METHOD FOR CALCULATING BEDLOAD SEDIMENT TRANSPORT RATE BY CORRECTING FRICTION COEFFICIENT IN BED SEDIMENT MOVEMENT

Abstract

A method for calculating the bedload sediment transport rate by correcting the friction coefficient in the bed sediment movement is provided, including the following steps: S1, creating a calculation formula of a friction coefficient; S2, determining a calculation bedload sediment transport rate formula per unit width; S3, transforming the calculation formula of the bedload sediment transport rate per unit width into a dimensionless form; and S4, substituting the calculation formula of the bedload sediment transport rate per unit width obtained in the S2 into the S3 to obtain a bedload sediment transport rate formula with a corrected friction coefficient.

Claims

1. A method for calculating a bedload sediment transport rate by correcting a friction coefficient in bed sediment movement, wherein the method comprises following steps: S1, creating a calculation formula of a friction coefficient: S11, determining a static friction coefficient, a recovery coefficient and a sediment particle temperature; and S12, determining volume weights of sediment particles and water flow, with the volume weight of the sediment particles being 2.65 g/cm.sup.3 and the volume weight of the water flow being 1.0 g/cm.sup.3, determining a particle size D and a settling velocity of the sediment particles, and determining a ratio m of an average height of bedload movement to the particle size of the sediment particles, and a calculation method of m is, wherein are a friction velocity and a critical fri U.sub.* and U.sub.*,c $m=7.3{\left(\frac{U\text{?}}{U\text{?}}\right)}^{0.6}\mathrm{ively};$ $\text{?}\text{indicates text missing or illegible when filed}$ S2, determining a calculation bedload sediment transport rate formula per unit width; S3, transforming a calculation formula of the bedload sediment transport rate per unit width into a dimensionless form; and S4, substituting the calculation formula of the bedload sediment transport rate per unit width obtained in step S2 into step S3 to obtain a bedload sediment transport rate formula with a corrected friction coefficient; wherein a method for calculating the friction coefficient in the step S1 comprises: $\begin{array}{cc}={}_0\left\{\mathrm{erf}\left(\frac{g_0}{\sqrt{2T_t}\stackrel{\_}{{}_0}}\right)-\frac{5k}{192}\frac{\sqrt{3}}{2}{R}_t\left[\frac{4}{\stackrel{\_}{{}_0}}\mathrm{erfc}\left(\frac{g_0}{\sqrt{2T_t}\stackrel{\_}{{}_0}}\right)+\frac{8}{\sqrt{}{g}_0}{\left(2T_t\right)}^{\frac{1}{2}}\left(1-\exp \left(-\frac{g_0^2}{2T_t\stackrel{\_}{{}_0^2}}\right)\right)\right]\right\}& \left(1\right)\end{array}$ wherein .sub.0 is the static friction coefficient, with values ranging from 0.4 to 0.6, D(du/dy)/{square root over (3T.sub.t)}, u is a velocity, y is a vertical coordinate, t is time, T.sub.t is the sediment particle e and b.sub.0 are vertical and tangential recovery coefficients, being 0.9 and 0.8 respectively, and g.sub.0 is an average velocity of contact points between the sediment particles and a $\stackrel{\_}{{}_0}=\frac{7}{2}\frac{1+e}{1+b_0}{}_0,$ $\begin{array}{cc}k={\frac{2}{\left(1+e\right)f_0}\left[1+\frac{4}{5}\left(1+e\right)f_{0}v\right]}^2+\frac{384v^2{f}_0\left(1+e\right)}{25}& \left(2\right)\end{array}$ bed surface, and k is a correction coefficient of suspended sediment particles to a viscosity coefficient, adopting a following calculation method: wherein f.sub.0 is a radial distribution function, , v.sub.m=0.64; v is a concentration of the sediment particles, and e is a vertical recovery coefficient; substituting formula (1) into Bagnold's bedload transport formula, obtaining the bedload sediment transport rate g.sub.b per unit width: $\begin{array}{cc}{g}_b=\frac{{}_s}{{}_s-}\frac{U_{*}-U_{*c}}{U_{*}}\frac{{}_0}{}\left[5.75U_{*}\log 30.2\left(\frac{mD}{K_s}\right)-\right]& \left(3\right)\end{array}$ wherein .sub.s and are the volume weights of the sediment particles and the water flow respectively, .sub.0 is a shear force of the sediment particles, with an expression of .sub.0=U.sub.*.sup.2, is a water flow density, K.sub.s is a bed roughness, D is the particle size of the sediment particles, m is the ratio of the average height of the bedload movement to the particle size of the sediment particles, and is the settling velocity of the sediment particles; in the step S3, the calculation formula of the bedload sediment transport rate per unit width is transformed into the dimensionless form by introducing shields number, and an expression is: $\begin{array}{cc}=\frac{{}_0}{\left({}_s-\right)D}& \left(4\right)\end{array}$ an expression of a dimensionless sediment transport rate is: $\begin{array}{cc}=\frac{g_b}{{}_s}\sqrt{\frac{}{\left({}_s-\right)g{D}^3}};& \left(5\right)\end{array}$ a bedload sediment transport rate formula after the friction coefficient corrected in step S4 is: $\begin{array}{cc}=\frac{\left(\sqrt{}-\sqrt{{}_{}}\right)\left[5.75\log 30.2\left(\frac{mD}{K_s}\right)-\frac{}{U_{*}}\right]}{{}_0\left\{\mathrm{erf}\left(\frac{g_0}{\sqrt{2T_t}\stackrel{\_}{{}_0}}\right)-\frac{5k}{192}\frac{\sqrt{3}}{2}{R}_t\left[\frac{4}{\stackrel{\_}{{}_0}}\mathrm{erfc}\left(\frac{g_0}{\sqrt{2T_t}\stackrel{\_}{{}_0}}\right)+\frac{8}{\sqrt{}{g}_0}{\left(2T_t\right)}^{1/2}\left(1-\exp \left(-\frac{g_0^2}{2T_t\stackrel{\_}{{}_0^2}}\right)\right)\right]\right\}}.& \left(6\right)\end{array}$

