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Article

Study on Parameters of Two Widely Used Cohesive Soils Erosion Models

The Key Laboratory of Urban Security and Disaster Engineering of Ministry of Education, Beijing University of Technology, Beijing 100124, China
*
Author to whom correspondence should be addressed.
Current address: College of Architecture and Civil Engineering, Beijing University of Technology, No.100, Pingleyuan, Chaoyang District, Beijing 100124, China.
Water 2021, 13(24), 3621; https://doi.org/10.3390/w13243621
Submission received: 8 November 2021 / Revised: 8 December 2021 / Accepted: 12 December 2021 / Published: 16 December 2021
(This article belongs to the Section Water Erosion and Sediment Transport)

Abstract

:
The erosion rate of cohesive soils was typically modeled with the excess shear stress model and the Wilson model. Several kinds of research have been conducted to determine the erodibility parameters of the two models, but few attempts have been made hitherto to investigate the general trends and range of the erodibility parameter values obtained by the commonly used Erosion Function apparatus. This paper collected a database of 177 erosion function apparatus tests to indicate the variability of all erodibility parameters; the range of erodibility parameters is determined by data statistics and parameter theoretical value derivation. The critical shear stress (τc) and erodibility coefficient (Z0) in the over-shear stress model have a positive proportional relationship when the data samples are sufficient. However, there is no such relationship between the erodibility coefficient (b0) and erodibility coefficient (b1) in the Wilson model. It is necessary to express the soil erosion resistance by considering all erosion parameters in the erosion model. Equations relating erodibility parameters to water content, plasticity index, and median particle size were developed by regression analysis.

1. Introduction

Erosion models represent the constitutive law of soils for erosion problems, much like a stress–strain curve represents the constitutive law of soils for settlement problems. The most commonly used erosion models up to date are the excess shear stress model and the Wilson model. The excess stress shear model can be expressed as [1]:
z ˙ = k D ( τ τ c ) α
where z ˙ is the erosion rate (m s−1), kD is the coefficient of erodibility ( m 3 / ( N × S ) ), τ is the applied shear stress (Pa), τc is the critical shear stress (Pa), and α is an empirical exponent sometimes assumed to be unity [2,3,4]. Some scholars proposed dimensionless nonlinear excess shear stress models to calculate the erosion rate [1,5,6,7]. The typical dimensionless excess shear stress model is defined as:
z ˙ = Z 0 ( τ τ c 1 ) α
where Z0 is the erodibility parameter of the dimensionless excess shear stress model (mm/h). However, it is difficult to predict the values of erodibility parameters due to the erodibility parameters (Z0 and τc) changing with the season [8,9].
Wilson (1993a, 1993b) proposed a mechanistic detachment model to provide a general framework for studying soil and fluid characteristics [10,11]. The advantage of the Wilson model over the over-shear stress model is that the factors affecting erosion can be considered and evaluated in greater depth; this has been studied extensively by related scholars, incorporating factors such as turbulence, roughness, seepage forces, material soil orientation, root effects, and negative pore water pressure effects into the Wilson model [12,13,14,15,16]. The Wilson model was based on the balance of all the forces and moments driving and resisting detachment that would be preferred for modeling the range of possible environmental conditions, which is expressed as:
z ˙ = b 0 τ ρ b [ 1 exp { exp ( 3 b 1 τ ) } ]
b 0 = ρ s k r K e K n k d d ( ρ s ρ w )
b 1 = ( π e v 6 ) k r ( K l s + f c ) K d g ( ρ s ρ w ) d
where ρ b is the bulk density of soil (g m−3),   ρ s and ρ w are the densities of particle and water (1000 kg m−3), respectively, Ke is the exposure of lower particle parameter, Kn is a combination and fluid factors, kr is the ratio of kv and ka (kr = kv/ka = 2/3), kdd is detachment distance parameter, Kd is dimensionless hydraulic drag parameter, Kls is the dimensionless bed and slope parameter that depends on particle (or aggregate) size, fc is the dimensionless cohesive force parameter, and ev is the coefficient of variation. Wilson suggested that the critical stress can be calculated by drag forces equaling time-average drag forces. The critical stress is expressed as:
τ c = k r K d ( ρ s ρ w ) d g ( K l s + f c )
Al-Madhhachi (2013) tested the appropriateness of the excess stress shear model and Wilson model for cohesive sediment using flume tests, “mini” JET tests, and JET tests [12]. It was found that the Wilson model fitted the observed data from the original and “mini” JET better than the excess shear stress model, while it was consistent with the excess shear stress model in fitting the observations from the flume tests. Then, the seepage force was introduced into the Wilson model to improve the prediction effect of cohesive soil [17,18]. The recent Erosion Function Apparatus (EFA) test by Gao X et al. (2019) showed that the Wilson and shear stress models could also be applied to the test [19].
In the application of the scouring model, the determination of its parameters is a significant problem. Hanson and Cook (1997) and Hanson et al. (2002) developed analytical procedures to directly estimate kD and τc based on diffusion principles of the circular jet scour test using an Excel spreadsheet [20,21]. Daly et al. (2013) proposed a new spreadsheet tool to solve for kD and τc values simultaneously [22]. Al-Madhhachi et al. (2017) used the solver routine in Microsoft Excel to derive erodibility parameters b0 and b1, which utilized the generalized reduced gradient method [23]. Hanson and Simon (2001) found inversely proportional between the critical shear stress and the erodibility parameter kD based on 83 jet-tests on cohesive streambeds in the Midwestern U.S., implying that one parameter can fully describe the soil erosion resistance [24]. An alternative relationship was proposed by Simon et al. (2011) based on hundreds of JETs on stream banks across the U.S [25]. However, other scholars found no correlation between erodibility parameter kD and critical flow shear stress [26,27]. These studies have different views on the relationship between each parameter, which needs further confirmation. In addition, for the data set of the Erosion Function Apparatus test, whether the above relationship is applicable still needs further verification.
Erosion resistance of soil is closely related to its parameters such as soil gradation, compaction, clay content, etc. [28,29]; Briaud (2005) found that soil porosity ratio, water temperature, soil temperature, sodium adsorption ratio, and other parameters are directly proportional to soil’s erosion resistance ability [30], while soil specific gravity, plastic index, particle proportion with particle size <0.075 mm and other parameters are inversely proportional to soil’s erosion resistance ability. The study shows that soil’s physical and mechanical parameters closely affect its scour characteristics [29]. Therefore, soil properties play an essential role in soil erosion resistance. For the parameters in the scour model, it is also vital to determine their relationship with soil parameters. Hasan and Al-Madhhachi (2018) investigated the effect of crude oil on erosion parameters (b0 and b1) [13]. For clean soil and polluted soil, parameter b1 increases with increasing water content. However, compared with clean soil, polluted soil has a more significant effect on parameter b0. Al-Madhhachi (2013) proposed that the scouring parameter Z0 is inversely proportional to water content in the scouring experiment of fine-grained soil [12]. In the scour experiment of silty clay and sand mixture, Z0 and α are positively proportional to dry density and inversely proportional to the void ratio [19,31]. Although there has been some advance in studying erosion in cohesive soils, further research is needed to estimate erodibility parameters accurately.
In this study, a database of 177 cohesive soil erosion function apparatus tests with soil properties was collected from the literature review. The Wilson model and the dimensionless over-shear stress model were further extended for applications in EFA devices. The range of scouring parameters in the EFA data set is determined based on the experimental data and the theoretical derivation of erosion parameters. The values of the erosion parameters under EFA equipment are summarized. The general trend of erosion parameters and the relationship between erosion parameters are further illustrated. The variability of the parameters and the importance of each parameter are revealed. The relationship between soil erodibility parameters (b0, Z0, and α) and soil engineering properties is proposed by regression analysis, which could be helpful for computer simulation analysis of Scouring failure.

