Soil Mechanics for Unsaturated Soils phần 3 doc

4.4 MEASUREMENTS OF MATRIC SUCTION 97 The MCS 6OOO sensors have been used for matric suction measurements in the laboratory and in the field (Pic- ornell et al., 1983; Lee and Fredlund, 1984). The sensors appeared to be quite suitable for field usage, being insen- sitive to temperature and salinity changes. Relatively accurate measurements of matric suction were obtained in the range of 0-300 kPa. Curtis and Johnston (1987) used the MCS 6OOO sensors in a groundwater recharge study. The sensors were found to be quite responsive and sensitive. The results were in good agreement with piezometer and neutron probe data. However, Moisture Control System Inc. discontinued production in early 1980, and the MCS 6OOO sensor is no longer commercially available. In 1981, Agwatronics Inc. in Merced, CA, commenced production of the AGWA thermal conductivity sensors. The design of the sensor was changed from previous designs, but was based on the research by Phene et al., (1971). There were several difficulties associated with the AGWA sensor that resulted in their replacement by a new design, the AGWA-I1 sensor in 1984. A thorough calibration study on the AGWA-I1 sensors was undertaken at the University of Saskatchewan, Canada (Wong et al., 1989; Fredlund and Wong, 1989). Several other difficulties were reported with the use of the AGWA- I1 sensors. These include the deterioration of the electronics and the porous block with time. The AGWA-I1 sensors have been ;sed for laboratory and matric suctions on several research et al., 1987; Sattler and Fredlund, 1989). field measurements of studies (van der Raadt 1989; Rahardjo et al., Theory of Opemtion A thermal conductivity sensor consists of a porous ceramic block containing a temperature sensing element and a min- iature heater (Fig. 4.66). The thermal conductivity of the porous block varies in accordance with the water content of the block. The water content of the porous block is de- Epoxy seal Temperature sensing integrated circuit Epoxy Epoxy backing . Plastic jacket - Heater resistor - Ceramic porous media Figure 4.66 A cross-sectional diagram of the AGWA-I1 thermal conductivity sensor (from Phew et al., 1971). pendent upon the matric suctions applied to the block by the surrounding soil. Therefore, the thermal conductivity of the porous block can be calibrated with respect to an applied matric suction. A calibrated sensor can then be used to measure the matric suction by placing the sensor in the soil and allowing it to come to equilibrium with the state of stress in the pore- water (Le., the matric suction of the soil). Thermal conductivity measurements at equilibrium am related to the matric suction of the soil. Thermal conductivity measurements are performed by measuring heat dissipation within the porous block. A controlled amount of heat is generated by the heater at the center of the block. A portion of the generated heat will be dissipated throughout the block. The amount of heat dissipation is controlled by the presence of water within the porous block. The change in the thermal conductivity of the sensor is directly related to the change in water content of the block. In other words, more heat will be dissipated as the water content in the block increases. The undissipated heat will result in a temperature rise at the center of the block. The temperature rise is measured by the sensing element after a specified time interval, and its magnitude is inversely proportional to the water content of the porous block. The measured temperature rise is ex- pressed in terms of a voltage output. Calibmtion of Sensors AGWA-I1 sensors are usually subjected to a two-point calibration prior to shipment from the factory. One calibration reading is taken with the Sensors placed in water (Le., zero matric suction). A second calibration reading is taken with the sensors subjected to a suction of approximately 1 atm. This calibration procedure may be adequate for some applications. However, it has been suggested that a more rig- orous calibration pmedure is necessary when the sensors are used for geotechnical engineering applications (Fred- lund and Wong, 1989). A more thorough calibration of thermal conductivity sensors can be performed by applying a range of matric suction values to the sensors which are mounted in a soil. Readings of the change in voltage output is a measure of the thermal conductivity (or the water content) of the porous block under the applied mattic suction. The matric suction can be applied to the sensor using a modified pressure plate apparatus (Wong et al., 1989; Fredlund and Wong, 1989). The sensor is embedded in a soil which is placed on the pressure plate (Fig. 4.67). The soil on the pressure plate provides continuity between the water phase in the porous block and in the high air entry plate. In addition, the soil used in the calibration must be able to change its water content at a low matric suction (i.e., low air entry value), as shown in Fig. 4.68. The matric suction is applied by 98 4 MEASUREMENTS OF SOIL SUCTION 30 - Calibration soil: 9Wo silt and 10% Ottawa sand 25 - -20 - P- 15- 8- c 3: g 10- E- c- - 5- - \Modified pressure plate Figure 4.67 Pressure plate calibration setup for thermal conductivity senson (from Fredlund and Wong, 1989). 