2. The method for calculating the bedload sediment transport rate by correcting the friction coefficient in the bed sediment movement according to claim 1, wherein a proportion of data points with the error of a calculated value of Bagnold's bedload sediment transport rate within a range of 0.5-2 times of a measured value after the friction coefficient is corrected is more than 60%.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0027] FIG. 1 shows a comparison between the measured and the calculated bedload sediment transport rate after the friction coefficient is corrected.

[0028] FIG. 2 shows a comparison of the ratio of revised Bagnold's formula calculation value to measured value and the ratio of original Bagnold's formula calculation value to measured value.

DETAILED DESCRIPTION OF THE EMBODIMENTS

[0029] The disclosure relates to a method for calculating bedload sediment transport rates by correcting friction coefficients in bed sediment movement, which includes the following steps: [0030] S1, creating a calculation formula of a friction coefficient: [0031] S11, determining a static friction coefficient, a recovery coefficient and a sediment particle temperature; [0032] S12, determining volume weights of sediment particles and water flow, with the volume weight of the sediment particles being 2.65 g/cm.sup.3 and the volume weight of the water flow being 1.0 g/cm.sup.3, determining a particle size D and a settling velocity of the sediment particles, and determining a ratio m of an average height of bedload movement to the particle size of the sediment particles, and a calculation method of m is, where are a friction velocity and a critical friction vel U.sub.* and U.sub.*,c

[00009]$m=7.3{\left(\frac{U_{*}}{U_{*,c}}\right)}^{0.6}$ [0033] S2, determining a calculation bedload sediment transport rate formula per unit width; [0034] S3, transforming the calculation formula of the bedload sediment transport rate per unit width into a dimensionless form; and [0035] S4, substituting the calculation formula of the bedload sediment transport rate per unit width obtained in the S2 into the S3 to obtain a bedload sediment transport rate formula with a corrected friction coefficient; [0036] where a method for calculating the friction coefficient in the S1 includes following steps:

[00010]$\begin{array}{cc}={}_0\left\{\mathrm{erf}\left(\frac{g_0}{\sqrt{2T_t}\stackrel{\_}{{}_0}}\right)-\frac{5k}{192}\frac{\sqrt{3}}{2}{R}_t\left[\frac{4}{\stackrel{\_}{{}_0}}\mathrm{erfc}\left(\frac{g_0}{\sqrt{2T_t}\stackrel{\_}{{}_0}}\right)+\frac{8}{\sqrt{}{g}_0}{\left(2T_t\right)}^{\frac{1}{2}}\left(1-\exp \left(-\frac{g_0^2}{2T_t{\stackrel{\_}{{}_0}}^2}\right)\right)\right]\right\}& \left(1\right)\end{array}$$={}_0\left\{\mathrm{erf}\left(\frac{g_0}{\sqrt{2T_t}\stackrel{\_}{{}_0}}\right)-\frac{5k}{192}\frac{\sqrt{3}}{2}{R}_t\left[\frac{4}{\stackrel{\_}{{}_0}}\mathrm{erfc}\left(\frac{g_0}{\sqrt{2T_t}\stackrel{\_}{{}_0}}\right)+\frac{8}{\sqrt{}{g}_0}{\left(2T_t\right)}^{\frac{1}{2}}\left(1-\exp \left(-\frac{g_0^2}{2T_t{\stackrel{\_}{{}_0}}^2}\right)\right)\right]\right\}$ [0037] in the formula, .sub.0 is the static friction coefficient, with values ranging from 0.4 to 0.6,
, u is a velocity, y is a vertical coordinate, t is time, T.sub.t is the sediment particle temp , e and .sup.b0 are vertical and tangential recovery coefficients, respectively, and g.sub.0 is an average velocity of contact points between the sediment particles and a bed surface, and k is a correction coefficient of suspended sed g.sub.0=u.sub.0+(D/2)nw viscosity coefficient, being calculated as follows:

R.sub.t=D(du/dy)/{square root over (3T.sub.t)}

[00011]$\stackrel{\_}{{}_0}=\frac{7}{2}\frac{1+e}{1+b_0}{}_0,$

[0038] In the formula, f.sub.0 is a radial distribution function,

[00012]$f_0={\left(1-\frac{v}{v_m}\right)}^{-5v_m/2},$

for sediment particles, v.sub.m=0.64; v is a concentration of the sediment particles, and e is a vertical recovery coefficient.