2. Methods

In the analysis of this paper, mean grain size and bulky soil density are normalized, and the data are converted into dimensionless data between 0 and 1. The remaining three parameters are expressed in decimal form, and then, regression analysis is conducted. The normalization formula is as follows:
x = x x min x max x min
where x is the normalized data, and xmax and xmin, respectively, represent the maximum and minimum values in this data group.
For the regression analysis model, the determination coefficient R 2 and F v a l u e were used to evaluate the model’s performance and determine the optimal parameter values [32,33]. The determination coefficient R 2 and F v a l u e are defined as:
R 2 = 1 ( y i y ^ i ) 2 ( y i y ¯ ) 2
where y i is the actual value of the sample, y ^ i is the fitting value, and y ¯ is the average value. R-square ranges from 0 to 1.0, which closer to 1.0 means better fit.
F v a l u e = ( f i y ¯ ) 2 ( y i f i ) 2 × ( D V 1 )
where D is the number of data points, and V is the number of independent variables. When the Fvalue is much higher than the critical value of the F test, the result of the regression equation is more reliable. The critical of Fvalue can be obtained from the F distribution table, and its significance level is set at 0.05.
Therefore, the combinations with higher R2 and Fvalue/Fstatistic are chosen as equations relating the erodibility parameters to the soil geotechnical properties.

