Soil parameters to predict the performance of off-road vehicles

Journal of Terramechanics, 1973, Vol. 9, No. 2, pp. 13 to 31. Pergamon Press

Printed in Great Britain.

SOIL PARAMETERS TO PREDICT THE PERFORMANCE OF OFF-ROAD VEHICLES B.-S. CHANG* and W. J.

BAKER~

SO1L parameters c, % kc, ke, and n are evaluated using combined penetrating and rotating motion of a circular plate. The device is called a Penetro-Shear apparatus. Data obtained by this method includes the effects of the slip-sinkage phenomenon. An equilibrium analysis of a rectangular traction element is compared to the analysis of a rotating and penetrating plate. The analogy between the results is shown and parameters to be used in the vehicle performance equations are derived. The performance of a full-scale M l I 3 track is predicted using soil parameters calculated from the Penetro-Shear apparatus data and compared to experimental determination of the drawbar pull-weight ratio vs. per cent of track slip. Agreement between .predicted and measured values is good. INTRODUCTION The interaction of a vehicle traction element with soft soil represents a complicated imposed stress path [1] on the soil where normal stresses and shear stresses are applied simultaneously by the traction element. The vehicle performance depends upon the amount of traction that can be developed from the soil and the amount of sinkage that the traction element will develop as a result of the imposed normal and shear stresses. Vehicle performance curves in the form of drawbar pull-weight ratio (DP/VV) vs. the slip (%) of the traction element have been used to evaluate the performance of various traction elements. The drawbar pull is:

(1)

DP = H - - (R~ + Rb)

where: H = total traction developed from the soil shear strength Rc ~- resistance to motion due to soil compaction (sinkage) R b = resistance to motion due to a bulldozing effect. The total traction, H, was originally evaluated by Micklethwait [2] who adopted the Coulomb [3] equation for soil shear strength. This was later modified [4-6] to account for the strength developed vs. slip relationship of the soil. The resulting equation is

H : (Ac + Wtanq~)[1

--

kiL(1

--

e)-~]

*Chief Supervisor, S.E. Asian Branch, Johnson and Anderson, Inc. ~Professor of Civil Engineering, University of Detroit. 13

(2)

14

B.-S. C H A N G and W. J. B A K E R

in which : L :~: the total contact length of the traction element K -- a soil shear deformation constant equal to the deformation at the intersection of the slope o f the eleastic portion o f the shear strength vs. deformation curve with the tangent to the plastic portion of the curve i per cent slip ~ (1 -- VvlVw) 100% Vv velocity of the vehicle Vw =-- velocity of the traction element A contact area of the traction element c =~ soil cohesion q~ ~ soil angle o f internal friction W -~ total vertical load on the traction element. The resistance due to sinkage was evaluated by Bekker [4] as 1

= (,, + i) (b S<) /

[-W-i "+~

z. J "

(3)

where n -- an exponent determined from curve fitting pressure/sinkage date from circular plate vertical loading tests k ~ k , . + k~ ~ soil values determined from curve fitting pressure/sinkage data b f r o m circular plates [7] b = diameter o f the plate. The sinkage of the traction element is

z =

(4)

W where p ~ bL ; average contact pressure.

Reece [8] modified the pressure/sinkage relationships to make the soil constants dimensionally consistent. Reece [8] also employed results o f bearing capacity analysis f r o m classical soil mechanics [9, 10] to c o m p u t e soil sinkage constants f r o m soil cohesion and internal friction. Most work in the evaluation o f soil properties has consisted of refinements o f the semi-empirical Bevameter method [4]. The results o f these plate load tests and ring shear tests on the ground yield the traditional land locomotion soil values, c, % kc, k~0 and n. Hence equations (2), (3) and (4) along with an expression for the bulldozing effect proposed by Hegedus [11] can be used to predict the performance curves for traction elements in various soils. The key to vehicle performance prediction lies in the proper evaluation of the land locomotion soil values. Substantial evidence exists [12, 13] to indicate that soil strength and deformation properties are dependent u p o n the imposed stress path. Considerable

