Soil Mechanics in Pavement Engineering SF BROWN
Soil Mechanics in Pavement Engineering SF BROWN
Soil Mechanics in Pavement Engineering SF BROWN
3, 383426
INTRODUCTION
383
384
BROWN
Granular
Soil
(a) Gravel road
Soil
(b) Sealed gravel road
Asphaltic
Concrete
Granular
Granular
Soil
(c) Asphalt pavement
Asphaltic
Cement treated or concrete
Granular
Soil
(e) Composite pavement
Concrete or brick
blocks on sand
Soil
(d) Concrete pavement
Concrete
Cement treated
Granular
Soil
Load
Surfacing
Rails on sleepers
Base
Ballast
Rail on sleepers
Sub-base
Asphaltic or cement treated
Granular
Soil
(g) Block pavement
Ballast (granular)
Sub-ballast
Foundation
Subgrade
Subgrade
(a)
(b)
Sub-Ballast (granular)
Soil
(h) Railway
385
386
BROWN
15
10
0.2
0.4
0.6
0.8
Time: s
(a)
120
100
80
60
40
20
0.2
0.4
0.6
0.8
1.0
Time: s
(b)
Fig. 3. In situ vertical stress measurements in subgrades: (a) below 165 mm asphalt construction at
Wakeeld; (b) below 350 mm granular layer at
Bothkennar
Theory
There has been extensive application of the
theory of elasticity to the analysis of layered
pavement systems. Burmister (1943) developed
the essential equations, and, following early sets
of tabulated solutions, (e.g. Acum & Fox, 1951)
various computer programs were developed to
assist in obtaining results in a convenient form.
387
x
p
1
h1
(x, z)
E2
h2
E3
h3
E4
4.0
3.0
2.0
1.0
0
0
1000
2000
3000
4000
5000
10000
5000
1000
5
10
20 30 40 50
1st stress invariant: psi
(b)
a
x
E1
5.0
Today the most widely used are the BISAR (de Jong
et al., 1973) and ELSYM 5 (Warren & Diekmann,
1963) programs originally developed by researchers
in the Shell and Chevron oil companies respectively. In both cases, the pavement layers are
assumed to be linear elastic and values of stress,
strain and deection components at any dened
points in the structure can be computed from given
geometry and surface loading. Typical details are
shown in Fig. 4. Wheel loading is represented by
uniformly distributed pressure over a circular area
and dual or multi-wheel congurations can be
accommodated.
In real pavements, loading is transient, the soil
and granular layers (the pavement foundation) have
markedly non-linear stressstrain relationships,
which are inuenced by a range of variables, and
the bituminous layer has properties which are
sensitive to loading rate and to temperature. Fig.
5(a) shows the shear stressstrain relationship for a
compacted silty clay determined from combining
in situ measurements of total stress and of strain
(Brown & Bush, 1972). These were obtained from
pilot-scale test pit experiments subjected to dynamic plate loading and superposition of in situ
measurements at various depths and orientations.
The non-linear stressstrain relationship is clearly
illustrated. Similar data from measurements in a
layer of compacted crushed rock are shown in
Fig. 5(b) in the form of Young's modulus plotted
against the rst stress invariant (Brown & Pell,
1967). Notwithstanding these non-linearities, the
ability to carry out linear elastic structural analysis
of pavements has proved extremely useful in
developing design methods, particularly as the real
characteristics of the constituent materials have
become better appreciated.
The main justication for using elastic theory is
(x, z)
( x, z)
z
p 5 contact pressure
E, , h 5 Young's Modulus, Poison's ratio and
E, , h 5 thickness for each layer
that under a single load application, most pavements will respond in a resilient manner. Any
irrecoverable deformations will be small relative to
the resilient component. Fig. 6 shows a vertical
strain pulse measured within a bituminous layer as
a result of a moving wheel load. There is a
delayed elastic response but no residual strain. The
validity of using linear elastic theory was the main
objective of many fulland pilotscale experiments carried out in the 1960s and 1970s. (e.g.
Brown & Pell, 1967, Bleyenberg et al., 1977).
