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Evaluating a Model for Seasonal Variation of Silty Sand Subgrade Resilient
Modulus with FWD Tests
Farhad Salour*
Pavement Technology, Swedish National Road and Transport Research Institute, VTI
581 95 Linköping, Sweden
&
Division of Highway and Railway Engineering, Royal Institute of Technology, KTH
SE-100 44 Stockholm, Sweden
Phone: + 46 (0) 13-20 41 11, Fax: +46 (0) 13-14 14 36
Sigurdur Erlingsson
Pavement Technology, Swedish National Road and Transport Research Institute, VTI
581 95 Linköping, Sweden
&
Faculty of Civil and Environmental Engineering, University of Iceland
IS-107 Reykjavik, Iceland
Phone: +35 (0) 45-25 46 54, Fax: +35 (0) 45-25 46 32
Claudia E. Zapata
Faculty of the School of Sustainable Engineering and the Built Environment, Arizona State
University, ASU
P.O. Box 873005, Tempe, Arizona, USA
Phone: +1 (480) 727-8514; Fax: +1 (480) 965-0557
Submitted for Presentation and Publication in the 94th
Annual Meeting of the Transportation
Research Board (January 11-15, 2015)
----------------------------------------------
Number of references: 25
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Word count: 4,336
Number of figures and tables: 10
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Total number of words: 6,836
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Submitted: July 29, 2014
Revised: October 31, 2014
*Corresponding Author
Salour, Erlingsson and Zapata 2
ABSTRACT The stiffness of unbound pavement material is one of the main input parameters in mechanistic
design and analysis of pavement systems. This material property is usually moisture dependent
and therefore, most of the unbound pavement layers exhibit seasonal variation in stiffness as the
pavement moisture regime changes throughout the year. Therefore, this variation should be taken
into account in any realistic pavement design. In unbound materials with high fine content,
change in moisture content can result in change in the stress state due to suction effects. In this
study, an enhanced predictive resilient modulus model that accounts for seasonal variation by
means of suction measurement is presented. A silty sand subgrade was tested using a modified
Repeated Load Triaxial (RTL) system under different moisture (suction) conditions and a set of
resilient modulus model regression parameters were determined. The capability of the model to
capture seasonal moisture variation effects was further evaluated using field data. A series of
Falling Weight Deflectometer (FWD) tests with multi-level loads were conducted on an
instrumented pavement structure where the moisture content of the subgrade was changed by
manipulating the pavement drainage condition. The resilient moduli obtained from the model
were compared to the backcalculated stiffness data obtained from FWD tests conducted at
different moisture conditions. Overall, a good agreement was observed between the
laboratory-based resilient modulus and the backcalculated stiffness. The resilient
modulus-suction model could efficiently capture the moisture content effects.
Keywords: Resilient modulus, backcalculation, falling weight deflectometer, seasonal variation,
moisture content, silty subgrade.
Salour, Erlingsson and Zapata 3
INTRODUCTION The stiffness of unbound pavement material, which is the elastic response of the material to
external loading, is one of the main input parameters in the mechanistic design and analysis of
pavement systems (e.g., stresses and strains). This material property is usually estimated directly
by conducting Repeated Load Triaxial (RTL) testing on materials under stress state that are
representative of the material conditions in pavement systems or indirectly by backcalculating
Falling Weight Deflectometer (FWD) deflection data. The mechanical behaviour of unbound
pavement materials is rather complex and depends on many factors such as gradation, particle
shape, surface texture, stress state, compaction degree, moisture content and environmental
conditions. In unbound materials and subgrade soils with a substantial amount of fines content,
the mechanical properties of the material can considerably be influenced by its moisture content.
Unbound layers moisture content in pavement structures is greatly dependent on the
environmental factors in the pavement surroundings (e.g. water table location, precipitation and
temperature) and soil properties at the site. Since the moisture regime in pavement structures is
continuously evolving with time towards a balance, proper consideration should be given to this
factor in a realistic pavement design and analysis.
In unbound pavement materials, moisture can affect mechanical properties through
different mechanisms: affecting the state of stress through suction or pore-water pressure
build-up in subgrade soils with high fine content, or reducing inter-particle friction and contact
forces due to water lubrication effects in coarse-grained materials (1, 2).
