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TRACTIVE FORCE STUDIES OF COHESIVE SOILS FOR DESIGN OF EARTH CANALS

by

E. J. Carlson P. F. Enger

Presented at the Eleventh Hydraulics Division Conference of the American Society of Civil Engineers

Davis, California

August 15-17, 1962

HYDRAULICS BRANCH

OFFICIAL FILE COPY

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TRACTIVE FORCE STUDIES

OF COHESIVE SOILS

FOR DESIGN OF EARTH CANALS

by

E. J. Carlson and P. F. Enger

A paper to be presented

at the Eleventh Hydraulics

Division Conference of the American Society of Civil

Engineers, Davis. Califor­nia, August 15-17, 1962

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TRACTIVE FORCE STUDIES OF COHESIVE SOILS FOR DESIGN OF EARTH CANALS

by E. J. Carlsonl / and P. F. Enger2 /

SYNOPSIS

The Bureau of Reclamation is conducting studies to establish better design criteria for earth lined and unlined canals in cohesive soil materials. Disturbed and undisturbed soil samples were taken from 46 test reaches on Bureau canals which had been in operation for a number of years. The samples were tested in the laboratory to determine dry densities., gradations, Atterberg limits.,, compaction characteristics., and vane shear values. A tractive force apparatus was developed in the laboratories and tests were made to determine critical hydraulic shear or tractive force values on 8-inch undis­turbed soil samples.

Soil characteristics were related to the critical hydraulic shear or tractive force values by a system of multiple linear correlations using an electronic digital computer. The best correlations of var­ious arrangements of independent variables (soils characteristics) with the dependent variable (hydraulic shear or tractive force) and details of the tests including the testing apparatus are given. Exam­ples showing how the critical tractive force for a cohesive soil is determined using the multiple linear correlations are included.

I/ Head., Sediment Investigations Unit., Hydraulics Branch., Division of Engineering Laboratories ., Bureau of Reclamation., Denver., Colorado. 2 /Hydraulic Engineer., Hydraulics Branch., Division of Engineering Laboratories., Bureau of Reclamation., Denver ., Colorado.

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INTRODUCTION

In 1950 the Bureau of Reclamation began an investigation of methods of improving the design of unlined canals constructed in earth mate­rials. (1), 1 / A method for designing stable· channels was developed which wasoased on distributing the tractive forces along the side slopes and bottoms of the channels > so that the force magnitude at all points on the perimeter would be sufficiently large to pr·event sedi­ment deposits in objectionable quantities and small enough to pre� vent objectionable scour. The method included the determination of channel slopes in coarse noncohesive materials which would result in a minimum of excavation. (2) Prior to this study, canals in earth materials were designed using limiting velocities as the main cri­teria. A summary of this work is given in Reference (3).

A similar method may be used in the design of canals in cohesive soils when the safe tractive force for the cohesive material can be determined. The distribution of tractive forces around the perim­eter of canals is considered, but the rolling down effect and angle of repose of particles on the side slopes is not applicable for cohe­sive materials. The main factors considered are the cohesion of the particles and the critical tractive forces for the cohesive mate­rials. (4)(5)(6)

The purpose of this paper is to present a method for determining tractive force values which can be used in the design of canals in cohesive materials.

Smerdon and Beasley( 7) made a study relating the critical trac­tive forces of 11 cohesive soil samples, measured in a 2. 5-foot hydraulic flume, with plasticity index, dispersion ratio, mean par­ticle size, and percent clay. They concluded that "the problem ·of the stability of open channels in cohesive soils can logically be approached on the basis of the tractive force theory." For the soils tested_, Smerdon and Beasley maintained--''the critical trac­tive force is best correlated with the plasticity index and the dis­persion ratio, although excellent correlation also exists with the mean particle size and percent clay. 11 Correlations were made using only two variables at a time.

Moore and Masch(B) made tests on cohesive earth materials to determine spour resistance from hydraulic forces. Their tests were made with a water jet impinging on the surface of ,a 5-inch circular sample submerged in a 3-foot-square tank. They assumed

1 /Numerals i-n parentheses--thus (l)--refer to-corresponding items in the Bibliography. - -. · . ·. . · -

the depth of scour to be proportional to the logarithm of the time of exposure and developed other relationships for depth of scour and a proportionality constant which was a measure of the rate of scour. Plots from their scour tests showed the proportionality factor to be related to the logarithm of the Reynolds number of the jet. Different ratios of height of jet to diameter of jet were used. The soil var­iables were lumped into a single constant called 11the scour resist­ance of the sediment, 11 and this single constant was related with the hydraulic variables. A rotating cylinder test apparatus for making scour tests was described, but no test results were given.

Dunn(9} studied the resistance to scour of cohesive ·soils using (a} a hydraulic jet flowing vertically downward on a soil surface and (b) a vane shear test on operating canal surfaces and on laboratory samples taken from the field. He determined the relationship between the critical hydraulic shear stress of the cohesive soil samples and the soil strength determined from the vane shear tests. He indicated that the vane shear strength, and consequently the crit­ical hydraulic shear stress, varied with the percent of fine parti­cles in the samples, the plasticity index, and the logarithmic prob­ability characteristics of the particle size curves. He concluded that (a} the most accurate method of estimating critical hydraulic shear stress, for soils with plasticity index between 5 and 16, is by use of his derived formula which includes the term "plasticity index, 11 (b} that predictions of critical tractive forces for cohesive soils can be based on the percent of silt and clay in the soil when the soil contains sand, and (c} that ''correlation of soil properties with grain size gave good results in this investigation because the effect of changes in strength due to differences in chemical and mineral-' ogical content, and due to differences in soil structure, are accounted for by the vane test. 11

EXPERIMENTAL WORK AND DATA OB TAINED F ROM FIELD TEST SITES

Data Obtained

The 46 test reaches selected on canals and laterals of varying size and discharge were located in five of the seven regions of the Bureau of Reclamation. A search was made in each case to locate a straight reach of canal in cohesive soil. From each of the selected test reaches soil samples were obtained for making lab­oratory tests. The samples included disturbed samples, 3-inch drive tube samples, 8-inch undisturbed hand cut samples, and deposited sediment samples (in the reaches where deposition had occurred). The disturbed soil samples were used to determine gradation, plastic properties, and the compaction characteristics

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of the soil materials. The 3-inch drive tube samples were used in unconfined compression tests. The 8-inch hand cut soil samples were used as erosion test specimens.

During operation at near peak discharge of the canals and laterals the following data were obtained from the test sections: canal water surface slopes; canal cross sections at the middle of the reach; velocity contours at the middle of the reach including veloc­ities near the canal boundary; amount of sediment being carried in suspension; temperature of the water; and shear resistance of the bank and bottom of the canal in place and in saturated condition. The shear resistance was determined by the vane shear tester shown in Figure 1. (10)

Photographs were made of each test reach showing the condition of the channel, both when it was flowing at near peak discharge and when there was no water in the test reach.

Water surface slopes were obtained using a water surface gage ., Figure 2, and an engineer's level. Velocity measurements were made using a Type A current meter. A pigmy-type current meter was used to measure velocities near the boundary. A DH-48 hand sediment sampler was used for obtaining samples of suspended sediment flowing in the canal.

Records of the highest sustained flow (maximum sustained dis­charge) for each year in each test section for a period of several years, were obtained from the project offices. It was assumed that the maximum sustained discharge would produce the most severe erosion or would expose the earth material to the most severe hydraulic forces. Cross sections of each canal test reach were obtained and used to determine whether the original shape had changed during operation.

Tractive Force Testing Apparatus

A laboratory tractive force testing apparatus was developed to measure tractive forces of undisturbed samples of soil material obtained from each of the test reaches. Appendix I describes the equipment and procedures used to determine critical tractive forces of cohesive materials. The critical tractive force values obtained were used as the dependent variable in analyzing the results of this study.

The tractive force apparatus includes a 35-inch-diameter tank, a variable speed air motor, a transparent lid, impeller blades., pressure gage, and a pressure regulator. An 8-inch round sat­urated soil sample is placed in the tank with only the surface

exposed on the bottom of the tank ., and covered with 12 inches of water. The impeller is started ., and rotating slowly, forces water to flow across the sample to create a tractive force of low value on the soil sample. After subjecting the sample to a low initial trac-­tive force for 3 minutes., the speed of rotation is increased and the corresponding increased tractive force is allowed to act on the soil for another 3 minutes. This procedure is repeated ., raising the speed of rotation in steps, until erosion begins. The speed of rotation of the impeller in revolutions per minute is recorded at the time erosion begins. Incipient erosion is judged by observa­tion through the transparent tank lid. The tractive force occur­ring on the surface of the sample, in terms of the velocity of rota­tion of the impeller in revolutions per minute was determined from calibration curves explained in Appendix I. Notes on the behavior of the soil undergoing the test and sketches of the eroded area are made when the sample has reached a point of general erosion. Photographs of the soil sample before and after the test are taken for comparison purposes. After completion of the erosion test ., soil density and vane shear strength are determined for the sample in the saturated condition. Mechanical analysis and standard soils Atterberg limits tests are also made on the same soil sample.

The tractive force developed when general erosion of the soil sam­ple begins is considered to be the critical tractive force ., and is the value used in the analysis presented in this paper.

Standard Soils Characteristics

Soil tests, including plasticity index ., liquid limit ., density, grada­tion factors, shrinkage limit, and percent maximum density were performed in conformance with procedures presented in the First Edition of the Bureau of Reclamation Earth Manual, July 1960. (11) Results are summarized in Table 2. Unconfined compression tests were performed on a few samples but the test results indicated that sufficient additional information could not be obtained to justify continuing this test. Density values (Column 4, Table 2) were obtained from the tractive force test specimens after they had been subjected to erosion tests in the tractive force machine. Vane shear values (Column 10 ., Table 2) were obtained using a vane shear apparatus having a four-bladed vane 4 inches high and 2 inches in diameter ., Figure 1. (1 0) Vane shear tests were also performed on tractive force test specimens after the erosion tests were completed.

Mechanical Analysis of Soils

The logarithmic probability analysis was used to explain the grada­tion of the soils. In this statistical method. the particle size

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distribution is assumed to follow a logarithmic normal probability curve. Mechanical analysis of soils can be described by deviations from this curve.

A special graph ruling, developed in the Bureau of Reclamation, provided a simple and rapid method of determining soils charac­teristics in relation to the logarithmic normal probability curve. By plotting a standard soils size analysis on the special graph paper, values of M (J, a- VJ, and k' (/J are quickly determined. M(J is a measure of the mean particle diameter. a- t/) is the standard deviation of the sample giving a measure of the particle distribu­tion or scatter of particles about the mean size, and the value of k' 0 gives a measure of the amount of fine particles in the soil.

In general, the mean particle size decreases as the value of Mt/) becomes greater; as a- 0 increases the spread or range of distri­bution of particles about the mean increases; and as k' 0 becomes greater the percentage of fine material in the sample increases. These three values were used in the multiple linear correlations obtained from the electronic digital computer.

A detailed description of the logarithmic probability method for describing the gradation of soils is given in Appendix II.

ANALYSIS OF LABORATORY DATA

Data obtained in the laboratory were analyzed by correlating the soils properties with the critical tractive force values obtained from the tractive force machine tests. The soils properties used were plasticity index, liquid limit, soil density, mechanical anal­ysis, shrinkage limit, vane shear values, and percent of maximum Proctor density.

Analysis of the laboratory data was first made using the method of deviations described by M. Ezekiel in his book, "Method of Correlation Analysis. "(12) In this method, many hand calcula­tions are required and a complete analysis is very time consum­ing. To make the analysis of many factors more practical, an electronic digital computer was used. A multiple linear correla­tion method, programed for the computer, was adapted for this study. The resulting computations provided the best linear equa­tion, standard deviations from the linear equation., a correlation coefficient., and standard deviations for the coefficients of each of the variables.

The correlation coefficient is a measure of the combined impor­tance of the several independent factors as a means of explaining

the differences in the dependent factor. In general for a linear cor­relatiop., the closer the correlation coefficient approaches unity the better the correlation becomes between the dependent variable and the independent variables. A coefficient of 1. 0 would show perfect correlation and a coefficient of zero would show no linear correlation.

Numerous correlation computations were made for all data together. Correlations were also made with the same data divided into zones which were arbitrarily drawn parallel to the "A'' line on the plasticity index-liquid limit chart shown in Figure 3. This chart has been accepted for use in the unified soils classification procedure and is a guide for estimating the erodibility of soils. The first correla­tions were made without using the liquid limit as a variable. It was believed that this property would not affect the correlation because it had been included in the plasticity index factor.

In the first analysis, 21 different correlations, Table 3, were made using tractive force as the dependent variable. Plasticity index, density, gradation factors k ';,, G t,, Mt), their product k' t,trt,Mt,; shrinkage limit, vane shear strength, and percent maximum density were the independent variables o Seven of these correlations, Num­bers 1, 2, 6, 7, 9, 10, and 13, gave the highest correlation coeffi­cients of O. 6 9 to O. 7 4 for all data, and al.so had high coefficients for the data in the separate zones.

It was decided to investigate the effect of the property liquid limit on the correlations. Additional multiple linear correlations were then made including the liquid limit as an independent variable.

Because of the computer program, it was comparatively simple to make a�ditional correlations by utilizing the initial computations and the already punched cards. Consequently, correlations for all of the data in a group and for the data divided into four zones par­allel to the "A" line on the liquid limit plasticity index chart were made adding the variable liquid limit. Seventeen additional corre­lations were made, Table 3A.

Higher correlation coefficients_ for all data were obtained than for the first analysis. This showed that even though plasticity index is the most important characteristic of plastic soils, the liquid limit is also important. Correlations Numbers 22 through 38 include liquid limit as an independent variable, Table 3A o

With the variable liquid limit ·added, the correlation coefficients for the best seven correlations were O. 71 to O. 79. The seven corre­lations, Table 3A, which give the highest correlation coefficients

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for all data are numbered 31, 32, 34, 35, 36 ., 37, and 38. The table below shows which variables are used to give these correlations.

Dependent Variables Percent Correla-

Corre- maxi- tion co-lation PI Density k'

f/J 0-0 M0 k' (/J a (/)M(/J SL vs mum LL efficient Num- den- for all hers sity data

31 X X X X X X • 78 32 X X X X X X • 76 34 X X X X X X • 79 35 X X X X X • 71 36 X X X X X • 78 37 X X X X • 76 38 X X X X • 78

PRACTICAL APPLICATION

An example of the determination of a critical tractive force value for a given soil, using the multiple linear correlation method., is given below:

Using Correlation Number 34 for all data, the general equation given at the top of Table 3 would be written:

TF = -0. 03414 + 0. 00001 PI+ 0. 00031 D + 0. 00029 k' f/J <Y·rJJM(/J + 0. 00325 VS+ 0. 00004 D% + 0. 00102 LL The numerical values are taken from Table 3A, Correlation Number 34 ., where

TF = critical tractive force for beginning general erosion PI = plasticity index D = density of the natural soil., pounds per cubic foot k' f/J = phi skewness a- (/J = phi standard deviation M0 = phi arithmetic mean diameter VS = vane shear value, pounds per square foot D% = percent of maximum Proctor density LL = liquid limit

A typical plastic soil may have the following values for soils properties:

PI = 12. 0 D = 91. 0 pounds per cubic foot k'¢ = 0.60, O-¢ = 3.07, M¢ = 5.70, k'¢ cr0M¢ = 10.5 VS = 0. 90 pound per square foot %D = 85. 3 percent LL = 32. 7

Inserting these values in the above equation and solving results in a computed critical tractive force, TF = 0. 037 pound per square foot.

