GEO-SLOPE International Ltd, Calgary, Alberta, Canada Rapid drawdown

Transcription

1 Elevation Introduction Rapid drawdown The objective of this illustration is to show how to model the rapid drawdown of a reservoir. It presents two cases one with instantaneous drawdown and another with drawdown over a period of time. This example also shows how to create a plot of factor of safety with time during and after the drawdown. Problem configuration The following diagram shows the problem configuration Core metres Figure The problem configuration 3 Analysis tree The analysis tree explains the steps used in the analyses. The first step is to establish the long term steady-state conditions with a full reservoir. The second step is to look at the case of instantaneous drawdown and how the factor of safety changes over a period of 30 days after the drawdown. The analysis is then repeated for the case where the reservoir is drawdown over a period of five days. SEEP/W Example File: Rapid drawdown.docx (pdf) (gsz) Page of 5

2 4 Instantaneous drawdown The instantaneous case is modeled with boundary conditions. The Point at the upstream toe is assigned a head-type boundary (H = 0.0). The remained of the upstream face below the initial reservoir level is assigned a potential seepage face type of boundary condition. The changing position of the piezometric line is shown Figure. Core Figure Changing positions of the piezometric line after instantaneous drawdown Figure 3 shows the condition at the end of Day-. Note how the excess pore-pressure remaining in the embankment after the reservoir has been removed is seeping out of the upstream face. Also, note the colored circles on the upstream face. These symbols show which nodes are H nodes and which Q nodes. The H nodes are red and the Q nodes are blue. Flow emerges from the upstream face at the H (red). These will change with each time step. Core Figure 3 Conditions at the end of Day- SEEP/W Example File: Rapid drawdown.docx (pdf) (gsz) Page of 5

3 Factor of Safety These results can now be used in SLOPE/W to look at the changing factors of safety with time after the drawdown. The SLOPE/W stability analysis becomes a child of the SEEP/W transient analysis as you can see in the Analysis Tree The key to computing factors of safety for all the time steps is to select (all) in the Time edit box as shown in the follow Analysis Dialog box. Using The Draw Slip Surface command in SLOPE, we can now create the following plot (Figure 4). Note how that removing the reservoir instantaneously causes the factor of safety to fall immediately below.0 but then recovers with time as the excess pore-pressure dissipates..8 Factor of Safety vs Time Figure 4 Factor of Safety versus time after instantaneous drawdown 5 Drawdown over time We can now repeat the process but simulate drawing down the reservoir over a five day period. This can be done with a boundary function such as in Figure 5. The reservoir head or reservoir level is specified as an H versus time function. SEEP/W Example File: Rapid drawdown.docx (pdf) (gsz) Page 3 of 5

4 Factor of Safety Total Head (m) Drawdown curve Figure 5 Reservoir drawdown curve Now the stability looks dramatically different (Figure 6). The margin of safety against failure drops as the reservoir is drawdown but then bottoms out at a safety factor above.0..8 Factor of Safety vs Time Figure 6 Factor of Safety versus time with drawdown over five days SEEP/W Example File: Rapid drawdown.docx (pdf) (gsz) Page 4 of 5

5 6 Commentary This example illustrates the power of the product integration by using the transient SEEP results in SLOPE to create factor of safety versus time plots. The example also illustrates that the instantaneous case is unrealistic and likely over conservative. Drawing down the reservoir over time is much more realistic and gives much more realistic results. SEEP/W Example File: Rapid drawdown.docx (pdf) (gsz) Page 5 of 5