Filter design problem Let's say that a soil with the following grain size distribution (GSD) needs to be retained at the t oe of a dam

Filter design problem Let's say that a soil with the following grain size distribution (GSD) needs to be retained at the t oe of a dam . Your goal is to design the filter soil; that is, to find the GSD of a soil that is capable to serve as a filter to protect this base soil. The GSD of the base soil is: dmm) 0.85 0.6 0.42 0.3 0.177 0.125 0.075 % finer than 100 57 38 25 14 9 5 The solution is as follows. 1. Plot the GSD of the base soil, using a computer. The graph space should look exactly like the one shown below. Print it in landscape so as to make the printout as large as possible. 100% l 90% vi Ill Ill E > e ..... C Ill .c i I 80% I I I I 70% I 60% 50% -- 40% a.I I C :.: 30% 20% I I - -----, I l I 10% . 0% 0.01 0.1 1 10 sieve diameter, d (mm) 2. Use the plotted GSD of the base soil to determine dss 8 • 3. Calculate the dis FRET to satisfy the retention criterion: dis FRET= 5 dss B 4. Draw a point, by hand, on the graph, with coordinates (dis 81 FRET, 15%). 100 S. Draw, by hand, a GSD curve that {l) is parallel to the base soil's GSD and (2) passes through the point drawn in step 4. Any soil with a GSD that lies to the left of this drawn GSD and is also parallel to the base soil's GSD satisfies the retention criterion. 6. Use the plotted GSD of the base soil to determine d1s a. 7. Calculate the d1s FFLow to satisfy the retention criterion: d15 F FLOW = 5 d15 8 8. Draw a point, by hand, on the GSD graph, with coordinates (d1s FFLow, 15%). 9. Draw, by hand, a GSD curve that (1) is parallel to the base soil's GSD and (2) passes through the point drawn in step 8. Any soil with a GSD that lies to the right of this drawn GSD and is also parallel to the base soil's GSD satisfies the flow criterion. 10. At this point, you should have three perfectly parallel GSDs on the printed graph. The leftmost one should be the GSD of the base soil (which was printed with the computer). The rightmost one is the GSD that you drew by hand, associated with the retention criterion. The middle one is the GSD that you drew by hand, associated with the flow criterion. 11. The middle and rightmost GSDs serve as limits for the range of soils that can serve efficiently to filter the given base soil. That is, any soil with a GSD that lies inside this range and is also parallel to the GSD of the base soil, works as a filter for the base soil. 82