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Relationship Between Erodibility and Properties of Soils (2019)

Chapter: Chapter 3 - Existing Correlations Between Soil Erodibility and Soil Properties

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Suggested Citation:"Chapter 3 - Existing Correlations Between Soil Erodibility and Soil Properties." National Academies of Sciences, Engineering, and Medicine. 2019. Relationship Between Erodibility and Properties of Soils. Washington, DC: The National Academies Press. doi: 10.17226/25470.
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Suggested Citation:"Chapter 3 - Existing Correlations Between Soil Erodibility and Soil Properties." National Academies of Sciences, Engineering, and Medicine. 2019. Relationship Between Erodibility and Properties of Soils. Washington, DC: The National Academies Press. doi: 10.17226/25470.
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Suggested Citation:"Chapter 3 - Existing Correlations Between Soil Erodibility and Soil Properties." National Academies of Sciences, Engineering, and Medicine. 2019. Relationship Between Erodibility and Properties of Soils. Washington, DC: The National Academies Press. doi: 10.17226/25470.
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Suggested Citation:"Chapter 3 - Existing Correlations Between Soil Erodibility and Soil Properties." National Academies of Sciences, Engineering, and Medicine. 2019. Relationship Between Erodibility and Properties of Soils. Washington, DC: The National Academies Press. doi: 10.17226/25470.
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Suggested Citation:"Chapter 3 - Existing Correlations Between Soil Erodibility and Soil Properties." National Academies of Sciences, Engineering, and Medicine. 2019. Relationship Between Erodibility and Properties of Soils. Washington, DC: The National Academies Press. doi: 10.17226/25470.
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Suggested Citation:"Chapter 3 - Existing Correlations Between Soil Erodibility and Soil Properties." National Academies of Sciences, Engineering, and Medicine. 2019. Relationship Between Erodibility and Properties of Soils. Washington, DC: The National Academies Press. doi: 10.17226/25470.
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Suggested Citation:"Chapter 3 - Existing Correlations Between Soil Erodibility and Soil Properties." National Academies of Sciences, Engineering, and Medicine. 2019. Relationship Between Erodibility and Properties of Soils. Washington, DC: The National Academies Press. doi: 10.17226/25470.
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Suggested Citation:"Chapter 3 - Existing Correlations Between Soil Erodibility and Soil Properties." National Academies of Sciences, Engineering, and Medicine. 2019. Relationship Between Erodibility and Properties of Soils. Washington, DC: The National Academies Press. doi: 10.17226/25470.
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Suggested Citation:"Chapter 3 - Existing Correlations Between Soil Erodibility and Soil Properties." National Academies of Sciences, Engineering, and Medicine. 2019. Relationship Between Erodibility and Properties of Soils. Washington, DC: The National Academies Press. doi: 10.17226/25470.
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Suggested Citation:"Chapter 3 - Existing Correlations Between Soil Erodibility and Soil Properties." National Academies of Sciences, Engineering, and Medicine. 2019. Relationship Between Erodibility and Properties of Soils. Washington, DC: The National Academies Press. doi: 10.17226/25470.
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Suggested Citation:"Chapter 3 - Existing Correlations Between Soil Erodibility and Soil Properties." National Academies of Sciences, Engineering, and Medicine. 2019. Relationship Between Erodibility and Properties of Soils. Washington, DC: The National Academies Press. doi: 10.17226/25470.
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Suggested Citation:"Chapter 3 - Existing Correlations Between Soil Erodibility and Soil Properties." National Academies of Sciences, Engineering, and Medicine. 2019. Relationship Between Erodibility and Properties of Soils. Washington, DC: The National Academies Press. doi: 10.17226/25470.
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Suggested Citation:"Chapter 3 - Existing Correlations Between Soil Erodibility and Soil Properties." National Academies of Sciences, Engineering, and Medicine. 2019. Relationship Between Erodibility and Properties of Soils. Washington, DC: The National Academies Press. doi: 10.17226/25470.
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Suggested Citation:"Chapter 3 - Existing Correlations Between Soil Erodibility and Soil Properties." National Academies of Sciences, Engineering, and Medicine. 2019. Relationship Between Erodibility and Properties of Soils. Washington, DC: The National Academies Press. doi: 10.17226/25470.
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Suggested Citation:"Chapter 3 - Existing Correlations Between Soil Erodibility and Soil Properties." National Academies of Sciences, Engineering, and Medicine. 2019. Relationship Between Erodibility and Properties of Soils. Washington, DC: The National Academies Press. doi: 10.17226/25470.
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Suggested Citation:"Chapter 3 - Existing Correlations Between Soil Erodibility and Soil Properties." National Academies of Sciences, Engineering, and Medicine. 2019. Relationship Between Erodibility and Properties of Soils. Washington, DC: The National Academies Press. doi: 10.17226/25470.
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Suggested Citation:"Chapter 3 - Existing Correlations Between Soil Erodibility and Soil Properties." National Academies of Sciences, Engineering, and Medicine. 2019. Relationship Between Erodibility and Properties of Soils. Washington, DC: The National Academies Press. doi: 10.17226/25470.
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Suggested Citation:"Chapter 3 - Existing Correlations Between Soil Erodibility and Soil Properties." National Academies of Sciences, Engineering, and Medicine. 2019. Relationship Between Erodibility and Properties of Soils. Washington, DC: The National Academies Press. doi: 10.17226/25470.
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Suggested Citation:"Chapter 3 - Existing Correlations Between Soil Erodibility and Soil Properties." National Academies of Sciences, Engineering, and Medicine. 2019. Relationship Between Erodibility and Properties of Soils. Washington, DC: The National Academies Press. doi: 10.17226/25470.
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Suggested Citation:"Chapter 3 - Existing Correlations Between Soil Erodibility and Soil Properties." National Academies of Sciences, Engineering, and Medicine. 2019. Relationship Between Erodibility and Properties of Soils. Washington, DC: The National Academies Press. doi: 10.17226/25470.
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56 It is well accepted that different soils have different critical velocities and different erosion rates beyond the critical threshold; therefore, soil erodibility depends on the soil’s properties. At the same time, a reliable and broadly accepted relationship between soil erodibility and soil properties has not been found. However, a number of attempts have been made on the basis of erosion test databases, which are more or less populated. Some of these attempts are reviewed in this chapter. 3.1 Existing Correlations Dunn (1959) carried out submerged JET examinations of remolded samples of sand and of fine-grained soils such as silty clay. He proposed a relationship between the critical shear stress obtained by using a 1-in2 steel plate in the location of maximum observed scour and two basic soil properties that he believed were the most influential parameters. This relationship was pro- posed for the soils with a plasticity index ranging from 5 to 16: 0.001 180 tan 30 1.73 PI (22)Sc v( ) ( )t = × + × + × where Sv = shear strength of the soil (psi), measured with a rotating vane; tc = critical hydraulic shear stress (psi); PI = plasticity index (%), and the unit of the angle in the tangent is degrees. Gibbs (1962) conducted flume tests on undisturbed samples [mostly clay of low plasticity (CL) and silt (ML)] from 45 case studies to assess the influence of field density on erosion resis- tance of the soil. Gibbs plotted his results versus field density and liquid limit. Recorded criti- cal shear stresses ranged from 0.7 Pa to 2.87 Pa. Gibbs observed that clays were more resistant to erosion than was coarser material. Also, the highly plastic samples generally showed more resistance to erosion as compared with low plasticity soils. Gibbs observed that gradation of a soil is an important parameter in the erosion resistance of coarser soils, while for finer samples, plasticity seems to be more effective. Although no good relation was found between dry density and critical shear stress, liquid limit generally seemed to be proportional to critical shear stress in several cases. Consequently, Gibbs (1962) recommended four categories based on the results of flume tests on the tested samples (Figure 29b). A few years after Gibbs (1962), Lyle and Smerdon (1965) performed some flume tests on seven Texas soils. They studied both the individual and combined influence of different engi- neering properties such as degree of compaction and PI on the erosion resistance of the soils. The soils tested in their study comprised two nonplastic soils (Amarillo fine sandy loam and C H A P T E R 3 Existing Correlations Between Soil Erodibility and Soil Properties

