Settlement due to Pumping Well

Transcription

1 1 Introduction Settlement due to Pumping Well A powerful and flexible feature in SIGMA/W is the ability to compute the volume change arising from an independently computed change in pore-pressure. The pore-pressure change could, for example, come from a SEEP/W analysis or a VADOSE/W analysis. SIGMA/W can then compute the associated volume change. This type of an analysis is, in essence, an uncoupled consolidation analysis. SIGMA/W forms and solves the coupled displacement and pore-pressure equations, but the known change in pore-pressure becomes a specified boundary condition. This example illustrates how an uncoupled consolidation or volume change analysis can be done using SIGMA/W. 2 Problem configuration and setup The problem involves computing the settlement that may occur due to the pumping from a well. The starting conditions are as shown in Figure 1. The watertable is 2 m below the ground surface Elevation - m Figure 1 Problem configuration Distance - m The pumping is considered to occur from a half-metre long well screen. A close up view is shown in Figure 2. The well screen is defined by drawing two Points and then drawing a Line to join the two Points. Using the Draw Mesh Properties command, a constraint is put on the Line such that there must be 5 divisions. With a global element size of about 1 m and the well screen Line constraint, the mesh shown in Figure 1 is automatically created. SIGMA/W Example File: Settlement due to pumping well.doc (pdf) (gsz) Page 1 of 5

2 Figure 2 Simulated well screen 3 Insitu conditions The initial conditions are required so that we can obtain the correct change in pore-pressures. The starting conditions can be set up with a SIGMA/W Insitu analysis. 4 Long-term seepage conditions The effect of the pumping is analyzed using a steady-state SEEP/W analysis. Boundary conditions are applied on the left and right ends, so that the water level remains at the initial watertable. The top elevation of the well screen is 6.5 m. We will make the assumption that the pumping will be controlled, so that the water level in the well will not drop below the top of the screen. This can be specified with an H-type boundary condition equal to 6.5 m. This means the water pressure will be zero at the top of the well screen and increase hydrostatically with depth within the well screen. The resulting long-term (steady-state) pore-pressure conditions are shown in Figure 3. Notice that the zero-pressure contour is above the well screen even though a zero-pressure was specified at the top of the well screen. This is the correct numerical solution, but perhaps not representative of actual field conditions. This response comes about in part due to the close proximity of the specified head conditions at the end. Physically, this means the end boundary conditions can supply sufficient water to create this situation. For actual field problems, the ends should be further away. The results are, however, adequate for this illustrative example. SIGMA/W Example File: Settlement due to pumping well.doc (pdf) (gsz) Page 2 of 5

3 Pumping well 14 Elevation - m Distance - m Figure 3 Steady state pore-pressure contours 5 Volume change analysis Now that the starting and final pore-pressure conditions are known, we can do a Volume Change analysis. The procedure is presented in the KeyIn Analysis dialog box. The Parent analysis is the SIGMA/W Insitu analysis The initial stresses and initial pore-pressures come from the Parent analysis The Analysis Type is Volume Change The final pore-pressure comes from the SEEP/W analysis; this is specified using the Browse button SIGMA/W Example File: Settlement due to pumping well.doc (pdf) (gsz) Page 3 of 5

4 Figure 4 KeyIn Analysis dialog box As noted earlier, SIGMA/W takes the initial and final pore-pressures and computes the pore-pressure change. The computed change in pore-pressure becomes a boundary condition in the SIGMA/W coupled deformation analysis. The resulting settlement or volume change is presented in Figure 5. Pumping well Figure 5 Settlement due to pumping (5X exaggeration) SIGMA/W Example File: Settlement due to pumping well.doc (pdf) (gsz) Page 4 of 5

5 6 Concluding remarks This simple example illustrates a very powerful feature in SIGMA/W. The uncoupled volume change analysis is attractive in that it makes it possible to study the changing pore-pressure conditions separately from the deformation analysis. This is particularly useful for complex saturated-unsaturated flow systems. It can lead to an understanding of the issues involved in a project in steps, rather then trying to do everything in one step. The difference between a uncoupled analysis and a fully coupled analysis is rather small for cases where there are no total stress changes; for example, a situation where the pore-pressure change is due to environmental changes as opposed to changes arising from applying loads. A complementary example that includes an uncoupled volume change analysis is the example called, Heave due to Infiltration. You can study this complementary example if you would like to obtain more information on uncoupled analyses. SIGMA/W Example File: Settlement due to pumping well.doc (pdf) (gsz) Page 5 of 5