DRAFT Stiffness, Strength, and Performance of Unbound Aggregate Material: Application of South African HVS and Laboratory Results to California Flexible Pavements Report produced under the auspices of the California Partnered Pavement Research Program by: H L Theyse CSIR Transportek PO Box 395 Pretoria, Republic of South Africa 0001 University of California Pavement Research Center July 2002
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DRAFT
Stiffness, Strength, and Performance of Unbound Aggregate
Material: Application of South African HVS and Laboratory
Results to California Flexible Pavements
Report produced under the auspices of the California Partnered Pavement Research Program
by:
H L TheyseCSIR Transportek
PO Box 395Pretoria, Republic of South Africa
0001
University of CaliforniaPavement Research Center
July 2002
ii
iii
TABLE OF CONTENTS
Table of Contents........................................................................................................................... iii
List of Figures ................................................................................................................................. v
List of Tables ................................................................................................................................. ix
Maximum Flakiness Index (%)§ 35 35Atterberg limits: maximum Liquid Limit (LL)**
maximum Plasticity Index (PI) ��
maximum Linear Shrinkage, % (LS) ��
2544
2563
Minimum compactionrequirements:
i) % Apparent Densityii) % mod. AASHTO compaction
86 - 88 -100 � 102 (G2)98 (G3, G4)
* Only applicable to G2 material, not G3 and G4 material.� 10% FACT (Fines Aggregate Crushing Value) is the the force in kN required to crush a sampleof aggregate passing the 13.2 mm and retained on the 9.5 mm sieve so that 10 percent of the totaltest sample will pass a 2.36 mm sieve.� The aggregate crushing value (ACV) of an aggregate is the mass of material, expressed as apercentage of the test sample which is crushed finer than a 2.36 mm sieve when a sample ofaggregate passing the 13.2 mm and retained on the 9.50 mm sieve is subjected to crushing undera gradually applied compressive load of 400 kN.§ Flakiness Index is a measure of the length to width ratio of aggregate particles** Liquid Limit is the moisture content of a soil expressed as a percentage of mass of the oven-dried soil, at the boundary between the liquid and plastic states. The moisture content at thisboundary is arbitrarily defined as the liquid limit and is the moisture content at a consistencydetermined by means of the standard liquid limit apparatus.�� Plasticity Index is the numerical difference between the liquid limit and the plastic limit of thesoil and indicates the magnitude of the range of moisture contents over which the soil is in aplastic condition.�� The linear shrinkage of a soil for the moisture content equivalent to the liquid limit, is thedecrease in one dimension, expressed as a percentage of the original dimension of the soil mass,when the moisture content is reduced from the liquid limit to an oven-dry state.
2.2.3 Quality requirement
The quality requirement for base aggregate is given in Table 6; that of subbase aggregate
is given in Table 7. The reference density for G1 aggregate is the apparent density of the course
and fine fractions combined; 86 to 88 percent of apparent density is equivalent to about 106 to
108 percent of maximum dry density (MDD) determined according to the modified AASHTO
(T-180) method.
9
Table 7 Quality Requirement for Subbase AggregateMaterial TypePropertyG5 G6
Maximum swell (%) at 100 % mod. AASHTO compaction 0.5 1.0Gradation requirement (maximum stone size)
Minimum gradation modulus
63 mm or2/3 of layerthickness
1.5
63 mm or2/3 of layerthickness
1.2Atterberg limits: maximum Liquid Limit (LL)
maximum Plasticity Index (PI)maximum Linear Shrinkage, % (LS)
30105
-12-
Min. Compaction requirements (% mod. AASHTO compaction) 95 95
2.3 Comparison of the California and South Africa Aggregate Specifications
2.3.1 Source of Material
The South Africa aggregate specification is more specific than the California
specification in terms of the origin of crushed stone aggregate and how the individual particles
are fractured, especially in the case of the South Africa specification G1 and G2 aggregates.
The California specification allows for a high percentage (up to 50 percent) of reclaimed
material in the aggregate. The South Africa specification allows for the use of reclaimed
pavement material as G4 to G6 material if the reclaimed material satisfies the specification for
these material categories. No clear indication is given on the use of reclaimed pavement material
for G1 to G3 material.
In the case of G1 material, the strict specification for this type of aggregate should rule
out the use of reclaimed material. However, a material that was originally placed as a G1 may
after years of service still comply with the specification for a G2 or G3 material and presumably
may be used as such.
10
2.3.2 Gradation Requirement
Although not identical, the gradation requirement for the California Class 2 aggregate for
base layers with a maximum size of 19 mm seems to be similar to the gradation requirement for
a G2/G3 material with a 26.5-mm maximum particle size. This similarity in gradation envelope
is illustrated in Figure 1. The colored solid squares in Figure 1 represent the control points for
the gradation of a 19-mm maximum size crushed stone aggregate according to the California
specification and the black lines represent the gradation envelope for a 26.5-mm maximum size
aggregate according to the South Africa specification.
0
10
20
30
40
50
60
70
80
90
100
0.01 0.10 1.00 10.0 100Sieve size (mm)
Perc
enta
ge p
assi
ng b
y m
ass
G1 to G3 crushed stone 37.5mm maximum size
AB 19 mm maximum size
Figure 1. Comparison of the gradation envelopes for a 19-mm maximum size base layeraggregate from California and a 26.5-mm maximum size base layer aggregate from SouthAfrica.