Existing Correlations Between Soil Erodibility and Soil Properties 57 (a) (b) Figure 29. (a) Flume test results of critical shear stress versus natural dry density and liquid limit and (b) proposed erosion categories (Gibbs 1962).

58 Relationship Between Erodibility and Properties of Soils Lufkin fine sandy loam), and five plastic soils (Reagan silty clay loam, San Saba clay, Houston black clay, Lake Charles clay, and Lufkin Clay). For each soil tested, the average particle size, percentage of clay, dispersion ratio, vane shear strength, and PI were measured. In addition to the physical engineering properties, the percent- age of organic matter, the calcium/sodium (Ca/Na) ratio, and the cation exchange potential were obtained for each soil. Lyle and Smerdon (1965) first studied the effect of compaction (void ratio), and linearly correlated the void ratio and the critical shear stress. Table 6, which refers to the void ratio of soil, shows the results of these linear regressions. After examining the test results, Lyle and Smerdon (1965) concluded that, in addition to the void ratio, the following parameters were also influential, in order of decreasing impact: PI, dispersion ratio, percentage of organic matter, vane shear strength, cation exchange potential, average particle size (D50), Ca/Na ratio, and percentage of clay. Thereafter, Lyle and Smerdon (1965) proposed linear regressions for each of these parameters combined with the void ratio. Table 7 shows the results of these linear regressions. Neither the R2 value nor any other param- eter representing the significance level of the proposed equations was reported along with the results. After these equations were established, further efforts were made to involve more param- eters; some link was observed between the Ca/Na ratio and the slope of the critical shear stress– void ratio plot. Smerdon and Beasley (1961) performed flume tests on 11 cohesive Missouri soils to investi- gate the relationships between the main engineering properties of soils and critical shear stress measured in the flume tests. The proposed empirical equations were as follows: 0.0034 (23)0.84Ic w( )t = 10.2 (24)0.63Dc r( )t = − 3.54 10 (25)28.1 50c Dt = * − 0.493 10 (26)0.0182c Pct = * where tc = critical shear stress (Pa) and D50 = particle size. Test Series No. Regression Equation t-value Significance Level 1 12.93 2 na 3 11.5 4 13.45 5 2.53 6 21.3 7 0.604 Note: psf = pounds per square foot; na = not applicable. 0.05 0.01 0.1 0.05 0.4 0.05 0.7 Table 6. Results of linear regression study on correlations between critical shear stress and void ratio (Lyle and Smerdon 1965).

