TRANSPORT AND ROAD RESEARCH LABORATORY Department of Transport

RESEARCH REPORT 300

Analyses of the performance of dead-weight rollers compacting soil

by M P O'REILLY

Crown Copyright 1991. The views expressed in this Report are not necessarily those of the Department of Transport. Extracts from the text may be reproduced, except for commercial purposes, provided the source is acknowledged.

Ground Engineering Division Structures Group Transport and Road Research Laboratory Crowthorne, Berkshire, RG11 6AU 1991

ISSN 0266-5247

Ownership of the Transport Research Laboratory was transferred from the Department of Transport to a subsidiary of the Transport Research Foundation on 1 st April 1996.

This report has been reproduced by permission of the Controller of HMSO. Extracts from the text may be reproduced, except for commercial purposes, provided the source is acknowledged.

CONTENTS

Page

Abstract 1

1 Introduction 1

2 Idealisation of the compaction process for pneumatic-tyred rollers 1

3 Smooth-wheeled rollers 2

3.1 Idealisation of compaction

with a smooth-wheeled roller 2

3.2 The pressures applied by steel rolls 2

3.3 Soil shear-strength relations 4

3.4 Calculated states of compaction 4

3.4.1 Cohesive soils 4

3.4.2 Granular soils 5

3.5 Assessment of theoretical calculations 6

3.5.1 Cohesive soils 9

3.5.2 Granular soils 14

4 Sheepsfoot and Grid rollers 18

4.1 Idealisation of compaction with sheepsfoot roller 18

4.2 Calculation of compaction achieved by sheepsfoot rollers 18

4.2.1 Cohesive soils 19

4.2.2 Gravel-sand-clay soil 20

4.3 Assessment of theoretical calculations for the sheepsfoot rollers 20

4.4 Calculated compaction achieved by a grid roller 21

5 Application of the analyses 21

5.1 Pneumatic-tyred rollers 21

5.2 Smooth-wheeled rollers 24

5.3 Sheepsfoot rollers 24

6 Conclusion 27

7 Acknowledgement 27

8 References 28

ANALYSES OF THE PERFORMANCE OF DEAD-WEIGHT ROLLERS COMPACTING SOIL

ABSTRACT 2.

In this report the methods used to analyse the compac- tion process using pneumatic-tyred rollers are developed and applied to smooth-wheeled, sheepsfoot and grid rollers. Calculations again using a shear stress with depth approach were applied on the cohesive soils while a bearing capacity method was used on the granular soils. Comparison of the calculated densities with measured results showed generally good agreement and that the idealisations and analyses developed were capable of determining the levels of compaction achieved by dead- weight rollers.

1. INTRODUCTION

Analytical approaches are useful when they improve the understanding of engineering processes and other phenomena. In the case of the compaction process where the underlying principles, ie the relation between dry density, moisture content and compactive effort, are straightforward (Proctor 1933; Road Research Labora- tory 1952) and there is a plethora of data on the perform- ance of compaction plant (see for example Johnson and Sallberg 1960; Ecole Nationale des Ponts et Chaussees 1980), the scope for obtaining added insights through an analytical approach is obviously limited. Indeed it would appear that only two attempts, by Lewis (1959) and by Yong and Fattah (1982), have so far been made to calculate the soil densities achieved by compaction from a knowledge of soil strength properties and behaviour.

With the methods used by Lewis (1959) to analyse the compaction achieved by pneumatic-tyred rollers as a starting point, methods for calculating the densities achieved by a wide range of compaction plant were developed by O'Reilly (1985). In this Report the analyses applicable to dead-weight rollers other than pneumatic- tyred rollers are described: compaction using smooth- wheeled rollers is treated in the first instance and sheepsfoot and grid rollers are then considered. A subsequent Report will deal with analyses for vibrating and impact compaction plant.

In their research Yong and Fattah (1982) used a finite element analysis to predict soil compaction under a model rigid roller in the laboratory and that approach is not considered further here.

IDEALISATION OF THE COMPACTION PROCESS FOR PNEUMATIC-TYRED ROLLERS

In the analysis of the studies at the Transport and Road Research Laboratory (TRRL) the compaction process for pneumatic-tyred rollers was idealised by Lewis (1959) in the following terms:

"When loose soil is traversed by a roller that exerts a bearing pressure in excess of the bearing capacity of the soil, compression of the soil will occur and it will be left in a higher state of compaction with an increased shear strength and hence increased bearing capacity. If the bearing capacity of the soil is still less than the bearing pressure of the roller, a further passage of the machine will produce additional compression of the soil but the magnitude of the ensuing increase in the state of com- paction will be less than that produced by the first pass because the soil will be over stressed by a smaller amount. As the soil is compacted by further passes of the roller, the bearing capacity will progressively increase at a decreasing rate until eventually an equilibrium situation will be reached when the shear strength or the bearing capacity of the soil balances the shear-stresses or bearing pressures produced by the roller. This condition is often termed 'compaction to refusal' ". It defines an upper limit to the dry density obtainable by a piece of compaction equipment at a given moisture content.

Using the above concept of compaction, two approaches were developed to calculate the states of compaction produced by pneumatic-tyred rollers. One was for "cohesive soils with no significant angle of shearing resistance" and the second for "soils with both cohesion and an angle of shearing resistance"; these latter soils are termedgranular soils in this Report.

For cohesive soils the basic assumption made by Lewis (1959) was that when the soil is compacted to refusal by the rollei', it has been compressed to a condition in which its shear strength is equal to the shear stresses induced by the roller in the layer being compacted. Further, a limiting condition occurs as the soil approaches satura- tion; here the shear strength of the soil is unable to sustain the shear stresses developed and serious plastic deformations, at constant volume, occur. Given relations between cohesion, moisture content and dry density and the shear stresses imposed by the roller, the maximum state of compaction that could be produced at any moisture content can be calculated.

With granular soils a different approach was employed since two parameters, apparent cohesion and the angle of shearing resistance, are needed to define their strength properties and the resistance to shear of the soils is a function of the normal stresses on the shear planes. In this case Lewis (1959) proposed a simplified approach in which the ultimate bearing capacity of the compacted soil is equated to the contact pressure applied by the roller tyre, ie the soil compacts until a bearing capacity equal to the applied pressure is developed. The method, therefore, only calculates an average density over some ill-defined depth beneath the source of the compaction pressure.

Agreement between measured and calculated states of compaction was excellent on the cohesive soils with the calculated dry densities and optimum moisture contents being on average 0.024 Mg/m 3 lower and less than one per cent higher respectively than the actual values. On the other hand discrepancies were greater on the granular soils and this undoubtedly reflects the limitation of the approach mentioned in the previous paragraph. On these soils the calculated maximum dry densities were on average 0.077 Mg/m 3 lower than measured values while the average optimum moisture contents were some 1.9 per cent higher.

3. S M O O T H - W H E E L E D R O L L E R S

Smooth-wheeled rollers are a commonplace sight on roadworks and indeed are almost invariably used for the compaction of bituminous pavement layers because of the smooth surface they produce.