Investigation of water impact on pavement materials and structures has been the subject
of many research works. These research studies have been conducted using different approaches
and at different scales; from laboratory-based studies (3-8) to large scale accelerated pavement
testing under controlled conditions (9,10) and in-situ measurements on pavements in service
using FWD (11-14).
Andrei (4) investigated the effect of moisture content on unbound materials resilient
modulus through triaxial testing. He observed that plastic subgrade soils in particular were
significantly affected by moisture. Simonsen et al. (6) conducted series of resilient modulus
laboratory tests on coarse- and fine-grained subgrade soils with full freeze-thaw cycles in an
environmental chamber. Depending on the soil type, about 20 to 60 percent decrease in resilient
modulus was reported after completed freeze-thaw cycles. Saevarsdottir and Erlingsson (10)
examined the water impact on the behavior of an instrumented flexible pavement in an
accelerated test using a Heavy Vehicle Simulator (HVS) where significant increase in the
development of permanent deformation was observed as water was added, particularly in the
subgrade layer. Jong et al. (13) investigated different field sites with different moisture contents
in Wisconsin using FWD. Their measurements showed that the base and subgrade modulus were
reduced by 35 and 65 percent, respectively, when thawing was completed, when compared to the
pre-freezing values. In a similar study in southern Sweden, Salour and Erlingsson (14) reported
48 and 63 percent reduction in the granular layer and subgrade stiffness, respectively, due to
spring-thaw effects. All these studies have indicated that moisture content is one of the most
influential factors in the deterioration of flexible pavement structures. Increase in moisture
content results in larger recoverable (resilient) and permanent deformations, if all other
conditions remain the same, which in return will lead to faster development of rutting and
cracking. Therefore, it is of great importance to improve the understanding of the behaviour of
unbound pavement materials (particularly materials with high fine content) that are subjected to
moisture content changes and develop more comprehensive response models.
Salour, Erlingsson and Zapata 4
Study Scope and Objectives
The overall objective of this study was to investigate the effects of matric suction on the resilient
modulus of silty sand subgrade soil (with high fine content) and the possibility of using the
matric suction parameter in modelling seasonal moisture variations and its effect on the subgrade
material resilient modulus. An attempt was also made to evaluate the proficiency of a
suction-resilient modulus model by conducting in-situ FWD measurements on an instrumented
test section with varying subgrade moisture condition.
RESILIENT MODULUS MODELLING OF SUBGRADE SOIL In recent decades, numerous research studies have been devoted to the characterization of the
resilient modulus of unbound pavement materials. The effort has focused on outlining
mathematical procedures for describing the stress dependency using various stress variables
through a total stress approach. A comprehensive revision of these models is summarized by
Lekarp et al. (1).
Several models, mostly empirical in nature, have been developed to take moisture
variations into account when estimating subgrade soil resilient modulus response (4, 15-18).
Among them is the model used in the MEPDG (4, 15) that adjusts a relative change in the
resilient modulus to variations in the degree of saturation. This model is expressed as following:
log �������
= + � ���������� � �⁄ ������� ������
(1)
where, !" is the degree of saturation at a given time, !"��� is the degree of saturation at the
optimum moisture content, #$ is the resilient modulus at a given time and #$%�& is the resilient
modulus at the optimum moisture content. , ' and () are the regression parameters. Figure 1
shows the prediction model given in Equation (1) for adjusting the resilient modulus of the
unbound materials due to variation in the degree of saturation.
FIGURE 1 Model used in the MEPDG for adjusting resilient modulus of unbound
materials due to moisture variation.