If all the soil properties used in the above computation are not known, a correlation can be chosen which includes the soil property data which is available. For the above soil, for example, if only the plasticity index, density and gradation factors were known, Correla­tion Number 38 for all data could be used to determine a critical trac-

• tive force value. For this case, the general equation at the top of Table 3 would become:

TF = -0. 03477 + 0. 00037 PI+ 0. 00038 D + O. 00548 k' ¢ + 0. 00095- LL

Inserting the values for the typical plastic soil in this equation results in a computed critical tractive force, TF = O. 039 pound per cubic foot. This value is probably not quite as reliable as the one from Correla­tion Number 34 but the two values are still very similar.

All of the correlations are given in Tables 3 and 3A. Whether to use the correlations for individual zones or the ones for all data is a mat­ter of judgment, depending on the exact knowledge of the soil in ques­tion.

A study of the correlations shows that the plastic properties, the gradation properties, and the density properties of the soils are all important when determining the safe tractive force of cohesive soils.

SUMMARY AND CONCLUSIONS

A field and laboratory study was made to develop a method for deter­mining critical tractive forces cf cohesive earth materials for the design of unlined and earth-lined canals. It is desirable to know the critical tractive force value of proposed earth canal materials and to use critical tractive force as a criterion in designing earth canals. Critical tractive force is a more precise value on which to base the design than estimated permissible canal velocities. When the criti­cal tractive force value is known. the methods of design outlined in

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References ( 1 ) , ( 2) , and ( 3 ) can be us ed to give the most efficient design for the canal.

Soil samples were obtained from 46 test reaches in various sizes of canals and laterals constructed on Bureau proj ects . Soil and hydraulic tractive force properties were measured and computed in the laboratory. The properties measured or computed were: critical tractive force from the hydraulic erosion machine, liquid limit, plasticity index, soil density, percent of maximum Proctor density, shrinkage limit, soil gradation using the logarithmic prob­ability method of analysis and unit vane shear values .

A multiple linear correlation was made using values of the var­iables obtained from the erosion and soil tests . The availability of an electronic digital computer and a program for making mul­tiple linear correlations made it possible to us e many groupings of the variables, obtain their equations, and determine correlation coefficients . The critical tractive force is the dependent variable and the measured soils properties are independent variables . The independent variables repres ent values obtained from standard tests that are easily made in the laboratory.

Data are arranged in four zones parallel to the ' 1 A" line on the soils plasticity chart. Correlations were made for data in each zone and for all data together. Some correlations within zones give the highest correlation coefficients . The correlations show that plas­ticity, gradation, and density are all important soils properties when considering erosion from hydraulic tractive forces .

Seven correlations which have high correlation coefficients for all the data, and also for the s eparate zones, were selected as the best correlations and are recommended for general use. For specific cases it may be desirable to us e a correlation in a sep­arate zone.

The dependent variable, critical tractive force, was measured on a soil erosion machine. The machine was calibrated to give criti­cal tractive force values using uniform sands and gravels . The c ritical tractive forces for noncohesive sands and gravel materials are known from many laboratory and field measurements. The critical tractive forces of cohesive soil samples were related to critical tractive forces of noncohesive sands and gravels by cali­bration curves described in Appendix I .

The logarithmic probability method of plotting and defining mechan­ical analysis of soils was us ed because it defines the properties on a statistical basis . This method of defining size analysis lends itself to mathematical treatment better than other methods .

Examples are given showing the practical application of determining critical tractive forces of cohesive soils for design of earth canals .

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BIBLIOGRAPHY

1 . Hydraulic Laboratory Report No. Hyd- 352 "Progress Report on Results of Studies on Design of Stable Channels , " Division of Engineer­ing Laboratories , Bureau of Reclamation, Denver, Colorado, June 1 9 52 .

2 . Hydraulic Laboratory Report No. Hyd- 325 "Stable Channel Profiles , 1 1 Division of Engineering Laboratories Branch, Bureau of Reclamation, Denver, Colorado, September 2 7 , 1 951 .

3 . Lane, E . W . ., "Design of Stable Channels , " Transactions American Society of Civil Engineers , Volume 1 2 0 ., page 1 234 ., 1 955 .

4 . General Report No. 21 , "Progress Report of Canal Erosion and Tractive Force Study- - Lower-Cost Canal Lining Program, 1 1 Divi­sion of Engineering Laboratories, Bureau of Reclamation, Denver ., Colorado, March 1 , 1 95 7 .

5 . General Report No. 2 2 , 1 1Progres s Report No. 2-- Canal Erosion and Tractive Force Study- - Lower- Cost Canal Lining Program, " Division of Engineering Laboratories , Bureau of Reclamation, Denver, Colorado, February 1 4 ., 1 958 .

6 . General Report No. 2 6 ., "Progress Report No. 3 ., Canal Erosion and Tractive Force Study ( Correlation of laboratory test data) - ­Lower- Cost Canal Lining Program, 1 1 Division of Engineering Laboratories , Bureau of Reclamation, October 28 , 1 9 60.

7 . Smerdon, E. T • ., and Beasley ., R. T . ., "The Tractive Force Theory Applied to Stability of Open Channels in Cohesive Soils, " Research Bulletin 71 5, University of Missouri, Agricultural Research Station, October 1 959 .

8 . Moore, Walter L. , and Masch, Frank D . ., Jr. , "Experiments on the Scour Resistance of Cohesive Sediments , 1 1 Journal of Geophysical Research, Volume 67 , Number 4, April 1 962 , The American Geophysical Union.

9 . Dunn, I. S . ., "Tractive Resistance of Cohesive Channels , 1 1

Journal of Soil Mechanics and Foundations ., Proceedings, American Society of Civil Engineers, June 1 959 .

1 0 . Hydraulid Laboratory .Report No . Hyd-43 4, "Design, Assembly, and Use of a Portable Vane Shear Tester, 1 1 Division of Engineering Laboratories, Bureau of Reclamation, Denver, Colorado, June 2 1 , 1 9 57 .

1 1 . Earth Manual, First Edition, U. S. Department of Interior, Bureau of Reclamation, Denver, Colorado, July 1 960.

12. Ezekiel, M. , "Methods of Correlation Analysis, 1 1 Second Edition, Wiley, New York, 1 941.

13. Soils Engineering Report No. EM-643 1 1A Study of Erosion and Tractive Force Characteristics in Relation to Soil Mechanics Properties, Earth Research Program, " Division of Engineering Laboratories, Bureau of Reclamation, February 23, 196 2.

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LOWER-COST CABAL LDIIG TBAc.rIVE FORCE FIELD AID LABOBAmlll S!UDI

CABAL AID LATERAL REACmS • . . :-Station or mile : Test . . . .

Samples No. :Region; ProJect . CaDal or lateral . at center : discharge: Soil type . . 18F- L reach: . . of reach . eta . . . . .

• . . . . . . 625-633 • 1-1 :Minidoka :Lateral PL lO-A-8248 . 33f00 . 3.79 : ML • . . 634-642 . 1-2 :Minidoka :Milner-GoodiDg Canal : 374+oo :l, 5lla . ML . . 643-651 . l-J :Minidoka :PA Lateral (Borth Side: 19+42 . 67.7 . ML . . .

: . . Pumping Co. ) . . . . . . . . 652-660 . l-4 :Yakima :PL Bo. 1.4 tLateral.) . 152+50 . 18.6 . ML . . . . 661-669 : l-5 :Yakima :PL Bo . 13 Lateral) . . 18. 4 . SM . . . 670-678 . l-6 :Yak:lma :Roza Main CaDal . *59 -l . 514 . ML • . . . · 679-687 . l-7 : Columbia Basin :WC Lateral. W27B . 24+90 : 26 .4 . ML . . . 688-696 . l-8 : Columbia Basin :WC Lateral W26A . 378+90 . 47 .1 . ML . • . . 6CTl-705 : l-9 : Columbia Basin. :EL Lateral 68T5 . 185-f()() . 5.81 : ML . . 435-439 . 2-1 :IOemth :Lateral M-2-A . 6+85 . 20.2 . Ml . • . . 440-443 . 2-2 :K.1 amath :Lateral M-2-A . 92+30 : 5 .6 . MB • . . : ·444-449 i 2-3 :Klamath :Lateral J-l-B . 6+50 . 18.1 . SM . . . , 450-455 • 2-4 :Klamath :Lateral J-13 . l5+oo . 27.4 . ML . . . . . · 456-459 : 2-5 : Central Valley : Friant-Kern CaDal . *37- 49 : 2,910 . CL-Cll . . 460-465 : 2-6 : central Valley :Friant-Xern CaDal . *39-82 : 2,62o . CL . . 466-471 : 2-7 ·: Central Valley :Madera Lateral 32.2 . 455+1'0 . 59.1 . ML-SM . . . 472-475 t 2-8 : central Valley :Madera Canal . *ll-35 . 692 . SC-cL . . . 476-481 • 2-9 : central Valley - :Madera Canal . *3l-50 . 488 . SC • . . . 510-517 : 4-1:men :Means . 24+17 . .289 . CL . • • 518-521 . 4-2: F,den :Means . 102..00 . 253 . SP • . . . 522-533 . 4-3: F,den :Means . 265+oo . 188 . SM • • . . 534-542 l 4-4:Eden : Eden . 3484-50 . 176 . SM . . . 543-554 : 4-5 :FA.en :men . : 355+83 . 16o . SC-CL . . 555-566 : 4-6:Eden :F.den . 1164+95 . 176 . CL-SC 567-578

. . . : 4-7:men :FA.en . 645f00 . 129 . CL-SC 579-586 . . . . 4-8 : Eden :men . 834+oo . 125 . SM • . . .

597-605 • 4-9:Paonia :Fire Mounta� . 419-fOO . 86. 3 . CL 606-614 . . . . . 4-lO: Paonia :Fire Mountain . 648+25 . 79.8 . CL 615-624 . . . . • i..-D.: Paonia : Fire Mountain . 1341+50 . 55 .2 : CL . . .

Samples No. l8F-

799-807 814-822 808-8]3

823-832 833-841 772-780' 781-789 '190-798 382-388 389-397 406-4]4 359-367 350-358 368-J'M-375-.381 398-405

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• . . . • • : Region: ProJect . Canal or lateral . • . • . : : . • • • . . • • . . t • • t

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5-1: 'fucum.cari : Conchas 5-2:i'Ucumcari : Conchas 5-3:Tuewacari : Conchas . . 5-4:Tucumcari :Hudson 5-5:!'ucumcari :Hudson 5-6:w. c. Autin :West 5-7:V. ·C . Austin :Altus 5-8:V. c. Austin :Ozark 7-1:Missouri River Basin:Bartley

· 7-2:Missouri River Basin:Bartley 7-3 :Missouri River BasiD: Cambridge 7-4:Missouri River Basin:Franklin Pump 7-5 :Missouri River Basill:Superior 7-6 :Missouri River Baaill: Prankliil 7-7 :Missouri River Basin: l'rankl!la 7-8 :Missouri River Basin: C&mbriclge

:Station or mile : Teat . • • at center : diacharge: Soil tn,e •

ot reach cfs • • . • 3215+00 68.6 . CL • . 3962+86 57. 4 CL . . lio56+o0 . 39.0 CL-with . . . : :Gravel Blanket .

• 274+57 . 138 . CL • . • . 1091.+oo 61..1 SC-c:L . . 188:t<>O . 78., . CL . . • . 799+50 . 160 . CL�CB . . • . 316+00 . 41.2 • CL-ell • . 263+00 72.6 . ML • . 762+36 . 36.1 : ML".'"CL . • . l.003+22 . 132.5 ML-CL . . . 215+57 . 18.0 ML . . . 1053+72 65 .3 . ML-CL . . . 947+24 . 99.1 ML-sM . . . :i,_949+24 . 54.6 ML-cL . . . l24Q+OO . 54.6 ML-eL . .

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reach

7-2 4-4 4-4 4-6 4-6 1-6 1-8 2-3 2-4 2-7 4-3 4-3 1-2 1-2 1-3

· 1-4 1-4 1-5 1-5 1-5 1-6 1-6 1-7 1-7 1-7 1-8 1-8 1-9 • • • • •

Table 2 Page 1 of 4

DATA OBTAINED FROM LABORMX>RI TEST SAMPLES Zone 2

: I : 2 � J :L J � � 4 : L : � �li : 1 : � · B � �: . 9 : 10 : 11 : 12 : Sam:ple :Most : : : : : : : : : : : No . :prob : PI :Density: k'+ : o; : M<,6 :k�6cf> M'P: SL :V.S� :1, Max• : LL : ( 18F-) :T.F. : : : : : : : : : density: . . . . . . . . . . . . . . . . . . . . . .

93. 4 : 1 .60:2 .88: 7. 54: 34-.8 :20.72 :2 .20: 85 .0 : 30 . 7 91. 7 : 0 .07:1 .16: 5 .12: o .416 : 22 .97:1 . 33: 84.6 : 22.2 95 . 7 : 1.00:2 . 72 : 4. 48: 12 .2 :20 .32:1. 15 : 88.4 :26. 7 96.6 : 0 . 50 :2 .16: 4.10 : 4.43 :24. 51 :1 .07: 85 .2 :29 . 3 89. 3 : 1 .20:2 .14:4.20:. 10. 8 :24. 53 :1 .48: 78. 7 :29 . 3 86.6 : o .ao:1 .26 : 5 .48: 5 . 52 :22 .21 :1 .10: ao.7 : 21. 3 95 . 3 : 0 .10:1. 59 : 5 .24: 0 .833:25 .11 :0 .66: 91.6 : 23 .1 94.5 : 1.04:2 .22: 3 .84: 8.87 :22 .85 :0 .82: 90.4 :23 .2

·361-1 :0 .053: 7 .2 : : 537 :0 .027: 0 .2 :

539" : 0 .038: 4.9 : : 571 :0 .038: 4.1:

572 :0 .0�: 6.7: : 673 :0 .023 : O : :. 691 :0 .028: o .4 :

445 :0.030: O 45() :0 .020: 0 468 :0 .033: O

: 75 � 3 : 2 .00:1 .41: 4.25: 11.99 :26 . 70 : 0 .90: 71 . 5 :21 .8 : 100.1 : 1 .4o:1 .93 : 3 .90: 10 . 54 :24. 5 :0 .66: 95 . 3 :20.1

: 525 :0 .018: o : 526 :0 .027: O

637 :0 .029 : O I 638 : 0 .017: 0 : 647 :0 .024: 0 : 656-1 :0 .032: o : 657-l :0 .045 : o I 664 :0 .03() : 0

· 665 :0 .03() : O 666 :0.017: () 673-2 :0 .028: 0 674 :0 .029 : 0 682 :0.024: 0 683 :0 .020: 0 684 :0 .025 : 0

I 692 :0 .022 : 0 I 693 : 0 . 025 : 0 : 700 :0 .021: 0 I 709-1 : 0 .018: 0 I 7].0-1 : 0 . 026: ·0 I 710-2 :0 .028: 0 I 7ll :0 .022 : 0 : 711-2 :0 .025 : 0

