To the Graduate Council: 
 
I am submitting herewith a thesis written by Tara Liyana Mallison entitled “Comparing 
In Situ Submerged Jet Test Device and Laboratory Flume Methods to Estimate Erosional 
Properties of Cohesive Soils for Bank Stability Models.” I have examined the final 
electronic copy of this thesis for form and content and recommend that it be accepted in 
partial fulfillment of the requirements for the degree of Master of Science, with a major 
in Environmental Engineering. 
 
 
 
 ______________________________ 
 John S. Schwartz 
 Major Professor 

 
 
 
We have read this thesis 
and recommend its acceptance: 
 
 
 
______________________________ 
Larry D. McKay 
 
 
 
______________________________ 
Randall W. Gentry 
 

 
 
 
 
 

 Accepted for the Council: 
 
 
 ______________________________ 
 Carolyn R. Hodges 
 Vice Provost and Dean of  
 the Graduate School 



 
 
 

Comparing In Situ Submerged Jet Test Device and Laboratory Flume Methods to 
Estimate Erosional Properties  

of Cohesive Soils for Bank Stability Models 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

A Thesis 
Presented for the  
Master of Science  

Degree 
The University of Tennessee, Knoxville 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Tara Liyana Mallison 
May 2008 

 



 ii

Acknowledgements 

Earning a masters degree in Environmental Engineering has been an arduous 

process and I could not have accomplished the goal without support from the University 

of Tennessee (UT), professors, family, and friends. First and foremost, I would like to 

thank the UT Center for Environmental Biotechnology (CEB) and the UT Institute for a 

Secure and Sustainable Environment (ISSE) for funding this research. I would especially 

like to thank my major professor, Dr. John Schwartz, for his intelligence, guidance, 

support, and motivation. When the research reached frustrating obstacles, he was present 

to turn things around and move things forward. Dr. Schwartz paid attention to my 

strengths and weaknesses so that he could best utilize and improve upon my abilities as a 

graduate student. Dr. Larry McKay and Dr. Randy Gentry have contributed their time and 

resources to help reach the research objectives. I would like to thank the two of them for 

serving on my committee and providing resources and guidance. 

Thanks to Andrew Simon, Brian Bell, and the rest of the crew at the National 

Sedimentation Laboratory for the use of their resources, equipment, and for the direction 

they provided, and to Dr. Tess Wynn in the Biological Systems Engineering Department 

at Virginia Tech for providing her expert opinion on the research topic. Larry Roberts 

and Ken Thomas have contributed a lot to this project. I would like to thank them for 

their incredible shop abilities in the construction and alteration phases of the flume. And, 

special thanks go to M. Patrick Massey for his unwavering support in the field and ability 

to keep things under control in the Perkins office. In the future, even though he won’t 

need it, Patrick will have me as a good reference for his character, quality of work, and 

determination. William Tyler Mallison, Nancy Roberts, Amanda Dunnavant, Keil Neff, 



 iii

and Dan Carter also helped with data acquisition or laboratory testing procedures. I 

appreciate their assistance with the research collection and analysis process. 

  Finally, I would especially like to thank my husband again, William Tyler 

Mallison, and my parents, Andy & Loretta Liyana and Tom & Sharron Mallison, for 

being supportive of continuing education and challenging me to succeed and attempt to 

learn as much as they already know. Without their love and continual support, I would 

not have had the time, strength, or determination to reach my goal of graduating from the 

University of Tennessee’s Environmental Engineering Masters program.  



 iv

Abstract 

In order to accurately predict the stability of riverbanks, model input parameters 

must be reliable bank failure estimators. Currently, bank stability models require two 

input parameters to predict bank erosion: critical erosion shear stress and erodibility 

coefficient. The investigation’s purpose was to compare two erosion estimation methods 

and improve the bank stability models for cohesive soil commonly found on the banks.  

To accomplish the objective, critical shear stresses and erodibility coefficients 

obtained using the in situ submerged jet test device (SJT) were measured against results 

from the closed-loop laboratory flume method for 12 cohesive bank sites. Additionally, 

SJT critical shear stress values were compared to values found via empirical relationships 

found in literature that incorporate plasticity index, median particle diameter, percent silt-

clay or percent clay content to compute critical shear stress. Particle size analysis and 

Atterberg limit determinations were run classify the sediment type collected. 

The critical shear stress values obtained ranged from 0.09 to 5.84 Pa and SJT 

erodibility coefficients varied from 0.37 to 10.07 cm3/N·s. From flume observations, 

cohesive soil erosion was influenced by interparticle forces and occurred in aggregate 

pieces and particle-by-particle. A few critical shear stress values appeared to be 

unreliable considering the critical shear stress threshold of 1.83 Pa found using the 

laboratory flume analysis and the limited erosion witnessed. Study results also indicated 

that sediment properties did not correlate directly with the SJT critical shear stress values 

or with each other. 

Flume observations and variations among experimental results suggest other 

influential factors exist besides critical shear stress and the erodibility coefficient when 



 v

quantifying the cohesive sediment erosivity. When empirical results were lower than the 

flume’s critical shear stress threshold, it was possible the mechanical soil property could 

not be transferred to the soil types tested or estimates incorrectly assumed zero physical 

and chemical influences. Because of its complexities, traditional experimental design 

may not reliably measure cohesive soil erosion. Only through the continued collaboration 

of various field and advanced degree professionals and the detailed, high-quality 

documentation of as many influential parameters as possible per project can the goal of 

estimating cohesive sediment erosion be accomplished.  



 vi

Table of Contents 

1 Introduction............................................................................................................... 1 
2 Literature Review ..................................................................................................... 5 

2.1 Noncohesive Material ......................................................................................... 6 
2.1.1 Shields Parameter........................................................................................ 6 
2.1.2 Alternate Form of Shields Diagram............................................................ 8 

2.2 Cohesive Material ............................................................................................... 9 
2.2.1 Flume Experiments ................................................................................... 10 
2.2.2 Submerged Jet Test Device....................................................................... 15 
2.2.3 Cohesive Strength Meter........................................................................... 19 
2.2.4 Relating Critical Shear Stress & Erosion Rate to Soil Properties............. 20 
2.2.5 Simple Relations ....................................................................................... 23 

2.3 Additional Effects on Erosion........................................................................... 23 
3 Device Descriptions................................................................................................. 26 

3.1 Submerged Jet Test Device............................................................................... 26 
3.2 University of Tennessee Closed-Loop Laboratory Flume................................ 27 

4 Methodology ............................................................................................................ 31 
4.1 Test Locations................................................................................................... 31 
4.2 Submerged Jet Test Device............................................................................... 36 

4.2.1 Field Setup & Data Collection.................................................................. 36 
4.2.2 Data Analysis ............................................................................................ 37 

4.3 Laboratory Flume.............................................................................................. 38 
4.3.1 Soil Sampling............................................................................................ 38 
4.3.2 Data Collection ......................................................................................... 39 
4.3.3 Data Analysis ............................................................................................ 41 

4.4 Critical Shear Stress Values Obtained from Empirical Relations .................... 43 
5 Results ...................................................................................................................... 45 

5.1 Submerged Jet Test Device Results.................................................................. 45 
5.1.1 Critical Shear Stress.................................................................................. 45 
5.1.2 Erodibility Coefficient .............................................................................. 45 

5.2 Closed-loop Laboratory Flume Results ............................................................ 47 
5.3 Critical Shear Stress Results from Empirical Equations found in Literature ... 48 
5.4 Compilation of Critical Shear Stress Results.................................................... 49 
5.5 Critical Shear Stress Correlations with Sediment Properties............................ 49 

6 Discussion................................................................................................................. 53 
References........................................................................................................................ 57 
Appendix.......................................................................................................................... 63 

Appendix A: Flume Construction and Initial Activation.............................................. 64 
Flume Construction................................................................................................... 64 
Equilibrium Test ....................................................................................................... 68 
Velocity Profiles ....................................................................................................... 75 
Bed Shear Computation ............................................................................................ 89 

 
 



 vii

List of Tables 

Table 1. List of parameters used to characterize cohesive material excluding biological 
effects (Winterwerp et al. 1990). .............................................................................. 11 

Table 2. Critical shear stress coefficients to account for vegetation (Julian and Torres 
2006). ........................................................................................................................ 22 

Table 3. Site information. ................................................................................................. 31 
Table 4. Median critical shear stress determined from submerged jet test device field 

data............................................................................................................................ 46 
Table 5. Median erodibility coefficients by site for the submerged jet test...................... 47 
Table 6. Submerged jet test critical stress shown with brief flume observations and root 

presence..................................................................................................................... 48 
Table 7. Critical shear stress values determined from empirical sediment relationships. 49 
Table 8. Critical shear stress result summary. .................................................................. 50 
Table 9. Percent difference between submerged jet test device critical shear stress and the 

analytical values........................................................................................................ 51 
Table 10. Sediment properties determined for each test location..................................... 51 
Table 11. Multivariate correlations for submerged jet test device critical shear stresses 

and soil properties. .................................................................................................... 52 
Table 12. Velocity data for trolling motor with half propeller on setting #1.................... 75 
Table 13. Velocity data for trolling motor with half propeller on setting #2.................... 77 
Table 14. Velocity data for trolling motor with half propeller on setting #3.................... 78 
Table 15. Velocity data for trolling motor with half propeller on setting #4.................... 80 
Table 16. Velocity data for trolling motor with half propeller on setting #5.................... 81 
Table 17. Velocity data for trolling motor with full propeller on setting #1. ................... 83 
Table 18. Velocity data for trolling motor with full propeller on setting #2. ................... 84 
Table 19. Velocity data for trolling motor with full propeller on setting #3. ................... 86 
Table 20. Velocity data for trolling motor with full propeller on setting #4. ................... 87 
Table 21. Flume bed shear stress values......................................................................... 117 

 



 viii

List of Figures 

Figure 1.  The Shields diagram as updated by Yalin and Karahan (1979). ........................ 7 
Figure 2. An alternate form of the Shields diagram for direct determination of critical 

shear stress (Sturm 2001)............................................................................................ 9 
Figure 3. Core sediment sample subjected to flow in a laboratory flume schematic (Julien 

1998). ........................................................................................................................ 11 
Figure 4. Plan and elevation view of in situ erosion flume (Krishnappan and Droppo 

2006). ........................................................................................................................ 14 
Figure 5. In situ flume (Debnath et al. 2007). .................................................................. 15 
Figure 6. Field testing of Beaver Creek Site #4 with the multiangle submerged jet test 

device. ....................................................................................................................... 26 
Figure 7. University of Tennessee closed-loop laboratory flume schematic.................... 28 
Figure 8. University of Tennessee closed-loop laboratory flume utilized for sediment 

research. .................................................................................................................... 29 
Figure 9. Acoustic Doppler Velocimeter 5.3-cm above sediment core sample................ 30 
Figure 10. Overall site map developed from Google Earth software. .............................. 32 
Figure 11. Closer view of the northern-most test sites compiled from Google Earth 

images. ...................................................................................................................... 33 
Figure 12. Defined Google Earth image of the Beaver Creek locations next to Halls 

Crossroads................................................................................................................. 33 
Figure 13. Initial inspection of three sediment core samples from upstream Beaver Creek.