Existing Correlations Between Soil Erodibility and Soil Properties 59 Partheniades (1965) proposed the following model to link the erosion rate to the shear stress of fine-grained soils. This model was used later on by Hanson and Cook (2004) with an exponent a equal to 1 and by Briaud et al. (2001b) with an exponent different from 1.  (27)z k td a c a( )= − t where z⋅ = erosion rate (m/s), kd = erodibility coefficient (m3/N * s), a = exponent typically assumed to be 1, tα = applied shear stress on the soil boundary (Pa), and tc = critical shear stress (Pa). Neill (1967) proposed an equation to predict the critical velocity of coarse-grained soils on the basis of experimental data on six sizes of graded gravels, two sizes of uniform glass balls, and cellulose acetate balls ranging in diameter from 6 to 30 mm. The depth of flow is included in the equation proposed by Neill (1967), which would indicate that critical shear stress is not merely a soil property (Clark and Wynn 2007). 2.50 (28) mc 2 0.20Y D D ds g gr γ =    − where Vmc = competent mean velocity for first displacement of bed material, Dg = effective diameter of bed grains, d = depth of flow, γs = g(rs − r), g = acceleration due to gravity, r = fluid mass density, and rs = bed-material mass density. Soil Property General Equation Plasticity index (Iw) Dispersion ratio (Dr) 10 10 Percentage of organic matter (Pom) 10 Vane shear strength (Sv) 10 10 Cation exchange capacity (CEC) Mean particle size (M) Calcium/sodium ratio (Rcn) Percentage of clay (PC) 10 Table 7. Proposed regression equations linking the critical shear stress with void ratio and other soil properties (Lyle and Smerdon 1965).

60 Relationship Between Erodibility and Properties of Soils Kandiah and Arulanandan (1974) also performed both flume tests and rotating cylinder tests on saturated and unsaturated Yolo clay loam. The influence of the sodium adsorption ratio (SAR) as well as the salt concentration of the sample on soil erodibility was investigated. SAR is defined in Equation 29. SAR Na 0.5 Ca Mg (29)[ ]( )( )[ ]= +++ ++ Kandiah and Arulanandan also studied the influence of the water content of the compacted samples on flaking. They concluded that an increase in salt concentration leads to a decrease in critical shear stress, whereas an increase in SAR would raise the critical shear stress. They also found that the water content of the sample in the saturated state does not have a significant impact on erodibility. However, in the case of an unsaturated compacted sample, it was observed that an increase in moisture content led to an increase in critical shear stress. Sargunan (1977) also used the rotating cylinder test to study the impact of mineralogy, soil pore fluid, and the chemistry of the eroding fluid on the erodibility of cohesive soils. However, this study did not lead to proposed regression equations. Sargunan tried Na instead of Ca or magnesium (Mg) and observed that the critical shear stress typically decreased when the SAR increased. Also, it was found that an increase in salt concentration at a given SAR led to an increase in critical shear stress. However, Sargunan indicated that the influence of mineralogy was more significant when the SAR was relatively high. Arulanandan and Perry (1983) challenged the contemporary filter design method, in which dam engineers of the time were using widely graded sand–gravel combinations as a filter for the core materials without taking erosion into account. Arulanandan and Perry concluded that using the classification plot based on plasticity proposed by Gibbs (1962) (Figure 29), was not sufficient to categorize erodibility, as some dam failures were observed in the “high resistance to erosion” zone of Gibbs’ (1962) proposed plot. Using flume tests and rotating cylinder tests, Arulanandan and Perry studied 29 dams that consisted of both dispersive and nondispersive core materials and performed erodibility tests on them. As a result, three general categories were proposed for the erodibility of core materials in dams: 1. Erodible soils. These are soils that have a critical shear stress less than 0.4 Pa. Filter tests are highly recommended to ensure the success of a filter in resisting erosion. 2. Moderately erodible soils. These are soils that have a critical shear stress between 0.4 and 0.9 Pa. Testing similar to that recommended for erodible soils is needed to certify the filter material. 3. Erosion-resistant soils. A regular filter design procedure can be implemented in these cases. Another finding of Arulanandan and Perry (1983) was that a nondispersive clay is not nec- essarily an erosion-resistant clay, owing to many factors such as clay type, composition of the eroding fluid as well as the pore fluid, pH, organic matter, temperature, and structure of the soil. This was also shown by Acciardi (1984), who found that some soils classified as dispersive clay on the basis of a pinhole test were found in the third category (erosion-resistant soils) of the Arulanandan and Perry category chart. Arulanandan and Perry proposed plots for saturated remolded soils to relate the critical shear stress and eroding fluid concentration. Figure 30 shows two of the proposed plots relating the eroding fluid concentration with the erosion rate and critical shear stress. Chen and Anderson (1987) investigated damages due to overtopping in 21 embankments in five U.S. states. They proposed the following equations for critical shear stress (tc) and erosion rate (E):

Existing Correlations Between Soil Erodibility and Soil Properties 61 (a) (b) Figure 30. Proposed charts by Arulanandan and Perry (1983) for relating erosion rate, critical shear stress, and eroding fluid concentration: (a) effect of eroding fluid on erosion rate and shear stress and (b) critical shear stress versus eroding fluid concentration. • Noncohesive material for a shear Reynolds number greater than 70: ( )t = γ − γ0.05 (30)50Dc s where γs = unit weight of soil, γ = unit weight of water, and D50 = median particle size of soil • Cohesive material (uncompacted, ranging from a silty loam soil to a highly cohesive clay soil): ( )t = 0.0034 PI (31)0.84c • Cohesive material (normally compacted): ( )t = 0.019 PI (32)0.58c