3. Erosion Function Apparatus Tests Database

The erosion function apparatus is currently one of the most commonly used soil erosion test equipment. It is used to investigate the erodibility of the non-cohesive soil, cohesive soil, and gravel. The EFA can measure the erosion rate curve and critical shear stress of cohesive soil [34].
The study collected a database of 177 tests. The coupling of various soil parameters influences the scour behavior of soil, and the scour mechanism is studied by investigating the influence of soil parameters on scouring behavior. The experimental data selected in this paper include the experimental data of scouring and soil parameters; some data lacking soil parameters are excluded. Among the database, eight tests were from Gao (2019), twelve tests were from ILIT (2006), eighty tests were from Shafii (2018), thirty-eight tests were from Briaud (1999, 2008), twelve tests were from Kwak (2000), six tests were from Park (2007), three tests were from Bernhardt (2011), five tests were from Govin (2009), and the thirteen tests were from Straub (2013) [19,28,35,36,37,38,39,40,41,42]. Table 1 shows the soil types according to the USCS classifications and the number of tests.
Figure 1 shows the soil samples main properties in the database, including plasticity index, percent fines, soil bulky density, water content, and mean grain size.

4. Results and Discussion

4.1. The Data Range of the Experimental Erodibility Parameters Values

In this study, the Wilson model’s erodibility parameters (b0 and b1) were derived using a curve fitting tool based on the principle of minimizing the error between predicted erosion data and measured erosion data. The critical shear stress τc is defined for this study as the interface shear stress corresponding to a very low erosion rate of 0.1 mm h−1. The value of the erodibility parameter (Z0) in equation 2 is equal to th e erosion rate when the hydraulic shear stress (τ) is equal to twice the critical shear stress (τc). After the critical shear stress and the erodibility parameter (Z0) were determined, the exponential term ( α ) was estimated using the curve fitting tool by minimizing the sum of squared errors between the predicted erosion data and the measured erosion data. The erodibility parameters (τc, Z0, and α ) of the dimensionless excess shear stress model and the erodibility parameters (b0 and b1) of the Wilson model are shown in Figure 2 and Figure 3, respectively.
The database was analyzed to obtain 177 Z0, τc, α, b0, and b1 values. Figure 2 shows that the erodibility parameters Z0, τc, and α of cohesive soils ranged from 0.10 mm h−1 to 117.23 mm h−1, from 0.11 Pa to 50.25 Pa, and from 0.26 to 2.75, respectively. Briaud (2017) analyzed 84 EFA tests carried out by Texas A&M University and TxDOT and obtained the range of critical shear stress values for various soil types [43]. The range of critical shear stress of cohesive soils is 0.15–20 Pa obtained from Briaud (2017), which is consistent with the range of critical shear stress obtained in this paper. Several studies have shown that α varies between 1.0 and 6.8 [43,44,45], consistent with the range of α values obtained in the current paper.
Figure 3 shows that the erodibility parameters b0 and b1 values of cohesive soils ranged from 0.09 g m−1 s−1 N−0.5 to 80.29 g m−1s−1N−0.5 and from 0.56 Pa to 267.26 Pa, respectively. Based on equation 3b, it can be shown that the erodibility parameter b0 is related to the bulk density of soil (ρb), the densities of the particle (ρs), the ratio of volume/area parameters (kr), the exposure of lower particle parameter (Ke), a combination and fluid factors (Kn), and detachment distance parameter (kdd). Wilson recommended that Wilson recommended that kr = 2/3 for spherical particles, kdd = 2. Wilson (1993b) defines a combination and fluid factors (Kn) as [11]:
K n = K t K d / k r
where Kt is the cumulation of instantaneous force. Wilson suggested that Kt = 2.5 and the dimensionless hydraulic drag parameter (Kd) is defined as:
K d = C d k f [ ln ( φ ) / κ + B ] 2 2
where Cd is the drag coefficient, Einstein and El-Samni (1949) suggested that the value of Cd is 0.2 [46]; kf is the fraction of exposed area, and Wilson recommended a value of 0.92; φ is the drag velocity fractional height, Einstein and El-Samni (1949) suggested φ = 0.35, while Yang (1973) suggested φ = 1 [46,47]; κ is the von Kannon constant, Wilson recommended κ = 0.4; B is the Log-velocity intercept parameter which ranges from 6.5 to 9.8 [11]. The maximum value of Kd is 8.84, and the minimum value is 1.38. Therefore, the maximum value of Kn is 33.15. Kothyari (2008) suggested that the density value of clay is 2.7 g cm−3 [48]. The influence of the exposure factor ke on the erosion parameter b0 is critical, but little information is available directly on the parameter ke [11,12]. The method of determination of this parameter needs to be further studied.
To obtain the maximum value of parameter b1, combine Equations (3c) and (4):
b 1 ( max ) = π τ c ( max ) e v 6
The value of ev in this study is 0.35. Due to the maximum value of τc being 50.25 Pa obtained from the database, the theoretical maximum value of b1 is 184.04 Pa. We can find that the range of theoretical values of the erodibility parameters (b0 and b1) includes the experimental values.
A comparison of erodibility parameters between high-plasticity clay (CH: PI ≥ 0.73(wL-20), PI ≥ 7, and wL ≥ 50) and low-plasticity clay (CL:PI ≥ 0.73 (wL-20), PI ≥ 7, and wL < 50) is shown in Figure 4 and Figure 5. Compared with the erodibility parameter b0 of high-plasticity clay, the erodibility parameter b0 of low-plasticity clay is higher. The range of erodibility parameters b0 of high-plasticity clay and low-plasticity clay mainly concentrates in 0.44–2.77 g m−1 s−1 N−0.5 and 1.35–4.6 g m−1 s−1 N−0.5, respectively (Figure 4a). The erodibility parameter b0 decrease with the water content increase due to the rise of soil cohesion (which increases Ke). Similar observations are reported for Z0. The range of erodibility parameters Z0 of high-plasticity clay and low-plasticity clay is mainly concentrated in 0.5–3.31 mm h−1 and 1–8.94 mm h−1, respectively (Figure 5b). The range of erodibility parameters Z0 of low-plasticity is higher than the range of erodibility parameters Z0 of high-plasticity. Therefore, b0 has a similar relationship with z0 relative to the liquid limit (Figure 4a and Figure 5b).
Compared with the erodibility parameter b1 of high-plasticity clay, the erodibility parameter b1 of low-plasticity clay is lower. The erodibility parameter b1 decreased as the liquid limit increased due to increasing soil cohesion (which increases fc). The range of erodibility parameters b1 of high-plasticity is mainly concentrated in 20.33–97.82 Pa, whereas the range of parameters b1 of low-plasticity clay is concentrated in 0.44–50.2 Pa (Figure 4b). Similar observations are reported for τc. The τc increase as the liquid limit increase due to increasing cohesion. The range of the τc of high-plasticity clay experimental data is mainly concentrated in 1.23–8.78 Pa, whereas the range of the critical shear stress of low-plasticity clay is primarily concentrated in 0.5–4.43 Pa (Figure 5a). We can find that the range of erodibility parameters τc of low-plasticity is lower than the range of erodibility parameters τc of high-plasticity. Therefore, b1 has a similar relationship with τc relative to the liquid limit (Figure 4a and Figure 5b).