91.4 : 1 . 55 : 1.64: 3 .44: 8.87 : 28. 31:0 .98: 83.6 : 27.2 88.9 : 2 .00:1 .15 : 3. 72 : 8. 56 :24.36 :0 .90: 81.2 : 23 .1 91.8 : 2 .00:1 .30 : 5 .20 : 13 . 52 :24.64:0 .66 : 100 :25 .4 78. 3 : o .S0:1 . 34: 5 . 34: 5 . 72 :28.16 :0 . 57: 85 . 7 :26.8 78. 6 : 2 .00:1.20 : 5 .20: 12.5 :27.08:0 .84: 73.8 :24. 5 93. 8 : 2 .00 :1. 54: 5 -50 : 16 . 94 :22 . 71 :1 .48: 92 .0 :23 . 5 96.6 : 1 . 50 :1 .45 : 5 .10 : 11 .09 :22 .18: 1 .93: 94. 8 :23 .8 92 . 5 : 1 . 50 ;1 .68:4.94: 12 .45 :21 .19 :0 .49: 86.5 :21 . 5 93. 9 : 2 .00:1 .10 : 4.40: 9 .68 :21 . 43 :0 .90: 87. 7 :22.3 74.o : 1 .40:1 .08:4 .20: 6 . 35 :24. 71:0 .66: 69 .2 :22 .0 88.2 : 1 .50 :1 . 39; 5 .40: 11.26 :22 .21 :1 .10: 81.9 :21 .5 86.6 : 1 .10 :1 . 36 : 5 .25 : 7 . 85 :21- 59 :0 .66: S0 .6 :22 .0 87 . 6 : 0 . 50 :2 .05 : 5 - 79: 5 .93 :25 . 87 :1. 31: 82.8 :25 . 5 &) . 7 : 0 .69 :1 .88: 5 .68: 7 . 38 :23 .26 :0 .98: 78.7 :23.0 86.8 : 0 . 81:1 .48: 5 . 79: 6 .95 :29 . 59 :1 .39: 79 . 4 : 24.o 84.8 : 0 .28 :1 .76 : 5 . 51 : 2 . 72 :22 .69 :0 .66: 81. 5 :24.2 89. 5 : 0 . 10 :1 . 56 : 5 .15 : 5 . 61 :25 . 9 :0 .98: 86.o :25 .1 85 .3 : -0 .2, : 1 .92 :6 .10 : -2 . 93 :27 .9 :1.64: 86.4 : 28.0 84. 5 : 1.00 :1 .38: 5 .60 : 7 .73 : 26 . 36:1.18: 81. 1 :24. 5 85 .0 : 1 .40: 1 . 39: 5 .48: 10 . 7 : 25 .88:0 . 90: 82 .3 :25 . 8 90.0 : 1 . 30 :1 .24: 5 -lt-O : 8 .69 :25 .88:1.31: 86.3 :25 . 5 82 .2 : 0 .85 : 1 . 52 : 5 . 75 : 7 .42 :26 . 32:1 .31: 78 .8 :27 .4 85 . 8 : 1 .30:1 .28: 5 -�: 9 .00 : 26 .32:1 .23: 82.3 :20.8

Notes : T .F . = most probable tractive force (pound per square foot) determined from tractive force machine

PI = plasticity index kq, = phi skewness 6<f, = phi standard deviation

M cJ, = phi arithmetic mean diameter SL = shrinkage limit VS = vane shear--pound per square foot LL • liquid limit

*Field data not obtained because of construction .

Region and

reach

7-5 7-5 7-6 7-1 7-2 7-8 7-3 7-3 4-1

4-3 4-8 1-1

1-1 1-3 1-3 2-4 2-7

Table 2 Page 2 of 4

DATA OBTAINED FROM LABORAroRI TEiT SAMPLES Zone J

l 2 : 3 : 4 5 6 : 7 : 8 : 9 : 10 : ll : 12 Sample :Most : : : : : : : : :

I I tJ.. No. :prob :P.I . :Density: k ip : 64> : M,t, :ktp 6cpM,j,:S.L. :V.S. :-,, 111ax. : LL __USF-) :T.F. : : : : : :densitz: . . . . . .

352-2 :0 .036: 10 .8: 359 :0.043:ll .3 : 370-1 :0 .025: o .8: 382 :0 .033: 6 .4: 391-1 :0 .042 :10 .2 : 4oo-l :0.043: 8.6 : 4o7-1 :0 .039: 5 . 4: 4o7-2 :0 .04o : 5 .6: 514 :0 .037: 9.7: 527 :0.04o: 8 .5 : 582 :0 .049: 4.8: 629 :0 .033: , . 3 : 630 :0 .041: 3 .3 : 646 :0 .028: 5 .6 : 648 :0 .04o: 3 . 5 : 451-1 :0.023: O 46J :0 .029: 0

. . . . . . . . . . . . . . 76 .0 : 1 .20:1.90:6.46: 14. 73 : 23 ,92 :l .8o: 76. 2 : 2 .10:1 .66:6.14: 21,4o :27 -12 :2 . 20 : 85 . 7 : 1 , 55 :2 .24: 5 ,19: 18.02 :15 , 45 : 1 , 45 : 72.1 : 1 .50 :2 .18: 5 . 50: 17.99 : 17 -71 :l .8o: 82.9 : 1 .50 :1.91:6.15 : 17.62 : 16.15 :1 .ao: 81.9 : 2 ,00:2.21:6 .6o: 29.17 : 19 .6o:l .50: 92. 5 : 2 .00:1.88:6.21: 23. 35 : 18.04 :1 .90: 84.2 : 2 .00:2 .07 :6 .49: 26.87 :18.04:1 .90: 73.4 : 1 ,57 :2 .76 : 5 .88: 25 .48 :19 ,31 :0 .41 : 91.6 : 2 .00:2 .46 :4, 54: 22. 34 :20.98 :0 .90: 99. 3 : 1 .40 :2 .41 :3.98: 13.43 :18 .3 :1 .64: 85 . 3 : 1 .00:1.81: 6.08: 11.0 :19.62:1 .43: 78.8 : 1.8 :2 .22 :6 .68: 26. 69 :20 .15 :1 .43: 78.7 : 0 .90:2 .81:4 .31: 10.9 : 19.67:0. 74: 91.6 : 1.10:1. 58 :5 .70 : 9.91 :22.01 :0 .98 : 76. 5 : 1 .90:1.31 :3 .29: 8.19 :22 .64:0 , 57 : 99.3 : o .6o:2 .20:3.6o: 4.75 : 24 .5 :o .9§:

. 67. 9 : 31 . 5 70 .1 : 34 .7 82 . 3 :19 .7 69. 8 : 26.0 79.1 : 30 .8 74.l. : 31,0 88.3 : 26 . 7 8o.2 :27 ,5 69.0 : 31.8 83. 8 : 29 , 5 84. 5 :24 .3 81. 3 : 24 .4 75 .2 :22.6 74.o : 25 . 5 85. 8 : 24.2 73.2 : 18.8 94.1 :19.5

"

�-·

L1,

,,..

.. '

Table 2

DATA OBTAINED FROM LABORAroRY �T S�

l -- : 2 : 3 : 4 : 5 : 6 : 7 : 8 9

PS£e 3 of 4

Zone 4 =- -10 : 11 : 12

Region : Sample :Most : : : : : : am : No. :prob :P.I. : Density: k� : 6p : M� :k'<f,6</, M<f,:S.L.

. . . . . .

reach : (18F-) :T.F. : : :V.S. :'1, fll&X• : LL

: densitl:

7-5 7-7 7-2 7-2 7-8 7-8 7-8 7-3 7-3 2-1 2-8 2-9 4-1 4-4 4-4 4-4 4-9 4-9 4-10 1-1 5-5 5-5 7-7

. . . . . . . . . . . . . . . . . . . . . . . . : 351-2 :0 .045 :11 .3 : 99. 5 : 1 .75 : 1 . 78 :6.27: 19.6 : 19.6 : l .8o : 88.8 : 31 ,3 : 375-1 :0 .042 : 6 .7 : 102 .0 : 2 .00:2 .00:4 .55 : 18.2 : 21 .2 : 1 . 45 : 94. 3 :22 .l : 389-1 :0 .050 :10.8: 112 .9 : 1 .90:2 .4o : 6.25 : 28. 5 : 25 .1 :l .8o: 100 :29 . 5 : 389-2 :0.042 :10 .9 : 72 . 7 : 2 .oo:2. 36 :6 .6o: 31.2 :25 .1 :1 .8o: 69.6 :29.1 : 398-1 : 0.046 :10 . 5 : 86.l : 2 .00:2 .75 :6 .98: 38. 4 : 19 . 7 : 1 . 50 : 83.1 : 28.1 : 398-2 :0 .042: 9 .9 : 84.4 : 1 . 56 :2 .05 : 6 . 30 : 20 .2 :19 . 7 : 1 . 50 : 81. 8 :29.2 : 399-1 :0 .053:16 .0 : 73. 7 : 1 . 70 : 3.00 : 7 . 38: 37.6 : 18.1 : l . 50 : 70 .6 : 35 - 2 : 406-2 ; 0 .057 :15 .4 : 81 .6 : 1 .70 : 3 .10 : 7 . 53 : 39. 7 : 15 - 2 : 1,90: 79. 5 : 35 - 2 : 408-1 :0 .046:16.8: 76.2 : 1 .10 : 2 .02 :6 . 56 ; 14 .6 :21.l ; l .90; 72.9 : 36.2 : 435 :0 .016: 9 .9 : 50 .8 : 0 .08: 2 . 34 :6 .44: 1 . 21 : 19 ,2 ;0 .61! 48.l : 29 .3 : 472 ;0 .030: 5 . 4: 93.2 : 0 . 50 : 3 .26 : 4. 55 : 7 . 42 : 18 .4 : 0 . 57: 86.3 :21 .7 : 478 :0 .037: 4 .4: 110 .1 : o .6o: 3.01 : 3 .67: 6 .64 :17.7 : 0 . 57: 98. 4 : 19 . 5 : 513 :0 .045 : 12 .0 : 91.0 : o .6o:3 .07: 5 . 70 : 10 . 5 : 17 .1 :0 .90: 85 . 3 : 32 . 7 : 53S :0 .050: 7 .9 : 103 .8 : 2 .00 : 3 .08: 4 . 76 : 29. 3 : 16 . 5 : l ,33: 95.7 :23.9 : 546 :0 .049:15.1: 68.2 : 1 . 45 : 3 .08 : 5 . 71 : 25 . 5 : 18 . 7 : 0 , 57: 65.0 : 35 . 1 : 547 : 0 .032: 6 . 5 : 98.7 : 1 .10 :2 .85 : 5 . 85 : 18. 4 : 15 .8 ;0 .82: 93. 8 : 25 . 4 : 6oo :0 .044:13.3; 112.2 : -0 .6 : 4. 5 : 5 , 1 : -13.8 : 20 .2 : 2 .05: 99. 8 : 33,l : 6o1 :o .o4o :16.9 : 81.9 : -0 .28: 3.14 :6 .44: -5 ,66 : 19 .8 :0 .98: 74.6 : 36 .5 : 610 :0 .042 :13.6: 96.2 : o . 4 : 2 .40 :6 .Bo: , . 53 : 20 . 2 : 2 . 30: 89.9 : 31 .7 : 628 :0 .030 : 4 .4 : 82.8 : 1 . 40 : 1.84:6.10 : 15 . 7 :14 . 4 :1 .15 : 79.0 : 22 . 4 : 836-1 :0 .015: 2 . 5 : 99.0 : -0 .9 : 2 . 70 :4 .61: -11.2 : 15 . 5 :1 .32: 89 .3 : 17.9 : 838-2 :0.025: 1 .3 : 104.8 : 1 .4 : 2 .6o: 5 ,0l: 18.2 : 14.2 : 1 . 32: 89.0 : 17 .6 : I{J-2_:o_.0_21: o _ __:__ 101.1 : 2 .00:1 .11 : 3 . 57 : 12 .2 : �3.0 : 1 . 45 : 84.o : 14.o

-----

Table 2 Page 4 of 4

DATA OBTAINED FROM LABORA'roRY TEST SAMPLES Zone 5

: l : 2 : 3 : 4 : . 5 : 6 : 7 : 8 : 9 : 10 : 11 =- -12 Region : Sample :Most : : : : : : : : :

I I d_ and : No. :prob :P.I. : Density: k¢ : 6tj, : M¢ : k,t, 6,p M;:s.L. :V.S. :,., max. : LL

reach : (18F-) : T.F. : ' : : : deusitz:

7-5 7-5 7-6 7-6 7-6 7-3 2-5 2-6 2-6 2-8 4-6 4-6 4-7 4-11 4-11 5-6 5-6 5-7 5-7 5-7 5-8 5-1 5-2 5-2 5-2 5-4 5-4 5�4 5-5 5-5 5-5 5-5 5-5 7-7

. . . . . . . . . . . . . . . . . . . . 351-l :0 .032 : 13 .6 : 87 . 4 : 1 . 70 :1 .90:6.26: 20.22 : 19 .6 : l .8o : 350-1 :0 .046 : 14.0: 88.1 : 2 .50 :2 . 78 :7 .22 : 50 .2 :20.8 : l .8o : 368-2 :0 .034: 7 , 5 : 98.0 : 2.0 : 3 .20 :4.21 : 26.94 : 13 . 7 : l , 45 : 368-3 :0 .04o : 10 . l: 93.9 : 2.0 : 3 , 75 : 5 ,4o: 4o . 5 :13 .7 : l.45: 369-1 :0 ,028: 9.6: 97.4 : 0.09 :2 .78:6.22: 1 . 56 :17.8 : l , 45 : 4o6-1 :0 .041 : 17 .3 : 74.o : 2.00:3 .30 : 7.62: 50 . 3 : 15 .,2 :l .90: 457 :0 .051 :21 .0: 81.2 : 1 .4 : 3 .68:4.68: 24.l : 16 . 4 : 0 . 41 : 461 :0 .036: 10 .0 : 106. 1 : o.So: 3.03 :4 .75 : 11. 5 : 16 . 5 : o . 82 : 462 :0 .034 :10 .0 : 103. 6 : 0 .50 : 3.06 :4 .76 : 7.28 : 16 . 5 : 0 .61 : �73 :0 .029 :10 .2 : 97 .1 : 0 : 3 .02 : 3.22 : 0 :21 . 9 :0 .66 :

: 559 :0 .027: 10 .2 : 85 .6 : o.62 :3 .98:6.4o : 15 .8 : 18. 4 : 0 .82 : 56o :0 .039 :13 .0 : 95 . 5 : 1.2 : 3.6o:5 .49: 23. 7 : 18 . 4 : l . 10 : 570 :0 .031:13 . 5 : 85 .2 : 1 .50 : 2 .50 :3 .98: 14. 9 :23 , 3 :2 .05 :

: 618 :0 .039 :12 . 5 : 95 .9 : 1.1 : 2 .38:6 .24: 17. 82 : 15 . 7 : 0 . 82 : : 62o :0 .053 : 16 . 5 : 118 .3 : 0 .60:2 .21:6 .90: 9.i5 : 17 , 7 : l - 97 :

775-1 :0.030 :24.8: 73. 6 : o .8o:4.i5 :8 .18: 27.2 : 8 . 5 : 0 .90: 777-1 :0 .042 : 22.8: 97 . 7 : 0 .66:3 .94 : 7 . 54: 19.6 :11 . 4 : 0 .82 :

: 785-1 : 0 .042 : 14.2 : 89.8 : 0 .86:3.61 : 7.61: 23.6 : 16 .3 : 0 . 39 : i 785-2 :0 .039: 14 .9 : 89. 8 : 0 .74 :3 .61 :7 .35 ; 19.6 : 16 . 3 : 0 . 41 : : 786-1 :0 .031 :14.8 : 82.2 : 1 . 4 :2 .84:6.4o : 25.4 : 16 . 1 : 0 , 39 :

793-1 :0 ,032 : 12 , 7: 109 .2 : 0 .89:3 .89 :6 .70 : 23.2 : 17 .8 : 0 .82: 799-1 :0 ,042 : 6 . 1 : 102 .9 : 1 .30 :6 .30 :8.68: 71.1 : 15 .0 : 0 . 41 :