SOIL PARAMETERS TO PREDICT PERFORMANCE

15

difference may result in the evaluation of the soil shear strength and the strain at failure between tests where principal planes are rotated and tests where principal planes are not rotated. Consequently, it is important to evaluate the strength and sinkage soil values from a test which closely approximates the stress path beneath a traction element. Since traction elements apply both normal and shear stresses to the soil in the process of sinking and developing traction for forward thrust, it seems reasonable to develop soil values by applying normal and shear stresses to the soil simultaneously. This has long been recognized as the slip-sinkage phenomenon [14-17]. In particular, vertical plate bearing tests without applied horizontal loads would not account for the additional sinkage that would occur when horizontal (shear) loads were added. Many attempts have been made to correct this; however, most proposed methods greatly complicate the original semi-empirical methods developed or require many additional tests. The method proposed in this paper retains the same simplicity as the Bevameter method, yet accounts for the slip-sinkage phenomenon and improves the prediction of traction element performance. The basic concept combines soil shear and soil penetration by applying a vertical load and a torque to a circular plate [18, 19] simultaneously.

ANALYTICAL CONSIDERATIONS Most of the major aspects of the stress path imposed on the soil by tracked vehicles are approximated reasonably well by the rotating and penetrating motion of the circular plate. Recently, Czako [20] proposed to adopt the track equations to calculate the performance of soft tires. Hence a wide range of traction elements may be evaluated using the proposed Penetro-Shear apparatus. In evaluating the traction, H, and the resistance to motion, Re, in equation (1) two important points must be considered. First, the shear stresses on the contact surface between the traction element and the soil must be determined. These will be approximated by the shear strength, only if the contact surface is also a slip surface. If the soil beneath the traction element slips on surfaces other than the contact surface, equation (2) can still be used if reduced values of c and tan q~ are evaluated. Second, the soil values kc, kq~ and n used to evaluate the resistance due to sinkage must be determined from pressure/sinkage data that includes the effects of shear forces applied perpendicular to the vertical forces. Experimental evidence [8] has shown that a soil prism with a nearly triangular cross-section generally slides with a shear plate on the horizontal surface of the soil. This suggests that essentially no relative motion occurs between the soil and a shear plate on the contact surface, and the slip surfaces are the inclined sides of the soil prism. This concurs with observations and assumptions made in bearing capacity tests and bearing capacity analyses made in classical soil mechanics [9, 10]. in the following analyses a traction element is modelled by a rectangular shear plate. Equilibrium equations for the plate and soil wedge are compared to the equilibrium equations for a circular shearing and penetrating plate forming an inverted cone of soil beneath the plate that moves with the plate as it rotates and sinks.

16

B.-S. C H A N G and W. J. BAKER

In the analysis o f the r e c t a n g u l a r s h e a r plate the f o l l o w i n g s i m p l i f y i n g a s s u m p t i o n s are m a d e w i t h r e f e r e n c e to Fig. I" I~

F

R ~

.-X

f

~ {

// P

(a )

O' z

,

F' ~ ~I ~ , f

2S~_[z><_ -

~,-_x

~ ~ ,/ ,,,

~.$~

]'

(b)

z

p surface

)rizontal is

ne~ ~s ~

FIG. 1. A vehicle model (a rectangular plate) in cohesionless soils (c = 0). (a) Vehicle model sinking motion due to weight. (b) Vehicle model travels in soft soils. (c) Relationship between the soil shear strength s and its components sh and s,..

SOIL PARAMETERS TO PREDICT P E R F O R M A N C E

17

(1) the plate is rigid, and the vertical pressure distribution over the contact surface is uniform and given b y f o r f ' (2) no relative motion occurs between the soil and the shear plate on the contact surface (3) the soil forms a prism beneath the plate. The side surfaces of the prism are failure surfaces and form an angle of ~3 = (45 ° ÷ q~/2) from the horizontal (4) the soil prism is treated as a rigid body (5) the stresses over the surfaces OAO' in Fig. l(c), are ignored and the passive earth pressure, p, acting on line O'A is uniform (6) frictionless soils (q~ = 0) and cohesionless soils (c = 0) are treated separately and the results may be superposed for mixed soils. From the equilibrium considerations and the geometry shown in Fig. 1 the vertical pressure on the contact area for penetration without shear is: f=p(1

+ t a n q ~ t a n ~).

(5)

For penetration with shear, the shear strength will develop to oppose the motion which now has a horizontal component, u, as well as a vertical component, v. The angle this motion vector makes with the vertical axis is

"~ = tan-1 ( ; ) .

