Estimation of Gravel Size Distribution using Contact Time

Transcription

1 ISSN Report of the Research Institute of Industrial Technology, Nihon University Number 97, 212 Estimation of Gravel Size Distribution using Contact Time Akira ODA*, Yuya HIRANO**, Masanori WATANABE*** and Minoru OCHIAI* ( Received June 13, 212 ) Abstract The sieve test is the main method used to measure the gravel size distribution for sabo (erosion control) planning. However, it is expensive to transport gravel from the field to the laboratory. Therefore, we devised an easy, economical method of measuring the gravel size distribution in the field based on the elastic wave between the gravel and an elastic body. We examined the relationship between the contact time from elastic wave and gravel diameter using an impact experiment involving glass and stone balls, natural gravel, and a hard plastic board (polyacetal board). This showed that the gravel diameter was proportional to the contact time. In addition, the count of the number of pieces of gravel was accurate. We estimated the size distribution of natural gravel by measuring the contact time and converting this into the gravel diameter. However, the resulting gravel size distribution determined from experiments was larger than that obtained from a sieve test. One possible cause is that natural gravel is not spherical. Therefore, we used a shape factor to adjust estimated value to real ones. The results showed that the gravel diameter determined from the contact time was correlated to the medium length of gravel for the ten largest pieces tested. When we estimated the size distribution of natural gravel using the shape factor, the resulting distribution matched that obtained from a sieve test. Key Words: elastic wave, contact time, gravel size distribution, method of measuring the gravel size distribution, polyacetal board 1. Introduction The sieve test is the main method of measuring the gravel size distribution for sabo and river planning. However, it is expensive to transport gravel from the field to the laboratory. Therefore, we looked for an easy, economical method of measuring the gravel size distribution indirectly. Different indirect methods of estimating the mean diameter of gravel have been evaluated, including using the sound of gravel colliding with a steel pipe called a hydrophone 1). Other studies about indirectly estimate method for the grain size distribution have been evaluated by a photograph of a dry river bed 2). Former method was shown the mean * Professor, Department of Civil Engineering, College of Industrial Technology, Nihon University ** Oji Real Estate Co., Ltd. *** HANABUSA Planning Office Co., Ltd. 1

2 Akira ODA, Yuya HIRANO, Masanori WATANABE and Minoru OCHIAI diameter of gravel, but the gravel size distribution was not shown. Latter method was shown the gravel size distribution, but it was measuring on dry river bed surface. However, the grain size distribution of the excavated also needs to be measured for sabo and river planning. In powder technology 3), indirect methods for determining the particle size distribution include laser diffraction and light-scattering methods, but these particles are smaller than 1 µm. In contrast, the gravel in rivers is much larger than 1 mm. This paper proposes a simple method for measuring the gravel size distribution in the field based on the contact time between the gravel and an elastic body. The contact time with an elastic body has been used to measure the deformation of various materials and the strength of concrete. Carino et al. 4) confirmed that the size of steel balls is correlated with the contact time with a concrete plate theoretically and experimentally. Therefore, we decided to utilize the principle of contact time for river material, i. e., gravel. To examine this possibility, we first conducted an impact experiment to examine the relationship between the contact time and gravel diameter using glass and stone balls, natural gravel, and a hard plastic board. We examined whether the number of pieces of gravel could be counted using the relationship between the contact time and gravel diameter. In addition, this number and a shape factor for gravel were used to estimate the gravel size distribution. Finally, we compared the effectiveness of this proposed method with a sieve test. 2. Experimental relationship between contact time and gravel diameter 2.1 Theory Equation (1) gives the contact time (Tc) between a steel ball and a concrete board based on Hertz s 5) impact theory by defining the contact time using the first half-cycle of an oscillatory wave(fig.1): r h T c (units: m-s) (1) where r is the radius of the steel ball and h is height of its fall. In a preliminary experiment 6) involving a perpendicular free fall from a height of cm onto Measure of amplitude(mv) Contact time(t c ) Time(µs) Fig.1 Definition of contact time. a piece of stainless steel, the contact time is directly proportional to the radius of the glass and stone balls. 2.2 Impact experiment to determine the contact time 6) In this experiment, the test material were glass and natural gravel. The elastic body was a hard plastic polyoxymethylene (POM) board of mm (length width thickness) because the oscillatory wave attenuation of POM is quicker than that of stainless steel. POM is often used to make gears in machines and has high friction and shock resistance. POM is also ideal for use in the field, because it is very light (the specific gravity of POM is 1.48). Here, we investigate the oscillatory wave by using the accelerometer. We evaluated the relationship between the contact time and the POM board in an impact experiment. A 3 slope was used (Fig.2). The glass balls and gravel were rolled from 2 cm from the top of the slope(3 ) to reduce the velocity at the time of collision with the POM. In a preliminary experiment with gravel, this distance of 2 cm made it possible to measure the contact time of each piece of gravel, enabling the pieces to be counted. The glass balls and natural gravel used in this experiment are listed in Table 1. We repeated our experiment three times in the same conditions. In the table, the diameter of gravel was that measured for the middle axis, and S. F. is a shape factor determined as follows 7) : c S. F. (2) ab where a, b, and c are the lengths of the long, middle, and short axes, respectively. For natural gravel, S. F..7 8). 2