0 increasing the air pressure in the pressure plate apparatus, but maintaining the water pressure below the pressure plate at atmospheric conditions. The change in voltage output from the sensor can be monitored periodically until matric suction equilibrium is achieved. The above procedure is repeated for various applied matric suctions in order to obtain a calibration curve. A number of thermal conductivity sensors can be calibrated simultaneously on the pressure plate. During calibration, 11'1 illl II"" Ill' the pressure plate setup should be contained within a temperature-controlled box. Figure 4.69 shows a typical response curve for the AGWA-I1 sensor resulting from the application of different air pressures during the calibration process. The curve indicates an increasing equalization time as the applied matric suctions increase. For the calibration soil indicated in Fig. 4.68, the sensor has an equalization time in the order of 50 h for an applied matric suction below 150 kPa. The 4.4 MEASUREMENTS OF MATRIC SUCTION 99 I I I 50 100 150 200 250 300 350 Elapsed time, t (hours) suction measurements above 175 kPa cornspond to the steeper portion of the calibration curve, which has a lower sensitivity to changes in thermal conductivity. AGWA-11 sensors have shown consistent, reproducible, and stable output readings with time (Fredlund and Wong, 1989). The sensors have been found to be responsive to both the wetting and drying processes. However, some failures have been experienced with the sensors, particularly when subjected to a positive water pressure. The failures are attributed to moisture coming into contact with the electronics sealed within the porous ceramic (Wong et al., 1989). Also, there have been continual problems with the porous blocks being too fragile. Therefore, the sensor must be handled with great am. Even so, there is a percentage of the sensors which crack or cnrmble during calibration or installation. lLpical Results of Mahic Suction Measunments Laboratory and field measurements of matric suctions using the MCS 6OOO and the AGWA-I1 thermal conductivity sensors have been made involving several types of soils. The soils have ranged from highly plastic clays to essentially nonplastic sands. The sensors have been installed either in an initially wet or an initially dry state. The results from the MCS 6OOO sensors are presented first, followed by the results from the AGWA-I1 sensors. Figure 4.69 Time response curves for a thennal changes in applied air pmssum (or matric suction). equalization time for a sensor is affected by the permeability and thickness of the calibration soil. In addition, the permeability and the thickness of the high air entry disks also affect the equalization times. More than 100 AGWA-I1 sensors have been calibrated and used at the University of Saskatchewan, Canada. Typ ical nonlinear calibration curves for the AGWA-I1 sensors are shown in Fig. 4.70. The nonlinear response of the sensors is likely related to the pore size distribution of the ceramic porous block. Similar nonlinearities were also ob- served on the calibration curves for the MCS 6OOO sensor. The nonlinear behavior of the AGWA-11 sensors may be approximated by a bilinear curve, as illustrated in Fig. 4.70. The bt.eaking points on the calibration curves are generally around 175 kPa. Relatively accurate measurements of matric suction dan be made using the AGWA-I1 sensors, particularly within the range of 0-175 kPa. Matric - 400- soil: 10% Ottawa sand - 9o%sik 5 3 300. I 7 I Sensor reading (mV) Figure 4.70 Calibration curves for two AGWA-Il thermal conductivity sensors. conductivity sensor (AGWA-II) subjected to The MCS 6OOO Sensors Lee (1983) studied the performance of the MCS 6OOO thermal conductivity sensor. The laboratory and field measurements of matric suctions in glacial till = shown in Figs. 4.71 and 4.72, respectively. The laboratory measurements 100 4 MEASUREMENTS OF SOIL SUCTION Desorption cycle saturated sensor &dry hole 1600 standard compaction 1400 - Absorption cycle dry - sensor &dry hole g 1200 standard compaction .