(6)

The resulting equations for vertical and horizontal stresses on the contact surface are f'--

P

(cos~ + t a n q ~ c o s ~ s i n f2)

(7)

COS ~

and Sh = p tan q~ sin 0 sin ~

(8)

where the angle f2 is shown in Fig. l(c). If the ratio of the vertical force to the horizontal shear force is defined as the developed soil coefficient of friction, tan q~', then it is clear that

tan q~' = .~'h; and q~ > q~' and the reduced friction angle, ? ' , should be used in equation (2). In addition to this the maximum vertical capacity of the soil is reduced when contact shear stresses are introduced since

f>~f'.

18

B.-S. CHANG and W. J. BAKER

,, p ,,,,,,

~ *

2

(a)

f,~RF ~ ~ ~ ~ z

Horzionta axi ls

(b)

FIG. 2. A vehicle model in ffictionless soils. (a) 1~ penetration motioa only. (b) In

penetration-shearing motion.

Similar results are obtained for frictionless soils (q~ ----0) shown in Fig. 2. The limiting vertical pressure without contact shear stresses is: f = (p +- cu). The limiting vertical pressure for the case with horizontal shear stresses is:

f'~

(

p+cucos

~sin ~

C6S~/

(9)

(10)

and the developed cohesion over the contact surface is: c'~ = cu sin ~ sin ~].

(11)

As in the case of the cohesionless soils the limiting bearing pressure is reduced and a reduced soil strength parameter c'u must be used in equation (2). By performing a similar analysis on a segment of the slip surface described by the soil cone beneath a circular rotating shear plate some important theoretical analogies become apparent. Applying analogous assumptions to the soil cone, the free body diagram for an incremental wedge section of the cone is shown in Fig. 3. In this case the horizontal component of the motion is not constant over the segment of the slip surface. The angle between the shear strength vector (i.e. direction along which full shear strength can be developed) and the z-axis is given by:

SOIL P A R A M E T E R S T O P R E D I C T P E R F O R M A N C E

19

t'O n-Io

8'~

Jo;j/

0 U'

,

ptonqbsin

o(b) ,Q, sin O' [

S.~O,

(c)

Sv .~Sh

~..p i O' z

o'

)

Sh:rL( ' ~RdJ~z,)(p¢on~s°n l~sn iO,)dz

i~--

R/cos/~(L)

S~:foL(R~Z')(PtOn~bs,n ~2sin 0')d:' FIG. 3.

Soil behavior beneath the PSA penetrating-shearing plates.

O' : tan -~ u_ : tan- 1 p~o__ 1,'

~

where p = radial coordinate on the contact surface (i.e. distance between point T and the z-axis) o~ = angular rotation rate of the plate v ----vertical component of motion. The horizontal component of motion over the segment of the slip surface varies linearly from Re0 at point A to 0 at point O' shown in Fig. 3. Defining as a constant a, for a given plate radius and specified rotation and penetration rate, the horizontal and vertical components of the shear stress opposing the motion may be integrated over the area of the segment of the slip surface as shown in Fig. 3. The resulting horizontal and vertical shear forces on the segment of the slip surface are:

R~o/v

_

R 2dn p t a n 0 IV/( 1 q_ a~ sinS [3) 2 cos [3 a sin [3 - - 1, log (a sin ~3) + ~/(1 + a 2 sin 2 [3)] a sin [3

(12)

and

sv_pRSdn 2cos[3

p tanqo [ ~ / ( l + a Z s i n 2 [ 3 ) _ l ] " a ssin[3

(13)

20

B.-S. CHANG and W. J. BAKER

From equilibrium conditions the limiting vertical force on the segment of the contact are represented by Rz/2 dn is: F' = p R~dn (cos [3 + 2 t a n 9 [ ~ / ( l + a " s i n 213)- 1] ~ c~ cos [3 k a z sin [3 f.

(14)

The ratio between the horizontal force and the vertical force, S~/F', on the elemental area will give the average developed coefficient of friction, tan 9 ' . For the case of frictionless soils (9 = 0) the developed cohesion is derived in a similar manner as:

{

, c.