0.0
0.5
1.0
1.5
2.0
2.5
3.0
-0.50 -0.40 -0.30 -0.20 -0.10 0.00 0.10 0.20 0.30
MR/M
Ropt
(Sr-Sropt)
Coarse-grained material Fine-grained material
Coarse-grained material a = -0.3123; b = 0.30; km = 6.8157
Fine-grained material a = -0.5934; b = 0.40; km = 6.1324
Salour, Erlingsson and Zapata 5
Cary and Zapata (4) have developed an enhancement to the universal MEPDG resilient modulus
model (19) which is a function of three stress state variables: bulk stress (*), octahedral shear
stress (+%,&) and material matric suction (-)). The proposed model is expressed as:
#$ = .�*� ∙ 1�+%,&� ∙ ℎ�-)� = (�3� �456� 789:;<=��=
��> �?�@�
�=+ 1�
�B ��C�D 8C���=
+ 1��E
(2)
where,
3� = atmospheric pressure (here chosen as 100 kPa)
*��& = * − 3H� = the net bulk stress (* =bulk stress = I� + IJ + I7 and H� = pore-air pressure)
ΔHL M�& = pore-water pressure build-up under a saturated condition (-) = 0)
+%,& = octahedral shear stress = 1 3O P�I� − IJ�J + �I� − I7�J+�IJ − I7�J
-)D = initial matric soil suction and Δ-) = relative change in soil matric suction with respect to
-)D due to pore-water pressure build-up under unsaturated condition (ΔHL M�& = 0)
(� ≥ 0,(J ≥ 0, (7 ≤ 0 and (S ≥ 0 are regression constants.
This model incorporates the effect of seasonal changes in the moisture content by introducing
matric suction as a fundamental variable within the stress state of unsaturated soil. Instead of
using a resilient modulus modification factor determined from degree of saturation (as in
Equation 1), variation in the matric suction is considered. The suction–resilient modulus
prediction model shown in Equation 2 was used in this study.
MATERIAL AND SAMPLE PREPARATION
Material Index Properties and SWCC
The subgrade soil used in this study was cored out from the instrumented test section in
Torpsbruk in southern Sweden (described further). It was classified as a non-plastic silty sand
(SM) according to the Unified Soil Classification System with 27.4% of fine content passing
through sieve No. 200 (75 µm). The subgrade had a maximum dry density, MDD= 2.07 gr/cm³,
optimum moisture content, OMC=7.6% (corresponding to !"��� =70.1% degree of saturation)
and specific gravity, SG=2.67. Figure 2(a) shows the grain size distribution curve of the
subgrade soil, whereas Figure 2(b) shows the soil-water characteristic curve (SWCC) of the
subgrade obtained with the odometer-type Fredlund apparatus. The SWCC describes the
relationship between the soil moisture content and the matric suction at equilibrium conditions
(20).
FIGURE 2 Subgrade grain size distribution (a) and soil-water characteristic curve (b).
Sample Preparation for Resilient Modulus
The subgrade soil was thoroughly mixed at its optimum moisture content and compacted into
cylindrical specimens of 102 mm in diameter and 203 mm in height. The specimens were
compacted in eight subsequent layers to the maximum dry density obtained from the standard
Proctor test (21). Studs that were further used for mounting the LVDTs were buried into the
specimen at the second and sixth compaction layers. After compaction, the samples were
extracted from the mold. In total, eight cylindrical specimens were prepared and pre-conditioned
for the resilient modulus tests.
Specimen Preconditioning
For the resilient modulus tests, four different target moisture contents with two replicates were
conducted. The target moisture contents tests were 3.6, 5.4, 7.6, and 10.4% corresponding to
degree of saturations of 30, 50, 70.1, and 97.1% respectively. This covered the moisture range
that could be experienced in the field and was considered suitable for the modelling procedure.
The matric suctions corresponding to these moisture contents were 316.0, 51.6, 23.3, and
0.0 kPa. After conditioning the specimen and once the moisture was close to its target value, the
membrane was assembled and the specimen was stored in a moisture-sealed bag for about 24
hours. Thereafter, the specimen was mounted on the triaxial cell pedestal and the matric suction
corresponding to the target moisture content obtained from the SWCC was applied using the
axis-translation technique. Under the applied suction, the specimen absorbed or released water
until the initial target moisture was reached. Once the specimen suction (moisture) reached
equilibrium the resilient modulus test was started.
