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Performance report on the simulator of erosion rate function

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Title:
Performance report on the simulator of erosion rate function
Series Title:
Performance report on the simulator of erosion rate function
Creator:
Ganju, Neil K.
Place of Publication:
Gainesville, Fla.
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Coastal & Oceanographic Engineering Dept. of Civil & Coastal Engineering, University of Florida

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University of Florida
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UFL/COEL-2000/011

PERFORMANCE REPORT ON THE SIMULATOR OF EROSION RATE FUNCTION
by
Neil K. Ganju Kevin M. Barry and
Ashish J. Mehta

September, 2000
Submitted to:
U.S. Army Engineering Research and Development Center Waterways Experiment Station 3909 Halls Ferry Road Vicksburg, MS 39180




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1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE 3. REPORT TYPE AND DATES COVERED
September, 2000 Final Report 2/12/99 5/15/00
4. TITLE AND SUBTITLE 5. FUNDING NUMBERS
PERFORMANCE REPORT ON THE SIMULATOR OF EROSION DACW39-99-P-0238
RATE FUNCTION
6.AUTHOR(S) Neil K. Ganju UF# 4511363-12
Kevin M. Barry
Ashish J. Mehta
7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATION
Coastal and Oceanographic Engineering Program REPORT NUMBER
Civil and Coastal Engineering Program UFL/COEL-2000/011
University of Florida
Gainesville, FL 32611
9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSORING/MONITORING
U.S. Army Engineering Research and Development Center AGENCYREPORTNUMBERS
Waterways Experiment Station
3909 Halls Ferry Road
Vicksburg, MS 39180
II. SUPPLEMENTARY NOTES
12a. DISTRIBUTION/AVAILABILITY STATEMENT 12b. DISTRIBUTION CODE
13. ABSTRACT (Maximum 200 words) Numerous rotating cylinder devices have been constructed to simulate the erosion characteristics of cohesive sediments. Typically, these devices consist of a rotating outer cylinder, which is filled with the chosen eroding fluid. A remolded or intact sample in the shape of a smaller cylinder is placed into the outer cylinder. While rotating, the outer cylinder imparts rotation to the fluid. which translates into a shear stress being uniformly imparted to the sample. The torque applied to the sample is measured and converted to the corresponding shear stress. Erosion of the sample follows, and a relation is obtained between shear stress and erosion rate. A rotating cylinder device the Simulator of Erosion Rate Function (SERF) was constructed and it's performance tested. SERF consists of an rotating acrylic outer cylinder filled with eroding fluid, and an inner stationary cylinder which holds the sample between brackets. A torque cell is connected to the stationary cylinder via a shaft, and measures the applied torque. A load cell connected in turn to the torque cell measures the weight of the sample. SERF was initially tested with aluminum cylinders representing dummy samples to calibrate for shear stress, following which three commercial types of ceramic clay samples were tested. Each sample was run by step-increasing the rpm and the loss in sample mass was recorded over each time-step. A relation (erosion rate function) between erosion rate and shear stress was obtained for the sample. The erosion rate function was found to be linear or piece-wise linear, depending on the degree of uniformity of the sample. Furthermore, increasing shear strength correlated with increasing density for all three clay types.

14. SUBJECT TERMS 15. NUMBER OF PAGES
31
16. PRICE CODE
17. SECURITY 18. SECURITY 19. SECURITY 20. LIMITATION OF ABSTRACT
CLASSIFICATION OF REPORT CLASSIFICATION OF THIS CLASSIFICATION OF PAGE ABSTRACT

NSN 7540-01-280-5500

Standard Form 298 (Rev. 2-89) Prescribed by ANSI St. Z39-18 298-102




UFL/COEL-2000/011

PERFORMANCE REPORT ON THE
SIMULATOR OF EROSION RATE FUNCTION
By
Neil K. Ganju Kevin M. Barry and
Ashish J. Mehta

Submitted to:
U.S. Army Engineering Research and Development Center
Waterways Experiment Station
3909 Halls Ferry Road, Vicksburg, MS 39180
Coastal and Oceanographic Engineering Program
Civil and Coastal Engineering Department
University of Florida Gainesville, FL 32611

