THE UNIVERSITY OF MICHIGAN COLLEGE OF ENGINEERING Department of Mechanical Engineering Progress Report CONTROL OF THE PROPERTIES OF RESEARCH SOIL SYSTEMS H. H. Hicks, Jr. E. Io Oktar Supervisor: E. T. Vincent ORA Project 02860 under contract with: DEPARTMENT OF THE ARMY U. S. ARMY ORDNANCE CORPS DETROIT ORDNANCE DISTRICT CONTRACT NO. DA-20-018-ORD-18955 DETROIT, MICHIGAN administered through: OFFICE OF RESEARCH ADMINISTRATION ANN ARBOR January 1962

TABLE OF CONTENTS Page LIST OF ILLUSTRATIONS v ABSTRACT vii INTRODUCTION1 SOIL VALUES 3 THE LABORATORY SOIL 5 Magnetic Soils 7 Glass Beads 8 TEST APPARATUS 9 PROCEDURE 13 RESULTS 15 DISCUSSION 23 Values of kc 23 Values of kS 25 Values of n 25 General 25 CONCLUSIONS 31 REFERENCES 33 iii

LIST OF ILLUSTRATIONS Table Page I EFFECT OF MOISTURE CONTENT ON SOIL PROPERTIES 5 II TYPICAL PROPERTIES OF BARIUM FERRITE 7 III SOIL PARAMETERS FOR INDICATED MATERIALS, OBTAINED WITH CIRCULAR AND RECTANGULAR FOOTINGS 21 IV CALCULATED MAXIMUM AND MINIMUM RELATIONS OF INDICATED PARAMETERS 21 V MATERIAL: 75% GLASS BEADS, 25% oSAND 29 Figure 1. Composition of the 3-component substance (water, clay, glycol) in equilibrium with humid air at 75~F, 1 atmos. pressure. 6 2, Diagram of test apparatus. 10 5. Electrical circuit. 11 4. One range of sizes of feet employed for plunger. 11 5. Pressure and sinkage relationship of sand with stirring. 12 6. Pressure.and sinkage relationship of nonmagnetic barium ferrite with stirring. 12 7. Pressure vs. sinkage of a flat plate in sand. 16 8. 100% sand. 17 9. 100o glass beads. 19 10, Poured magnetic barium ferrite. 20 v

LIST OF ILLUSTRATIONS (Concluded) Figure Page 11o Effect of speed of penetration in sand. 22 12. Averaged values of actual test points. 24 135 Magnetic barium ferrite. 27 14o Typical load-sinkage curves. 28 vi

ABSTRACT This report covers a series of experiments made with a precision bevameter on sand and mixtures of sand with other.materialso The object of the tests was to ascertain the range over which the cohesive and friction moduli of deformation of a soil can be controlled, thus exerting a controlling influence upon the dimensionless parameters employed during similitude testing of wheelso The results indicate that such control is possible to a moderate degree when using the types of materials studied. vii

i

INTRODUCTION A fundamental problem in land locomotion is the interaction of the wheelsoil system. Since the mechanics of this system involves the properties of all its constituents, the problem is related to the physical properties of the soil in contact with the wheel as well as that of the wheel itself, The soil can vary from a more or less plastic clay to sands and hard surfaces. Little is known about the science of soils, particularly about the complete range of possible soil values applicable to the soil-wheel system. The result is that an empirical approach is necessary to solve the immediate problems, at least for the present. One such approach is the Bekker1 soil-value system, represented by Eq. (1): P = (kc/b + k,)Zn (1) This relates the soil pressure P psi to sinkage Z in. by a physical dimension "b" ino of the measuring device employed: the narrow width of the imprint in the soil, or the radius of a circular foot if used, and three parameters kc, k1, and n. The latter three parameters are a function of the soil itself, These coefficients are defined as follows: kc = cohesive modulus of soil deformation kS = frictional modulus of soil deformation n = exponent of deformation It is well recognized by those working in the field that the pressure P and sinkage Z of the device is not accurately represented by the relation shown at all values of P and Zo However, the main error involved is at small values of Z, outside the range of vehicle sinkages at which trouble develops. Thus the relation permits considerable theoretical analyses and prediction, and the development of trends, saving much money and time. 1