SUCTION-CONTROLLED RESILIENT MODULUS TEST
RLT Test System and Procedure
The subgrade was tested using a custom built suction-controlled triaxial cell at Arizona State
University, which allowed for independent control/measurement of the pore-water and pore-air
pressures of the specimen during the resilient modulus test. The testing system consisted of four
main components: the unsaturated soil triaxial cell, a micro-console controller, a central pressure
unit and the measuring components. By means of pore-water and pore-air pressure control, the
matric suction of the specimens was controlled throughout the tests using the axis-translation
technique. In this technique, both the pore-air (H�) and pore-water (HL) pressures are translated
0
20
40
60
80
100
0.001 0.01 0.1 1 10
Passing [% by weight]
Sieve Size [mm]
0
20
40
60
80
100
0.01 0.1 1 10 100 1000 10000
Sr, degree of saturation [%]
Matric Suction [kPa]
Curve fitting _Fredlundand Xing (1994) model
Measured data points
(a) (b)
Salour, Erlingsson and Zapata 7
into positive pressure ranges, while their difference that is the matric suction (H� − HL) is
maintained to the test target value. The pore-air pressure was applied through the porous stones
imbedded into the top platen and the pore-water pressure was controlled through a saturated high
air entry (HAE) disk imbedded into the base pedestal. The specimen was placed directly on the
saturated-surface-dried HAE disk and a paper filter was placed between the specimen and the top
porous stone. The target matric suction for the RLT test was then applied to the specimen. Once
the suction (moisture) equilibrium in the specimen was reached, the LVDTs were set to zero and
the resilient modulus test was started (22).
Loading Sequences
The load sequences for granular subgrades in the NCHRP 1-28A test protocol (23) was used for
the resilient modulus test with some modifications that allowed for matric suction control
throughout the test (22). After applying 1,000 conditioning load repetitions, the test stress paths
consisting of 20 loading sequences were applied. Each sequence consisted of 100 load repetitions
with a haversine shaped load pulse with 0.2 second loading and 0.8 second rest periods. A
contact stress equal to 20% of the consequent peak stress was always applied to the specimen.
The resilient modulus for each loading sequence was calculated using the last five load pulses.
Model Parameters
The regression parameters in the model presented in Eq. (2) were calculated using a total of 150
test data points (22). The least square curve fitting method was used for determining the model
parameters along with the coefficient of determination, R2 (Table 1).
TABLE 1 Subgrade Resilient Modulus Model Regression Parameters
Model Parameters Goodness of Fit
TU TV TW TX YV
1524 0.774 -1.470 0.475 0.78
FIELD EXPERIMENTAL PROGRAM AND FWD TESTS
Field Measurements
A field study was carried out in order to evaluate the laboratory-based suction-resilient modulus
model. The instrumented test section in Torpsbruk was used for this purpose. This section is
located along a highly moist ground condition and is equipped with deep-drainage systems on
both sides of the road. By manipulating the drainage outlet pipes, the water discharge could be
impaired and the moisture condition in the pavement profile could therefore be changed. This
allowed for manually reproducing conditions in which pavements experience excess water
contents (e.g., spring-thaw periods, heavy rainfalls and floods). Under different moisture
conditions the pavement mechanical response was assessed by conducting FWD tests simulating
the traffic loads. The pavement system plan view and cross section are illustrated in Figure 3.
Salour, Erlingsson and Zapata 8
FIGURE 3 Schematic overview of the Torpsbruk test site and the pavement
instrumentation: Plan view (a) and pavement cross section (b).
Test Site Pavement Structure and Instrumentations
The Torpsbruk test section consisted of a three layer flexible pavement structure with 100 mm
Hot Mix Asphalt (HMA) layer, 160 mm crushed gravel base layer and 300 mm natural sandy
gravel subbase layer resting on a silty sand subgrade with bedrock at 3.0 to 3.5 m depth. The
HMA course was a dense graded mix with 16 mm maximum grain size. The test section was
instrumented with 6 pressure-cell groundwater level rods in the transverse direction of the road
and 2 subsurface moisture rods each consisting of 4 volumetric moisture probes (capacitance
type) at different depths with automatic data logging systems. The moisture rods were installed
at the unpaved shoulder of the road near the HMA layer edge with moisture probes at 50 cm
(bottom of granular layer) and 90, 120, and 150 cm depths (all three in the subgrade). The FWD
unit was a trailer-mounted KUAB 50 device with a combined two-mass and buffer loading
system (24).