11
Figure 2a shows the dry gradation of three actual aggregate samples obtained from
California base layers and sent to CSIR by the University of California Pavement Research
Center, plotted with the South Africa gradation control points for a 26.5-mm maximum size
crushed stone base layer aggregate as a reference. It is clear from this figure that the actual
gradation of the California aggregate complies with the South Africa specification except for the
larger particle sizes for which the actual gradation deviates slightly from the South Africa
specification. Figure 2b shows the dry gradation of the three samples plotted with the control
points for a dense aggregate gradation for a 19-mm maximum particle size material according to
the Talbot equation. The Talbot equation estimates the gradation that will result in the maximum
packing of particles for a given maximum aggregate size. It seems likely that the gradation of
the California aggregate is based on the dense aggregate gradation for a 19-mm maximum
particle size material.
Figure 3 shows the South Africa gradation envelope for a G4 aggregate and the
California gradation control points for a Class 1 subbase aggregate plotted on the same graph.
Although not exactly the same, there are similarities between the South Africa and California
gradation specification. The South Africa specification limits the maximum particle size to 53
mm while the corresponding value for the California specification is 75 mm.
2.3.3 Quality Requirement
It is not possible to make a direct comparison between the quality criteria of California
and South Africa aggregate as the parameters that are used to quantify the quality of the material
differ between California and South Africa.
There are, however, two factors that largely influence the quality of compacted aggregate
material: 1) the density levels to which the material is compacted, and 2) the moisture content of
12
0
10
20
30
40
50
60
70
80
90
100
0.01 0.10 1.00 10.00 100.0Sieve size (mm)
Perc
enta
ge p
assi
ng b
y m
ass
Sample 1
Sample 2
Sample 3Grading control points for G1 toG3 crushed stone, 26.5 mm max size
Figure 2a. Comparison of California samples with South Africa gradation control pointsfor a 26.5-mm maximum particle size aggregate.
0
10
20
30
40
50
60
70
80
90
100
0.01 0.10 1.0 10.0 100Sieve size (mm)
Perc
enta
ge p
assi
ng b
y m
ass
Grading control points for G1 to G3crushed stone, 19 mm max sizeSample 1Sample 2Samp le 3
Figure 2b. Comparison of California samples with dense aggregate gradation controlpoints for a 19-mm maximum particle size aggregate.
13
0
10
20
30
40
50
60
70
80
90
100
0.01 0.10 1.00 10.00 100.00
Sieve size (mm)
Perc
enta
ge p
assi
ng b
y m
ass
G4 aggregate
Class 1 subbase aggregate
Figure 3. Comparison of the gradation envelopes for Class 1 subbase aggregate(California) and G4 aggregate (South Africa).
the material. As stated in the Introduction, the objective of this report is to illustrate the validity
of this statement and to make this statement at this point is in a sense preempting the outcome of
this study. The South Africa specification for aggregate material quality is, however, based on
the principle that the density and moisture content of the material influences the quality of the
compacted material. Therefore, in order to fully appreciate the South Africa material quality
specification, it is necessary to provisionally accept this statement. Two examples of real data
are included in this section of the report to substantiate this statement. Additional information on
the effect of density and moisture content on the stiffness, strength, and plastic deformation of
unbound aggregate are presented later in this report.
14
Figure 4 shows the CBR results for the three aggregate samples sent from California to
CSIR compacted with the same amount of compaction energy at various moisture content levels.
Although the density of the samples varied slightly, the effect that the relatively large variation in
compaction moisture content had on the soaked CBR of the material overshadowed the effect
that the relatively small variation in density had on the CBR.
Figure 5 shows the soaked CBR results of a number of samples of a G2 crushed stone
aggregate from South Africa compacted with various compaction efforts. In this case the
moisture content of the samples are about the same but the density varied and the effect of the
density variation on the CBR of the material is clear.
The influence of density and moisture content on the quality (in the case of the examples,
measured in terms of CBR) of the material is amply illustrated by the examples given in Figures
4 and 5. The influence of these parameters on the quality of the compacted material is
incorporated in the South Africa specification for unbound aggregates. The minimum CBR for a
specific aggregate category is given for a certain relative density under soaked moisture
conditions. The minimum CBR for a G2, G3, and G4 classification is 80 percent at 98 percent of
maximum dry density (MDD) determined according to the modified AASHTO (T-180)
compaction method (see Table 6). The corresponding CBR values for a G5 and G6 classification
are 45 and 25 percent at 95 and 93 percent relative density, respectively (see Table 7). All of
these CBR values are soaked condition (4 days in a water bath) CBR values. The California
specification for unbound aggregate does not specify a reference density and moisture content at
which the R-value should be determined.
15
0
50
100
150
200
250
300
350
4 4.5 5 5.5 6 6.5 7 7.5 8
Moisture content (%)
CB
R (%
)
Sample 1
Sample 2
Sample 3
Figure 4. Combined CBR data for the three aggregates from California showing therelationship between compaction moisture content and CBR.
Figure 9. The effective stiffness modulus of crushed stone aggregate for the duration ofHVS test 398a4.
The low permeability of the crushed stone aggregate base largely prevented water from entering
the base layer.
3.2 Permanent Deformation Response of Unbound Aggregate Under HVS Testing
In addition to the depth deflection data, each MDD stack produced a set of permanent
vertical MDD displacement results. This is achieved by recording the voltage output from the
MDD modules at rest at various stages during the test. Various studies have been completed on
the analysis of the MDD displacement and permanent deformation data generated by an HVS
test.(7, 9, 10 ) In this case, the function listed in Equation 2 was fitted to the MDD displacement
data of the HVS tests listed in Table 8.