SOIL VALUES It has been indicated above that Eq. (1) can be used for the solution of land-locomotion problems provided that the soil values kc, ks,.and-.n are known for the soil in question. There is one other approach to the subject in which these parameters assume considerable importance: in dimensionless analysis where the object is to use the principles of similitude to employ small-scale tests in the laboratory to predict full-scale vehicle performance. In other words, the approach is to employ in land locomotion the equivalent of wind-tunnel tests of airplanes, a technique which has been employed for many years to check drag, stability, etc., of a model of the plane before its actual construction. Such similitude studies of land-locomotion problems have recently been made.24 To take complete advantage of these studies, with respect to their application to full-scale wheeled vehicles, examination of the relationships given below is necessary. kc = cidks (2) W = c2kddn+2 (3) D = c3d (4) These relationships should be met if the model rules are to be satisfied and complete similitude obtained under the conditions assumed in Ref. 2o Soil-value quantities must change as the scale of the model changeso Fortunately for the studies reported in Ref.'2,, the material employed was sand for which kc = O and useful work was accomplished without control of kc and k o To extend the studies to soils possessing values for both kc and kS it follows that means must be found to vary, independently, kc, k$, and n if at all possibleo The studies reported here, conducted with materials, other than natural soils, were aimed at obtaining sufficient variation in the laboratory soil-system parameters to permit the construction of dimensionless graphs from model tests, over a range of values which allow application to the range of wheel sizes currently used. To achieve the complete natural range of values of kc, kca, and n, it should be possible to prepare soils or their equivalent that would permit: kc to vary from 0 to > 20.0 kS to vary from 0 to >530.0 n to vary from 005 to >3.0 At the same time these soils must maintain their properties constant while in contact with the varying average laboratory atmosphere for extended periods of time 5

Research conducted at the Detroit Tank Arsenal Land Locomotion Laboratory on artificial soils5 provides a limited approach to the problem, but independent variation of kc, ks, and n would be difficult to achieve by this method alone. The experiments to be described represent a further attempt to produce stable soils accompanied with at least a moderate independent variation in both kc and ko and their ratio of the materials, using the Bekker Sinkage Parameterso 4

THE LABORATORY SOIL Various possible laboratory soils composed of clay, sand, and glycol are described in Refo 5. Various other possible soil ingredients were also proposed but not used, some of which are employed in the research now under discussion. The ideal soil mass, as defined in Ref. 5, should have the following characteristics: (a) Stability of the solid state regardless of time, oxidation, or other chemical interaction. (b) Controllability of the soil values and parameters. (c) Reproducibility of the mass in any quantity using standard or easily obtained materialso The materials employed at the Arsenal satisfy these requirements to a high degree, but the glycol is also hygroscopic, and thus will pick up moisture from, the atmosphere. The properties of the soil can change somewhat with time, particularly those mixtures representing viscous muds where high glycol contents are employed. Figure 1 shows the three-phase diagram of clay, glycol and water, plainly indicating the wide range of soil properties that could be expected from any one blended combination of clay and glycol, given sufficient time and atmospheric humidity. Fortunately, with proper organization the test data can be secured before such time elapse occurs. The importance of moisture content in a given soil (an average sandy farm soil of Wayne County, Michigan) can be seen from Table I.o TABLE I EFFECT OF MOISTURE CONTENT ON SOIL PROPERTIES Moisture, 4% Soil Properties $ deg c ks kc n 19 36 o6o 9.00 20o.00 0o16 20 38 0o53 7o00 16o00 0o17 22 36 0.25 2.20 2o50 0o18 It follows that stable soils under all conditions of time, temperature, and humidity are necessary, or else the magnitudes of the soil parameters must be determined at each testingo 5

0: C) t I Cd H I-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~C)Frc C% 6D rl 00 10 +-)~~~V 0 QL~~~~~~ r CD Cd CD sJ's ed m~~~~~~~~~~~~~~c r O t ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~~ m~~~~~~~~~. oo P -t~~~~~~~~~~~~~~~~~~~~~~~C a a c0 at 1Ce'b aO~C LLJ O* $~~~~~~~~~~~~~~~~~~~~C D c I \ \ \ 1 5~~~~~~~~~~~~~~~~~r YN+ ~~~~~~~~~~ a%~~~~~~~~~~~~~~~~~~~~~4)0 L 6P F~~~~~~~~~~~~~~~~~~~~~~DC 4 TlL~~~ Ln~~~ L ~~~~~~~~~~~ --- I I 0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~. ~~s ~ _ _ ~ ~ ~ \~ I o ) r