: 817-1 :0,04o: 8.2: 105 . 6 : 1 . 8 : 3 .85 :6 .15: 42.6 : 14.2 : 0 .84 : : 817-2 : 0 .034: 9 .4 : 103. 7 : 1 . 1 : 4.00:6 .32: 27.81 : 14.2 : 0 . 84:

818 :0 .039 : 5 . 3 : 103. 5 : 1.8 : 3 . 30 : 5 . 61: 33. 3 :14.5 : l,05: 826-1 :0 .034:11 .4 : 86.9 : 1.8 : 3.68:6 .18: 4o .9 : 18 .3 : 0 , 74 : 827-2 :0 .027: 7 . 5 : 88.7 : 2 .0 : 3.20:7 .08: 45 . 3 : 16 .1 : 1 .25: 828-1 :0 .021 : 10 .0 : So.9 : 0 . 9 : 3,10 : 5,68: 15.85 : 13 .9 : l. 25 : 837-1 : 0 .033 : 15 ,l : 88.9 : 0 . 7 : 3 ,00: 5 ,50: 11.6 : 15,0 :l .25 : 837-2 :0 .030: 8 .2 : 1o6 . 4 : 1 .5 : 3 .00.: 5 .36: 21� . 1 : 15 .0 : l .32 : 837-4 :0 ,022: 7 , 5 : 92 . 8 : 1 .8 : 3 , 10 : 5 . 48 : 30 . 6 : 15.0 : l . 32 : 838-1 :0 .039: 9 . 2 : 91 . 7 : 1 .50 :3 .30;5 .62 : 27.8 : 14.2 : l , 32: 838-3 :0 ,028: 9 .6 : 88.6 : 1.8 :2 .85 : 5 .20: 26. 7 : 14.2 : l .32 :

,;11-1 :0 .029: o : 117.2 : 2 .00:1.68:3.54: u.9 : 13.0 : l . 45 :

78.0 : 3l .l 79.0 : 30 .8 92.0 :21 .6 85 .5 :24 .4 85 . 7 :25 , 3 73.0 :33 .9 79.0 : 36 . 4 94.o :25 . 5 92 .0 :25 , 5 93.0 :25 .8 82.2 : 25 . 1 91. 7 :27.9 75 .2 :28.6 92. 4 :29 , 3

100 : 33.6 71. 3 : 42 . 9 94.6 :4o .6 83.0 : 29 . 4 83.0 :30 .1 75.9 : 29 .0 91.2 :25.2 83. 4 : 17.1 91.0 :22 .0 88.9 :22.0 88.5 : 18 .3 74.6 :25 ,0 76. 3 : 19 .4 69. 5 :23.1 ao.o : 30 , 7 95. 7 : 20 .3 8J .6 :20,l 82 . 7 : 22 . 4 79. 9 : 22.8 �8.0 :lJ.O

...

,.....,

c-.

.. ..

�

. . . . . .

Table 3

MULTIPLE LINEAR CORRELATION VALUES USING ELECTRONIC COMPUTER I I ,.,_M,. Values in General Equation : TF c a+b1 PI+b2D+b3k;p+b40-</'+b5Mq,+b6kq,�+b7SL+b8VS+b�r

0-n = standard deviation of variable

: . t

. : . lj, maximum . . .

Table 3 Sheet 1 of 4

k' 6'� Mf PI : Densitl . ct, . : . . . . . • . . . . Correlation : . : . • .

; 0-4 .

b5 0'"5 . .

b3 (j3 b4

. . k� cr� M� . SL . . . . . . . . . b6

. c:r6

. br

. <1'7

. vs b8 : era

• . . density - . . b9

. <1'9

a :Standard :Correlation :deviation :coefficient

b1 <r1 b2 CT2 . . . . . . . : : . . . : • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . : . . . : • . . . . . . . . • . . : • . . . . . . .

1 . Zone 2 :0.00246 :o.00046 : o.00014 :o.00010:o.00337 :o.00106 : -0.00122 :o.00223 : o.00223 :0.00011 : . . • . . . . . : . . . . : -0 . 05296 : 0 . 00336 : : -0.03268 : o.00460 : : -0 . 01559: 0 .00282 : : -0.03654 : 0.00552 : : -O .oo88o: 0 .00658 :

Zone 3 :o .oou1:o.ooo41: o.00052:0.00015 :o.00412 :o.00280: o.00077 :0.00308 : o.00190:0.00133 : Zone 4 : o.00202:0 .00020: o.00025 :o.oooo4 :0ooo802 : 0.00079: o.00366 :o.00125 : -0 .00106 :o.00096 : Zone 5 :o.00125 : 0.00027: o.00046:o.ooou:o.00530:0.00178 : o.00182 :0.00143 : o .00007 : 0.00098: All data:o.00099:0.00015 : o.00029:o.oooo6 :o.oo432 :o.00096 : -o.00138 :o.00102 : o.00129:0.00010: . . . . . . . . . . . . . . . . . . . . . .

. . • . . . . . . . . . . . . . . . . .

. . . • . . . . • . . . . . 0 . . . . .

. . •

: :

: . 0 . . . . . : . . : : : :

2 . Zone 2 :o.00311 :0.00061: :o.003o6 :o.00135 : -o.00053 :o.00282 : o.001o4 :o.ooo94 : :o.oo4o4 :o.00339 : o.00110 :0.00371: o.00124 :0 .00159 : : o.00782 :0 .00069: o.00324 :o.00109: -0.00142:o.00081: :o.00533 :0.00180 : o.00162 :0.00143 : o.00079:0.00099: :o.oo461 :o.00096 : -o.00074 :o.ooo96 : o.00116 :0.00068:

. . . . . . . . : o.00055 :0.00012 : -o.02937 : o.00422 : o.00048:o.00022 : -0.02450 : 0.00556

3 .

4 .

Zone 3 :0.00127 :0.00054 : . . Zone 4 : o.00203 : 0.00018 : . . Zone 5 : 0.00094 :0.00024 : : . . A11 data: 0.00099:0.00015 : . . . .

: . . Zone 2 : : Zone 3 . . . . Zone 4 . . • . Zone 5 : . . All data : : . . . . Zone 2 . . . . Zone 3 . . . • Zone 4 . . . . Zone 5 . .

0 . All data: . . . .

. . . . . . . . . . . . . . . . . . . . : o.00062 :o.00015 :o.oo425 :o .00143 : o.oo669:o.00212 : o.00218 :0.00105 : : o.00o46 :o.00018 :o.00578 :o.00341: o.oo489:o.00392 : o.00397:0.00145 : : o .00016 :o.ooou:o.00799:0.00191: o.00923 :0.00268 : o.Q04.54 :o.00175 : : o.00019:0.00011:o.00192 :o.00209: o.ooo83 :o.00185 : o.00210 :0.00111 : : o.00022 :o.00001 :o.oo478 :o.oou8 : o.00302 :0.00122: o.00283 :0.00078:

. • : : . . . •

. .

. . :

. . . . . .

. . . . . . . . • • • • • • 0 •

:o.00399:0.00168 : o.00888:0.00237 : o.00114 :0.00119: : :o .00556 :o.oo4o4 : o.00535 :0.00467 : o.00347 :0.00168 : : : o.00783 :0.00189: o.oo891:o.00267 : o.00438:0.00161: : : 0 .00294 :0.00200: 0 .00100 : 0.00173 ; 0 .00257: 0. 00lll: :

No correlation • • • • • • 0 . . . . . . . . .

. . . . . . . : : . . . . . . . . • . . . . . . . . . . : -o.00066:0.00039: : o.00056 :0.00051: : o.00016:0.00050: : o.()()()lf.6 :o.00046 : : o.00018 :0.00023 : . . . . . . : -o.00108 :0.00043 : : o.00059:0.00061: : 0.00075 :0.00049: : o.00058 :0.00043:

: . . . .

: . . : : : : :

. : . .. . . .

: o .00031:o.00004 : -0.01597 : 0.00244 : : o.00056 :0.00013 : -o.04102 : 0 .00555 : : o.00036 :o.00001 :-0.01399 : o.oo652 : . . . : . . . . . : -0 .03788 : o.00455 � • . : : : -0 . 05478 : 0 . 00560 . • : -o.04971 : o.oo677 . . . . : -0.00883 : 0 .00716 : . • . . : -0 . 01877 : 0 .00779 : . . . . . . . . . . : o .00031 :0.00015 : 0.00330: 0.00534 : : o.00033 :0.00024 : -o.04028 : 0.00655 : : 0 . 00022 : 0.00013 : -0 .. 05067 : 0 .00667 : : o .00042 :0.00015 : -o.03302 : o.oo667 :

. . . . • . . . . . 5 . Zone 2 : 0 .00190 : 0.00077 : :o.00353 :0.00168 : o .00379 :0.00333 : -o.00032 :o.00137 :

:o .00257 :0.00386: 0.00260:0.oo..45 : o.00038 :0.00199: :o .oo856 :o.001o8: o.00589 :o.00168 : -0.00312 :o.ool.26: :o.00286 :0.00232 : o.00097:0.00211 : 0.00035 :0.001.26 : :o.00363 :0.00102 : o.ool.61:o.00102 : -0.00002:o.00071:

. • • . . . : o.00589 :0.00312 : . : 0 .01151 : 0 .00529 : . : o.00412:0.00389 : : 0 . 01526 : 0 .00636 :

6 .

Zone 3 : 0 .00069:0.00056 : Zone 4 : 0.00179 :0.00028 : Zone 5 : 0.00061:0.00029: All data : 0.00073:0.00016 : . . . . . .

: . . . . :

Zone 2 :o.00162 :0.00042 : o.00059:0.00018 : Zone 3 :0.00072 :0.00040: O.OOlll:0.00037 : Zone 4 :o .00188 :0.00020: o.00021:0.00025 : Zone 5 :o .001� :0.00023 : o.00016 :0.00023: Al.l data:0.00077 :0.000U: -0.00009:0.00013 :

. . . . . . 0 . . . : . . . . . . . . . 0 . . . . . . . . . . . . . • . . . . . . . • . . . .

. 0 . 0 . 0 . . • . . 0

. . : . • . • :

: : . 0 . .

:0.00035 :0.00011 : : o.00037 :0.00016 : :0.00041:0.00005: :0.00025 :0.oooo6: :o.00021:0.00005 :

. . . . : . . . . . . . . . . . .. . .

• . : o.00436:0.00181: . : 0 .00903 : 0 .00390 : . : -0 .00070 :0.00340: . : 0.01964 : o.007� : . : o.00518 :0.00153 : . : 0.01437 : o.00684 : . • . . . . . . . . . . . : o.00320 :0.00115 : o.00003 :o.00011 :-0.03593 : 0.00339 : : o.00232 :o.00215 : -o.00084 :o.ooo46 : -o.00512 : o.oo4o4 : -0 .00153 :0.00175 : 0 .00012 :0 .00029:-0.01935 : 0 .00347 : : o.00061:0.00194 : o.00039:0.00029: -o.03375 : 0.00526 : : o.00502 :0.00130: o.00040:o.00011 : -0.00631: 0.00636 :

0 .91 0 .76 0 . 97 o .. 66 0.72

o.86 o .62 0.98 o.66 0 .73

0.83 0.61 0 .80 0 .23 0 . 57

0.16 0.38 o.Bo o.42

0.76 o.44 0.94 0.29 0.69

0.91 0.82 0. 95 0.70 0.74

.. , I:

Table 3--Continued

Table c Sheet 2 of

. . • • • • • • • cJ, IDELXimum • ; kq, ; cft ; Mct, ; k1

ct, 0-;M<(> ; SL ; VS ; density ; . . . .

: PI Correlation : __ ...:,.:_ ___

: Density

: b1 . . : 0"1

. . • b • • 2 • 0'2 . . : b3 : cr-3 : ba. : <1',. : b5 : o:5 : b6 : 6'.6 : b7 : <5:7 : bB : era : b9 : <St9 : . . . � . � · -----·�- . . . . . . . . .

a :Standard :Correlation :deviation :coefficient . . • • . . . . . . . . . .

7 . Zone 2 :0.00216 :o.0004,4 : o.00053 :0.00020: Zone 3 :o.001o4-:0.ooo44 : o.OOC>96:o.0004,3 : Zone 4 :o.00170:0.0CX>39:-o.ooo4o:o.ooo46 : Zone 5 :o.00095 :0.00028: o.00032:0.00027: A11 c1ata:o.00093 :o.ooou: o.00001 :0.00014 :

: a. Zone 2 :

Zone 3 : Zone 4 : Zone 5 : All data:

. . . • . . . .

. . . . . . : o.00090:0.00020: : o.00136 :0.00038 : : -o.00085 :0.00053: : -o.00036 :0.00025 : : -0.00001:0.000J.6 : . . . . . . . . . .

9 . Zone 2 :0.00183 :0.000lf.2: o.00062:0.00019: Zone 3 :o.00084 :0.00039: o.00112:0.00038: Zone 4 :0.00179:0.00017 : o.00022:0.00024 : Zone 5 :o.00104. :0.00023 : o.00017 :0.00022: All data:0.00081:0.000ll:-0.00005 :0.00014 : . . . . . . • . . . . .

10. Zone 2 :0.00249:0.0004,2: . • Zone 3 :0.00130:0.0()()lf.5 : : . • . . Zone 4 :0.00172 :0.00015 : . . Zone 5 :0.00094 :0.00019: . . • . All data:0.00081:0.00011: . . • • . .

ll. Zone 2 : Zone 3 : Zone 4 : Zone 5 : All data:

• • 12. Zone 2 :

Zone 3 : Zone 4 : Zone 5 . : All data:

. . . . . • . • . . • • • • . • • • :

. . . . . . : o.00067:0.00014 : : o.00038:0.00017 : : 0.00013 :0.000ll: : o.00016 :0.00011: : o.00011 :0.00007: . • • •

• . . • . • . . • .

. • . • . • • • • •

. . • . . • . . . • . • • . . • . . : • . . • . • • . • . • . • • . . . • . • • • . . . • • • . . . . . . . • . . • . . . • • . .

• • • . . . . • . • . . • • • • • • • • . . . • • . . • . . . . . . . • . . . • . . . • : . . . . . • . • • • . • . • • . . • . . • •

. . . . . . . . . . . . . . . 13 . Zone 2 :o.00243 :0.00035 : o .00066 :o.00010 :0 .00276 :o.00107 :

Zone 3 :0.00140:0.00035 : o.ooot..9:o.00015 :o.OC473:o.oozro: Zone 4 :0.00207:0.00016 : o.00032 :o.00005 :o.00657 :o.ooos3 : Zone 5 :o.00126 :0.00025 : o.00045 :o.ooou:o.00505 :0.00175 : All aata:o.00098:0.00010: o.00023:0.00005 :o.004.55 :o.00097:

. • • • . • • • . . . . . . . . . . . . . • : . . . . . • : . • . • . . . • • . . • • • . • . . • . . • . . . . • • . • . • . • • • . • • •

• • • • • • • •

. • . • • • : . . • . . • . • • . . . . • • . . • . • • •

. • . • . • . • . . • • • • . • • • : • • . . . • . • • • . • • - · . • • •

• • • • . . • • • • . •

• . . . • . . . . . . . • . • . • . . • . • . • . • . • • . . • . . • • . • . • . • • . . . . • • . . • . • . • • • . . . . .. .. . • • . . . . • . .. . • . • : • •

: . . • . • .

. • ' . . . • • • . • .

. . . . • . • . . • : . . . . . .

