Permeability of Sandy Soil CIVE 2341 Section 2 Soil Mechanics Laboratory Experiment #5, Laboratory #6 SPRING 2015 Group #3

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1 Permeability of Sandy Soil CIVE 2341 Section 2 Soil Mechanics Laboratory Experiment #5, Laboratory #6 SPRING 2015 Group #3 Abstract: The purpose of this experiment was to determine the coefficient of permeability of a sandy soil using the constant head method. The coefficient of permeability of a soil is a measurement of how a fluid can flow through the soil. The importance of this lab is to find the engineering properties characterized by the permeability, which relate to shrinkage, swelling and capillary action. The constant-head method was used to find the coefficient of permeability instead of the falling-head method as the soil was granular and not fine-grained. The sandy soil was placed in the permeability apparatus and compacted and then hooked up to the sink to establish steadyflow conditions. Once water was flowing through the apparatus, flow rate was measured for three different levels of head. Once all the data was collected and the results were analyzed, the average permeability coefficient at ambient temperature was found to be cm/s. The average permeability coefficient at 20 C was found to be cm/s. Group Members: Ian Greenbaum (Abstract/Reflection/Short Answer Questions, Ali Hayat (Introduction/Short Answer Questions, Lisa Hofgesang (Conclusion/Short Answer Questions, & San Kahn (Results & Analysis /Short Answer Questions Experiment Completed: 6 March 2015 Report Submitted: 19 March 2015

2 Introduction The objective of this lab was to determine the coefficient of permeability of a sandy soil using the constant head method. The permeability constant is a measure of how easily fluid can pass through a porous medium. The constant head method is used in this case since a granular soil is being tested. If a fine-grained soil was to be analyzed, the falling head method would have been used. The constant head method is paired with Darcy s Law to find the coefficient of permeability using flow rate, specimen area and the hydraulic gradient (Darcy s Law shown in equations. The procedure of ASTM D-2434 Standard Test Method for Permeability of Granular Soils (Constant Head was followed utilizing the key apparatus listed below to find the data. First, the mass of the permeability device was measured. Next, oven-dry sand was added to the device and compacted in three layers between two porous stones, one on each end of the specimen. The mass of the device and specimen was taken along with the length and diameter of the soil specimen. The device was then hooked up to a water supply that could supply water at a constant head. Water was run through the soil until fully saturated. The flow was then measured three times at a constant head using a stopwatch and a graduated cylinder to capture the volume. The temperature of each volume was also taken. Before each measurement, the air bubbles were removed. Flow was then measured at two more constant-heads, three times each. The data was recorded and analyzed. Key Apparatus: - Constant-head permeability device - Balance (sensitive up to 0.1g - Timer - Thermometer - Beaker for collecting water (1000mL - Graduated cylinder to measure water collected in beaker The expected coefficient of permeability was expected to be low, as it is typically difficult for fluid to flow through a soil. The k value of water flowing through a fine-grained soil may be 10 4 m/s or less. The k value for granular soils should be larger than that, perhaps in the range of 10 3 m/s. The given k value at 20 C was cm/s. There are many possible errors in the constant head test, making it largely unreliable for real world application. Most errors come in the form of the test not matching the field conditions. The effect of the entrapped air bubbles can cause considerable error in the lab. Results and Analysis In this section, the data, calculations and analysis necessary to determine the coefficient of permeability will be presented. Initial measurements of mass M d, diameter D and length L were taken of the device and specimen to determine area A, volume V, dry density ρ d and void ratio e (Eq. 1-5 and placed into Table 1. Once the device was hooked up to the water supply, flow and temperature were measured for three constant heads (Eq. 6 and placed into Table 2.