September, 2000




SUMMARY
Numerous rotating cylinder devices have been constructed to simulate the erosion characteristics of cohesive sediments. Typically, these devices consist of a rotating outer cylinder, which is filled with the chosen eroding fluid. A remolded or intact sample in the shape of a smaller cylinder is placed into the outer cylinder. While rotating, the outer cylinder imparts rotation to the fluid, which translates into a shear stress being uniformly imparted to the sample. The torque applied to the sample is measured and converted to the corresponding shear stress. Erosion of the sample follows, and a relation is obtained between shear stress and erosion rate. A rotating cylinder device the Simulator of Erosion Rate Function (SERF) was constructed and it's performance tested. SERF consists of an rotating acrylic outer cylinder filled with eroding fluid, and an inner stationary cylinder which holds the sample between brackets. A torque cell is connected to the stationary cylinder via a shaft, and measures the applied torque. A load cell connected in turn to the torque cell measures the weight of the sample.
SERF was initially tested with aluminum cylinders representing dummy samples to calibrate for shear stress, following which three commercial types of ceramic clay samples were tested. Each sample was run by step-increasing the rpm and the loss in sample mass was recorded over each time-step. A relation (erosion rate function) between erosion rate and shear stress was obtained for the sample. The erosion rate function was found to be linear or piecewise linear, depending on the degree of uniformity of the sample. Furthermore, increasing shear strength correlated with increasing density for all three clay types.
This work was supported by funds from The U.S. Army Engineering Research and Development Center, Waterways Experiment Station, Vicksburg, MS, through contract DACW39-99-P-0238.




TABLE OF CONTENTS
S U M M A R Y .................................................................................................... 2
L IST O F FIG U R E S ........................................................................................... 4
L IST O F T A B L E S ............................................................................................. 5
L IST O F S Y M B O L S .......................................................................................... 6
SECTIONS
1. In tro du ctio n ................................................................................................ 8
2. SE R F C haracteristics ...................................................................................... 8
3. SE R F C alibration .......................................................................................... 9
4 S E R F T estin g ............................................................................................. 1 1
5 S E R F R esu lts ............................................................................................. 13
6. C oncluding C om m ents ................................................................................... 15
7 R eferen ce s ................................................................................................ 17
APPENDIX USER'S MANUAL FOR SERF .......................................................... 19
A 1. SE R F C alibration ..................................................................................... 19
A 1. 1 T orque C ell C alibration ................................................................... 19
A .1.2 L oad C ell C alibration ...................................................................... 19
A 1.3 Shear Stress C alibration ................................................................... 20
A .2. Sam ple Preparation .................................................................................. 22
A .3. S am ple T esting ....................................................................................... 23




LIST OF FIGURES

2.1 Schem atic of SERF assem bly ..................................................................... 24
2.2a Front-view of SE R IF .................................................................................. 24
2.2b Photograph of acrylic outer cylinder and measurement cells .................................. 25
3.1 Calibration curve for large aluminum cylinder (dia. = 7.6 cm) ................................ 25
3.2 Calibration curve for medium aluminum cylinder (dia. = 7.2 cm) ............................. 26
3.3 Calibration curve for small aluminum cylinder (dia. = 6.8 cm) ............................... 26
3.4 Calibration curve for bottom disk ................................................................. 27
5.1 Erosion rate as a function of shear stress for clay type #10 .................................... 27
5.2 Erosion rate as a function of shear stress for clay type #20 .................................... 28
5.3 Erosion rate as a function of shear stress for clay type #75 .................................... 28
5.4 Erosion rate as a function of shear stress for clay type #10, with differing pore
fluid (tap w ater vs. saline w ater) ..................................................................... 29
5.5 Erosion rate as a function of shear stress for clay type #20, with differing pore
fluid (tap w ater vs. saline w ater) .................................................................... 29
5.6 Erosion rate as a function of shear stress for clay type #75, with differing pore
fluid (tap w ater vs. saline w ater) .................................................................... 30
5.7 Erosion rate constant as a function of shear stress for clay type #75 ........................ 30
5.8 Shear strength as a function of dry density for three clays ...................................... 31




LIST OF TABLES
5.1 Density, erosion rate constant, and shear strength values obtained for 15 clay
sam p le s ................................................................................................ 14




LIST OF SYMBOLS
A surface area (M2)
FT applied tangential force (kg)
R inner cylinder radius (m)
Re Reynolds number (-)
RPM revolutions per minute
T torque (kg-m, g-cm)
Ta Taylor number (-)
U annular peripheral velocity (mis)
d annular gap width (m)
g acceleration due to gravity (m/s2)
Am, change in dry sediment mass (kg)
r radius (m)
At time interval (s)
a empirical coefficient, Eq. 5.3 (-)
P3 empirical coefficient, Eq. 5.3 (-)
XS empirical coefficient, Eq. 5.2 (-)
E erosion rate (kg/m2-s)
EN erosion rate constant (kg/N-s)
ENO maximum erosion rate constant (kg/N-s)
As empirical coefficient, Eq. 5.2 (-)
p sediment bulk density (kg/m3)
Pd dry density (kg/m3)