Conventionally, each layer is characterized by a
value of Young's modulus and Poisson's ratio. In
view of the differences between real and idealized
behaviour of pavement materials, the parameter
`resilient modulus' was introduced in California
during the 1950s following the pioneering work of
Voltage: V
388
0.50
0.45
0.40
0.35
0.30
0.25
0.20
0.15
0.10
0.05
20.00
20.05
20.10
BROWN
Time: s
temperature conditions. Bituminous materials exhibit elastic, brittle behaviour at low temperatures
and short loading times, viscous behaviour at the
other end of the spectrum and viscoelastic response at intermediate conditions. For pavement
design calculations, when moving trafc is considered under normal temperatures, the response of
a bituminous mixture to a load pulse will be
essentially resilient as illustrated in Fig. 6. Fine
grained soils too, can behave in a viscoelastic
manner, as shown in Fig. 7 taken from repeated
load triaxial tests on saturated reconstituted silty
clay (Hyde, 1974).
Linear elastic analysis can be used with reasonable condence for pavements with thick bituminous or concrete layers but is inappropriate for
unsurfaced or thinly surfaced pavements unless
approximate account can be taken of non-linear
behaviour as discussed below. For bituminous
pavements under normal moving trafc conditions,
once a vehicle speed and, hence, loading time is
specied and a temperature condition known, the
bituminous layer may be assumed to behave in an
essentially linear elastic manner. Conversely, when
the pavement response to load is dominated by the
resilient properties of the granular materials and
soil, their non-linear characteristics must be properly taken into account in theoretical analysis.
The non-linear stressresilient strain characteristics of soils and granular materials under repeated loading are discussed in the section on
Behaviour of Soils and Granular Materials under
Repeated Loading. In pavement engineering, it
has been usual to express the resilient modulus
as a function of the applied stress level. To accommodate this in theoretical analysis, two general
approaches have been adopted. The simplest involves an iterative procedure using linear elastic
layered system solutions. The layers of granular
material and soil are subdivided into sublayers to
4
Deviator
stress
Axial
deformation
Elastic
deformation
Delayed elastic deformation
Fig. 7. Response of overconsolidated silty clay to bursts of undrained repeated loading (after Hyde, 1974)
389
390
BROWN
0 0.05 0.10
0.20
0.30
0.40
0.60
0.80
1.00
r: m
Pressure
600 kPa
0
0.05
Asphalt
Linear elastic
0.10
0.20
0.30
5 23 kN/m3
E 5 2000 MPa
5 0.35
Sub-base
5 21kN/m3
s 5 3 kPa
Ko 5 1.0
K- model, equation (22)
K1 5 8000
K2 5 0.70
( in kPa)
5 0.30
0.50
0.70
1.00
1.30
Subgrade
5 20 kN/m3
Brown's model, equation (6)
K 5 50 MPa
n 5 0.40
5 0.45
1.60
2.00
z: m
Fig. 8.
FENLAP
391
Wheel load
Stress
Strain
load
Wheel
Rail
Sleeper
Chord Modulus
Ballast
Overburden
Subballast
Subgrade layer 1
Subgrade layer 2
Secant moduli
Bedrock
Strain
(r 2 )
Corrected stresses (, )
*3
*1 = 1
(z, )
(z*, *)
FENLAP
(after
392
BROWN
Material type
Permanent deformation: mm
G4
G3
20
Water
removed
10
G2
Ingress
of water
Ingress
of water
G1
0
Number of load applications
393
Strain: %
0.5
Pavement structure
Vertical
stress
Shear
stress
1.0
Horizontal
stress
0
0.5
1.0
1.5
2.0
2.5
3.0
Typical pavement element
Time: s
(a)
(a)
60
Vertical stress
50
Stress
Horizontal stress
40
Shear stress when
wheel moves in
opposite direction
30
20
Time
10
Shear stress
0
0
0.4
0.8
1.2
Time: s
(b)
1.6
2.0
(b)
394
BROWN
(a)
LVDT
Actuator
Servo
hydraulic
supply
Piston
(b)
To
computer
Strain gauged
diaphragm
Load
cell
LVDTs
MT
Test
specimen
z
Pi
PO
(a)
Transducer
To
computer
Cylinder
Test
specimen
Proximity
transducers
LVDT
Actuator
Servo
hydraulic
supply
(b)
395
Hydraulic
supply
Load cell on
loading rod
Triaxial
cell
Actuator with
servo-value
Electronic
control
system
Pressure
sensor
Hand jack
Computer
(a)
180 mm
drainage
membrane
'o' rings to
seal membrane
150 mm
Strain ring
shown in
section only
300 mm
Hydraulic
supply
Pressure
cylinder
75 mm
Actuator with
servo-value
LVDT
Rod attached
to location stud
(b)
(AASHTO, 1986). Because soils testing is inherently more difcult to perform than asphalt testing,
simplied techniques present more of a challenge.