* Dry sensor &wet hole 7 lo00 standard compaction Dry sensor &dry ho!e modified compaction : 6 800 u) 600 - - 3 - 'g 3 400 0 L 200 0 10 14 18 22 26 3 t 3 28- c f 20- 8 z 12- P e' e 4 44 r Initially Glacial till I I111111 I IiIIIIII 11 .P 36 > t 3 28- c f 20- z 12- P e' e 8 4 83 hours 41 3 hours Initially Initially dry sensors Glacial till I I111111 I IiIIIIII 11 1 1 Water content, w (%) Time, t (min ) Figure 4.71 Laboratory measurements of matric suction in gla- cia1 till using thermal conductivity senson (MCS 6OOO). Figure 4.73 Equalization times for the MCS 6OOO sensors for glacial till and Regina clay compacted at various water contents. were performed on compacted specimens. Figure 4.71 indicates that the initially wet sensor gives a lower matric suction than the initially dry sensor for the same water content in the soil. The equalization times required for the MCS sensor are shown in Figure 4.73 for measurements in glacial till and Regina clay. The initially wet sensors have longer equalization times (Le., maximum 413 h) than the initially dry sensors (i.e., 83 h). This pattern was consistent in both soils . Unreliable suction measurements using thermal conductivity sensors have been attributed to poor contact between the porous block and the soil, the entrapment of air during installation (Nagpal and Boersma, 1973), and temperature and hysteretic effects. Poor contact between the porous 200 Shower Snowing VWVl I No reading when soil temperature below zero OC Depth = 0.1 5 m - g 120- b Sensor location changed r, V 3 100- L. 3 80- -"O 5 10 15 20 25 30 35 40 45 block and the soil will cause the sensor to read a high suction value (Richard, 1974). The temperature effects on the MCS 6OOO sensor readings in Regina clay are illustrated in Fig. 4.74. Tire AG WA-ZZ Sensors Results of laboratory measurements using the AGWA-I1 sensors on highly plastic clays from Sceptre and Regina, Saskatchewan are shown in Figs. 4.75, 4.76, and 4.77. The soils were sampled in the field using Shelby tubes. Matric suction measumments on compacted soils have also been performed on a silt from Brazil (Fig. 4.78). The results indicate that a considerably longer equalization time was required for the sensor to equilibrate when the water content of the specimen was low (Fig. 4.78) than when the water content of the specimen was high (Figs. 4.75, 4.76, and 4.77). The longer equalization time is attributed to the - m 500 2 100 a O"2O 22 24 26 28 30 32 Elapsed time, t (days) Temperature ("C) -re 4.72 Field measurements of matric suction in glacial till using thermal conductivity sensors (MCS-aooO). Figure 4.74 Temperature effect on the MCS 6ooo sensor readings in Regina clay. 4.4 MEASUREMENTS OF MATRIC SUCTION 101 Elapsed time, t (hours) Figure 4.75 Laboratory measurements of matric suction on a highly plastic clay from Sceptre, Sask., Canada (w = 39.3%). lower coefficient of permeability of the soil specimen as its water content decreases. Several laboratory measurements were conducted using two senson inserted into each soil specimen. One sensor was initially airdried, and the other was initially saturated. The initially saturated sensor was submerged in water for about two days prior to being installed in the soil. The sensors were inserted into predrilled holes in either end of the soil specimen. The specimen with the installed sensors was wrapped in aluminum foil to prevent moisture loss during the measurement. The responses of both sensors were monitored immediately and at various elapsed times after their installation. The results indicate that the time required for the initially dry sensor to come to equilibrium with the Elapsed time. t (hours) Figure 4.76 Laboratory measurements of matric suctions on a highly plastic clay from Sceptre, Sask., Canada (w = 34.1%). 102 4 MEASUREMENTS OF SOIL SUCTION 700 600 ;a 500 n 6 - I I Hi@hly plaStiC clay Water content: 35.1% Elapsed time, t (hours) Figure 4.77 Laboratory measurements of matric suction on a highly plastic clay from Darke Hall, Regina, Sask., Canada (w = 35.1%). soil specimen is less than the equilibrium time required for the initially saturated sensor to come to equilibrium. On the basis of numerous laboratory experiments, it would appear that the AGWA-I1 sensors that were initially dry yielded a matric suction value which was close to the comt value. In general, the initially dry sensor should yield a value which was slightly high. On the other hand, the initially wet sensor yields a value which was too low. Table 4.8 gives the interpretation of the results presented in Figs. 4.75-4.78 inclusive. On the basis of many laboratory tests, it is recommended that if only one sensor is installed in an undisturbed sam- ple, the sensor should be initially dry. If the sensors have been calibrated using at lest seven data points, the readings obtained in the labratoq should be accurate to within at least 15 kPa of the correct value, provided the matric suc- 700 Compacted silt from Brazil Water content : 15.2% 600 - initially dry sensor 1 \ I I I lnitiallv saturated I Elapsed time, t (hours) D Figure 4.78 Laboratory measurements of matric suctions on a compacted silt from Brazil (w = 15.2%). 