砂防ダムおよび水叩の設計に関する基礎的研究
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砂防ダムおよび水叩（水叩エ）の設計の合理化に重要な指針を提供するものとして，本研究では水叩コンクリート面に生ずる侵食痕跡に着目し，まずこれについての現地測定を，裁か国有数の土砂生産量を持つ天竜川上流々域内の114個所で行い，浸食部の開始点，最深点，終了点を各個所ごとに明らかにし，その後一部を再測して侵食の推移を示すとともに，水文観測値との対比から，侵食には大洪水のほか中小洪水も相当に関与することを示した．次に，模型水路実験を行い，渓床石礫のダムからの落ち方については，個別，集合の各落下間に大差がなく，石礫の質量が大きいぼど落下位置はダムに近く，それらは，一定関係で表われること,さらに水叩面に生じる侵食については，その形状と石礫の落下位置の分布が一致することより，侵食が流水ではなく石礫の衝突により形成されること，また侵食量は落下石礫の個数および質量の各々と比例し，水叩材料の圧縮強度とは負の相関関係を示すことなどを明らかにした.続いてこのような侵食の特性を考慮して，まず現地測定値をもとに，侵食の開始点まで砂防ダム下流のりを張り出すことにより，下流のりをより緩勾配にできること，またダムから侵食の終了点の位置までを必要な水叩の長さとして，この長さを従釆より短くできること，さらに侵食の最深点の探さに基づいて，水叩の厚さを必栗に応じて標準値以上にしなければならないことのそれぞれを，この流域における具体的な値とともに示した.次に，理論的な解析として，この現象にかかわる右礫のダム上の流送およびダムから水叩面の各地点への落下，侵食量に関与する落下石礫の運動エネルギーなどについての物理モデルを用いて，侵食形状を求める理論式を誘導し，この式の計算結果をもとに，これを砂防ダム下流のり勾配や，水叩の設計の基礎式として用い得ることを示した．最後に以上の考察をもとに砂防ダム下流のり勾配を，従来の定数から変数に換え，ダムの最小断面形を求める方法を線形計画法を応用した図解法により示すとともに，この方法によれば従来より断面積が平均1割程度減少し，また下流のり勾配に許容範囲が存在する場合も，これを付帯条件として，同様に解を求め得ることを明らかにした．With a view to rationalize the design of debris dam and apron, the erosion caused by floods on the apron surface was treated as a significant guide to design and by way of field surveys, model experiment and theoretical analysis of the erosion, a new design method was proposed. First of all, to clarify the characteristics of the erosion, field surveys were conducted at 114 spots of the 21 tributaries of the Upper Tenryu River Basin in 1975. These dams and aprons had been constructed about ten to thirty years ago in which the consequent erosion at the longitudinal section were generally arc-shaped, and the beginning, the deepest and the ending point of the erosion which indicate the shape directly were clarified in each spot. After five years, one of these spots was surveyed again and the transition of erosion was examined in contrast to the rainfall and discharge data of that period. It showed that the erosion has proceeded in the direction of depth rather than of the longitudinal length and is caused not only by great floods but also by medium and small floods, therefore erosions are frequent and significant phenomena of this basin. Secondly, the model experiment was conducted in open channel to clarify correlated factors of erosion. This experiment was composed of the gravels falling from the crown of debris dam and the erosion apron. As for the falling position of gravels, it was confirmed that gravels fall inside of the falling nappe and as the gravel mass become greater, the horizontal arrival distance become shorter. This was considered to be related with the area of the accepting water pressure before falling of the gravel. The two types of falling, individual, and collective, made little difference on the falling position. As for the erosion of apron, gravels were made to fall in aprons which were made of erosive soil concrete and in consequence, the surveyed shapes of erosion coincided with the distribution of afore mentioned falling position of gravels. Therefore the conclusion was that the erosion of apron is caused by the collision of gravel and is scarcely caused by collision of falling nappe or movement of the fallen gravel to downstream. The amount or erosion was proportional to both the number and the gravel mass, so it implies that the apron was eroded little by little. Conversely, it showed inverse interrelation to the compressive strength of the material of apron. Thirdly, basing on the results of the field survey and the model experiment, following studies were conducted aiming at the rationalization of the debris dam and apron designs. First, a case study was conducted based on the field survey data. In the upstream of the beginning point of erosion, the amount of falling gravels were so few that the downstream slope of dam is possible to be made gentler than the one actually in force (1 : 2 or 1 :0.3) especially in low dam. The depth of the deepest point which relates to the least required thickness of apron showed that the thickness should be thicker than the general value of 0.7 to 1m as the case may be. Most of the depths were less than 1m, but the depth of 1.5m could .be seen even in groundsel. The ending point of erosion nearly coincided with the maximum arrival distance of the falling nappe, so the distance from dam to this point indicates the