One of the principal problems is that of preparing
reliable and representative specimens. However,
recent work at Nottingham, in conjunction with
TRL, has endeavoured to develop practical tests for
soils and granular materials which could be adopted
for design purposes.
A pneumatically operated repeated load triaxial
Hollow brass
tube 5 mm dia.
'O' ring
Phospher
bronze strip
0.56 mm thick
Strain
gauges
Aluminium
block with
cup fitting
Adjustable
fixing
Specimen
BROWN
82 mm
396
Cruciform
vane
40 mm
Fig. 19. Simplied repeated load triaxial system for soils (after Cheung, 1994)
397
398
BROWN
Drop weight
Geophone
(a)
Drop weight
Loading plate/buffer
Geophone
Rubber
Deflection
300mm 200mm
500mm
500mm
(Typical dimensions)
500mm
(b)
and the peak load, an `effective foundation stiffness modulus' (Ef ) can be computed using the
equation:
2pa(1 2 )
Ef
(1)
d1
where p is the contact pressure below the plate, a is
the plate radius, is Poisson's ratio and d1 is the
measured plate deection.
The FWD is generally used for testing `inservice' pavements to assess structural integrity
(Brown et al., 1987). Analytical procedures have
been developed which involve a back-analysis of
the deected surface under the given load to
determine the effective resilient modulus of each
principal pavement layer. The layer thicknesses
need to be known and are obtained from coring
or can be estimated from ground radar surveys
(Highways Agency, 1994a).
399
Several analytical procedures have been developed in the form of computer programs for backanalysis of deection `bowls'. The most reliable
ones (e.g. Brown et al., 1986) take account of
the non-linear resilient properties of soils and,
where necessary, granular layers (e.g. Brunton &
d'Almeida, 1992) while bituminous or concrete
layers are treated as linear elastic. The central
analytical tools are those outlined previously but
nite element analysis is not used routinely because
of the computing time involved. This subject is
further discussed in the nal section. These procedures allow the parameters in simple non-linear
resilient soil models to be calculated and, by
matching theory to measurement by way of the
surface deection prole, provide a sound basis for
further theoretical analyses of the pavement.
The basic back-analysis procedure can also be
used when tests are conducted on pavement foundations, although the data tend to be less precise
because of the rough surface, compared with a
completed pavement, which can interfere with the
geophones.
The procedure was used on the Bothkennar haul
road experiments (d'Almeida, 1993) and on the
A564, Derby Southern By-Pass, some typical
results from which are presented on pp. 417418.
PAVEMENT FAILURE MECHANISMS
Cracking
Cracking of bituminous pavements under the
inuence of repeated wheel loading is a fatigue
phenomenon. Fig. 24 shows a typical failure
condition with a pattern of cracks in the wheel
paths. Hveem (1955) was the rst engineer to
identify the relationship between fatigue cracking
and the resilience of the supporting pavement
structure, which was principally inuenced by the
soil characteristics. For the thin surfacing commonly used in the 1950s, Hveem's theory, illustrated in Fig. 25, relates to surface cracking outside
the loaded area induced by horizontal tensile
Resistance in these
upper regions depends
upon flexural strength
(tensile, cohesion)
Load
Surface
Base
Weight of material
outside of load
also provides
restraint
Probable paths
of particle flow
Resistance in
this lower region is
primarily dependent
upon interparticle
friction (R-value)
16.5 kN
30 km/h
1s
Depth: mm
Temp.: C
22
30
23
Wheel position
20 cm right-hand side
80
20
140
19
BROWN
700
500
100
50
2 x 103
Test Series
Temp. C
104
105
Cycles to failure
106
107
+10
+10
+20
+30
Symbol
Test Series
Frequency
varies
Symbol
developed using linear elastic theory and incorporating this concept (e.g. Brown et al., 1985).