PI pore fluid density (kg/m3)
pi fluid mud density (kg/m3)
ps sediment granular density (kg/m3
r shear stress (Pa)
Tb sample shear stress (Pa)
rs shear strength (Pa)
v kinematic viscosity (m2/s)




PERFORMANCE REPORT ON THE
SIMULATOR OF EROSION RATE FUNCTION
1. Introduction
Numerous rotating cylinder devices have been constructed to simulate the erosion characteristics of cohesive sediment (Moore and Masch, 1962; Arulanandan et al., 1975; Croad, 198 1; Chapuis and Gatien, 1986). Lee and Mehta (1994) have provided a brief summary of the underlying design-and-operation concept. Typically these devices consist of a rotating outer cylinder, which is filled with the chosen eroding fluid A remolded or intact sample in the shape of a smaller cylinder is placed into the outer cylinder. While rotating, the outer cylinder imparts rotation to the fluid, which translates into a shear stress being uniformly imparted to the sample. The torque applied to the stationary sample is measured and converted to the corresponding shear stress. Erosion of the sample follows, and a relation (erosion rate function) is obtained between erosion rate and shear stress. The device requires calibration to convert the torque into an applied shear stress, as well as some method to measure the eroded mass. For the unit developed and tested, i.e., the Simulator of Erosion Rate Function (SERF), dummy aluminum cylinders were used to calibrate for the shear stress via the attached torque cell. A load cell allowed the eroded mass to be measured without removing the sample assembly from the outer cylinder. The inclusion of the load cell is an improvement over previous devices, which required removing either the sample or fluid to measure eroded mass. Three types of commercial clays were tested to gauge the performance of the SERF.
2. SERF Characteristics
Figure 2.1 shows the schematic of the SERF, and Figs. 2.2a,b show photographic views. The clay sample is molded into a cylinder with a diameter of 7.6 cm and a height of 9.6 cm. The cylinder is impaled on a shaft which secures an upper and a lower disk of equal diameters to the




two ends of the sample. The upper end of the shaft affixes to an Omega (Stamford, CT) model TQ201-10OZ torque cell, which is in turn connected to an Omega model LC601-5 load cell. When the acrylic outer cylinder is rotated, the chosen eroding fluid imparts a torque to the sample, and in turn the shaft and torque cell. The cell is connected to an Omega model DP25-S LED (light-emitting diode) display, and shows the applied torque in g-cm. The load cell is attached to the entire shaft/torque cell/sample assembly, and can be used to measure mass eroded after a given run. This unit can move vertically out of the outer cylinder for sample and water replacements.
The outer cylinder is capable of rotating at a maximum of 2,350 rpm, and a minimum of 150 rpm. The torque cell has a 1,800 g-cm capability, and the load cell can accommodate a maximum of 2.3 kg.
3. SERF Calibration
The torque cell is calibrated using an aluminum ring which affixes to the shaft of the cell. A two-point calibration is done using no load, and then with a 1,000 g weight hanging from the ring, which has a radius of I cm. This results in a calibration between 0 and 1,000 g-cm. The load cell is calibrated in the same two-point fashion, using a 1,000 g weight hung from the cell.
The calibration to convert torque into shear stress requires running the device with dummy samples. The SERF was run with three aluminum cylinders of varying diameter and identical height. The varying of diameters provides a relationship between the applied torque and the sample radius, considered to be necessary in instances when the radius of a sample decreases measurably during testing. For a given cylinder, the SERF was rotated from a standstill to a "reasonable" speed (up to 1,600 rpm) in time-step increments, and torque readings were taken at each rpm value, after steady-state was reached (typically within 3-5 seconds). Once at peak rpm,




