backcalculation models to evaluate light falling weight
TRANSCRIPT
BACK-CALCULATION MODELS TO EVALUATE THE LFWD MODULI
OF A ROAD FOUNDATION LAYER MADE WITH BOTTOM ASH
WASTE
By
Ahmed, Abdelkader T*
School of Engineering, University of Liverpool
Room 614, Brodie Tower, Brownlow Street,
Liverpool, L69 3GQ, UK
Email: [email protected]
Tel: 0151 7944896
Fax: 0151 7945218
Khalid, Hussain A
School of Engineering, University of Liverpool
Room 610, Brodie Tower, Brownlow Street,
Liverpool, L69 3GQ, UK
Email: [email protected]
Tel: 0151 7945222
Fax: 0151 7945218
Submission date: 22 /10/2010
*Corresponding author
Word Count (not include the title page): Abstract, 197; Text, 4650; Figures, 9; Table, 1
TRB 2011 Annual Meeting Paper revised from original submittal.
1
ABSTRACT
Incinerator bottom ash (IBA) is a residue from burning household waste that used to be
landfilled but now two-thirds of this ash is reused mostly in road construction. In this study, IBA
was mixed with limestone to produce a blend with acceptable properties for use as a road
foundation layer. In-situ simulative testing with a Light Falling Weight Deflectometer (LFWD)
and subsequent interpretation of the surface deflection data have enabled the evaluation of the
mechanical properties of the foundation and subgrade layers. This paper presents an
experimental and modelling study of the elastic dynamic response of a foundation layer of IBA
waste and limestone which was subjected to LFWD impact loading. Several parameters were
studied, such as IBA content, water content and curing time. Regression, mathematical and
three-dimensional finite-element models were developed to back-calculate the LFWD moduli of
the foundation layers. The modelling approach accounted for the static and impact nature of the
LFWD load. Results showed that IBA blends underwent less deflection, as a foundation layer,
than the control limestone blend. Back-calculated moduli results based on the dynamic effect of
the LFWD load produced different values from those calculated by Boussineq’s equation, which
is adopted by the LFWD manufacturer.
TRB 2011 Annual Meeting Paper revised from original submittal.
2
INTRODUCTION
Most developed countries nowadays face aggregate supply and waste disposal challenges. In the
UK, 25 % of household waste production is currently incinerated, which generates an annual
output of around one million tonnes of incinerator bottom ash (IBA) waste. In the past, this ash
was generally landfilled but in recent years, nearly two-thirds of the ash has been used mostly in
road construction (1). IBA has physical and chemical properties that make it amenable for use as
an aggregate substitute in different construction applications, such as compacted road base
material, structural fill in wind and sound barriers, and highway ramps, and asphalt applications
(2). Despite the multitude of feasible applications, IBA’s adoption in road pavement structures
has not been substantial. To enhance its use, the behaviour of IBA needs to be further examined
under representative field conditions.
In pavement foundation design, one of the most common equipment used to evaluate the strength
and stiffness of the material in the UK is the California Bearing Ratio (CBR). However, although
the CBR is widely adopted as a performance parameter, it is not considered satisfactory for
pavement design requirements, because deformations considered in the test are much higher than
what happens in situ due to wheel loading. The complexity and cost of other laboratory test
procedures prompted direct field tests to be explored. A direct measure like the Falling Weight
Deflectometer (FWD) of the performance parameters of the foundation materials, as they are
constructed in the field, provides a greater assurance of the design and efficiency of site
operations (3, 4, 5, 6). Recently, new light devices such as the Geogauge, Dynamic Cone
Penetrometer (DCP) and the Light Falling Weight Deflectometer (LFWD) have been used to
reliably measure the in-situ stiffness modulus of pavement layers.