Research into crack propagation has revealed
that, once a crack has been initiated, its rate of
propagation depends on the tensile stress at the
crack tip (Ramsamooj et al., 1972). There are,
therefore, conicting requirements between the
need to avoid crack initiation, which requires a
high asphalt stiffness, and to minimize crack
propagation, which requires a low stiffness. The
layer thickness is also inuential. The general
approach is to use low stiffnesses for bituminous
surfacing which is less than 100 mm thick and
high stiffnesses for the greater thicknesses which
embrace all modern major pavement construction.
Theoretical analysis allows an indication to be
obtained of the inuence which soil resilient
modulus has on the tensile stress and strain in
the bituminous layer. A sensitivity analysis reported by Dawson & Plaistow (1993) based on
computations with the FENLAP program revealed
that a change in the resilient modulus of the
subgrade from 40 to 90 MPa caused a change in
the asphalt tensile strain criterion of less than 2%.
Changes in the resilient characteristics of the
granular layer over a realistic range, using nonlinear models, were more signicant, causing the
asphalt tensile strain to vary by up to 70%. These
calculations involved bituminous layer thicknesses
between 100 and 250 mm with stiffness modulus
values of between 2 and 8 GPa. It would appear,
therefore, that the cracking phenomenon is not
greatly inuenced by soil resilience when a
reasonably thick bituminous layer is used. Conversely, the resilience of the supporting granular
layer is very signicant.
Rutting
The second trafc related failure mechanism in
exible pavements is rutting. This arises through
the accumulation of vertical permanent strains in
the wheel track (Fig. 28) which can, in principle,
include contributions from all layers in the pavement. Some typical data from eld experiments
carried out on the A1 by Lister (1972) are shown
in Fig. 29 to illustrate this point.
For thick asphalt pavements, rutting usually
arises from permanent deformations in the bituminous layers, often the surface course. Interpretation
of Lister's data for pavements with hot rolled
asphalt surfaces and base layers over traditional
foundations, by Brown & Brunton (1984) indicated
that a 20 mm rut might involve a 48% contribution from the bituminous layers. It is difcult to
generalize about this matter, since permanent
deformations will develop wherever there is a
weakness in the structure. For heavily trafcked
UK roads, this is likely to be in the surfacing, but
for pavements with thin bituminous layers, the
Rut depth
Load
Bituminous
Granular
Subgrade
1968
1969
2
Deformation: mm
400
1970
1971
Sub-base
Base +
surfacing
4
Subgrade
6
8 (100 mm)
Rolled asphalt
(150 mm)
Rolled asphalt
(150 mm)
Ballast
Heavy
clay
10
Total
401
Introduction
The foregoing discussion on failure mechanisms
in pavements suggests that an ability to design for
prevention of failure requires a knowledge of how
soils and granular materials respond to repeated
loading of the type imposed by moving trafc.
Under repeated loading, there are recoverable and
irrecoverable components of deformation. The
former dictate the value of resilient modulus,
which is required to carry out structural analysis
of pavements, while the latter needs to be quantied to deal with design to minimize rutting.
