GEO-SLOPE International Ltd, Calgary, Alberta, Canada www.geo-slope.com 1 Introduction Pressure Plate Drying and Wetting Axis translation is used in pressure plate measurements of the water content function to avoid cavitation. Water will undergo cavitation at negative water pressures of around 1 kpa, which is equivalent to a matric suction of 1 kpa under atmospheric conditions. As such, the axis is translated by increasing the air pressure, which allows large matric suctions to be generated without inducing a large negative water pressure. The objective of this example is to highlight the boundary conditions and material properties required to model a pressure plate test and to demonstrate the use of a coupled air-water transfer analysis using SEEP/W and AIR/W. 2 Feature highlights GeoStudio feature highlights include: Coupling SEEP/W and AIR/W Analysis of a high AEV disk Including multiple analyses in a single GeoStudio Project 3 Numerical Model Figure 1 presents 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. Water is expulsed from the sample and collected beneath the high air entry (AEV) disk. A high AEV disk is used in these experiments because the disk remains saturated under very large matric suctions due to the very uniform and small pore-size distribution of the stone. Axis of symmetry Air Pressure Line (u a = +ve) Silt 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 1 - Pressure plate apparatus and modeled section The analysis is set to axisymmetric, so the model domain represents half of the sample with the vertical line of symmetry at a radius of m (Figure 1). A silt material is placed above the 5 bar (5 kpa) disk. AIR/W Example File: Pressure Plate Drying and Wetting.docx (pdf) (gsz) Page 1 of 6
GEO-SLOPE International Ltd, Calgary, Alberta, Canada www.geo-slope.com This implies that the disk will remain saturated up to an air pressure of 5 kpa. The disk must remain saturated throughout the test cycle in order to allow water to drain from the soil through the outlet. Figure 2 presents the analysis tree. A steady-state coupled air-water analysis is used to establish the initial conditions. A pore-water pressure head of.1 m (1 cm) is applied to the base of the 1 cm thick stone, which establishes a zero pressure condition at the base of the sample. An air pressure of kpa is applied to the top, right and bottom edges of the domain such that atmospheric conditions exist through the sample at the onset of the analysis. Figure 2 Analysis tree for the project Each analysis forms the Parent for the subsequent analysis, which is demonstrated by the relative position of the analyses in the tree (Figure 2; parent-child relationship). Accordingly, the pore-water pressure and pore-air pressure initial conditions are set to the Parent (Figure 3). Figure 3 - Analysis settings for each child analysis in the tree The drying stage analyses are conducted by applying an air pressure boundary condition to the top and right edge of the domain (Figure 4). The water pressure and air pressure at the bottom of the column is maintained at.1 m and kpa, respectively, to allow free-drainage from the bottom. The final analysis in the tree is used to model re-wetting of the sample. The air pressure is set back to kpa, allowing the sample to imbibe water and return to the initial condition. AIR/W Example File: Pressure Plate Drying and Wetting.docx (pdf) (gsz) Page 2 of 6
GEO-SLOPE International Ltd, Calgary, Alberta, Canada www.geo-slope.com Figure 4 - Hydraulic (left) and air pressure (right) boundary locations A silt material was used in the region above stone, with the volumetric water content and hydraulic conductivity functions developed using the SEEP/W sample functions. The VWC function for the high AEV stone assumes a porosity of.334 and a hydraulic conductivity at saturation of.1 m/day. The air conductivity functions for the silt and disk were estimated in the software. Each stage in the analysis was modeled for a period of one day using fifty time steps. The small time steps are required such that the rapid changes in air pressure and water pressure can be captured by the analysis. The total duration of the analysis is therefore 6 days. 4 Results and Discussion Figure 5 and Figure 6 present the pore-air pressure and pore-water pressure, respectively, at a node located in the middle of the domain. The air pressure responds very quickly to the applied boundary condition because of the high air conductivity. At the onset, the water pressure increase is approximately equal to the air pressure increase. The low conductivity of the soil inhibits the movement of water. As such, the pore-water pressure dissipates more slowly as water drains out the bottom of the sample through the high AEV disk. Eventually, the water pressure drains back to the initial condition and a new air pressure increase occurs. AIR/W Example File: Pressure Plate Drying and Wetting.docx (pdf) (gsz) Page 3 of 6
Pore-W ater Pressure (kpa) Air Pressure (kpa) GEO-SLOPE International Ltd, Calgary, Alberta, Canada www.geo-slope.com Pore air pressure 16 14 12 1 8 6 4 2 Figure 5 - Pore-air pressure verses time in middle of the domain 8 Pore water pressure 6 4 2-2 -4 Figure 6 - Pore-water pressure verses time in middle of domain The pore-water pressure response is negative during the re-wetting stage. Recall that the air pressure boundary condition along the edges of the sample has been set to kpa. The air pressure in the sample immediately drops to kpa. The sample attempts to imbibe water, but cannot because the flow into the sample from below is controlled by the conductivity of the stone and soil sample at the end of the drying stage. Eventually, water moves back into the sample and the pore-water pressure diminishes back to nearly kpa. AIR/W Example File: Pressure Plate Drying and Wetting.docx (pdf) (gsz) Page 4 of 6
Matric Suction (kpa) Vol. Water Content (m³/m³) Air Content (m³/m³) GEO-SLOPE International Ltd, Calgary, Alberta, Canada www.geo-slope.com Figure 7 presents the air and water content at the same location. The water content decreases due to dissipation of pore-water pressure during drainage, while the air content increases by the same amount. The opposite happens during the re-wetting stage. Water contents.45.4.35.3.25.2.15.1.5 Time (day) air contents.35.3.25.2.15.1.5. Time (day) Figure 7 - Water content and air content verses time Figure 8 and Figure 9 present the matric suction time plot and cumulative water flow for the sample, respectively. The matric suction increase is in-keeping with the pore-water pressure and air pressure response presented above. The water and air pressures are approximately kpa at the start of the test, implying that the soil is tension saturated. The air pressure is then increased rapidly and sustained for each stage, while the water pressure increases and then dissipates back to the initial condition. As a result, the matric suction increases, which forces water out of the sample as indicated by Figure 9. 16 14 Matric suction 12 1 8 6 4 2 Figure 8 - Matric suction verses time AIR/W Example File: Pressure Plate Drying and Wetting.docx (pdf) (gsz) Page 5 of 6
C u m u la tive W a te r Flu x (m ³) GEO-SLOPE International Ltd, Calgary, Alberta, Canada www.geo-slope.com Water flow 1e-6-1e-6-2e-6-3e-6-4e-6-5e-6-6e-6 Figure 9 - Cumulative water flow 5 Summary and Conclusions A coupled SEEP/W and AIR/W analysis can be used to model the wetting and drying stages of a pressure plate test. The pressure plate makes use of the axis-translation technique, which shifts the reference air pressure to avoid cavitation in the water phase. The volumetric water content of a soil is a function of matric suction, which is the difference between the air pressure and water pressure. As such, the matric suction of a sample is increased by increasing the air pressure while maintaining the water pressure. The analysis demonstrates that the air pressure response within the sample is almost immediate. This causes an immediate and equal response in the pore-water pressure, which eventually dissipates back to the initial condition as water drains out through the high AEV disk. AIR/W Example File: Pressure Plate Drying and Wetting.docx (pdf) (gsz) Page 6 of 6