Bridge scour in bed materials other than cohesionless sediments
Part 1

Material Information

Bridge scour in bed materials other than cohesionless sediments Part 1
Series Title:
Bridge scour in bed materials other than cohesionless sediments Part 1
Sheppard, D. Max
Place of Publication:
Gainesville, Fla.
Coastal & Oceanographic Engineering Dept. of Civil & Coastal Engineering, University of Florida

Record Information

Source Institution:
University of Florida
Holding Location:
University of Florida
Rights Management:
All applicable rights reserved by the source institution and holding location.

Full Text

STATE JOB No. 99900-5000
CONTRACT No. B-B495 UPN No. 97050890 UF ACCOUNT No. 4910 451134112
CONTRACT PERIOD: 9/10/97 2/28/98

February 1998

LIST OF FIGURES ................................................................................. ii
1. INTRODUCTION ......................................................................... 1
1.1 Problem Statement .................................................................. 1
1.2 O bjective ............................................................................. 1
1.3 Scope and Purpose .................................................................. 2
2. PRELIMINARY INVESTIGATION ................................................... 3
2.1 Literature Search .................................................................... 3
2.2 Site V isits ............................................................................ 4
3.1 Cohesive Soils ....................................................................... 5
3.2 Rock Materials ...................................................................... 5
4. PRELIMINARY TESTS .................................................................. 6
4.1 Uniaxial Compression Tests ...................................................... 6
4.2 Preliminary Erosion Tests ......................................................... 8
5. EROSION TESTING DEVICES ....................................................... 9
5.1 Rotating Cylinder Device ......................................................... 9
5.2 Enclosed Flume Device .......................................................... 11
6. FDOT MEETING ........................................................................ 14
7. REFERENCES ............................................................................ 15

1 Uniaxial Comptression Test on Florida Limestone ................................. 7
2 Rotating Cylinder Erosion Testing Device ............................................. 10
3 Enclosed Flume Testing Device ...................................................... 12


1.1 Problem Statement
The soil at a number of bridge sites in the State of Florida is composed of materials other than cohesionless sediments (i.e. other than sand, loose shell, etc.). This includes cohesive materials (such as muds and clays), combinations of cohesive and cohesionless sediments, and harder materials such as limestone and coquina. The erosion
characteristics of these materials are quite different from those of cohesionless sediments and yet (due to our lack of understanding of their erosion characteristics) they are treated as cohesionless sediments in current design scour prediction equations in HEC- 18 (1993). Since the "erodibility" of these sediments can vary widely, the present approach could be overly conservative in some cases while for other cases scour depths could be under predicted. There is a clear need to improve the ability to predict design local and contraction scour depths in these types of materials.
1.2 Objective
The long-term objective of the work initiated in this proposed study is to provide a means of predicting aggradation and degradation, contraction, and local (structure-induced) sediment scour at bridge sites for the range of bed materials encountered in Florida. It is envisioned that either measurements of the bed material properties at the site or a laboratory analyses of bed material samples from the site would provide the necessary information for predicting the rates at which the material would erode as a function of flow conditions. Then, knowing the predicted ambient and design flow conditions (water velocities, depths, etc.) at the site, design scour depths can be estimated. As stated above, the bed materials to be investigated include cohesive sediments (and mixtures of cohesive and cohesionless sediments), and different types of limestone and coquina. The objectives of the present study can be summarized as follows:
1. To conduct a thorough literature and information search to determine what has been
and is being done to address this problem;
2. To obtain an overview of the sediments found in the upper 20 m of Florida's soil;
3. To design and construct two laboratory test apparatus for measuring erosion rates due
to shear flows;
4. To perform preliminary tests on field samples; and
5. To initiate a study which relates the "erosion properties" of these "non cohesionless"
sediments to properties of these materials that can be more easily measured (preferably, properties where standardized methods and procedures are already in

To establish these relationships, rate of erosion versus bed shear stress data for a range of sediments and sedimentary rock will be needed to guide and verify the theoretical work. The objectives of the second phase of the work initiated by the work reported here are as follows:
1. To obtain sediment and rock samples from a number of sites in Florida and perform
"rate of erosion" tests on these samples.
2. To continue the formulation of mathematical models relating erosion properties to
other (more easily measured) properties of the materials.
3. To use the data obtained in 1) to verify the models.
1.3 Scope and Purpose
The study was divided into two parts (Parts 1 and 2). The scope of Part 1 consisted of the following four tasks:
" Preliminary Investigation and Literature Search; Laboratory erosion testing device design; Presentation of results to FDOT;
* Summary Report.
This report summarizes those activities that were completed during Part 1, including the proposed laboratory erosion testing devices and the recommended approach for Part 2 of the study. Section 2 of this report describes the literature search that was conducted as well as the results of the search. Section 3 describes the rheological properties of cohesive sediments and rock materials that may affect the erosion rates. Section 4 describes the preliminary erosion tests and uniaxial compression tests that were performed on rock samples. Section 5 presents the basis of design of two erosion testing devices.


Two specific activities, a literature search and several site visits, were conducted during the preliminary investigation phase. Details of these activities are described below.
2.1 Literature Search
A thorough literature and information search was conducted to obtain information on the following:
" Shear stress (due to water flow) induced sediment scour in cohesive (and mixture of
cohesive and cohesionless) sediments;
* Correlations between rheological properties of cohesive sediments and their erodible
" Shear stress induced erosion of lime rock and coquina type materials with readily
measured properties of these materials; and
* Impact of suspended sand particles on the erosion rates of cohesive sediment beds.
To locate the information described above, several sources were investigated. Databases available at the University of Florida (UF) were searched and members of the UF faculty were consulted as to their knowledge of previous or similar efforts by other researchers.
An extensive database system is available through the University of Florida and the State University System (SUS) of Florida. Specifically, the following databases were searched for this project:
" GeoRef- A guide to materials and earth sciences; Cambridge Scientific Abstracts;
" GEOBASE Worldwide literature on geography and geology;
* LUIS Library information system for the University of Florida and the State
University System; and
* Journal of Rock Mechanics database.
In addition to the above databases, the Coastal Engineering Archives located in the Department of Coastal & Oceanographic Engineering at the University of Florida was also searched. The Coastal Engineering Archives contains extensive information relating to Florida's beaches and the physical processes that affect coastal areas.
As a supplement to the database search, faculty members at the University of Florida were also consulted. Faculty from the Departments of Geology, Materials Science, Engineering Mechanics, as well as Civil Engineering and Coastal & Oceanographic Engineering were consulted.
Based on a review of the available information obtained and gathered from the sources listed above during the literature search, it appears that a significant amount of work has

been performed in regards to cohesive sediment erosion. A summary of the previous work and literature search results is discussed in Section 3.
However, there appears to have been verry little research conducted in the scour of soft rock. Several articles were located that describe attempts to correlate rock erosion with stream power and an "erodibility index", but literature could not be located in which experiments were conducted to relate the properties of the rock materials and hydrodynamic shear stresses with erosion. Information regarding rock cutting with highpressure water jets has been obtained and reviewed. The search resulted in the following articles regarding the erodibility of rock:
* Erodibility (Annadale, 1995);
* On the Erodibility of Rock and Other Earth Materials (Annadale and Kirsten, 1994); Spillway and Dam Foundation Erosion: Predicting Progressive Erosion Extents
(Wittler et. al., 1995);
" Stream Bank Erosion: Application of the Erodibility Index Method (Annadale and
Parkhill, 1995);
" Preliminary Procedure to Predict Scour in Bedrock (Smith and Annadale, 1995); Preliminary Assessment of Local Scour Potential at Bridge Piers Founded on Rock
(Froehlich et. al., 1995);
* Preliminary Procedure to Predict Bridge Scour in Bedrock (Colorado DOT, 1994).
A study was located which attempted to predict bedrock scour around bridge piers through experimentation. The Canadian Hydraulics Centre (CHC) performed a laboratory experiment to evaluate the rate of erosion around proposed bridge piers founded in rock in the Northumberland Strait in Canada. The CHC attempts found that the erosion process was quite complex and as a result they were unable to reliably quantify erosion of these materials as a function of either near bed velocity or shear stress. However, the study was performed under contract to an engineering consulting firm and attempts are currently underway to obtain a copy of the report.
In addition to the above-cited work, researchers at the Oregon State University are attempting to relate rock erosion to existing geotechnical tests. An agreement to keep each other informed of our progress on these research projects has been made.
2.2 Site Visits
During the literature search process, it was discovered that several researchers have been experimenting with laboratory apparatus to measure the rates of erosion in cohesive sediments. Drs. D.M. Sheppard and A.J. Mehta of the University of Florida Coastal & Oceanographic Engineering Department (COE) made site visits to three universities from November 14 to November 19, 1997 where this research is currently being conducted. A description of the site visits is included in the Trip Report that has been included as Appendix A.