4.2. Relation between z0 and τc and between b0 and b1

As it is meaningful to explore whether there is a relationship between Z0 and τc and between b0 and b1, all datasets from each author have been plotted individually (Figure 6 and Figure 7). When the research data samples are small for the over-shear stress model, the discreteness between parameter Z0 and over-shear stress τc is significant (Figure 6a,b). In the case of sufficient data, the results of Shafii (2018) and Briaud (1999, 2008) showed that there was a direct proportional linear relationship between the parameter Z0 and τc. Additionally, this result has been confirmed in the research results of Hanson and Simon (2001), as shown in Figure 6c,d.
When the Wilson model is studied, this trend does not exist between b0 and b1. As shown in Figure 7a, b1 and b0 are highly discrete. While the number of data increases, the study samples of Gao (2019), Briaud (1999, 2008), and ILIT (2006) show an inverse proportional linear between the two parameters (Figure 7b). Criswell et al. (2016) also found an inverse relationship between b0 and b1 for gravels. However, this relationship is not confirmed in the studies of Shafii (2018), Straud (2013), and Govin (2009) (Figure 7c), which proves that there is no such relationship between parameters b0 and b1.

4.3. Multiple Nonlinear Regression Analysis

The multiple nonlinear model is used to study equations relating the erodibility parameters b0 and Z0 to the soil geotechnical properties in this research. The multiple no-nlinear model is shown in Equation (11):
Y = A × ( P 1 ) α 1 × ( P 2 ) α 2 × ( P 3 ) α 3 × × ( P n ) α n
where Y is the dependent variable; Pn is the soil geotechnical properties, including plasticity index, percent fines, wet density, water content, and mean grain size in this case. Many combinations between the erodibility parameters and the soil geotechnical properties can be selected to generate regression equations.
The correlation analysis of soil parameters and scour parameters in the database is carried out. The analysis results are shown in the following table. The correlation coefficient between soil parameter PI, WC, D50, and scour parameters is significant, so these three parameters can be used to analyze the relationship with scouring parameters.
According to the results of correlation analysis, we conducted regression analysis on WC, PI, and D50, with R2 and F test indexes as evaluation indexes. Table 2 summarizes the best regression equations for the erodibility parameters (b0, α, and Z0) of cohesive soils. According to Table 3, the relationship between parameters b0, α, and Z0 with the selected soil parameters is similar. They are inversely proportional to the plasticity index but directly proportional to water content and median grain size, which is consistent with the results of correlation analysis in Table 2. Figure 8a–c shows the comparison of predicted and measured values of the three parameters.