62 Relationship Between Erodibility and Properties of Soils • Highly cohesive soil such as clay (PI ≥ 10): ( )= t − t0.000086 (33)0.91E c • Low-cohesive soil such as sandy clay (PI ≤ 5): ( )= 0.00022 PI (34)0.43E • Noncohesive sand/gravel soil: ( )= 0.00324 PI (35)1.3E where E = erosion rate (cubic feet per second-foot), t = shear stress (pounds per square foot), tc = critical shear stress (pounds per square foot) γs = soil unit weight (pounds per cubic foot), γ = water unit weight (pounds per cubic foot), PI = plasticity index (percent), and D50 = mean grain size (inches). Chen and Anderson later created monographs using Equations 30 to 35 to predict the damage to embankments caused by flood overtopping. Shaikh et al. (1988a) used a flume system to study the erodibility of unsaturated compacted clay soils. Various mixtures of materials (e.g., Na-montmorillonite + silica) were used to prepare four samples with different percentages of clay (100%, 70%, 40%, and 10%). According to their tests on the four clayey samples, Shaikh et al. proposed empirical correlations for linking the erosion rate of the compacted clayey samples to the clay percentage and critical shear stress for the range of moisture content and saturation tested. They also found out that the compacted moisture content of the samples did not have a significant effect on erosion rates. The reason was that because the same compaction method was implemented, the orientation of particles was similar for all the samples. They first defined the erosion function as the following linear equation (Shaikh et al. 1988a):  = te (36)C where e . = erosion rate (N/m2/min), t = hydraulic shear stress, and C = erosion rate coefficient (1/min). Shaikh et al. (1988a) proposed the following relationships between the erosion rate coefficient, C (1/min), percentage of clay (PC), and torvane shear stress (S t) (MPa). ( )= × −4.14 PC (37)0.91C ( )= × −0.157 (38)1.338C St Shaikh et al. (1988b) tested Ca-montmorillonite (a nondispersive clay) and Na-montmorillonite (a dispersive clay) by using a flume system to study the relationships between dispersivity and erodibility of the soil. The dispersivity of the soils was measured according to Sherard et al.

Existing Correlations Between Soil Erodibility and Soil Properties 63 (1976). Again, the effect of the compacted moisture content was believed to be minimal. Shaikh et al. (1988b) proposed the following equation for relating erodibility to the chemistry of the pore water by using the SAR (mEq/L)0.5: ( )= × −4.41 SAR (39)1.34C Hanson (1992) and Hanson and Robinson (1993) used submerged jet tests in the laboratory to investigate the impact of compaction and associated moisture content on the erosion resis- tance of soils. The soils tested were clays and silty clays with a PI ranging from 7 to 12%. Both static and dynamic compaction methods were used to prepare 29 samples at different moisture contents and compaction efforts. Hanson and Robinson plotted dry density and moisture con- tent versus the unitless jet index (Ji) which was defined earlier by Hanson (1991): =    − 1 (40)0 0.931 D t J U t t s i where Ds = maximum scour depth, t = time of erosion, U0 = jet velocity at the nozzle, and t1 = time unit equivalent of 1 s. Hanson (1991) showed that Ji ≥ 0.02 refers to highly erodible materials, while Ji < 0.002 is associ- ated with very low erodible geomaterials. Comparison between the Ji values and the moisture content and dry unit weight indicated that Ji decreases (i.e., erosion resistance increases) when the dry density increases at a constant moisture content. Also, it was concluded that for a given dry unit weight, an increase in mois- ture content would decrease Ji (or increase the erosion resistance of the soil) for unsaturated soil samples. For saturated samples, however, an increase in moisture content increases the Ji value. Hanson and Robinson (1993) also compared the test results with the open channel tests conducted by Robinson (1990) on the same samples and found those results to be in agreement with their findings. Ghebreiyessus et al. (1994) performed flume tests on Mexico silty loamy soils to study the effect of vane shear strength and bulk density on soil erodibility parameters. Table 8 shows the Equation ledoMnoitauqEnoissergeR.oN R2 F-value Pr > F 1 = 1.8 + 0.21τ 2 = 41.3 + 0.5τ – 31 × ρ 3 = −4.0 + 5.9τ + 2.3 × ρ − 4.1 (τ × ρ ) 4 = 5.5 + 0.3τ − 0.5VE 5 = −1.4 + 1.3τ + 0.04VE − 0.07 (τ × VE) Note: = detachment rate (g m-2 s-1), ρ = bulk density (Mg/m3), τ = shear stress (Pa), and = vane shear strength (kPa). 0.25 4 0.07 0.68 11 0.002 0.97 108 0.0001 0.66 11 0.003 0.94 55 0.0001 VE Table 8. Predicted regression models for relationships between erosion rate, shear stress, bulk density, and vane shear strength (Ghebreiyessus et al. 1994).

64 Relationship Between Erodibility and Properties of Soils results of their regression analyses. The erosion or detachment rate is defined here as the rate of mass removal per unit area (g m−2s−1). Briaud et al. (2001a) and Briaud (2008) proposed a set of equations to predict the critical velocity and critical shear stress of coarse-grained soils on the basis of many erosion function apparatus (EFA) tests performed at Texas A&M University. ( ) ( )( )=m s 0.35 mm (41)50 0.45v Dc ( ) ( )t =Pa mm (42)50Dc Briaud (2008) concluded that for fine-grained soils, there is no direct relationship between critical velocity/shear stress and mean particle size. However, Briaud (2008) bracketed the data with an upper bound and a lower bound equation as follows: ( ) ( )( )= −Upper bound: m s 0.03 mm (43)50 1v Dc ( ) ( )( )= −Lower bound: m s 0.1 mm (44)50 0.2v Dc ( ) ( )( )t = −Upper bound: Pa 0.006 mm (45)50 2Dc ( ) ( )( )t = −Lower bound: m s 0.05 mm (46)50 0.4Dc Figure 31 shows the scattered data for both fine-grained soils and coarse-grained soils with the defined upper and lower bounds. Hanson and Simon (2001) proposed a relationship between the critical shear stress and the erodibility coefficient for soils with 50% to 80% silt size material. The results were based on 83 submerged jet tests in the midwestern United States. kd c= t−0.2 (47)0.5 where kd is the erodibility coefficient −     cm secN and tc is the critical shear stress (Pa). Wynn et al. (2004) investigated the influences of vegetation on stream bank erosion at 25 sites in Virginia. They used Hanson’s submerged jet test to measure the critical shear stress and erod- ibility of soils. The critical shear stresses measured ranged from 0 to 22 Pa. Wynn and colleagues concluded that bulk density is the most influential parameter in soil erodibility. Depending on the soil texture, other influential parameters were inferred to be moisture content, root density, pore and stream water chemistry, and freeze–thaw cycling. They categorized the data into three groups. Groups 1 and 2 included plastic soils, while Group 3 was made up of nonplastic soils. Group 1 included plastic soils with higher bulk densities, lower PI, and lower organic content than the soils in Group 2. Table 9 shows the results of regression analyses on the critical shear stress and some engineering properties. Amos et al. (2004) use two benthic annular flumes and soils from 24 sites to study the stabil- ity of the seabed in the Venice Lagoon. Water temperature, salinity, organic content, and bulk densities were controlled under different conditions. Amos and colleagues proposed an equation for natural lacustrine, estuarine, and marine muds that could link the critical shear stress and the wet sediment bulk density: ( )t = × r −−5.44 10 0.28 (48)cr 4 b