4.4 MEASUREMENTS OF MATRIC SUCT~ON 103 Table 4.8 Interpretation of Laboratory Matric Suction Measurements Initially Initially Water Dry Wet Best Soil Type No. (4%) Wa) orpa) (ea) Figure Content Sensor Sensor Estimate Sceptre clay 4.75 39.3 120 100 114 Sceptre clay 4.16 34.1 136 108 126 Regina clay 4.77 35.1 i6o 150 157 Brazil silt 4.78 15.2 100 68 90 tion reading is in the range of 0-300 kPa. It may take four- seven days before equilibrium is achieved. If the sensors are left in situ for a long period of time, the measurements should be even more accurate. Results from laboratory measurements of matric suction have been used to establish the negative pore-water pressures in undistuw samples of Winnipeg clay taken from various depths within a railway embankment (Sattler et al., 1990). The samples were brought to the laboratory for matric suction measurements using the AGWA-II sensors. The measured matric suctions were comted for the removal of the overburden stress, and plotted as a negative pore- water pressure profile (Fig. 4.79). The results indicated that the negative pore-water pressures approached zero at the average water table, and were, in gene&, more negative than the hydrostatic line above the water table. Field measurements of matric suction under a controlled environment have been conducted in the subgrade soils of a Department of Highways indoor test track at Regina, Sas- katchewan (hi et al,, 1989). The temperature and the rel- ative humidity within the test track facility were controlled. Twenty-two AGWA-I1 sensors were installed in the subgrade of the test track. The subgrade consisted of a highly plastic clay and a glacial till. The sensors were initially airdried and installed into predrilled holes at various depths in the subgrade. The sensor outputs were recorded twice a day. Typical matric suction measurements on the compacted Regina clay and glacial till subgrade are presented in Figs. 4.80 and 4.81. Consistent readings of matric suction rang- ing from 50 to 400 kPa were monitored over a period of more than five months prior to flooding the test track. The Pore-water pressure, u, (kPa) Figure 4.79 Negative pore-water pressures measured using the AGWA-II thennal conductivity sensors on undisturbed samples. 104 4 MEASUREMENTS OF SOIL SUCTION $7001 : ; I I ,!, i- ; 500 content = 7.4% - 1400 $300 In 8 200 ,: - 100 I IIIIbIII 0; ldo 260 300 40 5;)o & 760 80 40 Elapsed time, t (hours) Figure 4.80 Measurements of matric suction using the AGWA- I1 thermal conductivity sensors under a controlled environment in the test track facility (Department of Highways, Regina, Can- ada). sensor responded quickly upon flooding (Fig. 4.82). The results demonstrated that the AGWA-II sensors can pro- vide stable measurements of matric suction over a relatively long period of time. Matric suction variations in the field can be related to environmental changes. Several AGWA-I1 sensors have been installed at various depths in the subgrade below a railroad. The soil was a highly plastic Regina clay that exhibited high swelling potentials. Matric suctions in the soil were monitored at various times of the year. The results clearly indicate seasonal variations of matric suctions in the field, with the greatest variation occurring near ground sur- face (Fig. 4.83). Thermal conductivity sensors appear to be a promising device for measuring matric suction either in the laboratory or in the field. However, proper calibration should be performed on each sensor prior to its use. The calibration study on the AGWA-I1 sensors revealed that the sensors are quite sensitive for measuring matric suctions up to 175 kPa. It is possible that further improvements on thermal conductivity type sensors will further enhance their performance. For example, a better seal around the electronics within the sensor could reduce the influence of soil water. Also, a stronger, more durable porous block would pro- duce a better sensor for geotechnical engineering applications. These improvements would reduce the mortality rate of the sensor. 