BRIDGE SCOUR IN BED MATERIALS OTHER THAN COHESIONLESS
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
D. MAX SHEPPARD
COASTAL AND OCEANOGRAPHIC ENGINEERING DEPARTMENT
UNIVERSITY OF FLORIDA
TABLE OF CONTENTS
LIST OF FIGURES............................................................................ ii
1.1 Problem Statem ent..................................................... ..........1
1.2 O bjective..................................................... ....... ............. 1
1.3 Scope and Purpose..................................................... ..........2
2. PRELIMINARY INVESTIGATION .................................................. 3
2.1 Literature Search..................................................... ............
2.2 Site V isits..................................................... .................... 4
3. RHEOLOGICAL PROPERTIES AFFECTING EROSION RATES..........5
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......................................................
5. EROSION TESTING DEVICES................................. ...............9
5.1 Rotating Cylinder Device.................. ........................................9
5.2 Enclosed Flume Device ........ ................................... ......... 11
6. FDOT MEETING...................................................................14
APPENDIX A TRIP REPORT
APPENDIX B SURFACE EROSION OF FINE GRAINED SEDIMENT
LIST OF FIGURES
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.
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
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 theological 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
2. PRELIMINARY INVESTIGATION
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
* Shear stress (due to water flow) induced sediment scour in cohesive (and mixture of
cohesive and cohesionless) sediments;
* Correlations between theological 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 very 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 high-
pressure 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 ofRock 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
* 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
3. RHEOLOGICAL PROPERTIES AFFECTING EROSION RATES
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 Fine-
Grained Sediment Revisited by Mehta and Parchure. A copy of this paper is included as
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.
4. PRELIMINARY TESTS
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 e1 = (10
- 1) / 10 and the lateral strain s2 = (d0-d)/d0 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 deformation 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 2000
Strain x E-06
Figure 1. Uniaxial Compression Test on Florida Limestone
Stress vs. Volumetric Strain
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 high-
pressure 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
5. EROSION TESTING DEVICES
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
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 Rods --
1.75 in. x 3.59 in.
Annulus filled with fluid
Hollow Aluminum Tube
(pipe walls shown)
Upper End Piece
3/16-in. S.S. Supporting Pin
" Rotating Acrylic Cylinder
Lower End Piece
Rotating Aluminum Bottom platen
Variable speed motor drive
Figure 2. Rotating Cylinder Erosion Testing Device
Not to Scale
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
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
Shear stress sensors
iii .i" ii:i :
Removable bottom L -_ _
sediment storage ,
on Sample Advancement
4 Crystals (imbedded into test section directly over sample)
r Exit Section
Shear stress sensor (typ.) P
4|-- Load cell
SCohesive soil or
Hydraulic or Stepper Motor
Figure 3. Enclosed Flume Testing Device
Not to Scale
<'~ ~ 5,-' -
I _:_ ..
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 "pre-
loading" the load cell, which will calibrate the load cell for the o-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
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.
6. FDOT MEETING
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
Overall Problem and Objective
Specific Project Problem Statement
2. Project Approach
3. Preliminary Investigation Activities
Literature Review Results
Uniaxial Compression Tests
Preliminary Erosion Tests
4. Erosion Testing Apparatus Design
Annadale, G.W. (1995) "Erodibility," Journal of Hydraulic Research. Vol.33, No. 4,
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.
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
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:
1. The top of the sediment sample is located so as to be parallel with the bottom of
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. He 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
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:
1. 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
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:
1. 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
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.
Figure 1. Texas A&M and UC Santa Barbara Rate of Erosion Apparatuses.
Figure 2. UC Davis Rate of Erosion Apparatus.
Surface Erosion of Fine-Grained Sediment Revisited
Ashish J. Mehtat and Trimbak M. Parchure.
tCoastal and Oceanographic Engineering Department
University of Florida
Gainesville, FL 32611
'Coastal and Hydraulics Laboratory
U. S. Army Engineer Waterways Experiment Station
Vicksburg, MS 39180
U. S. A.
For applications in waters with low to moderate concentrations of suspended fine-grained sediments,
the formula of KANDIAH 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
ADDITIONAL INDEX WORDS: Cohesive sediments; critical stress for erosion; mud transport; sediment
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 flow-
induced 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 MEHTA et al. (1982). These stress-
based formulas are generally applicable to cases of low to moderate suspended sediment
concentrations. At high concentrations, exceeding anywhere between 4 and 20 g/1, 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 KANDIAH
e= E( -T (1)
in which E is the erosion rate or mass flux (mass eroded per bed area per unit time), tb is the bed
shear stress, t~ is the bed shear strength with respect to erosion, and the erosion rate constant, E,,
is equal to the value of E when Tb=2 :,. Equation (1) is characteristically applicable to homogenous,
uniform density, uniform shear strength beds, and indicates that E varies with the excess shear stress,
b- t,. Thus, a plot of e versus rb ideally appears as a straight line, as shown by, among others,
KANDIAH (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 E6
(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 ', with depth have been developed, e..g., by PARCHURE and MEHTA (1985).
