砂防ダムの下流法に関する研究

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In case of flood time it gives a very dangerous sight in Sabo-Dam, because overflowing sediments (mixtures of boulder, cobble, gravel and sand) carried over Sabo-Dam often destoroy the surface of downstream slope. If we should have a gentle angle of the downstream slope, the stability of Sabo-Dam may be more stronger and the cost will be more cheaper at the same time. So that, it is very important things for us to decide how to plan the reasonable Dam. Up to this time, the value of downstream slope has been guessed by both gravel's limiting velocity which the gravel begins to moving away on the stream bed, and planning theory based on the law of falling body. The conditional formula is expressed as follows, n=v_g√2/gH where, n is downstream slope, v_g is limitting velocity of gravel, g is acceleration of gravity, H is height of Sabo-Dam. v_g is estimated by following formula, v_g=√(γ_s-γ_w)dμcosθ/0.076γ_w (2) where, ys is a unit weight of gravel, γ_ω is a unit weight of flow water, μ is coefficient of friction, d is diameter of the smallest gravel among the overflowing sediments that damage to the suraface of downstream slope, cosθ is slope of stream bed. It has been believed that the impact-wear against the surface of downstream slope was decided by the specific size gravel. But, now, we have been clear that the impactwear was not due to the gravel's size but to the total weight of the overflowing sediments. Where, v_g is the velocity of flow and not that of the overflowing sediments. Therefore, for applying above mentioned formula, it is not reasonable to use the limiting velocity (v_g) in stead of the overflowing sediments from the downstream edge of Sabo-Dam. This paper aims to explain the movements about the overflowing sediments from the downstream edge of Sabo-Dam at the flood flow, and the mechanism of the impactwear against the surface of downstream slope caused by the overflowing sediments. Thus, we can decide reasonably to make the planning of downstream slope. 1) Discussion about the observations and experiments in the actuate spots where Sabo-Dam have been built. Based on our experimental data about the distribution of the overflowing sediments, we have analized the wear marks which had been traced by the overflowing sediments on the concrete front aprons in many Sabo-Dams at flood flow. From our experiments, it has been clear that: surface velocity at flood flow, bed flow velocity (velocity of the overflowing sediments from the downstream edge), minimum velocity of the overflowing sediments and relationship betweeen velocity of flow and velocity of the overflowing sediments. Those results show as follows, a) When the sediments overflow down from the downstream edge of Sabo-Dam at flood time, they flowed through clearly under the condition of tractive flow on the stream bed. And, their behaviour were realized as movement of singles. b) Overflowing sediments seem to conform to the velocity of the flow near the stream bed. c) At flood flow the bed flow velocity (v_s ) was estimated by an extent of 70～90 % of the surface velocity (v_0). d) At flood flow the amount of sediments that overflowed down from the downstream edge of Sabo-Dam were calculated about 60～70% of total mass, and they overflowed down including themselves within the nappe. The rest of sediments (30～40%) were dropping down outside of the nappe. 2) Hydraulics discussion The velocity of overflowing sediments (v_s) in the stream conformed to one of the stream flow (v) on the stream bed, so that, the relationship between v_s and v is expressed by following equation, which is given at the condition that the sediments begin to move against the frictional resistance by balance of power. v_s=v-√4(σ-ρ)gdμ/3C_Dρ (3) where, C_D is coefficient of drag, a is density of sediments, ρ is density of stream water, g, d, μ are above mentioned. C_D has been already calculated from many hydraulic experiments, its value is said to be similar to 0.4.μ is a range of 0.3～0.5,μ' is value of moving sediments in stream, it is not known. From this, we investigated μ' in our experiments, and we have obtained as follows. a) It is very reasonable for us to recognize that μ' grants for the appearance of friction's coefficient which puts together with ressistance against friction, fluid and flow's disturbance. b) The measured value of μ' have obtained 0.01～0.1 and considerabley smaller than μ. From our experiments about measurements of velocity of flow and overflowing sediments, it was confirmed that the change of sediment's velocity arising from difference of sediment's size at the downstream edge seems to be transitional phenomena caused by momentary acceleration in the stream flow. And we are able to explain by following equations. v_s=(v-b)(b+v-v_<s0>)+(v+b)(b-v+v<s0>)e-2abt/(b+v-v_<s0>)+(b-v+v_<s0>)e-2abc (4) t=1/2ablog_e(b+v-v_s){b-(v-v<s0>)}/(b-v+v_s){b+(v-v<s0>)} (5) Where, v_<s0> velocity of sediments before they are accelerated, that is, v_s=v_<s0> at t=0, and a=3C_Dρ/4σd, b2=4(σ-ρ)g d μ/3C_Dρ 3) Relationship