In gravel bed rivers, the shapes of bed sediments are important both from the sediment transport as well as river's ecological point of view. Resistance from large roughness elements and the flow variability are the main characteristics of gravel bed rivers. Morphological changes especially in gravel bed rivers are necessarily associated with the bed load sediment transport. For the gravel bed rivers, the prediction for sediment transport quantities can be improved if the transport parameters of models are determined with respect to the physical shape and movement characteristics of sediments. Both deterministic and stochastic methods are available to estimate the bed load transport rates. Unlike probabilistic methods, however, the deterministic methods mainly depends on the critical shear stress criterion which is easy to be applied but is relatively less efficient as it does not accounts for the entrainment probability and mobility of sediments. The latest stochastic model is capable of estimating the partial fractional transport rates, however, some parameters are ambiguously defined. A further improvement is suggested by defining these parameters for the four Zingg's shapes of sediments. Also the shape factors are used in various models but just as a multiplying factor to reduce the effective shear stress value. This practice is not sufficient for uncovering the geological and transport information that is hidden in the shapes of sediments. With the help of field study, laboratory experimentations and quantitative assessment, the targets of this research work are achieved.

In this research work, I planned to observe the sediment transport in the real rivers to check why software are deficient in estimating the transport quantities and finally to suggest and apply the improvements. To accomplish the tasks of research, field visits were conducted on Japanese gravel bed rivers where channel characteristics, flow characteristics, sediment transport phenomenon and dependency of large size sediments on stream habitat were observed. The Oppegawa River (おっぺ川) was selected as the study reach where geometric data (profiling, cross sectioning etc.), hydraulic data (velocity, depth, and discharge) and the sediment data (photo and sediment samples from surface and subsurface) were collected and analyzed by software to evaluate the efficiency of software.

Qualitative study of the gravel bed rivers and their analysis by various software revealed that shape of sediments is a key factor for entrainment from sub surface, partial mobility. As a result of comparison of software analysis, the stochastic approach was found to be relatively better than all other approaches, and it was felt that by including the shape effect the efficiency of the existing model can be improved.

Three parameters of the stochastic model are affected if particle shape are included i.e. the Vp,i (mean velocities of sediments), Yi (particles mobility factor) and the Δi (Subsurface entrainment factor). Here "i" is a diameter.

The Vp,i was extended for each gravel shape classified based on the Zingg's shapes category and renamed as Vp,im ("m" for Zingg's shapes category) as uni-size particles do not move with the same velocity. More than 300 mixed sized sediments from the Oppegawa River (4 mm to 32 mm) were colored in four Zingg's shapes and the mean velocities were computed in an acrylic glass flume (0.9 m x 0.038 m x 0.15 m) and plotted against the effective shear stress (θ'i). The final design curves of (θ'i vs Vp,im) were obtained by extrapolating the experimental relation.

The Yi was merged in the Vp,im, as it itself accounts for the partial fractional transport. The Yi as obtained in the original stochastic model can be eliminated when mobilization of sub fractions (shape groups) was defined by their mean velocities, however the impact assessment of this parameter comparison of sediment quantities was made with the original and modified stochastic model. Using it in conjunction with Vp,im the total transport quantities were found exaggerated.

The third and the last parameter of stochastic model that was studied for the modified stochastic model is the subsurface entrainment factor Δi. It shows the entrainment of sediments from the sub layers to the active layer. Validity of this parameter was studied in the (7 m x0.3 m x0.15 m) glass flume. The entrainment of subsurface sediments was accessed in terms of change in on bed sediment size distribution. The resulted curves revealed that effect of this parameter is not significant. No more entrainment from bottom layers were observed even for the laboratory sand whose fixity was much less than that of natural sediments, hence a uniform factor of 1 (no entrainment effect) can be used in the modified approach.

In addition to the improvement of the movement characteristics of sediment shapes, the physical characteristics of each grain like shape roughness were also included in the modified model by the Fourier shape analysis. First by modifying the open source code (Contour Analysis) (written in C #) to get the peripheral coordinates of sediments of size 4 mm to 32 mm then the Fourier shape coefficients were obtained for the required number of shape harmonics and finally the relative roughness of sediment shapes were worked out. By using this relative roughness, new parameter "shape deviation factor m" was suggested.

In gravel bed rivers, the mean velocity profile and shear velocity are significantly affected by gravel when water flow over large roughness elements. To count for this effect, the effect of deep and shallow flow layers was added by using both log law and tanh law. Gravel bed rivers also provides the natural habitat to the aquatic life. River habitat can be preserved by using the large size sediments, but they may affect the flow and can disturb the spatial distribution of sediments. Relations exist between the size distribution and blockage ratio. This relation was explored by laboratory experimentations, a relationship between blockage ratio and change in sediments size distribution between the wake and direct flow areas were obtained. For understanding the effect of boulders on bed changes, boulders were placed in different formations, then the effects could be explained qualitatively.