29
( )bNeaNmPD −−+= 1 (2)
Where PD = permanent vertical MDD displacementN = number of load repetitionsa,b,m = regression coefficientse = base of the natural logarithm
This function allows for two behavioral phases: an initial exponential bedding-in phase
and a long-term linear rate of increase in the permanent vertical MDD displacement as is
illustrated in Figure 10.
Equation 2 has an initial slope equal to the product of the two regression coefficients a
and b, a curvature determined by the value of b, an eventual linear slope equal to the regression
coefficient m, and an intercept with the Y-axis represented by the regression coefficient a. The
bedding-in phase, represented by the coefficient a and the eventual deformation rate, represented
by coefficient m are the two important parameters in the process of evaluating the permanent
MDD displacement data for an HVS test. Once the initial bedding-in (a) and the eventual rate of
permanent deformation (m) are known, it is possible to calculate the number of repetitions that
would be required to induce a certain amount of plastic strain in an unbound aggregate layer
bearing capacity.
Table 11 gives the bedding-in, eventual deformation rate, and the base bearing capacity
for 20 mm permanent base layer deformation for the HVS tests sections listed in Table 8 at a
number of MDD locations at which the permanent deformation of the aggregate base layer was
recorded.
The thickness of the base layers of the HVS test sections listed in Tables 8 and 11
differed and the results from Table 11 were converted to plastic strain values by dividing the
bedding-in deformation and the rate of deformation by the original thickness of the layer. Figure
11 shows the plastic deformation and base bearing capacity results obtained from this process.
30
N
PD
a
mN1
Eventualdeformationrate = m
a(1 - e )-bN
Initial deformation rate = ab
CurvatureBedding-indisplacement
Figure 10. Illustration of typical base permanent deformation (rutting) behavior.Note: PD = permanent deformation (rut depth or permanent vertical strain).
46.8
46.8
27.627.633.3
33.3
42.3
42.3
33.3
33.356.4
56.4
0
0.5
1
1.5
2
2.5
3
0 20 40 60 80 100 120
Dual Wheel Load (kN)
Even
tual
Pla
stic
Str
ain
Rat
e (%
/mill
ion
repe
titio
ns)
Figure 11a. Plastic strain rate.
31
27.6
46.8
46.8
56.4
56.433.333.3
42.3
42.333.333.3
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 20 40 60 80 100 120
Dual Wheel Load (kN)
Plas
tic S
trai
n B
eddi
ng-in
(%)
Figure 11b. Bedding-in plastic strain.
46.8
46.8
27.627.633.3
33.3
42.342.356.4
56.433.3
33.3
1.00E+05
1.00E+06
1.00E+07
1.00E+08
1.00E+09
0 20 40 60 80 100 120
Dual Wheel Load (kN)
Plas
tic S
trai
n B
eddi
ng-in
(%)
Figure 11c. Base bearing capacity for 20 mm plastic deformation of the base layer.
Figure 11. Bedding-in plastic strain, plastic strain rate, and bearing capacity results for anumber of crushed stone aggregate layers determined from HVS testing.
32
Table 11 Base Bedding-in Displacement, Deformation Rate, and Bearing CapacityResults for a Number of Crushed Stone Aggregate Base Layers from HVSTest Sections
The data labels associated with each of the data points indicate the moisture content of
the aggregate material expressed as a ratio of the field compaction water content over the
optimum compaction moisture content of the material (modified AASHTO compaction). An
increase in wheel load and moisture ratio causes an increase in the bedding-in plastic strain and
the eventual plastic strain rate of the unbound aggregate material.
No clear trend could be established between the density of the material and the plastic
deformation characteristics. The laboratory test results presented in Section 4 provide a better
33
opportunity for studying the effect of density and saturation on the permanent deformation
characteristics of unbound aggregate as these parameters are better controlled under laboratory
conditions.
3.3 Permeability of an Unbound Aggregate Base and Drainable Subbase on an HVSTest Section
It is evident from the data presented in Section 2 that the moisture content or degree of
saturation has an influence on the effective stiffness and permanent deformation of unbound
aggregate. The degree of saturation is in turn determined principally by the supply of water to
the material, and secondarily by the permeability of the material, which will allow or prevent the
moisture from entering the material.
Van der Merwe investigated the use of a permeable subbase drainage layer on HVS Test
Section 303a2.(11) The detail of the pavement structure for Section 303a2 is shown in Appendix
A. The subbase drainage layer was constructed from the same crushed stone aggregate used for
the base layer but the gradation was not adjusted to meet the requirement for G1 and G2
aggregate. The gradation of the base and subbase aggregate, which was basically from the same
source, influenced both the density to which the material could be compacted and the
permeability of the material. Table 12 provides information on the gradation, density, and
moisture content of the base and subbase layer aggregate for Section 303a4.
Figure 12 shows the gradation of the base and subbase aggregate compared to the
gradation envelope control points for a 37.5-mm maximum size aggregate for G1 to G3 material.
Table 13 lists the permeability coefficient of the base and subbase aggregate as a function of the
relative density of the material. The data from Table 13 is shown in Figure 13. The effect of
gradation and density on the permeability of unbound aggregate is clearly illustrated by the data
34
Table 12 Gradation, Density, and Moisture Content Properties of the Crushed StoneAggregate from the Base and Drainable Subbase Layers from Section 303a2
Pavement Layer Base DrainableSubbase
Maximum mod. AASHTO density(kg/m3) 2198 2027
Optimum moisture content (%) 7.7 9.9
Referencedensity andmoisturecontent Apparent density (kg/m3) 2658 2643
0.075 5.3 5.0Percent modified AASHTO maximumdry density 97.8 99.9
Percent apparent density 80.8 76.6
Field densityand moisturecontent Field moisture content (percent) 4.4 2.8
0
10
20
30
40
50
60
70
80
90
100
0.01 0.10 1.0 10 100Sieve Size (mm)
Perc
enta
ge P
assi
ng b
y M
ass
G1 to G3 crushed37.5 mm maxBas
Drainable
Figure 12. Gradation of the base and drainable subbase aggregate from HVS Test Section303a2.