3 Estimation of Gravel Size Distribution using Contact Time Rubber vibration insulator POM board 2cm θ=3 3. Experimental results 3.1 Relationship between the contact time and gravel diameter 5.5cm Fig.2 Schematic diagram of impact experimental setup. The relationship between the contact time Tc and gravel diameter d is shown in Fig.3. The contact time (Tc) between the glass balls and gravel, and the POM board, is given by Eq. (3): T c 2.25d r (units: mm-μs)(3) Table 1 Dimension list of glass balls and natural gravels. Glass ball Natural gravel Diameter (mm) S.F. Weight(N) where range of diameter is shown in Table 1 and the distance between the slope and the POM board is constant(5.5cm, see Fig.2). A power differs from a Eq.(1) may occur as the result of the difference in the quality of the material. The experimental conditions were similar to those in Carino et al. 4) The coefficient of determination was R 2 =.875. We used Eq. (3) to study the relationship between the number of gravel pieces, estimated diameter, and estimated gravel size distribution. Fig.3 Relationship between the contact time T c and gravel diameter d. 3.2 Estimating the amount of gravel This experimental condition (POM board, slope angle and slope distance) is the same as above 2.2. Gravels dropped fifty pieces simultaneously. The gravels used for the experiment are sampled from a river. Fig.4 shows an example of an oscillatory wave for the collision of gravel with the POM board. This result was used to count the number of pieces of gravel. Fig.5 shows the number of impacts (i. e., the number of piec- 3

4 Akira ODA, Yuya HIRANO, Masanori WATANABE and Minoru OCHIAI Number of gravel pieces The estimate average number of gravel pieces The actual number of gravel pieces.5 1.cm cm cm cm 2.5cm Gravel diameter range Number of impact Fig.4 Example of an oscillatory wave for the collision of gravel with POM board Experiment No. Fig.5 Number of impact for the collision of gravel with POM board. es of gravel) based on the oscillatory waves for each experiment. The number ranged from 4 55 pieces and averaged In fact, there were 5 pieces of gravel. One reason for the lower number is that some of the collisions with the POM board were simultaneous. It is also difficult to determine the peak waves because an oscillatory wave is very small. The high values could have resulted from multiple collisions between the same piece of gravel and the POM board. These problems might be solved by adjusting the angle of the POM board. Fig.6 compares the estimate average number with the actual number of gravel pieces for each gravel diameter range. The estimate gravel diameter was calculated from the experimentally observed contact time using Eq. (3). For a gravel diameter range of 15 2 mm, the error of experimental and actual number was 11.7%. For other gravel diameter ranges, the experimental result did not match the actual number. The error of experimental and actual number was 2-5%. This is likely due to the pieces within a gravel diameter Fig.6 Comparison of the number of gravel pieces for each gravel diameter range. range. For example, the average diameter in the gravel diameter range 5 1 mm was 9.2 mm based on a detailed check of the gravel used. This is near the upper limit of the range. Therefore, most of the gravel in this range would give results close to those for the next higher range (1 15 mm). Note that the shape factor (S. F.) depends on the gravel diameter range. For example, the S. F. for diameter range 2 25 mm is.58, while the values for other gravel diameters vary from Estimated gravel size distribution Fig.7 shows the gravel size distribution based on the gravel diameter determined using Eq. (3). In this study, the gravel was assumed to be spherical. The weight of the gravel was determined using the sphere diameter obtained with Eq. (3) and the specific gravity of the gravel, which was However, the shape of the gravel was not considered. The differences between the sieve test and this result were significant. The mean gravel diameter determined experimentally was dm = 6.2 mm, which was twice the mean diameter in the Cummulative percentage of gravel size (%) Sieve test Using Eq. (3) Gravel size (mm) Fig.7 Gravel size distribution. 4