between the relative velocity and the relative flow depth From the observations and experiments on many actual plots, we have acquired some knowledge of movements of overflowing sediments at flood flow, and those will be able to explain in view of hydraulics. But, our knowledgement is very qualitative on the other hand, it is very hard to seek for specific factors in applying theoretical formula. And then, we tried a experiment to guess a velocity of overflowing sediments (v_s) on the foundation of surface velocity of flow (v_0), because Va have been obtained comparatively easy from field work. At first, we calculated a relative velocity and a relative flow depth, relative velocity is expressed v_slv_0, relative flow depth do h_0/d, where, h_0 is flow depth on the downstream edge. And then, if the relationship between v_s/v_0 and h_0/d should be expressed as following equation, v_s/v_0=α(h_0/d)β (6) where, α, β are constant value obtained by experiments. Our experimental result will be showed as follows.Our experimental result will be showed as follows. v_s/v_0=0.68(h_0/d)0.148 (7) From this equation, we will be able to calculate the velocity of a given diameter sediments which overflow down from the downstream edge. (4) Invesitigation about impact-wear against surface of downstream slope (1) We investgated about the mechanism of the impact-wear against surface of downstream slope. Setting many sorts of slopes, we tried by our experimental machine. From our experiments, if value of W (ratio of impact-wear) were given as the ratio of inclination angle to horizontal place, it will be estimated by the following equation, W=(1+1.20sin2θ)cos2θ (8) where, θ is inclination angle of downstream slope. (2) It is very difficult for us to guess absolute amount of overflowing sediments from the downstream edge. And then, on the basis of peculiarity of the particle size distribution in stream difference of overflowing course by each size distinction within the nappe and sediment's velocity overflowing out from edge, we expected amount of sediments that strike against the surface of downstream slope in view of probability, and estimated a relative value of impact-wear for downstream slope. Those results are as follows: a) The impact-wear of downstream slope have been made mainly by overflowing sediments in case of higher classes floods. At this moment, we found, the particle size distribution of sediments at deposite was remarkabley similar to that of overflowing sediments. b) When we disucuss the particle size distribution curve about aboved deposite, average diameter of sediments (d_m) is given as follows: dm=p=100 Σ p=0 d ⊿p/p=100 Σ p=0 ⊿ Where, d is the hole width of a riddle, p is percentage of sediments of that pass through aboved riddle. ⊿p is percentage of the rest. Moreover, we examined for a smaller grains than average grains, and showed the percentage (P_m) that they took in total amount. It was estimated about 60～70 % regardless of avarage value. c) From the results of above mentioned 1)-d) and 4)-(2)-a), b), if we seek for the downstream slope on the basis of velocity of overflowing sediments as average grain diameter accumulating sediments on the stream bed, the overflowing sediments which strike against the downstream slope is an extnet of 30～40 %. d) Moreover, on the base of formura (8) and 4)-(2)-c), if we should give 0.6(inclineangle) to downstream slope, it will be guessed that the grade of that impact-wear is almost as much as one of spillway crown, and of front apron near side of the slope. Such a grade of downstream slope's wear will be able to allow in point of view of impact-wear on Sabo-Dam. And it is suggestive of possibility for us that a part of overflowing sediments will be allowed of making against the surface of downstream slope. 5) The decision of downstream slope for Sabo-Dam's planning From mentioned, experimental and actual investgations, we believe that the downstream slope of Sabo-Dam is decided by following process: a) At first, we estimate the planning flood discharge (Q) from the Rational formula, Q＝0.278 A r a (m3/sec) where, A is watershed area(km2), r is precipitation per hour(mm), α is runoff coeffi cient. b) When h_0 is flow depth on the downstream edge of Sabo-Dam, it is estimated by following formula, h_0=3√(Q/5.1B)2 (m) where, Q is aboved, B is width of overflow section. c) When v_0 is suraface velocity at flood flow, it is estimated by following formula, v_0=5.1√h_0 (m/sec) d) When we estimate the average diameter of grain size(dm) on the sediments of the stream bed, the relationship between d_m and D_m is showed as follows: d_m＝(D_m-11.3)/2.38 (cm) Where, D_m is the maximum diameter of sediments. e) We estimate the overflowing sediment's velocity(v_s) by following experimental equation, v_s=0.68(h_0/d_m)0.148 (m/sec) f) From above mentioned, we obtained, the downstream slope of Sabo-Dam(n) is decided by following formula. n=v_s√2/gH
信州大学農学部附属演習林の論文

砂防ダムの下流法に関する研究

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信州大学農学部附属演習林 | 論文

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