This section presents a brief discussion of those factors that may affect the rates of erosion in cohesive soils and rock materials.
3.1 Cohesive Soils
An extensive and thorough literature search and discussion on those factors affecting the erosion rates of cohesive soils is presented in a paper titled Surface Erosion of FineGrained Sediment Revisited by Mehta and Parchure. A copy of this paper is included as Appendix B.
3.2 Rock Materials
Rocks are a mixture of various solid mineral or organic grains bound together by binding agents. Typical for rocks is the presence of microcracks and pores. The inelastic properties exhibited by most rocks may be explained by the mechanisms of closure and/or opening of microcracks (and pores), and their multiplication and coalescence. In situ, the rock is subjected to a vertical load due to the weight of the overburden, to horizontal stresses, and to the stresses induced by the bridge weight. Under this stress field the rock deforms, and a progressive damage takes place. The newly created microcracks are oriented parallel to the maximum compressive stress. On the other hand, the damage evolution is influenced by the water flow. Thus, the first step towards relating the characteristic properties of the rock under the existing stress field to the erosion process is to characterize the mechanical behavior of the rock. To this end, laboratory compression tests were performed. These tests give preliminary information regarding the deformability characteristics and strength of the material. A description of the tests and the results are presented in Section 4.


Preliminary tests were performed on rock samples for an indication of the nature of the rock materials and their resistance to erosion. Samples of a lime rock material were obtained from the Florida Department of Transportation (FDOT) District 2 office in Gainesville, Florida. The samples came from borings completed to depths ranging from 80 to 100 ft below grade from a proposed bridge site (both on land and submerged) in the northwest (Panhandle) part of the state. Two types of tests were then performed:
" Uniaxial compression tests; and
" Preliminary erosion tests.
A description of these tests is given below:
4.1 Uniaxial Compression Tests
The experimental program consisted of a series of uniaxial compression tests on Florida limestone. The tests were carried out on cylindrical specimens of diameter d and height h, the aspect ratio being between 1. 19 and 1. 5. During each test both the axial strain c 1 =(10
- 1) / 10 and the lateral strain 62 = (d0-d)/do were recorded. Here, and throughout the text compressive stresses and strains are noted as positive. First, monotonic standard uniaxial compression tests were performed. The uniaxial compressive strength was found to be 1.47 MPa. To obtain information concerning the deformation and damage mechanisms in the rock, tests with several unloading-reloading cycles were conducted. Figure 1 presents the results of such a test that consists of three subsequent loading steps. Before passing from loading to unloading the axial force was held constant for a certain time interval (from 10 to 15 minutes) to allow the material to reach a quasi-stable state by creep. In this way, the hysteresis effects were practically eliminated, thus permitting an accurate evaluation of the elastic characteristics of the material. Several conclusions can be drawn from the results of these tests:
* The stress-strain curves are strongly non-linear;
* Unloading reveals the onset of irreversible strain deformnation at very small stress
levels, the yield stress being practically zero;
* Time effects are significant: upon constant load the rock creeps within minutes;
* The rock is compressible up to failure.
Under uniaxial loading conditions, microcracks oriented parallel to the axis of the specimen (parallel to the direction of the maximum applied compressive stress) form and ultimately lead to failure (axial split of the specimen).

Uniaxial Compression Test No. 3
Stress vs. Volumetric Strain

0 500 1000 1500
Strain x E-06


Figure 1. Uniaxial Compression Test on Florida Limestone
Stress vs. Volumetric Strain

180 160
140 120 100
40 20

2500 1

4.2 Preliminary Erosion Tests

In addition to the uniaxial compression tests, preliminary erosion tests were performed on samples of Florida limestone. A cylindrical sample of the limestone was cut into a cube with equal sides. The preliminary erosion tests were then performed by using a highpressure washer on different faces of the samples. The purpose of these tests was to qualitatively evaluate the resistance of the rock materials to direct hydraulic pressures and shear stresses. It was discovered that erosion of the sample occurred quickly (within a matter of minutes). However, it was also noticed that the rate of erosion varied depending on which side of the sample the test was performed. This is most likely due to the non-homogeneity of the rock materials. It appeared that the sample orientation (that is, which plane of the material is being tested) has an effect as to the erosion rate. Therefore, it will be necessary to test samples in the same orientation as they appear in the field.

Two laboratory testing devices are proposed to evaluate the rate of erosion for rock and cohesive sediments: a rotating cylinder device and an enclosed flume. A description of each of these laboratory devices and the basis of the designs are presented below.
5.1 Rotating cylinder device
The first laboratory erosion testing apparatus is the rotating cylinder device, shown in Figure 2. The purpose of this device is to generate a range of shear stresses on a sample and subsequently measure the resulting erosion rate for each shear stress. This is accomplished by placing a 1.75-in diameter by 3.5-in long cylindrical sample (the sample could be either a cohesive soil or rock sample) within an acrylic cylinder. The acrylic cylinder is between two aluminum plates with a threaded tie rod. The acrylic cylinder/aluminum plate assembly is connected to a motor that rotates the assembly freely. The sample to be tested is fastened to a hollow aluminum cylinder that is free to deform under a torque but does not rotate. The annulus between the sample and the acrylic cylinder/aluminum plate assembly is filled with water.
A motor with a variable speed drive then rotates the assembly while the sample inside the assembly remains stationary. It is anticipated that the assembly will rotate at speeds up to 3000 revolutions per minute (RPMs). As the assembly is rotating, the water inside the cylinder is also rotated as momentum is transferred from the assembly to the fluid. Once the flow has reached equilibrium a constant shear stress is applied to the face of the sample by the moving water. This shear stress will cause the face of the sample to erode. It is anticipated that the higher the shear stresses applied to the sample, the higher the erosion rates.
To measure the average shear stress acting on the face of the sample, a strain gage rosette is attached to the hollow aluminum cylinder as shown on Figure 2. The shear stress exerted by the fluid on the sample causes a torque on the sample and subsequently on the hollow aluminum cylinder. The strain gage rosette, which is four strain gages oriented along the principle planes of the aluminum tube, provide a measure of the amount of torque being exerted. By knowing the radius of the sample, the average shear stress acting on the sample face can be calculated.
To measure the erosion rate, the sample and hollow aluminum cylinder are connected to a load cell to measure the weight of the sample. Prior to initiating the test, the sample weight is obtained. As the test progresses, the weight of the sample is recorded continuously. The reduction of the sample weight is the amount of erosion of the sample.
Therefore, the rate of erosion on the sample can be obtained for the average shear stress acting on the sample face. One advantage of the rotating cylinder erosion device is that large shear stresses can be easily generated. Large shear stresses will be necessary for the harder rock materials.


