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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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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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55 CHAPTER 3 3. EXISTING CORRELATIONS BETWEEN SOIL ERODIBILITY AND SOIL PROPERTIES 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 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 tests databases which are more or less populated. Some of these attempts are reviewed next. 3.1. Existing Correlations Dunn (1959) carried out submerged JET tests on remolded samples of sand and of fine grain soils such as silty clay. Dunn proposed a relationship between the critical shear stress obtained 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 proposed for the soils with PI ranging from 5 to 16. 0.001 180 tan 30 1.73 (22) Where, Sv refers to the shear strength of the soil (psi) which was measured using a rotating vane, is the critical hydraulic shear stress (psi), PI is the plasticity index (%), and the unit of the angle in the tangent is degrees. Gibbs (1962) conducted flume tests on undisturbed samples (mostly CL and ML) from 45 case studies to assess the influence of field density on erosion resistance of the soil. Gibbs plotted his results versus field density and liquid limit. Recorded critical shear stresses ranged from 0.7 Pa to 2.87 Pa. Gibbs observed that clays are more resistant to erosion compared to coarser material. Also, the highly plastic samples generally showed more resistance to erosion in comparison 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 there was no good relation found between dry density and the critical shear stress, liquid limit generally seemed to be proportional to the critical shear stress for several cases. Consequently, Gibbs (1962) recommended four categories based on the results of flume tests on the tested samples (right plot in Figure 29).

56 Flume test results of the critical shear stress versus natural dry density and liquid limit Proposed Erosion Categories by Gibbs (1962) Figure 29. Flume test results of the critical shear stress versus natural dry density and liquid limit and the proposed erosion categories (Gibbs, 1962) A few years after Gibbs (1962), Lyle and Smerdon (1965) performed some flume tests on seven Texas soils. Lyle and Smerdon studied both the individual and combined influence of different engineering properties such as degree of compaction and PI on the erosion resistance. The soils tested in their study consisted of two non-plastic soils (Amarillo fine sandy loam and 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, the percent clay, the dispersion ratio, the vane shear strength, and the PI were measured. In addition to the physical engineering properties, the percent organic matter, the 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 shows the results of these linear regressions. In Table 6, e refers to the void ratio of soil.

57 Table 6. Results of linear regression study on correlations between critical shear stress and void ratio (Lyle and Smerdon, 1965). Test Series No. Regression Equation t value Significance level 1 0.0255 0.00714 12.93 0.05 2 0.0279 0.00316 - 0.01 3 0.0271 0.00577 11.5 0.1 4 0.036 0.01778 13.45 0.05 5 0.07387 0.0338 2.53 0.4 6 0.0323 0.00653 21.3 0.05 7 0.0640 0.00959 0.604 0.7 After examining the test results, Lyle and Smerdon (1965) concluded that in addition to the void ratio, other influential parameters are, in order of decreasing impact: plasticity index, dispersion ratio, percent organic matter, vane shear strength, cation exchange potential, average particle size (D50), Ca-Na ratio, and clay percentage. 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. The R-square values or any other parameter representing the significance level of the proposed equations were not reported along with the results. After these equations were established, further efforts were made to involve more parameters; some link was observed between the Ca-Na ratio and the slope of the critical shear stress-void ratio plot. Table 7. Proposed regression equations linking the critical shear stress with soil properties with having void ratio included in all (Lyle and Smerdon, 1965) Soil property General equation Plasticity index, Iw 0.00771 0.0233 1.2 0.00079 0.00035 1.2 Dispersion ratio, Dr 0.0322 0.0086 1.2 10 0.00452 10 . . Percent organic matter, Pom 0.0105 0.0124 1.2 0.765 10 . . Vane shear strength, Sv 0.0140 0.00192 1.2 10 0.205 10 . . Cation exchange capacity, CEC 0.00429 0.0136 1.2 0.0140 0.00116 1.2 log Mean particle size, M 0.01199 0.0101 1.2 0.00589 0.0009 1.2 log Calcium-sodium ratio, Rcn 0.02024 0.0235 1.2 0.00264 0.00812 1.2 log Percent clay, Pc 0.0141 0.0075 1.2 10 .