Properties of the subgrade
The mechanical properties of the subgrade are
inuenced by the imposed stress regime. This must
be considered in two parts; that resulting from the
equilibrium conditions established after construcTraffic: GN
0
0.8
25
50
75
225
20
Settlement
Subgrade
Sub-ballast
Ballast
Tamping
Settlement: in
0.6
Cumulative Traffic
15
0.4
Ballast
10
0.2
Subgrade
Settlement: mm
Total
Sub-ballast
0.0
10
15
20
0
25
Traffic: MGT
402
BROWN
Pavement surface
Pore pressure
ve
Formation level
+ve
Sandy
clay
Hydrostatic
line
Silty
clay
Sandy clay
Sandy
Gravel
Formation level
Area E
0
Formation level
Hydrostatic
line
Sandy
clay
Silty
clay
Sandy clay
Sandy
Gravel
Area G
25
20
15
10
Fig. 33. Pore pressure measurements in RRL experiments below sealed surfaces (after Black et al., 1958)
Water table
deviator stress q 9v 9h
(3)
(4)
403
Deviator stress, q
C
Compression
Swelling
Deviator stress, q
Swelling line
A
Pavement
construction
P
D
P
Lowering
water
table
Removal of overburden
Specific volume, v
Compression
P
P
A
C
Swelling
pA
pc
404
BROWN
CSL (failure)
Deviator stress, q
Q
O
Specific volume, v
Compression
Q
X
C
Swelling
CSL (failure)
Deviator stress, q
C
q
F
Wheel loading
qr
Q (Fill)
q
Wheel loading
E
qr
ESP
Time
TSP
P (Cut)
405
2.5
2.0
1.5
qr = 125 kPa
1.0
Locus of
values for
qr = 30 to
75 kPa
0.5
0
1
101
102 103
104
105
Number of load cycles
(a)
106
107
6.0
5.0
4.0
qr = 175 kPa
3.0
2.0
Locus of
values for
q = 40 to
130 kPa
1.0
0
1
101
102 103
104
105
Number of load cycles
(b)
106
107
50
40
Soil type
Keuper Marl
London Clay
Gault Clay
30
20
10
0
0
10
20
30
40 50 60
Suction: kPa
70
80
90
100
406
BROWN
1.0
Permanent axial strain: %
difcult. However, a pragmatic approach is suggested in the nal section of this paper. If the
actual value of accumulated plastic shear strain
after N cycles is required, Cheung proposed the
following relationship based on testing up to 1000
cycles
q b
(5)
p (N) A r (log N B)
s
where A, b and B can be dened for the particular
soil. Although equation (5) is only valid for
relatively few load applications, this could still
be of use in pavement foundation design where
the number of construction trafc movements is
limited.
Much more research has been devoted to the
measurement of resilient soil properties under
repeated loading. The parameter, resilient modulus,
was introduced by Seed et al. (1962) and dened
as repeated deviator stress divided by recoverable
(resilient) axial strain in the triaxial test. They
demonstrated that it varied with the magnitude of
the repeated deviator stress, as shown in Fig. 41.
Later work by Dehlen & Monismith (1970) showed
that suction also had an important inuence. The
rst attempt to relate resilient modulus to the
effective stress was reported by Brown et al.
(1975) who, working with reconstituted silty clay,
obtained the data in Fig. 42 for a range of initial
specic volumes, overconsolidation ratios and
initial effective stresses. These data were used to
deduce the empirical relationship:
n
p90
Er K
(6)
qr
where K and n depend on the soil type, p90 is the
initial mean normal effective stress and qr is the
16000
14000
for subgrades to prevent any signicant contribution to permanent deformation in the pavement.
This would involve ensuring that the ratio of
deviator stress to mean normal effective stress or
soil suction was kept below a critical value. Brown
& Dawson (1992) used this approach for design
and suggested a ratio of 2 for pavement foundations, recognizing that some plastic strain in the
subgrade at this stage in the construction is
permissible. They also noted that the reconstituted
soil specimens (Brown et al., 1987) had been
tested at a higher frequency than the compacted
specimens (Loach, 1987), which will have inuenced the result in view of the noted viscous
behaviour.
Later, more extensive testing by Cheung (1994)
on compacted clays using the apparatus shown in
Fig. 19, produced data such as those shown in
Fig. 40. These resulted from tests involving 1000
cycle bursts of repeated deviator stress at 2 Hz on
compacted, unconned specimens of Keuper Marl
and London Clay, two of the soils tested by Loach
(1987). The suction for the specimen featured in
Fig. 40 was 44 kPa leading to a threshold deviator
stress, according to Loach, of 22 kPa. This point is
seen to coincide with the sharp change in slope of
the line in Fig. 40. However, not all of Cheung's
data demonstrated this clear change in slope.