Rotating Aluminum Top Pie
Threaded Tie Rods1.75 in. x3.59 in.Rock Sample
Annulus filled with fluid

- Hollow Aluminum Tube
(pipe walls shown)
Upper End Piece
3/1 6-in. S.S. Supporting Pin
Rotating Acrylic Cylinder
Lower End Piece

Rotating Aluminum Bottom platen

I Variable speed motor drive Figure 2. Rotating Cylinder Erosion Testing Device
Not to Scale 10

False Bottom with Holes to collect eroded material

A few points should be noted for this type of erosion testing device. The first point is regarding the sample size. As discussed in Section 4, the orientation of the sample is important in calculating its rate of erosion for rock materials. Specifically, it is desirable to evaluate the rate of erosion of the rock materials with respect to the same orientation to the flow as in the field. Borings collected in the field, from which samples will be taken and tested, are advanced perpendicular to the flow. To test the face of the sample that would be exposed perpendicular to the flow, smaller samples will be cored into the side of the sample. Standard boring sizes for samples are 4-in in diameter. Samples cored from the sides of the sample will be 1.75-in in diameter and 3.5-in in length.
Secondly, in order to minimize the effects of secondary flows on the shear stress applied to the test sample surface the flow regime needs to be either be fully laminar (which occurs at Taylor Numbers less than 41.3) or fully turbulent (which occurs at Taylor Numbers greater than 400). The Taylor Number characterizes the stability of rotational flows in an annulus. It is anticipated that most of the tests will occur in the fully turbulent range.
The laboratory rotating erosion device is similar to the one used by several researchers including Dr. Krone at the University of California at Davis. Appendix A contains a description of Dr. Krone's device.
5.2 Enclosed Flume Device
The second laboratory testing apparatus is the enclosed flume device, shown in Figure 3. Just as with the rotating cylinder device, the purpose of this apparatus is to generate a range of shear stresses on a sample and subsequently measure the resulting erosion rate for each applied shear stress. This is accomplished by advancing either a cohesive sediment or rock sample through the bottom of an enclosed flume with a rectangular test section. Water is then pumped through the flume section under pressure past the sample to generate a shear stress on the sample.
The size of the sample to be tested depends on the type of material being tested. Cohesive sediments will be collected or placed in a Shelby Tube (which is approximately 3-in in diameter). As described in the preceding section, the rock samples will be 4-in in diameter. The rectangular flume test section will be configured to accommodate both sizes of samples. A hydraulic or stepper motor is then used to advance the sample into the flow field of the test section. An o-ring seal will be used as a seal between either the Shelby Tube or rock sample and the test section.
The sample will be advanced at the rate needed to maintain the sample flush with the bottom wall of the rectangular test section, as shown in Figure 3. As the water is flowing past the sample, a shear stress will act of the face of the sample exposed to the flow. This shear stress will cause material to erode from the face of the sample.
The sample will be advanced and kept flush with the bottom of the rectangular test section by utilizing a hydraulic or stepper motor controlled by the average of four

PlexiGlasR Test Section
Shear stress sensors
Entrance Section

into test section directly over sample)

Exit Section


Cohesionless sediments injection port
Cohesionless sediment storage


sensor (typ.)

Cohesive soil or rock sample (cylindrical)

Hydraulic or Stepper Motor


Figure 3. Enclosed Flume Testing Device
Not to Scale

Valve (typ.)


Discharge Piping

Discharge Piping
Sediment Chamber
- Baffles Clean out

acoustic signals emitted by four piezoelectric crystals. These four crystals will be mounted flush with the top of the rectangular test section and will be situated over the top of the sample. An acoustic signal will be sent from the crystals to measure the the distance between the top of the test section and the sample surface. The resulting depths will be averaged across the sample face to obtain an average distance. As the sample erodes, the distance will increase. A feedback control system will use the signal from the crystals to control the stepper motor that advances the sample. The rate of advancement will be such that the distance remains approximately constant (i.e. the top of the test sample remains flush with the bottom of the flume. The rate at which the sample rises is the rate of erosion.
To evaluate the shear stress that is acting on the sample, the sample will be connected to a load cell as shown in Figure 3. The sample will also be connected to a pivot by the motor that will allow the sample to rotate in the direction of flow only. As the flow exerts a shear stress on the sample face, the sample will exert a force on the load cell. By "preloading" the load cell, which will calibrate the load cell for the 0-ring between the sample and the test section, the amount of load that is registered is that caused by the force exerted by the water on the sample. By knowing the area of the sample exposed to the flow, the average shear stress can be determined. A variable speed controller will be provided for the pump motor to allow for varying flows and shear stresses to be examined.
In addition, a port will be provided in the discharge piping that will allow cohesionless sediment to be injected upstream of the test section. This will allow tests to determine the effect of cohesionless sediment on erosion rates of cohesive and rock sediments.
A reservoir has also been provided with baffles to assist in settling out suspended particles. The reservoir will assist in protecting the pump from exposure to suspended sediments and therefore, increase the service life of the pump.
The advantage of the enclosed flume testing device is that it minimizes the occurance of secondary flows and more closely approximates prototype flow conditions.
This type of device is similar to the erosion testing devices being utilized at Texas A&M University and the University of California at Santa Barbara. A description of these devices is included in Appendix A.


A meeting was held on January 23, 1998 with representatives of FDOT in the FDOT's offices in Tallahassee, Florida. The purpose of the meeting was to discuss the results of the information summarized in this report. The agenda of the meeting is presented below:
1. Introduction.
Overall Problem and Objective Specific Project Problem Statement Project Team
2. Project Approach
Cohesive Soils Rock Materials
3. Preliminary Investigation Activities
- Literature Review Results
- Uniaxial Compression Tests
- Preliminary Erosion Tests
- Site Visits
4. Erosion Testing Apparatus Design
Rotating cylinder Flume
5. Discussion


Annadale, G.W. (1995) "Erodibility," Journal of Hydraulic Research. Vol.33, No. 4, 1995, 471-493.
Annadale, George W. and Hendrik A.D. Kirsten (1994) "On the Erodibility of Rock and Other Earth Materials," Proceedings from the 1994 ASCE Hydraulic Engineering Conference, Buffalo, NY, August 1-5, 1994, Vol. 1, 68-72.
Wittier, R.J., B.W. Mefford, S.R. Abt, J.F. Ruff, G.W. Annadale (1995) "Spillway and Dam Foundation Erosion: Predicting Progressive Erosion Extents," Proceedings from the ASCE First International Conference on Water Resources Engineering, San Antonio, TX, August 14-18, 1995, Vol. 2, 1011-1015.
Annadale, George W. and David L. Parkhill (1995) "Stream Bank Erosion: Application of the Erodibility Index Method," Proceedings from the ASCE First International Conference on Water Resources Engineering, San Antonio, TX, August 14-18, 1995, Vol. 2, 1570-1574.
Smith, Steven P. and George W. Annadale (1995) "Preliminary Procedure to Predict Scour in Bedrock," Proceedings from the ASCE First International Conference on Water Resources Engineering, San Antonio, TX, August 14-18, 1995, Vol. 2, 971-975.
Froehlich, David C., Tommy C. Hopkins, and Tony L. Beckham (1995) "Preliminary Assessment of Local Scour Potential at Bridge Piers Founded in Rock," Proceedings from the ASCE First International Conference on Water Resources Engineering, San Antonio, TX, August 14-18, 1995, Vol. 2, 976-980.
Colorado Department of Transportation (1994) "Preliminary Procedure to Predict Bridge Scour in Bedrock," Interim Report, Report No. CDOT-R-SD-94-14, December 1994.


