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Tractive performance and compaction effect of a road roller running on a weak sandy soil
Pergamon
Journal of Terramechanics, Vol. 32, No. 5, pp. 245-261, 1995 Published by Elsevier Science Ltd Copyright ~ 1996 ISTVS Printed in Great Britain. All rights reserved 0022-4898/95 $9.50+0.00 0022-4898(95)00020-8
TRACTIVE PERFORMANCE AND COMPACTION EFFECT OF A ROAD ROLLER RUNNING ON A WEAK SANDY SOIL T. MURO* and Y. HOSHIKA t Summary--This study aims to investigate the tractive performance of a two-axle, two-wheel vehicle with rear-wheel drive or brake and the compaction of a decomposed granite soil. The effects of traction or braking, the change of sinkage, the slip ratio of the front and rear roller, and the number of passes of the road roller were studied. A number of tests were conducted and the experimental data were compared with the theoretical analysis results. It was observed that the amount of sinkage on the front and rear roller took the minimum value when the front roller was in the unpowered rolling state and the slip ratio of the rear roller was almost zero. When the absolute value of the slip ratio of rear roller increased, the amount of sinkage on the front and rear rollers, the absolute value of the driven or braking force of the rear roller and the absolute value of effective tractive or braking effort of the road roller increased. When the front roller was in the unpowered rolling state and the rear roller was in the braking state at - 5 % skid, the compaction density of the soil was at a maximum. Copyright © 1996 ISTVS. Published by Elsevier Science Ltd.
INTRODUCTION To compact effectively a loose sandy soil using a road roller, it is important to know the effect of the tractive performance of the road roller running over the soil on the degree of compaction of the soil. The main tractive performance feature of the road roller is the effective driving or braking force, which is the difference between the driving or braking force exerted by the rollers and soil strength, and the locomotion resistance arising from the compaction resistance. This depends on the density of the soil and the soil-wheel system constants [1]. The purpose of this paper is to investigate both the tractive performance of a two-axle, two-wheel road roller of 4.76 kN weight, running on a loose decomposed granite soil and the compaction property of that soil. Several tests were conducted with a road roller whose front roller was in the unpowered rolling state while the rear roller was in the driving or braking state. These experimental test results were compared with the theoretical analysis results. The amount of sinkage, the driving or braking force, the compaction resistance and the effective driving or braking force were calculated from the trochoid rolling locus of the roller. The soil-wheel system constants were measured for the various compacted soils after each pass of the roller. The amount of sinkage of the front and rear roller, the driving or braking force of the rear roller and the effective tractive or braking effort
*Faculty of Engineering, Ehime University, 3 Bunkyo-Cho, Matsuyama, Japan, 790-77. tToyo Construction Co. Ltd, 3-7-1 Nishikimachi, Kanda, Chiyodaku, Tokyo, 101, Japan. 245
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T. Muro and Y. Hoshika
were measured with the number of passes of the road roller. Finally, the compaction test was conducted for the same sandy soil as that used for the tractive performance test. The dry density of the soil was measured by using a cone penetrometer of 5 cm height, 30 ° apex angle and a 6.61 cm 2 base area. The depth ranged from 0 to 15 cm, the slip ratio from - 3 3 . 7 to 25.5% of the rear roller and the number of passes of the road roller N , ranging from 0 to 10.
D E T E R M I N A T I O N O F S O I L - W H E E L SYSTEM C O N S T A N T S
Plate loading and unloading test A soil sample of the air-dried decomposed granite soil with grain size below 4.75 mm was used. The size of soil bin used for this test was 120 cm length, 10 cm width and 35 cm height. The plate loading and unloading test was executed under the condition of plane strain state on the loose decomposed granite soil accumulated in the soil bin, and then on the compacted soil after two, four, six, eight and 10 passes of a steel roller of 32 cm diameter and 160 N/cm line pressure. The shorter length of the plate was varied from 5 to 15 cm. The average dry density of the compacted soil Pd (g/cm3), was measured at the surface of the terrain by using a tube sampler of 5 cm diameter and 10 cm length after each pass of the roller. The relationship between the pressure p (kPa), and the sinkage z (cm) can be predicted by Bekker's equation which considers the size effect of the plate [2] as follows: p =
+ ke z 0 -
b
where z0 is the initial amount of sinkage at the unloading state. The constants kc, kcr (N/cmn+l), depend on the cohesive strength of the soil, ke, ker (N/cm n+2) depend on the internal angle of friction of the soil, n and nr are the indices of sinkage respectively, and b is the length of the shorter side of the loading plate. Based on the experimental data obtained, the relationships between the soil-wheel system constants kc, kcr, kq, k~r, n, n r and the dry density of soil Pa (g/cm3) were obtained by a regression analysis as follows: 51.5(pd -- 1.46) k c = 1.41 + --0.890(pd -- 1.46) + 0.216' kcr = 213 -
78.7(pd - 1.46) --4.80(p d -- 1.46) + 1.00'
(3)
51.5(pd -- 1.46) ke = 5.64 + --3.69(pd -- 1.46) + 2.21' k(0 r =
32.3 +
51.5(pd -- 1.46)
(2)
(4) ,
(5)
--5.35(pd -- 1.46) + 1.21 5.25(pd -- 1.46) n = 0.867 + 5.15(pd -- 1.46) -- 3.16'
(6)
nr = 0.174.
(7)
and
Tractive performance and compaction effect
247
These equations are valid for the air-dried decomposed granite soil having a dry density ranging from 1.40 to 1.70 g/cm 3. Plate traction test
The relationship between the shear resistance r (kPa), the average normal stress p (kPa), and the amount of slippage j (cm) was presented by Janosi and Hanamoto [3] as:
= (mc + mfp){1 - e x p ( - a j ) } ,
(8)
where mc (kPa), mf and a (1/cm) are the soil-wheel system constants. The relationship between the amount of slip sinkage ss (cm), the average normal stress p (kPa), and the amount of slippage js (cm) was presented by Muro et al. [4] as:
(9)
Ss = copC'j c~',
where Co, Cl and c2 are the soil-wheel system constants. The plate traction test was conducted under several average normal stresses using a loading plate of 30 cm length and 10 cm width on the same soil as that mentioned previously for the plate loading and unloading test. The relationships between the soil-wheel system constants me, mf, a and Co, Cl, c2 and the dry density of the soil Pd (g/era3), were determined for the same air-dried decomposed granite soil as mentioned previously:
a Co
= (
=
mc = 0,
(10)
mf = 0.434,
(11)
5.25(Pd -- 1.46) , 1.59 + --8.82(Pd -- 1.46) + 1.98
0.431 -
5.25(pd-- 1.46) } x (1)c,, --0.683(pd -- 1.46) + 2.47
c 1 = 0.812 --
0.0945(Pd -- 1.46) 1.00 - 4.80(Pd -- 1.46)'
CZ = 1.591 --
0.346(pd -- 1.46) 1.00 -- 4.80(pd -- 1.46)'
and
(12) (13) (14)
(15)
As mentioned above, the soil-wheel system constants vary with the dry density of the soil and hence it is important to measure the dry density at the surface of the terrain. The relationship between the dry density Pd (g/cm3) and the cone index qc (kPa) at the surface of the terrain was measured in the compaction test of the loose decomposed granite soil using the test vehicle as follows: Pd
=
0.517(qc - 121) . 1.46 + 2.03(qc -- 121) + 514
(16)
The soil-wheel system constants could be determined by substituting the dry density Pd, given in equation (16) into equations (2)-(6) and (12)-(15). The cone index qc, was measured just after the final pass of the test vehicle (front roller skid--6.6%, rear roller skid--38.1%) for each number of compaction stage. Table 1
248
T. Muro and Y. Hoshika
C
×
g g Z g ~ g g g g g g ~ g g ' ' g ' ' g b bbb E
¢ I
.-7+
Z
Z
-
-
~
~
~
~
~
Z
z
~E
~
~
~
~
~
, ~
Tractive performance and compaction effect
249
shows the relationship between the soil-wheel system constants and the number of passes of the road roller N, in which the N - F line shows the values after the pass of the front roller and the N - R line shows the values after the pass of the rear roller.