In this work, IBA waste was mixed with limestone to produce a blend with acceptable
specifications for a minimum required surface stiffness modulus for use as a road foundation
layer. LFWD tests were adopted to study the elastic properties of IBA blends. The LFWD is a
portable falling weight deflectometer that has been developed as an alternative in-situ testing
device to the plate load test. In-situ testing using the LFWD and the subsequent interpretation of
the surface deflection data via rational analysis techniques has provided pavement professionals
with a convenient methodology for evaluating the mechanical properties of foundations and their
supporting subgrades (7). The LFWD is a non-destructive test that has experienced increased
popularity due to its light weight and quick measurements. In the UK, recent specifications have
recommended using the LFWD apparatus to measure the surface modulus for most foundation
materials (8). LFWD tests normally use the deflection measured by a centre geophone coupled
with a static, linear-elastic half space theory to calculate one elastic modulus for the whole
composite soil and foundation system, which is not representative of the elastic modulus of the
separate layers. With the possibility of measuring surface deflection at different points away
from the load application point by using extra geophones, the back-calculated moduli would be a
quick, convenient and more accurate way to express the layers’ moduli.
TRB 2011 Annual Meeting Paper revised from original submittal.
3
Very little research has been performed to evaluate the LFWD test with extra geophones and its
back-calculated moduli from the deflection basin (9, 10). In previous studies, back-calculated
moduli were accounted for by FWD applications, which is different from LFWD in load and
deflection values. A number of these studies (11, 12, 13) relied mainly on the static analysis of
linear elastic theory for a multilayered pavement system subjected to FWD loads, in which each
layer is characterized by its Young’s modulus and Poisson’s ratio. Surface deflections are
calculated and matched with measured deflections, and moduli are adjusted until the percentage
of matching error is reduced to an acceptably low value. However, some other studies depended
on a dynamic analysis due to the dynamic nature of FWD loads. Based on elasto-dynamic
analysis, Mamlouk et al. (14) concluded that dynamic deflections under FWD tests were greater
than the corresponding static displacements due to local amplification in the pavement system.
Zaghloul et al. (15) conducted a nonlinear dynamic analysis of FWD testing and showed that the
dynamic deflection basin computed from a finite element model compared reasonably with
measured deflection data. Al Qadi et al. (16) developed a finite element model to investigate the
dynamic behaviour of thin flexible pavement responses under the impulsive loading of the FWD
test. It was concluded that the dynamic analysis resulted in slightly greater predicted pavement
responses in comparison to the quasi-static analysis. In some cases, the difference between the
dynamic and static analysis is negligible, especially if the assumed subgrade layer in the model is
deep enough.
In this study, different approaches were adopted to find the best matching modulus of the
foundation layer by using regression and finite element models. A three-dimensional finite
element model was developed using a commercially available package, known as LS-DYNA, to
determine the back-calculated moduli taking into account the impact nature of the applied load.
The main objective of this work was to use LFWD test in a large box constructed in the
laboratory to reproduce field conditions in order to study the mechanical properties of IBA
blends serving as road foundation layers. The objectives can be summarized as follows:
Evaluate the stiffness properties of compacted IBA blends.
Predict the moduli of the foundation layers by using the deflection bowl from
experimental data based on a number of back-calculation approaches.
EXPERIMENTAL PROGRAMME
An experimental programme was undertaken to study the effect of various parameters, such as
IBA content, moisture content and curing time on the resulting moduli. LFWD test results
represent the average of four determinations at four different positions on the same layer and
each of them is the average of three readings recorded in the same position after discarding the
first three readings. Thus, each layer result represents the average of twelve readings taken on the
layer’s surface.
TRB 2011 Annual Meeting Paper revised from original submittal.
4
Equipment
Test equipment consisted of the LFWD device, two extra geophones and two identical wooden
square boxes to reduce the overall project duration; each of them is 1000 mm long and 1000 mm
deep. The two boxes were lined internally by plastic sheets to provide waterproofing. The LFWD
device 100 has a load range of 1–15 kN, i.e. up to 450 kPa stress with a 200 mm diameter
loading plate and up to 200 kPa with a 300 mm plate, which was used in this work. The large
plate was adopted in this work because it has been found to produce more consistent results due
to separating load over a wider area (17).
Sample preparation
Three materials were used in this study: IBA, limestone and natural subgrade soil. IBA was
supplied in two sizes: 20-10 mm and 10 mm. Limestone was chosen as the control aggregate in
the mixtures. It was supplied in six sizes: 20, 14, 10, 6, 4 mm – dust and filler. Gravelly silt clay
was collected from a site near the laboratory in Derbyshire, UK, and used at its natural water
content as the subgrade layer in the experiments. Four blends were used in this study, with four
different IBA contents, called A with limestone only, B, C and D with 30, 50 and 80% IBA by
mass respectively. Further details of all blends were presented by Ahmed and Khalid (18).