the device was slowed in time-step increments and torque readings were taken again. This procedure was done three times for each cylinder, the shaft and cylinder being removed and reinstalled each time in order to gauge the precision of the device after re-installment of samples. The bottom disk of the sample holder was also tested in this manner. By subtracting the bottom disk torque from the total torque, the torque applied to the sample area only can be obtained. The meniscus must be located just below the upper disk (Fig. 2.1), so the fluid is acting on the cylinder and the bottom disk. It is sometimes necessary to add or remove water to obtain an appropriate meniscus.
A trendline was plotted for the variation of torque with rpm for the disk, and the corresponding relation (Eq. 3. 1) was used to determine the torque provided by only the sample area of the cylinder, by subtracting the bottom disk torque (Fig. 3.4) from the overall torque. This adjusted torque value was converted into shear stress using Eqs. 3.2 and 3.3: T =0.O86RPM 1 (3.1)
FT=T (3.2)
r
*r=gFT (3.3)
A
where T is the torque reading in kg-in (g-cm for Eq. 3. 1), r is the cylinder radius in m, FT is the applied tangential force in kg, r is the shear stress in Pa, g is the acceleration due to gravity in m/s 2, and A is the cylinder surface area in M2 The shear stress values were then plotted versus rpm to yield calibration curves for three cylinders (Figs. 3.1, 3.2, 3.3). The spread in data is attributed to slight, inevitable changes in the alignment of the cylinders with respect to the




central axis, due to the removal and re-installment of the shaft/cylinder assembly between runs. This procedure of removal/re-installment was carried out in order to identify the degree of precision of the device. Overall, the small and large cylinders followed a power fit, and the medium cylinder followed a linear trend (Figs. 3.1, 3.2, 3.3). Fitting a power function to the medium cylinder resulted in overestimation of shear stress at high rpm (>1,000).
For the large, medium, and small cylinder, respectively, the following relations were obtained:
- = 4.9 x 10-6 RPM1' (3.4)
,t = 4.7 x 10-3RPM 1.32 (3.5)
= 8.0 x 10.8 RPM263 (3.6)
As an illustration of the differences among the above relations, note that a 10% decrease in surface area from the small cylinder to the large cylinder leads to a 67% increase in shear stress at an rpm of 1,000 for the small cylinder. This results from the decreased moment arm of the small cylinder leading to an increased tangential force and therefore increased shear stress.
4. SERF Testing
Once the relation of shear stress to rpm was determined, clay samples could be tested for their erosion rate as a function of applied shear stress. Three ceramic clays were obtained from Bennett Pottery Supply (Orlando, FL), #10, #20, and #75. The company did not provide any information concerning the compositions of these clays. In any event, each clay was molded to




two different bulk densities (both lower than initial) by adding tap water and working by hand. This procedure was repeated twice, resulting in four densities tested for each clay. A third set was prepared by molding two equal amounts of clay with water, one with tap water and another with 35 ppt salt (sodium chloride) water. Water was added in equal amounts to yield a similar density. Since the clays arrived with existing pore water, the actual salinity of the pore water was less than 35 ppt.
The first set of clays was shaped into cylinders of the same diameter as the medium cylinder, hence the medium cylinder calibration curve was used. The second set of samples was shaped into the diameter of the large cylinder, as was the third set. The volume and surface area of each sample was known, and the mass of the sample was determined by weighing the sample with the bracket and lid (Figs. 2.1, 2.2b), and weighing only the bracket and lid. This provided the density of each respective sample.
Once a sample was prepared it was lowered into the outer cylinder, and the load cell was zeroed. After 5 to 15 minutes of rotation at a given rpm, the device was stopped and allowed to rest for approximately one minute. The time-step was chosen based on observation of the erodibility of a given sample during the previous time-step. In most cases the maximum speed was 1,500 rpm. Above this speed, the possibility of mass erosion (i.e., large class being eroded) was present, which could have resulted in an imbalance and excessive torque, thereby damaging the torque cell. After reaching steady-state, the load cell displayed the loss in material in grams.
The load cell displayed the loss of sediment as well as the internal pore fluid which was also released. Since the load cell is measured buoyant mass, only the mass loss of solids was being displayed. If the pore fluid were assumed to be of similar density as the eroding fluid, then




the load cell displayed the loss of dry sediment mass. This value, along with the time-step and the surface area resulted in the erosion rate:
A ms (4.2)
where Ams is the dry sediment mass loss, A is the sample area in in2, and At is the time interval in seconds.
5. SERF Results
Eighteen clay samples were tested in total, and erosion rate as a function of shear stress was obtained (Figs. 5.1 through 5.6) for all but three samples (#2, 9, and 15) whose erosion was undetected by the load cell. Linear (or piece-wise linear) trendlines were fitted to each set of results with the following form:
6 = EN rT- TO) (5.1)
where c is the erosion rate in k g/rn -s, r, is the sample shear strength in Pa, EN is the erosion rate constant in kg/N-s (=e when Trb = 2 r,), and Trb is the shear stress, also in Pa Table 5. 1).
The composite plots (Figs. 5.1 through 5.6) for each clay show a general trend towards increasing shear strength with increasing density for all three clays. For the case of saline pore fluid versus fresh pore fluid, the saline samples tended to have greater erosion rates at the same shear stress than the fresh samples, thus implying a loss of soil strength due to the addition of sodium chloride. Unfortunately, because clay compositions were not available, an explanation for this effect of sodium chloride cannot be deduced. Some of the results show a two-line trend as opposed to a single-line trend. This Type 1/Type 2 erosion phenomenon (Mehta, 1981) possibly results from the non-uniformity of the sample, whereby the erosion rates are not constant between different density zones of the sample. The hand-molding of the clay samples