THEORETICAL ANALYSIS
Tractive performance The mechanism of tractive performance of the road roller running on the loose decomposed granite soil is considered as the combination of the effective braking force [5] of the unpowered front roller and the effective driving force [6] during driving action (or the effective braking force during braking action [5] of the rear roller). Figure 1 shows the vehicle dimensions and forces acting on the road roller running on a loose sandy terrain. The vehicle weight W acts vertically on the center of gravity G of the road roller, and the front and rear axle load Wf and Wr act vertically on the front and rear axle Of and Or, respectively. The position of the center of gravity G is located on the amount of eccentricity e D from the central axis of the road roller and on the height hg perpendicular to the line O f O r. D is the wheel base, Rf and R r a r e the radii of the front and rear rollers, respectively. The driving torque Q = Qrd or braking torque Q = Qrb < 0 acts around the rear axle Or. The position of the application point F of the effective tractive effort T = TD or effective braking effort T = TB of the road roller is located at a distance L from the central axis of the vehicle and at a height of application H from the line O f O r. The pure rolling resistance Lfcb acts horizontally on the front axle Of, and the effective driving force Trd o r effective braking force Trb acts horizontally on the rear axle Or as shown in the figure.
V
o cos 8t
Front wheel width Bf
~ r (Qrd/Rr)sinOr~ Rear wheel Wr-(Qrb/Rr)sin#reb width Br erd ~_ erb
Fig. 1. Several forces acting on rear-wheel drive or brake road roller running soil.
on loose
decomposed granite
250
T. Muro and Y. Hoshika
The vehicle trim angle 0 t is defined as the angle between the line Of Or and the horizontal plane. For the amounts of sinkage sf and Sr of the front and rear wheel at the b o t t o m - d e a d - c e n t e r Mf and M r respectively, the vehicle trim angle 0 t is calculated as: 0t = sin -1 Rf - uf + Sr - Rr D
(17)
where uf is the amount of rebound of the terrain at the front roller. On the forward contact part of the front roller, the horizontal compaction resistance Lfcb and the vertical ground reaction Wf act in the distance of amount of eccentricity eft, = Rfsin 0eb and /fb = Rfcos 0fe b. On the forward contact part of the rear wheel, the horizontal compaction resistance Lrcd during the driving state or Lrcb during braking action, the tangential driving force Qrd/Rr or braking force Qrb/Rr < 0, and the vertical ground reaction W r - QrdSinOred/Rr or W r - Q r b × sin Oreb/Rr act in the distance of amount of eccentricity erd = Rr sin 0red and /rd = R r COS 0red or erb ----R r sin 0reb and /~b = Rr cos 0reb. Bf and Br are the widths of the front and rear rollers respectively.
Rear-wheel drive road roller For the vehicle speed V, the angular velocity (of and (or of the front and rear roller, the skid ifb of the front roller and the slip ratio ird are expressed as follows: ifb --
Rf(of
1,
(18)
V V ird = 1 -- - - . (19) Rr(or F r o m the force balances in the horizontal and vertical direction, the following relationship can be obtained: TD --
Qrd
c o s 0re d -
Lrc d -
Lfc b = Trd -
Lfcb,
(20)
Rr W = Wf .4_ W r.
(21)
F r o m the m o m e n t balance around the rear axle Or, the following equation can be obtained:
WfDcosOt + LfcbDsinO t - w { D - ( e D
+ hgtanOt)}cosOt + HTDcosOt-
L -
TDsin0t = 0 .
(22)
The effective tractive effort TD of the road roller given in equation (20) can be calculated from the effective driving force Trd and the compaction resistance Lfcb. The relationships between T D and irc; Trd and ird; Qrd and ird; sf, Sr and ird could be determined by means of simulation [7].
Rear-wheel brake road roller For the vehicle speed V, the angular velocity (of and (or of the front and rear roller, the skid ifb of the front roller and the skid irb are expressed as follows:
Tractive performance and compaction effect Rfr.of
ifb -- - V irb -
RrtOr
V
251
1,
(23)
1.
(24)
From the force balances in the horizontal direction, the effective braking effort TB of the road roller can be calculated from the effective braking force Trb and the compaction resistance Lfcb as follows:
Qrb c o s
0re b - L r c b - L f c b = Trb -- L f c b. (25) Rr From the moment balance around the rear axle Or as mentioned previously, the relations among TB and irb; Trb and irb; Qrb and irb, Sf and irb could also be determined. TB -
Analytical result The tractive performances of the road roller were simulated using the soil-wheel system constants given in Table 1 and the vehicle dimensions of the road roller given in Table 2. Figure 2 shows the relationship between the driving or braking force Q/Rr (Qrd/Rr or Orb/Rr) of the rear roller, the effective tractive or braking effort T (TD or TB) of the road roller and the slip ratio i (ird or irb) of the rear roller during the first pass of the road roller ( N = 1). Q/Rr is always larger than T for the whole range of the slip ratio i and Q/Rr increases with the increment of the slip ratio i. At the unpowered rolling state of the rear roller Q/Rr becomes zero at i - - i r b = - - 2 . 1 % . At the self-propelling state of the road roller T becomes zero at i = ira = 8.3%. T takes the maximum value 0.22 kN at ird = 18.3%. Figure 3 shows the relationship between the amounts of sinkage sf of the front roller, sr of the rear roller, s of the road roller, and the slip ratio i (ird or irb) of the rear roller during the first pass of the road roller ( N = 1). The soil-wheel system constants for N = 1 - F were used to calculate the tractive performance of the front
Table 2. Vehicle dimensions of a given road roller Item
Symbol
Unit
Vehicle weight Radius of front roller Radius of rear roller Width of front roller Width of rear roller Eccentricity of center of gravity G Height of center of gravity G Distance between central axis of vehicle and point F, acting effective tractive or braking effort T Height of application of effective tractive or braking effort T Peripheral speed of rear roller Wheel base from front to rear wheel axle Line pressure of front roller Line pressure of rear roller
W Rf R~ Bf Br e hg L
4.76 kN 16 cm 16 cm 60 cm 60 cm 0 19 cm + 55 cm
H Rr~Or D
W/2B~ W/2Br
0 cm 9.56 cm/s 60 cm 39.7 N/cm 39.7 N/cm
252
T. Muro and Y. Hoshika
1.0
Q/R~
Q/R~ T
T 0.5
(kN)
/,,~7r
-0.5
-1.0 -50
/ -30
-I0
10
30 i
50 (%)
Fig. 2. Theoretical results of driving or braking force Q/Rrof rear roller, effective tractive or braking effort T of road roller and slip ratio i of rear roller.
i
-50 O,
-30
-i0 0 10
(%)
30
50
--Sf -Sr
0.5 1.0 1.5 S
2.0 (cm) 2.5 Fig. 3. Theoretical results of amounts of sinkage st of front roller st, or rear roller s of road roller and slip ratio i of rear roller.
roller, while those for N = 1 - R were used to calculate that of the rear roller. The total amount of sinkage s of the road roller can be calculated as: S = Sf -- Uf + Sr -- U r.
(26)
sf increases slightly with the increment of slip ratio ird during driving action of the rear wheel because the skid lifbJ of the front wheel during the unpowered rolling state i.e. the amount of slip sinkage, increases gradually with ird. On the other hand, during braking action of the rear roller, sf decreases slightly and s and Sr increase with the increment of the slip ratio ird or skid tirbl due to the increasing amount of slippage [4].