5. Conclusions

A database of 177 EFA tests of cohesive soils with soil properties is present. The database is used to derive the erodibility parameters (Z0, τc, and α) of the dimensionless excess shear stress model and the erodibility parameters (b0 and b1) of the Wilson model to obtain a new database of 177 erodibility parameters (Z0, τc, α, b0, and b1). The new database is used to determine the range of all erodibility parameters (Z0, τc, α, b0, and b1). The parameters Z0, τc, and α values of cohesive soils ranged from 0.10 mm h−1 to 117.23 mm h−1, from 0.11 Pa to 50.25 Pa, and from 0.26 to 2.75, respectively. The parameters b0 and b1 of cohesive soils ranged from 0.09 g m−1 s−1 N−0.5 to 50.25 g m−1 s−1 N−0.5 and from 0.56 Pa to 267.26 Pa, respectively.
The new databases were categorized according to the USCS (Briaud, 2013) classifications [49]. It found that the range of Z0, τc, b0 and b1 values of high-plasticity clay is mainly concentrated in 0.5–3.31 mm h−1, 1.23–8.78 Pa, 0.44–2.77 g m−1 s−1 N−0.5, and 20.33–97.82 Pa, respectively, whereas the range of Z0, τc, b0, and b1 values of low-plasticity clay are mainly concentrated in 1–8.94 mm h−1, 0.5–4.43 Pa, 1.35–4.6 g m−1 s−1 N−0.5, and 0.44–50.2 Pa. The experimental values obtained from the low-plasticity clay show that the τc and b1 values are lower than the high-plasticity clay values. In comparison, their Z0 and τc values are higher than the high-plasticity clay values. Therefore, erodibility parameters b0 and b1 have a similar relationship with Z0 and τc relative to the liquid limit, respectively.
The new databases are also used to develop regression equations that link the erodibility parameters (Z0 and b0) to the index soil parameters, such as the mean grain size, the water content, the percent fines, the plasticity index, the bulk density, and the plastic limit. It is found that z0 and b0 values consistently decreased when the plasticity index increased, while water content and mean grain size decreased. Therefore, the Wilson model parameter b0 had a similar relationship but a different magnitude, as parameter Z0 relative to the water content, the mean grain size, and the plasticity index. These results apply to EFA devices and may not be applicable to other devices such as jet erosion tests and hole erosion tests.

Author Contributions

All authors contributed extensively to the work presented in this paper. Conceptualization, Q.W.; Funding acquisition, Q.W.; Investigation, J.F.; Methodology, Q.W.; Project administration, Q.W.; Supervision, S.Q.; Validation, P.Z.; Visualization, P.Z.; Writing—original draft, J.F.; Writing—review and editing, P.Z. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by National Natural Science Foundation of China, grant number 52130905; 51679003 and the APC was funded by 51679003.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Informed consent was obtained from all subjects involved in the Study.

Data Availability Statement

The data were obtained from the summary of other scholars’ research papers; all data can be obtained from the figures of this paper.

Acknowledgments

This work was financially supported by the National Natural Science Foundation of China (Grant No. 52130905; No.51679003). The authors want to thank the anonymous reviewers and editors for their valuable comments and suggestions that significantly contributed to this manuscript’s improvement.

Conflicts of Interest

The authors declare no conflict of interest.