=

C•2

2 +

2 log[~ -

a"

k

÷~/(I+ /2

a2"l l

(~5)

2

where: C. -- soil cohesion or shear strength for 9 -- 0 condition a : Ro~/v : tan 0 t(max ) The developed shear parameters tan 9 ' and c ' , on the contact surface of the rectangular shear plate were found to depend on the soil friction component of strength tan 9 and the soil cohesion, c,, respectively as well as the geometry of the soil wedge and the direction of motion, ~, of the traction element model. Similar results were found for the developed shear resistance on the contact area of the rotating-penetrating plate; however, since the direction of the resisting shear stresses varies over the slip surface the equations are related to the direction of the outer edge of the circular plate, 0'(max), where a - tan 0'(max~ = Ro~/v was taken as a constant for a particular Penetro-Shear apparatus. The results are compared over the range of ~ and 0'(max) of interest in Fig. 4. Hence the approximate analysis indicates that the rotating and penetrating plate represents a reasonable way of evaluating soil values for traction elements. In addition to the method of evaluating soil parameters 9 ' and c' for equation (2) suggested by the preceding analysis, the sinkage parameters kc, k~ and n required for equation (3) will also be determined from pressure sinkage data in exactly the same way as the Bevameter method, and will include the effects of slip sinkage. THE PENETRO-SHEAR APPARATUS (PSA) Since the ratio of the horizontal velocity to the vertical velocity of a traction element varies over a narrow range, i.e. 0 in Fig. 1 will be relatively large for most practical cases, the Penetro-Shear apparatus was designed to maintain a constant ratio between the velocity of angular rotation and the velocity of vertical penetration. This is accomplished by applying a vertical thrust to a helically grooved shaft connected to the circular bearing plate as shown in Fig. 5. The shaft is mounted in a housing and turns by engaging roller bearings in the helical groove. By measuring the vertical force at the plate, the torque in the shaft, and the sinkage of the plate, a pressure/ sinkage curve and a shear resistance/normal stress curve can be developed simultaneously. By curve fitting the data for different sizes of plates as done in the Beva-

SOIL PARAMETERS TO PREDICT PERFORMANCE

21

45

4 0 --.

~ = 85 ° l

35

8 =.85 °

/ / / / / /

__

30

~ =75 °

/ /

25 --

/~"

~

/

.~" ~" ~__. _ _ _ _ __

~/~"

__

20

~-

O ~ : 75

"1- -~ ~

u

~ ~

g~ o

-- .

o ~

°

81= 6 0 ° 8 = 60 °

15

I0

> c~

5

I

~

5

0

~

I0

15

Soil

~

25

1

30

fr~ction ongle ,

tan0': tan~= FIG. 4(a).

1

20

Soil

I

35

I

40

Rw/V(Circular plate) U/V ( R e c t a n g u l a r t r a c t i o n slip-sinkage

45

~ (deg)

friction

element-)

parameter.

I'0

~]~ 0.8

g

._

~ u

0.6 "~

~ X~

~

Traction

element

°~

.~= ~

~

02

40

50

60 --

80r8

F ~ . 4(b).

Soil slip-sinkage

I

~

70

80

90

deg

cohesion

parameter.

meter m e t h o d a consistent set o f soil values will be developed to predict vehicle performance. The pressure/sinkage curves are derived in a straight forward manner f r o m the data. The shear resistance vs. normal force curve to evaluate c ' . and tan ?' require additional assumptions. As indicated in Figs. 5(a)-(d) the m o m e n t about the z-axis due to the shear stresses distributed over the plate contact area m u s t be in equilibrium

22

B.-S. C H A N G and W. J. BAKER

with the applied torque, T. To simplify the relationships the pressure distribution is assumed to be uniform over the contact area and the effect of side friction on the edges of the plate is assumed negligible. The applied torque can be related to the applied vertical force, Ft, the measured vertical force at the plate, F', the radius of the helical shaft, r, and the helical angle 0 by: T = r (F t -

F ; ) c o s O c s c O.

With the above assumptions the resisting torque over the contact surface will be: T

2/3 n R 8 sh

=

where: shear stress R ~ radius of contact area, plate. Hence the shear stress is given by: sh =

s~ =

3r - - - cot 0 (F, -- F ' ) 2nR ~

(16)

i

I

/"

Rd~ '~

q

s

.....

4\

~ ,,

/

T= "~R)(~R)%Rd~ ,

Fro. 5(a).

The design concept of shear plates for PSA, and the assumption of the shear stress distribution.