3.1 IDEALISATION OF COMPACTION WITH A SMOOTH-WHEELED ROLLER

Unlike the pneumatic-tyred roller, where the contact area between wheel and soil remains constant throughout the compaction process, with the smooth-wheeled roller the contact area between the steel rolls and the soil reduces progressively until an equilibrium is finally reached when 'compaction to refusal' is achieved. At the commence- ment of rolling the steel-tyred wheel sinks into the loose soil and compresses it until the area of roll in contact with the layer being compacted is 'balanced' by the bearing capacity of the soil. In succeeding passes the soil is further compressed and strengthened and the contact area between the wheel and the soil reduces, ultimately reaching a constant value: thus the pressure applied to the soil surface increases during the compaction process until a maximum pressure is reached. The relation between contact area, uniform bearing pressure and maximum shear stress distribution with depth for a constant load on a progressively reducing contact area - simulating the steel tyred wheel of roller - is shown in Figure 1. It is based on the fact that to a depth equal to a

half the width of the strip the maximum shear stress is equal to p/~ where p is the load per unit area; below this level the maximum shear stress is given by p sin ot./~ where (z is as shown on the inset in Figure 1 (Poulos and Davies 1974).

3.2 THE PRESSURES APPLIED BY STEEL ROLLS

At the condition of compaction to refusal the soil and wheel can be considered as an elastic system. Timosh- enko and Goodier (1970) consider the general case of the pressure between two elastic bodies and O'Reilly (1985) applied this to a cylinder i.e. the smooth wheel roll, resting on a flat surface, i.e. the material being com- pacted. For this case using the notation in Timoshenko and Goodier the area of contact is a narrow rectangle, the half width, b, of which is given by:-

b = (4P'(kl +k2)R,) o.s (1)

where

P' is the load per unit length of the surface of contact,

R 1 is the radius of the cylinder

E 1 and E 2 are the elastic moduli of the material of the cylinders and the flat surface respectively

"01 and "02 are the corresponding Poisson's ratios of the

material of the cylinder and flat surface

1 - "02 1 - '022 k 1 - k2 =

~E~ and ~E2

For a steel-tyred roller compacting soil the assumption is made that the E value of the roll is large compared with the E value of the soil layer so that k 1 is small by compari- son with k 2 and can be neglected. Then by taking "02, Poisson's ratio of the soil, as 0.5 equation (1) reduces to:-

b=0 .977 ( P'R, )0.5 (2)

In analysing the results of compaction plant trials the contact width, 'w', rather than the half width, b, is of more interest so that the above equation is more conveniently expressed as:-

vvo

I - s o i l Esoit

where 'W' is the load per unit width on the roll, R and D are the radius and diameter of the roll respectively and Esoil is the elastic modulus of the soil layer being com- pacted.

2

E v =,

O

0

0

50 - -

100 --

150 --

200 --

250 --

300

Fig. 1

i i I - -

I

C o n t a c t C o n t a c t w i d t h pressure m m W / u n i t area

3 0 4 . 8 0 . 0 8 3 W

152 .4 0 . 1 6 7 W

76 .2 0 . 3 3 3 W

5 0 . 8 0 . 5 0 W

2 5 . 4 1 . 0 0 W I I I

M a x i m u m shear stress - W / u n i t area

0 .1W J 0 .2W 0 . 3 W

W = Load per un i t w i d t h o f ro l l

2b

Ix,z)

Relation between contact width, maximum shear stress and depth below surface

The uniform pressure, q unif, developed under the roll is given by

W E 0,5 ( ,°,/ q unif = 0.51 ~ - -

(4)

Information on the values of elastic moduli of soils is limited. Values obtained during the course of pavement design research at TRRL gave a range of dynamic Eso , values of 35 to 160 MN/m 2 (Jones 1958 and 1959; Croney 1977). A wider range of values from 10 to 300 MN/m 2 is given by Barkan (1962) and subsequent measurements (Marsland 1973; Jardine et al 1984) do not alter that range. Recent compressional wave-velocity

* The description of the rollers used in the the original sources referring back and to aviod any confusion

measurements at TRRL would put the zero strain Eso , somewhat higher but suggest that the above range would be realistic where significant deformation occurs.

Details of the two smooth wheeled rollers used in the full- scale compaction plant trials at TRRL are given in Table 1A; similar details are given in Table 1B for the two vibrating smooth-wheeled rollers which were tested on the cohesive soils as dead weight rollers with their vibrating mechanisms inoperative. Also shown are the calculated contact widths, w, using equation (3) for the range of modulus values considered above; these range from 59.6mm for the rear roll of the 8-ton smooth- wheeled roller to 8.7mm for the front roll of the 23/~-ton" smooth-wheeled roller.

have been used throughout this report for ease in

3

TABLE 1A

D.etails of the smooth-wheeled rollers studied

Roller 8-ton * 23/~-ton *

Gross weight - kg 8624 2794 Weight on front rolls - kg 3548 864 Weight on rear rolls - kg 5076 1930 Width of front roll - m 1.0668 0.6096 Width of rear roll - m 0.4572 0.3810 Load per metre width:- Front roll - kg/m 3326 1417 Rear rolls - kg/m 5551 2533 Diameter of front roll - m 1.0668 0.8636 Diameter of rear roll - m 1.3716 0.9144 Calculated contact widths Modulus 40 MN/m 2 Front roll - mm 40.7 23.9 Rear roll - mm 59.6 32.9 Modulus 160 MN/m 2 Front roll - mm 20.4 12.0 Rear roll - mm 29.8 16.4 Modulus 300 MN/m 2 Front roll - mm 14.9 8.7 Rear roll - mm 21.8 12.0

* See Will iams and Maclean (1950) and Lewis (1954)

TABLE 1B

Details of the vibrating rollers studied

Roller 8V2-ton* 33A-ton * Towed Tandem

Gross weight - tonne 8.59 3.89 Weight on vibrating roll - tonne 8.59 2.79 Weight on non-vibrating roll - tonne Nil 1.10 Static load per metre width on vibrating roll - kg/m 4500 2786 Diameter of vibrating rol l- m 1.6002 0.8890 Calculated contact widths on vibrating roll - mm Modulus 40 MN/m 2 58.0 34.0 Modulus 160 MN/m 2 29.0 17.0 Modulus 300 MN/m 2 21.2 12.4

* See Lewis (1961) and Parsons et al (1962)

3.3 SOIL SHEAR-STRENGTH RELATIONS

Whenever dry-density measurements were made on the two cohesive soils during the course of the full-scale compaction tests using pneumatic-tyred compaction plant at TRRL 'undisturbed' soil samples were obtained and tested in unconfined compression (Lewis 1959). From the results of these test families of curves relating shear strength - taken as one-half of the unconfined compres- sive strength - moisture content and dry density were produced and these are reproduced as Figures 2 and 3.

For the granular soils, a well-graded sand and a gravel- sand-clay, where the shear, strength is characterised in terms of apparent cohesion and the angle of shearing resistance, a series of laboratory triaxial compression tests were carried out on specially compacted specimens of these two soils. The families of curves relating appar- ent cohesion and angle of shearing resistance with moisture content and dry density derived from these tests are reproduced in Figures 4 and 5. These data were reported in imperial units and this format has been retained to avoid rounding errors with metric equivalents appended for the reader's convenience.

3.4 CALCULATED STATES OF COMPACTION

Given that the E values of the soils used in the full-scale compaction trials at TRRL are only known in very general terms and not for each individual test, calculations were made for roll contact widths of 25.4, 38.1 and 50.8mm (1, 11/2 and 2 inches respectively) since the soil strength/ density/moisture content data (Figures 2-5) as has already been mentioned was originally presented in imperial units.

