b    n = 0.398 Lab 1st  0.080 0.075 0.314
Lab 2nd 0.075
Lab 3rd 0.073
Average K 0.076
Sand Sample c    n = 0.299 Lab 1st  0.034 0.033 0.179
Lab 2nd 0.031
Lab 3rd 0.028
Average K 0.031
Table 4.2 Comparison of Porosity and Hydraulic Conductivity from each procedures.


Table 4.2 compares the hydraulic conductivities obtained by the Hazen's method, Krumbein and Monk equation, and falling head permeability test for these samples, and the porosities measured (Table 4.1) before these practices. The hydraulic conductivities from the falling head permeability test (0.297, 0.076, and 0.031 cm/sec) were much closer to Hazen's approximation (0.312, 0.075, and 0.033 cm/sec) than to the Krumbein and Monk equation (0.262, 0.314, and 0.179 cm/sec).



4.2.7 Measurements of Specific Yield and Retention

The specific yield of a saturated soil is the ratio of the volume of water which it will yield by gravity, to its total volume. Specific retention represents the water retained against gravity drainage. The specific yield and retention when added together are equal to the water-filled porosity of the soil. The purpose of this laboratory is to assist the VG model simulation by providing estimates of the specific yield and retention values in the vadose zone.

In the experimental setup for this study, two different plastic columns (5.8 cm inside diameter and 100.00 cm length for sample a, 2.54 cm inside diameter and 122.50 cm length for sample b, and 2.54 cm inside diameter and 30.50 cm length for sample c) filled with de-ionized water were prepared and loaded with air-dried Ottawa sand samples (grain size of 0.725 ± 0.125 mm, 0.337 ± 0.087 mm, and 0.627 ± 0.552 mm for samples a, b, and c, respectively). The samples were the same sand as used in previous procedures. The columns were open to the atmosphere at the top and had a stopper which could be disconnected from the bottom of the column as shown in Figure 4.6.

Figure 4.6 Experimental Setup for Specific Yield and Retention Measurements.

As shown in Figure 4.6, the columns, which were filled with 100-cm to 122-cm of sand from the bottom of the columns, were saturated with de-ionized water up to the surface of the sand columns. After that, the bottom stopper was released and the water allowed to drain. At the same time, the discharge of drained water was measured as a function of time. This procedure was repeated seven times. In this study, the total volume of sand, saline water and electrical conductivity of water were measured before and after saturation. The specific yields (0.26 for sample a, 0.27 for sample b, and 0.24 for sample c) were measured and the specific retentions (0.10, 0.09, and 0.05, respectively) of the sand samples were calculated based on the effective porosities (0.32, 0.35, and 0.21) and the specific yield as shown in Table 4.3. Those column settings were utilized in the lab column studies for validating the VG model.


(1) Inside Diameter of Column 5.80 (cm) 2.54 (cm) 2.54 (cm)
(2) Cross-sectional Area of Column, A 26.42 (cm2) 5.07 (cm2) 5.07 (cm2)
(3) Length of Sand in Column, L 100.00 (cm) 122.46 (cm) 30.49 (cm)
(4) Total Volume of Sand, VT 2642.08 (cm3) 620.51 (cm3) 154.50 (cm3)
(5) Specific Density of Sand 2.65 (g/cm3) 2.65 (g/cm3) 2.65 (g/cm3)
(6) Effective Porosity (Saturation) 0.320 0.348 0.210
Sample a b c
Before Test Saline (ppt) 0.00 0.00 0.00
Conductivity (ms) 3.58 3.00 2.80
Temp. oC Lab 15.25 12.50 10.50
Water 14.02 10.50 9.50
W_s, Mass, (g) 4637.50 987.30 290.75
V_m = W_s/{\rho}_s (cm^3) 1750.01 372.56 109.72
V_v = V_T-V_m (cm^3) 892.07 247.98 44.78
Total Water (ml) 865.65 216.00 50.00
D_w, Drained Water (ml) 699.50 167.54 37.00
Volumetric Porosity, n = V_V/V_T 0.34 0.40 0.29
Specific Yield, S_y = D_w/V_T 0.26 0.27 0.24
 Specific Retention, S_r 0.08 0.12 0.05
After Test Saline (ppt) 0.10 0.00 0.00
Conductivity (ms) 113.95 99.90 89.90