................................................................................................................................... 34 
Figure 14. Facing upstream of Beaver Creek site #4........................................................ 35 
Figure 15. Beaver Creek site #2 off of Dry Gap Road. .................................................... 35 
Figure 16. Beaver Creek site #3 off Afton Road. ............................................................. 36 
Figure 17. Extruder utilized to extract sediment core samples from stainless steel 

cylinders.................................................................................................................... 39 
Figure 18. Initial photo of soil sample #1 from Beaver Creek downstream site. ............. 40 
Figure 19. Sample from Beaver Creek Site #6 in the unconfined compressive strength test 

device. ....................................................................................................................... 44 
Figure 20. Five samples during hydrometer analysis. ...................................................... 44 
Figure 21. One-way analysis of critical shear stress from submerged jet test by site 

location...................................................................................................................... 45 
Figure 22. One-way analysis of erodibility coefficient from submerged jet test by site 

location...................................................................................................................... 46 
Figure 23. Graphical representation of shear stress values obtain by submerged jet test 

device and soil parameter relationships. ................................................................... 50 
Figure 24. Scatterplot matrix for multivariate correlation data. ....................................... 52 
Figure 25. Typical velocities for the deposition, transport, and erosion of various particle 

sizes (Pidwirny 2006). .............................................................................................. 54 
Figure 26. Support structure for flume with sediment bed cut-out and hydraulic jack 

section. ...................................................................................................................... 64 
Figure 27.  Sediment core jack system. ............................................................................ 65 
Figure 28. Polyvinyl chloride utilized to weld the sheets of PVC together...................... 65 



 ix

Figure 29. Construction of the inside wall and the first vane. .......................................... 66 
Figure 30. Closed-loop flume during testing procedure. .................................................. 67 
Figure 31. Acoustic Doppler Velocimeter over cylindrical test section with plexiglass 

window...................................................................................................................... 68 
Figure 32. Equilibrium profile for trolling motor setting #1. ........................................... 69 
Figure 33. Equilibrium profile for trolling motor setting #2. ........................................... 70 
Figure 34. Equilibrium profile with trolling motor setting #3. ......................................... 71 
Figure 35. Equilibrium profile with trolling motor setting #4. ......................................... 72 
Figure 36. Long duration equilibrium profile with trolling motor on setting #3.............. 74 
Figure 37. Velocity profile for trolling motor with half propeller on setting #1. ............. 76 
Figure 38. Velocity distribution for trolling motor with half propeller on setting #1. ..... 76 
Figure 39. Velocity profile for trolling motor with half propeller on setting #2. ............. 77 
Figure 40. Velocity distribution for trolling motor with half propeller on setting #2. ..... 78 
Figure 41. Velocity profile for trolling motor with half propeller on setting #3. ............. 79 
Figure 42. Velocity distribution for trolling motor with half propeller on setting #3. ..... 79 
Figure 43. Velocity profile for trolling motor with half propeller on setting #4. ............. 80 
Figure 44. Velocity distribution for trolling motor with half propeller on setting #4. ..... 81 
Figure 45. Velocity profile for trolling motor with half propeller on setting #5. ............. 82 
Figure 46. Velocity distribution for trolling motor with half propeller on setting #5. ..... 82 
Figure 47. Velocity profile for trolling motor with full propeller on setting #1............... 83 
Figure 48. Velocity distribution for trolling motor with full propeller on setting #1. ...... 84 
Figure 49. Velocity profile for trolling motor with full propeller on setting #2............... 85 
Figure 50. Velocity distribution for trolling motor with full propeller on setting #2. ...... 85 
Figure 51. Velocity profile for trolling motor with full propeller on setting #3............... 86 
Figure 52. Velocity distribution for trolling motor with full propeller on setting #3. ...... 87 
Figure 53. Velocity profile for trolling motor with full propeller on setting #4............... 88 
Figure 54. Velocity distribution for trolling motor with full propeller on setting #4. ...... 88 



 x

List of Equations 

Equation 1. Dimensionless particle number. ...................................................................... 8 
Equation 2. Critical shear stress for noncohesive sediment................................................ 9 
Equation 3. K factor developed by Hanson. ..................................................................... 18 
Equation 4. Erosion rate.................................................................................................... 18 
Equation 5. Shear stress related to plasticity index........................................................... 20 
Equation 6. Critical shear stress related to the dispersion ratio. ....................................... 20 
Equation 7. Critical shear stress related to the mean particle size. ................................... 20 
Equation 8. Critical shear stress related to the percentage of clay.................................... 20 
Equation 9. Neill's equation. ............................................................................................. 21 
Equation 10. Critical shear stress based on silt-clay content. ........................................... 22 
Equation 11. Estimate of soil erodibility coefficient. ....................................................... 23 
Equation 12. Logarithmic definition of dimensionless “y” to solve for the ultimate scour 

depth.......................................................................................................................... 37 
Equation 13. Logarithmic definition of dimensionless “x” to solve for the ultimate scour 

depth.......................................................................................................................... 37 
Equation 14. Logarithmic velocity distribution. ............................................................... 41 
Equation 15. Region where viscous-sublayer velocity distribution applies. .................... 42 
 



 1

1 Introduction 

Considering the significant role of sediment in water quality and management of 

river systems nationally, there is an urgent need to improve sediment erosion models for 

the complexities of cohesive soils (Huang et al. 2006). Heavy metals, pesticides, 

nutrients, and harmful bacteria can absorb to cohesive materials on banks and disperse in 

surface water when that riverbank fails (Huang et al. 2006). Certain levels of sediments 

themselves can reduce the presence of aquatic life in rivers and can raise water treatment 

costs (Huang et al. 2006). From the output of bank stability model results, stream 

conditions can be properly restored by evaluating sediment best management practices 

such as: landuse management alternatives, amount of vegetation, streamside buffers, and 

in-stream grade control structures (Langendoen 2000). Because several studies have 

found up to 90% of the sediment in streams are from bank erosion sources, improving the 

bank stability components to these models are critical to the success of stream restoration 

or maintenance projects (Prosser and Winchester 1996; Wallbrink et al. 1998; Wasson et 

al. 1998).  

River mechanics, stream morphology, and sediment transport concepts are the 

basic components of erosion models (Langendoen 2000). To specifically estimate 

channel erosion, bank stability models use the excess shear equation which can be related 

to flow hydraulics (Langendoen 2000). To estimate channel sediment erosion, the bank 

stability models require two input parameters, the critical erosion shear stress (τc)  and 

erodibility coefficient (kd), which, unfortunately, can be difficult to estimate or measure 

for cohesive sediment (Langendoen 2000). Critical shear stress is the primary factor in 

determining whether soil will resist the forces of a concentrated flow, and the erodibility 



 2

rate determined from the erodibility coefficient, applied, and critical shear stress defines 

how quickly fine-grained sediments will erode (Sturm 2001). Currently, critical erosion 

shear stress and erodibility coefficients are estimated from empirical relationships 

developed from flume studies that related critical shear stress to basic soil properties, or 

determined by available testing methods, including the in situ submerged jet test device 

(Smerdon and Beasley 1961; Hedges 1990; Stein el al. 1993; Hanson and Simon 2001; 

Mazurek 2001; Julian and Torres 2006; Wynn and Mostaghimi 2006a; Clark and Wynn 

2007) and subjecting a sediment core sample to an erosion test in a specially-design 

flume (Briaud et al. 2004; Huang et al. 2006; Krishnappan and Droppo 2006; Debnath 

2007). The typical critical shear stress range for cohesive sediment found by the 

Transportation Research Board during their pier and scour depth study on cohesive soils 

was 0.5 N/m2 to 5 N/m2 (Briaud et al. 2004). The range was comparable to the critical 

shear stress values commonly obtained for sands (Briaud et al. 2004). 

The objective of this research was to compare and evaluate two methods of 

collecting critical shear stress and the erodibility parameter of cohesive sediment to 

enhance the erosive input parameters of bank stability models. To reach this goal of 

improving the erosion model input, the critical shear stresses and erodibility coefficients 

obtained using the in situ submerged jet test device were compared to results from the 

laboratory flume method for twelve cohesive test sites in East Tennessee. Three study 

locations were used for this investigation: Beaver Creek (Knox County, TN), Hines 

Branch (Knox County, TN), and Abrams Creek (Blount County, TN). All locations were 

second to third-order streams with cohesive riverbanks and each of the twelve sites are in 

Watts Bar Lake watershed. At least four runs were performed with the submerged jest 



 3

test device at each site to account for the variability of bank material. Twelve 6-inch long, 

2-inch diameter core samples were collected at each of the 12 locations for closed-loop 

flume method and soil analysis. In addition to that comparison, the submerged jet test 

device’s critical shear stress values were weighed against values found via empirical 

relationships found in literature based on flume and soil property experiments (Smerdon 

and Beasley 1961; Julian and Torres 2006). The properties related to the hydraulic 

erosion of cohesive sediment utilized to compute critical shear stresses are plasticity 

index, median particle diameter, percent silt-clay and percentage of clay present. 

Correlations were explored between the submerged jet test critical shear stresses and 

sediment properties to explore connections between the outcome of this research and past 

projects.  

Because each of the methods exhibit strengths and weaknesses during the data 

collection process, the procedure and outcome of each testing method are presented. As 

presented later in this paper, the in situ procedure uses a submerged jet test device to 

generate a scouring jet stream of water perpendicular to the bank. Besides the intense jet 

impact on the sediment surface, the placement of the submerged jet test device can affect 

the values obtained. Vegetation, habitat, soil structure, and soil gradation under the 

footprint of the device can lead to under- or over-estimated critical erosion shear stress 

and erodibility rates. Another test used to determine the erosive properties of cohesive 

sediment utilized was a sediment core subjected to flow in a laboratory flume. The flume 

test is not run on-site, but incorporates the hydraulic flow field and the viscous sublayer 

present in stream networks. While it is important to consider the hydraulics involved in 

data collection of erosive input parameters, erosion tests on cohesive material that do not 



 4

incorporate the soil and water chemistry influences are questionable due to the manner in 

which cohesive soil erodes (Wynn and Mostaghimi 2006a).  

From the comparison of methods and results obtained, the cohesive sediment 

erosion phenomenon was explored and recommendations towards finding a reliable 

method to estimate cohesive soil erosional properties were made. The erosive properties 

produced from two testing procedures and the computed empirical values were further 

evaluated by exploring the hydraulics of the river systems and effects present to influence 

the process of cohesive sediment erosion. Hydraulic engineers and fluvial 

geomorphologists involved in river restoration projects will be able to utilize the 

investigation results to enhance computer models incorporating the differences between 

noncohesive, semi-cohesive, and cohesive bank stability input parameters. 