likely left a surface layer of non-uniform and possibly lower density than the interior of the sample in these cases.
Table 5.1. Density, erosion rate constant, and shear strength values obtained for 15 clay samples
Sample Density, p EN (kg/m2-s) T, (Pa)
#, type (kg/m3)
1, 1Of 1665 5.00 x 105 3.14
3, 1Of 1710 1.91 x 10-5 3.38
4, 1Of 1859 1.23 x I05 4.49
5, 10s 1928 1.73 x 10-5 0.60
6, 1Of 1928 1.20 x 10.5 1.67
7, 20f 1435 3.93 x 10-5 1.93
8, 20f 1537 1.19 x 10-5 2.81
10, 20f 1721 7.72 x 10.5 3.02
11,20s 1894 1.73 x 10. 1.58
7.00 x1 I___O____12, 20f 1905 7.10 x 10-6 2.00
13, 75f 1675 4.80 x 10.5 1.39
14, 75f 1698 3.217 x 10.5 1.73
16, 75f 1806 1.14 x 10.5 1.76
3.20 x 10-5,
17,75s 1940 6.89 x 10-5 3.27
18, 75f 1963 9.85 x 10-6 1.88
Note: s indicates saline pore fluid, f indicates tap water pore fluid
The erosion rate constant is plotted versus shear strength (Fig. 5.7) for one set of tests
with clay #75, and the trend in this case follows the fit provided by Mehta and Parchure (2000).
The equation contains two empirical coefficients and is represented as
EN = ENO exp (-z/s ) (5.2)
where ENO is selected to be 0.2 kg/N-s based on the analysis of Mehta and Parchure, and Zs = 7.45
and A, = 0.5 are obtained as best-fit values.




The shear strength of each sample was plotted versus the dry density, and a fit of the following form (Mehta and Parchure, 2000) was applied to each clay type (#10, #20, #75): r = aO(pd-pI/ (5.3)
where a and )6 are empirical coefficients, pd is the dry density in kg/m3, and pi is 64 kg/m3 (selected to represent the dry density of fluid mud with no shear strength). The dry density was calculated from the mass balance
Pd = P-Pf A (5.4)
For the #10 and #20 clays, a = 3.20 x 103, and /3=1, and for #75, a = 1.30 x 10-3, and f=l were obtained (Fig. 5.8).
It should be pointed out that the selected group of samples did not erode enough to significantly decrease the sample radius, and only one cylinder calibration curve was used for each sample. For example, sample #6, with a bulk density (wet) of 1928 kg/m3, lost a total of 3 g during the entire test. This corresponds to a reduction in thickness of 0.007 cm, or 0.18% thickness lost (based on large cylinder volume).
6. Concluding Comments
A comment is in order concerning the operating speed range of SERF, the generation of Taylor vortices in the annular gap between the outer cylinder and the sample, and the development of turbulence in this gap. When a certain Reynolds number has been exceeded in the gap between two rotating concentric cylinders, vortices appear in the flow. The axes of these vortices are along the circumferences of the cylinders, and they rotate in alternately opposite




directions (Schlichting, 1968). The Taylor number is used to predict the formation of these irregularities, and is defined as
To= Udd (6.1)
v R
where U is the peripheral velocity of the cylinder, d is the gap width, R is the inner cylinder's radius, and v is the kinematic viscosity of the fluid. Taylor vortices are formed in the range 41.3 With the characteristic Reynolds number defined as Ud
Re = (6.2)
V
using a peripheral velocity of 0.8 m/s and the same fluid and gap width, Re=18,880 is obtained. The SERF is typically operated above this speed, and in these tests the lowest Re attained was 100,000 at a speed of 4.3 m/s (at 800 rpm). Operating above the Taylor vortex regime and above the laminar flow regime, one can expect a comparatively uniform distribution of shear stress over the sample surface area.
The SERF is capable of producing coherent results on the rate of sample erosion as a function of applied shear stress, even with small amounts of erosion (tenths of a gram). It should be feasible to use the apparatus to test a variety of cohesive samples, both intact from the field and remolded. The inclusion of a load cell directly attached to the apparatus considerably reduces the time necessary to obtain results, and ensures accuracy by not requiring periodic