: 0.00054 :0.00012 : :0.00047 :0.00016 : :o.00034 :0.00013 : :0.00022:0.00008: :o.00034 :0.00005 : . . . . • . :0.00039:0.000ll : :0.00041:0.000l.6 : :o.00039:0.00005 : : 0.00025 :0.00006: :0.00022:0.00005 : . . . • • • :o.00035 :0.00013 : :o.00033 :0.00020: :o.00038 :0.00005 : :0.00026 :0.00006: :0.00022:0.00005 :

. • . • . . • . . • • . . . . • • • . . . . • . . • • • • . . . . • . • . . • . • • . .

. . . . . . . . . . . . . . : 0ooo4.12 :0.00197: 0.0OOll :0.00019: -0.03520 : 0.00388 : : o.00336 :o.00245 :-o.00071 :0.00053 : 0.00016 : o.004.71 : : o.00157 :0.00338 : o.00085 :0.00055 : -o.01318 : o.oo692 : : o.00000:0.00234 : o.00001:o.00033 :-o.ooa71 : 0.00638 : : o.00531:0.00140: o.00025 :o.00018:-0.00121: o.00686 . . . . . . . . . . . . . , : o.00506 :o.00205 : -o.00023 :o.00019:-0.04341 : o.00414 : : o.00339:o.00224 : -o.ool26 :o.ooo43: 0.00758 : 0.00439 : : o.00620:0.00311 : o.00114 :0.00066: 0.00718: 0.00836 : : o.00011:0.00248: o.00081:0.00035 : -o.00529 : 0.00675 : : o.00603 :0.00156 : o.00025 :0.00020 : 0.00119 : 0.00766 : • . . . • • . . . • . • • • . . : • • . •

: . . . • . . • • • . • • . . : . .

. . . . . . . . . . : o.00002 :o.00011 :-0.03432 : 0.00353 : : -o.00081:0.00046 : -o.00615 : o.C>Oll.07 : : o.00016 :o.00029:-0.01850: 0.00345 : : o.00038:o.00028 :-0.03256 : 0.00518 : : o.00037 :o.00018 :-0.00169: 0.00678 : . . . . . . . . . . : o.00051:o.00011:-0.02053 : o.00408 : : o.00046 :o.00020: -0.01361 : 0.00513 : : o.00042 :0.00006 :-o.01896 : 0.00343 : : 0.00057 :0.00012:-0.03192 : 0.00514 : : o.00030 :0.00007 :-o.00124 : 0.00675 : . . . . . . • • . • . . . . . . . . .

:o.00059:o.00011:-0.00060,o.00039: : 0.00069:0.00021: 0.00051:0.000ll-9: :o.00045 :0.00012: o.00124 :0.00058: :o.00016 :0.00008: o.00028:o.ooo4-4 : :o.00033 :0.00006:-o.0000'7 :0.00020: . . . . . . . . . . :o.00060:o.00016 :-0.00110:o.00044 : :o.00064:0.00024 : o.0004,9:0.<>0056: :0.C>OOll-4 :0.00012: o.00123:0.00057 : : 0.<X>021:0.00008: 0.00035 :0.()()()4.2: No correlation . . . . • • • • • .

• •

: • • • • • .

• • • • . • • • • . • .

• • • • . . • . • . . •

• . . • • • • •

. • • • : . • . • • • • • • . . . • .

• •

. • • • • .

• . . • • .

. . . :-0.02229 : o.00449 : : -0.01831 : 0.00571 : : -0.00298: o.0084.8 : : o.ol.126: 0.00717 : : 0.01386: 0.00820 : . . . . . . . . . .

: o.00038:0.00015 : 0.01736 : 0.00546 : : o.00025 :o.00022:-0.004.76 : 0.00635 : : o.00020:0.00014 : -o.00756 : 0.00831 : : o.00036 :o.00015 : -0.00707: 0.00679 :

• . : . . • • • • • .

• • • • • . . • • • . .

• • . . • . :-0.03570 : 0.00372 : :-0.02071:, o.00461 : : -0.01749: 0.00347 : : -0.�75 : 0.00555 : : -0.00005 : o.00666 :

o.88 0.75 0.79 0.50 0.69

o.86 0.78 o.66 o.4o 0.59

0.90 0.82 0.95 0.71 0.70

0.87 0.69 0.95 0.71 0.70

o.84 0.59 0.65 0.22 0.51

0.74 o.44 0.67 0. 38

0.89 0.76 0.95 o.66 0.71

. ,

... ,.:-

Table 3--Continued

Table i Sheet 3 ot s

• • • • • • • • • ;r ....avimum • • • • r • • I • • • JO � •

: PI : Density : krp : <Y¢ : Mp : kp <YpM<J> : SL : VS : density : Correlation : : : : : : : : : : : : : : : :

: b1 : <r1. : b2 : cr-2 : b3 : cr-3 : b4 : cr-4 : b5 : cr5 : b6 : 66 : b-r : 6'7 : be : 6a . .

b9 69 : a

:Standard :Correl.a.tion :deviation:coefficient

. . . . . . . . . . 1.4. Zone 2 :0.00252 :0.00042: o.00056:0.00022:

Zone 3 :O.OOl.28:0.00042: 0.00095 :0.00044:

15 .

Zone 4 :o.00179:o.00034: -0.00037:0.ooo45: Zone 5 :0.00095:0.00027: o.00032:0.00021: All data:0.00099:0.0001.l: 0.00005 :0.00015 :

. . Zone 2 : Zone 3 : Zone 4 : Zone 5 : All data:

.

.

. .

. . : o.00098:0.00025 : : 0.00131:0.00047: : -0.00135 :0.00057: : -o.00018:0.00026: : o.00020:0.00018:

. . . . . , . . . .

16. Zone 2 :0.00181:0.00037: o.ooo64 :0.00010: Zone 3 :0.001.20:0.00036: o.00049:0.00014: Zone 4 :o.00183 :0.00016: o.00036 :0.00005 : Zone 5 :0.00114:0.00022: o.00044:0.00010: All data:o.00078:0.00011: o.00021:0.00006:

. . . . 17. Zone 2 :o.00242:0.00038: o.ooo66:0.000ll:

Zone 3 :0.00153:0.00037: o.00045 :0.00015 :

18.

19 •

Zone 4 :o.00199:0.00033: o.00030:0.00010: Zone 5 :0.OC>Q96 :0.00025 : 0.00034:0.000ll: ..All data: O. 00096 : 0. 00011: 0. 00021: 0. 00006 :

Zone 2 :o.003o6 :0.ooo40: Zone 3 : O. 00160: 0. ooo44: Zone 4 :o.00192 :0.00030: Zone 5 :o.00076:0.00023: All data:0.00100:0.00011:

Zone 2 : Zone 3 Zone 4 : Zone 5 : All data:

. .

. . • . . . . . . . . . : :

: : . .

. •

. .

. .

. .

. .

. .

. .

. .

. .

: . .

. .

. .

. .

. .

. .

. . :

. . : . . :

. .

. .

. .

. .

. .

. .

. .

. . : . .

. .

:

. .

. .

. .

. . : . .

. .

. .

. . : . . :

. .

. .

. .

. .

:

. .

: . .

. .

. .

. .

:

. .

. .

. .

. .

. .

. .

. .

. .

. .

. .

:

. .

. . :

. .

. . :

. .

. .

. . : . . . .

. .

. . : . . . .

. .

. .

. .

. .

. .

• .

:0.00039:0.000ll: :o.00037:0.00017: :0.ooo40:0.oooo4: :0.00022:0.00006: :0.00020:0.00005 :

. .

. .

. .

. .

. .

. .

. .

. .

. .

. . . . : . .

. . . . . .

: . .

: o.00010:0.00020:-o.03297 : o.oo410 : : -o.ooo65 :o.00054 : o.00008: o.00486 : o.ooo83:o.00054 :-o.01391: o.'"'0678

o.00001:0.00032: -o.00871: o.O<.i527 : o.00021:0.00019: 0.00393 : 0.00729

. . . . . . . . . . . . . .

: o.00186 :o.00244 :-o.00025 :o.00024 :-o.o4662 : 0.00521 : : o.00558:o.00263: -0.00134 :o.00053 : 0.02422: 0.00546 : : o.00826:o.oo415 : o.00168:0.00011: 0001037 : 0.00957 : : -o.00039:0.00211: o.00044:0.00036 : 0.01485 : 0.00739 : : o.oo693 :o.00178 :-o.00001:o.00023: 0.01318 : 0.00882 :

. .

. .

. .

. .

. .

. . :-0.03422 : 0.00347 : : -0.01869: o.oo438 : : -0.01753: 0.00338 : :-0.02630: 0.00525 : : 0.00577 : o.00688 :

:-0.03247: o.oo405 : :-O.Olo61: 0.oo493 : :-0.00773 : 0.00701 : : -O.oo853 : 0.oo617 : o.008o7: 0.00730 : . . . .

o.00054 :o.0001.2 :-0.02054 : o.oo446 o.00044 :o.00021: -0.00753: 0.00544 o.00040:0.00012:-o.01.271: o.oo672 o.00037:o.00014:-0.00584 : 0.00632

: 0.00028 :0.ooooB : 0.00356 : 0.00726 : . .

. . : -o.00168:0.00049: :-o.00003:0.00062: : o.00144 :0.00012 : : o.00012 :o.ooo44 : : -o.ooo60:o.00020 :

: o.00038:0.00018: 0.03697: o.oo645 : : 0.00002 :0.00025 : 0.03524 : 0.00756 :

o.00014 :0.00018: 0.00050: o.01o62 : o.00023:0.00015: 0.01346 : 0.00733 : o.00013:0.00009: 0.03421: 0.00910 :

0.87 0.73 0.80 0.52 o.64

0.77 o.64 0.52

Imginary 0.37

Oo91 0.78 0.95 0.70 0.69

0.87 0.72 0.78 0.54 o.64

o.84 o.64 0.80 0.51 0.65

0.61 Imaginary

0.31 o.08 0.29

.. -""

�

A

o_

. . . . . . . k4,

. • PI . Densit;x: • . . • . •

Correlation : • . . . . • . • . 62

. b3

. a: • • b1 . 61 . b2 . • . . • • . • • . . . . . . . . . . • . • . • .

20. Zone 2 . . : Ooooo68:0.00017 : • . • • . • Zone 3 . . : 0.00019:0.00021: . . . • . . Zone 4 . . : o.00005 :0.00014 : . • . . . . Zone 5 • . : o.00011:0.00011: . • • . • • All data : . : o.00011 :0.00008: . . . . •

• . . • • . . • . . . . . • 21. Zone 2 :o.00306 :0.00050: . :0.00274 :0.00159: .

Zone 3 :0.00099:0.00043: . :o.00326 :0.00349: . Zone 4 :o.00161:0.00024 : . :o.oo634 :o.0014o: . Zone 5 :o.00066 :0.00025 : . :o.00260:0.00202: . Ul data :0.00094 :0.00011 : . : o.�i1 :o.00103 : .

Notes : PI = plasticity index . D = density, lbs per square foot .

kct, == phi skewness . 6 ct, = phi standard deviation . M ct, = phi arithmetic mean diameter . SL = shrinkage limit . VS = vane shear, pounds per square toot . rJ1, == percent maximum density .

. • O""f • • • •

b4 • • • • . • • • . • • . . . • • • . . . . . • • • . . . . . • . . . . . • . . . . • . • . . . • . . . .

Table 3--Continued

• . • • k1� cr�Mf

• • M� • • SL . • • • . . • • . . . .

b6 .

0-6 .

l>-r . .

• . • . a: • bs . • . . • . . . • • . . . . • • • . . . : -O.OOll4 :0.0004-6 : • • • • • . : -o.00001:0.00060: . • . • • • : o.00143 :0.00074 : . • • • . . : 0.00011:0.0004-5 : • . • . • . : -o.00055 :0.00020: • . • • • . . • • • . . . • • . . . . . • . • . • . . . . . . . . • . . • • • . . . . . • . . . . . • • • . . . . . . . . . • . . . . . • . • • . • •

• • J maximum vs • • density

• • . <5's

. . . • • -

()9 b9 • • • • • . . . • • . • . . . . . • . • • • . . . • : • • . • • • • • • . • . • . . • . • • • . . : • • • . • . . • • • • •

. • • • • .

Table i Sheet 4 ot

. :Standard :Correlation . . :deviation :coefficient . • • • . • • . . . . . . : -0.00465 : 0.00563 : 0.73 : o.02o8o : 0.00736 : Imaginary : o.008o9: 0.01076 : 0.27 : 0.02228 : 0.00746 : Imaginary : o.o'.3445 : 0.00909 : 0.29 . • • . • . : 0.02238 : 0.00552 : 0.74 : 0.02569 : 0.00603 : 0.52 : 0.01674 : 0.00586 : 0.85 : 0.02390: Oooo68l : 0.38 : 0.02216 : 0.00714 : o .66

.. ,,.

-·�

TABLE J A

CONTINUATION OF TABLE J -- MULTIPLE LINEAR CORRELATION VALUES USING ELECTRONIC CCMPUTER (LL) Liquid Limit is Added as en Independent Variable

Values in General Equation TF = a+b1PI +b2D+b3k�+b4 cr�+b5Mq,+b6k�CV>Mt, +�SL+bgVS+bgD,C+b1oLL

Independent Variable . . : . . PI k.'tj, Correlation . . . . I I

22.

23.

24.

25 .

26.

'rl.

: b . � : b . . . . Zone 2 : 0.00]76: 0.00066: Zone j : -0.00091:0.00208: Zone 4 : 0.00400:0.00200: Zone 5 : -0.00017 :0.00126: All data : O.OCff/4 : 0.00018:

: . .

. . . : . . : . . . . . . . . . . : . . . . .

: . . . . . . . . . . . . . . . . . . . :

Zone 2 : 0.00286: 0.000,0: o.ooos.0.00011: . . . . Zone J : 0.00023:0.00179: 0.00043:0.00016: . : . Zone 4 : 0.00352: 0.00177 : 0.00028 :0.00010: . . . . Zone 5 : 0.00070:0.00117 : O.OOOJJ: 0.00011: . . . . All data : 0.00050:0.00017': O.OOOJl :0.00006: . . . . . . . : : . . . . . . . Zone 2 : 0.00361 :0.00066: . :0.00244:0.00162: . Zone J : -0.00043:0.00231: . :0.00216: 0.00397: . Zone 4 : 0.00335 :0.00145 : : : 0 .00615 : 0.00139 : Zone 5 : -0.00035 :0.00124: : :O .002.88 :0 .00206: All data : 0.00068 : 0.00017 : . : 0.00447 : 0.00103: . . . --:-._ . . . . . . . . . . Zone 2 : 0.00299 : 0.00071: : . . . . . . Zone 3 : -0.00024 :0.00221: : . . . . . . Zone 4 : 0 .00335 :0.00152: : . . . . . . Zone 5 : -0.00154: 0.00128: . . . . . . . . All data : 0.00032: 0.00019 : . : . : . . . . . . . . . . . . . . . . Zone 2 : 0.0024J:0.00076: : . : : . Zone J : -0.00131: 0.00220: . . . . . . . . Zone 4 : 0.00399:0.00213: . . . . . . . . Zone 5 : -0.00008: 0.00132: . . . . . . . . All data : 0.00061:0.00030: . . . • . . . . . : . . . . . . . . . . . Zone 2 : 0.00340:0.00063: . . . . . . . . Zone 3 : -0.00100:0.00202: . . : . . . . Zone 4 : 0.00339 :0.00205: . . . . : . . Zone 5 : -O.OOOJ6: 0.001J7: . . . : . . . All data : 0.00076:0.00017 : . . . . . . . .

o'n= Standard Diviation of the Variable

. : . . . . . C5"<J> . M ¢ SL vs

I b . <S . b : . . . . . . . . . . . . . : : . : : : . . . . . . . . : . . : . . . . . . . . . . . . . . . . : : : : : : . . . . . . . . : . . . . . . . . . . . . . . .