References

  1. Partheniades, E. Erosion and deposition of cohesive soils. J. Hydraul. Div. ASCE 1965, 91, 105–139. [Google Scholar] [CrossRef]
  2. Hanson, G.J. Surface erodibility of earthen channels at high stresses part I-open channel testing. Trans. ASAE 1990, 33, 127–131. [Google Scholar] [CrossRef]
  3. Hanson, G.J. Surface erodibility of earthen channels at high stresses part II-developing an in situ testing device. Trans. ASAE 1990, 33, 132–137. [Google Scholar] [CrossRef]
  4. Hanson, G.J.; Cook, K.R. Apparatus, test procedures, and analytical methods to measure soil erodibility in situ. Appl. Eng. Agric. 2004, 20, 455–462. [Google Scholar] [CrossRef]
  5. Gailani, J.; Ziegler, C.K.; Lick, W. Transport of suspended solids in the Lower Fox River. J. Great Lakes Res. 1991, 17, 479–494. [Google Scholar] [CrossRef]
  6. Lin, Q.; Wu, W. A one-dimensional model of mixed cohesive and non-cohesive sediment transport in open channels. J. Hydraul. Res. 2013, 51, 506–517. [Google Scholar] [CrossRef]
  7. Wicks, J.M.; Bathurst, J.C. SHESED: A physically based, distributed erosion and sediment yield component for the SHE hydrological modelling system. J. Hydrol. 1996, 175, 213–238. [Google Scholar] [CrossRef]
  8. Henderson, M.B.; Wynn, T.M.; Vaughn, D.H. Changes in streambank erodibility and critical shear stress due to subaerial processes. In Proceedings of the 2006 ASABE Annual Meeting American Society of Agricultural and Biological Engineers, Portland, OR, USA, 9–12 July 2006. [Google Scholar]
  9. Wynn, T.M.; Henderson, M.B.; Vaughn, D.H. Changes in streambank erodibility and critical shear stress due to subaerial processes along a headwater stream, southwestern Virginia, USA. Geomorphology 2007, 97, 260–273. [Google Scholar] [CrossRef]
  10. Wilson, B.N. Development of a fundamentally based detachment model. Trans. ASAE 1993, 36, 1105–1114. [Google Scholar] [CrossRef]
  11. Wilson, B.N. Evaluation of a fundamentally based detachment model. Trans. ASAE 1993, 36, 1115–1122. [Google Scholar] [CrossRef]
  12. Al-Madhhachi, A.T.; Hanson, G.J.; Fox, G.A.; Tyagi, A.K.; Bulut, R. Deriving parameters of a fundamental detachment model for cohesive soils from flume and jet erosion tests. Trans. ASABE 2013, 56, 489–504. [Google Scholar] [CrossRef]
  13. Hasan, M.B.; Al-Madhhachi, A.T. The influence of crude oil on mechanistic detachment rate parameters. Geosciences 2018, 8, 332. [Google Scholar] [CrossRef] [Green Version]
  14. Abbood, A.A.; Al-Madhhachi, A.T. Quantifying mechanistic detachment parameters due to humic acids in biological soil crusts. Land 2021, 10, 1180. [Google Scholar] [CrossRef]
  15. Al-Madhhachi, A.T.; Mutter, G.M.; Hasan, M.B. Predicting mechanistic detachment model due to Lead-Contaminated soil treated with Iraqi Stabilizers. KSCE J. Civ. Eng. 2019, 23, 2898–2907. [Google Scholar] [CrossRef]
  16. Criswell, D.T.; Al-Madhhachi, A.T.; Fox, G.A.; Miller, R.B. Deriving erodibility parameters of a mechanistic detachment model for gravels. Trans. ASABE 2016, 59, 145–151. [Google Scholar]
  17. Al-Madhhachi, A.T.; Fox, G.A.; Hanson, G.J. Quantifying the erodibility of streambanks and hillslopes due to surface and subsurface forces. Trans. ASABE 2014, 57, 1057–1069. [Google Scholar]
  18. Al-Madhhachi, A.T.; Fox, G.A.; Hanson, G.J.; Tyagi, A.K.; Bulut, R. Mechanistic detachment rate model to predict soil erodibility due to fluvial and seepage forces. J. Hydraul. Eng. 2014, 5, 04014010. [Google Scholar] [CrossRef] [Green Version]
  19. Gao, X.; Wang, Q.; Ma, G. Experimental investigation on the erosion threshold and rate of gravel and silt clay mixtures. Trans. ASABE 2019, 62, 867–875. [Google Scholar] [CrossRef]
  20. Hanson, G.J.; Cook, K.R. Development of excess shear stress parameters for circular jet testing. In Proceedings of the American Society of Agricultural Engineers Meetings Papers, Minneapolis, MN, USA, 10–14 August 1997. [Google Scholar]
  21. Hanson, G.J.; Robinson, K.M.; Cook, K.R. Scour below an overfall: Part II. Prediction. Trans. ASAE 2002, 45, 957–964. [Google Scholar] [CrossRef]
  22. Daly, E.R.; Fox, G.A.; Al-Madhhachi, A.T.; Miller, R.B. A scour depth approach for deriving erodibility parameters from jet erosion tests. Trans. ASABE 2013, 56, 1343–1351. [Google Scholar]
  23. Al-Madhhachi, A.T. Variability in soil erodibility parameters of Tigris Riverbanks using linear and non-linear models. Al-Nahrain J. Eng. Sci. 2017, 20, 959–969. [Google Scholar]
  24. Hanson, G.J.; Simon, A. Erodibility of cohesive streambeds in the loess area of the Midwestern USA. Hydrol. Process. 2001, 15, 23–38. [Google Scholar] [CrossRef]