 



 5

2 Literature Review 

To better understand the concept of critical shear stress and its applicability, the 

topic is presented for both noncohesive and cohesive material. Features of cohesive 

sediment that set it apart from noncohesive sediment are its high composition of clay-

sized material and strong interparticle forces (Huang et al. 2006). The high strength of 

interparticle forces is a result of surface ionic charges (Huang et al. 2006). Interparticle 

forces become the dominant factor affecting the behavior of sediment rather than gravity 

as the particle size decreases because the specific surface area (i.e. surface area per unit 

volume) increases concurrently (Huang et al. 2006). A clear boundary between cohesive 

and noncohesive does not exist, but particle sizes less than 2 μm are commonly labeled 

cohesive clays (Huang et al. 2006). Particles larger than 60 μm are cohesionless coarse 

sediment and sediment sizes in between 2 μm and 60 μm are classified as silts (Huang et 

al. 2006). Notably, silt sediment is between cohesive and cohesionless soils (Huang et al. 

2006).  

Since the presence of clay is mostly responsible for cohesive properties of silt 

sediment, practicing engineers consider both silt and clay as cohesive material (Huang et 

al. 2006). Included in this section is a detailed study of methods to determine the erosion 

parameters of cohesive and noncohesive sediment including Shields parameter, 

submerged jet test device, laboratory flume methods, and experimentally-derived soil 

parameter relationships. In addition to the procedures available to determine the critical 

shear stress and erodibility rate of site-specific sediment, additional factors that effect 

streambank erosion of cohesive soils are discussed. 



 6

2.1 Noncohesive Material 

Most erodibility experiments have been preformed on noncohesive sand, stream 

beds where flume and field methodology is clear (Haan 1994; Huang et al. 2006). From 

experience, Shields parameter, the ratio of the shear stress to a particle’s submerged 

weight per unit of surface area at critical conditions, is a reliable tool to provide a precise 

estimate of critical shear stress for noncohesive sediment (Shields 1936; Haan 1994). As 

described below, the behavior of noncohesive sediment erosion is well-defined and 

predictive models from those inputs are assumed reliable. Therefore, Shields parameter is 

typically used to determine the critical shear stress of cohesionless soils in practice. First, 

one indirect and then one direct method of obtaining critical shear stress using Shield’s 

parameter is presented in this section. 

2.1.1 Shields Parameter 

A noncohesive soil’s resistance to the critical shear stresses caused by a 

concentrated flow of water has been studied extensively both in the field and laboratory. 

As a result, the critical shear stress of a noncohesive soil can be ascertained from a few 

soil and fluid properties. Because the submerged specific weight of the sediment, 

sediment grain size, fluid density and dynamic viscosity have been found to control the 

erodibility of noncohesive soil, Shields parameter (τ*c) can be utilized to determine the 

critical shear stress (Sturm 2001). The parameter is dimensionless and developed from 

the compilation of various flume experiments on a wide range of grain sizes (Shields 

1936).  

Shields, the American that collected, developed, and presented critical shear stress 

results for various grain sizes, concluded that the noncohesive particles begin rolling and  



 7

 
 

 
Figure 1.  The Shields diagram as updated by Yalin and Karahan (1979). 

 
sliding at various locations along the soil face, just as the threshold of sediment 

movement is exceeded (Sturm 2001). Illustrated in Figure 1, he created the Shields 

diagram that presented results obtained during the experiments. While the original 

diagram did not account for particles with low specific gravity and small particle 

diameter, Mantz (1977) altered the graph to include smaller sediment sizes. The 

information needed to determine Shields parameter can be found from soil and water 

variables. 

According to Sturm (2001), a weakness of Shields diagram is that how incipient 

motion was defined by Shield’s to compute the critical shear stresses is unknown. Two 

ways that determine the value are: (1) visual observation of the initiation of movement, or 

(2) extrapolation of measured sediment transport rates to zero (Sturm 2001). In addition 

to uncertainties of which method Shield used, other controversies in using Shields  



 8

parameter (τ*c) are his use of both mean and median grain sizes and the presence of bed 

forms in part of the data (Sturm 2001). The diagram was based on a representative 

particle diameter and assumes zero influences between individual particles (Clark and 

Wynn 2007). Since the variability among sediment sizes is great, interaction between 

particles exist, and the bed form inclusion can lead to overestimation of τc, Shields 

diagram is considered very generalized for the initiation of motion (Clark and Wynn 

2007). 

2.1.2 Alternate Form of Shields Diagram 

Julien (1995) proposed an alternate form of the Shields diagram in order to 

directly compute the critical shear stress. Rather than having to iterate between critical 

shear stress and Reynolds number which both contain Shields parameter, an additional 

dimensionless parameter was introduced. First to compute the critical shear stress, a 

dimensionless particle number must be calculated utilizing Equation 1: 

3/1

2

3
50

*
)1(

⎥
⎥
⎦

⎤

⎢
⎢
⎣

⎡ −
=

v
gdSGd  (1)   

in which d* = dimensionless particle number, SG = specific gravity of 

sediment, g = gravitational constant, d50 = particle size with 50% passing, 

and ν = kinematic viscosity of the fluid. 

Then, the ratio of shear stress to the submerged weight of a particle per unit of surface 

area at critical conditions, τ*c, is obtained from the diagram presented in Figure 2. And, 

the corresponding critical shear stress using Shields parameter, the unit weight of 

soil, unit weight of the fluid, and the diameter with 50% passing, can be found using the 



 9

 
Figure 2. An alternate form of the Shields diagram for direct determination of critical shear stress 

(Sturm 2001). 

 

relationship in Equation 2 (Sturm 2001): 

csc d *50)( τγγτ −=   (2) 
 

where τc = critical shear stress, γs = unit weight of sediment, γ = unit 

weight of the fluid, d50 = diameter with 50% passing, and τ*c  = 

dimensionless critical shear stress.  

Even though the alternative form obviously contains the same limitations of Shields 

parameter, this relationship between specific unit weight and particle size has become a 

widely used practice for determining the critical shear stress of noncohesive sediment 

(Haan 1994). 

2.2 Cohesive Material 

Values of critical shear stress and erodibility rates are more complicated for 

cohesive soils than noncohesive sediment because of surface charge forces (Huang et al. 

2006). Due to the effects from soil shear strength, soil salinity, moisture content, 

percentage of clay, particle size and other related parameters on the resistance to shearing 



 10

forces, the method used to analyze cohesive sediment erosive properties should 

incorporate soil and site water conditions (Wynn and Mostaghimi 2006a). Judging from 

the methods presented below, the flume and field experiments utilized during the 

development of Shields parameter that does not apply to fine-grained sediment and the 

concept of critical shear stress set a precedence for designing experiments involving 

cohesive sediment (Shields 1936). Therefore, during the research projects preformed on 

the erosive properties of cohesive sediment, considerations were not always made for the 

28 parameters in Table 1 that currently characterize cohesive soil (Winterwerp et al. 

1990). With the erosive behavior of noncohesive soils in mind, the following methods 

were developed for determining the erosional parameters of fine-grained soils. 

2.2.1 Flume Experiments 

2.2.1.1 Laboratory Open-Channel Flow Test 

For cohesive soils, a laboratory open-channel flow test with a soil sample on the 

bed is an erosion measurement technique to determine the critical shear stress and 

erodibility rate of cohesive sediment. Figure 3 illustrates the experimental setup. After the 

soil sample is placed in a flume and the test has begun, the critical shear stress can be 

determined visually or graphically (Clark and Wynn 2007). A weakness with the visual 

method is that the point of failure is difficult to observe and even harder to separate from 

the individual’s definition of failure. The visual point is a subjective observation. In the 

paper, Methods for Determining Streambank Critical Shear Stress and Soil Erodibility: 

Implications for Erosion Rate Predictions, Clark and Wynn (2007) summarized three 

different interpretations of the point of failure from various sources. Dunn (1959) 

determined that the critical shear stress was met as “the water becomes cloudy.”  



 11

Table 1. List of parameters used to characterize cohesive material excluding biological effects 
(Winterwerp et al. 1990). 

 

 

 
Figure 3. Core sediment sample subjected to flow in a laboratory flume schematic (Julien 1998). 



 12

Alternatively, Smerdon and Beasley (1961) observed the critical shear stress when 

“general movement of the soil composing the channel bed was observed.” Many years 

later, Kamphuis and Hall (1983) reported that the critical value was reached at “pitting of 

the surface” during their flume observations. In order to avoid this subjectivity, Clark and 

Wynn (2007) determined it was best to graphically represent the erosion rate versus the 

shear stress.  

To graphically represent the erosion rate versus the shear stress, the variables to 

obtain the parameters from the laboratory flume method must be defined. The depth of 

sample eroded and the time passed from start to finish of erosion period is necessary to 

determine the erodibility rate (Briaud et al. 2004). And, using measurements of velocities 

and respective elevations, the vertical velocity profile can be developed (Briaud et al. 

2004). The velocity profile is utilized as a major component of the calculation of critical 

shear stress (Briaud et al. 2004). Through the addition of a best-fit line, a value that 

equals the critical stress can be found where the line crosses the x-axis (Clark and Wynn 

2007). 

Overall, laboratory flumes enable researchers to control the environmental and 

flow conditions more easily than field tests; however, it is impossible to transport the 

bank material into a flume without causing disturbance (Hanson et al. 1999; Hanson and 

Cook 2004). Also, erosion tests on cohesive material that do not incorporate the soil and 

water chemistry influences are questionable due to the manner in which cohesive soil 

erodes (Clark and Wynn 2007). In situ experimental processes that do not require the 

disturbance of the fine-grained soil and incorporate the exact physical, chemical and 



 13

biological state of the field, more easily and adequately represent the critical shear stress 

and erodibility rate of cohesive sediment (Krishnappan and Droppo 2006). 

2.2.1.2 In Situ Flumes 

Benthic in situ flumes are set up over stream sediment to measure erosive 

properties of cohesive soils (Black and Paterson 1997). The procedure is similar to the 

laboratory flume test, but the sediment samples do not require transport (Black and 

Paterson 1997). Even though the in situ flumes are a good approach, many uncontrollable 

influences can lead to uncertainty of soil parameter estimates (Julian and Torres 2006). 

Published in a 2006 issue of Geomorphology, Julian and Torres (2006) dealt with the lack 

of controls by choosing a study site based upon the location of the water table, soil with 

low silt-clay content and an entrenched channel, low vegetation component, and warm 

climactic region without the freeze-thaw component. During their in-situ flume study, 

bank erosion measurements were collected from cohesive banks over a 14-month 

duration (Julian and Torres 2006). From prior bank cohesive bank erosion studies, a 

conceptual model was developed that defined three categories (Julian and Torres 2006). 

When the channel banks contain greater than 40% of silt-clay content, the erosion was 

controlled by sub-aerial erosion and the hydraulic shear considered negligible (Julian and 

Torres 2006). When the silt-clay percentage was between 20% and 40%, a combination 

of the subaerial and shear stresses had an impact on the erosion of channel banks (Julian 

and Torres 2006). Lastly, hydraulic shear stress became the controlling erosional process 

of silt-clay soils with less than 20% of fines (Julian and Torres 2006). Utilizing the 

conceptual model with the three categories of erosivity influences and the data collected 



 14

using the in-situ flume, Julian and Torres (2006) found for sites with moderate τc (1.93-

4.08 N/m2), event peak is strongly related to bank erosion, while low τc (0.95 N/m2) 

values indicated a stronger correlation of variability with bank erosion.  