Tractive performance and compaction effect
253
ROAD R O L L E R TRACTIVE PERFORMANCE
Experimental apparatus As shown in Fig. 4(a), a 4.76 kN weight road roller was drawn by a 3.7 kW winch under driving action on a surface of terrain. During the driving state, the trolley mounted with a roller can be pushed away to the moving direction of V from the winch, because the peripheral speed of the rear wheel RrtOr is larger than the vehicle speed V. Figure 4(b) shows that the road roller was also drawn by the winch under braking action on the surface of terrain. During braking state, the trolley can be pulled out by the winch to the moving direction of V, because the peripheral speed of the rear wheel RrtO r is smaller than the vehicle speed V. The terrain was made artificially of the same decomposed granite soil mentioned before, using another large soil bin of 540 cm length, 150 cm width and 60 cm height. The soil bin was filled up to 37 cm with the air-dried decomposed granite soil. The road rollers have dimensions of 110 cm length x 90 cm width x 79 cm height. (Other dimensions are already shown in Table 2.) The road roller consists of the unpowered front roller and the rear roller driven or braked by a controllable speed 0.75 kW motor mounted on the road roller by use of a chain, as shown in Fig. 5. (a) ii
V
Ultrasonic Transducer
/\
Winch
(b) Excavator \ \ \
Ultrasonic Transducer
_ ~ Measuring Position oI \ Amount of Sinkage at \
:i
i:
Winch V
Measuring Position of L
~
~
Amount of Sinkage at I [ 6 ~ ) ~ Front Roller ..... / [-[ ~ ~ ~ r-
ii
i
IY
Fig. 4. (a) Experimental apparatus for rear-wheel drive road roller tractive performance and compaction test during driving action (Rroh > V). (b) Experimental apparatus for rear-wheel brake road roller braking performance and compaction test during braking action (RrCOr< V).
254
T. Muro and Y. Hoshika
Fig. 5. General view of 4.76 kN weight road roller.
Experimental method The effects of the number of passes and the slip ratio of the rear roller on the amount of sinkage of the front and rear roller, the driving or braking force of the rear roller, and the effective tractive or braking effort of the road roller were investigated. For each of 10 passes of the road roller, the tractive performances were measured for five combinations of the skid and slip ratio of the front and rear rollers. The amount of sinkage of the front roller sf and that of the rear roller Sr could be measured respectively by the use of an ultrasonic transducer. The driving or braking torque Q was measured by the use of strain gauges attached to the shaft (3 cm in diameter) of the rear roller. The effective tractive or braking effort T was measured by the use of a load cell of 4.9 kN capacity, as shown in Fig. 4. The actual slip ratio or skid of the rear roller ird or irb was calculated from equation (19) or (24) by measuring the running distance of the road roller during one revolution of the rear roller. The actual skid of the front roller ifb was also calculated from equation (18) or (23) by measuring the running distance of the road roller during one revolution of the front roller.
Amount of sinkage Figure 6 shows the relationship between the amount of sinkage of the front roller se, the total amount of sinkage of the road roller s and the slip ratio or skid i r of the rear roller, for the first pass of the road roller ( N = 1). In general, the total amount of sinkage of the road roller s is always larger than that of the front roller sf because the value of s is measured as the sum of the preceding amount of sinkage of the front roller s f - u f and the amount of sinkage Sr of the rear roller including the large amount of slip sinkage. Both the front roller and the road roller sinkages take the minimum values respectively at the slip ratio of the rear roller i r - 0%. Both of them
Tractive performance and compaction effect
i~ -30
-50 0
-10 0 10
255
(%) 30
50
O Sf
N=I S
0.5 1.0 1.5 sf s
2.0 (cm) 2.5
J
Fig, 6. Experimental test results of amount of sinkage of front roller sf and that of road roller s and slip ratio ir of rear roller.
increase with the increase of the absolute value of the slip ratio or skid of the rear roller due to the increasing amount of slip sinkage. Figure 7 shows the relationship between the total accumulated amount of sinkage of the road roller S and the pass number of the road roller N for five combinations of front and rear roller slip. The total accumulated amount of sinkage of road roller S was directly measured as the distance from the level of the original terrain surface to the depth of bottom-dead-center of the rear roller. In general, the total accumulated amount of sinkage S increases with the increment of the number of passes N, but the gradient IdS/dN I decreases gradually with the increase of N. With the increment of the absolute value of the slip ratio or skid of the rear roller lirl, the total accumulated amount of sinkage S increases mainly due to the increase of the amount of slip sinkage of the rear roller. This depends on the dilatancy phenomenon of the loose N 2
S (cm)
4
o-7.7
18. I
• %2
7.?
0-3.6'
0.3
6
8
10
• -4. t3 % 5 '~ -5.2 -18.7
5 Fig. 7. Experimental test results of total accumulated amount of sinkage of road roller S and number of passes N.
256
T. Muro and Y. Hoshika
decomposed granite soil, i.e. the volume reduction during the shear deformation of the soil.
Driving or braking force During the driving or braking action and the unpowered rolling state of the rear roller, the relationships between the effective tractive or braking effort T of the road roller, the horizontal component of the driving or braking force of the rear roller (Q/Rr)h, and the land locomotion resistance L of the road roller could be expressed as;
T = (Q/Rr)h -- L.
(27)
Figure 8 shows the relationships between the driving or braking force of the rear roller Q/R~, the effective tractive or braking effort of the road roller T and the slip ratio or skid ir of the rear roller, for the first pass of the road roller (N = 1). In general, IQ/Rrl and IT I increase with the increase of [irl, but the gradients td(Q/R,.)/dirl and ldT/dirl decrease gradually with li~l respectively. When the effective tractive effort T becomes zero at the slip ratio i r = 4 % , the road roller is running at the self-propelling state. At the skid ir = - 7 % , the driving force Q/Rr becomes zero and the road roller is rotating at the unpowered rolling state. The land locomotion resistance L increases with the increment of the absolute value of the slip ratio I/rj and it takes the minimum value at the slip ratio i r - 0%. Figure 9 shows the relationship between the driving or braking force of the rear roller Q/Rr and the number of passes of the road roller N for five combinations of front and rear slip. Generally speaking, both the values of the positive driving force and the negative braking force took almost the same values with the increment of the pass number of the road roller N. The absolute value of Q/R~ tends to increase with the increment of the absolute value of slip ratio i r of the rear roller as shown previously in Fig. 8. Figure 10 shows the relationship between the effective tractive or braking effort T of the road roller and the number of passes N for five combinations of front and rear roller slip. 1.0
Q/Rr T
N=I
0.5 (kN) 0.0
-0.5
j
o__o_~/
o Q/R. *
-1.0 -50
-30
-10 0 10
T
50
30 Jr
(%)
Fig. 8. Experimental test results of driving or braking force of rear roller Q/R~, effective tractive or braking effort of road roller T and slip ratio of rear roller it.
Tractive performance and compaction effect
257
0.50
Q/R~ (kN) 0.25
i~ o -7.2 -0.25
* -4.7 o -3.6 * -4.6 -5.2
i ~ (%) 18.1 7.7 0.3 -4.5
-18.7
-0.50~
2
4
8
6
10 N
Fig. 9. Experimental test results of driving or braking force of rear roller road roller. 0.50
i~ o -7.? • -4.7 <> -3.6 • -4.6 a_5.2
T (kN) 0.25
Q/Rrand number of passes N of
i r (%) 18.1 7.7 [3.3 -4.5 -18.7
-0.25
-0.50
0
2
4
6
8
10 N
Fig. 10. Experimental test results of effective tractive or braking effort of road roller T and number of passes N. In general, both the values of the positive effective tractive effort and the effective braking effort T do not change any more with the increment of number N. Especially, the absolute value of the effective braking effort T of roller increases with the increment of the absolute value of the skid irb of roller due to the increasing land locomotion resistance.
negative the pass the road the rear
R O A D R O L L E R C O M P A C T I O N TEST
Experimental apparatus For the road roller compaction test, the same soil bin filled with the air-dried decomposed granite soil and the same road roller of the two-axle, two-wheel and rear-wheel drive or brake vehicle as mentioned previously in the road roller tractive
258
T. Muro and Y. Hoshika
performance test were used. In order to measure the dry density of the air-dried decomposed granite soil in the direction of the depth, a cone penetrometer mounted with a small cone of 2.9 cm base diameter, 5.0 cm height and 30° apex angle was used.