removal and weighing of the sample assembly. The device is operated at sufficiently high Reynolds numbers (>100,000 at 800 rpm) to ensure a comparatively uniform shear stress distribution.
With regard to the clay samples tested the following conclusions can be drawn:
1. Linear and piece-wise linear erosion rate functions were observed for three types of
commercial clays,
2. The clays displayed a general trend toward increasing shear strength with density,
3. The use of saline pore fluid resulted in a greater erosion rate constant than samples
prepared with tap water.
A user's manual for SERF is included as Appendix.
7. References
Arulanandan, K., Loganathan, P., and Krone, R.B., 1975. Pore and eroding fluid influences on
surface erosion of soil. Journal of Geotechnical Engineering Division, ASCE 101 (1), 51
66.
Chapuis, R.P., and Gatien, T., 1986. An improved rotating cylinder technique for quantitative
measurement of the scour resistance of clays. Canadian Geotechnical Journal, 23(1), 8387.
Croad, R.N., 1981. Physics of erosion of cohesive soils. Ph.D. Thesis, University of Auckland,
New Zealand.
Lee, S.C. and Mehta, A.J., 1994. Cohesive sediment erosion. Report DRP-9406, U.S. Army
Engineer Waterways Experiment Station, Vicksburg, MS, 12-15.
Mehta, A.J., 1981. A review of erosion functions for cohesive sediment beds. Proceedings of the
First Indian Conference on Ocean Engineering, Vol. 1, Madras, 122-130.




Mehta, A.J. and Parchure, T.M., 2000. Surface erosion of fine-grained sediment revisited. Muddy
Coast Dynamics and Resource Management, B. W. Flemming, M.T. Delafontaine, and
G. Liebezeit, eds., Elsevier, Oxford, UK (in press).
Moore, W.L., and Masch, F.D., Jr., 1962. Experiments on the scour resistance of cohesive
sediments. Journal of Geophysical Research, 67(4), 1437-1449.
Schlichting, H., 1968. Boundary-Layer Theory, 6th edition, McGraw-Hill, New York, 500-503.




APPENDIX-USER'S MANUAL FOR SERF

A. I SERF Calibration
The SERF requires three calibrations: torque cell calibration, load cell calibration
and shear stress calibration.
A. 1. 1 Torque Cell Calibration
Remove the torque cell by unscrewing the single hex screw which connects the
torque cell to the load cell (Fig. 2. 1). Use caution in handling the torque cell, which can be damaged if over-torqued. Secure the torque cell base to a horizontal surface with a vise, keeping the shaft of the torque cell aligned in the horizontal direction. Place the 1 cm radius ridged collar (provided with the apparatus) around the shaft, and tighten the collar hex nut so it secures to the shaft without rotating. Secure a loop of string to the collar; tighten it to prevent rotation. Follow the Omega-provided calibration instructions for the light-emitting diode (LED) display (Omega DP25-S), applying zero load for the 0% point, and a 1 kg mass for the 100% load. The readout will now display torque in gcm in the range of 0-1000 g-cm. To ensure proper calibration, secure an intermediate mass to the string, and the display should show the corresponding torque (500 g load should result in a 500 g-cm torque). Remove the load, string and collar, and set the torque
cell aside.
A. 1.2 Load Cell Calibration
Remove the load cell by unscrewing the two vertical hex screws at the rear of the
cell. Secure the load cell horizontally with a vise. Loop a string through the hole at the end of the cell. Securing the load to the end of the string, follow the provided calibration instructions for the LED display, applying zero load for the 0% point, and 1 kg for the