Although these formulas differ from Eq. (1), 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 rs to vary with
depth, i.e., by replacing T, by t,(z), where z denotes the vertical coordinate (HAYTER and
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, t,,
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
( = 'tb (2)
For 6 = 1, Eq. (2) reduces to Eq. (I). As seen from Table 1, experimental data at times have yielded
values of 6 close to unity. It should be noted that in Eq. (2), vb 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 -t 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 t, 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 rt and eM has been addressed on an exploratory basis, using
previous concepts and correlations.
EROSION SHEAR STRENGTH AND RATE CONSTANT
The quantities tr 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 Ts 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.
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 "r as a
measure of soil shear strength, as shown in Table 2 relations of the following general form have been
r = e4)> (3)
where 4 is the solids weight fraction, 4, is a limiting or minimum value of 4 at and below which
- = 0, and (, ( are sediment-specific coefficients. Thus, according to Eq. (3) t depends on the
excess solids weight fraction. Note that the upper Bingham yield strength (tg), 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, tr and tV are representatives of the bulk physical properties of the soil. T
is associated with soil theology, and has been used, for example, to determine the bottom slope
required to generate mud underflows (EINSTEIN, 1941). rv 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, tv
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 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 T,
and Tc is reflected by the values of the proportionality coefficient, C, which is considerably higher
for T (with a mean C equal to 1,200, excluding the data of MIGNIOT, 1968) than for r, (10.6).
Likewise, the exponent, 4, is also higher (2.88 versus 1.62 in the mean). With respect to the sole
correlation for tv we note that ( = 1. 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 (), 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 ,) (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 t, versus 4 and
extrapolating the linear relation (( = I) he obtained to v = 0 axis (when ( = ()). 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 ),, 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 t' for the data presented in Fig. 2.
Two significant factors on which C, 4 and 4 depend are bed sediment composition and fluid
chemistry. This dependence is reflected in the variability in C and ( associated with v, 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.
The erosion rate constant, M,, 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 E,, hence the rate of erosion,
e, should increase with increasing temperature in such a way that loge would vary linearly with 1/T,
where T is the absolute temperature. This behavior can be represented by the relation:
S= eT (4)
This so-called ARRHENIUS 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, 4, and,
especially with respect to A, on the applied bed shear stress. The ARRHENIUS 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 (278K) and at 30'C (303 K).
From Fig. 5 we obtain E = 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 = EM/s, and plotted it against "^ derived from erosion
tests on a large number of soil samples. Introducing this modified rate constant conveniently
redefines Eq. (1) in terms of eN and T,, i.e., E=EN(-b-s). The investigators found that despite
evident data scatter, in the mean eN decreased with ts 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 ts 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 r,, E decreases with increasing group number from 1 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 KANDIAH (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 1 to 34% for Group 7,
which correlates with a decrease in eN 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 1 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 meqL"' for Group 1 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 (1991), 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:
EN = EN0e
for which the value of eN0 is conveniently chosen as 200 g N''s"', and values of coefficients x and
X for 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 1 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 r .
Combining Eqs. 1, 3, 4 and 5 results in
e = ENOTe 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: ENO
= 200 g N's' ; x = 2.892; = 0.372; C = 1.65; ( = 1.00; 1,= 0; A = 27.0 and A = 10145. Now
consider a bed of density p = 1,545 kg m'' subjected to a flow-induced bed shear stress rb = I Pa at
a water temperature T = 27C (= 3000K). The solids weight fraction is obtained from:
40 =(P-P,)/(P, -P,), where p, is water density. Thus, with P, = 1,000 kg m"3 and p,= 2,650 kg m'3
(Table 2), we obtain t = 0.33. Eq. (6) then yields e = 2.98 g mrs '. 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 S 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 Ea = 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, physicochemical 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 MEHTA
(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 I Parameters for Eq. 2 For wave-induced erosion
Investigators) Mode of wave Sediment Parameter range Parameter values in Eq. 2
generation a (cm); ( (rad s'"):
k (cm') e t,
(g ms'') (Pa)
Alishahi and Krone Wind Bay mud 0.9 s a s 3.4 Test 1: 0.48 0.29 1.72
(1964) Test 2: 11.2 0.39 1.15
Thimakorn (1984) Mechanical River mud 3.1 s us 12.6 = CJ 1t,' Variable 1.00
0.16 s ak 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 ( 6.3 Mud: 30 Depth-varying 0.95
Mimura (1993) Mechanical Clays: bay 0.6 s a s 6.9 0.27 0.15 1.82
mud 4.8 s rs 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
investigators) Sediment Shear Strength (r) 40' C( Range"
Krone (1963) Estuary muds Upper Bingham yield (tB) N. D."; Assume 0 466 2.55 0.008 0.57
Migniot (1968) Marine muds Upper Bingham yield (T,) N. D.; Assume 0 Variable 4.00 0.094 -0.19
Owen (1970) Estuary mud Upper Bingham yield (Tr) N. D.; Assume 0 1,110 2.33 0.042- 0.11
Vinzon (1997) Shelf mud Upper Bingham yield (tB) N. D.; Assume 0 2,024 2.62 0.021 0.19
Hwang(1989) Lake mud Vane (T,) 0.06 22.6 1.00 0.060 0.26
Thom and Parsons (1980) Estuary muds Surface erosion(T) N. D.; Assume 0 37.5 2.28 0.014-0.12
Kusuda etal. (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 ('T) N. D.; Assume 0 1.65 1.00 0.10-0.38
Black(1991) Estuary mud Surface erosion (T,) 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 mi" for convening ( to density, p, except for the relation of Hwang (1989), for which p, = 2.140
b Not defined.