58 Smerdon and Beasley (1961) performed flume tests on 11 cohesive Missouri soils to investigate the relationships between main engineering properties of soils and critical shear stress measured in the flume tests. The proposed empirical equations were: 0.0034 . (23) 10.2 . (24) 3.54 ∗ 10 . (25) 0.493 ∗ 10 . (26) τc = critical shear stress (Pa) Iw = plasticity index Dr = dispersion ratio D50 = mean particle size (m) Pc = percent clay by weight (%) 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 (Hanson and Cook, 2004) with an exponent “a” equal to 1 and by Briaud (2001) with an exponent different from 1.   ad a cz k      (27) z  = erosion rate (m/sec) kd = erodibility coefficient (m3/N*sec) α = exponent typically assumed to be 1 τα = applied shear stress on the soil boundary (Pa) τc = critical shear stress (Pa) Neil (1967) proposed an equation to predict the critical velocity of coarse grain soils based on 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. In the equation proposed by Neil (1967), the depth of flow is included; this would indicate that the critical shear stress is not merely a soil property (Clark and Wynn, 2007). 0.202 2.50 gmc s g DV D d           (28) Vmc = competent mean velocity for first displacement of bed material Dg = effective diameter of bed grains d = depth of flow γs = g(ρs-ρ) g = acceleration due to gravity ρ = fluid mass density ρs = bed-material mass density Kandiah and Arulanandan (1974) also performed both flume tests and rotating cylinder tests on saturated and unsaturated Yolo lam clay. The influence of the Sodium Adsorption Ratio (SAR)

59 as well as the salt concentration of the sample on soil erodibility was investigated. SAR is defined in Eq. 29. SAR Na / 0.5 (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 the critical shear stress; while, 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, for unsaturated compacted sample, it was observed that an increase in moisture content leads to an increase in the critical shear stress. Sargunan (1976) also used the rotating cylinder test to study the impact of mineralogy, soil pore fluid, and the eroding fluid chemistry on the erodibility of cohesive soils. However, this study did not end up with proposed regression equations. Sargunan tried Na instead of Ca or Mg, and observed that the critical shear stress typically decreases when the SAR increases. 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 is 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 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), is not sufficient to categorize erodibility, since 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 which 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: which have a critical shear stress less than 0.4 Pa. Filter tests are highly recommended to ensure the success of a filter to resist erosion. 2) Moderately erodible soils: critical shear stress is between 0.4 and 0.9 Pa. Similar testing as in category 1 is needed to certify the filter material. 3) Resistant soils: regular filter design procedure can be implemented in these cases. The other findings of Arulanandan and Perry (1983) was that a non-dispersive clay does not necessarily refer to an erosion resistant clay, due to many factors such as clay type, composition of eroding fluid as well as pore fluid, pH, organic matter, temperature, and structure of the soil. This was also shown by Acciardi (1984) where some soils which were classified as “dispersive clay” using a pinhole test, were categorized in the third category (erosion resistant soils) of 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

60 two of the proposed plots relating the eroding fluid concentration with the erosion rate and critical shear stress. Effect of eroding fluid on erosion rate and shear stress Critical shear stress versus eroding fluid concentration Figure 30. Proposed charts by Arulanandan and Perry (1983) for relating erosion rate, critical shear stress, and eroding fluid concentration Chen and Anderson (1987) investigated the damages due to overtopping in 21 embankments in 5 states of the US. They proposed equations for the critical shear stress τc and the erosion rate E as shown below: - Non-cohesive material for a shear Reynolds number greater than 70: 0.05 (30) Where, , , - Cohesive material (un-compacted, ranging from a silty loam soil to a highly cohesive clay soil) with PI being the plasticity index 0.0034 . (31) - Cohesive material(normally compacted) 0.019 . (32) - Highly cohesive soil such as clay( 10) 0.000086 . (33) - Low-cohesive soil such as sandy clay( 5) 0.00022 . (34) - Non-cohesive sand/gravel soil 0.00324 . (35) Where E is the erosion rate in cubic feet per second-foot, τ and τc are the shear stress and the critical shear stress in pounds per square foot, γs and γ are the soil and the water unit weights in pounds per cubic foot, PI is the plasticity Index in percent, and D50 is the mean grain size in feet. Chen and Anderson later created monographs using Eq. 30 to 35 in order to predict the damages to embankments caused by flood overtopping.