Sample a

Mean Grain Size 0.725 ± 0.125 mm

Sample b

Mean Grain Size 0.337 ± 0.087 mm

Sample c

Mean Grain Size 0.627 ± 0.552 mm

Table 4.3 Specific Yield and Retention from Sand Column Tests


A quantitative representation of the water content profile after completion of drainage has been developed by using the volume of water drained or specific retention versus time relationship which was obtained during the drainage test shown in Figure 4.7. This relationship was initially quite linear and then became increasingly non-linear. Graphic representations of the specific yield and specific retention for the various lab test have been created by plotting the percent of drained water volume versus time relationship as shown in Figures 4.8, 4.9, and 4.10.

Figure 4.7 Profile of Water Content after drainage.

Figure 4.8 Profile of Specific Yield and Retention for Sample a.

Figure 4.9 Profile of Specific Yield and Retention for Sample b.

Figure 4.10 Profile of Specific Yield and Retention for Sample c.



4.3 Experimental Setup for Column Study

The experimental setup of the physical steady state flow setting is considered first shown in Figure 4.11 and 4.12. The physical soil properties used the same values as the lab practices of the previous section. The experimental study was conducted at the Soil Laboratory of Environmental Engineering Research and Training Center at University of Rhode Island for the purpose of the sediments characterization and verification of the VG model. These lab measurements were done on 1998 and 1999.

Sodium Chloride (NaCl) solution (480 ppm) was used because it is a conservative chemical and easily measured. Sodium Chloride is very soluble in water. NaCl is ionic and nonvolatile. There is no Henry's law constant for NaCl because it has no vapor pressure at normal temperatures. NaCl may be slightly soluble in octanol, but it should not partition into natural organic matter to any measurable degree. Na+ may be retarded in some systems by ion exchange, but Cl- should be conservative (Hemond and Fechner, 1994).

Figure 4.11 Experimental Setup of Vadose Zone Leaching Soil Column Studies for Homogeneous Layer of Ottawa Sand Sample (a) and (b).

Figure 4.12 Experimental Setup of Vadose Zone Leaching Soil Column Studies for Heterogeneous Layer of Ottawa Sand Sample (b) and (c).

In the experimental setup for this study, a clean plastic column inside diameter of 2.54 cm and length of 150 cm, syringes, recharge rate controller (controlled rate by clamp), irrigation tube, de-ionized water in bladder irrigation bag, and colored sodium chloride water (480 ppm of saline) in bladder irrigation bag have been prepared with air-dried Ottawa sand samples a (grain size of 0.725 ± 0.125 mm), b (grain size of 0.337 ± 0.087 mm), and c (grain size of 0.627 ± 0.552 mm) which were the same samples as used in practices of previous section. The column was open to the atmosphere. As shown in Figure 4.11 and 4.12, the column has syringe caps installed at every 7.62 cm (0.25 ft) from top to bottom of column sampling water using syringes. The bottom of the column has installed iron fine screen for holding the samples. This setup controls the recharge rate of top (in) and the discharge rate (1 cc/10 drops) of bottom (out) of the column by medical clamp, making it easy to switch from de-ionized water to saline water for leaching study.

As shown in Figure 4.11, the steady state recharge rates of sample (a) and (b) for homogeneous column study were 0.03 and 0.004 [cm/sec], respectively. The columns of these two samples consisted of 121.92 [cm] (4 ft) of length and 2.54 [cm] (1 in) of diameter. The soil properties and the setups of these tests were adapted from section 4.2.

As shown in Figure 4.12, the setup of the third test for heterogeneous study involved 0.002 [cm/sec] of steady state recharge rate in a heterogeneous layered sample. These samples consisted of three layers which were 30.48 [cm] (1 ft) of sample b, 30.48 [cm] (1 ft) of sample c, and 60.96 [cm] (2 ft) of sample b in order from the top surface of the soil column. Sample (c) was the same sample (grain size of 0.627 ± 0.552 mm) as used in the previous section. The soil properties of sample (c) were adapted from the section 4.2.

After a switch to the saline water with the same recharge rate, the concentrations at every 7.62 cm (0.25 ft) depth from the top of the column were measured as a function of time using the syringes and refractometer.


Last modified: Oct 15, 1999
VG Model / Samuel Lee / VADOSE.NET