The research on the value of the soil parameters, covered by this report, can be considered an investigation of the manner in which the individual parameters kc, ks, etc., can be controlled and varied by other means than the variation of moisture content or glycol constituent. Variations are introduced by controlling the shape of soil particle, the size of particle, or its cohesive force as measured by its degree of magnetization, i.e., the effect of artificial materials on the control of soil parameters is examined as seit -out below. MAGNETIC SOILS As already pointed out, it is very desirable to be able to vary kc without material change of ks, if the relationship given by Eq. (2) is to be satisfied for complete fulfillment of the model rules. At least the ratio of kc and kS must be variable over a wide range, even if individual variation proves impossible. In considering this problem, it occurred to us that a material capable of being magnetized might present a variable kc with little change in kq; in other words varying magnetic attraction between the particles might represent a soil with variable cohesion. To this end, a supply of barium ferrite was obtained from the D. M. Steward Manufacturing Company of Chatanooga, Tennessee, which gave the properties, listed in Table II, of the material when magnetized. TABLE II TYPICAL PROPERTIES OF BARIUM FERRITE Residual Induction, Br (gausses) 2190 Coercive Force, Hc (oersteds) 1850 Intrinsic Coercive Force, Hc (oersteds) 3450 Maximum Energy Product, BdHd 1.03 x 106 Permeance Coefficient, Bm/Hm-:at BdHd max 1.160 Temperature Coefficient of Residual Induction 0.18%/~C Coefficient of Linear Thermal Expansion 10 x 10-6/C Curie Temperature (~C) 450 Apparent Density 4.70 gr/cm3 Electrical Resistivity (ohm/cm at 25~C) 10 x 106 Samples of this material in the nonmagnetized state show very little cohesion. At the same time the angle of repose (W) is extremely small; a sample spreads out over a wide area and has little depth even in the center. When magnetized, it has considerable magnetic attraction which appears to have the same effect on a mass as cohesion. At the same time such a mass will form into a distinct cone-like mound having a definite angle of repose compared to the 7

nonmagnetic variety, which might indicate a change in kS also. It follows that variation of the degree of magnetization may produce a reasonably wide variation of kc, ks, and n. An additional advantage is relative economy, as compared with glycol. GLASS BEADS One other material considered for the control of soil properties was spherical glass beads, with an average diameter of OoO10 to 0,015 in. Thus in particle size the beads are approximately in the same range as the sand particles in use; but by themselves they have no value of 4, the angle of repose, since, being almost perfect spheres, they will roll out to a single layer, provided they are dry and not mixed with oil or other viscous or cohesive binder. But if they are mined with the sand employed in the routine tests, the frictional characteristics of the soil may change sufficiently to be of practical importance. The inclusion in plastic soils with or without the sand Qf Ref. 5 could also contribute to a possible increased range of kc, kS, etc. To study these effects, bevameter tests were run with a series of both circular and rectangular plates, with the object of obtaining the range of soil properties that could be produced by the use of the materials being considered. 8

TEST APPARATUS To obtain soil properties with a high degree of precision, and thus obtain closely reproducible test results, a special penetrometer had been developed at this laboratory. This equipment removed much of the scatter and many of the discontinuities of previous bevameters employed. The equipment consists of an hydraulically operated plunger to which the penetrating foot is attached, held in place by a sensitive ring gage to-which strain gages are attached to record the load on the footo Displacement of the foot is recorded by a linear potentiometer driven by the plunger movement. This equipment is similar to many others employed for the purpose in question. The differences are (1) the size, and thus the sensitivity of the ring; and (2) the supply of fluid to the plunger is via a constant-flow control valve, permitting accurate control of the plunger velocity regardless of the loads appliedo This appears to be responsible for the absence of steps in the curves. The pressure-sinkage data are plotted directly on an Autograf X-Y recordero Figure 2 is a diagram of the system. The electrical circuit is shown in Fig. 3. The feet employed for the plunger are shown in Figo 4, The size of the box containing the soil was considered large enough to render the boundary effects of both bottom and sides negligible as judged by the tests of Refs. 2 and 7~ The soil can thus be considered homogeneous with semi-infinite boundary conditions. Figures 5 and 6 show the type of data recorded for a sand and barium ferrite, respectivelyo The material was well stirred between runs. Several runs are superimposed on one another, indicating the degree of reproducibility, particularly when allowance is made for the difficulty if accurately determining the position of zero sinkage for the start of the grafto 9