[00013]$\begin{array}{cc}k={\frac{2}{\left(1+e\right)f_0}\left[1+\frac{4}{5}\left(1+e\right)f_{0}v\right]}^2+\frac{384v^2{f}_0\left(1+e\right)}{25}& \left(2\right)\end{array}$ [0039] substituting formula (1) into Bagnold's bedload transport formula, obtaining the bedload sediment transport rate per unit width g.sub.b:

[00014]$\begin{array}{cc}{g}_b=\frac{{}_s}{{}_s-}\frac{U_{*}-U_{*c}}{U_{*}}\frac{{}_0}{}\left[5.75U_{*}\log 30.2\left(\frac{mD}{K_s}\right)-\right]& \left(3\right)\end{array}$ [0040] in the formula, .sub.s and are the volume weights of the sediment particles and the water flow respectively, .sub.0 is a shear force of the sediment particles, with an expression of .sub.0=U.sub.*.sup.2, is a water flow density, K.sub.s is a bed roughness, D is the particle size of the sediment particles, m is the ratio of the average height of the bedload movement to the particle size of the sediment particles, and is the settling velocity of the sediment particles; [0041] in the S3, the calculation formula of the bedload sediment transport rate per unit width is transformed into the dimensionless form by introducing shields number, and an expression is:

[00015]$\begin{array}{cc}=\frac{{}_0}{\left({}_s-\right)D}& \left(4\right)\end{array}$ [0042] an expression of dimensionless sediment transport rate is:

[00016]$\begin{array}{cc}=\frac{g_b}{{}_s}\sqrt{\frac{}{\left({}_s-\right)g{D}^3}};& \left(5\right)\end{array}$ [0043] a bedload sediment transport rate formula after the friction coefficient is corrected in the S4 is as follows:

[00017]$\begin{array}{cc}=\frac{\left(\sqrt{}-\sqrt{{}_{}}\right)\left[5.75\log 30.2\left(\frac{mD}{K_s}\right)-\frac{}{U_{*}}\right]}{{}_0\left\{\mathrm{erf}\left(\frac{g_0}{\sqrt{2T_t}\stackrel{\_}{{}_0}}\right)-\frac{5k}{192}\frac{\sqrt{3}}{2}{R}_t\left[\frac{4}{\stackrel{\_}{{}_0}}\mathrm{erfc}\left(\frac{g_0}{\sqrt{2T_t}\stackrel{\_}{{}_0}}\right)+\frac{8}{\sqrt{}{g}_0}{\left(2T_t\right)}^{1/2}\left(1-\exp \left(-\frac{g_0^2}{2T_t\stackrel{\_}{{}_0^2}}\right)\right)\right]\right\}}.& \left(6\right)\end{array}$

[0044] The bedload sediment transport rate calculated based on the above steps is compared with the collected classical Meyer-Peter (1948) measured data and Meyer-Peter formula (see Table 1), and the results are shown in FIG. 1. From the FIG. 1, it can be seen that the results calculated by the corrected bedload sediment transport rate formula may be better consistent with the measured values. In addition, the results calculated by the corrected bedload sediment transport rate formula are in good agreement with the results calculated by the classical Meyer-Peter empirical formula.

[0045] On this basis, the variation law of the ratio of measured value to calculated value with shields number is further counted, and as can be seen from FIG. 2, the data points with the error of the corrected Bagnold's calculated value within the range of 0.5-2 times the measured value are greatly increased, and the proportion increases from 32.57% to 61.36%, with an increase of nearly 30%.

[0046] Based on the analysis of the above two aspects, it can be seen that the accuracy of the calculation formula of in Bagnold's bedload sediment transport rate considering the correction of friction coefficient has been greatly improved, which is in better agreement with the measured data, and it also shows that the disclosure has good and practical value.

TABLE-US-00001 TABLE 1 Comparison of water and sediment parameters and calculation results of different bedload sediment transport rates in Meyer-Peter bedload transport experiment indicates data missing or illegible when filed

[0047] Finally, it should be noted that the above is only used to illustrate the technical scheme of the present disclosure, but not to limit it. Although the present disclosure has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that the technical scheme of the present disclosure may be modified or replaced by equivalents without departing from the spirit and scope of the technical scheme of the present disclosure.