4.5 MEASUREMENTS OF OSMOTIC SUCTION Several procedures can be used to measure the osmotic suction of a soil. For example, it is possible to add distilled water to a soil until the soil is in a near fluid condition, and then drain off some effluent and measure its electrical conductivity. The conductivity measurement can then be linearly extrapolated to the osmotic suction corresponding to the natural water content. This is known as the saturation extract procedure. Although the procedure is simple, it does not yield an accurate measurement of the in situ osmotic suction (Krahn and Fredlund, 1972). A psychrometer can also be placed over the fluid extract to measure the osmotic suction, but this procedure, like- 1000 2000 3000 4 Elapsed time, t (hours) Figure 4.81 Measurements of matric suction using the AGWA-I1 thermal conductivity sensors under a controlled environment (Test track facility, Department of Highways, Regina, Canada). 4.5 MBASUREMENTS OF OSMOTIC SUCTION 105 - 1500 .E 1000 - _. ' Slrid' : ' :. : ., :.: ', ., :, : i : .; :., : :. i -Regina clay 865 901 .o 5 500 Reginsclay Sandz ij ,Sand-', 6 I, I al 0' 0 3000 8ooo Irkpermeable 'O0O Distance (mm) membrane L '*Oo0 50000 100000 150000 200000 Tim, t (min) (a) (b) Figure 4.82 Cross-section and location of measurements of matric suction using the AGWA-II thermal conductivity sensors under a controlled environment (a) sensor locations; (b) sensor responses, (Test track facility, Department of Highways, Regina, Canada). wise, gives poor results. It is the use of the pore fluid squeezer technique that has proven to give the most rea- sonable measurements of osmotic suction. 4.5.1 Squeezing Technique The osmotic suction of a soil can be indirectly estimated by measuring the electrical conductivity of the pore-water from the soil. Pure water has a low electrical conductivity in comparison to porn-water which contains dissolved salts. The electrical conductivity of the pore-water from the soil can be used to indicate the total concentration of dissolved salts which is related to the osmotic suction of the soil. The pore-water in the soil can be extracted using a pore fluid squeezer which consists of a heavy-walled cylinder and piston squeezer (Fig. 4.84). The electrical resistivity (or electrical conductivity) of the pore-water is then measured. A calibration cuwe (Fig. 4.85) can be used to relate the electrical conductivity to the osmotic pressure of the 700 800 500 2 E400 5 3 7 300 - 200 100 8 ONov Jan Mar May July Sept 1984 1985 Figure 4.83 Summary plot of matric suction measurements versus time of year for various depths in Regina clay in Saskatche- wan (from van der Raadt, 1988). soil. The results of squeezing technique measurements appear to be affected by the magnitude of the extraction pressure applied. Krahn and Fredlund (1972) used an extraction pressure of 34.5 MPa in the osmotic suction measurements on the glacial till and Regina clay. Figures 4.86 and 4.87 present the results of osmotic suction measurements on glacial till and Regina clay, respectively. The measurements were conducted using the squeezing technique. The measured osmotic suctions are shown to agree closely with the total minus the matric suction measurements. In this case, the total and the matric suctions were measumd independently. The discrepancies -L 6.4 T LU Rubber (neoprene disk) Perforated plate, 1.6 mm thick (filter paper support) tainless steel wire-screen isk, 1.6 mm thick Rubber (neoprene) washer 4.8 mm thick Effluent passage reamed to fit nose of syringe passage k54.04 Figure 4.84 The design of the pore fluid squeezer (from Man- heim, 1966). 106 4 MEASUREMENTS OF SOIL SUCTION Figure 4.85 Osmotic pressure versus electrical conductivity re- lationship for pore-water containing mixtures of dissolved salts (from U.S.D.A. Agricultural Handbook No. 60, 1950). shown at low water contents for the glacial till (Fig. 4.85) are believed to be attributable to inaccurate measurements of matric suction (Krahn and Fredlund, 1972). The close agreement exhibited in Figs. 4.86 and 4.87 indicates the reliability of the squeezing technique for osmotic suction measurements. The results also support the 2 600 k - Total minus matric suction By squeezing technique 0 9 11 13 16 17 19 21 Water content, w (%) Figure 4.86 Osmotic suction versus water content for glacial till (from Krahn and Fredlund, 1972). m - Total minus matric suction 600 k z 200 0 20 22 24 26 20 30 32 E I Water content, w (96) Figure 4.87 Osmotic suction versus water content for Regina clay (from Kmhn and Fredlund, 1972). validity of the matric and osmotic suctions being compo- nents of the total suction [Le., Eq. (4.3)]. It appears that the osmotic suction is relatively constant at various water contents (Figs. 4.86 and 4.87). Therefore, it is possible to use the osmotic suction as a relatively fixed value that can be subtmcted from the total suction measurements in order to give the matric suction values. [...]