Experimental method The tractive conditions, the number of passes of the road roller and the combination of the slip ratio and skid of the rear roller, were set in the same way as described previously. The average line pressure of the road roller was calculated from the relationship W/(Bf + Br) which was equal to 39.7 N/cm. The degree of compaction was evaluated as the dry density Pd related to the cone index qc [i.e. the strength of the soil shown previously in equation (16)]. The cone index qc could be calculated as the penetration load divided by the base area of the cone which was measured for each depth of the terrain. After the road roller tractive performance test at the number of passes, the cone penetration tests were conducted at the depth z being equal to 5, 8, 10 and 15 cm respectively. Then the dry density Pd could be calculated from the measured cone index qc for each depth of the terrain.
Effect of the number of passes on dry density Figure 11 shows the relationship between the dry density Pd, at the depth z = 5 cm and the number of passes of the road roller N, for five combinations of front and rear roller slip. In general, the dry density increased gradually with the increase of the number of passes, but the gradient dpd/dN decreased slowly with the increase of passes. These phenomena can be explained by the fact that the number of repetitions of an alternative shear stress increases with the increment of the number of passes. The occurrence of the alternative shear stress due to the alternative shear deformation developed just under the wheel is considered to be very effective to compact the soil [8]. The dispersion of the dry density of the soil due to the tractive conditions becomes largest at N = 2 and it decreases gradually as number of passes increases further.
Pa (g/cm 3)
Z=5c m
1"81 1.7
8"1(%) i,o -7. 7 1 • -4.7 717 1.6 o-3.6 0.3 * -4.6 -4.5 1.5 1.4' 1.3 0
2
4
6
8
N
10
Fig. 11. Experimental test results of dry density Pd and number of passes N.
Tractive performance and compaction effect
259
Effect of slip ratio on dry density Figure 12 shows the relationship between the dry density at the second pass and the slip ratio or skid of the rear roller ir at the depth z = 5, 8, 10 and 15 cm. As shown in this figure, the dry density takes a maximum value at the skid of the rear roller i r - - --5% for all the cases of the depth z. At this tractive condition, it is considered that the soil is compacted most effectively due to the occurrence of the alternative positive and negative shear stresses which develop just under the contact area of the front and rear roller during braking action. There are normally two flow zones beneath a towed roller. Each flow zone consists of a passive and active failure zone. For the forward flow zone, the soil particles move forward along the slip line and then backward along the peripheral surface of the roller; the positive shear stress acts then on the front part of the contact surface of the roller. On the other hand, for the backward flow zone, the soil particles move forward along the peripheral surface of the roller and then downward along the slip line; the negative shear stress acts on the rear part of the contact surface of the roller. This is because the soil particle under the towed roller is rotating about an instantaneous center situated below the bottom-dead-center [9]. If the alternative shear stress occurs moderately among the soil particles beneath the towed roller, the loose soil can be compacted due to the effect of the dilatancy. For the shallow depth z = 5 cm, the alternative shear deformation occurring in the soil was too large to increase the density of the soil when the absolute value of the slip ratio or skid Iirt became large. In this case, the soil cannot be compacted effectively because the density of the soil decreases to a value less than the critical density due to the effect of the kneading of soil. For the depth z -- 10 and 15 cm, the soil can be compacted effectively because the density increases beyond the critical density. In this case, the effect of the slip ratio on the dry density of the soil is almost lost because the alternative shear stress occurs moderately under the comparatively higher normal stress. Therefore, it was clear that when the road roller is towed by a bulldozer under the condition of the unpowered rolling state of the front roller and the skid of the rear
1.8 Od (g/cm3) 1.7
1.6 1.5
1.4 1.3 -50
-30
-i0 0 10
30 i~
50 (%)
Fig. 12. Experimental test results of dry density Pa and slip ratio of rear roller i,.
260
T. Muro and Y. Hoshika
roller (it being equal to about - 5 % ) , the terrain of the loose decomposed granite soil can be compacted most effectively.
Relationship between depth and dry density Figure 13 shows the relationship between the depth z, and the dry density of the soil Pa, after the second pass of the road roller for five combinations of front and rear roller slip. For the shallow depths z - - 5 and 8 c m , the dry density of the soil scatters noticeably according to the slip ratio or skid of the rear roller while the dry density reduces to some value regardless of the slip ratio or skid at depths of 10 and 15 cm.
CONCLUSIONS The following conclusions can be drawn from the results obtained in this investigation. 1. The soil-wheel system constants kc, kcr, k~, kcr, n, nr, me, mf, a, c 0, q , and c 2 can be expressed as a function of the dry density Pd of the loose decomposed granite soil. 2. The sinkages of the front and rear roller had minimum values at the slip ratio of the rear roller ir - 0%, and both of them increased with the increase of the absolute value of slip ratio or skid ]irl of the rear roller. 3. The absolute values of the driving or braking force of the rear roller ]Q/Rrl and the effective tractive or braking effort of the road roller ITI increased with the increment of the absolute value of the slip ratio or skid lirl of the rear roller. These gradients ]d(Q/Rr)/dirl and [dT/dirl decreased gradually with the increment of the absolute value of the slip ratio or skid ]irl of the rear roller. 4. When the road roller is towed by a bulldozer under the condition of the unpowered rolling state of the front roller and the skid of the rear roller being equal to about - 5 % , the loose decomposed granite soil can be compacted most effectively. P a
1.3
1.4
1.5
1.6
(g/cm 3) 1.7 1.8 N=2
10
15 Z (cm) 20
o -7.7 * -4.7 0-3.6 0.3 * -4.6 -4.5 " -5.2 -18.7
Fig. 13. Experimental test results of depth z and dry density Pd for five combinations of front and rear roller slip.
Tractive performance and compaction effect
261
5. The dry density of the soil decreased with the increment of the absolute value of the slip ratio or skid of the rear roller for the shallow depths of 5 and 8 cm, while the dry density was constant regardless of the slip ratio or skid at depths of 10 and 15 cm. 6. In general, the theoretical analysis results were in good agreement with the experimental data of the amount of sinkage of the front and rear roller, the driving or braking force of the rear roller, the effective tractive or braking effort of the road roller and the slip or skid ratio of the rear roller.
REFERENCES [I] T. Muro, Terramechanics--Land Locomotion Mechanics. pp. 31-74, Gihoudo Press, Tokyo, Japan (1993). [2] M. G. Bekker, Off-the-road Locomotion. pp. 25-40, The University of Michigan Press. Ann Arbor, MI (1960). [3] Z. Janosi and B. Hanamoto, The analytical determination of drawbarpull as a function of slip for tracked vehicles in deformable soils, Proc. 1st Int. Conf. on Terrain-Vehicle Systems, Torino~ Italy (1961). [4] T. Muro, K. Omoto and M. Futamura, Traffic performance of a bulldozer running on a weak terrain--vehicle model test. Proc. o f JSCE 397 VI-9, 151-157 (1988). [5] T. Muro, Braking performances of a towed rigid wheel on a soft ground based on the analysis of soil compaction. Soils and Foundations 33 (2), 91-104 (1993). [6] T. Muro, Tractive performance of a driven rigid wheel on soft ground based on the analysis of soil-wheel interaction. J. Terramechanics 30 (5), 351-369 (1993). [7] T. Muro and R. Fukagawa, The optimum height of application of force and eccentricity of a wheeled vehicle running on a loose sandy soil. J. Terramechanics 31 (5), 313-328 (1994). [8} S. Shaaban, Compaction of sand using ordinary off-road vehicles. Proc. 8th Int. Conf. of the 1STVS, Cambridge, U.K., pp. 725-735 (1984). [9] J. Y. Wong, Behaviour of soil beneath rigid wheels. J. Agric. Engng Res. 12 (4), 257-269 (1967).