SOIL PARAMETERS TO PREDICT PERFOR.MANCE

23

~v

0"~

Fla. 5(b).

P

The helical shaft and the soil behaviour beneath a penetration-rotating shear plate of the PSA.

~The RrCOS8

//

FIG. 5(c).

'

helical surface

~~

cos O

Rr COS~ ~

The two-dimensional view of the free-body diagram of the helical shaft.

24

B.-S. CHANG and W. J. BAKER

cos

O

The helical "(Oj ~surfOce

i/i

Rr R I1[1["~-~~ ~ ~ r~_~ ~ ~

FIG. 5(d). The three-dimensional view of the free-body diagram of the helical shaft.

and the normal stress is given by: F t

[" = - - - . •

(17)

~ R 2

The evaluation of the soil parameters depends upon certain physical characteristics of the apparatus. These characteristics are the shaft radius, plate radius and helical angle of the shaft groove. For a given plate size the term (3r/2 rt R 3) cot 0 is a constant. Pressure/sinkage curves and torque/sinkage curves were found to be essentially independent of this constant over a range of ± 33 per cent from a mean value, with the plate radius kept constant [21]. Details of the hardware development, data reduction techniques, and indirect methods of data recording using a pen and ink spring recorder which make the apparatus extremely portable are given elsewhere [18, 19, 21]. EXPERIMENTAL RESULTS Soil values were measured from a series of tests on several soils ranging from sand to plastic clay. The soil values using the Penetro-Shear apparatus were compared to those found using the standard Bevameter method [4]. Typical results for a moist Detroit loam are shown in Fig. 6. Figure 6(a) shows the vertical force applied to the soil vs. the plate sinkage. The curves F ' 4 and F' a represent data from 4 in. and 3 in. diameter plates on the Penetro-Shear apparatus. In these tests a torque was simultaneously applied as described, developing shear stresses over the plate contact area. Curve F4 represents the vertical force vs. sinkage curve for a 4 in. diameter plate~ however, a torque is not applied in this case and the penetration occurs without the addition of surface shear forces. The effect of the slip-sinkage phenomenon is obvious from these data. Figure 6(b) shows the applied torque vs. the sinkage. Figures 6(a) and 6(b) are combined to produce the Penetro-Shear apparatus (PSA) results shown in Fig. 6(c). These data are used to compute c' and tan ~ ' to be used in the prediction of traction performance in equation (2). Similar results using the standard Bevameter method are shown in Fig. 6(c) also. Using equations (12), (14) and (15) the soil cohesion and angle of internal friction can be evaluated from the PSA results c ' , and q~'. The computed values are shown on

SOIL PARAMETER.S TO PREDICT PERFORMANCE / / PSAII

200

Load

cell

D e t r o i ? l o a m , mois~r (a)

/

/

/ /

//

/

/// ~ I00

135

F~ P l a t e size

-

o

I

2

3

4

Sinkages z, PSAII

i00 ¸-- D e i ' r o i i

Torque loam

~n. /

cell

T4

I06

(b)

50

-

o ~3.

~

I

2

3

Sinkoges

f

Moist detroit loom -- x , , 3in. pla,, e~o 4in. plate Computed c : O . 5 6 p s , 28">~>32.5" Direct sheor c:o-so~si _

~:~o.,.

~ " ~ ~

e

z,

in,

Bev. % = 0 . 2 0 p s i , ~ , : 3 2 " ~ / ~

~

~

~

~

//

~

~L"

~

~

~s2, ' ~=o.,o~ i ~' : 2~"

8

O

(c)

I 5

~ IO Normal pressures,

I 15 in.

FIG. 6. The PSA direct method data reduction technique. (a) Force-sinkage curves. (b) Torque-sinkage curves. (c) Soil shear values in the moist Detroit loam.