35
Table 13 Permeability Coefficient of the Base and Subbase Aggregate from HVS TestSection 303a2 as a Function of Relative Density (Modified AASHTOCompaction)
Figure 13. Permeability coefficient of the base and subbase aggregate from HVS TestSection 303a2 as a function of relative density (modified AASHTO compaction).
36
in Figure 13. The subbase material had a much higher permeability than the base material and
the permeability of the base material reduced almost ten times with an associated increase in
relative density from 85 to 86.2 percent.
Van der Merwe concluded that the structural strength of an untreated drainage layer is
insufficient and the layer deformed under traffic. The permeability of the layer below the
drainage layer also needs to be low enough to prevent water from entering the layer below the
drainage layer. Although the permeability of the material below the drainage layer may be low
enough to prevent water from entering this layer, the effective permeability of the layer may be
much higher if cracks are present in the layer supporting the drainage layer.(11)
37
4.0 LABORATORY STUDIES ON UNBOUND AGGREGATE
The information in this section is largely based on three laboratory investigations of
unbound aggregate. Two of these studies conducted by Maree and Theyse concentrated on the
stiffness, static shear strength, and plastic deformation potential of unbound aggregate.(12, 13)
The third study conducted by Semmelink investigated the compaction potential of unbound
material including crushed stone and natural gravel aggregate.(14) Static and dynamic triaxial
testing formed the basis of the studies by Maree and Theyse.(12, 13)
4.1 The Stiffness of Unbound Aggregate Under Laboratory Testing
Maree investigated the effect of several variables on the relationship between the effective
stiffness or resilient modulus and the bulk stress given in Equation 2. Table 14 lists a summary
of his findings.
Maree concluded that the stress condition and degree of saturation are the most important
parameters determining the effective stiffness for crushed stone aggregate with density being the
third most important factor. He also speculated that the degree of saturation might become the
dominant factor in determining the effective stiffness of lower quality aggregate.
In addition to the stress-stiffening model from Equation 2, Maree also investigated the
model shown in Equation 3, which incorporates both a stress-stiffening and stress-softening
component linked to the octahedral normal and shear stress, respectively. This model is similar
to the one suggested by May and Witczak (15) and Uzan (16) shown in Equation 4. Maree
found a better correlation between the resilient modulus and the octahedral normal and shear
stress than between the resilient modulus and bulk stress alone.
38
Table 14 Factors Affecting the Relationship between the Resilient Modulus and theBulk Stress Condition of Unbound Aggregate
Influence onFactor Change in Factor K n MRDuration ofload pulse 0.1 to 1.0 s No effect No effect No effect
Frequency ofload pulse 0.3 to 1.0 Hz No effect No effect No effect
Number ofload cycles
Increase in loadcycles 0�20% higher No effect to a
slight reduction Up to a 20% increase
Load history - No effect No effect No effectConfiningpressure
Constant vs.pulsed
No uniqueeffect detected
No uniqueeffect detected
Constant pressure slightlyoverestimates MR
Sampledensity
increase from 82.6to 87.5% ofapparent density
100% increase 15% reduction 10% increase
Maximumparticle size 19.5 and 37.5 mm No effect No effect No effect
Percentagematerial <0.075 mm
Increase in fines Slight increase Slight increase Optimum at 9% fines
Particle shape Increase inangularity Not determined Not determined Slight increase
Surfacetexture More course Not determined Not determined Slight increase
Degree ofsaturation
increase from 20to 90%
Up to 80%decrease 25% increase Up to 60% decrease
( ) ( ) 321
koct
koctR kM τσ= (3)
Where MR = Resilient or effective stiffness modulus (MPa)θ = Bulk stress σ1 + σ2 + σ3 (kPa)σoct = Octahedral normal stress = θ/3 (kPa)τoct = Octahedral shear stress = 0.47 σd for the triaxial test (kPa)ki = Regression coefficients, i = 1 to 3
32
1
k
a
dk
aR pp
kM
= σθ (4)
Where MR = Resilient or effective stiffness modulus (MPa)θ = Bulk stress σ1 + σ2 + σ3 (kPa)σd = Deviator stress σ1 � σ3 (kPa)pa = Reference stress (kPa)ki = Regression coefficients, i = 1 to 3
39
Theyse tested a crushed stone aggregate in the repeated load triaxial test as part of a
laboratory project done in association with the HVS testing of several construction labor-
intensive base layers. Table 15 contains the secant modulus values representing the effective
stiffness or resilient modulus for a crushed stone aggregate obtained from dynamic triaxial tests
for different combinations of dry density and degree of saturation.
Table 15 Resilient Modulus Values for a Crushed Stone Aggregate at DifferentCombinations of Density and Saturation
Theyse investigated the effect of dry density and degree of saturation on the effective
stiffness of the crushed stone material in addition to the effect of the stress condition on the
effective stiffness. The stress condition is represented by the confining pressure, which will tend
to cause stress-stiffening behavior, and the stress ratio, which will cause a reduction in effective
stiffness as the maximum shear strength of the material is approached. The function in Equation
40
5 was fitted to the data from Table 15. Figure 14 shows a plot of the observed and predicted
values for the resilient modulus of the crushed stone aggregate that was tested.