Existing Correlations Between Soil Erodibility and Soil Properties 65 (a) (b) Figure 31. Plots of (a) critical velocity and (b) shear stress versus the mean particle size (D50) (Briaud 2008).

66 Relationship Between Erodibility and Properties of Soils where tcr is the critical shear stress (Pa), and rb is the sediment wet bulk density (kg/m3). Equa- tion 48 is based on 73 sets of data; the R2 value for Equation 48 is 0.46. Thoman and Niezgoda (2008) studied the stability of 25 channel sites in Wyoming. To do so, they conducted several in situ JET tests and measured the erodibility parameters; the geotechni- cal properties were obtained from parallel laboratory tests. They found that the most influential parameters were activity, organic content, cation exchange capacity, soil pH, and dispersion ratio. No linear correlation was found between the critical shear stress and each of the aforemen- tioned geotechnical parameters; however, combining all five parameters, Thoman and Niezgoda (2008) proposed the following equation: ( ) ( ) ( ) ( ) ( )t = + + − − +77.28 2.20 Act 0.26 DR 13.49 SG 6.40 pH 0.12 (49)wc where tc = critical shear stress (Pa), Act = soil activity (ratio of PI to percentage of clay), DR = dispersion ratio, SG = specific weight, pH = chemical index for acidity, and w = water content (%). The reliability of the proposed model can be seen in Figure 32. The dashed lines show the one standard deviation range. Winterwerp and van Kesteren (2004) presented a theoretical derivation of an erosion rate parameter M: 10 1 1 10 (50) ,0 dry 50 0 dry 50 M c D c c W D c v s u v s w u ( )= j r = + j j     r Soil Group Equation n p-value R2 All data τ = 1.79 + 0.47BD2.5 – 0.27 ln(KIF) – 0.85SWpH6 – 0.08WT Group 1 τ = 1.48 + 0.11σ – 0.00035sand2 Group 1 τ = –0.44 + 0.067σ + 0.64BD2.5 Group 1 τ = 1.36 + 0.078σ – 0.00018sand2 Group 3 τ = –0.24 + 1.26BD2.5 – 0.23MC–1 – 0.86S:C–0.4 Group 3 τ = 2.11 + 2.21AS5 – 1.07RDAM2 – 1.15SWpH6 – 0.00044SG8 Note: KIF = potassium intensity factor, WT = temperature of water (oC), BD = bulk density (g/cm3), σ = standard deviation of particle size distribution, sand = sand percentage, MC = moisture content, S:C = ratio of silt to clay in soil, SWpH = ratio of pore water to river water pH, AS = aggregate stability, SG = soil specific gravity, and RDAM = related to the difference between median and average periods frozen. 42 0.000 0.569 9 0.002 0.718 18 0.001 0.663 18 0.005 0.508 15 0.002 0.733 12 0.001 0.913 Table 9. Regression equations for soil critical shear stress in southwest Virginia (Wynn et al. 2004).

Existing Correlations Between Soil Erodibility and Soil Properties 67 where cv = vertical consolidation coefficient, js, 0 = volumetric concentration, W0 = water content, js = density of the primary sediment particles, jw = density of the water, rdry = dry bulk density, D50 = mean particle size, and cu = undrained shear strength. Julian and Torres (2006) developed an equation linking the critical shear stress in pascals to the silt and clay (SC) content (%): ( ) ( ) ( )t = + + −0.1 0.1779 SC 0.0028 SC 0.0000234 SC (51)2 3c Mostafa et al. (2008) developed a relationship between a nondimensional shear stress of mass erosion and a nondimensional soil parameter. * 23.67 17.28 (52)pt = − c + * 107.56 79.59 (53)mt = − c + with c = − LI 1SG Figure 32. Estimated versus actual critical shear stress from the Wyoming channels (Thoman and Niezgoda, 2008).