::3 in' 0. +~ 4-, A t k~~~t 10 gz,11II,' > 10. 0 >

Reference Chopper Cel l Servo Amp. BALANCE -Sr Y ATTEN [TER CI PEN I CARRIAGE SERVO TABLE -\ MOTOR. _ TABLE- __] BALANCE X l AT N. FLTERJ — CIRCUIT Fig. 3. Electrical circuit. x 913 -,75" 1 1.25" t A x One range of sizes employed. 2. 50" 1.OWI ~ 2.00"11.75" One range of sizes employed. Fig. 4. One range of sizes of feet employed for plunger. 11

CH 0 Pc 0 d - 1 -CH 1 ) o *H 0 U) Cd.ral t i -H 0 PA*rl (U) 0 Cd ) *H J -hD'ql'eaJOJl r12.H CZ fil,

PROCEDURE In all soil testing with a bevameter, there is one great difficulty in duplicating results, particularly when a relatively small sample of the soil, contained in a box of modest size, is concerned: assuring that the material is in exactly the same state as regards humidity, compaction, etc., at the start of each test. The barium ferrite employed was a rather fine powder and thus did not lend itself well to the air-lift method of reconditioning previously employed successfully; the air flow through this finely powdered soil deposited most of it outside the container. After considerable testing the method of "pouring" was chosen as quite acceptable for the small volumes involved in the tests. This consists of pouring the used sample into a second container and then pouring it back into the test container. This flow process removed stress and compaction satisfactorily. The container was then placed on the bevameter table and carefully leveled. The zero setting of the sinkage scale was determined. The test was then carried out with a plunger speed of 6 fpm, which was held constant for all the tests with the ferrite, sand, and glass beads. In each case a series of runs was made for each foot size. These results were then averaged for the points shown in the various graphs of the P-Z relationship. 13

RESULTS The results obtained from the apparatus are typified by the curves of Figso 5 and 6, which show that the reproducibility of the results is good. Such force-sinkage curves were then averaged and the results were plotted on log-log paper as shown in Fig. 7. For Eq. (1) to represent the recorded results exactly, the points of Fig. 7 should lie on a straight lineo A typical line has been drawn in; although it is not strictly through all the points, a close approximation to the straight line is seen over a portion of the graph, particularly if: (1) the first one or two points plotted from such figures as Figso 5 and 6, are neglected where the sinkage is small, say < 0.5 in.; (2) The last few points at high load are also disregarded, where the sinkage is > 4-5 in. These points can be neglected to a first approximation for the following reasons. (a) It is very difficult to determine the exact point at which the bevameter foot first touches the soil and the point at which pressure is exerted by it on the sand, since the top layer appears to be compressed to some extent and, in some cases, voids are taken up with practically no sinkageo Thus the zero setting of pressure and sinkage has some error; since the first point plotted on curves of the type shown in Fig. 7 has been for Z = 0,25 in., an error of 0~05, which is easily possible in the zero setting, would change the picture a great dealo (b) Secondly, it seemed that the upturn at the upper end of the diagram could be due to boundary effects from the bottom of the containing vesselo This was checked by running bevameter tests with soils of varying thickness relative to the size of the penetrometero The results are shown in Fig. 8; four depths of a given sand were employed and the P-Z relationships were obtainedo The graphs show a high degree of agreement, except at the readings for Z = 0,25 and for Z > 4-1/2 ino approx. The upper part of the curves show that, for a 6-ino depth of soil and a 2-1/2-ino diameter foot or r = 1-1/4 in., departure from the approximate straight line occurs at about Z = 3-1/2 in. or a(r/Z-D) = 005 approxo, where D = depth of soil above the hard surface to the penetrating plate at its point of departure from the straight lineo For the 9-ino depth, departure occurs at Z = 4-1/2 ino or r/Z-D = 0.28; for both the 12- and 14-1/2-ino depths;of soils, departure from the straight line occurs at about 5 in. or r/Z-D = 0'18 and 0.3. It is concluded that for a 2-1/2-ino-diam ft, the soil should be at least 12 ino deep. Basing the relationship on the radius of the foot, the required depth of soil below the foot at the maximum penetration should be about five times the dimension "b" of Eqo (1) if depth effect is to be avoidedo Since only one size 15