61 Shaikh et al. (1988) used a flume system to study the erodibility of unsaturated compacted clay soils. Various mixtures of materials (Na-montmorillonite + silica) were used to prepare four samples with different clay percentages (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 does 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 a linear equation shown below (Shaikh et al., 1988): (36) Where, is the erosion rate (N/m2/min), is the hydraulic shear stress, and C is defined as the erosion-rate coefficient (1/min). Shaikh et al. proposed the following relationships between C, percent clay (PC), and torvane shear stress (St). 4.14 . (37) 0.157 . (38) Where, PC is the percent clay and St is the torvane shear strength (MPa), and C is the erosion rate coefficient (1/min). Shaikh et al. (1988b) tested Ca-montmorillonite (which is a non-dispersive clay) and Na- montmorillonite (which is a dispersive clay) 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. (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 (using Sodium Adsorption Ratio). 4.41 . (39) Where, SAR is the sodium adsorption ratio (meq/L)0.5, and C is the erosion-rate coefficient (1/min). Hanson (1992) and Hanson and Robinson (1994) used submerged jet tests in the laboratory to investigate the impact of compaction and associated moisture content on the erosion resistance of soils. The soils tested were clays and silty clays with a plasticity index ranging from 7 to 12%. 29 samples were prepared at different moisture contents and compaction efforts using both static and dynamic compaction methods. Hanson and Robinson plotted the dry density and moisture content versus the unitless Jet Index (Ji) which was defined earlier by Hanson (1991): . (40) Where, refers to the maximum scour depth, t is the time of erosion, is the jet index (unitless), is the jet velocity at the nozzle, and 1 refers to time unit equivalent of 1 second. Hanson (1991)

62 showed that 0.02 refers to high erodible materials, while 0.002 associates with very low erodible geomaterials. Comparison between the Ji values and the moisture content and dry unit weight indicated that Ji decreases (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 moisture content would decrease Ji (or increases 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 also compared the test results with the open channel tests conducted by Robinson (1990) on the same samples and found it 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 the soil erodibility parameters. Table 8 shows the results of their regression analyses. The erosion or detachment rate is defined here as the rate of mass removal per unit area (g m-2 s-1). Table 8. Predicted regression models for relationships between erosion rate, shear stress, bulk density, and vane shear strength (Ghebreiyessus et al., 1994)  = detachment rate (g m-2 s-1) = bulk density (Mg/m3) = shear stress (Pa) = vane shear strength (kPa) Briaud et al. (2001) and Briaud (2008) proposed a set of equations to predict the critical velocity and critical shear stress of coarse grain soils based on many EFA erosion tests performed at Texas A&M University.  0.45500.35 ( )( / )c D mmv m s  (41) 50( ( ))c D mPa m  (42) Briaud (2008) concluded that for fine grained soils there is no direct relationship between critical velocity/shear stress and the mean particle size. However, Briaud (2008) bracketed the data with an upper bound and a lower bound equation as follows. Upper bound   1500.0(m/ s 3 ( ))c Dv mm  (43) Lower bound   0.2500(m/ .1) )s (c D mv m  (44) Upper bound   2500.00(Pa) 6 ( )c D mm  (45) Eq. Number Regression Equation Model R2 F- value Pr. > F 1 1.8 0.21 0.25 4 0.07 2 41.3 0.5 31 0.68 11 0.002 3 4.0 5.9 2.3 4.1 0.97 108 0.0001 4 5.5 0.3 0.5 0.66 11 0.003 5 1.4 1.3 0.04 0.07 0.94 55 0.0001