100% point. Since SERF is only concerned with small mass changes, the load cell does not have to be calibrated above I kg. If smaller changes in mass are anticipated, the cell can be calibrated to 500 g or less, and the decimal point can be moved for higher resolution ( 0. 1 gram finest resolution). Decimal point movement is explained in the LED display manual. Replace the load cell with the two hex screws, and replace the torque
cell, tightening slowly.
A. 1.3 Shear Stress Calibration
Attach the chosen aluminum cylinder to the shaft, securing it between the upper
and lower disks/brackets (Fig. 2. 1). The lower bracket should be flush with the shaft, and the upper bracket should tighten onto the cylinder. Screw one of the two hex nuts onto the upper portion of the shaft, so it tightens against the top of the upper bracket. Tighten with an adjustable monkey wrench. Screw the other nut onto the shaft, approximately two cm above the lower nut. Place the plastic lid (Fig. 2.2b) onto the assembly, and screw the shaft into the torque cell, twisting counter-clockwise slowly, until the shaft rests at the internal roof of the torque cell (The shaft will halt at the roof). Screw the upper nut counter-clockwise so it locks against the torque cell. DO NOT OVERTIGHTEN! The nut should be tightened until it just stops turning, no further. For maximum care, twist the torque cell by hand in the opposite (clockwise) direction to minimize the torque being applied to the cell. By keeping the LED display on, one can observe how close the cell is
to being over-torqued.
Fill the outer cylinder to approximately 1/3 of it's volume with the chosen eroding
fluid (e.g., fresh water). Lower the cylinder/bracket assembly into the outer cylinder by loosening the four rear-facing adjustment arms. The assembly should be brought to rest




on the square collar on the back of the post. Tighten the adjustment arms. Fill with more water until the upper bracket is just submerged.
Slowly spin the outer cylinder counter-clockwise (forward setting) at less than 400 rpm and observe the meniscus. A level meniscus is desired. Four horizontal screws (Fig. 2.2b) can be loosened to move the assembly left and right, and four vertical screws (Fig. 2.2b) can be loosened to move the assembly forward and back. Small alignment changes tend to affect the meniscus considerably. After the assembly is centered, the height of the meniscus should be adjusted so at a given rpm the meniscus is just below the upper bracket while spinning. It is ideal to start with a lower level at low rpm, and to add water as the rpm increases and the meniscus lowers.
Begin taking readings after setting the torque cell at zero rpm. Increase the speed in time-step increments, allowing the torque cell to reach steady-state before recording the torque value. Once at desired peak rpm (2,350 rpm is attainable, below 1,600 rpm is prudent), reduce the speed in increments and record torque values. Once this procedure is completed raise the assembly, loosen the shaft upper nut (clockwise), and unscrew the shaft from the torque cell (clockwise). Reattach the shaft and repeat the above procedure. Three runs in this manner are sufficient to obtain the mean trend.
To obtain the calibration for the bottom disk, remove all of the water, and repeat the above procedure, keeping only the bottom disk submerged at every rpm step. After obtaining a torque versus rpm trendline, at each selected rpm subtract the bottom disk torque from the cylinder torque. The residual torque is thus adjusted for the added stress effect of the bottom disk.




By dividing the adjusted torque readings by the radius of the cylinder, the
corresponding tangential force (in kg-multiply by g for N) is obtained. Dividing this quantity by the surface area (in 2 ) yields the shear stress in Pa. For each cylinder tested, plot shear stress versus rpm and obtain the required calibration curves by drawing a mean
trendline through the data points.
A.2. Sample Preparation
Whether using an intact field sample or a remolded sample, the sediment must be
in the shape of one of the three cylinder sizes so the obtained calibration curves can be applied. In addition, the volume of the sample must be known so it's density can be
measured.
Attach the selected aluminum cylinder to the bracket assembly as described in
Section A.1.3, and then remove the bottom disk and the aluminum cylinder. This is necessary to place the upper bracket at the correct elevation. Impale the sample on the shaft. Screw the lower bracket to the end of the shaft, until the shaft is flush with the bottom of the disk. Plastic sheeting, cut to the height and circumference of the cylinders, is provided with the apparatus to wrap the sample and ensure the sample has the correct volume. Trim with a putty knife any extra mass before weighing. Place the plastic lid on the assembly over the top of the shaft. Weigh the entire assembly. The bracket/lid combination can be weighed later to provide the weight of only the sample. This weight
divided by the volume gives the (wet) bulk density of the prepared sample.
In the same manner mentioned in Section A. 1.3, secure the assembly to the torque
cell.




A.3. Sample Testing
Fill the outer cylinder about 1/3 with the chosen eroding fluid. Lower the
assembly into the outer cylinder to the collar level. Add water under the lid until the upper bracket is just flush with the water level. In this case the exact water level is not very important as long as the sample is fully submerged. The shear stress on the sample will be independent of the water level, as long as the entire sample is being acted on by
the fluid.
Secure the black torque cell wire to the rear post using a strip of tape, so the load
cell is not affected by it's movement. Zero the load cell. Wait until fluctuations are no
more than 0. 1 g before starting rotation.
Rotate the outer cylinder at a given rpm for a given time-step. At the end of the
time-step, stop the device. The load cell usually takes one minute to reach a steady-state, and then it reads the mass lost during that time interval. Using Eqs. 4.1 and 4.2, the erosion rate can be determined. The rpm value can be converted to a shear stress via the
calibration curves.