Trip Report
On November 14 19, 1997, D.M. Sheppard and A.J. Mehta traveled to 1) Texas A&M University (College Station, TX), 2) University of California at Davis (Davis, CA), and 3) University of California at Santa Barbara (Santa Barbara, CA) for the purpose of reviewing existing laboratory apparatus for measuring rate of erosion in fine sediments.
Texas A&M
On the afternoon of Friday, November 14, 1997, we met with Suresh Perugu,
Ph.D. student of Professor Jean Louis Briaud and discussed his research using their rate of erosion apparatus (Erosion Function Generator, or EFG). We also visited the geotech laboratory where the erosion device is located and the hydraulics flume area where local structure-induced scour experiments in cohesive sediments had been conducted.
Texas A&M Erosion Apparatus
A schematic drawing of the EFG is given in Figure 1. The erosion apparatus consists of a straight, closed rectangular flow channel connected to a pump and fluid/sediment reservoir as shown in the figure. The channel's inside dimensions are approximately 20 cm wide by 10 cm high. The initial channel was constructed of plexiglass but this was replaced by welded aluminum because of problems with leaks under the high pressures required for the high velocity flows needed. The entrance section contains flow straightners (approximately 1.5 cm. diameter by 20 cm long aluminum pipes). The flow rate is controlled with a flow bypass valve which diverts a portion of the flow from the constant discharge pump back to the reservoir. A stepper motor lead screw device advances a cylindrical ("Shelby tube") sediment sample into the flow one millimeter at a time. The test section has clear plexiglass sides so that the surface of the sediment sample can be viewed. The test procedure is as follows:
I. The top of the sediment sample is located so as to be parallel with the bottom of
the flume.
2. The pump is started and the desired flow rate set (a paddle wheel flow meter in
located downstream of the pump and bypass).
3. The sediment samples tested to date are prepared clay mixtures. A company in
Austin, TX provides the sediment in rectangular blocks. A 3 in diameter core
sample is pushed into the block to obtain a test sample. The intent is to be able
to bring core samples from the site of interest directly to the apparatus for testing. The coring tube becomes part of the scour test apparatus and the
sediment is pushed into the test area by the stepper motor-lead screw devise.
4. The sediment sample is advanced upward one mm into the flow. A stopwatch is
used to measure the time required for the one mm to be eroded, then the core is
advanced upward one mm and the procedure repeated.

5. Since the sediment sample does not erode evenly, it is up to the person
conducting the test to determine (visually) when the average level of the
sediment surface is level with the channel bed.
6. Bed shear stress is calculated from the measured pressure drop across the test
section of the flume.
7. The data are presented in "rate of erosion" versus "bed shear stress" plots.
"Electric eye" sensors, that consisted of a horizontal light beam projected across the sample surface to a light sensor on the opposite side of the channel, were initially used for detecting when the layer was eroded. This was abandoned due to problems with the irregular shape of the eroding test sample surface.
The following morning (Saturday, November 15) we met with Professor Briaud in his office and discussed his sediment scour research program. This work is being funded by the Texas Department of Transportation and has similar objectives to ours. lHe agreed to test some of our rock samples for us so that we could obtain a better understanding of the range of shear stresses needed for our apparatus.
As noted, their initial tests have been performed with prepared sediment samples. A company in Austin, Texas prepares sediment cubes to their specifications. Their preliminary test results for cohesive sediments indicate the behavior shown in the following sketch.

Bed Shear Stress

At this point, they were not sure if the curve represents the actual behavior of the sediment being tested or if there is problems with the procedures or the methods of computing shear stress.
University of California at Davis:
From Texas A&M we traveled (flew and drove) to the University of California at Davis. There, we met with Professor Ray Krone (retired Associate Dean of Engineering). Some years ago he developed a rotating device for measuring rate of erosion of cohesive sediment samples and it is currently being used by another faculty member and his students. A schematic drawing of the device is shown in the following figure. It requires that the sediment being tested have sufficient shear strength to maintain its cylindrical shape during the test. Some of the advantages of the apparatus are 1) its relatively simple design, 2) the (average) shear stress (being applied to the surface of the sediment sample can be measured directly, and 3) it is relatively inexpensive to construct.
Rotating Rate of Erosion Apparatus:
A schematic drawing of the apparatus is shown in Figure 2. A cylindrical
sediment specimen is placed inside a larger cylinder, the annulus is filled with water and the outer cylinder rotated at a constant rpm. This subjects the outer surface of the specimen to a shear stress that can be computed from the torque exerted on the specimen. The specimen and connecting apparatus is supported by an air bearing to reduce friction and, thus, improve the torque measurement.
The procedure used to test samples is as follows:
I Obtain a cylindrical sediment sample approximately 8 cm in diameter by 12 cm
long. Note that the sediment must have sufficient shear strength to support
itself in the apparatus.
2. A hole is "drilled" through the center of the sample and two end plates attached
to the sample with a long bolt (mandrel) as shown in the figure below.
3. The sample is weighed and placed in the apparatus.
4. The annulus is filled with water (preferably from the site of the sediment).
5. The motor is turned on and the outer cylinder is made to rotate at the
predetermined rpm (or the rpm is increased until the desired average shear stress
is reached).
6. After a fixed period of time the motor is stopped and the sample removed and
weighed. The sample is then placed back in the apparatus and the process
repeated until the sample is severely eroded.
7. The rate of erosion is then computed from the weight loss versus time data.
This apparatus is relatively simple in design and cost, and can be used over a wide range of shear stresses.

University of California at Santa Barbara:

We next went to the University of California at Santa Barbara to see Professor Wilbert Lick. He has two flumes that are similar in concept and design to that of Professor Briaud at Texas A&M. They have been used in recent years to measure erosion rates in fine grained sediments. The differences in these flumes (called the "Sedfulme") and the EFG at Texas A&M are as follows:
I1. This flume has only been used for fine grained sediments and for lower shear
stresses (up to 6.4 Pa).
2. The aspect ratio (height to width ratio) of the flow channel is smaller ('-2 cm x
10 cm).
3. The sediment sample has a rectangular cross-section ('- 10 cm. wide by 7 cm
long) and spans the full width of the flume.
4. The entire channel and the rectangular sediment sample tube are constructed of
5. The shear stress is computed from pipe flow equations, not measured.
6. As with the EFG the operator visually monitors the erosion and advances the
sample up and into the flow. The attempt here, however, is to maintain the
sample surface level with the upstream bed.
7. This flume has been taken to the site (New York Harbor) in a rented trailer and
water from the stream used in a "once through" mode (i.e. the water was
discharge back into the stream).
We had a lengthy discussion with Professor Lick and his students about their experience with the apparatus and its strengths and shortcomings.
The information gathered on this trip will be most helpful in our work on this project. All of the researchers were very helpful and willing to share their experience with the design and operation of their equipment. Both designs have their strengths and weak points. The most significant problems with existing apparatus appear to be with instrumentation, i.e. 1) measurement of the shear stress applied to the sample, and 2) monitoring the rate of erosion. If one takes advantage of recent advances in instrumentation it appears that significant improvements can be made.

flow straighteners

pressure taps

sediment sample
motor for ient sample

Figure 1. Texas A&M and UC Santa Barbara Rate of Erosion Apparatuses.


sediment sample

outer housing rotates at constant rpm

Rotating Test
Figure 2. UC Davis Rate of Erosion Apparatus.