25

26

B.-S. CHANG and W. J. BAKER

Fig. 6(c) for the range o f horizontal to vertical m o t i o n ratios imposed by the different P e n e t r o - S h e a r devices. The measured soil cohesion a n d friction f r o m direct shear tests are also shown. These results indicate the reasonableness o f the a p p r o x i m a t e analytical representation o f the P e n e t r o - S h e a r a p p a r a t u s and traction element model. The results also show that the s t a n d a r d Bevameter m e t h o d should over-estimate the traction in equation (2) and under-estimate the resistance to m o t i o n due to sinkage in e q u a t i o n (3). To test this hypothesis a series o f full-scale d r a w b a r pull tests were p e r f o r m e d using a full-size M I13 track. The tests were p e r f o r m e d using the soil bin and Universal D y n a m o m e t e r at the l a b o r a t o r y o f the L a n d L o c o m o t i o n Branch, M o b i l i t y Systems L a b o r a t o r y o f the U.S. A r m y T a n k A u t o m o t i v e C o m m a n d o f W a r r e n , Michigan. The soil bins, d y n a m o m e t e r , a n d recording e q u i p m e n t have been described elsewhere [21, 22] and the m a j o r features o f the test e q u i p m e n t are shown in Fig. 7. The tests were p e r f o r m e d on D e t r o i t l o a m at three different moisture contents. The p e r t i n e n t soil i n f o r m a t i o n , Bevameter soil values, a n d P S A soil values are given in Table 1. The results o f the d r a w b a r pull tests are shown in Figs. 8, 9 a n d 10. T h e TABLE 1

Detroit loam Testing devices

Parameters Moist*

Medium wet

Wet

7"00 2.00

9'00 2"70

3"20 1.00

n ¢ (psi) q0

0"98 0"20 32"00

0"84 0"25 34"00

1'20 0" 15 24.00

k '~ k 'w n' c' (psi) q)'

4"50 0"25 1'05 0'40 24.00

6"00 1'60 0'90 0"30 25'00

1.20 0'52 1"22 0.40 19.00

k~ k~ Bevameter

PSA

Moist Med. wet Wet

= :=

8 to 9% 13 to 14% 17 to 18%

t

Moisture contents

Liquid limit 19.3 ~ Plastic limit = 13.7~ Plasticity index ~ 5.6. d~o = 0.12 mm (mean particle size). Uniformity coefficient = 10. d r a w b a r pull vs. slip curves are the result o f direct measurements. The sinkage a n d vertical force on the track are also m e a s u r e d d u r i n g the test. Figures 8, 9 a n d 10 also show the predicted d r a w b a r pull vs. slip using the Bevameter soil values a n d the P S A soil values. In the semi-plastic a n d plastic soil the P S A results represent the lower b o u n d o f the d a t a b a n d a n d the Bevameter results sub-

SOILPARAMETERS TOPREDICT PERFORMANCE Verfica~ toads

~ / _ ~ / C a r riage

channel N°'land 2"-"~F~l^"l'-' T~I

Horizon'l"al loads (DP) /

~. Channel No,.~and4 ~Carria~e

~'~'~ ~

//III

27

honnel No. 5

A~ L=IO~ in. (a)

~No.2

//I//

-~

C~ro i ge chonnel No.7~ ~~ speed

~i

~_

13in.

~

J ~ The firth wheel B=lfin. (b) A-A (c) F]~. 7. The draw-bar pull test ri~, ~113 track, and the fifth wh~l.

stantia]l~ owr-estimate the track p¢r£ormanc¢ at slip ~r¢at¢r than ]0 per cent. As the soil approaches the liquid limit both techniques owr-estimate the performance. The PSA results over-estimate between ]5 and 20 per cent while the Bevam¢ter results over-estimate between 30 and 40 per cent. Predicted sinkage o£ track at slip ~reater than 30 per cent compares extremely well with measured values when the slip-sinkage soil values derived £rom the PenetroShear apparatus are used. The bulldozin~ eEect was negligible in all three cases due to the trim an~]¢ and small sinkage at the £ront o£ the track. CONCLUSIONS

The model consistin~ o£ a wedge o£ soil movin~ with a traction element seems to represent actual conditions reasonably wall. This requires the use o£ reduced £riction parameters in computin8 the thrust developed ~or £orward motion over the contact area between the traction element and the soil Sinkas¢ is substantially increased due to the slip-sinkage phenomenon and can be evaluated reasonably well £rom the p¢netratin~-rotatin~ motion o£ a circular plate. The experimental results indicate that the Penetro-Sh¢ar apparatus provides soil in£ormation that allows reasonabl~ 8ood predictions o£ traction element performance, while maintainin~ the simplicity o£ the semi-empirical Bevam¢ter method.