3.4.1 Cohesive Soils

With these soils it was assumed as in Lewis (1959) that when the soil is compacted to refusal, the shear strength equals the shear stresses induced by the roller in the layer of soil being compacted. As the shear stress decreases quite rapidly with depth under a narrow strip loading (Figure 1) the 152mm (6 inch) thick compacted layer being considered was divided into a number of sub- layers, the dry densities in each of which were calculated using the shear strength/moisture content/dry density relations given in Figures 2 and 3 together with the maximum shear stress factors given in Table 2 which are for a uniformly applied load at the surface. As the soil approached the saturated condition it was again as- sumed that a small quantity of air remained entrapped and, thereafter, at progressively higher moisture contents it was taken that the compaction curve follows a constant air voids line of 2 per cent. Some sensible rounding off below the intersection of the rising leg of the compaction curve and the falling leg paralleling the zero air voids line completes the calculated dry density/moisture content relation.

4

E z

v

==

250

200

150

100

50

40

36

32

28

I 110 Ib/cu. ft. (1.76 Mg/m 3)

20

16

12

0 I 16 18

%

t 105 (1.68)

95 (1.52) % % >. ."

Heavy clay

100 (1.60)

I I I I I I I 20 22 24 26 28 30 ;.

Moisture content (per cent)

Fig.2 R e l a t i o n between shear strength of heavy clay and m o i s t u r e c o n t e n t o b t a i n e d f o r various dry densities (Lewis, 1959)

Consideration of. the load per unit width of roll and the value of (W/R) °-s led to the rear rolls of both smooth- wheeled rollers being used in calculating the dry densi- ties. Typical calculations for the vibrating rollers with the vibrating mechanism inoperative are shown in Table 3. The average maximum shear stress values shown have been calculated using the shear stress factors in Table 2 and are the values at the mid-depth of each of the sub- layers concerned. The average dry density over the 0- 152mm depth of layer is the weighted average of the values given for the four sub-layers, the upper two of which are 25.4mm thick and the lower pair are each 50.8 mm deep.

The calculated dry density/moisture content relations for towed vibrating rollers with the vibrating mechanism inoperative given in Table 3 are plotted in Fig 6 and 7 since the tests on these pieces of compaction plant were carried out on the same soils from which the strength data in Figs 2 and 3 were obtained. Dry of optimum moisture content the relations have a range of values depending on the contact width assumed; above and wetter than optimum the curves coalesce into a single line paralleling the zero air voids line.

3.4.2 Granu la r Soi ls "

With these soils which require.two parameters to define their strength properties and where the shearing resis- tance of the soil is a function of the normal stresses on shear planes, it was assumed as in Lewis (1959) that at compaction to refusal the ultimate bearing capacity of the soil was equal to the contact pressure beneath the steel- tyred roll. The ultimate bearing capacity'of a loaded strip resting on the soil surface for local shear failure is given by Terzaghi and Peck (1948) as:-

q = 0 . 6 7 c N c +0.5 3' BN'3 '

where: q = ultimate bearing capacity

(5)

c = apparent cohesion of the soil

B -~ width of the loaded area

N' c and N' are bearing capacity factors for local shear

and 3' = the bulk density of soil.

5

E z v

. E

250 --

200 --

150 m

100

50

0

40

36

32

28

24

20

16

12

8

4

Sandy clay

\ ~ 120 Ib/cu. ft. (1.92 Mg/m 3)

15 (1.84)

~ . ~ 1 1 0 (1.761

~ ' ~ . . 105 (1.68) 100 (1.60) ~ ~'%%

90 '~*

I I t I , 10 12 14 16 18 20 22 24

Moisture content (per cent)

Fig.3 Relat ion between shear strength of sandy clay and moisture content obtained for various dry densities (Lewis, 1959)

In the case of smooth-wheeled rollers the value of B is even smaller than for the pneumatic-tyred rollers so that the second term of the expression with a maximum value of about 30kN/m can be neglected. The expression for the bearing capacity for a strip then reduces to:-

q = 0.67 c N' c (6)

Using the relations between the apparent cohesion, angle of internal friction, dry density and moisture content for the well-graded sand and the gravel-sand-clay in Figures 4 and 5, the curves shown in Figures 8 and 9 were drawn relating the bearing capacity of a strip footing with moisture content and dry density. Values of N' c are only given for ~) values up to 40 ° in Terzaghi and Peck (1948) so N' c values for higher ~) values were derived from the values of N c given by Smith (1990) for angles whose tangent was 2/3 tan ~. From the data in Figures 4 and 5 and the derived values of N c the.dry densities cor- responding to various combinations of moisture content and bearing pressure were calculated. As with the cohesive soils the relation between dry density and moisture content was completed on the assumption that the compaction curve followed a constant air void line: a value of 2 percent air voids was chosen to accord

with practical experience on these granular soils (Wil- liams and Maclean 1950).

The calculations for the 8-ton and 23,~-ton smooth-wheeled rollers compacting the well-graded-sand and the gravel- sand-clay soils are shown in Table 4 for contact widths of 25.4, 38.1 and 50.8mm. The calculated dry density/ moisture content relations for the two rollers are shown in Figures 10 and 11. Again, dry of optimum moisture content there are a number of compaction curves depending on the contact width assumed but these coalesce at higher moisture contents into a single line which descends parallel to the zero air voids line.

3.5 ASSESSMENT OF THEORETICAL CALCULATIONS

With the exception of the three trials on the vibrating rollers (Figs 6 & 7) the full-scale trials of the smooth- wheeled rollers were all carried out on the five soils used in the initial compaction trials at TRRL (Williams and Maclean 1950) and there is no strength data available for them. In these circumstances comparison between calculated and measured values is most appropriately made in terms of relative compaction and the moisture

6

16

Z

f~

, j

L

8. 0 - ,<

100 --

75

50

25

0

~d 14

n 3 l

1 2 - -

1 0 ~

. i 5- 8 ~

2s

6 ~

4 ~

2 ~

o I I I I I I 4 5 6 7 8 9 10

50

125 12.001 =~ 40

~ 35

< 3 0

/ 2s ~ I I I I 7" I

5 6 7 8 9 10 Moisture content (per cent)

F ig .4 R e l a t i o n b e t w e e n c o h e s i o n and ang le o f shear ing resistance o f we l l - g raded sand and m o i s t u r e c o n t e n t o b t a i n e d f o r va r i ous d r y dens i t i es (Lewis , 1959)

30

1 O0 -- ~ ~ Gravel-sand-clay

75 20

. .

g 15

g so

115 11.84) ~ ~ . ~

o - I I I [ I I 3 4 5 6 7 8 9 10

45

40

== - o v

3s

30

~5

< 25

20

130 Ib/cu.ft. (2.08 Mg/m 3)

125 (2.00)

120 (1.92)

115 (1.84)

I I I I I 3 4 5 6 7 8 9 10

Moisture content (per cent)

Fig.5 Relation between cohesion and angle of shearing resistance of gravel-sand-clay and moisture content obtained for various dry densities (Lewis, 1959)

T A B L E 2

Shear stress factors for various depths and contact widths for uniform loading

Contact width w = 2b mm

Depth below surface

m m

in terms

b

Maximum shear stress

factor

Average maximum

shear stress factor

50.8

38.1

25.4

0 12.7 25.4 38.1 50.8 76.2 101.6 127.0 152.4 228.6 304.8

0 12.7 25.4 38.1 50.8 76.2 101.6 127.0 152.4 228.6 304.8

0 12.7 25.4 38.1 50.8 76.2 101.6 127.0 152.4 228.6 304.8

0 0.5b

b 1.5b 2b 3b 4b 5b 6b 9b 12b

0 0.67b 1.33b

2b 2.57b

4b 5.33b 6.67b

8b 12b 16b

0 b

2b 3b 4b 6b 8b 10b 12b 18b 24b

0.318 ) 0.318 ) 0.318 ) 0.294 O.255 ) 0.204 ) 0.150 ) 0.123 0.103 0.070 0.053

0.318 0.318 0.296 0.255 0.210 0.150 0.115 0.093 0.078 0.053 0.040

0.318 0.318 0.255 0.189 0.150 0.104 O.O78 0.063 0.053 0.035 0.027

0.318

0.290

0.203

0.125

0.313

0.254

0.156

0.095

0.302 ) ) 0.196, )

0.109

) 0.065

content relative to the optimum moisture content (Road Research Laboratory 1952); the BS Compaction Test 2.5kg rammer method has been taken as the appropriate reference point (British Standards Institution 1990). Separate assessments are made for the cohesive and granular soil groupings.