: : . . : : : : : : . . . . . : . : : : : : . . . . . : . : . . . . : : . . . . . . . : . : . . . : : : . . . . . . : : . : . : : . . . . . . . . . . . . : . : . . . . . . . . . . . . . . . : . : : : . . . . . . . . . : . : : : : . . . . . . . . . . . . . . . . . . . . . . . . . . : . . . . : . . : . . . . . . . . . : . : . : : . . : . . . . . . . : . . . . . . . . . . . . . . . . . . -:-- : : . . . . . . . . . . . . : . . : . . . . . . . . . . . . . . : . . : 0.00039 : 0.00017 : . . . . . . . . . . . . . : 0.00024:0.00026: . . . . . . . . . . . . . . : 0.00035 : 0.00008: . . . . . . . . . . . . . . : 0.00021 :0.00008: . • . . . . . . . . . . . : : 0.00026:0.00005 : . . . : . . . . . . . ...... __ �--- . . . . . . . . . . . . . . . . . . : : : : : -0.001J5 :0.00047 : : . . . . . . . . : -0.00035 :0. 00052: . . . . . . . . . . . . . : : 0.00001:0,00066: . . . . . . . . . . . : : : 0.00012:0 .00044: . . . . . . . . . . . : : -0. 00015 :0.00027: . . . . . . . . . . : . . . . . : . . . . . . . . . . : : : : . : : 0.00668: 0.00268 : . . . . . . . . . : 0.00405 : 0.00299: . . . . . . . . . . . . . : 0.00422: 0.00357 : . . . : . . . . . : : : . . : -O.OOlOJ: 0.00274 : . . . . : : . . : : . : 0.00532 :0.00149 : . . .

. . : . . . . : : : . . : : . . . . : . . . . . . : . . . . . . . . . . . . . . . . : : . . . . . . . . . . : : : : . .

Table 3 A Sheet 1 or 3

: LL

: : standard : Correlation . a : Deviation: Coetficient . . . . . . . . . . : -0.00077: 0.00048: 0.04402: 0.00556 . . : 0.00159: 0.00160: -0.00011: 0 �00601 . . : -0.00187: 0.00151: 0.05254: 0.00803 . . : 0.00059: 0.00097: 0.021'4: 0.00695 : : 0.00027: 0.00020: 0.02145 : 0.00761 . . . . . . . . . . : -0.00046: 0.00035 : -0.01926: 0.00400 . . : 0.00101 :0.00135 : -0.02804 : 0.00501 . . : -0.00119 : 0.00135 : 0.01214 : 0.00705 . . : 0.00019:0.00089 : -0.010J2: 0.00627 : : 0.00072: 0.00021: -0.0168J:0.00696 . . . . : . . . . : -0.00061 :0.00049: O.OJ744 : 0.00548 . . : 0.00115 :0.00183: 0.00532: 0.00617 . . : -0.00133:0.00109 : 0.0]708: 0.00579 . . : 0.00081:0.00097 : 0.01413: 0.00685 . . : 0.00039:0.00019 : 0.01326: 0.00703 . .

----- - :-· : . . - - - . . -- --- - : -: -0.00060:0.00046: O.OJ692: 0 .Q0,22 : : 0.00088:0.00178: 0.01043:0 .00604 . . : -0.00152 :0.00114: 0.04357 : 0.00608 . . : 0.00171:0.00100: 0.00262: 0.00641 : : 0.00057 :0.00020: 0.01220:0.00701 . . . . . . . . . . : 0.00010:0.00053: 0.05660: 0.00500 : : 0.00193: 0 .00171 : 0.00049: 0.00613 . . : -0.00186 :0.00157 : 0.05221 : 0.00824 . . : 0.00052:0.00102: 0.02030: 0.00706 . . : 0.00039: 0.00029: 0.02253: 0.00764 . . . . . . . . . . : -0.00106: 0.00046: 0.04412: 0.00513 . . : 0.00150:0.00156: -0.002'77: 0.00584 : : -0.00150:0.00153 : 0.04261 : 0.00795 . . : 0.00073:0.0010, : 0.02116: 0 .00705 . . : 0.00016:0.00020: 0.01806: 0 .00721 :

0.7j 0. 53 0.70 O . JJ 0.60

0. 87 0.71 0.78 0. 52 0.68

0.74 0.49 0.86 0. 36 0.67

0.77 0. 52 0.84 0.49 0.68

0.79 0.50 0.68 0. 28 0.60

0.78 0. 57 0.70 0.28 0.65

. • . k'�

. Otf, . .

Correlation . PI . Densit;y: . . . M, • . I I I I I b1 : d'1 . b2 . d'2 . bJ

. 6� . b{t

: d"ti . b5 . 65 . . . . . . . . . . . . . . . . : : . . . . . . . . . 28. Zone 2 : 0.00385 : 0.00049: . . . . . . . . . . . . . . . .

Zone 3 : 0.00029:0.00203: . : • . . : . : . . . . . Zone 4 : 0.00346:0.00169: : . : . : . . . . . . . . Zone 5 : 0.00092: 0.00124: : : : . : . : . . . . All data : 0.00069 :0.00017 : . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

29. Zone 2 . . : 0.00085 : 0.00015 : . . . . . . . . . . . . . . Zone 3 . . : 0.00042:0.00015 : . : . . : . . . . . . . Zone 4 . : : 0.00031:0.00011: . . . . : . . . . . . . Zone 5 . . : 0.00031:0.00011 : : : . . . : . . . . . All data : : : 0.00037:0.00006: . : . : : : . . . . . . . . : : : . . . . . .

.30. Zone 2 . . : 0.00085 : 0.00014:0.00J56: 0.00156: . . . . . . • . . . Zone J . . : 0.00045 : 0.00015 : 0.00371: 0.00284: . . . . . . . . . . Zone 4 . . : 0.00033:0.00006:0 .00677: 0.00101: . . . . . . . . . . Zone 5 : . : 0.00042: 0.00010: 0.00518: 0.00177 : . : . . . . . . All data : . : 0.00042: 0.00005 : 0.00578 :0.00090: . . . . . . . . . . • . . : . . . : • . . . . . . . . . .

31. Zone 2 : 0.00278: 0.00052: 0.000'72:0.00010: 0.00315 : 0.00106: -0.00089: 0.00222: 0.00239 : 0.00077: Zone J : 0.00154: 0.00191: 0.0005J:0.00016: 0.00446: 0.00J27: 0.00076: 0.00322: 0.00194 : 0.00141: Zone 4 : 0.00241 :0.00075 : 0.00025 : 0.00005 : 0.0079J :0.0008J: 0.00372: 0.00128 : -0.00082: 0.00107 : Zone 5 : -O.OOUJ: 0.00122: 0 ,00044 : 0.00010:0.00611: 0.00174: 0.003'72: 0.00166: -0.00014 : 0.0009.3: All data : 0.00007:0.00023: 0.00037: 0.00006: 0.00579 : 0 ,00092: 0.00152:0.00108: 0.00059: 0.00064:

: . . . . . . . . : . . . . . . . . . . 32. Zone 2 : 0.00]79: 0.00064: : :0.00258: 0.00127 : -0.00026: 0.0026.3: 0.00142: 0.00089 :

Zone 3 : 0.00143:0.00238: . : 0.00416: 0.00400: 0.00109:0.00389: 0.00125 : 0. 00168 : . Zone 4 : 0.002J6:0.00064: . : 0.00'775 : 0.00072: 0.00329: 0.00112: -0.00122 :0.00091: . Zone 5 : -0.00066:0.00131 : . : 0.00574: 0.00181: 0.00288: 0.00174: 0.00061: 0.00099: . All data : 0.00026:0.00023: . : 0.00573: 0.00095 : 0.00178: 0.00112: 0.00049:0.00066: . . . . . . . . . . : . . . . . . . . . . .

33. Zone 2 : 0.00258: 0.00081: . : 0 ,00296: 0.00162� 0.00417 : 0.00317 : -0.00011: 0.00lJl: . Zone J : -0.00094:0.00248: . : 0.00133:0.00436� 0 .00273:0. 00457 : 0.00017:0.00206: . Zone ·4 : 0.00162: 0.00110 : . : 0.00860: 0.00114 : 0.00587: 0.0017J: -O.OOJ2J: 0.00149: . Zone 5 : -0.00224:0.00156: : : 0.00422: 0.00234 : 0.00293: 0. 002.34: 0.00014:0.00121: All data : 0.00007: 0.00025 : . : 0.00460: 0.00102: 0.00398: 0.00123: -0.00067 : 0.000'71: .

�

. q_

: IS

1�Q$Mm . & I

b6 : d"6 . � : <f7 . . . : . . . . . . . . . : . . . . . : . . . . . . . . . . . . . . . . . . . .

: . . . . . : . . . : . . . . . : : . . . : . . . : . . . . . . . . . . . . . . . . . : . . . : . . . . . . . . . : . . . . . . . . . . . . . . . . . . . . . . . . : . . : . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . : . . . . : . . . • . . . . . . . . . . . . . : . . . . . . . .

Table 3 A Sheet 2 or 3

. . % Maximum . . : Standard : Correlation . . . . : IS . Densit;y: : l,I.. . a : Deviation: Coetticient I : bg . 6'g . b2 . 6'2 : b10 : 610 : . . . . . . . . . . . . . . . . . . . . . : 0.00056:0.00011: -0.00087 : 0. 000J6: -0.00092 : 0.00414 . 0. 86 . . . : . : 0.00041: 0.00022: 0.00100:0.00151 : -0.02391:0.00555 . 0. 62 . . : . : O.OOOJS :0.00012: -0.00119 : 0.00129: 0.00711:0.00675 . 0. 80 . . . : : O.OOOJ8: 0.00015 : -0 , 00012: 0. 00094: -0.00496 0.00642 . 0.49 . . . . : 0.00032 :0.00008: 0.00047 : 0.00020: -0.01058 : 0.00710 . o.66 . . . . . . . . . : : . . . . . . . . . . : 0.00086:0.00037 : -0.06893:0.00569 . 0.72 . . . . . : . . . : 0.00118:0.00027: -0.03080 :0.00484 . 0.73 . . . . : . . : : 0.00145: 0.00027 : -0.02915 :0.00755 . 0.74 . . . : . . : : 0.00071:0.00019 : -0.01399 : 0.00620 . 0.54 . . . : : : : : 0.00119 : 0.00013: -0.0.'.3093: 0.00719 . 0.65 . . . . . . . . . . . . . . . . . . : . . : 0.00102: 0 ,00036: -0.0'7652:0.0053J . 0.76 . . . . . . . . : 0.00107 : 0.00028: -0.03591 :0.00472 . 0.75 . . . . . . . . . : 0.00154 :0.00015 : -0.04129: 0.00424 . 0.93 . . . . . : . . . : o.ooc;6: o.00019 : -0.0370J:o.00;56 . 0.65 . . . . . . . . : O.OOlJl :0.00011: -0.04604: 0.00611 . 0.77 . . . . . . . . . . . . : . . . . . . . . . . . . . .: -0. 00039: 0. 00031: -0. 04250: 0. 00331 . 0.91 . . . . . . . . . : -O.OOOJ,4:0.00150: -0.02777 : 0.00482 . 0.73 . . . . . . : . . : -O.OOOJ3:0.00061: -0.0ll48: 0.00288 . 0.97 . . . . : . . . : 0.00188: 0.00094 : -0.06271: 0.00524 . 0.70 . . . . : : . : : 0.00110 : 0.00022: -0.04J54 : 0.00591 . 0.78 . . . : . . . . . . . . . . . . . . . : 0.00056: 0.00011: -0.00082: 0.000J6: -0.0l248: 0.00393 : 0.88 . . . : : 0.00049:0.00024: -0.00012: 0.0018J : -0.02275 : 0.00583 . 0. 57 • . . . : 0. 00031 : 0. 00005 : -0. 00027: 0 .00052: -0 .01249·: 0. 00249 . O .<n . . . . . : 0.00052:0.000lJ: 0.00126 : 0.00101: -0.0554J: 0.00550 . 0.66 . . • . . : 0.00039 : 0.00007: O.OOOOJ:0.00022: -0.0J687 : 0.0061J . 0.76 . . . : : : : : . . : . . : 0.00689: 0.00301: : : -0.00093: 0.00047 : O.OJ164: 0.0050J . 0.79 . : 0.00448: 0.00402: . : O.OOlJJ: 0.00196: -0.00803: 0.00652 : 0. 39 . : 0.00443:0.00194: : : 0.00014 : 0.00089: 0.00719 : 0.00402 . 0.93 . : -0.00173: 0.00331: . : 0.00227 : 0.00]2 2: -0.01257 : 0.00675 . 0. 39 . . : 0.00532: 0.00146: : : 0.00074: 0.0002J: -0.00405 :0.00655 . 0.72 .

• : : . . . k'�

. Correlation : PI

. Densit;r . . : I I b1 . 61 . b2 : 62 . bJ . O') . b4 . . . . .

: . . . . : . . . . 34 . Zone 2 : O .OOJJS: 0 .00055 : 0.00042: 0.00019 : . . . .

Zone 3 : 0.00046: 0.00170: O .OOlll: 0.00039 : : . . Zone 4 : 0 .00287:0 .00089 : 0 .00024: 0.00025 : . . . . Zone 5 : -0.00094: 0.00117 : 0 .00029 : 0 . 00023: . : . All data : 0.00001:0.00019 : O .OOOJl: 0.00015 : : . . . : . . : : : . . .

35. Zone 2 : 0 .00.308:0.00053: 0 .000.30: 0 .00021: . . . . Zone 3 : -0.00070:0.00176: 0 .00101: 0.00043: : . Zone 4 : O.OOJJJ :0 .00179: -0.00044: 0.00047: . : . Zone 5 : 0 .0006.3: 0 . 00142: 0 .00035 : 0 . 00030: : : All data 1 0.00055 : 0.00019 : 0 .00026:0.00017 : . . . . . . . . . . . . . . . .

36. Zone 2 : 0.002Jl :0 .00060: 0 .00052: 0 .00020: . . . . zone J : 0 .000'17:0 .00168: 0 .00112: 0 .000.39 : . . . . Zone 4 : 0.00269 :0 .00087: 0 .00019 : 0 .00024: : . . Zone 5 : -0 .00068 : 0 .00lOJ: 0 .00026 :0 .00022: : . . All data : -0.00008: 0 .00019 : 0 .00040: 0.00015 : . . . . . . . . : : . . . . . .

YI . Zone 2 : O.OOJ2J: 0 .0005J: . . : . . . . Zone 3 : O .OOlJS: 0 .00209: : . : : . Zone 4 : 0 . 00272:0.00086: : . . . . . . Zone 5 : -0.0005J: 0.0010J: : . : . . . All data : 0 . 00017 :0.00017 : . . . . . . . . . . . . . . . . . . . .