SRSRDM R 87.082.072.204.1496.527 3 −+−+−= σ (5)
R2 = 81.2 % and Standard Error of Estimate (SEE) = 45.4 MPaWhere MR = Resilient modulus (MPa)
RD = Relative density (% of apparent density)S = Degree of saturation (%)σ3 = Confining pressure or minor principal stress (kPa)SR = Stress ratio (applied shear stress expressed as a percentage of the shear
strength of the material at the specific confining pressure)
The four variables � relative density, degree of saturation, confining stress and stress
ratio � explain about 81 percent of the variation in the effective stiffness of the crushed stone
aggregate. According to the regression model, an increase in the relative density and confining
pressure will result in an increase in the effective stiffness of the material. In addition, an
300
350
400
450
500
550
600
650
700
300 350 400 450 500 550 600 650 700
Measured Stiffness (MPa)
Pred
icte
d St
iffne
ss (M
Pa)
Figure 14. The observed and predicted values of the resilient modulus for a crushed stoneaggregate.
41
increase in the degree of saturation and stress ratio will result in a decrease in the effective
stiffness of the material. The rate of change in effective stiffness associated with a unit increase
in relative density is the highest, followed by the rate of decrease associated with the degree of
saturation. The rates of change associated with a unit change in confining pressure and stress
ratio are of the same order of magnitude. The relative density therefore appears to be the
variable that will most influence the effective stiffness. The range of practical values for the
relative density (80�88 percent or apparent density) is, however, much narrower than that of the
degree of saturation (30�100 percent) and the degree of saturation may therefore have the biggest
impact on the effective stiffness of the crushed stone material.
The range of laboratory stiffness values reported in Table 15 agrees well with the range
of HVS back-calculated effective stiffness values reported in Table 10 and shown in Figure 8,
except for two relatively low values from HVS Tests 101a4 and 303a2.
In summary, it appears that the range of effective stiffness values for crushed stone
aggregate may be expected to vary from about 350 to 700 MPa based on HVS and laboratory
results. A major portion of this variation in effective stiffness may be explained by variation in
the relative density and the degree of saturation of the material and stress condition imposed on
the material. Most of the more recent resilient modulus models for unbound aggregate allow for
a combination of stress-stiffening and stress-softening behavior for unbound aggregate. The
stress-stiffening behavior is normally associated with an increase in the confinement of the
material that may be quantified by the minor principle stress, the bulk stress, or the octahedral
normal stress. The stress-softening behavior is normally associated with the level of shear stress
imposed on the material and may be quantified by the deviator stress, octahedral shear stress, or
42
the stress ratio expressing the applied shear stress as a percentage of the shear strength of the
material for the given value of the minor principle stress.
4.2 Static Shear Strength Parameters of Unbound Aggregate
Maree (17) re-analyzed existing static triaxial data and performed additional static triaxial
tests on several crushed stone and natural gravel aggregates from which the influence of several
parameters on the static shear strength parameters of unbound aggregate were identified. Table
16 gives a summary of these parameters and their influence on the shear strength parameters.
Table 16 Factors Affecting the Relationship Between the Resilient Modulus and theBulk Stress Condition of Unbound Aggregate
Figure 19a. Friction angle and cohesion results plotted against relative density and degreeof saturation for natural gravel aggregate; component effect: compaction
G4
G4
G9
G9
G4
G4/G5
G5
G5
G5
G5
35.0
40.0
45.0
50.0
55.0
60.0
20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0 100.0
Saturation (%)
Fric
tion
angl
e (d
eg)
Figure 19b. Friction angle and cohesion results plotted against relative density and degreeof saturation for natural gravel aggregate; component effect: saturation.
m = maximum allowable major principal stress (kPa) given C, φ and σ3σ1
w, σ1a = working or applied major principal stress (kPa)
σ3 = minor principal stress or confining pressure for the triaxial test(kPa)
Φ
Möhr-Coulomb failure envelope
ΦmbΦc
b ΦwbΦm
aΦca Φw
a
Internalfrictionangle, Ν
Stress ratio SR =Φm
a - Φca
Φwa - Φc
a
Φmb - Φc
bΦw
b - Φcb
Cohesion
Figure 22. Equal values for the stress ratio generated at different values of absolute stress.
59
Figure 23 shows typical examples of S-N (stress ratio - N) data sets for three plastic strain
levels (3, 7, and 13 percent) for crushed stone aggregate at 80.7 percent relative density (relative
to apparent density) and at 33.4 and 78 percent saturation. The large influence of the degree of
saturation on the number of load repetitions that can be sustained before a certain level of plastic
strain is induced in the material, is evident from the data shown in Figure 23. Dynamic triaxial
tests were also performed at 84.5 percent relative density and two levels of saturation to fully
investigate the effect of relative density and degree of saturation on the number of load cycles
that the crushed stone aggregate could sustain for different levels of plastic strain. The S-N data
for the four possible combinations of relative density and degree of saturation at which tests were
done were combined and a regression analysis was done for 3, 5, 7, 9 and 13 % plastic strain.
The regression model is given in Equation 13 and Figure 24 contains contour plots of the model
for different combinations of relative density and degree of saturation.
SRPSSRDN 02.007.007.029.043.13log −+−+−= (13)
R2 = 97.3 %; SEE = 0.313
Where:N = Number of load repetitionsRD = Relative density (%)S = Degree of saturation (%)PS = Plastic strain (%)SR = Stress ratio (%)
4.4 Compaction Potential of Unbound Aggregate
The plastic strain model for a crushed stone aggregate presented in the previous section
indicated that the density of unbound aggregate had a major influence on the plastic strain of the
aggregate when subjected to repeated loading. This section presents a brief overview on the
compaction potential of unbound aggregate from a study by Semmelink (14).
