顆粒級配對砂土滲透係數之影響

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Title:	顆粒級配對砂土滲透係數之影響
Other Titles:	The effect of grain gradation on the permeability of clean sand
Authors:	陳惠宜;Chen, Huei-Yi
Contributors:	淡江大學土木工程學系碩士班楊長義;Yang, Zon-Yee
Keywords:	滲透係數;碎形維度;砂土;級配;顆粒分佈;孔隙分佈;Coefficient of Permeability;Fractal dimension;Sand;Gradation;Particle size distribution;Void Size Distribution
Date:	2012
Issue Date:	2013-04-13 11:49:09 (UTC+8)
Abstract:	砂性土壤滲透係數(k)主要受顆粒之粒徑與級配形態之影響，k值大小為描述流體通過孔隙空間的難易程度，主要取決於土體中的孔隙大小和孔隙分佈聯通情況，而這又是由其組成顆粒的大小和顆粒的級配所控制。在求砂土滲透係數k之經驗公式中，對於顆粒組成的描述，常以單一粒徑(如有效粒徑D10)或利用任兩粒徑之比值(如均勻係數，Cu=D60⁄D10 )來代表整體顆粒大小之組成形態，但實際上僅擷取其中的幾個粒徑尺寸，常無法完整代表土壤的粒徑大小分佈整體狀況。因此，本研究將引用可反映整體顆粒級配形態之碎形維度值(Dg)，將此Dg值應用於土壤滲透係數之推估公式中。本研究試驗將對飽和狀態砂土，規劃不同的顆粒大小(即不同D10)、級配類型(Dg)及孔隙比(e)，並進行一系列室內定水頭滲透試驗，以探討三項參數對砂土滲透係數k的影響比重，並以此三項參數建議新的評估滲透係數的經驗公式。結果得致下列主要結論：(1)級配形態(Dg)、有效粒徑D10及孔隙比e三項參數與滲透係數k 均成正向關係，且經SPSS統計分析得知三項參數對k之影響比重為Dg：D10：e = 4：2：1。 (2)在e值及D10固定下，Dg值越大，表示試體顆粒尺寸分佈較廣趨向「優良級配」，內含有較多大於D10尺度的大顆粒，故k值較大。 (3)當e與級配形態(Dg)因素固定，而D10越大時，意即粒徑分佈曲線平行移動至較大粒徑之區域，顆粒組成大小均變大，表示顆粒所堆疊成之孔隙大小均將變大，故其滲透性變佳而k值變大。 (4)僅以有效粒徑(D10)預測k值結果差異最大，最多將有918%的相對差異；加入考慮孔隙比e參數次之；Hazen及Chapuis公式因為僅採單一個粒徑去代表整體顆粒大小狀況，故對於粒徑組成相近之均勻級配才有較好之預測結果。 (5)Amer & Awad公式考量D10、e、Cu三者其預測k較精準，顯示級配曲線型態考慮越完整對k值預測越精準。 (6)在相同的大小顆粒組成級配狀況(相同Dg)下，不論顆粒群相互堆疊的鬆緊及排列關係如何，其對應構成之孔徑大小分佈比例級配參數(Dp)是固定的，但在顆粒堆疊較鬆之狀況下，Dp雖不變，但其相對之孔隙大小分佈曲線會平移至孔徑較大區域。 (7)本研究試驗獲得滲透係數k之建議經驗公式為： k = (11 e D10)×[Dg ^(0.148((e D10)^(-1.3)))]，並初步獲得他人試驗資料之驗證。 The coefficient of permeability (k) of sands is to reflect the fluid behavior through the pore space among particles, which depends on pore size and pore connectivity. This pore connectivity is controlled by the size and gradation of the soil particles. Calculating the permeability coefficient (k) of sands using the empirical formula, it usually employs only the effective grain size (D10). Another approach considers two specified particle size such as using the coefficient of uniformity,(Cu=D60⁄D10) to represent the overall the composition of particle sizes. However, this index can’t completely represent the overall range of soil size. Therefore, this study employs the fractal dimension (Dg) concept to reflect the overall soil particle size distribution. An empirical formula involved the Dg is proposed to estimate the permeability coefficient. In this study, permeability tests in constant head condition for the saturated sands with different effective grain size, gradation and void ratio (e) are performed. It aims to study the influence of effective grain size, gradation and void ratio on the permeability coefficient. The following conclusions are drawn: (1) Particle gradation type (Dg), effective grain size (D10) and void ratio (e) all have a positive effect to the permeability coefficient. The result of SPSS statistical analysis shows the weighting ratio of Dg：D10：e influence on the permeability coefficient is 4：2：1. (2) Keeping both the particle gradation (Dg) and void ratio (e) as constant, the greater D10 case shows a large k value. (3) Keeping D10 and e as constant, the well-graded sand with large Dg case has a higher k value. (4) Using single particle such as the effective grain size (D10) to predict the k value, the difference between predictions and experimental results is up to 918%. This type of empirical formula such as the Hazen formula and Chapuis formula are proposed for the uniformly-graded cases. (5) Amer & Awad formula employed D10, e and Cu to predict the k value is more accurate. This indicates more describing the overall gradation curve will have a better prediction. (6) For a given particle mass with the same Dg value (i.e., the same particle size distribution), its corresponding fractal dimension of void size distribution Dp is the same. This means that the composition of void size distribution is independent of particle packing conditions. (7) This study proposes an new empirical formula as k = (11 e D10)×[Dg ^(0.148((e D10)^(-1.3)))] that involves the fractal index for describing the overall particle size distribution curve.
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