All blends were compacted on top of a 250 mm compacted natural soil, which served as a
subgrade layer and remained inside the box during the whole testing programme. IBA subbase
materials were dried and weighed as four sublayers, each weighing 125 kg, to form a 250 mm
thick foundation layer. Each IBA sublayer was mixed in a large mixer. The mixture was then
placed in the box, levelled and compacted. A vibratory hammer with 100 by 150 mm size foot
was used for a period of 20 seconds over each position to compact the material. The surface of
each layer was manually roughened before adding the next layer; in this way a good layer
interlock and a homogeneous blend was obtained. After finishing the four sublayers, the
materials were covered with a plastic sheet to prevent evaporation. Initial densities obtained for
the blends were 2.52, 2.43, 2.37 and 2.33 Mg/m3 for A, B, C and D respectively.
Test procedure
The LFWD device was set up on the layer’s surface at four different positions to determine the
dynamic modulus. At each test position, three readings were taken. Two geophones were used to
measure the deflection at two further points in addition to the loading point underneath the
LFWD base plate. Figure 1 shows the four test locations of the LFWD device and geophones on
the layer’s surface, this being the minimum recommended distance to avoid boundary effects on
the measured properties (17). The four positions were chosen to be offset from the box sides by
at least 300mm. Readings were taken immediately after compaction followed by further readings
after 1, 7, 14 and 28 days with the layer covered by a plastic sheet in between to keep its
moisture content constant.
TRB 2011 Annual Meeting Paper revised from original submittal.
5
FIGURE 1 LFWD test locations in the box.
EXPERIMENTAL RESULTS
Effect of IBA content
Figure 2 shows that the measurements of surface deflection at the three geophones for blends B
and C were either similar or more than that of limestone tested at seven days old and optimum
moisture content (OMC). However, blend D with 80% IBA showed lower deflection than the
limestone blend, especially at the first position, i.e. the loading point. This is probably due to the
high angularity of IBA particles, which provided a good interlock and, thus, less deflection.
Moreover, pozzolanic activity of IBA materials increased with increase in the blend’s IBA
content.
Effect of water content
Figure 3 presents the LFWD test results for blends A and D, at three different water contents:
OMC and OMC±2%, with OMCs being 5 and 7.4% respectively. The figure shows that the
surface deflection of blend D increased with increase in water content, blend A just as; however,
the drier limestone blend showed higher deflection values than those of the OMC case, which
was unexpected. The dry limestone blend was produced immediately after the compaction of the
subgrade layer and the latter was initially very soft and weak, which may explain the high
deflection values. In the following tests, however, the subgrade layer was modified by removing
some soft clay from the surface and recompacted to improve its properties.
1000 mm
1000 mm
≥300 mm ≥300 mm
300 mm
LFWD plate
Geophone
200 mm
200 mm
≥300 mm
≥300 mm
TRB 2011 Annual Meeting Paper revised from original submittal.
6
FIGURE 2 Effect of IBA content at OMC and seven days.
FIGURE 3 Effect of water content for blends A and D at seven days.
Effect of curing time
The blends’ surface was tested by LFWD at intervals of 1, 7, 14 and 28 days to monitor the
curing time effect. Figure 4 presents the deflection values for blends A and D. The figure shows
that both blends underwent an improvement in the deflection measurements with time. Blend A’s
deflection decreased after 28 days by 20% and blend D’s decreased by 25% in comparison to the
first day’s measurements. Both blends exhibited less deflection with time; however, blend D
underwent more improvement and less total deflection than limestone. These changes can be
attributed to the abundant presence of silicon and aluminium elements in the IBA, which aid its
pozzolanic activity especially in the presence of calcium from limestone (19).
0
100
200
300
400
500
600
0 100 200 300 400 500
De
fle
ctio
n (
µm
)
Distance from the LFWD centre (mm)
A, Limestone
B, 30% IBA
C, 50 % IBA
D, 80% IBA
0
100
200
300
400
500
600
0 100 200 300 400 500
De
fle
ctio
n (
µm
)
Distance from the LFWD centre (mm)
OMC-2%
OMC
OMC+2%
Blend A0
100
200
300
400
500
600
0 100 200 300 400 500
Distance from the LFWD centre (mm)
OMC-2%
OMC
OMC+2%
Blend D
TRB 2011 Annual Meeting Paper revised from original submittal.