, I l I I I 11 l l l1l1111 I I' I I 1,.11' Material: Sand Rectangular Plates 3"x 1" and 3"x 2" n =1.0 3x 2". -.. A^33x1" P 3.2 Z 1 3 kc=-10 k4 =3.7 Z, IN. Fig. 7. Pressure vs. sinkage of a flat plate in sand. 16

100 10 I I'1 I' 11 I' I' 80 60 t Larger circular plunger 14-114" depth used, 12" depth 40 AA =4.90 in2 9" depth d = 2-12 in 6" depth ^Y A n= 0.95 20 10 8 6 - 4.2-.S I I I 1 I INKAGE - I NCHES o1.2'.4.6.8 1 2 4 6 8 10 20 30 S I NKAGE - I NCHES Fig. 8. lO0 sand. 17

of foot was employed for Fig. 8, the values of kc and kS cannot be determined; however, for the sand in question we can write P = 355Z~095 which agrees well with other experiments with similar materialso As a result of the above tests, the analytical relationships between P, Z, and n which follow were all determined by neglecting the value of Z for sinkages < 05 and > 4 ino and using a total soil depth of at least 12 ino With the above limitations, tests with the following materials were carried out: (a) Sand (b) Nonmagnetic barium ferrite (c) Magnetic barium ferrite (d) Glass bead of from 0,010 to 0o015 ino in diam (approxo) (e) A mixture of 25% glass beads and 75% sand (f) A mixture of 50% glass beads and 50o sand (g) A mixture of 75% glass beads and 25% sand All the above materials were dryo It follows that the cohesive force would be expected to be quite small and kc ~ 0OOo Tests were made with three sizes of both circular and rectangular footings; theoretically, since kc is zero or at least quite small, all the P-Z curves should almost superimpose on one another and cross the line of Z = 1 ino almost at one pointo The results substantiate thiso Typical plots for some of the materials are shown in Figso 9 and 10, the former is for the circular plates and the latter for rectangular oneso The soil parameters obtained from all the graphs are as shown in Table IIIo Substantial agreement exists between the two types of footings. When more than one such set of curves are averaged (as was generally the case), the results tend to be closer than those given here. The effect of the speed with which the footing penetrated the soil was examined for any change of magnitude of n, kc, and k, that might have resulted. This effect is recorded in Figo 11o Table IV gives the maximum and minimum relations as calculated. Since the speed-effect curves for rectangular and circular feet are all recorded with but one size of plate, the individual values of kc and kS cannot be determined in this caseo But it is safe to assume kc 0 0o0 since this has been determined for this material by other tests. 18

100 I I' 80 60 Circular Footings 40 2-1/2, 2 and 1-112 in. diam. 20 2O 8 -.1,, Lar,,, Average Soil Parameters I k -n==0..='6: k =3.95 4 2 - SINKAGE -INCHES Fig.. 100 glass beads, 0.010 to 0.015 in. diam. 19 19

10 7 - Rectangular footings (in.) Ix 1/3 5' 1-1/2x 1/2 2-1/2x 3/4 3 - Average Soil Parameters Sm Smaller, kcn=1.04 MediumA kc = 0 43 L a.04.0..4Larger k4 = 1.05. - " 1-1/2 x 1/2x 1Q"~,~>^^//~~~'< 2-1/2x 3/4 Z8..4.4 - C-r-n=l.O.2.1 I IIIIl I I I 1 I11111 I I I I I I 111.04.1.2.4.6.8 1 2 4 6 8 10 SINKAGE Fig. 10. Poured magnetic barium ferrite. 20