68 Relationship Between Erodibility and Properties of Soils where tp* = nondimensional erosion resistance for particle erosion, t*m = nondimensional erosion resistance for mass erosion, c = nondimensional soil parameter, LI = liquidity index PI , PL= ω − ω and SG = specific gravity based on moist bulk density. Straub and colleagues (2010, 2013) studied the ultimate pier and contraction scour methods for cohesive soils at 30 bridge sites throughout Illinois. As part of this study, they showed that the unconfined compressive strength of the tested cohesive soils provided a good estimate of the critical shear stress obtained from the EFA (Equation 54): t = +0.1065ln 0.209 (54)Qc u where tc (psf) is the critical shear stress and Qu (tsf) is the unconfined compressive strength. Fleshman and Rice (2013) developed a piping erosion test device called the constant gradi- ent piping test apparatus and performed multiple tests on sandy soils to investigate the effect of grain size, gradation, and specific gravity on the critical hydraulic gradient required for piping to start. Although they did not propose a practical correlation equation, Fleshman and Rice (2013) showed that, in general, angular sandy soils have greater piping resistance. Greater piping resistance was also observed when the sandy samples were graded. The specific gravity was also shown to be directly proportional to the piping resistance. Bones (2014) developed a methodology for predicting critical shear stress by using the Uni- fied Soil Classification System categories. Shan et al. (2015) also proposed general relationships between critical shear stress, water content, unconfined compressive strength, PI, and fine con- tent on the basis of a limited range of cohesive soil. Singh and Thompson (2015) used the cohesive strength meter in soils with different moisture contents and measured the in situ critical shear stress in fields and grassed waterways. The study showed that the critical shear stress varies with moisture content and is not constant for a soil. It was also observed that critical shear stress is proportional to soil moisture until it is below the plastic limit. Singh and Thompson (2015) proposed the following equation for the case in which the soil moisture content is less than the plastic limit in grassed waterways. The R2 associated with Equation 55 is 0.68. t = × ( )×0.70 (55)0.06 moisture content, %ec Using the EFA and electrical resistivity tomography (ERT), Karim and Tucker-Kulesza (2018) evaluated the erosion resistance of 15 selected bridge sites in Kansas. They observed that the erod- ibility of a soil changed with the in situ electrical resistivity of the soil. Therefore, ERT could be used as an alternative quick tool for predicting the erodibility of a site instead of performing differ- ent erosion tests such as the EFA. By comparing the results of the EFA with ERT for highly erod- ible sites, Karim and Tucker-Kulesza (2018) indicated that when the electrical resistivity exceeds 50 Ωm, there is a 93% chance that the tested soil will be categorized as having high erodibility. ERT was introduced as a crude tool for identifying the critical locations prone to erosion at a site. The selected critical locations then would need further investigation to evaluate their erodibility. It is very important to evaluate the reliability of these equations, as the scatter in the data may be significant. In the next section of this chapter, the influence of each soil property is discussed in qualitative terms.

Existing Correlations Between Soil Erodibility and Soil Properties 69 3.2 Influence Factors on Erosion 3.2.1 Broad Geological Properties That Influence Erodibility The erodibility of soil can vary significantly; therefore, in general, erodibility depends on engi- neering soil properties. Some of the broad geological properties likely to influence erodibility include • Soil microstructure and macrostructure, • Lithification, • Strength of structural (cohesion) forces between particles and between water molecules and particles, • Lithology and anisotropy of soil at the different scales (laboratory and in situ), • Grain size distribution, • Mineral and chemical composition of soil, • Geotechnical properties, and • Presence of fissures in a given soil massive that affect at full scale the field behavior of clay. Scale, specifically, becomes a critical factor when the presence of fissures in the soil is consid- ered. Many laboratory tests are not able to capture the effects of fissures or joints because of the small size of the tested sample. It is clear that many factors can influence the erosion behavior of a soil. On the basis of the literature review conducted for this report, a list of typical properties that affect the erosion resistance of soils is given in Table 10. This table is divided into two categories: the more typically obtained properties and the less typically obtained properties. As mentioned earlier, the main goal of this project was to develop reliable and simple equations quantifying the erodibility of soils on the basis of soil properties. 3.2.2 Effects of Less Typically Obtained Parameters The fact that the following parameters are not typically obtained does not mean that they are not important when it comes to predicting erosion. 3.2.2.1 Mineralogy and Particle Size Distribution One of the very important parameters that needs to be carefully studied is the effect of min- eralogy and of particle size distribution on the erosion resistance of soils. In terms of grain size More Typically Obtained Properties Less Typically Obtained Properties • Plasticity index • Liquidity index • Unit weight • Water content • Undrained shear strength • Percentage passing sieve #200 • Percentage of clay particles • Percentage of silt particles • Mean grain size • Coefficient of uniformity • Percentage of compaction (for man-made soils only) • Soil swell potential • Soil void ratio • Specific gravity of solids • Soil dispersion ratio • pH (flowing water and pore water) • Salinity of eroding fluid • Organic content • Soil cation exchange cap • Soil clay minerals • Soil sodium adsorption ratio • Soil activity • Soil temperature • Density of cracks Table 10. Soil and water properties that influence the erosion resistance of soils.

70 Relationship Between Erodibility and Properties of Soils distribution, there are four major fractions—gravel, sand, silt, and clay—that affect the erosion resistance of soil under different flow conditions. Gravel Fraction (2–20 mm). The erosion behavior of the gravel fraction depends mostly on the correlation between the weight of the particle and the hydrodynamic force applied to the particle. The mineral composition of gravel is an issue as well and becomes important when the particle is formed by carbonate minerals (CaCO3). Leaching of carbonate minerals is likely to occur in the presence of aggressive carbon dioxide in aqueous form (CO2). The following reaction between carbonate minerals and water takes place: ( ) ( )+ + →CaCO H O CO aqueous Ca HCO (56)3 2 2 3 2 As a result of this reaction, lightly soluble calcium bicarbonate will form and go to an aqueous phase; thereafter, calcium carbonate is gradually destroyed. As a result, the content of hydrogen carbonate ion (HCO3) in the water increases as well as the content of calcium ion (Ca 2+). The erosion behavior of the gravel fraction in soil can be important for glacial (moraine) clayey soil containing these fractions. Sand Fraction (0.075–2 mm). The influence of sand particles on soil erosion is similar to that of gravel particles, as the most important factor that affects the erodibility of sand is the particle’s weight and its mineral composition. Silt Fraction (0.002–0.074 mm). The silt fraction is the least erosion resistant and soaking resistant of all the fractions. The presence of silt particles in soil may cause the collapse of the structure during wetting. For example, loess is less water resistant because it is made primarily of silt-sized particles (more than 70%). Some clayey soils in semiarid zones such as Texas contain a great amount of silt particles and could erode rapidly. Clay Fraction (<0.002 mm). In clayey soils, the individual clay particles can form micro- aggregates (from single to dozens of micrometers) and macroaggregates (from dozens to thou- sands of micrometers) (Osipov et al. 1989). Light microscopes and electron microscopes can be used to identify the microstructure of clayey soil. The erosion behavior of clayey soils depends on the presence of micro- and macroaggregates in the matrix, on the ability of the particles to coagulate, on the size and shape of the particles, and on the clay’s ability to resist disaggregation when submerged in water. The most active aggregate formation is associated with the smectite group (e.g., montmorillonite, nontronite, bentonite). In this case, the erodibility of clay contain- ing smectites depends on the strength between the clay aggregates. After the bonds between clay aggregates collapse, the erosion resistance depends on the force between individual clay particles and the strength of those forces. The clay fraction swells when it interacts with water. The swell potential typically increases with a decrease in water flow velocity. The presence of clay particles in sand creates a cohesion between sand particles that can significantly increase the resistance to erosion. The three major groups of clay minerals are kaolinite, illite, and montmorillonite. These minerals have very dif- ferent structures, including bonding between layers. Figure 33 shows four general different clay mineral microstructures. Many studies have been conducted to find out the potential relationships between erodibility and particle size. Particle size should be a factor considered only for coarse-grained soil. For fine-grained soils, particle size alone, without consideration of electrostatic and electromagnetic forces, is not an adequate representative. Working separately, Maslov (1968) and Justin (1923) obtained very similar results in study- ing the relationship between critical velocity and size of particles. Table 11 and Figure 34 show