Journal of Terramechanics, Vol. 32, No. 5, pp. 245-261, 1995 Published by Elsevier Science Ltd Copyright ~ 1996 ISTVS Printed in Great Britain. All rights reserved 0022-4898/95 $9.50+0.00 0022-4898(95)00020-8
TRACTIVE PERFORMANCE AND COMPACTION EFFECT OF A ROAD ROLLER RUNNING ON A WEAK SANDY SOIL T. MURO* and Y. HOSHIKA t Summary--This study aims to investigate the tractive performance of a two-axle, two-wheel vehicle with rear-wheel drive or brake and the compaction of a decomposed granite soil. The effects of traction or braking, the change of sinkage, the slip ratio of the front and rear roller, and the number of passes of the road roller were studied. A number of tests were conducted and the experimental data were compared with the theoretical analysis results. It was observed that the amount of sinkage on the front and rear roller took the minimum value when the front roller was in the unpowered rolling state and the slip ratio of the rear roller was almost zero. When the absolute value of the slip ratio of rear roller increased, the amount of sinkage on the front and rear rollers, the absolute value of the driven or braking force of the rear roller and the absolute value of effective tractive or braking effort of the road roller increased. When the front roller was in the unpowered rolling state and the rear roller was in the braking state at - 5 % skid, the compaction density of the soil was at a maximum. Copyright © 1996 ISTVS. Published by Elsevier Science Ltd.
INTRODUCTION To compact effectively a loose sandy soil using a road roller, it is important to know the effect of the tractive performance of the road roller running over the soil on the degree of compaction of the soil. The main tractive performance feature of the road roller is the effective driving or braking force, which is the difference between the driving or braking force exerted by the rollers and soil strength, and the locomotion resistance arising from the compaction resistance. This depends on the density of the soil and the soil-wheel system constants [1]. The purpose of this paper is to investigate both the tractive performance of a two-axle, two-wheel road roller of 4.76 kN weight, running on a loose decomposed granite soil and the compaction property of that soil. Several tests were conducted with a road roller whose front roller was in the unpowered rolling state while the rear roller was in the driving or braking state. These experimental test results were compared with the theoretical analysis results. The amount of sinkage, the driving or braking force, the compaction resistance and the effective driving or braking force were calculated from the trochoid rolling locus of the roller. The soil-wheel system constants were measured for the various compacted soils after each pass of the roller. The amount of sinkage of the front and rear roller, the driving or braking force of the rear roller and the effective tractive or braking effort
*Faculty of Engineering, Ehime University, 3 Bunkyo-Cho, Matsuyama, Japan, 790-77. tToyo Construction Co. Ltd, 3-7-1 Nishikimachi, Kanda, Chiyodaku, Tokyo, 101, Japan. 245
246
T. Muro and Y. Hoshika
were measured with the number of passes of the road roller. Finally, the compaction test was conducted for the same sandy soil as that used for the tractive performance test. The dry density of the soil was measured by using a cone penetrometer of 5 cm height, 30 ° apex angle and a 6.61 cm 2 base area. The depth ranged from 0 to 15 cm, the slip ratio from - 3 3 . 7 to 25.5% of the rear roller and the number of passes of the road roller N , ranging from 0 to 10.
D E T E R M I N A T I O N O F S O I L - W H E E L SYSTEM C O N S T A N T S
Plate loading and unloading test A soil sample of the air-dried decomposed granite soil with grain size below 4.75 mm was used. The size of soil bin used for this test was 120 cm length, 10 cm width and 35 cm height. The plate loading and unloading test was executed under the condition of plane strain state on the loose decomposed granite soil accumulated in the soil bin, and then on the compacted soil after two, four, six, eight and 10 passes of a steel roller of 32 cm diameter and 160 N/cm line pressure. The shorter length of the plate was varied from 5 to 15 cm. The average dry density of the compacted soil Pd (g/cm3), was measured at the surface of the terrain by using a tube sampler of 5 cm diameter and 10 cm length after each pass of the roller. The relationship between the pressure p (kPa), and the sinkage z (cm) can be predicted by Bekker's equation which considers the size effect of the plate [2] as follows: p =
+ ke z 0 -
b
where z0 is the initial amount of sinkage at the unloading state. The constants kc, kcr (N/cmn+l), depend on the cohesive strength of the soil, ke, ker (N/cm n+2) depend on the internal angle of friction of the soil, n and nr are the indices of sinkage respectively, and b is the length of the shorter side of the loading plate. Based on the experimental data obtained, the relationships between the soil-wheel system constants kc, kcr, kq, k~r, n, n r and the dry density of soil Pa (g/cm3) were obtained by a regression analysis as follows: 51.5(pd -- 1.46) k c = 1.41 + --0.890(pd -- 1.46) + 0.216' kcr = 213 -
78.7(pd - 1.46) --4.80(p d -- 1.46) + 1.00'
(3)
51.5(pd -- 1.46) ke = 5.64 + --3.69(pd -- 1.46) + 2.21' k(0 r =
32.3 +
51.5(pd -- 1.46)
(2)
(4) ,
(5)
--5.35(pd -- 1.46) + 1.21 5.25(pd -- 1.46) n = 0.867 + 5.15(pd -- 1.46) -- 3.16'
(6)
nr = 0.174.
(7)
and
Tractive performance and compaction effect
247
These equations are valid for the air-dried decomposed granite soil having a dry density ranging from 1.40 to 1.70 g/cm 3. Plate traction test
The relationship between the shear resistance r (kPa), the average normal stress p (kPa), and the amount of slippage j (cm) was presented by Janosi and Hanamoto [3] as:
= (mc + mfp){1 - e x p ( - a j ) } ,
(8)
where mc (kPa), mf and a (1/cm) are the soil-wheel system constants. The relationship between the amount of slip sinkage ss (cm), the average normal stress p (kPa), and the amount of slippage js (cm) was presented by Muro et al. [4] as:
(9)
Ss = copC'j c~',
where Co, Cl and c2 are the soil-wheel system constants. The plate traction test was conducted under several average normal stresses using a loading plate of 30 cm length and 10 cm width on the same soil as that mentioned previously for the plate loading and unloading test. The relationships between the soil-wheel system constants me, mf, a and Co, Cl, c2 and the dry density of the soil Pd (g/era3), were determined for the same air-dried decomposed granite soil as mentioned previously:
a Co
= (
=
mc = 0,
(10)
mf = 0.434,
(11)
5.25(Pd -- 1.46) , 1.59 + --8.82(Pd -- 1.46) + 1.98
0.431 -
5.25(pd-- 1.46) } x (1)c,, --0.683(pd -- 1.46) + 2.47
c 1 = 0.812 --
0.0945(Pd -- 1.46) 1.00 - 4.80(Pd -- 1.46)'
CZ = 1.591 --
0.346(pd -- 1.46) 1.00 -- 4.80(pd -- 1.46)'
and
(12) (13) (14)
(15)
As mentioned above, the soil-wheel system constants vary with the dry density of the soil and hence it is important to measure the dry density at the surface of the terrain. The relationship between the dry density Pd (g/cm3) and the cone index qc (kPa) at the surface of the terrain was measured in the compaction test of the loose decomposed granite soil using the test vehicle as follows: Pd
=
0.517(qc - 121) . 1.46 + 2.03(qc -- 121) + 514
(16)
The soil-wheel system constants could be determined by substituting the dry density Pd, given in equation (16) into equations (2)-(6) and (12)-(15). The cone index qc, was measured just after the final pass of the test vehicle (front roller skid--6.6%, rear roller skid--38.1%) for each number of compaction stage. Table 1
248
T. Muro and Y. Hoshika
C
×
g g Z g ~ g g g g g g ~ g g ' ' g ' ' g b bbb E
¢ I
.-7+
Z
Z
-
-
~
~
~
~
~
Z
z
~E
~
~
~
~
~
, ~
Tractive performance and compaction effect
249
shows the relationship between the soil-wheel system constants and the number of passes of the road roller N, in which the N - F line shows the values after the pass of the front roller and the N - R line shows the values after the pass of the rear roller.