3.5.1 Cohesive Soils

The maximum relative compaction and relative optimum moisture contents obtained on the heavy clay and sandy clay soils by measurement and calculation are shown in Table 5. Overall the calculated relative compaction values were 1.1 per cent higher than the measured

values with the results being very close on the heavy clay. The average difference in relative optimum moisture content was only 0.1 per cent but this results from an over-estimate of the measured optimum moisture content by an average of 2.7 per cent on the heavy clay and a countervailing under-estimate by 2.1 per cent on the sandy clay soil. Indeed the outcome on the heavy clay is probably somewhat better than the numbers indicate as the dry legs of the measured compaction curves for the two smooth-wheeled rollers had 'anomalous' reverse curvature as discussed by O'Reilly (1974) and probably due to difficulties of mixing in water during the trials.

9

0

.0

0 c-

Q~

o

J~

I-

-0

"6

0

c~

0

10

l

0

E

o)

n~

o

Q) 0

O_

~0 OJ

r- Q) 0

O_

0 0

OJ

Q~

0

O_

0

t- O 0

O_

CO

0 O_

I',- D--

~ ~ 0

~ ~ 0

~ ~ 0

~ 0 ~

~ 0 ~

~ 0 ~

0 ~

~ .

¢.0 O0

~ 0

~ 0

~ 0

, ~06~

0 0 tO

O0

(33 D--

__ 03 OD

~ ~ 0

~ ~ 0

~0 O0 ~r-

U') O0

CO O0

~ 0

~ 0 0

~ . ~ . ~ ~.

<

C~ LO

"T 0 o

¢.0 cO

c- O

"0 t- O o

0

c-

E

-0 Q) t- o

0o

tO

+ x m

1.65

Heavy clay

1.60

1.55

1.50

1.45

1.40 14

? U "\

a

Rol ler

3¾-ton

Compact ion curve

Calculated Measured

A-- ~1, t.. -~

I I I I I I 16 18 20 22 24 26

Moisture con ten t (per cent)

Fig.6 Calculated and measured compaction curves for the 3¾-ton vibrating roller without vibration on heavy clay soil

28

The iterative rhythm of the calculations in Table 3 gives valuable insights into the idealised concept of the com- paction process. At low moisture contents there is a considerable difference with depth in the calculated densities and in the topmost layer the narrower the contact width the higher the density. Measurements of density variation with depth has shown differences of as much as 0.32 to 0.48 Mg/m 3 over a 152 mm layer (Lewis 1954): in the calculations shown in Table 3 there are differences of up to 0.34 Mg/m 3 and up to 0.38 Mg/m 3 in the complete calculations (O'Reilly 1985).

With the calculated values, as optimum moisture content is approached, the upper layers are beginning to reach the limiting 2 per cent air voids condition - they are for practical purposes saturated and pore pressures can develop rapidly under stress. With further increases in moisture content the full-depth of the layer being com- pacted reaches the limiting air void condition.

Once this stage is reached the roller/soil combination no longer behaves elastically and the contact width under the roll will increase until it is in equilibrium with the bearing capacity of the now plastic soil. For example on "the heavy clay soil at a moisture content of 26 per cent when the maximum shear strength is of the order of 69kN/m 2 the bearing capacity for general and local shear failure are respectively 393 and 262kN/m 2 giving corre- sponding contact widths for the 8-ton roller of 14 and 21cm. Contact widths up to about 22 cm have been found under a steel tyre roll by Farzaneh (1983) on a silt soil at a moisture content 2 per cent above the optimum moisture content in the BS Compaction Test 2.5kg rammer method.

Measured and calculated compaction curves for the vibrating rollers with the vibrating mechanism inoperative are shown in Figures 6 and 7 since shear strength/ moisture content/dry density data (Figures 2 and 3) are available for soils on which these items of compaction

11

1.88

E

-8 => a

1.83

1.78

1 . 7 3 - -

1 . 6 8 - -

1.63 - -

1.58 10

Sand clay

4" \,,

/

Compaction curve

/ Roller Calculated_ ?easured

F i g . 7

I I l I I I 12 14 16 18 20 22

Moisture content (per cent)

Calculated and measured compaction curves for two vibrating rollers without vibration on sandy clay soil

24

12

2400 - 350

z

O

t n

2000

1600

1200

800

400

Fig.8

300

250

200

150

100

5O 3 4 5 6 7 8

Moisture content (per cent)

Relat ions between bearing capac i ty o f the wel l -graded sand and mois ture con ten t f o r various dry densities for a strip footing

10

-z.

O v

• ~ E

r n

2400

2000

1600

1200

800

400

Fig.9

36o

I / / o,

I (1'~92,\ \ Dry density Ib/ft. 3 (Mg/m 3)

3 4 5 6 7 8

Moisture content (per cent)

Relat ions between bearing capac i ty of the gravel-sand-clay and mois ture con ten t f o r various dry densities for a strip footing

9 10

13

TABLE 4

Calculations of dry densities achieved by smooth-wheeled rollers on well-graded sand and gravel-sand-clay soils.

Details of Rollers Load per

metre Soil Type Roller width Contact Bearing

on rear width pressure rolls kg mm kN/m 2

Calculated dry density at a moisture content of:-

4 5 6 7 8 9 10 11

Well-graded 8-ton 5551 25.4 2144 sand 38.1 1429

50.8 1072

~A-ton 2533 25.4 979 38.1 653 50.8 490

Gravel-sand 8-ton 5551 25.4 2144 clay 38.1 1429

50.8 1072

~A-~n 2533 25.4 979 38.1 653 50.8 490

1.84 1.94 2.02 2.10" 2.16 2.13 2.08 1.78 1.86 1.96 2.05 2.15 2.13 2.08

1.81 1.91 1.99 2.07 2.12 2.08

1.79 1.89 1.97 2.04 2.08 2.08 1.81 1.89 1.97 2.04 2.07 2.05 1.76 1.84 1.92 1.99 2.05 2.05

1.97 2.05 2.15" 2.20* 2.16 2.12 1.91 1.99 2.07 2.16" 2.16 2.12 1.86 1.94 2.02 2.08 2.15 2.12

1.92 2.00 2.07 2.13 2.12 1.86 1.92 1.99 2.04 2.10 2.07 1.81 1.89 1.96 2.02 2.07 2.07

1.84

Bold Type - indicates the soil has reached limiting air voids. Asterisk - indicates quesstimated value.

plant were tested. Agreement on the heavy clay soil is very good but less good, although still reasonable, on the sandy clay soil.

3.5.2 Granular Soils

The maximum relative compaction and relative optimum moisture contents obtained on the well-graded sand and the gravel-sand-clay are shown in Table 6. The highest relative compaction values in the Table correspond to a 25.4 mm contact width and have been used throughout for the calculated values. On this basis agreement on both soils is extremely good with calculated densities on average just one half a per cent lower than measured values and optimum moisture content values differing on average by 1/4 per cent. Had the lower dry density values associated with wider contact widths been used from Table 4 the agreement would, of course, have been poorer.