7
FIGURE 4 Effect of curing time for blends A and D at OMC.
MODULI of MATERIALS
Moduli values adopted by the equipment manufacturer
During LFWD tests, the falling mass impacts the plate producing a load pulse in the range of 1–
15 kN in about 15–20 ms. The measured deflection at the centre of the plate was used to
calculate the dynamic modulus, ELFWD, using Boussineq’s equation as follows:
ELFWD = 𝐶 1−𝑣2 σR
𝑑𝑐 (1)
where C = π/2 and 2 for rigid and flexible plates respectively; dc is centre deflection; σ is applied
stress; R is radius of the plate; and ν is Poisson’s ratio. In this work, equation parameters were
taken as: C is 2, R is 150 mm and ν = 0.35.
Regression back-calculated moduli
The LFWD modulus value depends on a number of factors, such as applied load, layer density,
curing time and water content, which were discussed in the previous sections. The effect of all
these parameters was reflected through the surface deflection values. Fwa and Chandrasegaran
(20) concluded that the deflection-based back-calculation solution, in the form of regression
equations, would have useful practical applications because of its speed and convenience in the
computation of the moduli. In an attempt to predict the moduli from the surface deflections and
applied loads, a back-calculation model based on measured deflections at the three points of the
deflection basin was derived using regression analysis. The statistical software package SPSS
was used to perform a comprehensive regression analysis on the LFWD results to establish the
best empirical relation between measurements and parameters. Analysis based on the work by Li
et al. (21) was adopted, in which the surface deflection, δr, of a point at a distance r from the
0
50
100
150
200
250
300
350
0 100 200 300 400 500
De
fle
ctio
n (
µm
)Distance from the LFWD centre (mm)
1 day7days14 days28 days
Blend A
0
50
100
150
200
250
300
350
0 100 200 300 400 500
Distance from the LFWD centre (mm)
1 day7days14 days28 days
Blend D
TRB 2011 Annual Meeting Paper revised from original submittal.
8
centre of the loading plate, as shown in Equations 2 and 3, is analysed to find the best correlation
between the deflection basin and elastic modulus using least square error models, coefficient of
determinations, R2, and standard error.
k =𝜎
δr𝑓 (2)
k ∝ 𝜎 𝑓1
δ1+
𝑓2
𝛿2+
𝑓3
𝛿3 (3)
where k is modulus of subgrade reaction; σ is applied stress from the loading plate; δ1, δ2 and δ3
are measured deflections in mm at radial distances of 0, 200 and 400 mm from the centre of
loading respectively; and f1, f2 and f3 are deflection factors depending on the distance from the
plate centre and equal to 1 at the plate centre.
In the case of loading plate on elastic half space, the relation between reaction modulus, k, and
Young’s modulus, E, can be described as follows (22):
𝐸 = 𝑘𝑚 1− 𝑣 𝐴 (4)
where A is loading plate area = π a2; a is plate radius and equals 150 mm; and m is shape factor
and equals 1 for the circular plate. Using these parameter values, the final relation between k and
E can be presented as in the following equation:
𝐸 = 0.233𝑘 (5)
The regression results produced the following equation to estimate layer moduli based on the
experimental data with the correlation coefficient, R2, being 0.998:
𝐸 = 0.233𝜎 995.22
δ1−
2.04
δ2+
2.14
δ3 (6)
Results from this and from subsequent models considered in this paper are presented in Figure 9,
which provides a comparative snapshot of the layer moduli calculated using different methods.
Mathematical back-calculated moduli
The aim of this part of the research was to back-calculate the layer moduli via a mathematical
relation between elastic modulus and deflection in beam structures due to an applied load. A
simple assumption was made for the soil strip underneath the loading plate to act as a simply
supported beam of 1210 mm span, 300 mm width and 500 mm thickness, as shown in Figure 5.
The relation between the elastic modulus and deflection can be derived via an analytical
procedure called the double integration method. In this method, when a beam is loaded
elastically, the longitudinal central axis of the beam becomes an elastic curve. Deflection of the
TRB 2011 Annual Meeting Paper revised from original submittal.