A Canadian in situ flume study by Krishnappan and Droppo (2006) involved a 

submerged pump attached and underwater video camera mounted onto a field flume 

setup. The plan and elevation view of the in situ erosion flume (Figure 4) shows the 

components of the instrument (Krishnappan and Droppo 2006). While this research 

project was a bed study and not bank testing, the outcome is influential towards 

understanding the effect of sediment deposition on erosion. Also, the experimental setup 

is similar to that of in situ flume bank erosion testing. The two sites measured in 

Hamilton Harbour found density variations as the explanatory variable for erosion rates. 

   

 
Figure 4. Plan and elevation view of in situ erosion flume (Krishnappan and Droppo 2006). 



 15

The density variations were a result of gas accumulation, biofilm 

development/degradation, and bioturbation (Krishnappan and Droppo 2006). Also, 

Krishnappan and Droppo (2006) found it prudent to run in situ tests because of the 

difficultly of mimicking the physical, chemical, and biological state of the sediment and 

the exact function of all on-site influences. 

From an in situ flume study, Debnath et al. (2007) concluded that the spatial and 

temporal variation of the sediment on the bed controlled the rate of erosion. The physical 

properties of the flume in Figure 5 did not have an effect. The data also showed an 

exponential decrease in the erodibility rate after the bed shear stress is reached depending 

on clay content, dry bulk density, and conductivity (Debnath et al. 2007).  

2.2.2 Submerged Jet Test Device 

Studies have been performed with the submerged jet test device on cohesionless 

sediment. Yet, as mentioned earlier, Shields parameter as a method to determine critical  

 

 
Figure 5. In situ flume (Debnath et al. 2007). 

 



 16

shear stress is more common. So, other researchers have begun to explore the 

complexities of testing cohesive soils with and exploring the scour properties of the 

submerged jet test device (Dunn 1959; Moore and Masch 1962; Mirstkulava et al. 1967; 

Dash 1968; Bhasin et al. 1969; Hollick 1976; Blaisdell et al. 1981; Stein 1993; Hanson 

1990; Hedges 1990; Mazurek et al. 2001). By determining critical shear stresses and 

erodibility coefficients from a wide range of submerged jet test results and determining 

the properties of the sediment at each of the test sites, some of the data collected was used 

to observe relationships between the soil properties and the erosivity of cohesive soil 

(Hanson and Simon 2001; Clark and Wynn 2007). While others observed the scouring 

effects of the jet test device such as the shape of the scouring hole formed, maximum 

scour depth, and the shear stress distribution underneath the jet (Blaisdell et al. 1981; 

Mazurek et al. 2001; Ansari 2003). 

Hanson and Simon (2001) analyzed the critical shear stress and erodibility 

coefficients from 83 submerged jet test runs in the Midwestern United States. The 

outcome of their testing resulted in critical shear stresses from 0.0 to 400 Pa and an 

erodibility coefficient of 0.001 to 3.75 cm3/N·s (Hanson and Simon 2001). Hanson and 

Simon (2001) determined a large variation in the values of critical shear stress and 

erodibility coefficients. The loess soils in the Midwest varied among erosion resistance 

within streambeds, from streambed to streambed, and across regions (Hanson and Simon 

2001). Clark and Wynn (2007) compared the submerged jet test device results against 

estimated critical shear stress values obtained from Shields diagram and empirical 

equations relating the τc to soil properties for 25 field sites near Blacksburg, Virginia. For 

the Virginia testing locations, the submerged jet test critical shear stress results were 



 17

larger than all of the other values obtained except for the silt-clay estimate (Clark and 

Wynn 2007).   

In depth research has been performed to study the scour properties of the device. 

Consistent with the relationship presented by Moore and Masch (1962) and assumptions 

of scour analysis made by Blaisdell et al. (1981), there exists a linear relationship 

between scour depth and logarithm of time. Dunn (1959) observed that the erosion first 

occurs away from the centerline of the jet nozzle and Moore and Masch (1962) describe 

the jet erosion of cohesive or consolidated clays as a process of mass erosion. 

Considering the pattern of submerged jet test erosion, two types of scour holes were 

observed by Moore and Masch (1962) and Hollick (1976): wide and shallow or narrow 

and deep. While Moore and Masch related the height of the jet above the sediment 

surface and the diameter of the nozzle to the hole type, Hollick found that other 

parameters influence the type of scour hole.  

2.2.2.1 Jet Test Erosion Coefficient 

An erodibility coefficient (kd) which is used to calculate an erodibility rate (ε) can 

be produced from the data collected of a submerged jet test device. In the 1990 

Transactions of the ASAE, G. J. Hanson wrote about the development of the submerged 

jet test device. While his design with an inner cylindrical baffle and a pin profiler is 

slightly different than the one being utilized for this research, the mechanics of the scour 

are the same. Four different soil types were analyzed and the data collected was used to 

calibrate the device based upon the Reynolds number of the submerged jet device 

(Hanson 1990). Summary tables of the soils’ physical properties and average compacted 

densities were tabulated and the experiment led to the development of the equation to 



 18

estimate the erodibility of other soils. Equation 3 developed by Hanson (1990) is used to 

solve for the K factor: 

μ

ρ
μ

μ
ρ

d

d
tVd

hVolK ×

⎟
⎟
⎟
⎟
⎟
⎟

⎠

⎞

⎜
⎜
⎜
⎜
⎜
⎜

⎝

⎛

⎟
⎟
⎠

⎞
⎜
⎜
⎝

⎛
⎟⎟
⎠

⎞
⎜⎜
⎝

⎛
=

25.7

065.0

2

67.0

3

00436.0

/  (3) 

 
where K = coefficient of erodibility, Vol = volume of material removed 

during a jetting event, h = elevation of jet above the soil surface, d = 

diameter of the jet nozzle, V = jet velocity, ρ = the mass density of the 

fluid, µ = absolute viscosity of the fluid, and t = time. 

The K factor is then related to the Reynolds number of the jet and the time factor and 

represented by a linear relationship on a logarithmic scale. In situ tests are compared 

against predicted values and the results are accurately represented. Clark and Wynn 

(2007) also used this least squares method. Their jet test scour depth data was fitted to the 

excess shear stress equation and the erodibility coefficient, kd, was produced (Clark and 

Wynn 2007). Along with the applied shear stress on the boundary and the critical shear 

stress determined from submerged jet test data, the erodibility coefficient can be plugged 

into Equation 4 and an erosion rate can be determined (Clark and Wynn 2007): 

a
cadk )( ττε −=  (4) 

 
where ε = erodibility rate (m/s), kd = erodibility coefficient (m3/N·s), a = 

exponent typically assumed to equal 1, τa = applied shear stress on the soil 

boundary (Pa), and τc = critical shear stress (Pa).  

For the Blacksburg, Virginia sites, the erodibility results collected using a submerged jet 

test device were effected by freeze/thaw cycling, root density, field moisture content, soil 



 19

texture and soil pore water in contact with stream water had influence on the streambank 

erosion (Clark and Wynn 2007). 

2.2.3 Cohesive Strength Meter 

2.2.3.1 Critical Shear Stress 

Since it is a fairly new in situ device, few researchers have performed experiments 

on soils utilizing the Cohesive Strength Meter (CSM). Set up on the exposed intertidal 

sediment, the claim is that the CSM can measure critical erosion shear stress (Paterson 

1989). The experimental set-up and hydraulics of the CSM are similar to the submerged 

jet test device. A 3-cm wide chamber is carefully pushed in perpendicular to the soil 

surface and filled with site water. Incrementally, the jet pressure, calibrated with a 

standard manometer, increases and the vertical jet causes erosion over a 700 mm2 area. 

The light transmission is read periodically to detect the increase of sediment in the 

chamber water caused by the erosion. As the amount of sediment increases within the 

chamber, the turbidity level increases which causes the light transmissivity to decrease. 

From the plot of transmission versus pressure, the critical erosion threshold is found 

when the light transmission falls just below 90% (Widdows et al. 2007). Eroding 

pressure is plugged into an empirical equation and used to determine the equivalent 

horizontal shear stress (Tolhurst et al. 1999). Widdows (2001) found no correlation with 

the CSM critical erosion shear stresses compared to the four other intertidal erosion 

devices. The four other devices analyzed were: (1) Plymouth Marine Laboratory’s (PML) 

annular flume (diameter 64 cm; area 0.17 m2), (2) PML’s mini-annular flume (diameter 

19 cm; area 0.026 m2), (3) National Oceanography Centre Southampton’s (NOC) 

EROMES erosion device (diameter 10 cm; area 0.0079 m2), and (4) NOC’s annular mini-



 20

flume (diameter 30.5 cm; area 0.032 m2). The CSM values were repeatedly higher than 

the others’ measurements (Widdows et al. 2007). 

2.2.3.2 Erodibility Rate 

Inferred by Widdows (2001), the CSM is not capable of measuring a rate of 

erosion. The device does not contain a sensitive optical backscatter sensor (OBS) and the 

intervals of the recording of the suspended sediment concentration (SSC) are not small 

enough. 

2.2.4 Relating Critical Shear Stress & Erosion Rate to Soil Properties 

2.2.4.1 Critical Shear Stress 

Smerdon and Beasley (1961) related critical shear stress to the plasticity index, 

dispersion ratio, mean particle size, and percentage of clay present from data collected 

during a flume study on eleven cohesive sediment types in Missouri. The equations that 

were developed by Smerdon and Beasley (1961) are shown in Equations 5 through 8: 

84.0)(16.0 wc I=τ  (5) 
 

63.0)(2.10 −= rc Dτ  (6) 
  

501.281054.3 D
c

−×=τ  (7) 
 

cP
c

0182.010493.0 ×=τ  (8) 
   

in which τc = critical shear stress (Pa), Iw = plasticity index, Dr = 

dispersion ratio, D50 = mean particle size (m), and Pc = percent clay by 

weight (%) (Smerdon and Beasley 1961). 

In Design Hydrology and Sedimentology for Small Catchments, Foster (1982) suggested 

the foundation of the Smerdon and Beasley equation be the dispersion ratio (Equation 6), 



 21

while Hirschi and Barfield (1988a) suggested the equation be based on percentage clay 

(Equation 8) (Haan 1994). Clark and Wynn (2007) considered the relationship between 

critical shear stress and plasticity index or dispersion ratio to be the best estimate since 

they found the two properties were directly related to the sediment’s ability to resist 

erosion. 

An experiment by Neill (1967) involved six particle sizes of graded gravels, 

uniform glass balls of two different sizes, and cellulose acetate balls. The cellulose 

acetate balls were of various diameters (6 to 30 mm) for a uniform flow over a wide 

channel with no slope (Neill 1967). Equation 9, which represented critical shear stress in 

terms of specific gravity, median particle diameter, and water depth, was developed from 

his experimental data (Neill 1973): 

( ) 3/13/2
50176090.0 dDSGc −= γτ  (9) 

   
in which τc = critical shear stress (Pa), γ = specific weight of water (N/m3), 

SG = specific gravity of soil, D50 = mean particle size (m), d = depth of 

flow (m) (Neill 1973). 