63 Lower bound   0.4500.05(m/ s )) (c D mm  (46) Figure 31 shows the scattered data for fine grain soils with the defined upper and lower bound, as well as for the coarse grain soils. Critical velocity as a function of D50 Critical shear stress as a function of D50 Figure 31. Plots of critical velocity and shear stress versus the mean particle size (Briaud, 2008) Hanson and Simon (2001) for soils with 50 to 80% silt size material proposed a relationship between the critical shear stress and the erodibility coefficient. The results were based on eighty- three submerged jet tests in the Midwestern US. 0.50.2d ck   (47) Where, kd = erodibility coefficient ( ) and τc = critical shear stress (Pa). Wynn et al. (2004) investigated the influences of vegetation on stream bank erosion for twenty- five (25) sites in Virginia. Wynn et al. used Hanson’s submerged jet test to measure the critical shear stress and erodibility of soils. Measured critical shear stresses ranged from 0 to 22 Pa. They concluded that bulk density is the most influential parameter in soil erodibility. Depending on the soil texture, other influencing 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 comprised of non-plastic 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.

64 Table 9. Regression equations for soil critical shear stress in southwest VA (Wynn et al., 2004)  KIF is the potassium intensity factor, WT refers to temperature of water (oC), BD is the bulk density (g/cm3), is the standard deviation of the particle size distribution, Sand refers to sand percentage, MC refers to moisture content, SWpH is the ratio of pore water to river water pH, AS is the aggregate stability, SG is the soil specific gravity, and RDAM is related to the difference between median and average periods frozen. Amos et al. (2004) studied the stability of the seabed in the Venice Lagoon using two benthic, annular flumes and soils from 24 sites. Water temperature, salinity, organic content, and bulk densities were controlled under different conditions. Amos et al. proposed an equation for natural lacustrine, estuarine, and marine muds which could link the critical shear stress and the wet sediment bulk density:  45.44 10 0.28cr b    (48) Where, is the critical shear stress (Pa), and ρb is the sediment wet bulk density (kg/m3). Eq. 48 is based on 73 sets of data, and the R-square value for Eq. 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 geotechnical properties were obtained from parallel laboratory tests. They found that most influential parameters are activity, organic content, cation exchange capacity, soil pH, and dispersion ratio. No linear correlation was found between the critical shear stress and each one of the aforementioned geotechnical parameters; however, combining all five parameters, Thoman and Niezgoda (2008) proposed the following equation:          77.28 2.20 0.26 13.49 6.40 0.12c Act DR SG pH w       (49) Where τc is the critical shear stress in Pascals, is the soil activity (ratio of % ), is the dispersion ratio, is the specific weight, is the chemical index for acidity, and is the water content (%). The reliability of the proposed model can be seen in Figure 32. The dashed lines show the one standard deviation range. Soil Group Equation n p- value R 2 All data 0.36 1.79 0.47 2.5 0.27 ln 0.85 6 0.08 42 0.000 0.569 Group 1 0.36 1.48 0.11 0.00035 2 9 0.002 0.718 Group 1 0.36 0.44 0.067 0.64 2.5 18 0.001 0.663 Group 1 0.36 1.36 0.078 0.00018 2 18 0.005 0.508 Group 3 0.36 0.24 1.26 2.5 0.23 1 0.86 : 0.4 15 0.002 0.733 Group 3 0.36 2.11 2.21 5 1.07 2 1.15 6 0.00044 8 12 0.001 0.913

65 Figure 32. Estimated versus actual critical shear stress from the Wyoming channels (Thoman and Niezgoda, 2008) Winterwerp and van Kesteren (2004) presented a theoretical derivation of an erosion rate parameter M  0,0 50 50 1 1 / 10 10 v dry s wv s dry u u c Wc M D c D c             (50) Where, is a vertical consolidation coefficient, , is the volumetric concentration, is the water content, is the density of the primary sediment particles, is the density of the water, is the dry bulk density, is the mean particle size, and is the undrained shear strength. Julian and Torres (2006) developed an equation linking the critical shear stress in Pa to the silt and clay content in percent (SC).      2 3τ 0.1 0.1779 0.0028 0.0000234c SC SC SC    (51) Mostafa et al. (2008) developed a relationship between a non-dimensional shear stress of mass erosion and a non-dimensional soil parameter. ∗ 23.67 17.28 (52) ∗ 107.56 79.59 (53) With: ∗ Non dimensional erosion resistance for particle erosion ∗ Non dimensional erosion resistance for mass erosion Non dimensional soil parameter Liquidity index ω ω Specific gravity based on moist bulk density