Rotating Acrylic Cylinder
10. 16 cm ID Upper Disk
0.476 cm. S.S. Supporting
Shaft
7.61 cm x 10. 16 cm Cohesive Sediment
Sample
Bottom Disk

Variable speed motor drive

Figure 2. 1. Schematic of SERF

Figure 2.2a. Front-view of SERF showing the rotating cylinder assembly, speed control panel (lower left) and digital readouts (lower right) for the torque cell and the load cell




Figure 2.2b Photograph of acrylic outer cylinder and measurement cells supported by a vertical member

0 200 400 600 800 1000
RPM
Figure 3.1. Calibration curve for large aluminum cylinder (dia.=7.6 cm)

1200 1400




6
- 5 (L
0
I
0200 400 600 800 1000
RPM
Figure 3.2. Calibration curve for medium aluminum cylinder (dia.=7.2 cm)
C. 4
3

'U
1
0
0 200 400 600 800
RPM
Figure 3.3. Calibration curve for small aluminum cylinder (dia.=6.8 cm)

1200 1400

1000




0 200 400 600 800 1000 1200 1400
RPM
Figure 3.4. Calibration curve for bottom disk

*#1 rho=1665 kg/mA3 #3 rho=1710 kg/m^3 X #4 rho=1859 kg/mA3

0 1 2 3 4 5
Shear Stress (Pa)

6 7 8 9

Figure 5.1. Erosion rate as a function of shear stress for clay type #10

1.80E-04 1 .60E-04 1.40E-04 1.20E-04 1.00E-04 8.00E-05 6.00E-05 4.00E-05 2.00E-05 0.00E+00




1.40E-04 1.20E-04 1.00E-04 8.00E-05 6.00E-05 4.00E-05 2.00E-05 0.OOE+00

0 1 2 3 4 5 E
Shear Stress (Pa)

Figure 5.2. Erosion rate as a function of shear stress for clay type #20

Oz
01 2 3 4 5
Shear Stress (Pa)

#13 rho=1675 kg/m^3 S#14 rho=1698 kg/m^3 X #16 rho=1806 kg/m^3

Figure 5.3. Erosion rate as a function of shear stress for clay type #75

*#7 rho=1435 kg/m^3
*#8 rho=1537 kg/m^3 S#10 rho=1721 kg/m^3

1.80E-04 1.60E-04 1.40E-04 1.20E-04 1.00E-04 8.00E-05 6.00E-05 4.00E-05 2.OOE-05 O.OOE+00




1.20E-04 1.00E-04 8.00E-05

* #10 fresh
6.00E-05
t- 15#10 saline
.0
m 4.00E-05
I-1
2.00E-05
0.00E+00 .
0 1 2 3 4 5 6 7 8
Shear Stress (Pa)
Figure 5.4. Erosion rate as a function of shear stress for clay type #10, with differing pore fluid (tap water vs. saline)

1.20E-04 1.00E-04 8.00E-05 6.00E-05 4.00E-05 2.00E-05 O.OOE+00

*#20 fresh M #20 saline

0 1 2 3 4 5 6
Shear Stress (Pa)

Figure 5.5. Erosion rate as a function of shear stress for clay type #20, with differing pore fluid (tap water vs. saline)




2.00E-04 1.80E-04
1.60E-04 1.40E-04 1.20E-04 1.00E-04 8.00E-05 6.00E-05
4.00E-05 2.00E-05 0.00E+00

Shear Stress (Pa)4 5 6 7
Shear Stress (Pa)

Figure 5.6. Erosion rate as a function of shear stress for clay type #75, with differing pore fluid (tap water vs. saline)
1.20E-04 1.00E-04

8.00E-05 6.00E-05
4.00E-05 2.00E-05

* #75 fresh S#75 saline

U.UUt+UU
1 1.2 1.4 1.6 1.8 2
Shear Strength (Pa)
Figure 5.7. Erosion rate constant as a function of shear strength for clay type #75




4
a
CD
CI)
0 .. . .
0 200 400 600 800 1000 1200 1400 1600 1800 2000
Dry Density (kg/m3) Figure 5.8. Shear strength as a function of dry density for three clays