Existing Correlations Between Soil Erodibility and Soil Properties 71 (a) (b) (c) (d) Figure 33. Clay mineral microstructure (Mitchell 1993 after Tovey 1971): (a) kaolinite, (b) halloysite, (c) montmorillonite, and (d) illite. that critical velocity decreases as the diameter of the particle decreases. It was also observed that erosion resistance increases as the number of particles with a diameter of less than 0.05 mm and greater than 0.001 mm increases. 3.2.2.2 Structural or Cohesion Forces The nature and the magnitude of structural or cohesion forces play a very important role in understanding the erodibility of clayey soils. The strength of the structural forces can vary significantly and depends on their nature and on the soil properties. Structural forces may be ion-electrostatic, molecular, magnetic, or chemical in nature. One of the strongest forces is the chemical force that exists in geomaterials such as igneous rock and clay if the natural water content of the clay is below the plastic limit (Table 12). The nature of this force is electrical interaction between atoms. Once this chemical force fails, it cannot be recovered.

72 Relationship Between Erodibility and Properties of Soils Diameter of Particles (mm) Critical Velocity (cm/s) Maslov Justin 5 NA 22.1 3 NA 17.3 1 10 9.85 0.8 NA 8.83 0.5 7 6.97 0.1 3 3.05 0.08 NA 2.79 0.05 2 2.19 0.03 0 1.74 0.01 0.5 0.98 0.005 0.12 NA 0.001 0.02 NA Note: NA = not available. Table 11. Critical velocity of water flow (Vcr) depending on diameter of particles (Maslov 1968 and Justin 1923). Figure 34. Critical velocity of water flow in different soils (Maslov 1968; Justin 1923). Molecular and ion-electrostatic (Coulomb) forces exist mostly in soft clays when the water content reaches the liquid limit. Molecular forces or van der Waals forces are weaker than chem- ical forces. The strength of the molecular force depends on the water content of the clay as well as on the dispersion ratio. With an increase in dispersion, the magnitude of molecular forces increases. The maximum strength of molecular forces is found in dry clay. As the water content of clay increases, the strength of the molecular force decreases. If the clay becomes wet, the dif- fusion layer of ions between and around particles causes the formation of the molecular-ion- electronic force, which is very likely to be destroyed by water flow. Mirzhulava (1967) obtained a relationship between the critical velocity and the cohesion of saturated soils (Figure 35) indicating that the critical velocity of saturated soils increases as soil cohesion increases. The results of this study also show that critical velocity increases with an increase in the undrained shear strength of clay (Su) (Figure 36).

Existing Correlations Between Soil Erodibility and Soil Properties 73 Figure 36. Relationship between critical velocity and undrained shear strength of clay (Mirzhulava 1967). Type of Clay Type of Cohesion Force Strength of Single Force (N) Clayey silt (W >> WL) Thixotropic and coagulation 10–3 to 10–2 10–8 to 10–9 Soft clay in quasi-liquid condition (WL > W > Wp) Thixotropic and coagulation, appearance of cementation 10–8 to 10–9 10–3 to 10–2 10–2 to 4 Clay in quasi-plastic condition (W ≈ Wp) Partially thixotropic and coagulation, partially cementation 10–2 to 4 10–3 to 10–2 10–7 to 10–2 Hard clay (like mudstone) (W < Wp) Cementation with subordinate significance of coagulation 10–2 to 4 10–7 to 10–2 10–3 to 10–2 Very hard clay (like slate) (W << Wp) Cementation Physical Nature of Force Molecular Magnetic Magnetic Molecular Ion-electrostatic Ion-electrostatic Molecular Chemical Ion-electrostatic Chemical Molecular Ion-electrostatic Chemical 10–2 to 4 10–7 to 10–2 Note: W = water content; Wp = plastic limit; WL = liquid limit. Table 12. Type of cohesion forces in fine-grained soils (clayey soils) (Osipov et al. 1989). Figure 35. Critical velocity versus cohesion for saturated soil (Mirzhulava 1967).