66 Straub and Over (2013) studied the ultimate pier and contraction scour methods for cohesive soils one thirty bridge sites throughout Illinois. As part of this study, Straub and Over (2013) showed that the unconfined compressive strengths of the tested cohesive soils provide a good estimate of the critical shear stress obtained from the EFA (Eq. 54) 0.1065 ln 0.209 (54) Where is critical shear stress, and (tsf) is the unconfined compressive strength. Fleshman and Rice (2013) developed a piping erosion test device called the constant gradient 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 no practical correlation equation was proposed, Fleshman and Rice (2013) showed that in general the angular sandy soils have greater piping resistance. Also, greater piping resistance was 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 to predict the critical shear stress using the USCS categories. Shan et al. (2015) also proposed general relationships between critical shear stress, water content, unconfined compressive strength, plasticity index, and fine content based on a limited range of cohesive soil. Singh and Thompson (2015) used the Cohesive Strength Meter (CSM) in different soil moisture contents and measured the in situ critical shear stress in field and grassed waterway. The study showed that the critical shear stress varies with moisture content and is not constant for a soil. Also, it was observed that the critical shear stress is proportional to the 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 Eq. 55 is 0.68. 0.70 . ,% (55) Karim and Tucker-Kulesza (2018) evaluated the erosion resistance of 15 selected bridge sites in Kansas using the EFA and Electrical Resistivity Tomography (ERT). It was observed that the erodibility of a soil changed with the in situ electrical resistivity (ER) of the soil. Therefore, ERT could be used as an alternative quick tool to predict the erodibility of a site instead of performing different erosion tests such as the EFA. By comparing the results of the EFA with ERT for high erodible sites, Karim and Tucker-Kulesza (2018) indicated that when the ER exceeds 50 Ωm, there will be 93% chance that the tested soil is categorized as high erodibility. ERT was introduced as a crude tool to identify the critical locations prone to erosion in a site. The selected critical locations then need further investigation to evaluate the 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.

67 3.2. Influence Factors on Erosion The erodibility of soil can vary significantly; therefore, in general, erodibility depends on engineering soil properties. Some of the broad geological properties likely to influence erodibility include:  Soil micro- and macro structure;  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;  Presence of fissures in a given soil massive that impact at a full-scale field behaviour of clay. Scale, specifically, becomes a critical factor when considering the presence of fissures in the soil. Many laboratory tests are not able to capture the effects of fissures/joints due to the small size of the tested sample. It is clear that many factors can influence the erosion behaviour of a soil. Based on the literature review conducted for this report, a list of typical parameters which affect the erosion resistance of soils is shown in Table 10. This table is divided into two categories: the more easily obtained parameters and the less easily obtained parameters. As mentioned earlier, the main goal of this project is to develop reliable and simple equations quantifying the erodibility of soils based on soil properties. 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.

68 Table 10. Influencing soil and water properties in erosion resistance of soils More typically obtained properties  Plasticity index  Liquidity Index  Unit weight  Water content  Undrained shear strength  Percent passing sieve #200  Percent clay particles  Percent silt particles  Mean grain size  Coefficient of uniformity  Percent compaction (for man-made soils only)  Soil swell potential  Soil void ratio Less typically obtained properties  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 Mineralogy and particle size distribution One of the very important parameters that needs to be carefully studied is the effect of mineralogy and of particle size distribution on the erosion resistance of soils. In terms of grain size distribution, there are four major fractions (i.e. gravel, sand, silt, clay) which affect 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: CaCO3+H2O+CO2 (aqueous) → Ca (HCO3)2 (56) As a result of this reaction, lightly soluble calcium bicarbonate will form which goes to an aqueous phase, and thereafter calcium carbonate is gradually destroyed. As a result, the content of hydro carbonate-ion (HCO3) in the water increases as well as the content of calcium-ion (Ca2+). The erosion behavior of the gravel fraction in soil can be important for glacial (moraine) clayey soil containing these fractions.