Cheung used an alternative approach to design
suggesting that the plastic strain after 1000 cycles
should be limited to 1%. The deviator stress
causing this (qt ) was related to soil suction,
yielding ratios of qt /s of 08 for Keuper Marl,
(wL 337%, wp 176%), 04 for Bothkennar
clay (wL 543%, wp 251%) and 05 for London Clay (wL 76%, wp 252%). The range of
soil suction for Cheung's specimens was 2080 kPa.
These various triaxial test results suggest that
the allowable transient deviator stress is a function
of the effective stress state of the soil. Since the
initial stress state, particularly for compacted soil,
is uncertain, precise application of these data is
0.8
0.6
0.4
12000
10000
8000
6000
4000
0.2
2000
0
0
10
20
30
40
50
Fig. 40. Plastic strain after 1000 cycles against repeated deviator stress for compacted silty clay (after
Cheung, 1994)
10
15
20
25
30
Deviator stress: psi
35
40
407
2
4
10
20
4
10
20
200
150
)
)
)
200
400
Asphalt
600
Granular
40
Case A
1
Subgrade
100
Case B
Depth: m
250
3
kPa
380
190
76
38
OCR
50
0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
2
Case B: Water table 1 m
Case B: below formation
4.0
qr /3
(8)
60
76
50
40
43
30
Key
32.5
20
19
10
0
10
20
30
40
50
(9)
BROWN
100
80
60
Line of equality
40
20
0
20
40
60
80
Measured resilient modulus: MPa
100
(11)
0.2
0.6
0.5
0.4
0.3
0.2
0.1
400
qr /p e
500
1
0.9
0.8
0.7
0
0.0001
0.001
0.01
0.1
Cyclic shear strain: %
300
0.1
200
100
0
0
1
0.1
po/pe
0.2
408
0.3
152
3 qr
sr 111 10
p90
Since
(12)
Gr
qr
3sr
(13)
Gr
293p90
034
sr
(14)
and
Gr p90 1 1
034
G0 58 R02
0 sr
(15)
for R0 18,
G0 034
r
p90 33 kPa
(17)
in which r is in % strain.
In Fig. 48 these relationships are plotted to
indicate the range of Brown et al.'s results. A
predicted relationship based on the data in Fig. 46
accumulated by Roblee et al., (1994) for a
plasticity index of 19% is shown for comparison.
It is seen to pass through the centre of the range
dened by Loach's model for his experiments. An
attempt was also made to use the Hardin &
Drnevich method to estimate G0 for Loach's soil
but this led to unrealistically high values.
The philosophy of expressing shear modulus in
terms of deviator stress or shear strain is worth
examining. In pavement engineering, the soil is
subjected to a stress-controlled environment except
for situations below very stiff pavements. This
means that the strain which develops in the soil
depends on the applied stress and the soil stiffness.
1.2
1
Gr /Go
0.8
0.6
0.4
0.2
0
0.001
po = 100 kPa, Ro = 6
po = 33 kPa, Ro = 18
0.01
0.1
Resilient shear strain: %
Prediction
409
(18)
@q
@p9
This led to the denition of expressions for resilient
bulk Kr and shear Gr moduli as follows
Kr
K 1 p9(1c)
1 (q=p9)2
Gr G1 p9(1c)
(19)
(20)
410
UR
E
BROWN
FA
IL
Er K 1 K 2
160
130
300
100
200
70
100
40
100
(15,6)
300
1400
300
Volumetric strain
(microstrain)
1200
100
0
UR
E
FA
IL
600
800
400
200
200
100
400
200
500
100
200
400
300
Normal stress p : kPa
(b)
(21)
(22)
400
Shear strain
(microstrain)
200
800
600
Pessimum
line of fit
400
200
0
50
100
Peak mean normal effective stress: kPa
150
Fig. 50. Resilient modulus for crushed dolomitic limestone as a function of applied stresses
411
sp f (N )lr (^
)
(23)
B
Failure
500
Limit of
resilient
strain
tests
400
300
200
100
100
200
300
1.2
1.0
0.8
0.6
0.4
A
0.2
C
0
1
10
103
104
102
Number of cycles
(b)
105
106
412
BROWN
ln _ 1p a b ln N
(24)
200
Deviator stress: kPa
100
where B is positive.