74 Relationship Between Erodibility and Properties of Soils 3.2.2.3 Disturbance of the Soil Structure Disturbance of the soil structure also has an impact on erosion resistance. Zhordaniaya (1957) studied the influence of disturbance on the erodibility of carbonated lean clay. Table 13 clearly shows that disturbing the soil structure decreases the critical velocity significantly. The critical velocity of the same carbonated lean clay at a given water content decreases by a factor of 3 to 5 times when going from the undisturbed to the disturbed state. Carbonate soils are prone to having strong cementation but are not very resistant to chemical processes such as dissolution and leaching. 3.2.2.4 Chemical Composition of Soil The chemical composition of soil has an impact on the erodibility of both fine- and coarse- grained soils. Erosion, especially suffusion, is likely to occur in sandy and clayey soils contain- ing soluble salts. This type of erosion corresponds to a dissolution of salt and to a collapse of the corresponding bonds in the soil. The more soluble cases would be those with chloride and sulfate in the soil. The presence of these salts in the chemical composition of the soil accelerates the erosion process, owing to the co-occurrence of mechanical and chemical erosion. Table 14 shows the solubility of different salts in water. 3.2.2.5 Organic Content of Soil Another influential factor in erosion is the presence in soil of biogenic forms (micro- organisms) and abiogenic material (organic matter in colloidal form). Organic colloids with a size of less than 0.0001 mm can clog the pore space and decrease the permeability of the soil. This is more important in coarse-grained soil (sand). The presence of organic colloids in the pore space can create some particle–particle cohesion as well as organic colloid–particle cohe- sion. This would lead to a decrease in water permeability and increase the resistance to erosion. The adhesion of microorganism cells to soil particles results in the formation of biofilms, which are extracellular substances glued to particles. This bond between the biofilm and the particle can help resistance against erosion. A microbial enzyme is a product of microbial activity and works to stabilize active clay parti- cles. It has a hydrophobic effect on the clay. Strengthening clayey soils by using enzyme technol- ogy is one of the soil improvement methods applied to decrease the hydrophilicity of clays and to protect them from erosion; however, in water erosion, the flow velocity at which the organic matter could be washed away may not be very high. 3.2.2.6 Presence of Cracks and Fissures (Micro- and Macroscale) In a fractured rock or fissured soil mass, water discharges through the existing cracks and fis- sures. An increase in water discharge through the fissured soil mass provides an increase in the Type of Salt Solubility in Water (g/100 g water) Sodium chloride (NaCl) 35.8 Potassium chloride (KCl) 34.2 Calcium sulfate (CaSO4) 0.2 Calcium carbonate (CaCO3) 0.0014 Sodium hydroxide (NaOH) 107.0 Sodium sulfate (Na2SO4) 32.8 Magnesium chloride (MgCl2) 35.3 Table 14. Solubility of different salts in water. Critical Velocity (m/s) Disturbed Structure 3–6 0.15 11–12 0.25 18–20 0.4 23–25 0.5 Undisturbed Structure 8–10 0.75 16–18 1.35 25–27 2.6 Water Content (%) Table 13. Critical velocity of water flow for carbonated lean clay (Zhordaniaya 1957).

Existing Correlations Between Soil Erodibility and Soil Properties 75 opening of the fissures by erosion. Table 15 shows the critical fluid velocity above which rock erodes, depending on the opening of the cracks in the rock mass. The erosion rate changes as the opening of the cracks increases. 3.2.2.7 Wet–Dry Cycles The wet–dry cycles are due to the weather and associated moisture migration in the soil profile by a thermal gradient during the year. These cycles have an impact on the soil erodibility. For example, the formation of shrinkage cracks and then water flowing through the cracks can erode a soil significantly. The density and size of the shrinkage cracks depends on the initial water con- tent of the clay and on its plasticity index. This is particularly important at shallower depths with problems such as overtopping of levees during hurricanes or floods, river bank erosion, surface erosion of highway embankments, and so forth. As mentioned earlier, the present study focuses on the influences of the most common geo- technical properties (Table 10). The selected properties are some of the more direct influences on erodibility and are commonly measured in the laboratory during geotechnical testing. Opening of Crack (cm) Options 0.1 0.2 0.5 1.0 2.0 Critical velocity (m/s) 0.15 0.075 0.03 0.015 0.0075 Critical gradient of head 0.5 0.063 0.004 5 * 10–4 6.3 * 10–5 Coefficient of actual velocity (m/s) 0.01 1.5 50 0.003 0.3 1.2 7.5 30 120 Note: Coefficient of actual velocity is an average velocity through a crack at a gradient equal to 1. Table 15. Critical fluid velocity above which rock erodes, depending on opening of cracks (Bogdanov and Smirnov 1972).

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Analysis of the erodibility of geomaterials is important for the study of problems related to soil erosion such as bridge scour, embankment overtopping erosion, and stream stability. Erodibility is the relationship between the soil erosion rate and fluid velocity or hydraulic shear stress. Since different soils have different geotechnical properties, their erosion rates vary.

The TRB National Cooperative Highway Research Program's NCHRP Research Report 915: Relationship Between Erodibility and Properties of Soils provides reliable and simple equations quantifying the erodibility of soils on the basis of soil properties.

The report presents a detailed analysis of the issue. In addition, the project that developed the report also produced a searchable spreadsheet that uses statistical techniques to relate geotechnical properties to soil erodibility. The spreadsheet, NCHRP Erosion, includes a searchable database that includes compiled erosion data from the literature review and a plethora of erosion tests. It contains equations that may be used to estimate the erosion resistance of soil and determine whether erosion tests are needed.

The following appendices to NCHRP Report 915 were published online in a single Appendices Report:

Appendix 1 – Erosion Test Results Spreadsheets

Appendix 2 – Geotechnical Properties Spreadsheets

Appendix 3 – First and Second Order Statistical Analysis Results

Appendix 4 – Deterministic Frequentist Regression Analysis

Appendix 5 – Probabilistic Calibration Results

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