69 Sand fraction (0.075-2 mm): The influence of the sand particles on soil erosion is similar to that of the gravel particles as the most important factor that affects 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 silts size particles (more than 70%). Some clayey soils in semi-arid 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 macro-aggregates (from dozens to thousands of micrometers) (Osipov et al., 1989). The microstructure of clayey soil can be identified using the light and electronic microscope. The erosion behavior of clayey soils depends on the presence of these micro- and macro- aggregates in the matrix, on the ability of the particles to coagulate, on the size and shape of the particles, and on the clay ability to resist disaggregation when submerged in water. The most active aggregate formation is associated with the smectite group (montmorillonite, nontronite, bentonite etc.). In this case, the erodibility of the clay containing 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 which can significantly increase the resistance to erosion. The three major groups of clay minerals are kaolinite, illite, and montmorillonite. These minerals have very different types of structure including bonding between layers. Figure 33 shows four general different clay mineral microstructures.

70 Figure 33. Clay mineral microstructure (Mitchell, 1993 after Tovey, 1971) a- kaolinite, b- halloysite, c- montmorillonite, d- illite. Many studies have been conducted to find out potential relationships between erodibility and particle size. Particle size should be a factor considered only for coarse-grain soil. For fine-grain soils, particle size by itself without considering the electrostatic and electromagnetic forces is not an adequate representative. Maslov (1968) and Justin (1923) working separately obtained very similar results when studying the relationship between critical velocity and size of particles. Table 11 and Figure 34 show that the critical velocity decreases as the diameter of the particle decreases. It was also observed that the erosion resistance increases with an increase in amount of particles with diameter of less than 0.05 and 0.001 mm.

71 Table 11. Critical velocity of water flow (Vcr) depending on the diameter of the particles (after Maslov, 1968 and Justin 1923) Figure 34. Critical velocity of water flow in different soils (Maslov, 1968; Justin 1923) Structural or Cohesion Forces The nature and the magnitude of the 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. These forces are held by forces which may be ion-electrostatic, molecular, magnetic, and chemical in nature. Diameter of particles, mm Critical velocity, cm/s After N.N. Maslov After D. Justin 5 - 22.1 3 - 17.3 1 10 9.85 0.8 - 8.83 0.5 7 6.97 0.1 3 3.05 0.08 - 2.79 0.05 2 2.19 0.03 0 1.74 0.01 0.5 0.98 0.005 0.12 - 0.001 0.02 -

72 One of the strongest forces is the chemical force which exists in geomaterials such as igneous rocks and clay if the natural water content (WC) of clay is below the plastic limit (PL) (Table 12). The nature of this force is electrical interaction between atoms. Once this chemical force fails, it cannot be recovered. Molecular and ion-electrostatic (Coulomb) forces exist mostly in soft clays when the water content (WC) reaches the liquid limit (LL). Molecular forces or Van der Waal’s forces are weaker than the chemical 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 the molecular forces increases. The maximum strength of the molecular forces is found in dry clay. With an increase in water content of clay, the strength of the molecular force decreases. If the clay becomes wet, the diffusion layer of ions between and around particles causes the formation of the molecular-ion-electronic force. This force is very likely to be destroyed by water flow. Table 12. Type of cohesion forces in fine grain soils (clayey soils) (Osipov et al., 1989) * W refers to the water content; Wp refers to the plastic limit; WL refers to the liquid limit. 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 with an increase in soil cohesion. The results of this study also show that the critical velocity increases with an increase in the undrained shear strength of clay (Figure 36). Type of clay Type of cohesion forces Physical nature of force Strength of single force, N Clayey silt (W>>WL) Thixotropic and coagulation Molecular Magnetic 10-3 - 10-2 10-8 - 10-9 Soft clay in quazi liquid condition (WL>W>Wp) Thixotropic and coagulation, appearance of cementation Magnetic Molecular Ion-electrostatic 10-8 - 10-9 10-3 - 10-2 10-2 – 4 Clay in quazi plastic condition (W≈Wp) Partially thixotropic and coagulation, partially cementation Ion-electrostatic Molecular Chemical 10-2 – 4 10-3 - 10-2 10-7 - 10-2 Hard clay (like mudstone) (W<Wp) Cementation with subordinate significance of coagulation Ion-electrostatic Chemical Molecular 10-2 – 4 10-7 - 10-2 10-3-10-2 Very hard clay (like slate) (W<<Wp) Cementation Ion-electrostatic Chemical 10-2 – 4 10-7 - 10-2