5 Estimation of Gravel Size Distribution using Contact Time sieve test, dm = 29.9 mm. This is likely due to the gravel shape. 3.4 Estimated gravel size distribution using gravel shape (S. F.) We solved this problem by using the shape factor (S. F.) for gravel. The lengths of the long, middle, and short axes, i. e., a, b, and c, respectively, of the ten largest pieces of gravel used in this experiment and their S. F. values are listed in Table 2. The relationships between the length of each axis and the gravel diameter calculated using Eq. (3) are shown in Fig.8. This result was correlated with the length of the long axis, which led us to hypothesize that the gravel diameters calculated using Eq. (3) were almost equal to the length of the long axis. One of the reasons for this might be curvature of stones which collides with a board. It remains to be seen whether this idea is right. Examining the relationship between the length of each axis in Table 2, there was a significant correlation between a and b(see Fig.9), which was as follows: b.749a (4) The shape of the gravel was assumed to be ellipsoid. The average shape factor (S. F.) of all of the gravel used in this experiment was.578. From Eqs. (2) and (4), the volume of ellipsoid pieces of gravel is given by: 3 V.624 a (5) Table 2 Dimension list of the ten largest pieces of natural gravel. Long axes a(mm) Middle axes b(mm) Short axes c(mm) S.F Considering gravel passing through a sieve, as observed experimentally, the long axis of the gravel passes through the sieve at right angles. It is assumed that the direction of the diagonal of the sieve openings is the same as the middle axis of the gravel (see Fig.1). In this case, the sieve opening length (gravel size d) is approximately as follows: d b 2 (6) The length of the long axis, a, was obtained from Eq. (3). Fig.11 compares the results calculated using Eqs. (3) and (6) and the values measured in the sieve test. The mean diameter was dm = 32. mm, which is closer The gravel diameter calculated using Eq. (3) (mm) Long axes(mm) Middle axes(mm) Short axes(mm) The length of each axis (mm) Fig.8 Relationships between the length of each axis and the gravel diameter calculated using Eq. (3). Middle axes : b (mm) b=.745a R² = Long axes : a (mm) Fig.9 Relationship between a and b. 5

6 Akira ODA, Yuya HIRANO, Masanori WATANABE and Minoru OCHIAI 1) Takuro SUZUKI, Hideaki MIZUNO, Nobutomo OSANAI, Ryosuke HIRASAWA and Yuji HASA- GAWA, Basic study on sediment rate measurement with a hydrophone on the basis of sound pressure data, Journal of the Japan Society of Erosion Control Engineering, Vol.62, No.5, pp.18-26, 21(in Japanese) 2) Masato UCHIO, Hajime NAKAGAWA, Toyoaki SAWADA, Koji YOKOYAMA, Mitsuaki UESU- GI and Yoshinori FUKUDA, Development of a measuring system for particle size distribution in gravel-bed rivers by using an image processing technique, Journal of the Japan Society of Erosion Control Engineering, Vol.58, No.2, pp.26-31, 25 (in Japanese). 3) The Society of Powder Technology, JAPAN, Measurement Technology of Particle, THE NIKKAN KOGYO SHIMBUN, LTD., pp.18-27, 1994 (in Japanese). 4) N. J. Carino et al., A Point Source-Point Receiver, Pulse-Echo Technique for Flaw Detection in Concrete, ACI Journal/March-April 1986, pp , ) Werner Goldsmith, IMPACT, DOVER PUBLICA- TIONS, INC., pp.83-91, 21. 6) Akira ODA, Yuya HIRANO, Masanori WA- TANABE, Minoru OCHIAI and Shigekatsu ENDO, EXPERIMENTAL STUDY ON EVALU- ATION OF GRAIN DIAMETER USING CONc b (3) The gravel size distribution measured using the shape factor matched that determined from the sieve test. Experimental results show that the proposed method applicable to estimate the size distribution of gravel for 15 mm or more in diameter. The development of an indirect method of measuring grain diameter is important for erosion control (sabo) and river planning. Further work is required to apply the method to actual flows. d=b Fig.1 The sieve opening and middle length of gravel b. Cummulative percentage of gravel size (%) Sieve test Using Eq. (3) Using Eqs. (3)-(6) to the mean diameter dm = 29.9 mm from the sieve test. Nevertheless, the calculated result still is slightly greater than the measured value. In particular, the difference for finer gravel was about 2%. This might arise because the shape factor is different for smaller pieces of gravel and it is that small gravels collision at same time to POM board. However, for the largest ten pieces of gravel, the calculated and measured values were in good agreement. Such a simple survey is applied to this method so that, the accuracy of grain size distribution can be improved. 4. Conclusions Our proposed method can be used to estimate the size distribution of gravel. We obtained the following results. (1) The relationship between the contact time Tc and gravel diameter d is given by Eq. (3). (2) The method was most accurate for gravel with a diameter range of 15 2 mm. 2 Gravel size (mm) Fig.11 Comparison of gravel size distribution. Acknowledgment This work was supported in part by Grant-in-Aid for Challenging Exploratory Research (No ). References 6

