Backcalculation Models to Evaluate Light Falling Weight ...

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.


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.


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.


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.


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


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

)


OMC-2%

OMC

OMC+2%

Blend A0

100

200

300

400

500

600

0 100 200 300 400 500


OMC-2%

OMC

OMC+2%

Blend D


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


1 day7days14 days28 days

Blend D


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


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


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


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


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.


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


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)


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


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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