required length of apron. It showed that the length could be made shorter than the value obtained from the practical use formula. This tendency become more conspicuous as the height of dam increases. Examples of definite values for this basin are : in thecase of a 3 m high dam, the allowable range of downstream slope is from 1: 0.3 to 1: 0.6, and the length of apron is from 2.0 to 5.0 m and for a 6 m high dam, the allowable range of downstream slope is from 1:0.25 to 1:0.4, and the length of apron is from 3.0 to 6.0 m. Next, the theoretical analysis was conducted using physical models such as water depth and flow velocity in a given discharge, sediment discharge by grain size on the upstream of dam, falling of gravel on apron surface by laws of motion and the kinetic energy loss which relates to the amount of erosion. Then the following theoretical expression was formed to calculate the longitudinal shape of erosion. \frac{δz}{δt}=A \times q(x,z) \times (H+z) \times {{{2-\frac{x}{H+z} \times {{\frac{δz}{δx}}}}}}^2 \times {{{1+{{\frac{δz}{δx}}}^2}}}^(-1) where t : time A: constant x: horizontal distance from the downstream end of the crown of debris dam to downstream z : vertical distance from the base of the downstream slope of debris dam to downward q: amount of falling gravel at the point (x, z) H: height of dam from the base of the downstream slope The results of calculation of this expression with required hydrographs, grain size distrbution of stream bed and constants showed the same property of the surveyed shape, and the position of the beginning, the deepest and the ending points of erosion coincided with those of the surveyed shape, therefore it was certified that this expression is useful for designing the downstream slope of debris dam and the length and the thickness of apron. Based on above studies, the downstream slope of daw which used to be taken as an invariable was changed to a variable and the methood of determining the cross section of minimum area was established using iconography with the linear programming method. By this method, the area of the section decreases about ten percent than that of the former type in which downstream slope was fixed as 1 : O.2. As solutions following three cases are given. 1) The minimum value of the arbitrary section in which the acting line of the external force of the planned overflow depth is on the downstream end of the middle-third, 2) The section in whcih the acting line of the external force of the planned overflow depth is on the downstream end of the middle-third and the horizontal component of the external force is equal to the multiplied value of the vertical component of the external force by the coeffient of friction between dam and ground, 3) The section in which the acting line of the external force of the planned overflow depth is on the downstream end of the middle-third and that of the section where no water stays is on the upstream end of the middle-third. For example, in the case of α (the ratio of the crown width to the height of dam)=0.2, β (the ratio of the overflow depth to the height of dam)= 0.4, the downstream and upstream slope are 1 : 0.672 and 1 : 0.041 (case 1) and the area of dam decreases approximately 14% compared with the former type in which the slopes are 1 : 0.2 and 1 : 0.660 respectively. In the case of α=0.4, β=0.6, the downstream and upstream slopes are 1 : 0.621 and 1: -0.092 (case 2) and the area decreases approximately 12% compared with the former type in which the slopes are 1 : 0.2 and 1: 0.2 and 1 : O.488 respectively. In the case of α=O.2, β=0.2, the downstream and upstream slopes are 1 : 0.624 and I : -0.034 (case 3) and the area decreases approximately 11% compared with the former type in which the slopes are 1 :0.2 and 1 : 0.552 respectively. If the downstream slope is restricted by the own condition of each spot, a collateral condition should be added in this method. By these studies, the design of debris dam and apron can be much more rationalizad than before.１．序論 １．１．研究の目的 １．２．既往の研究 １．３．論文の構成 ２．水叩の浸食についての現地調査および模型実験 ２．１．現地調査 ２．１．１．方法 ２．１．２．結果および考察 ２．２．模型実験 ２．２．１．方法 ２．２．２．結果および考察 ３．砂防ダム下流のり勾配および水叩の設計 ３．３．事例的考察 ３．１．１．砂防ダム下流のり勾配 ３．１．２．水叩の長さ ３．１．３．水叩の厚さ ３．２．理論的考察 ３．２．１．基本式の誘導 ３．２．２．計算例および考察 ４．砂防ダムの断面設計 ４．１．概説 ４．２．基本式の誘導 ４．３．計算例および断面表の作成 ４．４．諸条件の検証 ５．総括 参考文献