JS . Zone 2 : 0.00268:0.00048: 0 .00064: 0.00011: 0 . 00254 : 0.00111: Zone J : 0.00145 : 0 .00189 : 0.00049 : 0 .00016: 0.00476: 0.00320 : Zone 4 : 0.00279 : 0.00088: O .OOOJl:0 .00005 : 0.00648: 0.00084 : Zone 5 : 0 .00067:0 .00105 : 0.00044: 0 .00011: 0.00517 :0 .00178 : All Data : 0 . 0007/:0.00015 : 0 .00038: 0.00005 : 0.00548: 0 .00088:

'('·

-\

. . c5'1'

. . . Ah� . k'i6raMt I I . 64 . b5 : 6-5 . b6 : 6"6 . . . . . : . . . . . . . . . . . : . : 0. 00029:0 .000ll: . - · . . : : 0. 00036 :0 .00019: . . : : . : 0 .00040: 0.00005 : . : : : : O.OOOJQ: 0 .00006: : . . : 0 .00029:0.00005 : . . : : . . . . . . . . . . . . . . . . . . . : . : . . . . . . . . . . . . : : . : . : . . . . . : 0 .00036: 0 .00012: . . . . : . : 0 .00041 :0 .00018: . . . . : : 0.000.39 : 0.00005 : . . . . : : 0.00029:0 .00006: . . . . . : O .OOOJl : 0 .00005 : . . . . . : : . : . . . : : . : 0.00030:0 .00013: . : : : : O.OOOJJ:0.0002J: . . . : 0.00037: 0 .00005 : . . . : . . : 0.00030 :0.00006: . . : . . : O.OOOJl :0.00005 : . . . . . . . . . . . . . . . . . . . : : . . . . . . . . . . . . .

b7 c5'7

Table 3 A Sheet 3 ot 3

� % Maximum l)e_ns_it.z li1& a

: standard : Correlation : Deviation: Coetticient

bg d"g b9 : 0'"9 b10 : 610 . . . . . . . . . . . . . . 0 .00441 :0.00177: 0 .00018: 0.00018 : -0.00066: 0.000JJ: -0.01801 :0 .00322

: 0 .00236 :0 .00227: -0.00085 : 0 .00048: 0 .00020: 0 .00lJQ: -0.00822 :0 .00424 : -0 .00173: 0 .00174: 0.00015 : 0.00029: -0.00076: 0.00067: -0.00665 : 0.00344 : -0.00104: 0. 00210: 0 .00019 : 0.00030: 0.00160:0 .00092: -0.04723:0.00509 : 0 .00335 : 0 .00124: 0.00004 :0.00017 : 0 .00102: 0 .00022: -0.03414: 0.00580 . . . . . . . . . . . . . . . . : 0.00556:0.00187: 0 .00029: 0 .00019 : -0.00091 : 0.000J5 : -0.0l�: O.OOJ5.3 : : O .OOJJ6: 0 . 00245 : -0 .00081:0.00054: 0 .001J2: 0.00129: -0.02048: 0 . 00470 : O . OOllJ : 0.00342: 0.00087:0 .00055 : -0.00125 : 0.00134: 0.00735 :0 .00695 : -0.00028 : 0 .00267: -0.00002:0.00038: 0.00025 : 0 .00111 : -0.01025 :0 .00648

0 .00438 :0 .00142: 0 .00002: 0 .00020: 0 .00056: 0.00023: -0.01556: 0.00671 : : : : : : : 0.00010:0 .00019 : -0.000J7: 0.00034: -0.02J84: 0.00J52 : -0. 00081 :0 .00048: 0 . 00006: 0 .00130: -0.0Cfl07:0.00425 : 0 .00019 : 0.00029 : -0.00070: 0 .00066: -0 . 00685 : 0.00.344 : 0 .00024 : 0.00028: 0 .00139:0.00081 : -0.04709:0 .00502 : : -0 .00002: 0.00017 : 0 .00119 : 0 .00021: -0.0J621 : 0.00596

: : : : : : 0 .0005J: 0 .00010: -0.0007J: O.OOOJ4: -0 .00404 :0 .00J84 : 0 .00046:0.00021 : -0 .00006: 0 .00164 : -0.01266:0 .00534 : 0 .00041: 0.00006: -0 .00077 : 0 .00065 : -0.00605 : 0 .00.340 : 0.00055 :0 .00012: 0.00116: 0.00079 : -0 .047/5 : 0.00505 : 0 .00040: 0.00007 : 0 .00088: 0.00018: -0 .02952: 0.0061J . . . . . . . .

: -0.00026:0 .000J4: -0.0278J:0.007/4 : -O.OOOOJ:0 .00147 : -0.02017 :0.00479 : -0.00055 : 0 .00067 : -0.00807: 0.00350 : 0.00046: 0.00080: -0 .0JJ49 : 0.00561

0 .00095 : 0 .00018: -0.03477 : 0 .00596

0 . 92 e.so 0 .95 0 .72 0 .79

0 .90 0 .75 0 . 78 0.47 0 .71

0 .90 o.so 0 . 95 0.73 0.78

0 . 88 0 . 66 0 .95 0 .73 0.76

0 .89 0 .74 0 .95 0 . 65 0 .78

�

4 ...

APPENDIX I

EQUIPMENT AND PROCEDURE FOR PERFORMING TRACTIVE FORCE TEST ON COHESIVE MATERIALS

Tractive force or boundary shear may be defined as the force per unit a'rea exerted by a fluid flbwing past a stationary boundary. The force, acting on the surface of the boundary in the direction of flow, is dependent on flow conditions and the roughnes s characteristics of the boundary material . In an earth canal, tractive force is a pri­mary agent tending to cause erosion .

For every earth material there is a critical tractive force or range of tractive forces above which erosion will occur and below which the material will remain es sentially stable.

The magnitude of this critical tractive force is dependent upon the properties of the soil, including cohesion, size and shape of soil particles, range and distribution of particle sizes, and various unknown physical and chemical p roperties . The determination of critical tractive forces has, in the past, depended to a con­siderable extent on the judgment of the ob server. In some cases, initial movement of individual grains has been the criterion, whereas in other cases the criterion has been the beginning of general bed movement . In calibrating the tractive force tank, the experimenters tended toward the latter criterion.

During the l ast two decades, numerous experiments have estab­lished for noncohesive materials a fairly consistent relationship between critical tractive force and the mean diameter of particles composing the bed material . The majority of these experiments have been performed with uniform sand and gravels . However, no satisfactory relationship between tractive force and soil prop­erties has been obtained for cohesive materials, although it has been conceded that cohesive soil s are generally more resistant to erosion than are noncohesive soils.

The p rimary purpose of this laboratory investigation was to obtain data to assist in development of canal design criteria for cohesive

soils based on the tractive force theory. However, the test may be adopted as a: standard test for determining the erosion r esistance of soils , especially those soils proposed for use as canal lining material. The test may also be used to evaluate the stabilizing effect of chemical or other additives .

TEST APPARATUS

Description of Equipment

The tractive force test apparatus, including tank., motor, plastic lid, impeller, pressure gage, and pr essure regulator is shown in Figure 1 . Water is circulated in the cylindrical tank through rota­tion of the impeller . The plastic lid was added to confine the water surface and improve visibility. Pertinent data regarding basic com­ponents are :

1 . Tank

a. Diameter = 3 5 inches

b . Total height = 24 inches

c . Height from sample surface to tank top = 1 3 - 3 / 8 inches

d . Height from sample surface to bottom of plastic lid = 9 inches

e . Depth o f water used = 1 2 inches

2 . Three -blade impeller

3 .

a. Blade width = 3 mche.s

b . Blade length = 17 inches

c . Distanc e from sample surface to bottom of blade = 4 - 1 / 2 inches

Sample test well

a. Width = 12 inches

b. Length = 15 inches

c. Depth = 10 inches

4 . Sample container is a standard 8-inch-diameter plastic percolation test cylinder .

2

.._.,

_,

..,:

,. �--

5. Plastic lid is made of 3/ 8-inch clear plastic.

6. Pressure gage reads from O to 100 pounds per square inch.

7. Pressure regulator variable from O to 7 0 pounds per square inch.

8. The power source is a converted compressed air drill.

Additional equipment required for this test includes two stopwatches, one for accurate determination of the rotational velocity and the other for determining the time required for testing at each velocity incre­ment. A thermometer for reading the water temperature and var­ious tools such as trowels., screwdrivers , etc. , also are needed.

Calibration of Test Apparatus

A bank of four pitot tubes., mounted as shown in Figure 2., was used to determine magnitude and distribution of velocities occurring near the surface of the sample. The sample surface was represented by a smooth plastic plate set flush with the floor of the tank. It was assumed the logarithmic velocity di,stribution law applies in the immediate vicinity of the boundary.

Static pressures were read from s tatic pressure taps in the pitot tubes and at piezometer taps across the plastic lid. At given verticals there was close agreement between measured static pressures.

From preliminary tests the tendency of sand and gravel particles to deposit near the center of the tank indicated a secondary circula.­tion similar to that found in open channe 1 flow around curves. The resultant direction of velocity components was checked by means of short lengths of string fastened at three levels at various points across the sample. The levels ranged from O to 1 -3 / 4 inches above the s ample surface. Figure 3 shows the strings oriented along lines closely following arcs from the center of the tank. Orienta­tion of the strings remained essentially the same over the entire range of rotational velocities. It was concluded that effects of secondary currents were minor in comparison to primary currents. Pitot tubes were alined with the mean direction of flow indicated by the strings ..

Readings on the pres.sure gage were correlated with rotational velocities of the impeller. The purpose of this correlation was to provide a basis for immediate determination of rotational veloc­ities. Results of the correlation are plotted in Figure 4.

As a direct method for measuring boundary shear was not available, the rotational velocities required to move uniform sands and gravel were determined. The tractive force required to move these sands

3

and gravels was known. The procedure followed was e ssentially the same as that presented under the heading "Performing the Test 1 1

•

Figure 5 is a photograph of sand.s and gravels used in the tests . Table 1 shows their source location and size range. Results of the.se calibration tests are plotted in Figure 6 .

Analysis of Calibration

Relation of critical tractive force to mean diameter of material is given in Figure 7 . A relationship between rotational velocity of the impeller blade and resulting tractive force was established by combining calibration results shown in Figure 6 with this crit­ical tractive fore�. The combination results in the equation T0 = 0 . 000146 Vr

where

To = tractive force acting on sample, lb/ft 2

V r = rotational velocity of impeller blade, rpm

It is apparent that tractive force varies with distance from the cen­ter of the tank. During calibration runs with noncohe.sive materials , erosion was concentrated near the outer edge of the sample at a distance of approximately 1 . 1 5 feet from the center of the tank ( 1 . 7 5 inches from outer edge of sample) . Therefore, the equation applies only for the radial di.stance (r) equal to 1 . 1 5 feet.

As shear varies with the .square of the velocity, distribution of shear acro.ss the .sample wa.s determined with the aid of the veloc­ity distribution obtained from the pitot banks. The distribution indicated that at r = 1 . 1 5 feet, velocity of the water near the bound­ary was approximately 0 . 85 times the velocity of the blade, or Vw = O . 85 Vb. Combining equations with the Vw/Vr ratio for r = 1 . 1 5 feet results in:

and

as

and

V =

1 . 1 5 ( 27T) V b 60 r

T0 = 0 . 000 146 ( 8 . 30)2 Vb2

Vw Vb =

0 . 8 5

To = O . 000 146 (8 • 30) 2

V 2

(O . 85 )2 w

4

-.,

·.,

rt-;,

----

T0 = 0 . 0 140 Vw2

where

letting

Vw is the velocity of flow in ft/ sec near the boundary as determined by the pitot tubes

V C = o . 0 140 ( . w) 2

Vr

and combining with the preceding equation results in TO

= CV r 2 .

C is a factor which varies with the radial distance .

The variation of C across the sample is shown in Figure 8 ., in which the radial distance is expressed in terms of x., the distance in inches from the outer edge of the sample .

Figure 9 may be used to estimate the magnitude of the tractive force at any point on the sample area for various rotational veloc­ities . The zones corresponding to 2-inch increments of the x dis ­tance are as defined on the figure . It is doubtful whether the tractive force should be estimated to more than two significant figures.

TEST PROCEDURE

The procedures recommended for performing the tractive force test on samples of cohesive soil are based primarily on experience gained from preliminary tests. Consequently., the recommended procedures should be considered as tentative and subject to revision pending the gaining of additional experience . The foregoing re,ser­vation applies particularly to some of the quantitative testing criteria.

The recommended'" procedure together with a sample data sheet are presented in the following pages.

Preparat_ion for Test

Preparation of the sample involves saturation of the material and smootning the surface prior to beginning the test. Approximately 1-we ek total immersion should be sufficient to saturate most sam­ples . After removing the sample from the immersion tank., the surface should be smoothed off so as to be flush with the flange of the 8-inch percolation settlement cylinder . A trowel., putty knife., straight edge., or other suitable instrument may be used for- this purpose. The cylinder may now be placed in the sample well of the tractive force tank. Care should be taken to fill crack,s such as those between the cylinder flange and the sample well cover with modeling clay in order to obtain a smooth transition between the floor of the tank and the sample surface.

5

The tank is next filled with water to the level indicated by the black line on the wall of the tank. At this point, the water temperature is taken.

Performing the Test

The ultimate aim of the test is to determine, in terms o f the rota­tional velocity of the impeller blade, the tractive force required to cause erosion of the sample. The test procedure consists es.sen­tially of approaching the critical rotational velocity in systematic steps between which the velocity is held constant over specified intervals of time. Rotational velocities are expressed in revolu­tions per minute and are determined by counting the number of revolutions of the impeller blade occurring in a period of from 30 to 60 seconds as timed with a stopwatch. A second stopwatch is used to provide a continuous time record of the test. The rota­tional velocity may be set fairly accurately to a predetermined magnitude by means of the pressure- regulator valve and pre.ssure gage in accordance with the calibration curve .shown in Figure 4. Velocitie.s should always be varied by turning the pressure -regulator valve. The line valve is left open during the test.

The way in which the critical rotational velocity is approached con­stitutes an important part of the test. Increasing the velocity by large steps precludes the possibility of accurately determining the critical rotational velocity. However, if the velocity increments are too small, excessive time is consumed in performing the test. It is r�commended that velocity increments be varied from a max­imum of 5 to a minimum of 1 revolutions per minute, with incre­ments becoming progressively smaller as the critical condition is approached. Between steps, the velocity should be increased grad­ually, as a sudden acceleration may prematurely precipitate an unstable condition. Upon attainment, the desired rotational velocity should be held constant for a period of from 5 to 10 minutes before increasing the velocity another step.

When the critical rotational' velocity is reached, erosion tends to begin quite suddenly and to progress rapidly. This is true for sandy clay, lean clay, and plastic clay. There should be little question as to whether or not the critical condition has been reached.

When it becom�s apparent that critical rotational velocity has been attained or surpassed, the test should be stopped . The valve should be closed, the tank drained, and the lid removed . The distance from the outer edge of the sample to the center of the eroded area should be measured in inches and recorded as shown on the sample data sheet.

6

�.

'

�

ct.·

Summary of Procedure

In performing a laboratory test, it is easy to overlook details or to o.mit steps which may have a significant bearing on the outcome of the test . Errors or omissions can sometimes be avoided by frequent reference to a check list which summarizes test proce­dures . It is recommended the following outline be used as such a check list.

A. Preparations for test

1 . Preparation of sample

a . Saturate ( 1 -week immersion)

b . Smooth surface of sample

c. Place cylinder in sample well

d . Insure smooth transition between tank floor and sur­face of sample by filling cracks with modeling clay

2 . Fill tank to indicated level

3 . Take temperature of water

B. Performing the test

1 . Open line valve

2 . Start Stopwatch No. 2

3 . Open pres sure regulator valve (gradually until gage registers 3 pounds per square inch} ( about 10 revolutions per minute)

a. Check revolutions per minute with Stopwatch No. 1

b. Observe sample 5 to 10 minutes , writing down pertinent observations

c . Record cumulative time registered on Stopwatch No . 2 and increase velocity gradually to next step

4. Repeat Step 3, each time increasing the velocity by incre­ments varying from 5 down to 1 revolutions per minute , as many times as necessary until critical condition is reached and general erosion begins

5 . Record time on Stopwatch No . 2, shut off valve, drain tank, and remove lid

6 . Measure x distance (from outer edge of sample to center of eroded area)

7

SAMPLE DATA SHEET

Material Description- - CL Mod. Plasticity Laboratory Sample �o . ___ _ Temperature ., 16. 5 C

Cum. Revs . / I Vr

.secs . rpm P ! time.,

psi min.