Surface Erosion of Fine-Grained Sediment Revisited

Ashish JI Mehtat and Trimbak M. Parchure+,
tCoastal and Oceanographic Engineering Department
University of Florida
Gainesville, FL 326 1 t
'Coastal and Hydraulics Laboratory
U. S. Army Engineer Waterways Experiment Station
Vicksburg, MS 39 180
U. S. A.
For applications in waters with low to moderate concentrations of suspended fine-grained sediments, the formula of KANDI.AH for the rate of bed surface erosion remains a convenient model for simulating scour due to steady or quasi-steady flows. For a given bed sediment-fluid mixture, ARULANANDAN et al. showed that the two parameters characterizing this formula, namely the erosion rate constant and the bed shear strength with respect to erosion, seem to be related in such a-way that the rate constant decreases with increasing shear strength. Other studies have shown that the shear strength correlates with bed density. We have used these findings to develop a formula for estimating the rate of erosion from bed density for sediments that are largely inorganic. While this formula cannot replace the need for laboratory or prototype testing of sediment beds for an accurate determination of erosion rate, it may be used to obtain "first CUt" values of the rate characterizing parameters in situations where they are unavailable from measurements. Recent experimental results suggest that the same formula may also be applied for estimating the rate of erosion of organic-rich sediments.
ADDITIONAL INDEX WORDS: Cohesive sediments; critical stress for erosion; mud transport; sediment resuspension.
Modeling the erosion of fine-grained sediment beds continues to pose problems largely due to a lack of clear understanding of the exact way in which the bed-water interface responds to a flowinduced stress. For steady or quasi-steady, e.g. tidal, flows numerous formulas relating the rate of surface erosion to the bed shear stress have been proposed. In this mode of erosion, particles or particulate aggregates at the bed surface are detached and entrained in the flow, thus causing bed scour. Some of the earlier formulas have been summarized by N{EHTA et al. (1982). These stressbased formulas are generally applicable to cases of low to moderate suspended sediment concentrations. At high concentrations, exceeding anywhere between 4 and 20 g/l. settling of sediment becomes hindered and is controlled by the rate of upward seepage of interstitial water. Under these conditions, a layer of fluid mud may form over the bed due to deposition of suspended

sediment. The mechanism by which this layer erodes is not modeled well by stress-based formulations. In any event, to various degrees all such formulas are empirical-phenomenological approximations of very complex flow-particle interactions, which ultimately cause bed particles and aggregates to dislodge, rupture and entrain. Among the formulas, the one proposed by KAINDIAH (1974) is
E = Em Ts (1)
in which E is the erosion rate or mass flux (mass eroded per bed area per unit time), rb is the bed shear stress, -c is the bed shear strength with respect to erosion, and the erosion rate constant, EM' is equal to the value of E when b =2r. Equation (1) is characteristically applicable to homogenous, uniform density, uniform shear strength beds, and indicates that e varies with the excess shear stress, T b- Irs. Thus, a plot of e versus rb --r ideally appears as a straight line, as shown by, among others, KAND[AH (1974) through careful experimentation on the erosion of clay and clay/silt mixtures of uniform density in a laboratory apparatus. This is shown for example in Fig. 1, in which the erosion rate and the shear strength (as determined by the intercept of each line with the horizontal axis) is seen to depend on the percentage (by weight) of montmorillonite in the Yolo loam + montmorillonite mixture. Also observe that the effect of the highly cohesive montmorillonite was to decrease EM (line slope) due to an increase in the shear strength of the mixture.
For beds that are stratified with respect to density and shear strength, formulas which account for the variation in r, with depth have been developed, e..g., by PARCHURE and MEHTA (1985). Although these formulas differ from Eq. (I), in all of them the erosion rate varies with the excess shear stress. This similarity, as well as experience from modeling applications, suggest that Eq. (1) can also be used for stratified beds with a reasonable degree of accuracy by allowing -r, to vary with depth, i.e., by replacing -c by "rj(z), where z denotes the vertical coordinate (HAYTER and MEHTA, 1986).
Recently, VINZON (1997) used measured time-series of near-bed velocities and suspended sediment concentrations at sites on the Amazon Shelf off Brazil to develop the linear plot shown in Fig. 2, which is qualitatively akin to the lines in Fig. 3, and therefore conforms to Eq. (1), but with a considerably greater scatter of data points, as would be naturally expected. The shear strength, '",, was obtained from a formula noted later. Finally, in reference to Eq. (1) it is also interesting to note that a compilation of erosion rate formulas for wind- as well as mechanically-generated waves in laboratory flumes indicates the validity of the form of Eq. (1) for wave-induced resuspension (MEHTA, 1996). This information is summarized in Table 1, in which characteristic parameters are given for the following expression
( I (2)
= EM Is

For 8 = 1, Eq. (2) reduces to Eq. (I). As seen from Table I, experimental data at times have yielded values of 8 close to unity. It should be noted that in Eq. (2),'rb is the peak value of the bed shear stress during the wave cycle, and that c, can differ from that associated with current induced erosion due to the effect of cyclic loading on the soil matrix (MAA and MEHTA, 1987; MIMURA, 1993).
For applying Eq. (1) to erosion by steady or quasi-steady flows, it is essential that -r and EM be determined for every site-specific situation. In general this process tends to be tedious in the laboratory, and more so in the field (LEE and MEHTA, 1994). It is therefore natural to ask if a generalized even though approximate, formula can be developed to assist in an initial estimation of the values of "r, and EM, particularly for those situations in which no data other than bed density are available. It appears that past studies along these lines can be helpful in this context, and in what follows the question of estimation of rs and EM has been addressed on an exploratory basis, using previous concepts and correlations.
The quantities 'r. and e,, depend on sediment composition and the stress history of the bed, and also on the chemistry and temperature of the pore and eroding fluids. An extensive review of influential factors and parameters (LEE and MEHTA, 1996; LEE et al., 1994) has revealed that over one hundred such factors/parameters have been examined in the literature. Despite this finding, significant site-specificity of conditions for erosion makes it impractical to develop multi-variate expressions relating these or fewer factors/parameters to -r, and em. For coastal and brackish water bodies BERLAMONT et al. (1993) reduced these to a total of twenty-eight. MEHTA and LI (1997) recommended six measurements: particle size distribution (of dispersed sediment), settling velocity of (non-dispersed) sediment, mineralogical composition, organic content, cation exchange capacity and salinity. These are primarily meant to characterize the bed and the fluid environment, rather than "r, and EM as such.
Shear Strength
Although shear strength and the bed density are neither uniquely related in the physical sense, nor are dimensionally homogeneous, attempts have been made to correlate these two parameters empirically, recognizing that denser the soil the harder it is likely to erode. In general, given 't as a measure of soil shear strength, as shown in Table 2 relations of the following general form have been used
where 4) is the solids weight fraction, ) is a limiting or minimum value of 4 at and below which c = 0, and are sediment-specific coefficients. Thus, according to Eq. (3) 'r depends on the excess solids weight fraction. Note that the upper Bingham yield strength (tB), the vane shear strength ("r,) and -c have all been used, although only the last is of direct interest to the present