A limitation of Neill’s equation is that it considered the flow conditions in addition to the 

soil properties. Therefore, studies have concluded that Neill’s equation is difficult to 

compare to other estimation processes (Clark and Wynn 2007). 

From work presented by Dunn (1959) and Vanoni (1977), Julian and Torres 

(2006) related critical shear stress to the percentage of silt and clay (SC), which are 

defined by particles sizes less than 0.063 mm. Equation 10 is the third order polynomial 

fitted to the critical shear stress and silt-clay content data: 

 



 22

32 )(534.2)(0028.0)(1779.01.0 SCESCSCc −−++=τ   (10) 
 

where τc = critical shear stress (N/m2), SC = silt-clay (<0.063 mm) content 

(%), and E = erodibility rate (cm/s) (Julian and Torres 2006). 

The critical shear stress in Equation 10 could also be multiplied by a coefficient to 

account for vegetation. Table 2 lists the vegetation coefficient which ranges from 1 to 

19.20 (Julian and Torres 2006). 

In the “USDA Water Erosion Prediction Project: Hillslope Profile Model 

Documentation,” authors relate the critical shear stress of cohesive soils to shear strength, 

soil salinity, and moisture content (Alberts et al. 1989). Alternatively, Lyle and Smerdon 

(1965) related the erosive parameter to percentage clay, mean particle size, dispersion 

ratio, vane shear strength, organic matter content, cation exchange capacity, and calcium-

sodium ratio. 

2.2.4.2 Erosion Rate 

Typically, the erodibility rate of fine-grained sediment is predicted using Equation 

4. However, the parameters that affect the critical shear stress such as moisture content 

and percent clay can also affect the erosion rate, causing the critical shear stress and 

erodibility coefficient to be variable (Clark and Wynn 2007). 

 

Table 2. Critical shear stress coefficients to account for vegetation (Julian and Torres 2006). 

Bank vegetation τc coefficient 
None 1.00 
Grassy 1.97 
Sparse trees  5.40 
Dense trees 19.20 



 23

2.2.5 Simple Relations 

2.2.5.1 Critical Shear Stress Assumed Zero 

Considering a worst-case condition, the critical shear stress can be considered 

zero. One approach to determining the erosive properties of sediment does just that  

(Clark and Wynn 2007). Because many people believe it is difficult to define the point of 

incipient motion, critical shear stress is often assumed to be insignificant and set equal to 

zero (Foster et al. 1977; Hanson 1990; Temple 1992; Hanson et al. 1999), or assigned a 

constant value base upon soil properties as suggested in earlier sections of this literature 

review. 

2.2.5.2 Erodibility coefficient function to determine erodibility rate  

In the Midwestern U.S. where the stream beds were 50% to 80% silt, an intensive 

jet test study was performed by Hanson and Simon (2001). The critical shear stresses 

ranged from 0.0 to 400 Pa and the erodibility coefficient varied from 0.001 to 3.75 

cm3/N·s. From the analysis of the data set, Hanson and Simon (2001) identified that kd 

was inversely related to τc and determined that the following equation could be utilized as 

an estimate of the erodibility coefficient: 

5.02.0 −= cdk τ   (11) 
  
 in which kd = erodibility coefficient (cm3/N·s) and τc = critical shear stress (Pa). 

For other projects where the erodibility coefficient was not available, Equation 11 

provided a good approximation (Hanson and Simon 2001).  

2.3 Additional Effects on Erosion 

Other pertinent studies involved the effects of vegetation, soil structure, soil 

gradation, soil chemistry, and water chemistry on streambank erosion (Wynn and 



 24

Mostaghimi 2006a). When studying the erosivity of cohesive sediment banks, the factors 

cannot be avoided (Wynn and Mostaghimi 2006a). Using a submerged jet test device to 

study the effect of soil vegetation on the erodibility properties of sediment, Wynn and 

Mostagimi (2006a) ran 48 submerged jet test device runs in a variety of Virginian soils. 

During the study, cohesive soils tended to erode by aggregates so the stability of the 

particle compounds had an effect on the critical shear stress (Wynn and Mosaghimi 

2006a). The salinity of the soil pore water influenced the clayey soils’ dispersion (Wynn 

and Mosaghimi 2006a). Therefore, the soil and water chemistry was found to affect the 

pattern of bank erosion (Wynn and Mosaghimi 2006a). Clark and Wynn (2007) also 

determined the soil chemistry, structure, and water chemistry affected the pattern at 

which a bank sample erodes.  

Specifically, a few of the cohesive properties of cohesive sediment have been 

studied. Bulk density was found to impact the critical shear stress value obtained 

significantly (Wynn and Mosaghimi 2006a). Previous research by Asare et al. (1997) 

found that as the bulk density increases, the shear strength of sediment increases 

concurrently. Root density, soil freezing, and soil texture have also been found to impact 

the erodibility of soils (Wynn and Mosaghimi 2006a). In addition, the range of particles 

diameters found by soil classification methods affects the erosion of soils. As the amount 

of sand size particles decreases, the critical shear stress of cohesive sediment is increased 

(Wynn and Mosaghimi 2006a). The results of an in situ erosion test by Debnath et al. 

(2007) showed an exponential decrease in the erodibility rate after the bed shear stress is 

reached depending on clay content, dry bulk density, and conductivity.  



 25

In addition to the sediment property impacts on erosion results, the footprint of 

the device or size of sample used for analysis can also affect results. Investigations of 

various in-situ and laboratory erosion experiments made by Cornelisse et al. (1994) 

determined that the as the surface area of the test increased, the reproducibility also 

improves. Both the shear stress of cohesive and cohesionless sediment can be influenced 

by the presence of vegetation, freeze-thaw cycles, and soil texture; however, the amount 

of factors impacting erosion increases with cohesive soils when considering the critical 

shear stress and the erodibility coefficient (Wynn and Mosaghimi 2006a).   



 26

3 Device Descriptions 

In order to understand the procedures utilized to collect the soil erosional 

properties for this study, a detailed description of the equipment is necessary. The 

following information summarizes the device components and capabilities. 

3.1 Submerged Jet Test Device 

A method of utilizing a submerged vertical circular turbulent impinging jet device 

exists to determine the erodibility of cohesive sediments. The multi-angle submerged jet 

test device, shown in Figure 6, scours the bank sediment with a highly turbulent jet 

stream of water at a 90 degree angle from the soil surface. A submerged jet test requires 

the following components: pump & motor, steel cylinder with a diameter of 30.5 cm, 

outer jet tube, nozzle, point gauge, and hammer. The system also requires tubing for the 

inlet, outlet, and jet components and gate valves for head control.  

 

 
Figure 6. Field testing of Beaver Creek Site #4 with the multiangle submerged jet test device. 



 27

 

The steel cylinder is pounded into the soil 7.6 cm with a hammer and the inflow, outflow, 

and jet hoses are attached to the pump. After the initial setup, the pump is turned on and a 

constant jet stream of water begins scouring the riverbank. In theory, the velocity of the 

water coming out of the jet nozzle remains constant and causes shear stress on the 

sediment surface. The pressure head created by the pump system controls the applied 

shear stress. At regular intervals, the scour depth is measured with a point gage until a 

maximum depth or the final time period is reached.  

While the device allows for direct field measurements, the amount of equipment 

required adds a level of difficultly when considering the widespread use of the 

submerged jet test device. Moreover, vertical or steep riverbanks can restrict the 

placement of the pump motor. Depending upon the elevation of the streambank and the 

placement of the intake, a restriction can be placed on the minimum pressure head 

allowed which leads an unavoidable increase in applied shear stress during testing. Also, 

because of the turbulent nature of the flow perpendicular to the bank, the submerged jet 

test device is criticized. The jet stream of water impinges perpendicular to the streambank 

ignores the presence of the viscous sublayer. 

3.2 University of Tennessee Closed-Loop Laboratory Flume 

Recently, a small-scale hydraulic flume was built to facilitate the project. Figure 7, 

the schematic of the closed-loop laboratory flume, shows the aerial view of the outside 

and inside wall dimensions along with key features of the design. Additional images of 

the flume during construction phases and initial testing can be viewed in Appendix A. As  

 



 28

 

Figure 7. University of Tennessee closed-loop laboratory flume schematic. 

 
 
seen in the development of velocity profiles and the calculation of bed shear stresses in 

Appendix A, the flume is capable of producing bed shear stresses (τ b) from 0.34 to  1.83 

Pa. 

The table that supports the flume is 11-feet by 6-feet. The outside length and 

width of the widest portions of the flume are 10-feet by 5-feet. The inside diameter of the 

semi-circular segments are 3-feet in diameter. As seen in Figure 8, four major vanes are 

located around the bend prior to the test section to prevent differential local velocities and 

vortexes from forming. Each of the vanes was spaced to allow an equal area of flow and 

lined on the bottom with gravel to increase bed roughness. At the start of the test section, 

eight-inch vanes were placed to aid in the development of laminar flow. Approximately 

23-inches after the test section, one major vane was located around the second bend in the 



 29

 

Figure 8. University of Tennessee closed-loop laboratory flume utilized for sediment research. 

 

flume to facilitate the flow pattern. The closed-loop design enables the mimicking of 

river hydraulics without varying flow rates or highly turbulent flows. It is important to 

note that sediment can be recirculated through the flume without much disturbance if 

necessary. The test section is 5-feet in length by about 1-foot in width and is free from 

flow impedance. A 2-inch diameter cylindrical test chamber is located 55-inches from the 

beginning of the test section and a 17-inch long, 11.8-inch wide, and 2-inch deep 

sediment chamber is located 30-inches from the beginning of the test section. When 

sediment pans are not being tested, a removable plate that is flush with the flume bed is 

placed over the sediment box. 



 30

 

Figure 9. Acoustic Doppler Velocimeter 5.3-cm above sediment core sample. 

 

A SonTek Acoustic Doppler Velocimeter (ADV), shown 5.3-cm above the sample 

volume in Figure 9, was used to measure the local mean flow and turbulence in three-

dimensions. The Acoustic Doppler Velocimeter’s sample volume is 5-cm down from the 

probe head and the ADV has the ability to measure a sample volume within 2-mm of the 

boundary. The last two components of the closed-loop flume is an 8-Ton hydraulic bottle 

jack which was utilized to raise the 2-inch cylindrical soil sample into the flow field and 

Minn Kota trolling motor. 



 31

4 Methodology 

 Twelve field sites were chosen in East Tennessee to perform the submerged jet 

tests and collect soil samples for soil characterization and laboratory flume analysis. The 

test locations are described below and the procedure for data collection is presented.  

4.1 Test Locations 

The streams chosen were second to third-order streams with cohesive riverbanks. 

All 12 sites have the hydrologic unit code in the Watts Bar Lake watershed of 06010201 

(USGS 2007). The selected locations have a longitude between 35°35’30.52” N and 

36°4’55.14” N and latitude between 83°49’34.83” W and 84°8’15.04” W. A description, 

latitude, longitude, and the side of bank tested for each site is listed in Table 3. 