It is not altogether unexpected that the bearing capacity approach has proved better in this instance than in the case of the pneumatic-tyred rollers. Given the narrower contact areas of the rolls, the depth of soil involved in a bearing capacity failure would be more comparable with the depth of layer being considered in the field measure- ments. However, very little 'feel' for the compaction process emerges and unlike the maximum shear stress method in Table 3, few insights are obtained.

The measured dry density/moisture content relations obtained in the full-scale trials have been superposed on the calculated values in Figs 10 and 11. While no adjust- ment was necessary for the gravel-sand-clay soil, the curve for the well-graded sand was adjusted to allow for the differences in maximum dry density in the BS Com- paction Test 2.5kg rammer method between the soil used in the trials and that for which shear strength data was available. As well as the good agreement between maximum measured and calculated values, the rising legs of the compaction curves are remarkably similar on both soils.

It is to some extent surprising that the values predicted by the bearing capacity method using the local shear failure approach have correlated so well with measured dry densities. However, it must be remembered that the use of contact widths of 25.4, 38.1 and 50.8 mm is to a considerable extent arbitrary and very similar results would have been obtained using a general shear failure approach with contact widths of half the above values. The argument for keeping the local shear failure ap- proach is that although agreement between measured and calculated values was not good for the pneumatic- tyred rollers (Lewis 1959) it would have been considera- bly poorer had the general shear failure formula for bearing capacity been used.

14

2.18

E

¢

E3

2.14

2.10

2.06

2.02

1.98

1.94

1.90

1.86

0

i'i / f /

II // 4

- /

I/ / II /

II, I I 4 6

t /

/ /

/ Roller

Well-graded sand

Compaction curve

Calculated Measured and adjusted "~

8-ton 0 " '~= " 0 O 0

2¾-ton Ak~ ~== ~ z ~ 1

9(" See Section 3.5.2

I I I 8 10 12 14

Moisture content (per cent)

F ig. lO Ca lcu la ted and 'measured" c o m p a c t i o n curves f o r s m o o t h - w h e e l e d rol lers on we l l -g raded sand soi l

16

1 5

2.24

2.20

2.16

2.12

2.08 --

" o

=> D 2.04

2.00 m

1 . 9 6 - -

1 . 9 2

1.88

2

G ravel-sand-clay

t 1

/ ,//

4

H / / / /

/ / / / / /

1 f/ / / /

/ /

1 , , I I I 6 8 10 12

Moisture content (per cent)

Compaction curve Roller

Calculated Measured

8 - t o n 0 " ~ " 0 0 0

2¾-ton Ak= ~ =dk ~. -~

14

Fig. 11 C a l c u l a t e d a n d m e a s u r e d c o m p a c t i o n curves f o r s m o o t h - w h e e l e d

ro l l e r s o n g rave l - sand -c lay so i l

16

16

TABLE 5

Comparison of calculated and measured compaction on cohesive soils for smooth-wheeled rollers

Soil type

Details of rollers

Load per Weight unit width Tons of rear

roll kg/m

BS Optimum - roller optimum per cent

Maximum relative compaction moisture content per cent

Measured Calculated Difference Measured Calculated Difference

Heavy clay 8 5551 23A 2533

3 ~ # 2786

107 106 1 6 3 3 98 99 -1 5 -1 6 99 100 -1 -2 -1 -1

Average difference -0.33 Average difference 2.67

Sandy clay 8 5551

2 ~ 2533

8V~ 4500 33/~ 2786

107" 5* 101+ 0+

Avg 104 107 -3 Avg 2.5 4 -1.5

106* 4* 99+ -2 ÷

Avg 102.5 102 0.5

105 106 -1 101 104 -3

Average difference -1.63

Avg 1 2 -1

0 3 -3 -2 1 -3

Average difference -2.13

Key: # = Vibrating roller without vibration * = Silty clay + = Sand clay

TABLE 6

Comparison of calculated and measured compaction on granular soils for smooth-wheeled rollers

SoilType

Well- graded sand

Gravel- sand- clay

Details of Rollers

Load per unit

Weight width of tons rear roll

kg/m 3

8 5551

2¾ 2533

8 5551

23A 2533

Maximum relative compaction per cent

Measured

BS Optimum - roller optimum moisture content - per cent

Calculated Difference Measured Calculated Difference

-3 -2 1

-1 -1 0

Average difference 0.5

109 109 0

105 105 0

Average difference 0

107 106 1

104 103 1

Average difference 1

-2 -2 0

-1 -1 0

Average difference 0

17

4. S H E E P S F O O T AND GRID R O L L E R S

Sheepsfoot rollers consist of a cylindrical steel drum which can be ballasted with water or sand, and on which projecting feet are mounted.

They are very popular in the drier regions of the USA and large self-propelled multi-drum versions have been developed: for example, Johnson and Sallberg (1960) show a machine weighing 41.1 Mg and another with foot pressures of 5902kN/m 2. Towed vibratory sheepsfoot rollers were introduced around 1960 (Forssblad 1981).

The towed grid roller came into use extensively in the USA and other parts of the world in the late 1950s both for the compaction of soils and for the crushing and compaction of soft rocks in situ for road bases (Parsons 1959). It consists of two grid rolls composed of a heavy steel mesh of square pattern mounted on a box beam framework.

4.1 IDEALISATION OF COMPACTION WITH SHEEPSFOOT ROLLERS

Two types of sheepsfoot roller were tested during the initial compaction plant trials at TRRL, a club-foot and a

taper-foot roller (Williams and Maclean 1950). Subse- quently the performance of two vibrating sheepsfoot rollers was studied both with and without vibration (Cross 1962; Parsons 1962). Details of these four sheepsfoot rollers are given in Table 7.

Sheepsfoot rollers apply pressure to the soil being compacted through feet which are either square (or nearly square) or circular on plan. Given the similarities between the compaction processes, the writer applied the methods put forward for pneumatic-tyred rollers by Lewis (1959) to compaction using sheepsfoot rollers. Again a maximum shear stress gradient with depth approach is used to calculate densities in the cohesive soils while a bearing capacity method is applied on the gravel-sand- clay soil. Sand soils were not considered since sheepsfoot rollers are ineffective on this type of soil and there is little measured data with which to make compari- sons.

4.2 CALCULATION OF COMPACTION ACHIEVED BY SHEEPSFOOT ROLLERS

The method of calculation developed by Lewis (1959) for pneumatic-tyred rollers can be applied unaltered to estimate the states of compaction produced by dead-

TABLE 7

Details of sheepsfoot rollers studied at TRRL

Dead-weight

Type of Sheepsfoot Roller

Weight (empty) kg Total weight on roll kg Number of feet Size of feet mm Area of foot mm 2 Equivalent radius mm Foot-pressure kN/m 2 Minimum number of passes to give complete coverage Maximum shear stresses:-

Club-foot

3214 4994+

128 101.6 x 76.2mm

7742 49.5 793 11

Taper-foot*

2774 4572+

176 57.15 x 57.15 mm

3266 32.3 1717

20

5-ton**

5080

101.6mm diam 8107 50.8

1365 (static)

Depth mm

0-25.4 25.4-50.8 50.8-101.6 101.6-152.4

Factor Shear Stress kN/m 2

0.295 234 0.218 172 0.122 97

Factor Shear Stress kN/m 2

0.275 469 0.161 276 0.063 110

Factor

Vibrating

Shear Stress kN/m 2

0.296 407 0.221 303 0.124 172 0.054 76

41/2_ton ***

4267 98

79.38mm diam 4949 39.7

2413(static) 15

Factor Shear Stress kN/m 2

0.287 690 0.193 469 0.092 221 0.034 83

* See Williams and Maclean (1950), Lewis (1954) ** See Cross (1962) *** See Parsons (1962)

+ Water-ballasted

1 8

weight sheepsfoot rollers with different approaches being required for the two cohesive soils and the gravel-sand- clay soil.