analysis. Among these, r. and -r. are representatives of the bulk physical properties of the soil. "r. is associated with soil theology, and has been used, for example, to determine the bottom slope required to generate mud underflows (EINSTEIN, 1941). r, is a measure of the bulk strength of the soil and has been is also used, for instance, in geotechnical evaluations of cohesive soil consistency. Thus, ANNANDALE (1995) has suggested the following classification: Soil Identification Vane Shear
Consistency Strength, -cv
Very soft Easily molded by fingers. 0-80
Soft Moulded by fingers with some pressure. 80-140
Firm Very difficult to mold. Can be penetrated by hand-spade. 140-210
Stiff Requires hand pick for excavation. 210-350
Very stiff Requires power tool for excavation. 350-750
Most studies on the erosion of submerged soils in estuarine and marine environments are limited to very soft cohesive materials. This is so because wave- and current-induced bed shear stresses in these environments are usually not large enough to require testing for the of erodibility of stiffer soils. On the other hand, in rivers with high flow velocities, even firm soils can erode significantly over long durations on the order of months to years. Thus, the vane shear strength is a convenient and commonly used parameter to assess the erosion potential of cohesive soils in a given flow environment, even though it is not highly accurate (LEE, 1985).
In contrast to -rB and :,, rs is related to the strength of surface aggregates, and is a transport characterizing quantity. Referring to the results in Table 2, the characteristic difference between -r. and r, is reflected by the values of the proportionality coefficient, C', which is considerably higher for tcB (with a mean equal to 1,200, excluding the data of MIGNIOT, 1968) than for r, (10.6). Likewise, the exponent, is also higher (2.88 versus 1.62 in the mean). With respect to the sole correlation for rv we note that = I. Note however, this low value may not be representative of beds that are predominantly inorganic, because this relationship of HWANG (1989) was developed for a (lake) mud which contained a high amount of organic fraction (39% by weight).
In a strict sense, 4) should represent the volume fraction of the sediment aggregates rather than weight fraction, because the inter-particle bond strength depends primarily on the degree of space-filling by the soil matrix. The use of solids weight in lieu of aggregate volume is an approximation which is introduced to obviate the usual difficulty in estimating aggregate volume. In any event, conceptually the minimum value of 4), namely 4,, is analogous to the space-filling weight fraction at which the sediment matrix begins to exhibit a measurable shear modulus of elasticity, which increases with increasing 4) (>4,) (JAMES et al., 1988). The same "threshold" condition may apply for the development of normal effective stress in the soil (ROSS and MEHTA, 1990). HWANG (1989) determined 4),=0.06 from the plot of measured r, versus 4) and

extrapolating the linear relation ( = I) he obtained to'-r = 0 axis (when = 4,). He further showed that this value (0.06) was commensurate with the sediment density below which the mud he tested was in a fluid-like state, and therefore was devoid of measurable vane shear strength. As seen from Table 2, others did not report 4,,, which has therefore been assumed to be zero in applying Eq. (3) to their data. An example of data conforming to Eq. (3) is shown in Fig. 3, based on the work of KUSUDA et al. (1984) using mud from the Chikugo River estuary in Japan. The relationship of VINZON (1997) was used for calculating 'r, for the data presented in Fig. 2.
Two significant factors on which C, and 4,, depend are bed sediment composition and fluid chemistry. This dependence is reflected in the variability in and associated with -c, in Table 2. The relative influences of composition and chemistry cannot be sort out easily in these cases, because the shear strength of a soil of given mineral composition can be vastly influenced by the chemical composition of water. Furthermore, even though salinity is reported in most investigations on marine muds, other chemical parameters can also exert influences on the soil fabric, and hence on its erodibility. Thus, for example, Fig. 4 shows the results of KANDIAH (1974) for a montmorillonite in terms of the Sodium Adsorption Ratio (SAR), a ratio of sodium ions to the sum of calcium and magnesium ions in the bed pore fluid. The plot shows that the state of this montmorillonite could be altered between dispersed and coagulated (or flocculated) merely by changing the pH of the pore fluid either by holding SAR constant, or by holding constant the total cation concentration in the pore fluid (reported in milliequivalents per liter). Since a dispersed clay bed can erode with considerably greater ease than a coagulated bed of the same clay, KANDIAH's example shows that sediment composition alone cannot be a unique, or even dominant, determinant of bed erosion potential.
Rate Constant
The erosion rate constant, EM, generally depends on the same factors/parameters which influence -c A noteworthy effect studied in the laboratory is the variation of EM with fluid temperature. In that context, it should be noted that surface erosion of cohesive beds has been treated as a mechanism phenomenologically akin to the rate process for chemical reactions. In this concept, erosion is considered to occur when a threshold "energy of activation" is exceeded and inter-particle chemical bonds broken. Following this concept it can be shown that EM, hence the rate of erosion, E, should increase with increasing temperature in such a way that loge would vary linearly with l/T, where T is the absolute temperature. This behavior can be represented by the relation: aA
T (4)
This so-called ARRHENrUS relation was in fact shown to hold for the erosion of a bed of grundite by KELLY and GULARTE (1981), as seen from Fig. 5. The coefficients A = 34.7 and A = 10145 defining the line are specific to the sediment-fluid mixture used, and were obtained at a constant eroding flow velocity (0.18 ms'). Their magnitudes conform to the units use for e and T in Fig. 5.

Whereas A is an erosion rate scaling parameter, A characterizes the rate of decay of the erosion rate with decreasing temperature. In general, these coefficients can be expected to depend on the physicochemical properties of the sediment and fluid, on the solids weight fraction, and, especially with respect to A, on the applied bed shear stress. The ARRHEN1US plot highlights the difference in the rate of erosion as might occur between temperate waters and cooler waters in the higher latitudes. To illustrate this difference, consider water at 5C (2780K) and at 301 C (30Y K). From Fig. 5 we obtain = 33 and 730 g m'2s, respectively, which indicates a 22-fold increase in the rate of erosion due to a 25C rise in temperature. As LAU (1994) has noted, an increase in temperature affects the van der Waals attractive force at the particle surface only in a minor way, but the inter-particle repulsive force increases significantly. As a result, particle-particle bonds rupture more easily at higher temperatures, thereby leading to enhanced erosion.
Based on the observation that the rate of erosion decreases as the shear strength increases, ARULANADAN et al. (1980) defined EN = EMI[rs' and plotted it against vs derived from erosion tests on a large number of soil samples. Introducing this modified rate constant conveniently redefines Eq. (I) in terms of EN and "r., i.e., e=EN(rbd s). The investigators found that despite evident data scatter, in the mean EN decreased with "r, monotonically. This finding naturally raises the question as to whether such a correlation can be established, even though in an approximate way, using a wider set of erosion data, since it would essentially mean that, on account of Eq. (3), the sediment density (hence the solids weight fraction) would be the principal physical parameter characterizing Eq. (1). Given the convenience in modeling erosion that such a correlation would entail, this question is addressed here next.
Table 3 lists selected laboratory erosion studies, the apparatuses used and the sediment sources. Important features of the apparatuses have been'summarized elsewhere (LEE and MEHTA, 1994). An examination of the erosion rate data showed that the EN versus '7, relation of ARULANANDAN et al. (1980) could be very approximately sorted into seven groups, as shown in Figs. 6, 7 and 8 (LEE and MEHTA, 1994). The groups are arranged in such a way that for a given value of "., EN decreases with increasing group number from I to 7. The principal characteristics thought to relate significantly to bed erosion for each group are summarized in Table 4. This table provides information on bed density, clay content, total salt concentration and cation exchange capacity (CEC). While in most studies the salt concentration was the same in the bed pore fluid and the ambient eroding fluid, in many of the tests of KANDIAI (1974) as well as ARULANANDAN and coworkers, salts were confined to the pore fluid; the eroding fluid being salt-free water. Also, unlike most other studies, these investigators chose to impregnate pore water with mono- as well as di-valent cations (e.g. sodium and calcium). This meant that in many cases they used salts other than sodium chloride. In order therefore to report data from the various studies in units common to all, salt concentration is reported in milliequivalents of salt per liter of solution.
Since the mean density did not vary substantially or systematically from Group I to 7, the influence of density independently of its effect on c: was not apparently not significant. Clay content, a measure of bed cohesion along with the CEC, also did not vary substantially or systematically although. overall, clay content increased from 24% for Group I to 34% for Group 7,