60
1.00E+05
1.00E+06
1.00E+07
1.00E+08
40% 50% 60% 70% 80% 90% 100%
Stress Ratio
Load
cyc
les
3% 7% 13%
Figure 23a. Stress ratio � N data set for crushed stone aggregate, 80.7 percent relativedensity and 33.4 percent saturation.
1.00E+02
1.00E+03
1.00E+04
1.00E+05
40% 50% 60% 70% 80% 90% 100%
Stress Ratio
Load
cyc
les
3% 7% 13%
Figure 23b. Stress ratio � N data set for crushed stone aggregate, 80.7 percent relativedensity and 78 percent saturation.
61
0.00E+00
1.00E+072.00E+07
3.00E+074.00E+07
5.00E+07
6.00E+077.00E+07
8.00E+079.00E+07
1.00E+08
0 20 40 60 80 100
Stress Ratio (%)
Bea
ring
Cap
acity
(loa
d re
petit
ions
)
3
5
7
9
11
13
Plastic strain (%)
Figure 24a. Contour plot of the permanent deformation bearing capacity model for theunbound aggregate tested by Theyse, 86 percent relative density, 70 percent saturation.
0.00E+00
1.00E+072.00E+07
3.00E+074.00E+07
5.00E+07
6.00E+077.00E+07
8.00E+079.00E+07
1.00E+08
0 20 40 60 80 100
Stress Ratio (%)
Bea
ring
Cap
acity
(loa
d re
petit
ions
)
3
5
7
9
11
13
Plastic strain (%)
Figure 24b. Contour plot of the permanent deformation bearing capacity model for theunbound aggregate tested by Theyse, 86 percent relative density, 45 percent saturation.
62
0.00E+00
1.00E+072.00E+07
3.00E+074.00E+07
5.00E+07
6.00E+077.00E+07
8.00E+079.00E+07
1.00E+08
0 20 40 60 80 100
Stress Ratio (%)
Bea
ring
Cap
acity
(loa
d re
petit
ions
)
3
5
7
9
11
13
Plastic strain (%)
Figure 24c. Contour plot of the permanent deformation bearing capacity model for theunbound aggregate tested by Theyse, 88 percent relative density, 70 percent saturation.
0.00E+00
1.00E+072.00E+07
3.00E+074.00E+07
5.00E+07
6.00E+077.00E+07
8.00E+079.00E+07
1.00E+08
0 20 40 60 80 100
Stress Ratio (%)
Bea
ring
Cap
acity
(loa
d re
petit
ions
)
3
5
7
9
11
13
Plastic strain (%)
Figure 24d. Contour plot of the permanent deformation bearing capacity model for theunbound aggregate tested by Theyse, 88 percent relative density, 45 percent saturation.
63
The compaction potential is the expected practical maximum compaction that can be
achieved for a given material. It is largely determined by the particle size distribution of the
material. A higher density can be achieved with a continuously graded material than with a
uniformly graded material of the same type. Semmelink therefore investigated the possibility of
developing empirical predictive models for the maximum achievable density of an unbound
aggregate, based on the particle size distribution of the material. The smallest sieve size used for
routine grading analysis in South Africa is the 0.075 mm sieve. Instead of using the actual
particle size distribution of the minus 0.075 mm fraction, which would have required hydrometer
testing, in his models Semmelink used the liquid limit (LL) and linear shrinkage (LS) to
characterize the minus 0.075 mm fraction material.
The approach followed by Semmelink deviates from that of Fuller and Talbot in the sense
that they prescribe the requirements that the grading of the material has to meet in order to
ensure that the maximum density is achieved. The grading of an aggregate from a natural source
is, however, a given and it is not always possible or economically feasible to alter the grading.
Semmelink therefore approached the problem with the aim of predicting the maximum
achievable density for a given particle size distribution. The level of compaction that is achieved
also depends on the compaction energy that is employed. Semmelink therefore developed
models for modified AASHTO and vibratory table compaction effort. Each of these compaction
methods has an optimum moisture content (OMC) associated with it. In addition to the density
models, Semmlink also developed predictive models for estimating the optimum compaction
moisture content for a given material and compaction effort.
Where:C = (percentage passing the 0.425 mm sieve/100)/(LL/100)0.1
GF = Σ(percentage passing a particular sieve size/nominal sieve size)/100 forthe 75 mm, 63 mm, 53 mm, 37.5 mm, 26.5 mm, 19 mm, 13.2 mm, 4.75mm, and 2 mm sieves
LS = linear shrinkageLL = liquid limit
All of the above models had correlation coefficients higher that 90 percent and provide
good estimates of the maximum achievable density of a material for which particle size
distribution and Atterberg limits are known.
65
5.0 CONCLUSIONS AND RECOMMENDATIONS
Although the methods of specification for unbound granular material in South Africa and
California differ, the basic materials seem to be similar for certain aggregate classes. The end
product that is placed in a pavement layer is, however, expected to have different stiffness,
strength, and performance levels because of the differences in specification. Data presented in
this document illustrate the effect of the moisture content and density of an unbound material on
the bearing strength of the material. The South Africa specification allows this to be taken into
consideration when an unbound granular material is used in different pavement layers. The
specification requires a higher density and bearing strength for layers closer to the pavement
surface than for layers deeper down. The California specification does not incorporate the
influence of density and moisture content on the bearing strength of the material. Furthermore,
the California method for determining the reference density for compaction control effectively
utilizes the wet density of the material. The following specific recommendations are therefore
made regarding the California specification for the use of unbound granular material in
pavements:
• The influence of density and moisture content on the bearing strength of the material
should be incorporated in the specification. Bearing strength requirements for
different pavement layers should be specified at specific density and moisture content
levels.