4.2.1 Cohesive soils

On these soils, circles of equal area were substituted for the rectangular and square feet of the club-foot and taper-foot sheepsfoot rollers respectively, to calculate the maximum shear stress gradient with depth (Poulos and Davis 1974). As in the case of the smooth-wheeled rollers, the reduction in shear stress with depth was quite rapid and the layer was again divided into a number of sub-layers and a weighted average dry density obtained. In the trials of the club-and taper-foot rollers, 102mm (4

inch) deep density holes were used (rather than the 152mm deep holes used with the other items of compac- tion plant), because of the loose tilth of soil remaining after compaction with these rollers and which had to be removed before density determinations were made (Williams and Maclean 1950): for these two rollers, therefore, calculations were carried out for a 102mm thick layer. On the other hand, with the vibrating sheepsfoot rollers tested in the non-vibrating mode, the normal 152 mm deep density holes were used and so densities have been calculated over this depth of layer.

The calculations shown in Table 8 for the four rollers on the heavy clay soil were made by equating the maximum

TABLE 8

Calculations of dry densities achieved by sheepsfoot rollers on heavy clay soil

Average Depth of maximum

Sheepsfoot Layer shear Roller stress

mm kN/m 2

Calculated maximum dry density (Mg/m 3) at a moisture content of:-

Club-foot

Taper-foot

0-25.4 234 25.4-50.8 172

50.8-101.6 97

0-101.6 Average dry

density

0-25.4 469 25.4-50.8 276

50.8-101.6 110

0-101.6

5-ton 0-25.4 Vibrating 25.4-50.8 without 50.8-101.6 vibration 101.6-152.4

0-152.4

41/2-ton 0-25.4 Vibrating 25.4-50.8 without 50.8-101.6 vibrations 101.6-152.4

0-152.4

Average dry

density

18 per 20 per 22 per 24 per 26per cent cent cent cent cent

1.70 1.75 1.68 1.63 1.57 1.62 1.67 1.68 1.63 1.57 1.44 1.51 1.55 1.62 1.57

1.55 1.61 1.62 1.63 1.57

1.81 1.75 1.68 1.63 1.75 1.75 1.68 1.63 1.49 1.54 1.60 1.63

1.63 1.64 1.64 1.63

407 1.81 1.75 1.68 1.63 303 1.76 1.75 1.68 1.63 172 1.62 1.67 1.68 1.63 76 1.39 1.44 1.52 1.55

Average dry

density 1.60 1.62 1.63 1.60

690 1.81 1.75 1.68 1.63 469 1.81 1.75 1.68 1.63 221 1.68 1.75 1.68 1.63 83 1.41 1.46 1.52 1.57

Average dry

density 1.63 1.65 1.63 1.61

Bold type indicates the soil has reached limiting air voids

19

average shear stress in any sub-layer to the shear strength, density and moisture content of the soil using the relations given in Figure 2; calculations were also made for the club- and taper-foot rollers for the sandy clay soil.

As saturation was approached, the same assumption of a limiting condition of 2 per cent air voids as has been made previously, was again adopted although the indications from the full-scale trials were that a limiting value of 5 per cent might have been more appropriate for the club-and taper-foot rollers.

4.2.2 Gravel-Sand-Clay Soil

On the gravel-sand-clay soil the foot pressures given in Table 7 for the club-and taper-foot rollers were equated with the ultimate bearing capacity in local shear failure using the relations given for circular contact areas by Lewis (1959), i.e. the bearing capacity in local shear was taken as 0.87 c N' c. In making the calculations (O'Reilly 1985) the assumption is made based on experience that as saturation is approached a minimum air voids content of 4 per cent is reached (Williams and Maclean 1950).

4.3 ASSESSMENT OF THEORETICAL CALCULATIONS FOR THE SHEEPSFOOT ROLLERS

In comparing the measured and predicted states of compaction achieved by sheepsfoot rollers in Table 9, the relative compaction method has again been used because the compaction trials of the club- and taper-foot rollers were undertaken on soils for which shear strength/

dry density/moisture content relations were not available. On the other hand, the trials without vibration of the two vibrating sheepsfoot rollers were made on soils for which such data are available.

The striking disparity between the two sets of results on the heavy clay soil is immediately apparent. For the club- and taper-foot rollers tested in the initial trials, the calculations under-estimate the relative compaction achieved by 8 per cent, while the calculated optimum moisture contents are some 10 per cent wetter: there is very poor agreement between the measured and pre- dicted values (see Table 9). By contrast, in the later series of compaction plant trials, the agreement between measured and calculated values was much better although still not as good as for the pneumatic-tyred rollers.

The anomalous behaviour of the sheepsfoot rollers on the heavy clay soil in the initial series of compaction plant trials carried out on the covered circular track at TRRL does raise questions as to the quality of these trials and to the use of relative compaction as a method of normal- ising results. It also means that much greater confidence can be placed in the results of the later TRRL compaction trials carried out on the same soils for which shear strength/dry density/moisture content relations are available.

Despite the above comments on the poor agreement between measured and calculated values for the club- and taper-foot rollers on the heavy clay, the agreement between predicted and measured values was reasonable on the sandy clay~and gravel-sand-clay soils. On the sandy clay soils the calculations (O'Reilly 1985) indicated

TABLE 9.

Comparison of calculated and measured compaction for.sheepsfoot rollers . L

Detai ls o f Soil Type Sheepsfo_ot rol lers .

M a x i m u m relative compact ion - pe r cent

BS Optimum-rol ler opt imum moisture content - pe r cent

Heavy clay

Measured Calculated Difference _Measured Calculated Difference

Club-foot 110 102 8 10 -1 11 Taper-foot 11.0 102 8 11 1 10 5-ton Vibrating 100 102 -2 6 1 5 without vibration 41/2-ton Vibrating 100 103 -3 7 3 4 without vibration

Sandy clay Club-foot Taper-foot

Gravel-sand- Club-foot clay

Taper-foot

107" 105 2 4* 2 2 107" 106 1 4* 3 1

100 101 -1 3 0 3

99 103 -4 4 1 3

*Average for silty and sandy clay soils in initial compaction plant trials (Williams and Maclean 1950)

20

relatively flat compaction curves while the measured curves shown by Williams and Maclean (1950) on the analogous silty and sandy clay soils are distinctly peaked; agreement is therefore not quite as good as would be inferred from the comparison in Table 9. On the other hand, the slope of the measured and calculated compac- tion curves dry of optimum on the gravel-sand-clay soil are very similar.

4.4 CALCULATED COMPACTION ACHIEVED BY A GRID ROLLER

The grid roller studied in the compaction plant trials at TRRL weighed nearly 13.7 Mg when fully ballasted: the grid was formed from 41 mm bars with 86 x 86 mm clear openings and the load per metre width of roll was 8429 kg/m (Parsons 1959). By analogy with the smooth- wheeled rollers in Section 3, this roller could be idealised as a strip loading 41 mm wide.

Calculations have been made on this basis (O'Reilly 1985) for the grid roller using the maximum shear stress with depth method for the two cohesive soils and the bearing capacity approach for the two granular soils using the data given in Figures 2, 3, 8 and 9. The maximum shear stress gradient beneath the 41 mm strip was interpolated from the stress factors given in Table 2.