Table 3. Summary of selected erosion experiments.
Espey (1963) Roaing cylinder
Parheniades (1965) Straight flume
Christensen and Daa (1973) Drill-hole device
Raudkivi and Hutchisoa (1974) Closed conduit
Kandiab (1974) Rotating cylinder
Arulanandan et al. (1973) Rotating cylinder
Arlanandan et al. (1975) Rotating cylinder
Gularte et al.. (1977) Closed conduit
Fukuda (1978) Annular flume
Thorn and Parsons (1980) Straight flume
Alanandan et al. (1980) Straight flume and rotating cylinder
Gularte et al. (1980) Closed conduit
Vilaret and Paulic (1986) Annular flume
Hwang (1989) Annular flume
Wincrwerp et al. (1993) Straight flume and annular flume
- -- --------
Loam: clays; bay mud: mixtures
River and bay muds
Grundite and silt
Kaolinite; estuary mud
Kaolinite; estuary mud
Table 4. Characteristics of selected data groups
Group Bed Densily, p Clay Content Total Sail Concentration Cation Exchange Capacily
No. (kgm') (%) (nwqL')b (1mq/100 g)'
Range Mean S. 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. Coefficient values for Eq. 5 and main characteristics of Groups 1-7
Group No. Coefficients in Eq. 5' Mean Clay Mean Total Mean Cation
Content Salt Exchange
(%) Concentration Capacity
1 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'.
Table 6. Erosion parameters for organic-rich sediments.
Locaiion/Invesigatoi(s) Organic Mixture Elosion Rate Comtant, eN 4 Range
Fraction Granular (gN's ')
by Weight Density, p,
(%) (kg ') Mean S. D.
Lake Okecchobee (Hlwang, 1989) 39 2,140 0.06 1.0 0.2 N. I. N. I. 0.06 -0.17
Rodman Reservoir (Mclta ci al., 1994) 45 1,914 N. ).; Assume 0 0.105 0 4.95 8.0 0.02 0 28
Lower Kissimamee River Uasin (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, b (Pa)
Figure 1. Erosion rate versus bed shear stress for mixtures of Yolo loam
and montmorillonite. Percent indicate montmorillonite (by weight)
(adapted from Kandiah, 1974).
Amazon Shelf Mud
3.5 ------------- --........... ............... .. ..-- --
3 -------------1 ----------- --- ----_
2 0 --------------------------
0 0 0
S" t .--------- ---- -------------- .0 ----------- ------
o i : o
g o-^<. --_ o -- :- -:
0 0.05 0.1 0.15 0.2
Excess Shear Stress, b-,, (Pa)
Figure 2. Erosion rate versus excess bed shear stress based on field data
analysis reported by Vinzon (1997).
Water Content (%)
0.03 0.05 0.1 0.2
Solids Weight Fraction, 4
Figure 3. Bed shear strength versus solids weight fraction (and water
content) for Chikugo estuary (Japan) mud (after Kusuda et al., 1984).
z 30. opH4-5
S+ pH 6.5 7.5
S5 pH 10 -11
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).
Se/T = exp(A-A/T)
A = 34.7 A = 10145
0.0032 0.0033 0.0034 0.0035 0.0038
Inverse Temperature 1/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.
2 "\ x xGroup 4
SGroup 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.
3 10 Er si Group 6
a .t. group 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
0 2 4 6 8 10
Bed Shear Strength, ;, (Pa)
Figure 9. Erosion rate constant versus bed shear strength nomogram.
0.12 0 o
0. % + +o Mean of All Data
-7 0.1 -o -- -
S + +
2 0.04- o: Rodman Reservoir
+: Lower Kissimmee River
0 I I I
0 -------'------- -------> -----i---
0 0.1 0.2 0.3 0.4 0.5
Solids Weight Fraction, (
Figure 10. Erosion shear stress versus solids weight fraction for organic-rich