9
beam is so small, such that the elastic curve radius is very large. The elastic curve is an arc of a
circle of radius ρ, in which the beam is deformed only by a bending moment. The relation
between the bending moment, M, elastic modulus, E, moment of inertia, I and deflection, y, at
any distance x is described in the following differential equation:
1
𝜌=
𝑑2y
𝑑𝑥 𝟐=
𝑀𝑥
𝐸𝐼 (7)
The double integration method was used to solve Equation 7 for the deflection, y as a function
of distance x along the beam. The constants of integration are evaluated by applying the
boundary conditions, in which a known set of values of x and y at a specific point in the beam is
defined. Consequently, after normal integration steps to find the value of the deflection, y, using
simple calculus and with the assumption that the sub layer curved with the same radius as the top
layer, the equation for the elastic modulus of the soil layers due to the applied load is given by:
E =Pbx
6yIL L2 − b2 − x2 For 0 ≤ x≤ a (8)
where P=applied load; L=beam length; and b is a distance between load and one of the beam
supports. y1 is a deflection under load. Figure 9 presents layer moduli results based on Equation
8 for blends A and D using the parameter values of P=7 kN; I=312500 cm4; b=32.4 cm; and L=
121cm.
FIGURE 5 Section details of the soil beam.
500 mm
y 1 y 2 y3
b=324 mm a=886
mm
L=1210
mm
x
P=1-15 kN
y
300 mm
1000 mm
1000 mm
300 mm
y 1
L=1210
mm 300 mm
TRB 2011 Annual Meeting Paper revised from original submittal.
10
3D-FEM back-calculated moduli
The LFWD equipment produces an impact load, yet most back-calculation analyses assume that
the moduli can be estimated using static analysis. It has been prove that static and dynamic
responses are different, as expected, due to the inertial effects associated with the latter (12, 23,
24). The finite element method offers a powerful tool for developing back-calculation models for
evaluation of pavement surface deflection basins generated by pavement deflection equipment.
In this study, an explicit dynamic 3D-FE back-calculation model was developed using the LS-
DYNA solver software to back-calculate the moduli of a two-layer model relying on the dynamic
nature of the applied impact loads. During model design trials, it was found that the physical
simulation of the falling weight on the layer is closer in terms of the generated deflection results
to LFWD experiment values than that of applying propagating monotonic loads as a simulation
for the impact load. Thus, the model was designed to provide a physical simulation of the impact
load applied by the LFWD equipment, in which the weight falls from a specified height as was
the case during the experiment. Figure 6a describes the impact stress applied by the equipment
and simulated by the model. The two layers were modelled using 8-node solid brick elements
with 24 degrees of freedom per element. After mesh refinement trials, each layer comprised 4840
nodes and 4000 elements, and 528 elements were used for modelling equipment parts. Boundary
conditions were chosen to represent box conditions in experiments as the box base was fixed and
the sides were hinged to allow vertical displacements for the layers. A friction coefficient of 0.3
was applied at the interface between the two layers. Figure 6b presents details of the 3D-FE
model.
Model results
In the 3D-FE back-calculation model, an attempt was made to match the measured surface
deflection of the layers in the laboratory boxes with the calculated surface deflection generated
from an identical layer structure using assumed layer stiffness moduli. Table 1 presents the
geometry details and material inputs for the FE model. Initially, generated deflection values were
inaccurate; thus, the assumed layer moduli in the calculated model were adjusted until they
Table 1. Geometry details and material inputs for 3D-FE model
Model parts
Geometry Initial properties Dimension
(mm)
Thickness (mm)
Elastic
modulus
(MPa)
Poisson’s
ratio Density
(Kg/mm3)
Subgrade layer 1000x1000 250 50-70 0.45 2.6E-6
IBA layer 1000x1000 250 100-700 0.32 2.05E-6
Limestone layer 1000x1000 250 100-600 0.34 2.1E-6
Base plate Diameter: 300 20 210000 0.30 7.85E-6
Falling weight Diameter: 150 75 210000 0.30 7.85E-6
Rubber pad Diameter: 150 20 10000 0.45 9.0E-7
TRB 2011 Annual Meeting Paper revised from original submittal.