The measured and predicted maximum dry densities and optimum moisture contents are compared in Table 10. On the two cohesive soils the calculated maximum dry densities are both some 0.06 Mg/m 3 higher and the optimum moisture content some 3-4 per cent drier than the measured values. This indicates that the shear stresses induced are less than those generated by a 41 mm strip load: possible explanations are that the node points of the mesh might act as Iocalised footings like the feet of a sheepsfoot roller, or that some of the load on the roll is transferred to the ground by the circumferential bars of the mesh as well as the transverse bars, or that some clogging of the mesh with soil occurs during the compaction process.

On the other hand, agreement between measured and calculated values on the granular soils could not have been better with the maximum dry densities and optimum moisture contents being equal in both cases. As the bearing capacity approach was used, this can only mean that the depth of soil involved in a bearing capacity failure was very similar to the 152 mm layer of soil over which the densities were determined.

The measured and calculated dry density/moisture content relations for the cohesive and granular soils are shown in Figures 12 and 13 respectively. As indicated above, agreement on the cohesive soils is poor and the rising portions of the calculated compaction curves were not defined. On the other hand, on the granular soils the slopes of the measured and predicted compaction curves were virtually identical.

5. A P P L I C A T I O N OF T H E A N A L Y S E S

Compaction of soil is a relatively simple and easily understood process amenable to the experimental approach and engineers can happily interpolate within their data framework in the knowledge that the errors are unlikely to be large. However, when extrapolating outside this framework, as in the development of new methods or equipment, theoretical analyses which provide an insight into the underlying behaviour and processes can be very useful. As a first practical example the analyses devel- oped by Lewis (1959) for pneumatic-tyred rollers are considered before applying the analyses set-out in this report to other dead-weight compaction plant.

5.1 PNEUMATIC-TYRED ROLLERS

In the studies of the states of compaction achieved by pneumatic-tyred rollers, Lewis (1959) concluded that it was possible to make a reasonable estimate of the likely

TABLE 10.

Comparison of calculated and measured compaction for grid roller

Soil type Maximum dry density - Mg/n~

Measured Calculated Difference

Optimum moisture content - per cent

Measured Calculated Difference

Heavy clay 1.70

Sandy clay 1.86

Well-graded sand 2.13

Gravel-sand-clay 2.16

1.76 -0.06 21 18 3

1.92 -0.06 16 12 4

2.13 0 8 8 0

2.16 0 7 7 0

21

1.94

- o

(3

1.90

1.86

1.82

1.78

1.74

1.70

1.66 B

1.62

10

&.,,.

\ \

\

Z

Grid roller

Soil type

Heavy clay

Sandy clay

Compaction curve

Calculated Measured

O m ~ O O

I I 12 14

%0 \

\ \

o \

! I I I 16 18 20 22

Moisture content (per cent)

Fig.12 Calculated and measured compaction curves for grid roller on the cohesive soils

22

2.18

E

=> E3

2.14

2.10

2.06

2.02

1.98

1.94

1.90

1.86

I I

I I

I I

I I !

I

/ I

I I

I ?

I I

I I

I

I I

I I

I

Grid roller

Compaction curve

Soil type Calculated Measured

Well-graded sand • u ~ • 0 0

Gravel-sand-clay A u ~ • z& z.~

I I ! I

Fig.13

6 8 10

Moisture content (per cent)

12

Calcu la ted and measured c o m p a c t i o n curves f o r gr id ro l le r on granu lar soi ls

14

2 3

performance of such a roller from a knowledge of the contact areas and pressures of the tyres and the relations between either shear strength or bearing capacity, dry density and moisture content of the soil. He showed that the shear stress depth relation for a 14.7 Mg wheel load with a tyre-inflation pressure of 6.2 bar as used on the heaviest pneumatic-tyred roller then manufactured on any significant scale in the UK, was very similar to that of the 10.2 Mg wheel load with a tyre-inflation pressure of 9.7 bar tested at TRRL. On this basis he suggested that the compaction results obtained with the latter roller could also be applied with reasonable confidence to the roller with the 14.7 Mg wheel load and 6.2 bar tyre-inflation pressure.

Although not done by Lewis, it is of interest to use the results of his theoretical calculations to predict the maximum dry densities achieved by the 10.2 Mg wheel load with a tyre-inflation pressure of 9.7 bar from the actual results on the lightest roller with a wheel load of 1.35 Mg and a tyre-inflation pressure of 2.5 bar. When the difference in calculated values of maximum dry density are added to the actual maximum dry density achieved with the lightest roller to give a prediction for the heaviest roller, the predicted values are all within + 0.016 Mg/m 3 of the true value. This is a surprisingly good outcome which demonstrates the value of the analytical method when extrapolating from experimental results.

5.2 SMOOTH-WHEELED ROLLERS

Following from the above it is perhaps easiest to consider how well the actual results obtained on the 8-ton smooth- wheeled roller could have been predicted from the full- scale trial results on the 23A-ton roller and the calculated compaction curves; in this instance it must be remem- bered that because of a lack of strength/dry density/ moisture content data for the soils used in the plant trials, a relative compaction approach has to be adopted and that this may introduce some added uncertainty into the prediction process. Using the calculated data in Table 5 and 6, the performance of the heavier roller is predicted with + 2 per cent relative compaction on the two cohesive soils while both predicted and measured values were identical on the two granular soils.

The 81/2-ton and 33/~-ton smooth-wheeled vibrating rollers were tested on the sandy clay soil without vibration and thus behaved as simple dead-weight smooth-wheeled rollers. The data for these tests are given in Table 5 and since the measured and calculated results are for the same soil there is no need to resort to the use of the relative compaction approach. In these instances, when the maximum dry density achievable by the heavier roller is predicted as outlined above, the predicted value underestimates the measured value by just 0.016 Mg/m 3.

In Table 11 a comparison is made of the states of compaction produced in the USA (Aaron et a11944), India (Central Road Research Institute 1953; Gokhale and Rao (1957) and East Africa (O'Reilly 1974). In the trials carried out in the USA the states of compaction achieved equalled those found at Scheme No. 4 in East

Africa and also in the full-scale compaction plant trials at TRRL. In India, however, the states of compaction achieved were some 8 per cent relative compaction lower and were similar to the results obtained on Schemes Nos. 7 and 9 in East Africa. These differences are most easily accounted for in terms of differing Esoit values of the supporting layer which, if the soil is considered to behave elastically as assumed by the writer in the derivation of equation 3, would alter the contact width under the rolls and hence the distribution of maximum shear stress with depth. Rather similar results were obtained in the full- scale compaction plant trials at TRRL where an 8-ton smooth-wheeled roller compacting 609.6 mm (24 inch) thick loose layers of a gravel-sand-clay (Lewis 1954) produced maximum relative compactions of 101 and 88 per cent in the 0 - 152.4 mm and 152.4 - 304.8 mm layers respectively, compared with 106 per cent in the top 152.4 mm when 228.6 mm (9 inch) loose layers, resting on previously compacted layers, were being compacted.

This influence of supporting soil Eso~ value would apply to all rollers with steel rolls, vibrating as well as dead- weight. On the other hand, with pneumatic-tyred rollers, apart from tyre-wall stiffness effects which would not be expected to be large at the manufacturer's recommended tyre pressure, contact areas are constant and thus contact pressures should be independent of soil modulus. This is confirmed by Lewis (1959) who shows that the density achieved in the top 152.4 mm of soil by pneu- matic-tyred rollers is unaffected by the depth of the layer being compacted. If site trials are to be used to validate the performance of new types of compaction plant, then it would seem appropriate to specify pneumatic-tyred plant as the reference compactor, since this would ensure that the correct state of compaction was achieved in the reference section irrespective of the standard of compac- tion of the supporting layers. It would suggest too, that it is unwise to carry out compaction trials in bays with concrete floors, as happened in the initial studies at TRRL.