Table 3. Site information. 

Site 
Designation Description Latitude  Longitude Bank Tested  
Abrams 
Creek Abrams Creek 35°35'30.52" N 83°49'34.83" W Left 

BC_DS 
Beaver Creek, 
Downstream 36°4'55.14"   N 83°55'27.87" W Left 

BC_Site2 Beaver Creek, Site 2 36°3'30.33"   N 83°58'26.06" W Left 
BC_Site3 Beaver Creek, Site 3 36°4'47.22"   N 83°56'0.86"   W Left 
BC_Site4 Beaver Creek, Site 4 36°1'38.65"   N 84°1'37.99"   W Left 
BC_Site5 Beaver Creek, Site 5 35°59'50.46" N 84°5'5.26"     W Right 
BC_Site6 Beaver Creek, Site 6 35°58'18.99" N 84°8'15.04"   W Right 

BC_US1 
Beaver Creek, 
Upstream #1 36°4'51.22"   N 83°55'23.83" W Right 

HB_DS 
Beaver Creek at 
Halls, Downstream 36°4'47.22"   N 83°55'12.74" W Right 

HB_Site1 Hines Branch, Site 1 36°4'7.37"     N 83°56'35.94" W Left 

HB_US 
Beaver Creek at 
Halls, Upstream 36°4'47.28"   N 83°55'10.82" W Right 

HB_USB 
Beaver Creek at 
Halls, US of bridge 36°4'47.28"   N 83°55'11.16" W Right 



 32

 
Figure 10. Overall site map developed from Google Earth software. 

 
More specifically, eleven of the locations are in the Beaver Creek Watershed which is in 

Knox County, Tennessee (USGS 1). The predominant landuse observed of these Knox 

County stream areas tested is residential/urbanized. Labeled a third-order stream, Abrams 

Creek is the only test site located outside of Knox County and is part of the Great Smoky 

Mountain National Park river system (USGS 1). The predominant landuse around the site 

tested is forested. An overall site map (Figure 10) depicts the locations the sites. Due to 

the extent of the locations, Figure 11 shows a closer view of the northern-most sites and 

Figure 12 is more defined picture of the Beaver Creek locations next to Halls Crossroads. 



 33

 
Figure 11. Closer view of the northern-most test sites compiled from Google Earth images. 

 

 
Figure 12. Defined Google Earth image of the Beaver Creek locations next to Halls Crossroads. 



 34

Each study site location was at least 5 m wide and was visually inspected for 

homogeneity. Later, the homogeneity was checked via soil tests and observation of the 

soil samples. The first time the soil samples’ depth can be checked visually was after 

extrusion (Figure 13). According to the data collected and the triangular classification 

chart introduced by the U.S. Bureau of Reclamation (1974), bank materials ranged from 

clay, silty clay, and sandy & silty clay. Figure 14, Figure 15, and Figure 16 provide a 

visual of typical study sites’ physical characteristics. The bank angles where the 

submerged jet test device is placed ranges from 20-75°, and the amount of vegetation 

present where testing occurred ranged from none to low. The tests and samples collected 

avoided contact with roots unless otherwise noted on the data sheets. Runs with apparent 

vegetative influences are discarded from data analysis. 

 

 
Figure 13. Initial inspection of three sediment core samples from upstream Beaver Creek. 

 

 
 



 35

 
Figure 14. Facing upstream of Beaver Creek site #4. 

 
 

 
Figure 15. Beaver Creek site #2 off of Dry Gap Road. 



 36

 

 
Figure 16. Beaver Creek site #3 off Afton Road. 

 
Each of the submerged jet test and sample collection location is carefully chosen to avoid 

contact with roots or habitat. However, the three previous figures displayed the difficultly 

encountered when choosing a wide enough, visually homogeneous area to perform four 

complete jet tests and accrue twelve 6-inch long, 2-inch diameter samples. 

4.2 Submerged Jet Test Device 

4.2.1 Field Setup & Data Collection 

In order to remain in close proximity to the moisture content of the soil samples 

tested within the flume and in situ methods, the submerged jet tests were limited to the 

submerged bank or toe of the bank. Therefore, the soil under each footprint of the test had 

a high moisture content. Every multi-angle submerged jet test device run had a 30 minute 



 37

duration with reading intervals every minute. Each time the reading was taken with a 

point gage, the gage tip plugged the nozzle opening; therefore scour ceased during those 

measurements. At least four jet test device runs were conducted at each of the field sites. 

In cases where vegetation, soil strength, or habitat influenced the outcome of the tests, 

additional information was collected. 

4.2.2 Data Analysis 

Since the maximum scour depth can take hours or days to reach, the critical shear 

stress can be computed from the data collected by utilizing the Blaisdell Method 

(Blaisdell et al. 1981; Hanson and Cook 1997). As suggested by Blaisdell et al. (1981), 

the hyperbolic logarithmic method of analysis is utilized to provide the best-fit equation 

and produce a prediction of the ultimate scour depth based on data collected in the early 

stages of the scour. The basic equations for the submerged jet data processing are 

provided as Equation 12 and Equation 13: 

p

p

p

m

p

p

P

m

D
tV

D
Z

D
tV

D
Z

y logloglog −==  (12) 

 

p

p

D
tV

x log=  (13) 

 
in which Zm = the maximum depth of scour measured from the tailwater 

surface, Vp and Dp = the jet velocity and diameter at the point where the 

jet plunges in to the tailwater surface, and t = the time passed since the 

beginning of the scour.  



 38

Utilizing a least squares method, an erodibility coefficient (kd) can be produced from the 

data collected of a submerged jet test device (Hanson and Cook 1997). In most cases, the 

bank angles restricted the placement of the pump and motor; therefore, the applied shear 

stress was relatively high.  

4.3 Laboratory Flume 

 Seven soil samples were collected at each site for testing in the laboratory flume. 

A major difference between the flume and submerged jet device methods was the 

location of testing. A submerged jet test was run at the field site and the laboratory flume 

required an undisturbed sample to be taken and bought back to the laboratory for 

analysis. In addition to the testing location difference, the hydraulic component of the 

equipment varied. While the submerged jet test device impinged a jet stream of water at a 

90-degree angle, the flume allowed for the flow to run horizontally over the sample and 

did not directly interfere with the viscous sublayer.  

4.3.1 Soil Sampling 

For the laboratory flume method, seven 2-inch diameter sediment cores were 

collected from each of the field sites with 6-inch soil stainless steel tubes, a sampler head, 

and hammer. Immediately after collection, each sample was sealed with a labeled plastic 

cap and duct tape around the cap provided another means of preventing moisture loss. 

The samples were placed in labeled Ziploc bag and drove back to the laboratory where 

they were extracted by standard methods. As depicted in Figure 17, each sediment core 

sample was extracted from stainless steel cylinders using an extruder. Then, the  



 39

 

Figure 17. Extruder utilized to extract sediment core samples from stainless steel cylinders. 

 

samples were sealed back into labeled Ziploc bags and brought immediately to a moisture 

room. In the moisture room, the sediment cores were placed vertically with the top of the 

soil sample facing upward and stored until testing.  

4.3.2 Data Collection 

 Per equilibrium and velocity tests that were conducted on the University of 

Tennessee’s closed-loop flume, the following procedures were followed to determine the 

soil erosional properties of critical shear stress and erodibility rate using a laboratory 

flume. 

1. Clean flume prior to use and fill 12 inches with tap water. 

2. Shear one-inch off the top of the soil sample and discard the one-inch trimming. 



 40

3. Place the rest of the sample in flume for at least 12 hours to promote saturation. 

Make sure the top of the sample collected is at the highest elevation within the 

test cylinder. 

4. Set up Acoustic Doppler Velocimeter directly over the test cylinder to measure 

the mean velocity 10-cm above flume bed. 

5. Record the initial temperature of the water. 

6. Turn the trolling motor on to the position necessary for the shear stress required 

and wait 5 minutes for equilibrium within the flume. 

7. Take an initial turbidity measurement. 

8. Crank the soil sample up using the 8-ton hydraulic jack until the soil is 1.5-mm 

above the flume bed, take an initial photo similar to Figure 18, and start timing 

the scour rate. 

9. Begin recording the mean velocity with the ADV for approximately 10 minutes at 

the beginning of the test. 

 

 
Figure 18. Initial photo of soil sample #1 from Beaver Creek downstream site. 



 41

10. When the soil sample is eroded approximately 1.5-mm, take an additional picture 

and crank the soil sample up an additional 1.5-mm. Record the time interval each 

time the soil sample is raised. 

11. Repeat steps 1 through 10 until an accurate erodibility rate is obtained. 

12. Record the mean velocity with the ADV for approximately a 10 minute duration 

during the end of the testing process. 

13. Take final temperature and turbidity readings. 

14. Turn off equipment, extrude soil sample from flume, and repeat the procedure for 

the next soil sample. 

As seen by the calculations present in Appendix A, the flume has the capability of 

producing bed shear stresses in a range of 0.3 to 1.83 Pa. Depending on the soil sample, a 

range of values were tested in order to predict a critical shear stress for the site. For this 

process, one to seven values of critical shear stress should be tested per site for solving or 

categorizing the critical value.  

4.3.3 Data Analysis 

From modern fluid mechanics research on turbulent mixing length by Prandtl and 

von Karman’s hypothesis of turbulence similarity, the law of the wall (Equation 14) was 

developed (Sturm 2001): 

oz
z

u
u ln1

* κ
=  (14) 

 
where u* = shear velocity, κ = von Karman’s constant = 0.40, zo = constant 

of integration, and u and z are the point velocity and distance from the 

wall, respectively. 



 42

The law of the wall presents a logarithmic distribution of velocities from the bed to the 

near-wall region where z/h < 0.2 (Sturm 2001). The “h” in the near-wall region considers 

the boundary-layer thickness and z is the point distance from the wall. The region where 

the equation applies is not the full thickness of the flow, but the transition between the 

viscous sublayer and the region where turbulent shear stresses govern entirely. Because 

the viscous sublayer is a region where only viscous shear applies, the thickness is 

determined via Equation 15 and then the logarithmic overlap layer between the viscous 

sublayer and the fully turbulent region is utilized to find the logarithmic best-fit line and 

solve for the bed shear stress (Sturm 2001):  

5* <
v

zu
  (15) 

where u* = shear velocity, z = point distance from the wall, and v = 

kinematic viscosity of the fluid (Sturm 2001). 

Because the selection of depth for the no-slip (zero velocity) condition strongly 

influences the estimated bed shear, Equation 15 is applied and the thickness of the 

viscous sublayer is computed for 70°F, the average temperature of the fluid during 

testing. Considering the bed shear stress is the shear stress acting on the soil sample, the 

bed shear value computed from the law of the wall equation in the transition zone 

between the viscous sublayer and turbulent flow is the critical shear stress for each flow 

rate.  

An erodibility rate was measured simply by measuring the depth of sediment 

eroded and dividing the depth by the time passed. Many depth and time measurements 



 43

were required to account for variability in sediment samples. Also, three samples were 

tested at a single flow rate to test for repeatability. 