• It is strongly recommended that the method for determining the reference density for
compaction control should be changed to a method that utilizes dry density and that
the compaction effort for the test should be increased above the currently required 95
66
percent relative to CTM 216, or a modified wet density such as in the Bureau of
Reclamation manual (18).
As far as the effective stiffness of unbound granular material is concerned, HVS test
results indicate that there is an increase in stiffness associated with an increase in the stress
condition to which the unbound material is subjected. The correlation between resilient modulus
and the bulk stress determined from the back-calculation of depth deflection results is, however,
relatively poor although there is a general increase in resilient modulus as the bulk stress
increases. There are several possible explanations for the relatively poor correlation. The bulk
stress is calculated from linear elastic theory, which may lead to some error in the value of the
bulk stress. The laboratory test results presented in this report indicate a strong dependency of
the effective stiffness of unbound granular material on the density and moisture content of the
material. These factors are often difficult to quantify for HVS tests and their effects on the back-
calculated resilient modulus were not included in the correlation between the resilient modulus
and bulk stress calculated from HVS data. The following parameters were identified as having
an influence on the resilient response of unbound aggregate based on the HVS and laboratory
data presented:
• The dry density of the material expressed as a percentage of the solid density of
the material. The rate of change in the resilient modulus of unbound aggregate
associated with a unit change in the relative dry density of the material is higher than
the rate of change associated with changes in other parameters. The range of realistic
values for the dry density of unbound aggregate is, however, limited to a range of
values between about 78 and 88 percent of apparent density, thus limiting the overall
effect on the resilient modulus.
67
• The degree of saturation of the unbound aggregate. The degree of saturation of
the unbound material has a significant influence on the resilient modulus of the
material. Realistic values for the degree of saturation can vary between 30 and 100
percent, thereby having a relatively large influence on the resilient response of the
material.
• The level of confinement of the unbound material. An increase in the level of
confinement of unbound aggregate causes the material to respond in a stiffening
manner with an associated higher value for the resilient modulus of the material. The
confinement may be quantified by the minor principal stress, the octahedral normal
stress, or the bulk stress.
• The shear stress imposed on the material. In addition to the stress stiffening
behavior of unbound material, there is also a reduction in stiffness as the shear
strength of the material is approached. The imposed shear stress may be quantified
by the deviator stress, the octahedral shear stress or the stress ratio.
The static shear strength of unbound aggregate is influenced by the relative dry density
and degree of saturation of the material. The friction angle of crushed stone aggregate shows a
general increase as the relative dry density increases and the cohesion decreases as the degree of
saturation increases. There are, however, other factors that have an influence on the static shear
strength parameters of the material, such as the particle size distribution and the characteristics of
the course and fine particles in the material. Predictive models relating the shear strength
parameters of unbound materials to the particle size distribution of the material and the
characteristics of the course and fine aggregate particles should be investigated.
68
The permanent deformation of unbound granular material is affected by the following
parameters:
• the relative dry density of the material;
• the degree of saturation of the material, and
• the combined level of confining and shear stress imposed on the material. This
combined confining and shear stress condition is best represented by the stress ratio
concept as defined in this report. The stress ratio is, in turn, determined by the shear
strength parameters of the material, which depend on the relative dry density and
degree of saturation of the material.
Predictive models for the permanent deformation bearing capacity of unbound aggregate
incorporation the effect of relative dry density, degree of saturation, and stress ratio are presented
in this report. These models were calibrated for specific aggregates with a relatively high degree
of accuracy, but need to be extended to cover a wider range of materials used in California.
69
6.0 REFERENCES
1. California State Department of Transportation (Caltrans). Caltrans Highway DesignManual. Sacramento, California. November, 2001.
2. Caltrans. 1999. Test Plan for CAL/APT Goal 5. University of California at BerkeleyPavement Research Center, Transportek, and Dynatest Consulting, Inc.
3. Bejarano, M. O., J. T. Harvey, A. Ali, M. Russo, D. Mahama, D. Hung, and P. Preedonant.Performance of Drained and Undrained Flexible Pavement Structures under WetConditions Accelerated Test Data Test Section 543�Drained. Report prepared for CaliforniaDepartment of Transportation by the University of California Pavement Research Center.August 2002.
4. Bejarano, M. O., J. T. Harvey, A. Ali, M. Russo, D. Mahama, D. Hung, and P. Preedonant.Performance of Drained and Undrained Flexible Pavement Structures under WetConditions Accelerated Test Data Test Section 544�Undrained. Report prepared forCalifornia Department of Transportation by the University of California Pavement ResearchCenter. August 2002.
5. Bejarano, M. O., J. T. Harvey, A. Ali, M. Russo, D. Mahama, D. Hung, and P. Preedonant.Performance of Drained and Undrained Flexible Pavement Structures under WetConditions Accelerated Test Data Test Section 545�Undrained. Report prepared forCalifornia Department of Transportation by the University of California Pavement ResearchCenter. August 2002.
6. Bejarano, M. O., J. T. Harvey, A. Ali, D. Mahama, D. Hung, and P. Preedonant.Performance of Drained and Undrained Flexible Pavement Structures under Conditions ofSaturated Base - Accelerated Pavement Testing Evaluation Goal 5 HVS. Report prepared forCalifornia Department of Transportation by the University of California Pavement ResearchCenter. August 2002.