The modified model was calibrated with the Manning's "n" for the water discharge and with optimum harmonic number for shape deviation factors" Sm" for the sediment discharge.

Excel VBA code was written for all sections of computations i.e. image processing, Fourier shape analysis and finally for the comparative computations of two models i.e. original and the modified stochastic model.

For the evaluation of the modified approach, the online sediment transport data for the two gravel bed rivers i.e. Big Wood River near Ketchum and Salmon river below Yankee fork of Idaho State, USA was used. This data was collected by the USDA Forest Service - RMRS - Boise Aquatic Sciences Lab. The results of analysis were improved when compared with original method and in reasonably good agreement with the field measurements.

本論文は,日本の急流河川によく見られる礫床の河川における流砂量の算定方法をいかにして改善するかを検討したものである.流砂量の算定は,河川管理上極めて重要であるにも関わらず,未だに十分な精度での算定には至っていない.特に,河川生態系の保全や再生を考える上では,よりミクロな土砂の動態を捉えなければならないため,既往の土砂動態の算定法は適用できていないのが現状である.

こうした背景を踏まえ,河川における土砂の堆積状況の観察,河床形状及び河床材料の調査,水理実験を行った結果,既往のモデルでは球体として扱われている礫の形状を丁寧に考慮しない限り,実際の土砂動態を表せていないのが問題ではないかとの結論に達した.こうした背景を踏まえ,これまでにない新たな流砂量算定手法を提案したのが本論文であるが,次の四つの項目を新しい着眼点として挙げることができる.

一つ目は,存在割合がさほど多くなくとも,水深に比して粒径の大きな材料が河床に存在する場合には,通常用いられる対数則ではなく,双曲線正接(ハイパボリックタンジェント)型の分布形を用いた方が良いというKatulの手法をモデルに組み込んだ点である.たいていの場合,流れの計算は平面二次元で行われ,水深方向の平均流速から底面剪断力を算定する際には上記対数則を仮定しているため,このような流速分布形の違いは流砂量の算定において極めて大きな影響を及ぼす.実際に細粒土砂からなる水路床に大きめの材料を配置した水理実験を行った結果,流量や勾配といった条件が同じでも,細粒分の流出量が著しく減少することが確認でき,水深と84%通過粒径の比が7より大きいか否かで上記二種類の流速分布を使い分けるというルールをモデルに組み込んだ.

二つ目は,礫の形状によって河床材料を分類し,分類群ごとに剪断応力と粒子の移動速度の関係を求めた点である.具体的には,まず長径と中径の比が1.5より大きいか否か,中径と短径の比が1.5より大きいか否かに応じて,礫の形状を4つのタイプに分類するというZinggの方法を適用することから始める.こうして分類された4つのタイプによって,同じ水理条件でも土粒子の移動速度や挙動が異なることを実験によって確認し,剪断力と土粒子の移動速度との関係を粒径ごとに定量的に求めている.

三つ目は,礫の形状を考慮した有効剪断応力の算定手法を提案した点である.この四つのタイプのそれぞれに属する複数の礫の輪郭(半径の分布)に対して,フーリエ解析を行って礫の形状を定量化する.こうして得られた礫表面の凹凸の度合いについて,4つの形状間で比を求め,この比率を河床にかかる平均的な剪断応力に掛け合わせることで有効剪断応力とした.単に掛け合わせるだけでよいか否かは今後検討を続ける必要があるが,凹凸が大きい方が表面積が大きくなり,それだけ剪断力の影響を受けやすいという仮定である.

四つ目は,通常表面を流れる砂の量しか考慮しないものの,河床材料の粒度分布の幅が広い場合は,大半の河床材料が静止している下層からも細粒分が表層に持ち出されるという点を考慮すべきだとし,この影響をモデルに組み込んだ点である.しかしながら,今回行った水理実験では,その量が有意ではなかったため,モデルに組み込めるようにはしつつも,その定量的な影響についてはまだ含めていない.

こうした四つの作業を組み合わせた流砂量算定モデルを提案し,すでに流砂量のデータが公開されているアメリカの河川に適用した結果,計算結果は礫の形状を考慮する前より観測値の傾向を再現することに成功した.モデルにおける各種パラメーターの選択に任意性が残されているものの,上記四つの観点は従来の流砂量の算定では組み込まれていない。本論文で問題提起された流砂量における礫の形状の役割は、それ自体が重要な問題提起であると同時に,本論文で提案されたモデルは、まだ不完全な部分を残しているものの、今後の流砂に関する学術研究の新たな展開に結びつくものであると認められる.

よって本論文は博士(工学)の学位請求論文として合格と認められる.