28

B.-S. C H A N G

and W. J. B A K E R

De'i'roit loam moisf ( w = 8 - 5 % ) Normal loads o e . : 1 3 , 0 0 0 Ib 0'8 _ X

,~. ~7:8~:~:)0 Ib

0¸6

8evamefer

\ \~7\\

0.4

-

~

~ ~ ~ ~ ~--~,~

0'2

~

C

~

I

\ \~x",~,,,~,

~ ; ,

~

sinka~ Calculated PSA ~vameter

85in. 7~ ~

I0

\ \ ,', \ \ \ \ \ \, \ \ \ x \ \ \ x ~ ~ \,

PSA

~9-Oin

~

\\ \ \\\

. . . . . ~,,,~ . . . . . . . . . . . ~ . . . . . .

~

Track

~

\ \\,x\\,

~

~

~sured ( i ~ %)

~

~

'

~~ g,~"

20

30

in

:

I

I

40

50

60

~ 70

Slip i, % FIG. 8.

Vehicle p e r f o r m a n c e curves for M113 in the moist Detroit loam.

Bevameter Rc = 720 lb Slip (%) 5 10 15 20 30 50 80 W = 13,000 lb.

H (lb) 3300 5450 6580 7110 7830 8350 8430

P S A Re = 810 lb

DP (lb)

DP/W

H (lb)

DP (lb)

2580 4730 5860 6390 7110 7630 7710

0.198 0-364 0'450 0.492 0.547 0'586 0.593

2818 4060 4780 5235 5880 6285 6430

1808 3250 3770 4225 4870 5275 5420

DP/W 0.139 0.234 0.290 0.325 0.378 0.405 0.416

SOIL PARAMETERS

TO PREDICT PERFORMANCE

Defroit loam medium wet

29

(~=14%)

Normal loads x z,, ~ I3 e la:lS,O00 Ib @ 0 E]:8,~:~O0Ib

o.8I O6

B e v a m e ~ ~"

/

~..~.~_~ \ ...~0\\ (~. . . . . . . . . .

~

~

0.4

/

~ ~ ~ _ ~ ~ ~ f ~

0'2

I0

~

~

~.~\\

..... ~

~

.

~

~

~

Track sinka~ M~sured Cal~leted (~30%) ~ B~ter tllO~. ~'7in 8-9in

20

50

Slip i, F~G. 9.

~]~. . . . . .

~.,P.~,~.~,,~

40

50

60

70

%

Vehicle p e r f o r m a n c e curves for M113 in the m e d i u m wet Detroit loam.

Bevameter Rc = 635 lb.

P S A Rc = 830 lb.

Slip

(%)

H (lb)

DP (lb)

DP] W

H (lb)

DP (lb)

DP/W

5 10 15 20 30 50 80

4225 6005 7205 7815 8565 9005 9135

3590 5370 6570 7180 7930 8370 8500

0"276 0"412 0"505 0'554 0"610 0"643 0'654

2770 4210 5005 5480 5910 6360 6540

1940 3380 4175 4550 5080 5530 5710

0"149 0"260 0'321 0"350 0'391 0'425 0.440

W = 13,000 lb.

30

B.-S. C H A N G and W. J. BAKER

0.~--

Detroit loam, wet (w:±17.5%) Normal loads ~500 lb

0.6--

" ~

o_

0"

4

I

/

/

~

~

~

~

°

o

~" _,#e0~,', d ~ a "~'~O" 2 [~

Track sin~oges

,~,,~k/.,~'-

I , ~

IVleasured

~

Calculated Es~ ~evameter ,i.,io.

~i-~%)

r/J~-~

0

I0

20

30

Slip i,

FIG. 10.

40

50

60

70

%

Vehicle performance curves for M113 in the wet Detroit loam.

Bevameter R, = 100 lb.

PSA Rc = 235 lb.

Slip (%)

H (lb)

DP (lb)

DP/W

H (lb)

DP (lb)

5 10 15 20 30 50 80

675 1080 1310 1470 1633 1780 1792

575 980 1210 1370 1533 1680 1692

0'164 0'280 0"346 0"392 0'438 0'480 0"484

625 932 1242 1380 1495 1670 1710

390 697 1007 1145 1260 1435 1475

DP/14/ 0"111 0"199 0"287 0'327 0"360 0'410 0'420

W = 3500 lb.