Field Condition and Test Procedure
Groundwater Level and Moisture Content Data
The drainage outlet pipes on both side of the road were clogged for about three months (from
June 7 to September 15, 2011). Drainage clogging resulted in rapid groundwater level rise from
2.5 m to about 1.0 m below the road surface. Figure 4(a) shows registrations by the six
groundwater rods across the pavement profile. Rise in the groundwater level also influenced the
moisture condition of the material above the groundwater level as registered by the moisture
probes (Figure 4(b)). The moisture probes at 120 and 150 cm depths were below groundwater
table as the drainage was clogged and therefore showed a very sharp rise. However, the moisture
probe at the 90 cm depth showed a more gradual increase, most likely due to gradual increase in
(a)
(b)
Salour, Erlingsson and Zapata 9
the capillary moisture content at that depth. The same trend was observed in the moisture probe
registration in the granular layer measured by the probe at 50 cm depth.
FIGURE 4 Groundwater level (a) and volumetric moisture content (b) measurements at
Torpsbruk test site.
FWD Tests
The response of the pavement structure under variable moisture conditions was evaluated by
conducting frequent FWD tests with multilevel loads (Table 2). The FWD tests were conducted
during the stable draining hydrological condition, the stable non-draining hydrological condition
and the changeover period between these two conditions (24).
In total, 11 series of FWD measurements were conducted; one before the drainage
clogging (May 11), five during the clogged period (June 13 and 20, July 4, August 1, and
September 14), and five after the drainage unclogging (September 16, 19, 22, and 26 and
October 13). The FWD tests were conducted along the outer wheel path of the road in both
directions at 10-m intervals (Figure 3). For this study, FWD data obtained from eight stations
(four in each direction) closest to the moisture sensors were used. The first two FWD
measurements (May 11 and June 13) had a different setup and consisted of 11 stations with 2-m
intervals in one direction of the road adjacent to the moisture sensors (24).
(a)
(b)
Salour, Erlingsson and Zapata 10
All FWD tests were conducted at 30, 50, and 65 kN load levels and deflections were
measured by seven accelerometers at 0, 200, 300, 450, 600, 900, and 1,200 mm distance from
the center of the loading plate (150 mm in radius). For each load level, the average value of all
the FWD stations was used.
Response Modelling
In order to analyse the unbound granular and subgrade layer properties at different moisture
contents and stress states, a series of FWD tests with multilevel loads were conducted. The
surface deflection data obtained were further used to backcalculate the stiffness and nonlinear
parameters of the unbound layers. The response of the pavement to external FWD load was
calculated using the ERAPave computer program (25) in which the unbound granular layer and
the subgrade soil were modelled using the k-θ nonlinear Universal Model (19). This model
effectively captures the stress dependent behavior of unbound materials and is expressed as:
#$ = (�Z3� �7�
�=��>[ �?�@�
�=+ 1�
�B[ (3)
where #$ denotes the resilient modulus, 3 is the mean normal stress including the material
self-weight and lateral earth pressure; 3� is the atmospheric pressure (100 kPa), +%,& is the
octahedral shear stress and (�Z , (J
Z and (7Z are regression constants. The ERAPave program
divides the nonlinear layers into a desired number of sub-layers and employs an iterative
procedure to determine the nonlinear stiffness of the sub-layers (25).
In the backcalculation procedure, the HMA layer and the bedrock were treated as linear
elastic materials. Stiffness of the HMA layer was determined using the layer mid-depth
temperature during the FWD tests. A fixed stiffness of 3,500 MPa was assigned to the bedrock.
Both the unbound granular layer and the subgrade were treated as nonlinear material using
Equation 3. In the backcalculation procedure, the unbound granular material was modelled using
the simplified k-θ universal model where (7Z = 0. This simplified model is often used for the
granular layers and is known to capture the overall stress dependent (stress-hardening) behavior
of unbound granular materials (24). A constant (JZ = 0.35 was used for the granular layer for all
of the FWD tests, while (�Z was varying depending on the moisture content of the layer (24).