... verified in the unsaturated soil in a similar manner to its verification for a saturated soil However, the volume of water (or water content) should be constant while the hydraulic head gradient is varied Experiments to verify Darcy’s law for unsaturated soils have been performed, and the results are presented in Fig 5.5 (Childs and Collis-George, 1950) A column of unsaturated soil with a uniform water... volumetric water content, 8, (Buckingham, 1907; Richads, 1 931 ; Moore, 1 939 ) A coefficient of permeability function, k,(8,), has been proposed 114 5 FLOWLAWS Table 5.1 Suggested Values of the Constant, 6, and the Pore Size Distribution Index, A, for Various Soils Soils 6 Values X Values Source Uniform sand Soil and porous rocks Natural sand deposits 3. 0 4.0 3. 5 2.0 4.0 00 Irmay [19541 Corey [1954] Avejanov [19501... suction form for water flow However, the elevation head component has then been o i t d mte The flow of water through a soil is not only governed by the pressure gradient, but also by the gradient due to ele107 108 5 FLOWLAWS FLOW SYSTEMS COMMON TO UNSATURATED SOILS Air diffusion through water Water Occluded air bubbles (Compressible pore fluid flow) Figure 5.1 Flow systems common to unsaturated soils. .. applied to unsaturated soils In an unsaturated soil, however, the magnitude of the coefficient of permeability will differ for different volumetric water contents, e,, as depicted in Fig 5.5 5.1 .3 Coefficient of Permeability with Respect to the Water Phase The coefficient of permeability with respect to the water phase, k, is a measure of the space available for water to , flow through the soil The coefficient... constant for a specific saturated soil Elq (5.9) can also be written for the x- and z-directions The negative sign in Elq (5.9) indicates that water flows in the direction of a decreasing hydraulic head Darcy’s law also applies for the flow of water through an unsaturated soil (Buckingham, 1907; Richard, 1 931 ; Childs and Collis-George, 1950) However, the coefficient of permeability in an unsaturated soil. .. Hillel et al (1972) The method is also suitable for situations where the water table is deep and the soil is nonhomogeneous The method is most suitable for soils of low plasticity Numerous problems have been reported when using the test for highly plastic swelling soils The test procedure by Watson (1966) and Hillel et ai (1972) considers a column of saturated soil that undergoes internal drainage while... where 25 50 'm Case 2 1 Unsaturated soil UW -150- -200 (ua - uw) 150 I 150 p w = density of water When the water density, pw, is constant, Eq (5 .3) takes Assume: P,= constant g = constant ( Elevation = y Pressure = u , Velocity = v w Density = pW Case 3 US I I ~loo-T;~~!d Unsaturated uw (u - uw) 30 0 200 Figure 5.2 Pressure and matric suction gradients across an unsaturated soil element I Arbitrary... permeability, k, is con, stant for various hydraulic head gradients (Le., in this case, only the gravitational head was varied) applied to the unsaturated soil In other words, the rate of water flow through an unsaturated soil is linearly proportional to the hydraulic head gradient, with the coefficient of permeability being a constant, similar to the situation for a saturated soil This confirms that Dmy’s... head gradient as the fundamental driving potential The hydraulic head gradient in a specific fluid phase is the driving potential for flow in that phase This is equally true for saturated and unsaturated soils 5.1.1 D i i g Potential for Water Phase rvn The driving potential for the flow of water defines the energy or capacity to do work The energy at a point is com- E g = MwgY (5.1) where Eg = gravitational... the soil structure is assumed to be negative slope of the effective degree of saturation, incompressible Se, versus matric suction, (u, - uw), curve There are three soil parameters that can be identified from Soils with a wide range of pore sizes have a small value the matric suction versus degree of saturation curve These are the air entry value of the soil, (u, the residual for h The more uniform . Index, A, for Various Soils Soils 6 Values X Values Source Uniform sand 3. 0 00 Irmay [ 19541 Soil and porous rocks 4.0 2.0 Corey [1954] Natural sand deposits 3. 5 4.0 Avejanov. Darcy’s law for unsaturated soils have been performed, and the results are presented in Fig. 5.5 (Childs and Collis-George, 1950). A column of unsaturated soil with a uniform water. the driving potential for flow in that phase. This is equally true for saturated and unsaturated soils. 5.1.1 Driving Potential for Water Phase The driving potential for the flow of water

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