The parameter A was shown to relate to the
peak applied stress ratio as follows
A
(26)
c d
in which c and d are constant for the material and
c/d f , the stress ratio at failure. This hyperbolic
relationship is similar to that proposed by Lentz &
Badady (1980) for sands. Equation (26) implies
that as approaches failure, A, and therefore the
accumulated strain, become very large.
Although empirical models have been developed
to match the measured data for repeated load
triaxial tests on granular materials, in particular
cases, testing is still needed to determine the
various parameters. The models therefore only
provide a framework within which experience
suggests that the data may be interpreted. Thom
& Brown (1988) proposed a series of stress paths
that could be applied to evaluate routinely both
resilient and plastic strain characteristics. These are
illustrated in Fig. 52 and show 19 stress paths to
deal with resilient response, all of which involve
peak values below the threshold, and a single,
20th, path to characterize plastic strain. Finally,
unless failure has developed under repeated loading, a monotonic test can follow to measure shear
strength. About 20 cycles on each of the paths
for resilient strain are adequate, while the more
damaging paths for plastic strain could be applied
for 104 105 cycles. A frequency of 1 Hz is appropriate.
Chan's (1990) experiments with the Hollow
Cylinder Apparatus demonstrated that shear reversal (rotating principal planes) does inuence plastic
strain accumulation under repeated loading. This is
illustrated by the data in Fig. 53 from Chan &
Brown (1994) showing the increased rate of strain
when shear reversal is introduced to a specimen
initially subjected to triaxial stress conditions.
0
0
100
200
Mean normal effective stress: kPa
p1 A[1 (N=100)B ]
0.5
Triaxial
With shear
reversal
Recoverable
strain
0.4
0.3
0.2
Permanent
strain
0.1
0
5
10
25
Number of load cycles
50
Fig. 53. Inuence of shear stress reversal on accumulation of plastic strain in a dry crushed rock (after
Chan & Brown, 1994)
Head
Penetration
piston
90 0 10
80
70
60
20
30
40
3 in2 area
Tapered
lugs
6 Cylindrical
mould
Testing machine
413
414
BROWN
(27)
300
20
40
100
60
80
100
u s p
200
0
0
10
CBR: %
(a)
120
arl
er M
p
Keu
M=
80
10
CB
R
7. 6 CB
Mr = 1
London Clay
40
Gault Clay
0
0
6
CBR: %
10
(b)
(29)
0. 64
(28)
(30)
(31)
415
Plunger load: kN
1.0
0.75
0.5
0.25
0
3
4
5
Penetration: mm
416
BROWN
100R 1 (h =v ) (=1 )
(33)
(34)
where 1 v and q v h 2
Notwithstanding the disputed factor of two, R is
seen to be a reasonably fundamental measure of
Head of testing machine
Piston for
applying
load to specimen
Load
Pressure
gauge
Dial
gauge
Displacement
pump
Test
specimen
Liquid
Adjustable
stage
Flexible
diagram
Platen of
testing machine
417
500
1000
Asphalt
layer
Granular
layer
0.5
Subgrade
Depth: m
1.0
Surface deflection
under centre of load = shaded area
1.5
2.0
418
BROWN
Effective Er : MPa
Select aggregate(s)
90
70
3200
240
200
200
if aggregate
is unsatisfactory
Design foundation
Prepare subgrade
NO
Performance satisfactory?
YES
Place aggregate?
Introduction
This section outlines an approach to pavement
foundation design based on the use of theoretical
concepts and measured properties of the soil and
granular layer. It is based on research carried
out for the TRL reported by Thom et al. (1993) and
Dawson et al. (1993). The objective was to produce
a relatively simple, implementable system using
reasonably priced facilities which could be adopted
by design laboratories.