A Poisson’s ratio of 0.35 was assigned to the HMA layer, the unbound granular layers
and the bedrock. For the subgrade layer, a Poisson’s ratio of 0.4 was assigned. In the pavement
structural model used for the backcalculations, the granular layer was always modelled as a
single layer. The moisture content of the granular layer was determined using the average
measurements of the moisture sensors at 50 cm depth at the time of the FWD tests. However, the
subgrade material was divided into different sublayers, depending on the moisture content
measurements at different depths. The number of subgrade sublayers and the thickness of every
sublayer can be seen in Figure 5. For the FWD measurements conducted on 11 May, 16, 19, 22
and 26 September as well as 13 October, the subgrade was treated as a single layer with a
moisture content equal to the average of the three moisture measurements in the subgrade
(Figure 5(a)). This was due to the fact that the moisture contents measured at different depths
were practically identical (see Figure 4).
For the FWD measurements conducted on 20 June, 4 July, 1 August and 14 September,
the subgrade layer was divided into two sublayers (Figure 5(c)). The moisture content of the
upper 50 cm-thick subgrade sublayer was determined from the moisture sensor at 90 cm depth
Salour, Erlingsson and Zapata 11
and the moisture content of the bottom subgrade sublayer was determined by taking the average
of the moisture sensor measurements at 120 and 150 cm depths. As illustrated in Figure 5(b), for
the FWD measurements that were conducted on June 13, the subgrade layer was divided into
three sublayers in which the moisture content of the subgrade sublayers were individually
determined by moisture sensors at 90, 120 and 150 cm depths.
FIGURE 5 Pavement structure cross sections used in backcalculation in ERAPave and the
backcalculated response measurement points in the subgrade layer.
TABLE 2 Backcalculation RMSEs for FWD Tests Performed under Different Drainage
Conditions and Different Load Levels
Date 11
May
13
Jun
20
Jun
4
Jul
1
Aug
14
Sep
16
Sep
19
Sep
22
Sep
26
Sep
13
Oct
Drainage condition* ○ ● ● ● ● ● ○ ○ ○ ○ ○
FWD
load
level
30 kN 1.96 2.19 0.92 1.30 1.86 1.25 1.61 1.16 1.14 1.03 1.83
50 kN 2.10 3.15 1.14 1.24 1.48 1.75 1.95 2.01 1.96 2.45 1.77
65 kN 2.28 2.12 1.51 1.80 1.31 2.62 1.96 2.19 1.50 1.46 1.41
* ○ = open drainage, ● = clogged drainage
For all three load levels of each FWD test date, the model parameters for each
layer/sublayer were manually changed through an iterative procedure until the surface
deflections computed by the ERAPave program were best matched to the measured deflections
and the criterion was fulfilled. The criterion used for the backcalculation was that the
11 May; 16, 19, 22
and 26 Sep; 13 Oct
13 Jun 20 Jun; 4 Jul;
1 Aug; 14 Sep
(a) (b) (c)
Salour, Erlingsson and Zapata 12
root-mean-square error (RMSE) between the calculated and the measured deflections from
sensors at 450, 600, 900 and 1,200 mm be less than 3.5 % for each test and load level (Table 2).
The rationale behind using only the last four set of deflection sensors in the convergence
criterion of the backcalculation procedure was that they mainly represent the deeper layers in the
pavement structure being the granular and subgrade layers. This would result in more precise
stiffness backcalculation and reduced calculation time. The backcalulation algorithm for
determination of the pavement response and unbound materials nonlinear parameters is depicted
in Figure 6.
FIGURE 6 Backcalculation algorithm of moduli, response and nonlinear parameters.
RESULTS AND DISCUSSION
FWD vs. Laboratory Measured Resilient Modulus
In the backcalculation process, both the unbound granular and the subgrade material were
modelled using the nonlinear resilient modulus model presented in Equation 3. The ERAPave
accounts for the stress dependency of the unbound materials by calculating the in-situ stress state
of the material due to both the geostatic load and the FWD impact load. Therefore, the resilient
modulus of the unbound layers varies with depth as both the bulk stress and the octahedral shear
stress due to static overburden load and FWD-induced impact loads vary with depth. Using the
FWD data with multilevel impact loads the in-situ resilient modulus of the subgrade material and
the responses (stress states) at 4 selected depths (80, 130, 180 and 230 cm) were backcalculated.
These selected depths were within the subgrade sublayers used in the backcalculations
(Figure 5).
