1 Introduction Pressure Plate Drying and Wetting This air flow example illustrates how the process of axis translation, which is used in pressure plates to measure the water content function, can be modeled. Boundary conditions are critical to obtaining good modeled results, which indicates that they are therefore critical to obtaining good laboratory results. Very slight changes in the elevation of the outlet drainage relative to the base of the soil (or top of ceramic disk) can have a significant impact on water extraction at any given applied air pressure. 2 Feature highlights GeoStudio feature highlights include: Air pressure and water pressure coupling (Ua-Uw) Water balance in a drying / wetting soil sample Verification with known solutions. 3 Geometry and boundary conditions Figure 3-1 shows a schematic of a pressure plate cell and the corresponding model geometry. The cell is designed such that positive air pressure can be applied at the top, and forced out water collected from beneath the high air entry disk below. The model cross section in this example is an axisymmetric view, which means it considers that the cross section rotates about the vertical axis.in this example, a silt material is placed above the 5 bar (5 kpa) air entry ceramic disk. This disk is designed such that an air pressure of 5 kpa can be applied to it without forcing out any of the trapped water. The disk must remain saturated throughout the test cycle. Axis of symmetry Air Pressure Line (u a = +ve) Spring High Air-Entry Disk SOIL SPECIMEN Outlet Line (u w = ) 5 bar AEV disk 1 2 3 Inlet Line Radius (m) (x.1) Figure 3-1 Pressure plate apparatus and modeled section In this test model, the initial conditions are established as if the soil were able to drain under gravity to a zero pressure condition at the base of the sample. This is equivalent to specifying a pressure of.1 kpa at the base of the 1 cm thick ceramic stone. Once initial conditions were established using a steady state AIR/W Example File: Pressure plate drying and wetting.doc (pdf) (gsz) Page 1 of 5
analysis, five incremental drying stages plus a single re-wetting stage were linked together, as shown in Figure 3-2. Figure 3-2 Drying and wetting analyses The pressure plate makes use of a technique called Axis Translation, in which a positive air pressure is applied to push water out the bottom as opposed to a negative water pressure to suck it out. The actual stress stage variable in an unsaturated soil is matric suction, which is the difference between air and water pressure, or (Ua Uw). To move water, you have the choice of altering Uw or Ua. Since it is very hard to create a water suction of more than 1 kpa due to cavitation, it is more practical to create a positive air pressure and push the water out. For each incremental load in Ua, the soil is allowed to drain. All drained water is collected and weighed, such that the total volume of water leaving the sample is known. At each stage, when the drainage stops, a new load can be applied to drive more water out. It is important to allow full drainage before incrementing the applied air pressure. In this example, the air pressure is increased on the top and sides of the sample according to the values shown in the figure above. The air pressure was applied to the side of the sample, because quite often in these tests a small shrinkage of the soil away from the walls of the sample ring will occur, which allows air to enter all sides of the sample. Figure 3-3 Hydraulic (left) and air pressure (right) boundary locations AIR/W Example File: Pressure plate drying and wetting.doc (pdf) (gsz) Page 2 of 5
Figure 3-3 above shows the hydraulic boundary condition of.1 kpa applied to the base of the ceramic stone. On the right of the image are the applied positive air pressure BC on the top and sides of the sample, as well as an atmospheric BC along the base of the stone. 4 Material properties The material models used in this example are as follows. For the soil, the sample function for was chosen and the Ksat was adjusted to be.1 m/day as shown below. 1.e-1.45 1.e-2.4 X-Conductivity (m/day) 1.e-3 1.e-4 1.e-5 1.e-6 1.e-7 Vol. Water Content (m³/m³).5 1.e-8.1.1 1 1 1 1..1.1 1 1 1 1 The water content for the silt is on the right in the above image. The ceramic stone was modeled using a water content function that ensures 1% saturation to a suction above 5 kpa as shown below. The conductivity of the stone was set at a uniform value of.1 m/day for all suctions. 5 bar aev stone Vol. Water Content (m³/m³) 1 1 1 1 1 The air conductivity function for the stone is not important, because the stone will remain saturated. It is sufficient to use any function with a low K air. AIR/W Example File: Pressure plate drying and wetting.doc (pdf) (gsz) Page 3 of 5
5 Discussion of results The applied pore-air pressure is shown below on the left, and the response computed pore-water pressure is shown on the right. These data values are for a location in the middle of the sample. You can see that the air pressure responds very quickly, but that the pore-water pressure is a little lower in magnitude. You can also see that the pore-water pressure dissipates after every applied air pressure increment. Since the air pressure is constant, it is the dissipation of the excess pore-water pressure that is causing the drainage. Pore air pressure Pore water pressure Air Pressure (kpa) 16 14 12 1 8 6 4 2-2 Pore-Water Pressure (kpa) 8 6 4 2-2 -4-6 The air and water contents at the sampled location are shown below. You can see that as the water contents decrease due to dissipation of pressure and drainage, the air volume increases by the same amount. This is the correct observation, given the assumption that the soil skeleton is incompressible. Water contents air contents.45.4 Vol. Water Content (m³/m³) Air Content (m³/m³).5.5. The final two images below show the matric suction over time, as well as the total mass flow out of and back into the sample. You can see that the matric suction is the difference between air and water pressures, and that it is a positive value when the soil is unsaturated. As the matric suction approaches zero, the soil nears saturation. The figure on the right below is the mass balance for the full drying and wetting cycle. You can see that the process in this case is 1% reversible. This means that no hysteretic effects have been considered. With the new Add-In functions in Geo-Studio 27, it is possible for the user to create a hysteretic water content function and have it applied in the solver. This is left for a user or keen graduate student to undertake. AIR/W Example File: Pressure plate drying and wetting.doc (pdf) (gsz) Page 4 of 5
16 Matric suction.5 Water flow 14 12 1 8 6 4 2 Cumulative Water Flux (m³). -.5 AIR/W Example File: Pressure plate drying and wetting.doc (pdf) (gsz) Page 5 of 5