which correlates with a decrease in E N in an expected way, because of increasing contribution of cohesion to erosion resistance. It interesting to note that the mean CEC did increase from 13 to 23 from Group I to 7 in a systematic way with the exception of its value for Group 2. This increase too is consistent with the observed decrease in eN. Finally, the (mean) total salt concentration showed a noteworthy effect. Thus, observe in Table 3 that the total salt concentration decreased (in the mean) from 54 meqLl for Group I to 3 meqL for Group 7. The influence of pore fluid salt on bed stability is not independent of the composition of the sediment, hence a general statement concerning the dependence of erosion rate on salt concentration cannot be made. Thus, with respect to the data in Table 3, the influence of salt concentration on EN must be viewed in tandem with changes in clay content and CEC. However, we must refrain from examining these influences further, because any quantification of correlations based on data in Table 3 alone, without considering the diversity of the experiments in terms of the influential factors/parameters not analyzed here, can lead to speculative answers. Also note that since the salt used was not sodium chloride in all cases, a common basis for comparison of the effect of salt does not occur in general.
Further in the above context, we note that numerous secondary factors/parameters may have influenced the results on erosion rate including fluid temperature (not always reported) and, as reported by ROHAN and LEFEBVRE (199 1), flow characteristic of the apparatus used to measure erosion. A tentative observation made by LEE and MEHTA (1994) was that whether the bed sample was undisturbed or remolded influenced the erosion rate, although they did not quantify the effect. In any event, it appears that the state of the bed may also play a noteworthy role in determining the rate of erosion.
The curves in Figs. 6, 7 and 8 are based on the following relation:
E= oe-zr1 (5)
for which the value of eN is conveniently chosen as 200 W Ns", and values of coefficients X and Afor each group are given in Table 4. Also given (from Table 4) are the mean values of three noteworthy properties, namely clay content, total salt concentration and CEC. In Fig. 9, portions of curves for all groups are plotted together. Each curve is essentially applicable only over the range of cs covered in Figs. 6 through 8. In any event, these curves, represented as a nomogram, highlight the wide range of values of EN that can occurs for a given v
Erosion Rate
Combining Eqs. 1, 3, 4 and 5 results in
E NTe T e(6

The application of Eq. (6) can be illustrated by the following example. Assume that the bed and fluid conditions for which E is to be calculated conform to Group 2 (Tables 4 and 5), and that the shear strength can be obtained from the relation of VILLARET and PAULIC (1986) in Table 2. Accordingly, values of the coefficient required for solving Eq. (6) will be selected as follows: rNO
- 200 g N's' ; x = 2.892; = 0.372; = 1.65; = 1.00; 1= 0; A = 27.0 and A = 10145. Now consider a bed of density p = 1,545 kg m"3 subjected to a flow-induced bed shear stress rb = I Pa at a water temperature T = 27C (=300'K). The solids weight fraction is obtained from: (0 =(P-p,,)/(p, -p,), where p, is water density. Thus, with p,, = 1,000 kg m"3 and p,= 2,650 kg m3 (Table 2), we obtain (0 = 0.33. Eq. (6) then yields E = 2.98 g rs "'. This value is comparable to what is measured in the laboratory (e.g., Fig. 1) and field (Fig. 2).
Natural incorporation of organic material into inorganic fine-grained sediment characteristically reduces the granular density of the mixture, and in the case of clays the overall effect of inter-particle cohesion is reduced, even though organic particles in aggregates are mutually bound through intertwining and by biogenic adhesives such as mucopolysaccharides.
In Table 6, erosion rate parameters from three studies are summarized. All were conducted in laboratory apparatuses using muds from water bodies in Florida. These waters receive organic sediments from a variety of sources, but the majority of material appears to be locally generated (MEHTA et aL, 1997). Observe that the exponent g of Eq. 3 is 0.2 for sediment from Lake Okeechobee with 39% organic matter (by weight). This may be compared with the mean value of 1.62 from Table 2 for largely inorganic sediment beds. The Rodman Reservoir (45% organic content) and the Lower Kissimmee River basin (50% organic content) samples showed practically no dependence of the shear strength on density. This is illustrated in Fig. 10, in which it is also seen that the mean of all data points is 0. 1 Pa, a very low shear strength in relation to its characteristic range (Fig. 9). MEHTA et al. (1994) and RODRIGUEZ et al. (1997) further observed that the erosion rate constant showed no systematic variation with shear strength, even though the rates were high (mean EN = 4.95 and 2.02 gN'ls") in relation to the range in Fig. 9.
The high erosion potential of organic-rich sediments is no doubt due to the comparatively light and weakly bound nature of the aggregates. The lack of significant dependence of erosion on bed density may be explained by the following scenario. Unlike clayey beds, whose interface with water can be reasonably well defined especially for dense beds, the organic-rich bed-water interface tends to develop a layer of "fluff consisting of aggregates released from bed. When fluid stress is applied it is this layer of weakly interconnected particles, with a low negative buoyancy, that is entrained. Further, as the layer, having a thickness on the orders of a few aggregate diameters, continues to erode it is replenished by continual generation of aggregates from within the bed as it is disturbed by flow-induced deformations. Then, since the density of the fluff layer is determined by the "released" aggregates rather than the bed, the erosion rate is largely unaffected by bed density.


Equation 6 must be used with great caution because of the inherent and possibly unquantifiable uncertainties arising from experimental measurement, as well as the effects of numerous physical, physicochemnical and biological factors associated with the sediment and the pore and eroding fluids in the natural environment. The observation, such as that of LEE and MEEHTA (1994), that remolded beds may erode differently from undisturbed ones in laboratory setups, has led to increasing reliance on in situ devices in recent times. A case in point is the Sea Carousel developed by MAA (1993), which can be lowered on to the sea bottom. Such devices, which generate their own flow field over the natural bed, tend to measure the shear strength and the erosion rate of the top, typically a few millimeter thick, layer of the bottom. This is usually adequate in comparatively low energy environments were a significant thickness of the bottom, e.g, on the order of several centimeters, does not scour. In high scour situations, e.g., due to river flows, or where wave action can intensely disturb the bottom, it becomes necessary to determine the erodibility of thick layers of the bed as a function of depth. As one approach, McNEIL et al. (1996) and JEPSEN et al. (1997) have reported erosion data obtained in a ducted flume ("Sedflume"), using sediment cores collected from field sites. The core is gradually "fed" to the flume from beneath at the same rate at which it erodes at the top. Since the flow velocity and hence the bed shear stress in the flume can be varied over a wide range, it is possible to analyze fine-grained sediment cores ranging in consistency from soft to stiff. Knowing the density profile of the core material, the parameters which characterize Eq. 6 can be determined. A limitation which cannot be easily obviated is that the coring procedure itself may affect the in situ shear strength (LEE, 1985). Although in the Sedflume fluid temperature cannot be varied, in general ducted flumes can be conveniently used to control fluid temperature, as in the case of KELLY and GULARTE (1981). This can be advantageous when dealing with samples collected from widely different water temperatures.
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Table 1 Parameters for Eq. 2 For wave-induced erosion

Investigators) Mode of wave Sediment Parameter ranges' Parameter values in Eq. 2
generation a (cm): a (rad s"'):
k (cm') e ,
(g m s"') (Pa)
Alishabi and Krone Wind Bay mud 0.9 a s 3.4 Test 1: 0.48 0.29 1.72
(1964) Test 2: 11.2 0.39 1.15
Thimakom (1984) Mechanical River mud 3.1 1 ais 12.6 = 08/2Tb Variable 1.00
0.16 s ak s 1.60
Man and Mehta Mechanical Kaolinite; 1.4 sa s 3.7 Kaolinite: 131 Depth.varying 1.15
(1987) bay mud 3.3 s s 6.3 Mud: 30 Depth-varying 0.95
Mimura(1993) Mechanical Clays; bay 0.6 s as 6.9 0.27 0.15 1.82
mud 4.8 s a 8.2
a = wave amplitude; w = wave frequency; k = wave number. b = amplitude of bottom orbital velocity; 6b = wave boundary layer thickness.