Salour, Erlingsson and Zapata 13
Effect of Moisture in the Field Data
The FWD tests were conducted on a pavement structure with varying moisture content within the
unbound layers. In the universal k-θ model, the effect of stress state on resilient modulus is taken
into account through bulk and octahedral shear stresses while moisture effects is not directly
incorporated into the model. However, (�Z parameter in this model usually varies with moisture
in a similar way as in the adjusted model in Equation 1. Figure 7(a) shows the effect of moisture
content variation of the silty sand subgrade on the (�Z parameter of the universal k-θ model that
was used in the backcalculation of the FWD data. Increase in the moisture content (degree of
saturation) resulted in decrease in the (�Z parameter and therefore in the resilient modulus of the
subgrade material.
FIGURE 7 TU
Z parameter (a) and \�]^� term (b) variations due to moisture changes.
In the enhanced resilient modulus model by Cary and Zapata (8) presented in Equation 2,
the moisture effects on the resilient modulus is taken into account by the last term of the equation
which is the matric suction term (ℎ�-)�). This term accounts for adjusting the resilient modulus
of the material with respect to its moisture content (suction). Figure 7(b) shows the variation of
the adjustment factor due to changes in the subgrade moisture content on the FWD test dates.
This figure is produced using the in-situ subgrade moisture content measurements and SWCC
presented in Figure 2(b). Here, the suction factor in Equation 2 increased the resilient modulus
by a factor of 1.3 as the subgrade degree of saturation was reduced from 100 % to about 46 %.
The backcalculated subgrade stiffness at the selected response depths obtained for all of
the FWD test dates and load levels were compared with the resilient modulus results obtained
from the laboratory-based model expressed in Equation 2 (Figure 8). Both the field
measurements and the laboratory tests confirm the stress and moisture dependence of the
subgrade material modulus. In general, good agreement was observed between the moduli. The
field and laboratory data showed a good correlation for all the measured moisture states
(R2=0.82). The enhanced resilient modulus model in Equation 2 appeared to reliably capture the
effect of the stress state and moisture content of the subgrade material on the resilient modulus.
Salour, Erlingsson and Zapata 14
FIGURE 8 Laboratory versus backcalculated moduli using nonlinear model in ERAPave.
SUMMARY AND CONCLUSION In unsaturated subgrade materials with high fine content, variation in the matric suction is known
to be the main factor for seasonal variation of the resilient modulus which is caused by moisture
content changes. This factor should therefore be taken into account in any realistic resilient
modulus predictive model. In this paper, the laboratory-determined regression parameters of an
enhanced resilient modulus predictive model for a silty sand subgrade are presented. This model
incorporates matric suction as stress state variable to account for seasonal variation of moisture
content within the subgrade material. To evaluate this model, series of in-situ FWD test were
conducted along a pavement test section in which the moisture content of the silty sand subgrade
layer was manually changed by manipulating the drainage system of the section. The subgrade
degree of saturation during the FWD tests varied between 45% to full saturation. The FWD field
data were then used to backcalculate the stiffness of the subgrade soil at different moisture
contents and depths using the universal resilient modulus model.
For the range of the subgrade degree of saturation measured in the field (!"= ~ 45 to
~100%) the matric suction accounted for about 30% of the variation in the subgrade resilient
modulus. The enhanced predictive resilient modulus model by Cary and Zapata (16), which
includes the matric suction parameter, seemed to successfully capture the moisture content
variation effects on the resilient modulus. In general, a good agreement was observed between
the subgrade resilient modulus calculated from the enhanced predictive model and the
backcalculated stiffness obtained from the FWD field data, concluding that the modulus-suction
model could efficiently capture the seasonal variation effects.
It is believed that once a more extensive database with more tests and materials is
obtained, the approach used in this study together with the SWCC analytical models can be
adapted for developing more comprehensive resilient modulus predictive models for subgrade
soils that account for seasonal moisture variations.
0
50
100
150
200
250
300
0 50 100 150 200 250 300
Backcalculated subgrade stiffness [MPa]
(ERAPave)
Predictive Model Stiffness [MPa]
13-Oct
26-Sep
22-Sep
19-Sep
16-Sep
14-Sep
1-Aug
4-Jul
20-Jun
13-Jun
11-May
R2 = 0.82, n=165
Salour, Erlingsson and Zapata 15
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