TABLE III SOIL PARAMETERS FOR INDICATED MATERIALS, OBTAINED WITH CIRCULAR AND RECTANGULAR FOOTINGS I ~n k. k Material - _ - k Circular Rect. Circular Rect. Circular Rect, Dry Sand 0.95 0.95-1o0 -0.60 -o064 3.1 353-357 100% Glass Beads o09-0o91 0.91-1.06 +0.175 +.182 1 96 196 25% Glass Beads and 75% Sand o09 0.95 -0.7 -0.53 3595 3.68 50% Glass Beads and 50%o Sand 1.0 1o0 -0.36 -0.48 2.97 3501 75% Glass Beads and 25% Sand lo0 6 1 06 -0.703 -Oo461 2.79 2 43 Nonmagnetic Barium Ferrite 0.68 0.65 0.93 1.21 0.37 0.69 Magnetic Barium Ferrite 1.0 1.00 0,34 o.43 1.22 o 05 TABLE IV CALCULATED MAXIMUM AND MINIMUM RELATIONS OF INDICATED PARAMETERS Circular Footing, 2 ino Diam Speed, fpm n k 5~0 0.95 2.9 6.5 0.95 3.0 21

4 I I I I iI I I I I! I Average Relation 2 P-3.0Z.95 n0.95. 10 6S Z CL 4 -~ Circular Foot 3.03w~ * ~Upper Limit Sinkage, Z, In. Fig. 11. Effect of speed of penetration in sand. 22

DISCUSSION The values of kc and kS obtained from such diagrams as Figs. 9 and 10 resuit in ke varying from positive to negative for the same material in different tests. This is considered to be because, for the materials in question, kc 000 and small errors in the observed data or even in drawing the curves through the points produce positive or negative values for kc in such cases. But it must be admitted that some doubt exists about the correctness of this explanation, due to the accuracy with which the observed data were repeated in subsequent check tests, and the consistently small negative values obtained0 In Figo 12 the actual test points are plotted to show the rather tight grouping of most of the points at their averaged values, plus a few scattered results which in almost all cases still do not change the sign of the coefficientso The values given in Table III result from the averaging of several runs using the straight-line log-log relationship P = (kc/b + kR)Zn in the conventional manner0 Employing the appropriate values from Table III in this formula and calculating the pressure and sinkage values, the calculated points do fit in very well with the mean plotted valueso It is concluded that no major error in kc and k, exists by employing the average of a number of runs with small, medium, and large plates, at least for Z between 07 and 4[5 ino Table III indicates that for the range of materials examined change in the value of "n" for all these dry, large-particle materials is negligible. But for the fine powdery barium ferrite this parameter has been reduced to n = 0o68, which, when magnetized, is re-established at lo0 as for the other materials o VALUES OF kc The object of the tests was to produce an independent variation in the magnitude of kco The average data indicate a possible variation of its magnitude from -7O to +0o93 for circular plates and -0o53 to +1.21 for rectangular one s o The variation produced in kc is small as is to be expected since all the materials, with the exception of the barium ferrite, were granular, with little if any cohesion0 A cohesive coefficient of o09 to 1.2 was recorded with the magnetic barium ferrite. In general, it was observed of all the test results that there was less variation between tests for rectangular plates than for circular oneso 23

M lo o'1 = ~D C l so sanleA \ o 3 ^ -- 7 "" -- n m-IcT- ^}Ln Cow r — CH 24) rd a) bO 7^nLn *rL_ _a CD L + o o senleA LL L. o o +'-~ C

VALUES OF kS The corresponding variation of kX is from 0.37 to 53.95 for circular plates and from 0o69 to 357 for rectangular oneso Here a significant change of values has been achievedo Taking the sand and bead combinations only, where for sand kS = 31o to 537 and for beads kS = 196, a variation of about 1.8:1 is seen, a range of considerable interest as far as similitude study is concerned. If the ferrite is included, a range from 005 to 355 or 7:1 is possible. VALUE OF n Table III shows that the value of "n" in Eq. (1) changes from 0.65 to 1.06o If the nonmagnetic barium ferrite is neglected, the range is from 0.9 to lo06. In other words, "n" for the materials so far tested is approximately constant at n = 1. GENERAL The analysis so far has been based on the fact that Eqo (1) represents the relationship between P and Z with sufficient accuracy for a soilo This equation is an approximation of the results obtained by soil-penetration tests in the manner described; yielding important results for an engineering approach to the problem of soil-vehicle relationshipso The relationship employed departs from the test results mainly at very low sinkage of little importance in practical problems The question arises what, if anything, could be added to Eqo (1) to lend a more scientific approach to the whole load-sinkage relationshipo In parallel work at The University of Michigan,8 the equation P = C + (kc/b + k,)Zn was suggested as a refinement of the Bekker relationship, in which the magnitude of "C" depends on the width "b" of the plate employed in the tests, The addition of such a constant'C" does not raise any particular problem for the soil-value-system parameters, but it would seriously complicate the equations for wheel sinkage, etc., deduced from its use in any theoretical considerationso The effect of general soil stress state on the bevameter parameters, also examined in Refo 8, should also result in some further modification of Eqo (1) if bevameter tests are to be represented completelyo Turning again to the main problem of this report, it may be an advantage to list the similitude relationships in a slightly different form. If W, D, d, and L are considered the independent variables and Z and R the dependent ones, 25