THEORETICAL ANALYSIS
Tractive performance The mechanism of tractive performance of the road roller running on the loose decomposed granite soil is considered as the combination of the effective braking force [5] of the unpowered front roller and the effective driving force [6] during driving action (or the effective braking force during braking action [5] of the rear roller). Figure 1 shows the vehicle dimensions and forces acting on the road roller running on a loose sandy terrain. The vehicle weight W acts vertically on the center of gravity G of the road roller, and the front and rear axle load Wf and Wr act vertically on the front and rear axle Of and Or, respectively. The position of the center of gravity G is located on the amount of eccentricity e D from the central axis of the road roller and on the height hg perpendicular to the line O f O r. D is the wheel base, Rf and R r a r e the radii of the front and rear rollers, respectively. The driving torque Q = Qrd or braking torque Q = Qrb < 0 acts around the rear axle Or. The position of the application point F of the effective tractive effort T = TD or effective braking effort T = TB of the road roller is located at a distance L from the central axis of the vehicle and at a height of application H from the line O f O r. The pure rolling resistance Lfcb acts horizontally on the front axle Of, and the effective driving force Trd o r effective braking force Trb acts horizontally on the rear axle Or as shown in the figure.
V
o cos 8t
Front wheel width Bf
~ r (Qrd/Rr)sinOr~ Rear wheel Wr-(Qrb/Rr)sin#reb width Br erd ~_ erb
Fig. 1. Several forces acting on rear-wheel drive or brake road roller running soil.
on loose
decomposed granite
250
T. Muro and Y. Hoshika
The vehicle trim angle 0 t is defined as the angle between the line Of Or and the horizontal plane. For the amounts of sinkage sf and Sr of the front and rear wheel at the b o t t o m - d e a d - c e n t e r Mf and M r respectively, the vehicle trim angle 0 t is calculated as: 0t = sin -1 Rf - uf + Sr - Rr D
(17)
where uf is the amount of rebound of the terrain at the front roller. On the forward contact part of the front roller, the horizontal compaction resistance Lfcb and the vertical ground reaction Wf act in the distance of amount of eccentricity eft, = Rfsin 0eb and /fb = Rfcos 0fe b. On the forward contact part of the rear wheel, the horizontal compaction resistance Lrcd during the driving state or Lrcb during braking action, the tangential driving force Qrd/Rr or braking force Qrb/Rr < 0, and the vertical ground reaction W r - QrdSinOred/Rr or W r - Q r b × sin Oreb/Rr act in the distance of amount of eccentricity erd = Rr sin 0red and /rd = R r COS 0red or erb ----R r sin 0reb and /~b = Rr cos 0reb. Bf and Br are the widths of the front and rear rollers respectively.
Rear-wheel drive road roller For the vehicle speed V, the angular velocity (of and (or of the front and rear roller, the skid ifb of the front roller and the slip ratio ird are expressed as follows: ifb --
Rf(of
1,
(18)
V V ird = 1 -- - - . (19) Rr(or F r o m the force balances in the horizontal and vertical direction, the following relationship can be obtained: TD --
Qrd
c o s 0re d -
Lrc d -
Lfc b = Trd -
Lfcb,
(20)
Rr W = Wf .4_ W r.
(21)
F r o m the m o m e n t balance around the rear axle Or, the following equation can be obtained:
WfDcosOt + LfcbDsinO t - w { D - ( e D
+ hgtanOt)}cosOt + HTDcosOt-
L -
TDsin0t = 0 .
(22)
The effective tractive effort TD of the road roller given in equation (20) can be calculated from the effective driving force Trd and the compaction resistance Lfcb. The relationships between T D and irc; Trd and ird; Qrd and ird; sf, Sr and ird could be determined by means of simulation [7].
Rear-wheel brake road roller For the vehicle speed V, the angular velocity (of and (or of the front and rear roller, the skid ifb of the front roller and the skid irb are expressed as follows:
Tractive performance and compaction effect Rfr.of
ifb -- - V irb -
RrtOr
V
251
1,
(23)
1.
(24)
From the force balances in the horizontal direction, the effective braking effort TB of the road roller can be calculated from the effective braking force Trb and the compaction resistance Lfcb as follows:
Qrb c o s
0re b - L r c b - L f c b = Trb -- L f c b. (25) Rr From the moment balance around the rear axle Or as mentioned previously, the relations among TB and irb; Trb and irb; Qrb and irb, Sf and irb could also be determined. TB -
Analytical result The tractive performances of the road roller were simulated using the soil-wheel system constants given in Table 1 and the vehicle dimensions of the road roller given in Table 2. Figure 2 shows the relationship between the driving or braking force Q/Rr (Qrd/Rr or Orb/Rr) of the rear roller, the effective tractive or braking effort T (TD or TB) of the road roller and the slip ratio i (ird or irb) of the rear roller during the first pass of the road roller ( N = 1). Q/Rr is always larger than T for the whole range of the slip ratio i and Q/Rr increases with the increment of the slip ratio i. At the unpowered rolling state of the rear roller Q/Rr becomes zero at i - - i r b = - - 2 . 1 % . At the self-propelling state of the road roller T becomes zero at i = ira = 8.3%. T takes the maximum value 0.22 kN at ird = 18.3%. Figure 3 shows the relationship between the amounts of sinkage sf of the front roller, sr of the rear roller, s of the road roller, and the slip ratio i (ird or irb) of the rear roller during the first pass of the road roller ( N = 1). The soil-wheel system constants for N = 1 - F were used to calculate the tractive performance of the front
Table 2. Vehicle dimensions of a given road roller Item
Symbol
Unit
Vehicle weight Radius of front roller Radius of rear roller Width of front roller Width of rear roller Eccentricity of center of gravity G Height of center of gravity G Distance between central axis of vehicle and point F, acting effective tractive or braking effort T Height of application of effective tractive or braking effort T Peripheral speed of rear roller Wheel base from front to rear wheel axle Line pressure of front roller Line pressure of rear roller
W Rf R~ Bf Br e hg L
4.76 kN 16 cm 16 cm 60 cm 60 cm 0 19 cm + 55 cm
H Rr~Or D
W/2B~ W/2Br
0 cm 9.56 cm/s 60 cm 39.7 N/cm 39.7 N/cm
252
T. Muro and Y. Hoshika
1.0
Q/R~
Q/R~ T
T 0.5
(kN)
/,,~7r
-0.5
-1.0 -50
/ -30
-I0
10
30 i
50 (%)
Fig. 2. Theoretical results of driving or braking force Q/Rrof rear roller, effective tractive or braking effort T of road roller and slip ratio i of rear roller.
i
-50 O,
-30
-i0 0 10
(%)
30
50
--Sf -Sr
0.5 1.0 1.5 S
2.0 (cm) 2.5 Fig. 3. Theoretical results of amounts of sinkage st of front roller st, or rear roller s of road roller and slip ratio i of rear roller.
roller, while those for N = 1 - R were used to calculate that of the rear roller. The total amount of sinkage s of the road roller can be calculated as: S = Sf -- Uf + Sr -- U r.
(26)
sf increases slightly with the increment of slip ratio ird during driving action of the rear wheel because the skid lifbJ of the front wheel during the unpowered rolling state i.e. the amount of slip sinkage, increases gradually with ird. On the other hand, during braking action of the rear roller, sf decreases slightly and s and Sr increase with the increment of the slip ratio ird or skid tirbl due to the increasing amount of slippage [4].