Table 2. Expressions relating a characteristic shear stress to solids weight fraction
Invesdtigator(s) Sediment Shear Strength (v) t ( Range"
Krone (1963) Estuary muds Upper Bingham yield (') N. D.6; Assume 0 466 2.55 0.008 0.57
Migniot (1968) Marine muds Upper Bingham yield (TB) N. D.; Assume 0 Variable 4.00 0.094 -0.19
Owen (1970) Estuary mud Upper Bingham yield (rB) N. D.; Assume 0 1.110 2.33 0.042-0.11
Vinzon (1997) Shelf mud Upper Bingham yield (r') N. D.; Assume 0 2,024 2.62 0.021 0.19
Hwang (1989) Lake mud Vane (?,,) 0.06 22.6 1.00 0.060 0.26
Thorn and Parsons (1980) Estuary muds Surface erosion ( Ts) N. D.; Assume 0 37.5 2.28 0.014-0.12
Kusuda et al. (1984) Estuary mud Surface erosion (T ) N. D., Assume 0 6.50 1.60 0.032-0.11
Villaret and Paulic (1986) Bay mud Surface erosion (Ts) N. D.; Assume 0 1.65 1.00 0.10 0.38
Black (1991) Estuary mud Surface erosion (Ts) N.D.; Assume 0 1.88 2.30 0.13 0.25
Berlamont et al. (1993) Marine muds Surface erosion ( T) N. D.; Assume 0 5.41 0.90 0.02 0.07
SUse p, = 2,650 kg m for converting (0 to density, p, except for the relation of Hwang (1989), for which p, = 2,140
kgm .
I Not defined.

Table 3. Summary of selected erosion experiments. Investigaor(s) Apparatus
Espey (1963) Rocuing cylinder
Pautheniades (1965) Straight flume
Christensen and Das (1973) Drill-hole device
Raudkivi and Hutchison (1974) Closed conduit
Kandiab (1974) Rotating cylinder
Arulanandan et al. (1973) Rotating cylinder
Arulanandan et al. (1975) Rotating cylinder
Gularte eat al.. (1977) Closed conduit
Fukuda (1978) Annular flume
Thorn and Parsons (1980) Straight flume
Anlanandan et al. (1980) Straight flume and rotating cylinder
Gularte et al. (1980) Closed conduit
Villaret and Paulic (1986) Annular flume
Hwang (1989) Annular flume
Winterwerp et al. (1993) Straight flume and annular flume

Sediment Mari
Bay mud Knolinite Kaolinite
Loam; clays; bay mud: mixtures Loam
River mud Lake mud River and bay muds Various soils Grundite and silt Kaolinite; estuary mud Lake mud
Kaolinite; estuary mud

Table 4. Characteristics of selected data groups
Group lied Densily. p Clay Content Total Sail Concentration Cation Exchange Capacity
No. (kgm.') (%) (neqL)b (mc1Wq/100 g)
Range Mean S. D.d Range Mean S. D. Range Mean S. D. Range Mean S.D.
I (7)' 1,440-2.270 1,910 460 5-53 24 16 1-205 54 87 9-20 13 4
2(16) 1,420-20,80 1,730 170 12-46 27 12 2-145 27 42 7-28 18 6
3(34) 1,480-1,860 1.670 160 6-50 28 10 4-40 19 7 9-23 15 5
4(20) 1,270-1.990 1,820 210 12-42 23 10 1-205 31 64 8-30 IS 5
5(26) 1.350-2.090 1,820 200 11-53 27 II 2-205 22 42 8-26 15 5
6(23) 1,070-2,240 1,740 310 6-80 33 26 2-33 7 9 8-25 16 6
7(26) 1,100-2,400 1,730 380 6-94 34 19 1-6 3 2 5-100 23 23
' Numbers within parentheses are number of data points.
b milliequivalents per liter.
'milliequivalents per 100 grams of sample.
' Standard deviation.

Table 5. Coelficient values for Eq. 5 and main characteristics of Groups 1-7
Gioup No. Coefficients in Eq. 5' Mean Clay Mean Total Mean Cation
Content Salt Exchange
(%) Concentration Capacity

I 1.345 0.368
2 2.892 0.372
3 3.905 0.356
4 4.938 0.355
5 6.594 0.382
6 9.011 0.386
7 10.582 0.252
'These values of X and I apply when T, is in Pa and EN is in gN's-'.

54 27 19
31 22 7 3

(meq/100 g)
13 18
15 15

Table 6. Erosion parameters for organic-rich sediments. Location/Invesigator(s) Organic Mixture ( ( Eiosion Rate Constant, eN Range
Fraction Granular (gN's ')
by Weight Density, p,
(%) (kgm ') Mean S.D.
Lake Okecchobee (llwang, 1989) 39 2,140 0.06 1.0 0.2 N. i. N. I. 0.06 -0.17
Rodman Reservoir (Meita ci al., 1994) 45 1,914 N. D.;)4 Assume 0 0.105 0 4.95 8.0 0.02 0 28
Lower Kissimamee River iasian (Rodriguez et al., 1997) 50 1,586 N. D.; Assume 0 0.099 0 2.02 10.1 0.08 0.38
' Not included in this table; see Table 3.


0 2 4 6 8
Shear Stress, rb(Pa) Figure 1. Erosion rate versus bed shear stress for mixtures of Yolo loam and montmorillonite. Percents indicate montmorillonite (by weight) (adapted from Kandiah, 1974).
Amazon Shelf Mud
3.5 ------------- -- O .... --
-. . . . ... .....- . . ... . . . .
'3 ------------1 -----------
0 0 -------------------a2.5 o----o
0 0 0
2 0
S : o ------------0
0.5 -- -- -------------10-------0oo00
0 0.05 0.1 0.15 0.2
Excess Shear Stress, rb-, (Pa) Figure 2. Erosion rate versus excess bed shear stress based on field data analysis reported by Vinzon (1997).

Water Content (%)


0.02 1
0.03 0.05 0.1 0.2
Solids Weight Fraction, $ Figure 3. Bed shear strength versus solids weight fraction (and water content) for Chikugo estuary (Japan) mud (after Kusuda et al., 1984).
S30 opH4-5 Montmorillonite
~ 30 opH4-5
+ pH 6.5 7.5
5 pH 10 11
a 20
.2 Dispersed
'* 15
5 Coagulated
0 10 20 30 40 50
Total Cation Concentration (meq L )
Figure 4. Coagulation-dispersion boundary curves for a montmorillonite at three pH ranges (after Kandiah, 1974).

o e/T = exp(A-A/T)
S* A = 34.7 A = 10145

0.0032 0.0033 0.0034 0.0035 0.0038
Inverse Temperature I/T (*K') Figure 5. Arrhenius plot for a grundite (after Kelly et al., 1980).

0 10 20 30 40 50 60 70
Bed Shear Strength, :, (Pa) Figure 6. Erosion rate constant versus bed shear strength for Group 1 data.

2xl 02
, 10
o o
S10 **o* Group2
& ** Group 3
.4 10 x
p group 4
Group 5 x
0 2 4 6 8 10
Bed Shear Strength, ', (Pa) Figure 7. Erosion rate constant versus bed shear strength for Groups 2, 3, 4 and 5 data.
-- 10
z I
0 0*
Fi3r 8. osio Iaecntn essbdsersrnt o Groups n
a: *
a 10 si Group 6
soo w 02roup 7
0 0.5 1 1.5 2
Bed Shear Strength, r, (Pa)
Figure 8. Erosion rate constant versus bed shear strength for Groups 6 and 7 data.

1 ----.........
o ---- -0---2
0 2 4 6 8 10
Bed Shear Strength-, (Pa) Figure 9. Erosion rate constant versus bed shear strength nomogram.
0.12-o 0 +
01 %+ +0 Mean of AUData
q+ +
0.08 ++
*1 + +
. 0.04 o: Rodman Reservoir
+: Lower Kissimmee River
0 0.1 0.2 0.3 0.4 0.5
Solids Weight Fraction, (0 Figure 10. Erosion shear stress versus solids weight fraction for organic-rich sediment samples.