Acknowledgements--The authors wish to acknowledge the cooperation and encouragement of Dr. Ernest Petrick, Chief Scientist of U.S. Army Tank Automotive Command. Special thanks are given to Mr. Zoltan J. Janosi (TACOM), Mr. Ronald Liston (formerly TACOM) and Mr. E. Hawes (TACOM), for their continued cooperation during the period of this work. Acknowledgements are also given tb the Michigan Technological University for constructing two models of the PSA and to Mr. William Doebbler, Yuma Proving Ground, U.S. Army Testing and Evaluation Command. The major portion of the testing program was carried out in the facilities of the Land Locomotion Division, Mobility Systems Laboratory. U.S. Army Tank Automotive Command, Warren, Michigan. REFERENCES [1] T . W . LAMBE, Stress path method. ASCE, J. Soil Mech. Found. Div. 93 (SM6), 309-331 0967). [2] E . W . E . MICKLETHWAIT, Tracks for Fighting Vehicles, School of Tank Technology (1944). [3] C . A . COULOMB, Essais sur une application des r~gles des maximis et minimis 5, quelques problems de statique relatif 5. l'architecture. Mere. Acad. Royal. Pres Divers. Say. 5.7, Paris (1776). [4] M . G . BEKKER, Theory of Land Locomotion, University of Michigan Press. Ann Arbor (1956). [5] Z. JANO$I and B. HANAMOTO, The analytical determination of drawbar pull as a function of slip for tracked vehicles in deformable soils. Proc. First International Conference of Soil-l/ehicle Systems, Turin, Italy (1961). [6] T . F . CZAKO and Z. JANOSI, State of the art of vehicle mobility prediction. U.S. Army Tank Automotive Command Rex. Report, LLD, No. 6 (1966).

SOIL PARAMETERS TO PREDICT P E R F O R M A N C E

31

[7] Staff, U.S. Army Tank Automotive Command, A soil value system for land locomotion mechanics. L L Research Report No. 5, Warren, Michigan 0958). [8] A. R. R.EECE, Problems of soil-vehicle mechanics. Land Locomotion Lab. Report LL No. 97, U.S. Army Tank Automotive Command, Warren, Michigan (1964). [9] K. TERZAGHi, Theoretical Soil Mechanics. Wiley, New York (1943). [10] G . G . MEYERHOF,The ultimate bearing capacity of foundations. Geotechnique 2, 301-332 (1951). [11] E. HEGEDUS, A simplified method for the determination of bulldozing resistance. Land Locomotion Laboratory, Report No. 61, U.S. Army Tank Automotive Command, Warren, Michigan (1960). [12] C . C . LADD, Strength parameters and stress-strain behaviour of saturated clays. Dept. Civil Engineering Res. Report R71-23, Soil Mechanics Division, M.I.T., Cambridge, Mass. (1971). [13] H . K . Ko and R. R.. SCOTT, Deformation of sand in shear. ASCE, J. Soil Mech. Found. Div. 93 (SM5), 283-311 (1967). [14] M . G . BEKKER, Introduction to Terrain-Vehicle Systems. University of Michigan Press, Ann Arbor (1969). [15] A . R . REECEand R. ADAMS,An aspect of tracklaying performance. A S A E (1962). [16] A. SOLTVNSKI, Slip-sinkage as one of the performance factors of a model pneumatic-tired vehicle. J. Terramechanies 2, (3) (1965). [17] L . L . KAIAFIATH,On the application of land locomotion theories and experimental results in problems of lunar locomotion. Grumman Research Dept. Men. RM. 454 (1969). [18] B.-S. CHANG, The Penetro-shear apparatus. Land Locomotion Div. Rep. No. 131, U.S. Army Tank Automotive Command, Warren Michigan (1968). [19] E. HAWES, The Penetro-shear apparatus. U.S. Patent No. 3552194 (1971). [20] T . F . CZAKO, Methods of vehicle soft soil mobility evaluations bases on the soil-vehicle interaction. Proceedings First International Conference on Vehicle Mechanics. Wayne State University, Detroit, Michigan (1968). [21] B.-S. CHANG, A method of predicting soft soil performance of off road vehicles. Dissertation, College of Engineering, University of Detroit (1971). [22] R . A . LISTON,The Land Locomotion Laboratory. J. Terramechanics 2, (4) (1965).