Tractive performance and compaction effect
253
ROAD R O L L E R TRACTIVE PERFORMANCE
Experimental apparatus As shown in Fig. 4(a), a 4.76 kN weight road roller was drawn by a 3.7 kW winch under driving action on a surface of terrain. During the driving state, the trolley mounted with a roller can be pushed away to the moving direction of V from the winch, because the peripheral speed of the rear wheel RrtOr is larger than the vehicle speed V. Figure 4(b) shows that the road roller was also drawn by the winch under braking action on the surface of terrain. During braking state, the trolley can be pulled out by the winch to the moving direction of V, because the peripheral speed of the rear wheel RrtO r is smaller than the vehicle speed V. The terrain was made artificially of the same decomposed granite soil mentioned before, using another large soil bin of 540 cm length, 150 cm width and 60 cm height. The soil bin was filled up to 37 cm with the air-dried decomposed granite soil. The road rollers have dimensions of 110 cm length x 90 cm width x 79 cm height. (Other dimensions are already shown in Table 2.) The road roller consists of the unpowered front roller and the rear roller driven or braked by a controllable speed 0.75 kW motor mounted on the road roller by use of a chain, as shown in Fig. 5. (a) ii
V
Ultrasonic Transducer
/\
Winch
(b) Excavator \ \ \
Ultrasonic Transducer
_ ~ Measuring Position oI \ Amount of Sinkage at \
:i
i:
Winch V
Measuring Position of L
~
~
Amount of Sinkage at I [ 6 ~ ) ~ Front Roller ..... / [-[ ~ ~ ~ r-
ii
i
IY
Fig. 4. (a) Experimental apparatus for rear-wheel drive road roller tractive performance and compaction test during driving action (Rroh > V). (b) Experimental apparatus for rear-wheel brake road roller braking performance and compaction test during braking action (RrCOr< V).
254
T. Muro and Y. Hoshika
Fig. 5. General view of 4.76 kN weight road roller.
Experimental method The effects of the number of passes and the slip ratio of the rear roller on the amount of sinkage of the front and rear roller, the driving or braking force of the rear roller, and the effective tractive or braking effort of the road roller were investigated. For each of 10 passes of the road roller, the tractive performances were measured for five combinations of the skid and slip ratio of the front and rear rollers. The amount of sinkage of the front roller sf and that of the rear roller Sr could be measured respectively by the use of an ultrasonic transducer. The driving or braking torque Q was measured by the use of strain gauges attached to the shaft (3 cm in diameter) of the rear roller. The effective tractive or braking effort T was measured by the use of a load cell of 4.9 kN capacity, as shown in Fig. 4. The actual slip ratio or skid of the rear roller ird or irb was calculated from equation (19) or (24) by measuring the running distance of the road roller during one revolution of the rear roller. The actual skid of the front roller ifb was also calculated from equation (18) or (23) by measuring the running distance of the road roller during one revolution of the front roller.
Amount of sinkage Figure 6 shows the relationship between the amount of sinkage of the front roller se, the total amount of sinkage of the road roller s and the slip ratio or skid i r of the rear roller, for the first pass of the road roller ( N = 1). In general, the total amount of sinkage of the road roller s is always larger than that of the front roller sf because the value of s is measured as the sum of the preceding amount of sinkage of the front roller s f - u f and the amount of sinkage Sr of the rear roller including the large amount of slip sinkage. Both the front roller and the road roller sinkages take the minimum values respectively at the slip ratio of the rear roller i r - 0%. Both of them
Tractive performance and compaction effect
i~ -30
-50 0
-10 0 10
255
(%) 30
50
O Sf
N=I S
0.5 1.0 1.5 sf s
2.0 (cm) 2.5
J
Fig, 6. Experimental test results of amount of sinkage of front roller sf and that of road roller s and slip ratio ir of rear roller.
increase with the increase of the absolute value of the slip ratio or skid of the rear roller due to the increasing amount of slip sinkage. Figure 7 shows the relationship between the total accumulated amount of sinkage of the road roller S and the pass number of the road roller N for five combinations of front and rear roller slip. The total accumulated amount of sinkage of road roller S was directly measured as the distance from the level of the original terrain surface to the depth of bottom-dead-center of the rear roller. In general, the total accumulated amount of sinkage S increases with the increment of the number of passes N, but the gradient IdS/dN I decreases gradually with the increase of N. With the increment of the absolute value of the slip ratio or skid of the rear roller lirl, the total accumulated amount of sinkage S increases mainly due to the increase of the amount of slip sinkage of the rear roller. This depends on the dilatancy phenomenon of the loose N 2
S (cm)
4
o-7.7
18. I
• %2
7.?
0-3.6'
0.3
6
8
10
• -4. t3 % 5 '~ -5.2 -18.7
5 Fig. 7. Experimental test results of total accumulated amount of sinkage of road roller S and number of passes N.
256
T. Muro and Y. Hoshika
decomposed granite soil, i.e. the volume reduction during the shear deformation of the soil.
Driving or braking force During the driving or braking action and the unpowered rolling state of the rear roller, the relationships between the effective tractive or braking effort T of the road roller, the horizontal component of the driving or braking force of the rear roller (Q/Rr)h, and the land locomotion resistance L of the road roller could be expressed as;
T = (Q/Rr)h -- L.
(27)
Figure 8 shows the relationships between the driving or braking force of the rear roller Q/R~, the effective tractive or braking effort of the road roller T and the slip ratio or skid ir of the rear roller, for the first pass of the road roller (N = 1). In general, IQ/Rrl and IT I increase with the increase of [irl, but the gradients td(Q/R,.)/dirl and ldT/dirl decrease gradually with li~l respectively. When the effective tractive effort T becomes zero at the slip ratio i r = 4 % , the road roller is running at the self-propelling state. At the skid ir = - 7 % , the driving force Q/Rr becomes zero and the road roller is rotating at the unpowered rolling state. The land locomotion resistance L increases with the increment of the absolute value of the slip ratio I/rj and it takes the minimum value at the slip ratio i r - 0%. Figure 9 shows the relationship between the driving or braking force of the rear roller Q/Rr and the number of passes of the road roller N for five combinations of front and rear slip. Generally speaking, both the values of the positive driving force and the negative braking force took almost the same values with the increment of the pass number of the road roller N. The absolute value of Q/R~ tends to increase with the increment of the absolute value of slip ratio i r of the rear roller as shown previously in Fig. 8. Figure 10 shows the relationship between the effective tractive or braking effort T of the road roller and the number of passes N for five combinations of front and rear roller slip. 1.0
Q/Rr T
N=I
0.5 (kN) 0.0
-0.5
j
o__o_~/
o Q/R. *
-1.0 -50
-30
-10 0 10
T
50
30 Jr
(%)
Fig. 8. Experimental test results of driving or braking force of rear roller Q/R~, effective tractive or braking effort of road roller T and slip ratio of rear roller it.
Tractive performance and compaction effect
257
0.50
Q/R~ (kN) 0.25
i~ o -7.2 -0.25
* -4.7 o -3.6 * -4.6 -5.2
i ~ (%) 18.1 7.7 0.3 -4.5
-18.7
-0.50~
2
4
8
6
10 N
Fig. 9. Experimental test results of driving or braking force of rear roller road roller. 0.50
i~ o -7.? • -4.7 <> -3.6 • -4.6 a_5.2
T (kN) 0.25
Q/Rrand number of passes N of
i r (%) 18.1 7.7 [3.3 -4.5 -18.7
-0.25
-0.50
0
2
4
6
8
10 N
Fig. 10. Experimental test results of effective tractive or braking effort of road roller T and number of passes N. In general, both the values of the positive effective tractive effort and the effective braking effort T do not change any more with the increment of number N. Especially, the absolute value of the effective braking effort T of roller increases with the increment of the absolute value of the skid irb of roller due to the increasing land locomotion resistance.
negative the pass the road the rear
R O A D R O L L E R C O M P A C T I O N TEST
Experimental apparatus For the road roller compaction test, the same soil bin filled with the air-dried decomposed granite soil and the same road roller of the two-axle, two-wheel and rear-wheel drive or brake vehicle as mentioned previously in the road roller tractive
258
T. Muro and Y. Hoshika
performance test were used. In order to measure the dry density of the air-dried decomposed granite soil in the direction of the depth, a cone penetrometer mounted with a small cone of 2.9 cm base diameter, 5.0 cm height and 30° apex angle was used.