10 / 56. 0 1 10 . 7 I 3 . o

10 / 55. 4 5

Observations

No perceptible movement

10 / 4 1 . 3 I 14. 5 I 4 . 0 I I Not much change. A few loose sand particles leaving at first. Surface

10 I 4 1 . 0 I 14. 6 I I 10 I of s_ample still stable

10 / 3 1 . 1 I 19. 3 I 6. 0 I I No significant change. A few loose sand particles left at

1 o / 3 2 . o I 18 . 8 I I 1 8 I first

20/ 52 . 2 I 23 . 0 I 8. 0 I I No perceptible movement. All loose sand particles s e em to have

20 I 5 1 . 9 I 23 . 1 I I 26 I left

20/48 . 8 1 24 . 6 I 9. o

20 I 48 . a I 24 . 6 I I 36

No perceptible change

20/ 45. 8 26, 2 10, 0 I No perceptible change

20 / 46. 0 26 . 1 46

20/ 43 . a I 27 . 4 1 10 . 8

20 I 43 . 6 I 27 . 5

5 2

Surface of sample appeared stable at first. Small chunk broke loose after 3 minutes . Chunks continued to leave . Water becoming cloudy. Sizable cavity formed after 5 minutes at this speed . Past critical tractive force . Test stopped after 6 minutes

8

Critical V r = 27 rpm "J

-_o

'·'

,.-

Upon. completion of a tractive force test, the critical rotational velocity and the x - distance are known. Critical tractive for ce may be determinea with the aid of Figure 9. Suppose, for example , the critical rotational velocity for a particular sample was 34 revolutions per minute , and the distance from the outer edge of the cylinder to the center of the eroded area me asured 3 inches . According to the foregoing definitions, V r = 34 revolutions per minute and x = 3 inches . The �alue of C in Figure 8 corresponding to x = 3 inche s is 0. 00013 . Using Equation 1 , the critical tractive force would then be :

T = CV 2 o r

= 0. 000 13 X ( 34.) 2 = 0. 1 5 lb / ft2

Figure 9 may be used for a direct estimation of the critical tractive for ce . In Figure 9, the sample is divided into four zones which correspond closely to 2-inch increments of the x - distance . Repeat­ing the above example with V = 34 revolutions per minute and x = 3 inches, it is seen that file center of the eroded area lies in the center of Zone 2 . Entering Figure 4 with V = 3 4 revolutions per minute, the tractive force at the center of Zone 2 is seen to be O . 1 5 pound/foot2 which agrees with the method based on Figure 8 . Considering assumptions made in evaluating calibration data, it would seem the critical tractive force can be estimated with suf­ficient accuracy from Figure 4 .

9

Table 1

SANDS AND GRAVE LS USED IN CALIBRATING TRACTIVE FORCE TANK

Particle diameter, No . I Source I mm

1 Clear Creek o. 59 - 0. 7 1

2 I Clear Creek I 1 . 19 - 1. 41

3 I Clear Creek I 2. 38 - 2. 83

4 I Color ado River I 2. 38 - 2 . 83

5 I Clear Creek 4. 00 - 4. 76

6 I Colorado River 4. 00 - 4. 76

7 I Clear Creek I 7 . 93 - 9. 42

8 I Colorado River I 7 . 9 3 - 9. 42

9 I Clear Creek 1 5 . 9 - 19. 1

10 I Colorado River 1 5 . 9 - 19. 1

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FIG UR E I

Air supply .... , \ i '

Pressure

;-Plastic lid

TRACTIVE FORCE FIEL D AND LABORATORY STUDY TRA C TI VE FORCE TEST TA NK

Figure 2

TRACTIVE FORCE FIELD AND LABORATORY STUDY ARRANGEMENT FOR CALIBRATING TRACTIVE

FORCE TANK

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TRACTIVE FORCE FIELD AND LABORATORY STUDY

4

9

SANDS AND GRAVELS USED IN CALIBRATING THE TRACTIVE FORCE TANK

5

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6000

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Line representirio relations of tractive forces .lbsjft�•0.5 �lometer in jr711· hes � -Tractive force Ko/Ml • diameter in centimeters (approxlmotelyh

I I I I I I I I I ,' i

-10.6

-105

I I I I I I I I I ;Oil

Recommended volue tor corio ls with high content of fine sediment in the water., -u.S.S.R. conols with Ql "lol -,0.3 I I I I I I I I I I \ . .

/ - Fortier & Scobey - Recommended for conols in tine sand wit� : l=-=*Z::Z::,::i:z;:i:q:q::,a,,¥::z:::a./4:l• colloids '" woter

,' water containing colloids : N � 1000

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with low content of fine - 700 w -',,----+----t--+--t-+---r---r--t--r-------'-'--+---t---.-,....t--,�;,"'-+--ii"'--t,,'#-.-,r,-;---- sed iment in the water --1---+---+--+--l

.... w == l­e.)

600 � Schoklitsch - Recommended 1--i---t-t-t-t-------,1-�.,,,...t-�.-f'"'.-,...t--J,'7"t"7"1-,t�-----t----+---t---t---+--t-1-t--t \ for canals in sand - -- - . . ·---- Recommended values for canals in

500'

400

' ' coarse, non· cohes ive material __ _,_ ... size 25o/. - lon;ier

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1cano

i's with � le�r ":ot�r

389

50

· · · ·-Strou b values of cri tical tractive force ,1 1 I I I

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APPENDIX II

A L OGARITHMIC- PROBABILITY GRAPH METHOD F OR DESCRIP TION OF MECHANICAL ANALYSIS OF

S OILS USED IN TRACTIVE FORCE STUDY

Particle sizes of cohesive soils are not uniform . Generally , a s ample i s analyzed and the re sults are plotted on standard p aper as percent in weight pas sing a given sieve size versus particle s iz e . By inspection, it is intuitively felt there is som e law which governs the variability of size s . Listing a few generalities regard­ing a given soil s ample, we find : 1 . Particle sizes are usually con­fined to a ce rtain range . 2 . Some siz e interval s contain many grains , while other size interval s contain only a few grains . 3 . There i s always one size interval which contains the largest numbe r of p articles . 4. For all other size interv als there will be fewer particles , their numbers decreasing toward the ends of the size range s . A mathematical l aw which describes the s e gen­e ralities is immediately recognized as the mathematical probabil ­ities normal density function or normal frequency curve ( 1 ) ,:� . The p robl em is to find a fast and convenient way of exp res sing this law with regards to size analysis . While the function may b e expressed in s eve ral w ays , one given by Krumbein ( 2 ) in t e rm s of the ordinate y and the indep endent var�able x is

1 e

y = O"x /tTr

- (x- M )2 X

2 er 2 X ( 1 )

where Mx i s the arithmetic mean of the x v alues and a- x i s their standard deviation . A gene ral plot of a curve of this natu re is shown in Figure 1 .

By general observations , we s ee that if the number of particles belonging to a general area is large , the effect of a misclas sifica­tion of a particle is small . However, if the number of p articl e s belonging t o an area i s very small, a s i s the case near the ends of the curve , the effect of misclas sification of a p article may be very l arge . W e also note that the Normal Frequency Curve is bell shaped and symmetrical about its mean value , Mx.

��Number s in p arentheses refe r to Bibliography at end of Appendix .

In 1 9 3 8 , Krumb ein ( 2 ) introduced a new variabl e into the normal frequency curv e :

r/J = - log2l . . . . . . . . . . . . . . . ( 2 )

where

e = the piamet er in mm

0 = a new variable = the negative log2 of e M 0 = its arithmetic mean (the phi mean)

a (/J = its standard deviation (the phi standard d eviation)

These were substituted into Equation 1 , and a normal phi curv e w as defined as : - ( ¢ - M0 )2

- 1 Y - er� Jzn

e 2 (j02

. . . . . . . . ( 3 )

Krumbein then treats this curve similar to the Gau s si an cu rve (Normal Frequency Curv e ) . The negative logarithm to the B as e 2 was cho s en to simplify the geometric grade scales ; i . e . , if clas s intervals are of the range 2 - 1 , 1 - 1 / 2 , 1 / 2 - 1 / 4 , 1 / 4 - 1 / 8 millimeter, etc . , then - log2 2 = - 1 , -log2 1 = 0, -log2 1 / 2 = + l , - lo g2 1 / 4 = +2 , etc . The negative log was us ed in the definition of � b ec au s e the re are more fine- grained than coarse- grained soil s .

Using the idea o f Krumbein, and a method pres ent e d b y Otto ( 5 ) , the Hydraulic Laboratory designed a modified logarithmic probability graph for the interpretation of mechanical analyse s of sediments in 1 9 5 0 . The m echanical analysis shown on Figure 2 , is plotted as Curve 1 , on a she et of the special graph paper in Figu re 3 . The curve in Figure 3 is plotted in a manner similar to that in Figure 2 ; the sieve size , or geometric mec!'n diameter 1 s plotted against the percentage finer or perc entage coarse r . The percent age finer or coarser scale is a probability sc ale and the geometric mean size a logarithmic scale . The method of determining p arameters from the graph paper follows .

2

�o

•

):

DETE RMINATION OF PARAM ETERS IN PHI PROBABILITY GRAPH Ref er to Figure 3

To Obtain M e) : (phi arithmetic mean diamete r)

Draw a straight line AB connecting the int ers ections of the fitted curve and the 1 5 . 9 and 8 4 . 1 perc ent dotted line s . 68 . 2 perc ent of the weight of the material fall s b etween the valu es 1 5 . 9 to 8 4 . 1 . This is the range for one standard deviation e ach side of the geo ­metric mean or two standard deviations . Wh ere the 5 0 p erc ent line c ro s s e s the lin e AB, draw a horizontal line CD int ers ecting the diameter sc ale us ed in plotting the analysis . Read off the value of M = 1 . 1 1 , on the arithmetic phi scale and the co rresponding geom etric mean diameter, 0 . 469 millimeter, from the geometric s c ale.

t/J is any diameter defined by the expre s ssion r/J = -log2 { where ! is the diameter

in millimeters

To Obtain a- r/J : (phi standard deviation )

Draw a line H F parallel t o AB th rough th� c enter o f the small circle ne ar the middle of the graph. Extend the line HF to the phi standard deviation sc ale on the s ame side of the graph as th e s c ale u s ed for plotting the analysis . The O' r/) scale is the sl ant scal e along the lower l eft corner of the graph . Read the value of a 0 , = 1 . 2 , at the inte r ­section o f line E F with the scale .

To Obtain kr/J : (phi skewne ss)

S et a p air of dividers to the length GH on the vertic al 4 p erc.ent line b etween its inters ection with the EF and the horizontal line pas sing through the circl e at the middl e of the graph . Next, l ay off the distanc e DI, equal to GH, on the 50 percent line starting at its inters ection with the line AB. From Point I draw a horizontal line IJ inters ecting the fitted curv e . Read the percent age 9 1 . 2 perc ent at the intersection . On the kr/J s c al e near the lower right corner of the graph read the value of skewne s s - 1 . 6 , corresponding to the p erc entage· just obtained . Simil arly, loc ate I ' and J' and dete rmine the kr/J ' value, - 0 . 8 1 , from the l eft corner of the graph.

3

INTERPRETATION OF ANALYSES

The value of M0 is an indication of the position of the curve on the graph. For the sample in Figure 2., M0 = 1 . 1 1 and the correspond­ing geometric mean diameter = 0. 469 millimeter. It will be noted that the geometric mean diameter" is not the diameter at which 50 per­cent by weight is larger and 50 percent smaller. As the mean size becomes smaller ., the value of M© becomes greater and as the value of the mean particle size increases M© approaches zero or becomes negative. On standard gradation charfs ., an increase in value of M0 will move the gradation curve to the left ., while a decrease in value of M¢ will move the curve to the right.

As may be seen from a close study of the phi probability graph ., a variation in a- 0 is a measure of distribution ., or scatter of the parti­cles about the median. In other words ., a- 0 is a measure of the fre­quency of size range of particles present. For the example (j 0 = 1. 2 This value is shown plotted on Figure 2., as 1 . 2 to each side of the mean. As the size range present between 84. 1 and 15. 9 percent becomes smaller., the numerical value of (j 0 decreases ., and as the �ize range between 84. 1 and 15. 9 percent becomes greater ., (j 0 increases.

Variation in the kt, values describe changes in the shape of the curves. k0 describes the tail of the curve in the region where particle size is largest. In general ., as the percentage of coarse material increases k0 tends to relatively large negative values. On standard gradation analysis paper., this would result in a flattening of the upper end of the curve ., and the curve above the 50 percent size would tend to have a more pronounced S shape. As the percentage of coarse material decreases; k0 tends to a relatively large positive value., and on stand­ard paper ., the curve tends to become straighter above the 5 0 percent size range.

k' 0 values describe the tail of the curve in the region of small parti­cles. Generally, as the percentage of fine material increases ., k ' ¢ tends to relatively large positive values. On the standard gradation paper., this would result in a flattening of the lower end of the curve ., and the curve would tend to have a more pronounced S shape below the 50 percent size. As the percent of fine material decreases ., k ' m tends to negative values ., and on standard analysis paper ., the curve tends to become straighter. It may also be observed that if a straight line fits all the plotted points ., the skewness is zero or k0 and k ' 0 equal zero. Values of k0 for the example are shown on Figure 2.

Obviously ., these data are not directly applicable to every type curve ., but from the previous discussion ., it is evident that if phi probability data are known the gradation curve on standard gradation paper can usually be rapidly sketched.

4

-s

•

>: II

BIBLIOGRAPHY TO APPENDIX II

1 . Feller ., W . ., An Introduction to Probability Theory and Its Applications ., Volume 1 ., Second Edition ., pp 1 64 - 1 65 ., Wiley, 1 9 57

2 . Krumbein ., W . C . ., Application of Logarithmic Moments to Size Frequency Distributions of Sediment ., Journal of Sedimentary Petrology ., Volume 6 ., pp 3 5 -47 ., 1 9 3 6

3 . Kottler., F . ., Journal Franklin Institute ., Volume 2 50 ., pp 339 .,

419 ., 1 9 50

4 . Otto ., G. H . ., A Modified Logarithmic Probability Graph for the Interpretation of Mechanical Analyses of Sediments , Journal of Sedimentary Petrology ., Volume 9 ., No. 2 ., pp 62 - 7 6 .,

August 1 9 3 9

..

): ,

....

Table 1

TABLE FOR PLOTTING SIZE ANALYSIS OF SEDIMENTS USING LOG- PROBABILITY METHOD

Size mm

0 . 00 1 0 . 0 02 0 . 005 0 . 009 0 . 0 19 0 . 0 3 7 0 . 074 0 . 149 o . 29 7 0 . 590 1 . 1 9 2 . 3 8 4 . 7 6 9 . 5 2

19 . 1 38 . 1 7 6 . 2

1 27 . 0 1 5 2 . 0 200 . 0

U . S . Standard sieve series

200 100 50 30 1 6 8 4

3 / 8 inch 3 /4 inch

1 - 1 / 2 inches 3 inches 5 inches 6 inches 8 inches

¢ units - Log2 (size in mm)

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- 1 . 25 - 2. 25 - 3 . 25 -4. 26 - 5 . 26 - 6 . 26 - 6 . 99 - 7 . 26 - 7 . 66

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