where W = Load on wheel, lb D = Depth of soil above hardpan, in. d = diameter of wheel, ino a = aspect ratio of wheel Z = Depth of sinkage, ino R = Drag of wheel, lb, then for similitude the following conditions must be met: d = Constant (5) kc W k-dn+2 = Constant (6) D d = Constant (7) When kc 0 O, Eq. (5) disappears and thus, for sand where kc = 0, model work is a possibility by the use of Eqs. (6) and (7). It follows that the main importance of the present test program arises as soon as kc has some magnitude. Then to provide a sufficient band of model tests to cover all practicable wheels, as d is varied the ratio ks/kc must also vary if true similitude is desired for all caseso The work to date has shown that there are some possible ways in which the cohesive and deformation moduli of the Bekker soil-value system can be varied independently, at least over a moderate range of valueso The important feature is the ratio of the two [see Eq. (5)], Figure 13 shows the range of kc and k., together with values of their ratio for the magnetic soil (the degree of magnetization is unknown). For the sand and glass bead combination, the value of kc is so close to zero, actually varying from positive to negative values, that it is believed that the ratio of the parameters loses some of its significance. But the variation of kS is a reasonable amount and could have a significant effect in extending the range of similitude testing for full scale and models, particularly when the limitation arising from Eq. (5) is taken into account for a given soil bin with a fixed value of D, the soil deptho If the curve of Fig. 12 for kc is taken as drawn, then the ratio k//kc varies from -4.4 for pure sand to +9.7 for glass beads. The major change occurs as the composition approaches 100o glass beads. Typical load-sinkage curves with various sizes of rectangular plates are shown in Figso l4a, 14b, and 14c. The initial portion of the record consists of an almost vertical rise in load with a negligible deformation, Examining the initial part of the curves on the basis of the pressure per unit area under the plate, one obtains the data of Table Vo An approximately constant stress 26

1.3 1. 2 k c 0.9 0.80.7_ kko 0. - 0. 5 _ -*. —. _. _.. 04- ko 4 circle kcll X) laverage kClkj,- Y 3.0 o rest kclk. magnitude nonmagnetic x unknown 2.0 l. -----— DEGREE OF MAGNETIZATION Fig. 1. Magnetic barium ferrite. 27

130 I' 120 C 110 100 -/ 90 80 70 L Large Rect b 3-314" x 60 [ -1z / 50 24 240 a 30 20 10 1 2 3 4 5 SINKAGE, IN. Fig. 14. Typical load-sinkage curves. 28

TABLE V MATERIAL: 75% GLASS BEADS, 25% SAND Plate and Load, Penetration, Stress, psi Area sq in. lb Z, ino 2-1/4" x 3/4"1 Too small to 10687 sq in, 1.2 read 0.71 2-1/2" diam Too small to 1.767 sq in. 1.5 read 0.85 31" x 1" 3 sq in. 2.7 o015 0.90 2" diam 3.14 sq in. 2.5.021" 080 3-3/4" x 1-1/4" 4.675 sq in. 4.7 o02"1 0.99 2-1/2" diam 4.906 sq in. 5 o0.02" 1.02 under the various plates is seen. The exact process occurring during this phase of the load-sinkage curve is difficult to establisho In Refo 8 the initial visible effect is claimed to be a compaction accompanied with a gradual increase in the boundary-layer development; however, this definitely involves a displacement which according to Fig. 14 has not yetoccurred. It follows that the very first load increase must take place with an almost negligible sinkage, perhaps as follows: (a) The sand is left in some state of particle arrangement and density for some depth by the soil-conditioning process employed. (b) When load is applied, no penetration occurs until a force is exerted sufficient to cause the uppermost sand particles to reorientate themselves against the friction between particles, and to slide or shear on one another an insignificantly small amount to produce a more or less rigid solid surface in contact with the penetrating plate on one side and the sand at greater depths on the other. (c) Further increase in load produces an increased boundary layer attached to the plate accompanied by some small measurable sinkage resulting 29