73 Figure 35. Critical velocity vs. cohesion for saturated soil (Mirzhulava, 1967) Figure 36. Relationship between the critical velocity and the undrained shear strength for clays Disturbance of the Soil Structure Disturbance of the soil structure also has an impact on erosion resistance. Gordaniaya (1957) studied the influence of disturbance on erodibility of carbonated lean clay (Table 13). This table clearly shows that disturbing the soil structure decreases significantly the critical velocity. 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 have strong cementation but are not very resistant to chemical processes such as dissolution and leaching.

74 Table 13. Critical velocity of water flow for carbonated lean clay (Gordaniaya, 1957) Chemical Composition of Soil The chemistry of soil has an impact on both fine-grain and coarse-grain soil erodibility. Erosion, especially suffusion, is likely to occur in sandy and clayey soil containing 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 soils. The presence of these salts in the chemical composition of the soil accelerates the erosion process, due to the co-occurrence of mechanical and chemical erosion. Table 14 shows the solubility of different salts in water. Table 14. Solubility of different salts in water Organic Content of Soil Another influencing factor in erosion is the presence of biogenic (microorganisms) and abiogenic (organic matter in colloidal form) in soil. 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 Disturbed structure Undisturbed structure Water content, % Critical velocity, m/s Water content, % Critical velocity, m/s 3-6 0.15 - - 11-12 0.25 8-10 0.75 18-20 0.4 16-18 1.35 23-25 0.5 25-27 2.6 Type of salt Solubility in water, (g/100 g of water) NaCl 35.8 KCl 34.2 CaSO4 0.2 CaCO3 0.0014 NaOH 107.0 Na2SO4 32.8 MgCl2 35.3

75 coarse-grain soil (sand). The presence of organic colloids in the pore space can create some particle-particle cohesion as well as organic colloid-particle cohesion. This would lead to a decrease in water permeability and increase the resistance to erosion. The adhesion of micro- organisms cells on soil particles result in the formation of biofilms which are extracellular substances glued to particles. This bond between the biofilm and the particle can help resist against erosion. Microbial enzyme is a product of microbial activity and works to stabilize active clay particles. It has a hydrophobic effect on the clay. Strengthening clayey soils using enzyme technology is one of the soil improvement methods applied to decrease 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. Presence of Cracks and Fissures (Micro- and Macro-Scale) In a fractured rock or fissured soil mass, the water discharges through the existing cracks and fissures. An increase in water discharge through the fissured soil mass provides an increase in 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. Note that the erosion rate would change as the opening of the cracks increases. Table 15. Critical fluid velocity above which rock erodes depending on opening of cracks (Bogdanov et al., 1972) 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 content 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 banks erosion, surface erosion of highway embankments and so on. As mentioned earlier, this study will focus on the influences of the most common geotechnical parameters (Table 10). The selected parameters are some of the more direct influences on erodibility and are commonly measured in the laboratory during geotechnical testing. Options Opening of crack, cm 0.01 0.1 0.2 0.5 1.0 2.0 Critical velocity, m/s 1.5 0.15 0.075 0.03 0.015 0.0075 Critical gradient of head 50 0,5 0,063 0,004 5*10-4 6,3*10-5 Coefficient of actual velocity, m/s 0.003 0.3 1.2 7.5 30 120 Note. Coefficient of actual velocity is an average velocity through a crack at the gradient equals to 1

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TRB’s National Cooperative Highway Research Program (NCHRP) has released the pre-publication version of NCHRP Research Report 915: Relationship Between Erodibility and Properties of Soils, which provides reliable and simple equations quantifying the erodibility of soils based on soil properties.

The report 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 which 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 Statically Analysis Results

Appendix 4 – Deterministic Frequentists’ Regression Analysis

Appendix 5 – Probabilistic Calibration Results

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