3 For each head, three trials were averaged to determine the temperature and flow to use in the succeeding calculations. Next, the hydraulic gradient, discharge velocity and seepage velocity were calculated for each case (Eq These values were then used to calculate the coefficient of permeability at the given temperature and 20 C for each case (Eq The average of each case was taken and is presented as the final coefficient. These measurements were placed in Table 3. M d = M 2 M 1 (Eq. 1 Where M 2 is the mass of the device + soil specimen and M 1 is the mass of the device. A = D2 π (Eq. 2 4 V = A L (Eq. 3 ρ d = M d π 4 D2 L (Eq. 4 e = G sρ w ρ d 1 (Eq. 5 Q = Volume collected t (Eq. 6 i = h L L (Eq. 7 v d = Q A v s = v d n (Eq. 8 (Eq. 9 Where n = porosity = e (1 + e (Eq. 10 k = QL Ah L (Eq. 11 k 20 = k T η T η 20 (Eq. 12 Where η T is the viscosity of water at temperature T and η 20 is the viscosity of water at 20 C

4 Table 1: Initial Measurements Specific Gravity, G s 2.65 Specimen Height, L (cm 11 Specimen Diameter, D (cm 6.35 Permeability Device, M 1 (g 2173 Permeability Device + Soil, M 2 (g Specimen Dry Weight, M d (g Area of Specimen, A (cm Volume of Specimen, V (cm Dry Density of Soil, ρ d (g/cm Density of Water, ρ w (g/cm Viscosity of Water at 20 C, η20 (g/cm*s Initial Void Ratio, e Table 2: Constant Head Tests Constant Head Test No. 1 Constant Head, h L (cm Trial No. t (s Volume (cm 3 T, ( C Q (cm 3 /s Average Constant Head Test No. 2 Constant Head, h L (cm Trial No. t (s Volume (cm 3 T, ( C Q (cm 3 /s Average Constant Head Test No. 3 Constant Head, h L (cm Trial No. t (s Volume (cm 3 T, ( C Q (cm 3 /s Average

5 Discharge Velocity (cm/s Table 3: Combined Test Data Test No Constant Head, h T (cm Water Temperature, T ( C Volume of water per unit time, Q (cm^3/s Viscosity of Water at T C, η T (g/cm*s Hydraulic Gradient, i Discharge Velocity, v d (cm/s Seepage Velocity, v s (cm/s Permeability Coeff. at Ambient T C, k T (cm/s Permeability Coeff. at 20 C, k 20 (cm/s Avg. Permeability Coefficient at Ambient T C Avg. Permeability Coefficient at 20 C Once the data was collected, Figure 1 was created by plotting Discharge Velocity vs. Hydraulic Gradient. A linear trend-line was then fitted to the data. Hydraulic Gradient vs. Discharge Velocity y = x Hydraulic Gradient Figure 1: Hydraulic Gradient vs. Discharge Velocity

6 Reflection Our results of k T = cm/s and k 20 = cm/s were off by one order of magnitude from the given results of and 0.092, respectively, which is seemingly a large amount. However, the lab manual states It is rare for the value obtained to be correct within one order of magnitude due to the many possible errors. One of the most influential errors is entrapped air in the sample. Even after releasing the air bubbles as the ASTM procedure states for about 5 minutes before each measurement, whatever air was left in the sample seems to have thrown our numbers off by an order of magnitude. Further, the lower coefficient (i.e vs 9.2 produced by our results is probably due to the compaction that our group was instructed to perform which differed from other groups. Since compaction leads to less voids in the soil for which the water to flow through, the permeability coefficient would be lower as was found. Short Answer Questions 1. Why is the permeability test important in soil mechanics? Explain. It is important to obtain the coefficient of permeability to understand how a specific soil will react to the influence of water. For example, one would use a soil with low permeability when building a land fill, as it is necessary to keep the contents contained. It is also good to know how much water will end up in a soil under a road in the winter to better account for frost action. 2. What are the factors influencing the accuracy of the test? Is it an accurate test? Explain. Test conditions are often different from the field conditions. Hydraulic head in the laboratory may be much larger than field hydraulic head, leading to turbulent flow. Darcy s Law is not always linear. The entrapped air offers a lot of error. Because of the many possible causes for error, this test is not accurate. 3. Do all sands have the same permeability? Suppose that the same sand is under testing but compacted at different degrees will the permeability be the same in all compaction cases? Why or why not? Not all sands have the same permeability. They can differ greatly due to grain size distribution and compaction. The more compact a soil is, the fewer amounts of voids exist, making it harder for water to flow through the soil, resulting in a lower coefficient of permeability. 4. Is clay more permeable than sand? Explain. Clay is less permeable than sand due to the smaller amount of voids between the smaller particles, as explained in question 3.