5.3 SHEEPSFOOT ROLLERS

The analyses present in this Report can contribute much to explaining the results of the two major full-scale studies of these rollers at TRRL (Williams and Maclean 1950) and by the U.S. Corps of Engineers summarised by Johnson and Sallberg (1960). For the former the calculated shear stresses under the feet of the four sheepsfoot rollers particularly approaching the bottom of the compacted layer being considered (see Table 7) were of similar magnitude so that maximum dry densities were also similar.

In the case of the U.S. tests, the premise that the level of compaction achieved depends on the shear stresses developed under the feet of the rollers provides a unifying concept considering the factors involved. Thus, the area and pressure exerted by the foot interact so that the increasing shear stresses with depth due to increased area of contact can explain the increasing maximum densities in Figure 14, although the contact pressure of 1724 kN/m 2 was constant for the three tests.

24

, ,J E l

I--

E r r

I'-.. o b

_>,

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O m . E

<

c E ~ O

(I) ,'~ • .~-

o ~ o c"

-o ~ -, g ~ .

r - < . ~ ._o E

E O O

o E

¢ mg

c E O O m O

E O

O

c- O

O O

- J

._ ,~ " 6 ~ - ~ 6 ~ ~ -o

~ o "~ ~ ~ _o -~ ~ o C --- ~ CL~ -- O (D

:S~o~ ~ ~ o ~ ~o_~° =~,~° ~

o~ ~. o o E~ E E 8 o° = = ~ E o 7 o o

O O u ' ) ~ ( . O C O t -

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aid

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(D . _

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7".

2

2 5

E

E3

E3

E

E3

1.80

1.70 --

1.60 10

1.80

1.70

1.60 10

1.70 --

1.60 10

Fig.14

~ 13548 mm 2 foot area / ~ ~ ~ . . . . 6 passes

/ ~ ~ ~ - - - - - 12 passes

I I ' k I "~ 15 20 25 30

~ 9032 mm 2 foot area / ~ ~ . . . . 6 passes / ~ ~----- 12passes

/ ~X~.~ ~ - - - - 24 passes / / ~ ~ Zero air voids

/ i I [ \ 15 20 25 30

"X• ~ 4516 mm 2 foot area / ~ ~ - - - - - - 6passes

/ J _ ~ . . ~ ~ - - - - - 12 passes

/ / . / - ~ " ~ ~ Zero air voids y . - " \ \ =2-72

I / I I I %

15 20 25 30

Moisture content (per cent)

Roller compaction curves for a lean (silty) clay soil for sheepsfoot rollers having 7-, 14- and 21-sq in foot contact area, a constant maximum contact pressure of 1724 kN/m 2 for 6, 12 and 24 passes (Johnson and Saliberg, 1960)

26

6. CONCLUSION

In determining the pressures applied by pneumatic-tyred rollers, Lewis (1959) simply substituted circular contact areas for the pneumatic-tyred wheel. For the two cohe- sive soils, the maximum shear stress distribution with depth beneath the wheel was then determined assuming the soil was uniform and elastic. The discrepancy between measured and calculated values, on average 0.024 Mg/m 3, could be attributed in the main to the higher E values induced in the upper levels of the soil by the greater stresses and, hence, increased densities there. However, the fact that the contact area of a pneumatic- tyred wheel is essentially independent of the ground on which it rests, means that these secondary effects are not large : it also means that pneumatic-tyred plant would provide the best reference compactor for comparative trials of compaction plant in the field.

The progression to the smooth-wheeled roller involved the substitution of a strip contact area which progres- sively decreased in width during compaction for the steel roll, the contact width of which in elastic conditions depends on the elastic modulus of the soil and varies with both its moisture content and dry density (O'Reilly 1985). As information on this variability was very limited, the strip was considered to reduce to a width of 25.4 - 50.8 mm when compaction to refusal was attained. On this basis agreement between measured and calculated values was excellent on the heavy clay but less good on the sandy-clay soil.

On the granular soils, the bearing capacity approach which had not proved very successful with the pneu- matic-tyred rollers (Lewis 1959), came into its own and agreement between calculated and measured maximum dry densities was excellent when the strip was taken to be 25.4 mm wide.

After the excellent agreement on the heavy clay with both the pneumatic-tyred and smooth-wheeled rollers, it was disappointing that the calculated maximum dry densities for the club-and taper-foot sheepsfoot rollers tested in the initial full-scale compaction studies at TRRL fell far short of the measured values. This was particularly so since the contact pressures and areas were well defined for these items of plant. On the other hand, agreement was quite good to fair on the sandy clay and gravel-sand-clay; of perhaps greater significance, agreement was also quite good for the vibrating sheepsfoot rollers operated without vibration and tested during the later compaction trials at the laboratory on the heavy clay and gravel-sand- clay soils.

It is indeed possible that the presence of a concrete floor to the test bays used in the initial full-scale compaction studies at TRRL may have affected some results. For all subsequent compaction research the floor of the soil bays were left as natural soil to approximate as closely as possible conditions in the field. It is also fairly clear from the general regularity and scatter of the results, that the later series of compaction plant trials at TRRL were as

would be expected, where a learning process is involved, of a higher standard than those carried out initially in the circular covered track (Lewis 1954); for example, reverse curvature of the dry leg of the compaction curves is almost completely absent, an indication of more efficient moisturising and conditioning of the soils prior to compac- tion trials.

Lastly for the grid roller, while the calculated and meas- ured maximum dry densities were identical for the two granular soils, the calculated values exceed the meas- ured results by some 0.064 Mg/m 3 on the two cohesive soils. In these latter cases a 41.3 mm wide strip loading was assumed: it would require a redistribution of less than 10 per cent on the roll to other parts of the grid in possible contact with the ground to correct this disparity.

Both the analytical approaches used the shear strength/ moisture content/dry density relations for the soil ob- tained by conventional laboratory testing procedures using relatively low rates of strain of the order of 1.27 mm/min (Lewis 1959). The fact that agreement using them was as good as it is suggests that when compaction to refusal is approached at the lower moisture contents the strains induced by succeeding passes of the compac- tion are not large and the behaviour of the soil is essen- tially elastic and undrained.

It is to some extent surprising that such good agreement was obtained with the two approaches since the distribu- tion of maximum shear stress with depth assumes the soil behaves elastically while the bearing capacity approach assumes it behaves plastically. However, there is a long history of the use of stress distributions derived from elastic analyses in essentially plastic situations in soil mechanics. In the case of the pneumatic-tyred rollers on the cohesive soils, a change from the shear stress with depth to the bearing capacity approach would have resulted in the reduction of the calculated maximum dry densities of some 0.048-0.080 Mg/m 3. Since the values calculated using the shear stress approach already underestimate the measured values by an average of 0.024 Mg/m 3 on these soils there are clear indications that where both approaches are possible, the shear stress with depth approach is the better.

7. ACKNOWLEDGEMENTS

The work described in this report forms part of the research programme of the Ground Engineering Division of the Structures Group of TRRL. Many of the staff at the laboratory have carried out research on the compaction of soils from the 1940's onwards; particular acknow- ledgement is due to Mr A W Parsons for most useful discussion and advice.

27

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