Experimental method The tractive conditions, the number of passes of the road roller and the combination of the slip ratio and skid of the rear roller, were set in the same way as described previously. The average line pressure of the road roller was calculated from the relationship W/(Bf + Br) which was equal to 39.7 N/cm. The degree of compaction was evaluated as the dry density Pd related to the cone index qc [i.e. the strength of the soil shown previously in equation (16)]. The cone index qc could be calculated as the penetration load divided by the base area of the cone which was measured for each depth of the terrain. After the road roller tractive performance test at the number of passes, the cone penetration tests were conducted at the depth z being equal to 5, 8, 10 and 15 cm respectively. Then the dry density Pd could be calculated from the measured cone index qc for each depth of the terrain.
Effect of the number of passes on dry density Figure 11 shows the relationship between the dry density Pd, at the depth z = 5 cm and the number of passes of the road roller N, for five combinations of front and rear roller slip. In general, the dry density increased gradually with the increase of the number of passes, but the gradient dpd/dN decreased slowly with the increase of passes. These phenomena can be explained by the fact that the number of repetitions of an alternative shear stress increases with the increment of the number of passes. The occurrence of the alternative shear stress due to the alternative shear deformation developed just under the wheel is considered to be very effective to compact the soil [8]. The dispersion of the dry density of the soil due to the tractive conditions becomes largest at N = 2 and it decreases gradually as number of passes increases further.
Pa (g/cm 3)
Z=5c m
1"81 1.7
8"1(%) i,o -7. 7 1 • -4.7 717 1.6 o-3.6 0.3 * -4.6 -4.5 1.5 1.4' 1.3 0
2
4
6
8
N
10
Fig. 11. Experimental test results of dry density Pd and number of passes N.
Tractive performance and compaction effect
259
Effect of slip ratio on dry density Figure 12 shows the relationship between the dry density at the second pass and the slip ratio or skid of the rear roller ir at the depth z = 5, 8, 10 and 15 cm. As shown in this figure, the dry density takes a maximum value at the skid of the rear roller i r - - --5% for all the cases of the depth z. At this tractive condition, it is considered that the soil is compacted most effectively due to the occurrence of the alternative positive and negative shear stresses which develop just under the contact area of the front and rear roller during braking action. There are normally two flow zones beneath a towed roller. Each flow zone consists of a passive and active failure zone. For the forward flow zone, the soil particles move forward along the slip line and then backward along the peripheral surface of the roller; the positive shear stress acts then on the front part of the contact surface of the roller. On the other hand, for the backward flow zone, the soil particles move forward along the peripheral surface of the roller and then downward along the slip line; the negative shear stress acts on the rear part of the contact surface of the roller. This is because the soil particle under the towed roller is rotating about an instantaneous center situated below the bottom-dead-center [9]. If the alternative shear stress occurs moderately among the soil particles beneath the towed roller, the loose soil can be compacted due to the effect of the dilatancy. For the shallow depth z = 5 cm, the alternative shear deformation occurring in the soil was too large to increase the density of the soil when the absolute value of the slip ratio or skid Iirt became large. In this case, the soil cannot be compacted effectively because the density of the soil decreases to a value less than the critical density due to the effect of the kneading of soil. For the depth z -- 10 and 15 cm, the soil can be compacted effectively because the density increases beyond the critical density. In this case, the effect of the slip ratio on the dry density of the soil is almost lost because the alternative shear stress occurs moderately under the comparatively higher normal stress. Therefore, it was clear that when the road roller is towed by a bulldozer under the condition of the unpowered rolling state of the front roller and the skid of the rear
1.8 Od (g/cm3) 1.7
1.6 1.5
1.4 1.3 -50
-30
-i0 0 10
30 i~
50 (%)
Fig. 12. Experimental test results of dry density Pa and slip ratio of rear roller i,.
260
T. Muro and Y. Hoshika
roller (it being equal to about - 5 % ) , the terrain of the loose decomposed granite soil can be compacted most effectively.
Relationship between depth and dry density Figure 13 shows the relationship between the depth z, and the dry density of the soil Pa, after the second pass of the road roller for five combinations of front and rear roller slip. For the shallow depths z - - 5 and 8 c m , the dry density of the soil scatters noticeably according to the slip ratio or skid of the rear roller while the dry density reduces to some value regardless of the slip ratio or skid at depths of 10 and 15 cm.
CONCLUSIONS The following conclusions can be drawn from the results obtained in this investigation. 1. The soil-wheel system constants kc, kcr, k~, kcr, n, nr, me, mf, a, c 0, q , and c 2 can be expressed as a function of the dry density Pd of the loose decomposed granite soil. 2. The sinkages of the front and rear roller had minimum values at the slip ratio of the rear roller ir - 0%, and both of them increased with the increase of the absolute value of slip ratio or skid ]irl of the rear roller. 3. The absolute values of the driving or braking force of the rear roller ]Q/Rrl and the effective tractive or braking effort of the road roller ITI increased with the increment of the absolute value of the slip ratio or skid lirl of the rear roller. These gradients ]d(Q/Rr)/dirl and [dT/dirl decreased gradually with the increment of the absolute value of the slip ratio or skid ]irl of the rear roller. 4. When the road roller is towed by a bulldozer under the condition of the unpowered rolling state of the front roller and the skid of the rear roller being equal to about - 5 % , the loose decomposed granite soil can be compacted most effectively. P a
1.3
1.4
1.5
1.6
(g/cm 3) 1.7 1.8 N=2
10
15 Z (cm) 20
o -7.7 * -4.7 0-3.6 0.3 * -4.6 -4.5 " -5.2 -18.7
Fig. 13. Experimental test results of depth z and dry density Pd for five combinations of front and rear roller slip.
Tractive performance and compaction effect
261
5. The dry density of the soil decreased with the increment of the absolute value of the slip ratio or skid of the rear roller for the shallow depths of 5 and 8 cm, while the dry density was constant regardless of the slip ratio or skid at depths of 10 and 15 cm. 6. In general, the theoretical analysis results were in good agreement with the experimental data of the amount of sinkage of the front and rear roller, the driving or braking force of the rear roller, the effective tractive or braking effort of the road roller and the slip or skid ratio of the rear roller.
REFERENCES [I] T. Muro, Terramechanics--Land Locomotion Mechanics. pp. 31-74, Gihoudo Press, Tokyo, Japan (1993). [2] M. G. Bekker, Off-the-road Locomotion. pp. 25-40, The University of Michigan Press. Ann Arbor, MI (1960). [3] Z. Janosi and B. Hanamoto, The analytical determination of drawbarpull as a function of slip for tracked vehicles in deformable soils, Proc. 1st Int. Conf. on Terrain-Vehicle Systems, Torino~ Italy (1961). [4] T. Muro, K. Omoto and M. Futamura, Traffic performance of a bulldozer running on a weak terrain--vehicle model test. Proc. o f JSCE 397 VI-9, 151-157 (1988). [5] T. Muro, Braking performances of a towed rigid wheel on a soft ground based on the analysis of soil compaction. Soils and Foundations 33 (2), 91-104 (1993). [6] T. Muro, Tractive performance of a driven rigid wheel on soft ground based on the analysis of soil-wheel interaction. J. Terramechanics 30 (5), 351-369 (1993). [7] T. Muro and R. Fukagawa, The optimum height of application of force and eccentricity of a wheeled vehicle running on a loose sandy soil. J. Terramechanics 31 (5), 313-328 (1994). [8} S. Shaaban, Compaction of sand using ordinary off-road vehicles. Proc. 8th Int. Conf. of the 1STVS, Cambridge, U.K., pp. 725-735 (1984). [9] J. Y. Wong, Behaviour of soil beneath rigid wheels. J. Agric. Engng Res. 12 (4), 257-269 (1967).