7 5. Is Darcy s Law always effective? If no, explain the proper case for its application. If yes, explain why it is effective. Darcy s Law is not always effective as it is not always linear. With small values of hydraulic gradient i, the equation is v = ki. With larger values of hydraulic gradient i, the equations is v = ki n. Conclusion The constant head permeability test was performed on a sample of sand by compacting it in a constant-head permeability device and measuring the water flow through the device from three constant head levels. All data was recorded and analyzed to produce the tables and figures in the results and analysis section. The findings were used in collaboration with class notes and the lab manual to answer the short answer questions. The average permeability coefficient at ambient temperature was found to be cm/s. The average permeability coefficient at 20 C was found to be cm/s. These results were only one order of magnitude off of the expected results. This is an acceptable range of error, as the test has been proven to be inaccurate.

8 Appendices Equations, sample calculations, tables and plots of the experiment: Equations: M d = M 2 M 1 (Eq. 1 Where M 2 is the mass of the device + soil specimen and M 1 is the mass of the device. A = D2 π (Eq. 2 4 V = A L (Eq. 3 ρ d = M d π 4 D2 L (Eq. 4 e = G sρ w ρ d 1 (Eq. 5 Q = Volume collected t (Eq. 6 i = h L L (Eq. 7 v d = Q A v s = v d n (Eq. 8 (Eq. 9 Where n = porosity = e (1 + e (Eq. 10 k = QL Ah L (Eq. 11 k 20 = k T η T η 20 (Eq. 12 Where η T is the viscosity of water at temperature T and η 20 is the viscosity of water at 20 C

9 Sample Calculations: Eq. 1: = Eq. 2: = (6.352 π Eq. 3: = Eq. 4: = π 4 ( Eq. 5: = Eq. 6: = 75 Eq. 7: = Eq. 8: = Eq. 9: = Eq. 10: = ( Eq. 11: = ( /( Eq. 12: =

10 Reference Tables: Table 1: Initial Measurements Specific Gravity, G s 2.65 Specimen Height, L (cm 11 Specimen Diameter, D (cm 6.35 Permeability Device, M 1 (g 2173 Permeability Device + Soil, M 2 (g Specimen Dry Weight, M d (g Area of Specimen, A (cm Volume of Specimen, V (cm Dry Density of Soil, ρ d (g/cm Density of Water, ρ w (g/cm Viscosity of Water at 20 C, η20 (g/cm*s Initial Void Ratio, e Table 2: Constant Head Tests Constant Head Test No. 1 Constant Head, h L (cm Trial No. t (s Volume (cm 3 T, ( C Q (cm 3 /s Average Constant Head Test No. 2 Constant Head, h L (cm Trial No. t (s Volume (cm 3 T, ( C Q (cm 3 /s Average Constant Head Test No. 3 Constant Head, h L (cm Trial No. t (s Volume (cm 3 T, ( C Q (cm 3 /s Average

11 Discharge Velocity (cm/s Table 3: Combined Test Data Test No Constant Head, h T (cm Water Temperature, T ( C Volume of water per unit time, Q (cm^3/s Viscosity of Water at T C, η T (g/cm*s Hydraulic Gradient, i Discharge Velocity, v d (cm/s Seepage Velocity, v s (cm/s Permeability Coeff. at Ambient T C, k T (cm/s Permeability Coeff. at 20 C, k 20 (cm/s Avg. Permeability Coefficient at Ambient T C Avg. Permeability Coefficient at 20 C Reference Figure: Hydraulic Gradient vs. Discharge Velocity y = x Hydraulic Gradient Figure 1: Hydraulic Gradient vs. Discharge Velocity

Darcy's Law. Laboratory 2 HWR 531/431

Darcy's Law. Laboratory 2 HWR 531/431 Darcy's Law Laboratory HWR 531/431-1 Introduction In 1856, Henry Darcy, a French hydraulic engineer, published a report in which he described a series of experiments he had performed in an attempt to quantify