  25. Simon, A.; Bankhead, N.L.; Thomas, R.E. Development and application of a deterministic Bank-Stability and Toe-Erosion Model (BSTEM) for stream restoration. In Stream Restoration in Dynamic Systems: Scientific Approaches, Analyses, and Tools; American Geophysical Union: Washington, DC, USA, 2011; pp. 453–474. [Google Scholar]
  26. Laflen, J.M.; Elliot, W.J.; Simanton, J.R.; Holzey, C.S.; Kohl, K.D. WEPP Soil erodibility experiments for rangeland and cropland soils. J. Soil Water Conserv. 1991, 46, 39–44. [Google Scholar]
  27. Mamo, M.; Bubenzer, G.D. Detachment rate, soil erodibility and soil strength as influenced by living plant roots part II: Field study. Trans. ASAE 2001, 44, 1175–1181. [Google Scholar] [CrossRef]
  28. Bernhardt, M.L. 2008 Midwest Levee Failure: Erosion Studies. Ph.D. Thesis, Texas A&M University, College Station, TX, USA, 2011. [Google Scholar]
  29. Kimiaghalam, N.; Clark, S.P.; Ahmari, H. An experimental study on the effects of physical, mechanical, and electrochemical properties of natural cohesive soils on critical shear stress and erosion rate. Int. J. Sediment Res. 2016, 31, 1–15. [Google Scholar] [CrossRef]
  30. Briaud, J.L. Erodibility of fine grained soils and new soil test. In Erosion of Soils and Scour of Foundations; Geo-Frontiers Congress: Austin, TX, USA, 2005; pp. 1–10. [Google Scholar]
  31. Wang, Q.S.; Su, R.L.; Gao, X.J. Study on the starting test of remolded clay soils and soils with different sand and gravel contents. J. Hydraul. Eng. 2018, 49, 975–985. [Google Scholar]
  32. Pennell, K.D.; Hornsby, A.G.; Jessup, R.E.; Rao, P.S.C. Evaluation of five simulation models for predicting aldicarb and bromide behavior under field conditions. Water Resour. Res. 1990, 26, 2679–2693. [Google Scholar] [CrossRef]
  33. Hession, W.C.; Shanholtz, V.O.; Mostaghimi, S.; Dillaha, T.A. Uncalibrated performance of the finite element storm hydrograph model. Trans. ASAE 1994, 37, 777–783. [Google Scholar] [CrossRef]
  34. Briaud, J.L.; Chen, H.C. Erosion function apparatus for scour rate prediction. J. Geotech. Geoenviron. Eng. 2001, 127, 105–113. [Google Scholar] [CrossRef]
  35. Team, I.L.I. Investigation of the Performance of the New Orleans Flood Protection Systems in Hurricane Katrina on August 29, 2005. 2006. Available online: https://digitalcommons.calpoly.edu/cgi/viewcontent.cgi?article=1032&context=cenv_fac (accessed on 12 December 2021).
  36. Shafii, I. Relationship between Erodibility and Properties of Soils. Ph.D. Thesis, Texas A&M University, College Station, TX, USA, 2018. [Google Scholar]
  37. Briaud, J.L. Case histories in soil and rock erosion: Woodrow wilson bridge, Brazos River Meander, Normandy Cliffs, and New Orleans Levees. J. Geotech. Geoenviron. Eng. 2008, 134, 1425–1447. [Google Scholar] [CrossRef]
  38. Briaud, J.-L.; Ting, F.C.K.; Chen, H.C.; Gudavalli, R.; Perugu, S.; Wei, G. SRICOS: Prediction of Scour Rate in Cohesive Soils at Bridge Piers. J. Geotech. Geoenviron. Eng. 1999, 125, 237–246. [Google Scholar] [CrossRef]
  39. Kwak, K. Prediction of Scour Depth versus Time for Bridge Piers in Cohesive Soils in the Case of Multi-Flood and Layered Soil Systems. Ph.D. Thesis, Texas A&M University, College Station, TX, USA, 2000. [Google Scholar]
  40. Park, N. A Prediction of Meander Migration Based on Large-Scale Flume Tests in Clay. Ph.D. Thesis, Texas A&M University, College Station, TX, USA, 2007. [Google Scholar]
  41. Govin-dasamy, A.V. Simplified Method for Estimating Future Scour Depth at Existingbridges. Ph.D. Thesis, Texas A&M University, College Station, TX, USA, 2009. [Google Scholar]
  42. Straub, T.D.; Over, T.M.; Domanski, M.M. Ultimate Pier and Contraction Scour Prediction in Cohesive Soils at Selected Bridges in Illinois; National Technical Information Service: Springfield, VA, USA, 2013.
  43. Briaud, J.L.; Govindasamy, A.V.; Shafii, I. Erosion charts for selected geomaterials. J. Geotech. Geoenviron. Eng. 2017, 143, 04017072. [Google Scholar] [CrossRef]
  44. Van Klaveren, R.W.; McCool, D.K. Erodbility and critical shear of a previously frozen soil. Trans. ASAE 1998, 41, 1315–1321. [Google Scholar] [CrossRef]
  45. Knapen, A.K.; Poesen, J.; Govers, G.; Gyssels, G.; Nachtergaele, J. Resistance of soils to concentrated flow erosion: A review. Earth-Sci. Rev. 2007, 80, 75–109. [Google Scholar] [CrossRef]
  46. Einstein, H.A.; El-Samni, E.A. Hydrodynamic forces acting on a rough wall. Rev. Mod. Phys. 1949, 21, 520–524. [Google Scholar] [CrossRef] [Green Version]
  47. Yang, C.T. Incipient motion and sediment transport. J. Hydraul. Div. 1973, 99, 1679–1704. [Google Scholar] [CrossRef]
  48. Kothyari, U.C.; Jain, R.K. Influence of cohesion on the incipient motion condition of sediment mixtures. Water Resour. 2008, 44, W04410. [Google Scholar] [CrossRef]