4.4 Critical Shear Stress Values Obtained from Empirical Relations 

In order to classify the sediment collected and compute critical shear stress values 

relating to soil properties, the following soil analyses were preformed:  Standard Test 

Methods for Unconfined Compressive Strength of Cohesive Soil (ASTM D 2166-00), 

Standard Test Methods for Liquid Limit, Plastic Limit, and Plasticity Index of Soils 

(ASTM D 4318-00), and Standard Test Method for Particle-Size Analysis of Soils 

(ASTM D 422-63). Each of tests is run according to the ASTM standard and documented 

accordingly.  

The unconfined compressive strength test device is shown with a sample from 

Beaver Creek Site #6 in Figure 19 and the hydrometer analysis setup is depicted in Figure 

20. Due to the inconsistency of results from the unconfined compressive strength, 

possibly a result of strain rate, only the physical properties and characteristics of the site  

obtained during preparation of the unconfined compressive strength samples were 

utilized in characterizing the soil samples. 

As mentioned earlier, other studies have found relationships between critical 

shear stress and soil parameters such as plasticity index and percentage of clay present. 

The parameters collected during soil characterization are plugged into the respective 

equation (Equation 5, Equation 7, Equation 8, or Equation 10) and critical shear stress 

values were computed for each site. 



 44

 
Figure 19. Sample from Beaver Creek Site #6 in the unconfined compressive strength test device. 

 
 

 
Figure 20. Five samples during hydrometer analysis. 

 



 45

5 Results 

5.1 Submerged Jet Test Device Results 

5.1.1 Critical Shear Stress 

 In order to determine the presence of outliers affecting the submerged jet test 

results, a one-way analysis of the four test runs for each test site is preformed. The 

graphical results are depicted in Figure 21 and the values in Table 4 present the median 

critical shear stresses determined from the submerged jet test device. The values outside 

of the 95% confidence interval were considered outliers and a result of vegetative or 

habitat influences on the test run. In all cases, three out of four test runs were compiled to 

compute the average critical shear stress for each location.  

5.1.2 Erodibility Coefficient 

 Erodibility coefficients were computed from the submerged jet device 

  

1

1.5

2

2.5

3

3.5

4

C
rit

ic
al

 s
he

ar
st

re
ss

,  
(N

/m
^2

)

A
br

am
s 

C
re

ek

B
C

_D
S

B
C

_S
ite

2

B
C

_S
ite

3

B
C

_S
ite

4

B
C

_S
ite

5

B
C

_S
ite

6

B
C

_U
S

1

H
B

_D
S

H
B

_S
ite

1

H
B

_U
S

H
B

_U
S

B

Site Location
 

Figure 21. One-way analysis of critical shear stress from submerged jet test by site location. 



 46

measurements. The erodibility coefficients are visually presented in a quartile plot 

(Figure 22) and presented numerically in Table 5.   

 

Table 4. Median critical shear stress determined from submerged jet test device field data. 

Site Location τc, SJT (N/m2) 
Abrams Creek 1.33 
BC_DS 1.84 
BC_US1 2.06 
BC_Site2 2.96 
BC_Site3 2.35 
BC_Site4 2.09 
BC_Site5 1.86 
BC_Site6 2.51 
HB_DS 2.23 
HB_Site1 2.41 
HB_US 2.48 
HB_USB 2.09 

*Note: SJT = submerged jet test device. 
 
 

0

5

10

15

E
ro

di
bi

lit
y

C
oe

ffi
ci

en
t (

cm
3/

N
-s

)

A
br

am
s 

C
re

ek

B
C

_D
S

B
C

_K
E

IL
_U

S
1

B
C

_S
ite

2

B
C

_S
ite

3

B
C

_S
ite

4

B
C

_S
ite

5

B
C

_S
ite

6

H
B

_D
S

H
B

_S
ite

1

H
B

_U
S

H
B

_U
S

B

Site Location
 

Figure 22. One-way analysis of erodibility coefficient from submerged jet test by site location. 

 



 47

 Table 5. Median erodibility coefficients by site for the submerged jet test. 

Site Location 
Submerged Jet Test Device 

Erodibility Coefficient (cm3/N*s) 
Abrams Creek 5.66 
BC_DS 2.63 
BC_Site2 0.66 
BC_Site3 4.77 
BC_Site4 3.89 
BC_Site5 3.43 
BC_Site6 4.13 
BC_US1 10.07 
HB_DS 2.45 
HB_Site1 3.59 
HB_US 1.52 
HB_USB 0.37 

 

5.2 Closed-loop Laboratory Flume Results 

 During the experimental procedure of the flume method, the values of bed shear 

stress are found to be insufficient to provide a numerical comparison between the values 

obtained during the jet test data collection and the values computed from empirical soil 

parameter relationships. However, the observation and experience during the laboratory 

flume method is valuable and summarized next to the submerged jet test device results in 

Table 6. Generally, the soil samples did not continue to erode throughout the flume 

testing; therefore, the critical shear stress of each of the sites tested is assumed to be 

greater than 1.83 Pa. Critical shear stresses at three sites, as determined by the submerged 

jet tester were within the range of τc that the flume could generate, however only minimal 

disturbance was observed during the flume tests. 

 

 



 48

Table 6. Submerged jet test critical stress shown with brief flume observations and root presence. 

Site 
Location 

Submerged Jet 
Test τc (Pa) 

Erosion Observation in Closed Loop 
Flume* 

Roots Presence, 
(Y or N)* 

Abrams 
Creek 1.33 

Disturbance-induced on 2/3rds of the 
samples. None on 1/3rd. N 

BC_DS 1.84 
High erosion on 1/3rd of the samples. 
None on 2/3rds. N 

BC_Site2 2.06 
Minimal disturbance-induced on 
2/3rds of the samples. None on 1/3rd. N 

BC_Site3 2.96 None N 
BC_Site4 2.35 None (1/3) Y (2/3) N 
BC_Site5 2.09 None N 

BC_Site6 1.86 
Disturbance-induced on 2/3rds of the 
samples. None on 1/3rd.. N 

BC_US1 2.51 
High erosion on 1/3rd of the samples. 
None on 2/3rds. (1/3) Y (2/3) N 

HB_DS 2.23 
Disturbance-induced on 2/3rds of the 
samples. None on 1/3rd. N 

HB_Site1 2.41 
Each sample had few aggregate 
pieces erode followed by no erosion. (1/3) Y (2/3) N 

HB_US 2.48 
High erosion on 1/3rd of the samples. 
Minimal erosion on 2/3rds. N 

HB_USB 2.09 None Y 
* Note: Fractions are used to represent portion of samples that did or did not experience 

erosion and amount of samples tested where roots were encountered during flume testing. 
 

5.3 Critical Shear Stress Results from Empirical Equations found in 
Literature 

 
From the soil properties obtained by the Unconfined Compressive Strength of 

Cohesive Soil (ASTM D 2166-00), Standard Test Methods for Liquid Limit, Plastic 

Limit, and Plasticity Index of Soils (ASTM D 4318-00), and Standard Test Method for 

Particle-Size Analysis of Soils and the erodibility rate obtained using the jet tester, the 

following critical shear stresses in Table 7 were computed. As mentioned previously, the 

empirical equations were developed by Smerdon and Beasley (1961) and Julian and 

Torres (2006). 



 49

 
 

Table 7. Critical shear stress values determined from empirical sediment relationships. 

Site Location 
τc, PI 

(N/m2) 
τc, D50 

(N/m2) 
τc, PC 

(N/m2) 
τc, SC 

(N/m2) 
Abrams Creek 1.62 1.93 2.64 3.91 
BC_DS 2.28 2.34 3.84 4.42 
BC_US1 1.86 2.52 5.84 4.29 
BC_Site2 2.05 2.29 4.01 4.77 
BC_Site3 1.88 2.51 4.64 3.32 
BC_Site4 2.49 2.06 3.39 2.18 
BC_Site5 1.64 1.26 2.42 3.85 
BC_Site6 0.82 2.03 3.39 4.84 
HB_DS 2.52 2.10 3.69 4.56 
HB_Site1 0.09 1.18 1.59 2.52 
HB_US 0.29 1.74 2.99 4.70 
HB_USB 0.16 2.03 3.84 3.67 

    *Note: PI = plasticity index, D50 = median particle diameter (mm), PC = percent clay, 
and SC = percent silt-clay. 

 
 
5.4 Compilation of Critical Shear Stress Results 

All of the critical shear stress result are compiled in Table 8 and presented 

graphically in Figure 23. Then, the percent differences between the critical shear stress 

determined from submerged jet test device and the empirical equation results. By site 

location, the percent differences are summarized in Table 9. 

5.5 Critical Shear Stress Correlations with Sediment Properties 
 

Previous research had shown a strong relationship between critical shear stress and 

bulk density or other soil characteristics. In order to determine if the presence of similar 

findings exists for this project, data was collected to determine the sediment properties 

summarized in Table 10. Then, multivariate correlations were found for the submerged 



 50

jet test device critical shear stresses and soil properties. The correlation results are listed 

in Table 11 and Figure 24 is a scatterplot matrix depicting the correlations. 

  

Table 8. Critical shear stress result summary. 

Site Location 
τc Threshold, CLF 

(N/m2) 
τc, SJT 

(N/m2) 
τc, PI 

(N/m2) 
τc, D50 

(N/m2) 
τc, PC 

(N/m2) 
τc, SC 

(N/m2) 
Abrams Creek 1.83 1.33 1.62 1.93 2.64 3.91 
BC_DS 1.83 1.84 2.28 2.34 3.84 4.42 
BC_US1 1.83 2.06 1.86 2.52 5.84 4.29 
BC_Site2 1.83 2.96 2.05 2.29 4.01 4.77 
BC_Site3 1.83 2.35 1.88 2.51 4.64 3.32 
BC_Site4 1.83 2.09 2.49 2.06 3.39 2.18 
BC_Site5 1.83 1.86 1.64 1.26 2.42 3.85 
BC_Site6 1.83 2.51 0.82 2.03 3.39 4.84 
HB_DS 1.83 2.23 2.52 2.10 3.69 4.56 
HB_Site1 1.83 2.41 0.09 1.18 1.59 2.52 
HB_US 1.83 2.475 0.29 1.74 2.99 4.70 
HB_USB 1.83 2.09 0.16 2.03 3.84 3.67 

*Note: CLF = closed-loop laboratory flume, SJT = submerged jet test, PI = plasticity index, D50 = median 
particle diameter (mm), PC = percent clay, and SC = percent silt-clay. 

 
 

0

1

2

3

4

5

6

Abra
ms C

ree
k

BC_D
S

BC_U
S1

BC_S
ite

2

BC_S
ite

3

BC_S
ite

4

BC_S
ite

5

BC_S
ite

6

HB_D
S

HB_S
ite

1

HB_U
S

HB_U
SB

Site Location

C
rit

ic
al

 S
he

ar
 S

tre
ss

, N
/m

^2

τc Threshold, CLF (N/m2)
τc, SJT (N/m^2)
τc, PI (N/m^2)
τc, D50 (N/m^2)
τc, PC (N/m^2)
τc, SC (N/m^2)

 
Figure 23. Graphical representation of shear stress values obtain by submerged jet test device and 

soil parameter relationships. 