7. Shackelton M C. 1995. Modelling of the Permanent Deformation of Untreated PavementLayers. M Eng thesis, University of Pretoria, Republic of South Africa.
8. Maree, J H, van Zyl, N J W and Freeme, C R. 1982. �Effective Moduli and StressDependence of Pavement Materials as Measured in some Heavy Vehicle Simulator Tests.�Transportation Research Record 852, Transportation Research Board, Washington D.C., pp.52�60.
9. Wolff H. 1992. Elasto-Plastic Behaviour of Granular Pavement Layers in South Africa. Ph.D. thesis, University of Pretoria, Republic of South Africa.
10. Theyse H L. 1997. �Mechanistic Empirical Modelling of the Permanent Deformation ofUnbound Pavement Layers.� Proceedings of the Eighth International Conference on theStructural Design of Asphalt Pavements. Seattle, University of Washington, pp 1579�1594.
70
11. Van der Merwe, C J. 1988. Some aspects of road subsurface drainage in South Africa. Ph.D. thesis, University of Pretoria, Republic of South Africa.
12. Maree J H. 1982. Aspekte van die Ontwerp en Gedrag van Padplaveisels metKorrelmateriaalkroonlae. (Aspects of the Design and Behavior of Road Pavements withGranular Base Layers). Ph. D. thesis, University of Pretoria, Republic of South Africa.
13. Theyse, H L. 1999. Laboratory Design Models for Materials Suited to Labour-intensiveConstruction. Contract Report CR-99/038, Transportek, CSIR, Pretoria, Republic of SouthAfrica.
14. Semmelink ,C J. 1991. The Effect of Material Properties on the Compactability of SomeUntreated Road-building Materials. Ph. D. thesis, University of Pretoria, Republic of SouthAfrica.
15. May, R W and Witczak, M W. 1981. �Effective granular modulus to model pavementresponse.� Transportation Research Record 810, Transportation Research Board,Washington D.C., pp. 1�9.
16. Uzan, J. 1985. �Characterization of Granular Materials.� Transportation Research Record1022, Transportation Research Board, Washington D.C., pp. 52�59.
17. Maree J H. 1978. Ontwerpparameters vir Klipslag in Plaveisels. (Design Aspects forCrushed Stone in Pavements). M Eng. thesis, University of Pretoria, Republic of SouthAfrica.
18. California State Department of Transportation (Caltrans). Standard Specifications.Sacramento, California. July 1999.
71
APPENDIX A: PAVEMENT AND INSTRUMENTATION DETAIL OF HVS TESTSECTIONS
HVS-section Nr: Region: Road Nr: Year of test:Pavement structure Instrumentation detail Pavement material information
Test section point
MDD anchorat 3 m depth
MDD anchorat 3 m depthDepth (mm)
Layer Type
(UCS, CBR, MDD, OMC,etc) class
Material properties TRH14
Load sequence detail: Related reports:
303A2 Macleantown, Eastern Cape TR86 1986
van der Merwe C J, Horak E. 1986. East London HVS experimental sections: Objectives and
preliminary investigation. National Institute of Transport and Road Research (NITRR), CSIR.
(Technical Note TPC/1/86)
From To Wheel load Tyre pressure Water added
Repetitions Test information
0 411 413
411 413 531 896
100 kN 690 kPa
40 kN 520 kPa
No
Yes
0 2 4 6 8 10 12 14 16MDD
Topcap
MDD180
MDD330
MDD630
0
100
200
300
400
500
600
700
800
900
1000
MDDTopcap
MDD180
MDD330
MDD630
van der Merwe C J, de Villiers E M, Horak E. 1987. HVS aided evaluation of a drainable subbase
layer in the Eastern Cape. NITRR, CSIR. (Research Report RR486)
HVS-section Nr: Region: Road Nr: Year of test:Pavement structure Instrumentation detail Pavement material information
Test section point
MDD anchorat 3 m depth
MDD anchorat 3 m depthDepth (mm)
Layer Type
(UCS, CBR, MDD, OMC,etc) class
Material properties TRH14
Load sequence detail: Related reports:
341A2a Richmond, Central Cape TR9-7 (N1) 1988
Nienaber C J. 1988. Planning of the HVS test on Road TR9-7 (N1) between Three Sisters and
Richmond. (In afrikaans) Division for Roads and Transport Technology, CSIR. (I/FP/19/88)Du Doit G J. 1988. Interim report on the behaviour of crushed stone base layers - Report on the
HVS test at Richmond-Three Sisters (Road TR9-7). (In afrikaans) Division for Roads and
Wright, B G and Horak E. 1988. Report on the crushed stone section at Umgababa in Natal.
Division of Roads and Transport Technology, CSIR. (Unpublished report.)
Selectedsubgrade
In-situsubgrade
In-situsubgrade
Yes, points 0 - 8
(kg/cub m)Density MC
(%)
Field
75
HVS-section Nr: Region: Road Nr: Year of test:Pavement structure Instrumentation detail Pavement material information
Test section point
MDD anchorat 3 m depth
MDD anchorat 3 m depthDepth (mm)
Layer Type
(UCS, CBR, MDD, OMC,etc) class
Material properties TRH14
Load sequence detail: Related reports:
398A4 Cullinan, Gauteng Road 2388 1997
From To Wheel load Tyre pressure Water added
Repetitions Test information
MDD anchorat 3 m depth
Theyse H L. 1997. The construction of the HVS experimental sections on Road 2388 near Cullinan. Transportek, CSIR. (Confidential Contract Report CR-97/071)Theyse H L. 1999. Laboratory design models for materials suited to labour-intensive construction. Transportek, CSIR. (Confidential Contract Report CR-99/038)