  49. Briaud, J.L. Geotechnical Engineering: Unsaturated and Saturated Soils; John Wiley & Sons: Hoboken, NJ, USA, 2013. [Google Scholar]
Figure 1. Soil properties of samples: wet density (a); plasticity index (b); D50 (c); percent fines (d); water content (e).
Figure 1. Soil properties of samples: wet density (a); plasticity index (b); D50 (c); percent fines (d); water content (e).
Water 13 03621 g001aWater 13 03621 g001b
Figure 2. Erodibility parameters of the excess stress shear model: the critical shear stress (τc) (a); the erodibility parameters Z0 (b); an empirical exponent α (c).
Figure 2. Erodibility parameters of the excess stress shear model: the critical shear stress (τc) (a); the erodibility parameters Z0 (b); an empirical exponent α (c).
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Figure 3. Erodibility parameters of the Wilson model: the erodibility parameters b0 (a); the erodibility parameters b1 (b).
Figure 3. Erodibility parameters of the Wilson model: the erodibility parameters b0 (a); the erodibility parameters b1 (b).
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Figure 4. The range of derived parameters b0 (a) and b1 (b) for high-plasticity clay and low-plasticity clay.
Figure 4. The range of derived parameters b0 (a) and b1 (b) for high-plasticity clay and low-plasticity clay.
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Figure 5. The range of derived parameters τc (a) and Z0 (b) for high-plasticity clay and low-plasticity clay.
Figure 5. The range of derived parameters τc (a) and Z0 (b) for high-plasticity clay and low-plasticity clay.
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Figure 6. The erodibility coefficient (Z0) as a function of critical flow shear stress (τc) under identical experimental conditions: Sub-dataset 1 (a), Sub-dataset 2 (b), Sub-dataset 3 (c), and Sub-dataset 4 (d).
Figure 6. The erodibility coefficient (Z0) as a function of critical flow shear stress (τc) under identical experimental conditions: Sub-dataset 1 (a), Sub-dataset 2 (b), Sub-dataset 3 (c), and Sub-dataset 4 (d).
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Figure 7. The erodibility parameter b1 as a function of the erodibility b0 under identical experimental conditions: Sub-dataset 1 (a), Sub-dataset 2 (b), and Sub-dataset 3 (c).
Figure 7. The erodibility parameter b1 as a function of the erodibility b0 under identical experimental conditions: Sub-dataset 1 (a), Sub-dataset 2 (b), and Sub-dataset 3 (c).
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Figure 8. The results of b0 (a); b1 (b) and α (c) regression analysis were compared with the measured values.
Figure 8. The results of b0 (a); b1 (b) and α (c) regression analysis were compared with the measured values.
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Table 1. List of the USCS classifications related to 177 texts.
Table 1. List of the USCS classifications related to 177 texts.
USCS ClassificationNumber of Samples
Low-plasticity clay (CL)99
High-plasticity clay (CH)56
CH with sand2
CL with sand20
Table 2. Correlation analysis results of scouring parameters and soil parameters.
Table 2. Correlation analysis results of scouring parameters and soil parameters.
Parameterb0b1Z0 τ c   α
PI−0.392 **0.004−0.2310.056−0.371 **
ρ s −0.172−0.107−0.316 **−0.069−0.085
WC0.1410.393 **0.304 **0.333 **0.593 **
Pf−0.0320.130−0.0810.0430.077
D500.439 **−0.1140.391 **−0.1160.076
Note: The number in the table represents the correlation between parameters, ** represents significant correlation, and the significance level is 0.01.
Table 3. Results of multiple nonlinear regression.
Table 3. Results of multiple nonlinear regression.
Dependent
Variable
Model ExpressionNumber
of Data
R2Fvalue/
Fstatistic
b0
(g m−1 s−1 N−0.5)
b0 = 3.66 × WC1.65 × PI−0.53 × D500.72540.6310.82
Z0
(mm h−1)
z0 = 0.123 × WC2.37 × PI−0.86 × D500.39540.639.23
α α   =   0 .094 × WC1.26 × PI−0.19 × D500.25540.6792.21
Note: D50 (mm)—mean particle size; WC (%)—water content; PI (%)—plastic index.
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Wang, Q.; Zhou, P.; Fan, J.; Qiu, S. Study on Parameters of Two Widely Used Cohesive Soils Erosion Models. Water 2021, 13, 3621. https://doi.org/10.3390/w13243621

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Wang Q, Zhou P, Fan J, Qiu S. Study on Parameters of Two Widely Used Cohesive Soils Erosion Models. Water. 2021; 13(24):3621. https://doi.org/10.3390/w13243621

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Wang, Qiusheng, Pengzhan Zhou, Junjie Fan, and Songnan Qiu. 2021. "Study on Parameters of Two Widely Used Cohesive Soils Erosion Models" Water 13, no. 24: 3621. https://doi.org/10.3390/w13243621

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