11
FIGURE 6 (a): Impact stress applied by falling weight in LFWD experiments, and (b): 3D-
FE model details.
0
20
40
60
80
100
120
0 5 10 15 20 25
Imp
act
stre
ss (
kPa)
Time (ms)
250 mm
250 mm Subgrade
IBA blends
1000 x 1000 mm
Falling weight
Base plate Rubber pad
b
a
TRB 2011 Annual Meeting Paper revised from original submittal.
12
produced a surface deflection that closely matches the measured one. The final values of
assumed layer stiffness that were obtained were then assumed to be the IBA blends’ layer
moduli.
One of the advantages of the 3D modelling approach is the ability to follow the propagation of
the stress and displacement through any layer and at any point in the model. Figure 7 shows
snapshots of Von Mises stress and vertical displacement fringes for the IBA model at 10 ms,
which is the peak impact moment. The figure shows that the top layer experienced significant
localized compressive stresses because the impact load affected it locally underneath the plate;
however, its effect was distributed over the whole of the bottom layer, which confirms that
deflection values at the extra geophone positions express the bottom layer deflections rather than
the surface layer. Due to the unbound interface between IBA and subgrade layers in the model
and even with the friction applied between them at the time of the impact, the material rose
against its own weight. This deformation feature was captured only during the impact moment,
as observed in Figure 7b. The same behaviour was noted during the experiments, as layers
bounced during load application.
Figure 8 shows deflection results of the FE simulations for the LFWD impact load on the layers
made from blends A and D. These results correspond to the three nodes located at the central
area of the plate and the two geophone positions in the experiment, as shown in Figure 1. From
Figure 8, the FE model was able to match the results for blends A and D reasonably well. The
moduli values produced by the FE model were higher than aforementioned back calculated
moduli. This is probably due to the fact that, in these models, static analysis was used for the
applied load while the FE model adopted the impact effect of the load.
Comparison between different back-calculation models
Figure 9 shows a comparison between the modulus results of different back-calculation models
used in this study. The 3D-FE model showed completely different values from the other models
due to the fact that, in these models, static analysis was used for the applied load while the 3D-
FE model adopted an impact effect. The figure shows that Equation 8 provides the closest
moduli values to those from laboratory triaxial test results on the same blends, which were
presented by Ahmed and Khalid (19). Whilst Boussineq’s equation is seen to underestimate the
modulus value, Equation 8 can be considered as a convenient approach to generate reasonable
estimates of the modulus from LFWD measurements.
TRB 2011 Annual Meeting Paper revised from original submittal.
13
FIGURE 7 Snapshot of 3D-FE model at impact time for blend D, (a): Von misses stress
contours and (b): vertical displacement contours.
a: IBA layer a: subgrade
IBA layer Subgrade b: IBA layer b: subgrade
TRB 2011 Annual Meeting Paper revised from original submittal.
14
FIGURE 8 Experimental and FE simulation deflection for blends A and D.
FIGURE 9 Back-calculated moduli for blends A and D.
CONCLUSIONS
From the results obtained in this work, the following remarks can be made.
IBA blends underwent less deflection, as a foundation layer, than the control limestone
blend.
The deflection values of blend D increased with increase in the water content.
The deflection values of blends A and D decreased with increase in curing time.
0
100
200
300
400
0 100 200 300 400 500
Defl
ecti
on
(µ
m)
Distance from the LFWD centre (mm)
Experiment results, A
Simulation results, A
Experiment results, D
Simulation results, D
0
100
200
300
400
500
600
700
Ela
sti
c m
od
ulu
s (
MP
a)
Back-calculation method
Blend A
Blend D
Equ.1 Equ.6 Equ.8 3D-FEM Triaxial
TRB 2011 Annual Meeting Paper revised from original submittal.
15
Moduli results from back-calculation models based on the LFWD readings were higher
than those calculated by Boussineq’s equation, which is adopted by the LFWD
manufacturer.
Finite element analysis resulted in higher values for the foundation layer moduli in
comparison to those obtained using static analysis models.
ACKNOWLEDGEMENT
The authors are indebted to Aggregate Industries for the technical and financial support of this
investigation. The award of a study scholarship by the Egyptian government to pursue this
research programme is gratefully acknowledged.
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TRB 2011 Annual Meeting Paper revised from original submittal.