 51

Table 9. Percent difference between submerged jet test device critical shear stress and the analytical 
values. 

Site Location τc, SJT (N/m^2) 

τc, PI 
Difference 

(%) 

τc, D50 
Difference 

(%) 

τc, PC 
Difference 

(%) 

τc, SC 
Difference 

(%) 
Abrams Creek 1.33 9.73 18.33 32.92 49.22 
BC_DS 1.84 10.61 11.96 35.24 41.25 
BC_US1 2.06 -5.21 10.05 47.87 35.12 
BC_Site2 2.96 -18.21 -12.66 15.03 23.40 
BC_Site3 2.35 -11.07 3.34 32.76 17.17 
BC_Site4 2.09 8.65 -0.83 23.71 2.04 
BC_Site5 1.86 -6.20 -19.34 13.16 34.81 
BC_Site6 2.51 -50.73 -10.59 14.90 31.70 
HB_DS 2.23 6.06 -2.94 24.60 34.31 
HB_Site1 2.41 -92.85 -34.32 -20.38 2.27 
HB_US 2.475 -79.26 -17.35 9.40 30.99 
HB_USB 2.09 -85.78 -1.47 29.54 27.39 

Average Percent Difference (%) -26.19 -4.65 21.56 27.47 
*Note: SJT = submerged jet test, PI = plasticity index, D50 = median particle diameter (mm), PC = percent clay, and 

SC = percent silt-clay. 
 
 
 

Table 10. Sediment properties determined for each test location. 

Site 
Location 

Bulk 
Density 
(g/cm3) D50 (mm) G 

LL 
(%) 

PL 
(%) 

PI 
(%) 

Percent 
silt (%) 

Percent 
clay 
(%) 

Percent 
silt-clay 

(%) 
Abrams 
Creek 1.93 0.00940 2.93 43 27 16 50 40 90 
BC_DS 1.85 0.00640 2.80 47 23 24 45 49 94 
BC_Site2 1.88 0.00670 2.50 41 20 21 43 50 93 
BC_Site3 1.93 0.00530 2.59 43 24 19 43 54 97 
BC_Site4 1.60 0.00840 2.65 57 31 26 39 46 85 
BC_Site5 1.98 0.01600 2.93 33 17 16 35 38 73 
BC_Site6 1.83 0.00860 2.44 31 24 7 44 46 90 
BC_US1 1.89 0.00525 2.31 40 21 19 38 59 97 
HB_DS 2.00 0.00805 2.55 47 20 27 47 48 95 
HB_Site1 1.88 0.01700 2.40 27 26 1 49 28 77 
HB_US 2.02 0.01095 2.59 26 24 2 53 43 96 
HB_USB 1.97 0.00860 2.39 25 24 1 39 49 88 

*Note: D50 = mean particle diameter, G = specific gravity, LL = liquid limit, PL = plastic limit, and PI = 
plasticity index. 

  
 



 52

Table 11. Multivariate correlations for submerged jet test device critical shear stresses and soil 
properties. 

 

Critical Shear 
Stress, SJT 

(N/m^2) 

Bulk 
Density 

(g/cm^3) D50 (mm) G PI (%) 
Percent silt 

(%) 
Percent 
clay (%) 

Percent silt-
clay (%) 

Critical Shear Stress, 
SJT (N/m^2) 1.0000 0.0156 -0.0884 -0.4751 -0.0237 -0.1518 0.2671 0.1690 
Bulk Density 
(g/cm^3) 0.0156 1.0000 0.1821 0.0390 -0.3520 0.2852 -0.0549 0.1410 
D50 (mm) -0.0884 0.1821 1.0000 0.2157 -0.5082 0.1142 -0.9192 -0.8638 
G -0.4751 0.0390 0.2157 1.0000 0.3520 0.0483 -0.2978 -0.2720 
PI (%) -0.0237 -0.3520 -0.5082 0.3520 1.0000 -0.2845 0.4602 0.2751 
Percent silt (%) -0.1518 0.2852 0.1142 0.0483 -0.2845 1.0000 -0.3739 0.3084 
Percent clay (%) 0.2671 -0.0549 -0.9192 -0.2978 0.4602 -0.3739 1.0000 0.7669 
Percent silt-clay (%) 0.1690 0.1410 -0.8638 -0.2720 0.2751 0.3084 0.7669 1.0000 

Note:  D50 = mean particle diameter, G = specific gravity, and PI = plasticity index. 
 
 

1.5
2

2.5
3

1.6

1.8

2

0.0075

0.0125

0.0175

2.4
2.6
2.8

3

5

15

25

35

45

55

30
40
50
60

75

85

95

Critical ShearStress, SJT (N/m^2)

1.5 2 2.5 3

Bulk Density(g/cm^3)

1.6 1.8 22.1

D50 (mm)

.0075 .015

G

2.42.62.8 3

PI (%)

510 20 30

Percentsilt (%)

3540 5055

Percentclay (%)

30 40 50 60

Percentsilt-clay (%)

75 85 95
 

Figure 24. Scatterplot matrix for multivariate correlation data. 



 53

6 Discussion 

Due to the low bed shear stress values produced in the laboratory flume, percent 

differences between the critical shear stresses and erodibility parameters produced by the 

submerged jet test device method and laboratory flume method could not be determined. 

However, the submerged jet test results could be compared to the laboratory flume’s 

threshold. The in situ test produced an estimate above the laboratory flume’s threshold at 

each test site location except for Abrams Creek, and two Beaver Creek sites were near the 

flume maximum τc. Even though none of the complete flume test runs continually eroded 

at the max shear stress applied, the flow rate within the flume had the ability to transport 

gravel placed on the bottom of the flume for roughness. Because the velocity required to 

transport some gravel sizes is less than the speed needed to cause erosion in clay and silt 

sediment, the ability of the flume to transport gravel without causing erosion in the core 

sample can be explained. The illustration in Figure 25 of deposition, transport, and 

erosion velocities for different particles sizes best represents the flume’s ability to move 

gravel particles without eroding the sediment core sample. The transport of gravel can 

occur at lower flow velocities than erosion of clay particles. During the initial rise of the 

cylinder, when aggregate eroded quickly and then the sample remained intact, the cause 

was assumed to be a drag force induced. 

When considering the concept of shear stress and erodibility coefficient being the 

controlling factor of the erosion of cohesive sediment, this flume study found that it did 

not adequately describe the pattern of cohesive sediment erosion. In fact, the soil sample 

face and the moisture level affected the ability of the flume to erode the sediment. If a  



 54

 
Figure 25. Typical velocities for the deposition, transport, and erosion of various particle sizes 

(Pidwirny 2006). 

 

sample had a jagged face or high moisture content, the weak plane of soil sheared most 

times. When another sediment core from the same site had a smooth face or lower 

moisture content, no erosion would occur, not even in the initial rise of the cylinder. 

According to the flume observations and outcome witnessed, cohesive sediment erosion 

estimates should incorporate the effects of soil structure, gradation, physical and 

chemical properties which have been found to effect cohesive sediment erosion. 

With the submerged jet test device, the presence of organic matter and habitat 

affected the runs and accounted for part of the variability within the results. While some 

wildlife presence was accounted for by correcting the data collected for crawfish holes or 

moving the jet test cylinder’s location when roots were encountered, the field testers may 

not realize other wildlife impacts. Also, the jet test device eroded sediment very quickly 

and aggregate collected on the bottom of the scour hole. From both an objective and 

subjective standpoint, this piling effect could also affect scour rates and measurements. 

Limitations aside, the submerged jet test data returned similar critical shear stresses and 

erodibility rates in three out of the four test runs per site. 



 55

Considering the empirical estimates of critical shear stress, the values obtained 

from the percent clay or percent silt-clay parameters returned the highest estimates of the 

erosive property. Also, the plasticity index equation to find critical shear stress produced 

the lowest critical shear stress at a few of the test sites. Apparently, the equation based on 

plasticity index did not apply to half of the sediments sample collected because they were 

considerably lower than the flume’s critical shear stress threshold. Erosion was not 

usually witnessed in the flume from the samples collected at those sites. The critical shear 

stress calculated from the mean particle diameter was closest to the submerged jet test 

result most often with an average percent difference of -4.65%. 

Soils properties determined did not correlate well with each other or with 

erosional properties found by the submerged jet test method. Bulk density does not take 

into account sediment composition, salinity, or other physiochemical properties of the 

soil. While previous studies (Wynn and Mosaghimi 2006a; Asare et al. 1997) found a 

relationship between critical shear stress and bulk density, the results of this experiment 

failed to do so. It is possible that results from other studies which linked soil properties to 

the erosive parameters could not be transferred to the soil types tested for this project. 

With the closed-loop laboratory flume having zero slope, it was difficult to 

achieve critical shear stresses that reliably and continually produced a constant rate of 

erosion. Because a fraction of the samples at most sites experienced some form of erosion 

in the flume while others samples from the same site location did not, the lack of a 

measurable pattern of erosion in the laboratory flume suggest that the critical shear stress 

and erodibility are not the primary considerations when dealing with cohesive sediment. 

Considering the observations of the two procedures, the submerged jet test device was the 



 56

best available testing method. Since the soil structure, soil gradation, and chemistry of the 

soil and water apparently influenced the erosion of cohesive sediment, any in situ method 

that had been carefully designed would be the better representation than the laboratory 

result based upon erosion observations of this experiment. While the submerged jet test 

device is field intensive, the in situ test uses a practical amount of site water and does not 

include the sampling or transport disturbance that the laboratory method requires. As for 

the submerged jet test device not accounting for the viscous sublayer, the results have 

shown that there are more influential factors on the erosion of cohesive sediment.  

Many important advances in understanding the erosive behavior of cohesive 

sediment have been made in the past decade. However, the connection between values 

obtained using analytical equations, in situ devices, or laboratory experiments is subject 

to great uncertainty unless the influential parameters that dominate the behavior of 

cohesive sediment erosion are measured and detailed along with the experimental results. 

Judging from experiences with this project, in situ testing over a wide range of soil types 

with careful accounting of cohesive parameters is recommended for future research on 

improving erosion prediction and measurement.  



 57

References 



 58

Alberts, E.E., Laflen, J.M., Rawls, W.J., Simanton, J.R., and Nearing, M.A. (1989). Soil 
component. In “USDA Water Erosion Prediction Project: Hillslope Profile Model 
Documentation,” Chap. 6, NSERL Report No. 2. National Soil Erosion 
Laboratory, USDA-ARS, W. Lafayette, IN. 

 
Asare, S.N., R.P. Rudra, W.T. Dickinson, and G.J. Wall. (1997). Frequency of Freeze-

Thaw Cycles, Bulk Density, and Saturation Effects on Soil Surface Shear and 
Aggregate Stability in Resisting Water Erosion. Canadian Agricultural 
Engineering 39(4):273-279. 

 
ASTM. (2003). Standard test method for Liquid Limit, Plastic Limit, and Plasticity Index 

of Soils. No. D4318-00. ASTM International, West