from further compaction and slip with the start of flow away from the stressed region to places of no stress, most probably toward the sand surface as shown in Ref, 8. (d) When the attached boundary has been completely formed to the penetrating plate, the remaining operation is mainly one of flow from below the boundary layer outward and upwardo The result is the curves as shown in Figo 14, with little or no sinkage for a given increase in load, followed by a fairly rapid increase in sinkage for a further moderate increase in load, and finally a more or less constant functional change of P and Z approximating Eqo (l)o One other explanation could be the assumption of an initial elastic phase where the modulus of compression would have to be of very considerable magnitudeo This does not seem to fit all the observations, That this initial change of stress without sinkage is in some manner assoiated with the material of the soil is established by comparison of FigSo 5 and 6 (the latter showing the load-sinkage curve for nonmagnetic barium ferrite)o For this material, due to its finely powdered state, there is little or no need to apply load of much magnitude to reorient the particles and produce a flowo Also due to the fine nature of the material and its powdered condition, its density is probably below that of its natural compacted state, that is, unless it has been consolidated. It follows that the first portion of Figo 6 shows a very small vertical rise followed by sinkage, producing mainly compaction, With little or no applied pressure, some of this sinkage is definitely due to flow of the finely powdered loose surface material; how much, is difficult to sayo It is seen that after some consolidation the load-sinkage curve does assume the normal shapeo The great difference between Figs. 5 and 6 establishes that the soil itself and its preparation does control the resulting curves obtained in bevameter testso 50

CONCLUSIONS As a result of analysis of the test data herein reported, it can be concluded that: 1. It is possible to control the values of kc and kS with some degree of independence over a range of values that should prove useful for similitude testing when employing frictional materials. 2. The value of the ratio kp/kc can be varied from approximately -4.0 to +10.0 by the use of various combinations of sand and glass beads of approximately the same particle size. 3. By the use of barium ferrite in the nonmagnetized and magnetized states, the values of ke and kS can be moderately varied; however, the ratio kj/kc varies only from 0.28 to 0.34 in the process. 4. Additional tests with materials having greater magnitudes of kc are desirable to evaluate fully the usefulness of the methods employed. 5. To cover the total possible variation of the parameters and their ratios, further test work should be undertaken, such as: (a) variation of bead size in relation to sand particles; (b) variation (and measurement) of the degree of magnetization; (c) combinations of these materials with clays and loams, etco 31

REFERENCES 1. M. G. Bekker, Theory of Land Locomotion, Univ. of Mich. Press, Ann Arbor. 2. H. H. Hicks, Jr., D. K. Kapur, and E. T. Vincent, A Similitude Study of the Drag and Sinkage of Wheels Using the Sinkage-Parameter System of Soil Values, Univ. of Mich. ORA Report 02860-27-P, April, 1961. 35 C. J. Nuttall, The Rolling Resistance of Wheels in Soil, Stevens Inst. of Tech., Expt. Towing Tank Report No. 418, Hoboken, N. J., July, 1957. 4. C. J. Nuttall, Scale Model Testing in Non-Plastic Soil, Stevens Insto of Tech., Expt. Towing Tank Report No. 394, Hoboken, N. J., 1949. 5. B. Hanamoto, Artificial Soils for Laboratory Studies in Land Locomotion, U. S. Army Ordnance Corps, Land Locomotion Research Branch, OoToAoC. Report No. 20, November, 1957. 6. M. G. Bekker, Off-The-Road Locomotion, Univ. of Mich. Press, Ann Arbor. 7. E. To Vincent, H. H. Hicks, Jr., and D. K. Kapur, Research in Vehicle Mobility, Univ. of Mich. ORA Report 02544-31-F, July, 1960. 8. R. Leis, Soil-Value System as Determined with a Precision Bevameter, Univ. of Mich. ORA Report 03026-2-P, December, 1961. 33

UNIVERSITY OF MICHIGAN 3 9015 03025 4406