7 Estimation of Gravel Size Distribution using Contact Time TACT TIME WHEN GRAVEL COLLIDES WITH ELASTIC PLATE, Annual Journal of Hydraulic Engineering, JSCE, Vol.55, pp.s1165-s117, 211 (in Japanese). 7) J. S. McNown, J. Malaika and H. R Pramanik, PARTICLE SHAPE AND SETTLING VEROCI- TY, INTERNATIONAL ASSOCIATION FOR HYDRAULIC RESEACH FOURTH MEETING, BOMBAY, INDIA, pp , ) Saburo KOMURA, SEDIMENT HYDRAULICS 1 [POD edition], Morikita Publishing Co, Ltd., p.4, 25(in Japanese). 7

8 礫の接触時間を用いた粒度分布の推定 小田晃, 平野雄也, 渡邉真矩, 落合実 概 要 河川 砂防の分野での粒度分布の計測方法は, ふるい分け試験 が主である しかし, この方法は現地から砂礫を運搬し, さらに乾燥させるなどの作業を必要とし, 粒度分布を得るためには時間と費用がかかる そのため, より簡易に粒度分布を推定する方法が模索されている 本研究は, 砂礫と弾性体の衝突時の弾性波を用いることにより簡易に粒度分布を推定する方法を提案するものである 砂礫と弾性体の接触時間に基づいた粒度分布の推定法についての実験を実施した 単独のガラス球, ならびに単独の石球による弾性体 ( 硬質プラスチック (POM) 板 ) との衝突実験では, 弾性波計測結果から得られる接触時間と粒径の関係について検討した その結果, 接触時間と粒径の間に良い相関が示された また, 個数の計数も良好な結果であることが示された この実験から, 個々の礫の接触時間を読み取り粒径に換算して粒度分布を推定した しかし, この粒度分布はふるい分け試験の結果よりも平均粒径で約 2 倍大きい結果となることが示された この原因のひとつとして, 自然の礫が球体ではないことがあげられる 礫が弾性体に衝突 接触する箇所の形状が影響しているのではないかと考えた そこで, 礫の形状を数値化するため形状係数を用いた 使用した礫の最大径から上位 1 個の形状係数を用いて検討した結果, 接触時間から推定した粒径が礫の中軸長と最もよい相関であった 形状係数, ならびに推定した粒径と中軸長の関係を考慮して粒度分布を推定した結果, 推定した粒度分布はふるい分け試験の結果とほぼ一致することが示された このことから, 本研究で提案した間接的な粒度分布推定法が, 現地での粒度分布の推定に有効であることが示された 8

9 Biographical Sketches of the Authors Akira Oda Born March 15th 196 Finished Doctor Course program without dissertation, Graduate School of Nihon University, Doctor of Engineering. Main Research Subjects : Outburst of Landslide dam, Development of Measuring Bedload Discharge, Study on Evaluation of Grain Diameter Using Contact Time When Gravel Collides with Elastic Plate. Outside Contributions : Committee of mid Niigata Prefecture Earthquake Sediment Disasters Investigation Study of JSECE, Research Fellow of Civil Engineering Research Laboratory, Committee of Sabo Hydraulic Research of Civil Engineering Research Laboratory, Chairman of Conference of Sakuda River Area Chiba Prefecture, Committee of Chiba Prefecture Tsunami Prevent Engineering Department(River). Academic society : Japan Society of Erosion Control Engineering (JSECE) and Japan Society of Civil Engineers (JSCE). Yuya Hirano Born January 11th 1987 Master Course, Graduate School of Nihon University, Master of Engineering. Main Research Subjects : Study on Evaluation of Grain Diameter Using Contact Time When Gravel Collides with Elastic Plate. Academic society : Japan Society of Civil Engineers (JSCE). Masanori Watanabe Born September 21th 1987 Master Course, Graduate School of Nihon University, Master of Engineering. Main Research Subjects : Study on Evaluation of Grain Diameter Using Contact Time When Gravel Collides with Elastic Plate. Academic society : Japan Society of Civil Engineers (JSCE). 9

10 Minoru Ochiai Born March 6th 1954 Master Course, Graduate School of Nihon University, Doctor of Engineering. Main Research Subjects : Material diffusion and environmental impact assessment in the ocean by using the ocean circulation model, CO2 diffusion technology for the ocean isolation of carbon dioxide, Development of hydraulic structure in consideration of impact on ecosystem in waters, Experimental and numerical analysis of turbulent flow field with fluctuation of free water surface. Outside Contributions : Trustee of Japan Society of Civil Engineers (JSCE) Kanto Branch, Committee of Kashiwa City General Plan Council, Committee of Kashiwa City Urban Plan Council, Chairman of Council of Kashiwa Police Station. Academic society : Japan Society of Civil Engineers (JSCE), International Association for Hydro-Environment Engineering and Research, Japan Society for Marine Surveys and Technology. 1