Philosophy
Fig. 59 shows the sequence of design and
testing proposed by Dawson et al. (1993). It includes laboratory testing of representative samples
of the subgrade and the aggregates(s), design
calculations using analytical techniques and eld
measurements as construction proceeds to provide a
check on the design.
Materials testing
The simplied repeated load triaxial apparatus
in Fig. 19 can be used to determine resilient
properties and permanent deformation characteristics of soils. These are modelled by equation (8)
for the resilient modulus and a simplied version
Table 2. Equivalent foundation stiffness values for
road on embankment
Test on
Subgrade
Capping
Sub-base
Equivalent foundation
stiffness: MPa
30
50
90
NO
Performance satisfactory?
YES
Foundation Complete
(35)
419
Rut depth: mm
Analytical techniques
A quasi-failure analysis using the wedge model
in Fig. 60 is proposed to deal with rutting in the
granular material. The force P required to push
the central wedge down by the allowable rut depth
(say 40 mm) is computed using static equilibrium
techniques. Resistance to P is mobilized by the
values of apparent cohesion c and angle of
shearing resistance, for the aggregate layers
and the allowable deviator stress on the subgrade
qa . This is determined from equation (35) using an
allowable plastic strain of 06% for the required
number of load applications N. This strain level is
regarded as a tentative suggestion at present. Full
details of the wedge model are described by Thom
et al. (1993). An iterative computation is used to
obtain a solution.
For the situation where the rutting is entirely
contributed by the subgrade and for the determination of equivalent foundation resilient modulus,
linear elastic layered system analysis is used. The
non-linear resilient properties of the materials are
accounted for by using the iterative approach
described on p. 389. This allows compatibility of
stresses and resilient moduli to be established. For
the subgrade rutting criterion, the deviator stress at
formation is calculated and equation (35) used to
check whether the allowable strain of 06% is
exceeded.
The equivalent foundation stiffness is determined using the computed surface deection for
the layered system and calculating the resilient
modulus for an equivalent semi-innite elastic half
space using equation (1). The analysis described
above can be performed using the PAFODE computer program developed by Dawson & Thom (1994).
Rut depth: mm
0
10
20
Ash
30
Sand &
40 Gravel
50
Granodiorite
predicted
60
measured
70
80
1
10
100
Number of passes
(a)
0
10
20
30
40
50
60
70
80
10
Limestone
1000
Granite
(550 mm)
Gravel
(400 mm)
predicted
measured
100
1000
10 000
(b)
Fig. 61. Predicted rut depths compared with measurements at full-scale (after Dawson et al., 1993) (a)
Loughborough trials; (b) Bothkennar trials
2r
Rcb
Rba
Fcb
B
Fb
Rb
Fba
Ra
Fig. 60. Proposed `wedge model' for calculating rutting in pavement foundations (after Thom et al., 1993)
420
BROWN
kennar the model overpredicted rutting. The laboratory test data to support the Bothkennar calculations
were less complete than for the Loughborough tests.
The method clearly needs to be used more extensively for a wider range of materials and conditions and to be rened. It is, however, considered
to provide the basis for improved design of
pavement foundations in the future.
Railtrack design
Li (1994) presents a good summary of procedures for the determination of granular layer
thicknesses in railtrack. He describes a method
developed at the University of Massachusetts
which uses the GEOTRACK program for modelling
response to wheel loading. The design criteria are
vertical plastic strain and vertical permanent
deformation at formation level. The former is to
prevent plastic ow, which leads to progressive
failure of the top of the subgrade, while the latter
relates to the overall deformation of the subgrade.
Varying the thickness of the granular layers
inuences the transient deviator stress level in
the subgrade and, hence, the plastic strain p . The
plastic strain after N cycles is computed by the
following equation, derived from repeated load
triaxial tests on clays
1p A(qr =cu )m N b
(36)
421
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BROWN
425
426
practical designs which could lead to a more
theoretical approach than is currently used in the
UK. Some empiricism would remain, but at a
lower level in the hierarchy.
We have been privileged to hear an acknowledged master of his subject demonstrate clearly
the role of soil mechanics in pavement engineer-
BROWN