Total positivity in some classical groups

published_or_final_versionMathematicsMasterMaster of Philosoph

拋石保護控制固床工趾部局部淘刷之研究

An array of 1:50 scaled groundsill models was installed in a semi-circulating flume to study scour mechanics and effectiveness of riprap protection lengths and riprap sizes. Results of this study show that riprap protection at the toe of a groundsill is unable to completely eliminate the local scour, but it is capable of reducing scour depth and scour length. A dimensionless relationship was also derived in this study to help select riprap protection lengths and riprap sizes. The maximum percent of scour depth reduction can be reduced from 83% to 76% with respect to the increase of riprap size to channel sediment size ratio when riprap protection covers 1/4 of the groundsill interval. Percent of reduction remains fairly constant when riprap protection covers 1/2 of the groundsill interval. On the other hand, the maximum percent of scour length reduction increases from 64% to 84% with respect to the increase of riprap size to channel sediment size ratio.本研究利用 1:50 縮尺之系列固床工模型進行水工實驗，以探討拋石保護段長度及拋石粒徑大小對減 輕固床工趾部渠床淘刷的效益。除了瞭解拋石保護措施下渠床局部淘刷的縮減與淘刷機制外，更透過因次分 析，尋求拋石保護段長度與拋石粒徑之無因次設計公式。研究結果顯示，拋石雖可以減輕固床工趾部渠床的 局部淘刷，但並不能完全消除。當拋石保護段的長度為固床工間距的 1/4 時，渠床淘刷深度的最大縮減百分 比隨著拋石粒徑與渠床床砂粒徑比的增加而從 83% 降低為 76%；當拋石保護段的長度為固床工間距的 1/2 時，淘刷深度的最大縮減百分比則大致持平。至於淘刷坑長度的最大縮減百分比，則隨著拋石粒徑與渠床床 砂粒徑比的增加由 64% 提高為 84%