Experimental Behaviour of Concrete Box Culverts · 2019-05-10 · culverts (Yang 2000). Therefore,...

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Experimental Behaviour of Concrete Box Culverts - Comparison with Current Codes of Practice

Journal: Canadian Geotechnical Journal

Manuscript ID cgj-2018-0506.R1

Manuscript Type: Article

Date Submitted by the Author: 20-Aug-2018

Complete List of Authors: Cristelo, Nuno; Universidade de Tras-os-Montes e Alto Douro, CQ-VRFélix, Carlos; Instituto Politecnico do Porto Instituto Superior de Engenharia do Porto, CONSTRUCT-LABESTFigueiras, Joaquim; Universidade do Porto Faculdade de Engenharia, CONSTRUCT-LABEST

Keyword: Earth Pressure, Culverts, Numerical Analysis, Structural Instrumentation

Is the invited manuscript for consideration in a Special

Issue? :Not applicable (regular submission)

https://mc06.manuscriptcentral.com/cgj-pubs

Canadian Geotechnical Journal

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September 2018

Experimental Behaviour of Concrete Box Culverts - Comparison

with Current Codes of Practice

a,* Nuno Cristelo; b Carlos Félix; c Joaquim Figueiras

a CQ-VR, Department of Engineering, University of Trás-os-Montes e Alto Douro, 5001-801

Vila Real, Portugal* Corresponding author

Telephone: + 351 259 350 643

E-mail address: [email protected]

b CONSTRUCT-LABEST, School of Engineering, Polytechnic Institute of Porto, 4249-015

Porto, Portugal


c CONSTRUCT-LABEST, Department of Civil Engineering, Faculty of Engineering, University

of Porto, 4200-465 Porto, Portugal


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mailto:[email protected]



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Abstract

It is now accepted that current expeditious models for determining earth pressures on flexible

underground structures under compacted layers do not include several technical nuances of the

soil-structure interaction. Thus, these models are not capable of delivering an optimised design.

The present paper compares the results from the well-known AASHTO model with two different

numerical models – a user-friendly elastic model and a more robust finite element model, and

with the results retrieved from a full-scale monitoring of a concrete box culvert, 5.5 m high and

3.77 m width, over which a 15 m high embankment was built. This structure was selectively

instrumented, over a period of almost 1 year, during which several parameters were recorded,

including earth pressures and structural deformation. Results have shown that the two most

significant drawbacks associated with the use of the AASHTO model are the inadequate

evaluation of the vertical pressure on the top slab and the coefficient of earth pressure, which

results in a significant over-estimation of the lateral pressures and, consequently, into an overall

inefficient design of the structure.

Keywords: Earth Pressure; Culverts; Numerical Analysis; Structural Instrumentation

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1. Introduction

The mechanical behaviour of buried structures is strongly influenced by soil-structure interaction.

It is obvious that the stresses in the structure depend on the earth loads, but these earth loads are

also a function of the structure’s deformation, which in turn depends on the structural stresses. It

is this complex iterative process, together with the fact that the earth load depends not only on the

geotechnical parameters of the embankment but also on the construction procedures (e.g.

compaction energy), that makes the estimation of the stresses acting on the structure a sequence

of assumptions, which can result in a far from accurate, usually over-conservative, structural

design (Ebeling and Mosher 1996; Hansen et al. 2007; Chen et al. 2010, 2016; O’Neal and

Hagerty 2011; Oshati et al. 2012). However, although it is well-known that classic theories to

predict geometry and magnitude of earth pressures around a box culvert (BC) are more than

likely to produce results substantially different from reality, a more satisfactory model is yet to be

developed. The difficulty associated with the determination of the true value of the soil pressures

around the BC is also related with the complex soil-structure interaction, which includes the

development of an arch effect in the soil, especially in buried structures such as a BC.

The fundamentals of the similar theories tackling the soil-structure complex and combined

behaviour were derived in the first half of the 20th century (Marston and Anderson 1913; Marston

1930), aiming the estimation of the geostatic pressure distribution around steel pipes in trenches.

In essence, the main principle is that the pressure from the soil is given by the total weight, of the

soil above the structure, multiplied by a soil-structure interaction factor, which depends mainly

on the relative stiffness of the soil above and on the sides of the structure.

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Nevertheless, it is important to note that the trench type installation (Figure 1a) creates a positive

arching effect that is the opposite, in terms of soil pressure redistribution, of the embankment

type installation (Figure 1b), which generates a negative arching effect (Chen et al. 2010; Oshati

et al. 2012; Chaloulos et al. 2015). The positive arch effect transfers the load from the soil

directly above the trench to the side fills. However, for this positive arch effect to occur, it is

necessary that the soil in the trench is more compressible than the adjacent soil (which is usually

the case due to the lower compaction energy used in the trench area, immediately above the

buried structure), and thus the central soil volume becomes ‘suspended’ on the lateral volumes.

This mechanism enables a stress transfer from the softer central area to the stiffer lateral areas. A

similar effect can be achieved if the buried structure has a low stiffness compared with the soil

stiffness on the side fills.

On the contrary, for embankment type loadings, the negative arch effect transfers the soil weight

from the side fills to the central fill above the structure, not only because the thickness of the area

directly above the BC is smaller than the thickness of the side fills, resulting in higher absolute

settlements of the latter, but also due to the higher stiffness of the concrete structure supporting

the central fill, relatively to the stiffness of the foundation soil beneath the side fills. The load

transfer between soil blocks happens through the shear stress 1, which creates an additional

stress on the top slab of the BC (Figure 1b). The magnitude of the transfer increases with the

stiffness of the foundation soil and decreases with the compaction efficiency of the lateral soil (in

this case, assuming that such lateral soil will not suffer further compaction, during its service

life). It is also exacerbated when a high-stiffness concrete structure is used, just like the one

described in this paper.

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Figure 1: Relative displacement around a trench type installation (a) and an embankment type installation (b)

The American Association of State Highway and Transportation Officials (AASHTO)

publications ‘LRFD Bridge Design Specifications’ (AASHTO 2010) and ‘Standard

Specifications for Highway Bridges’ (AASHTO 2002), propose Eq. (1) to estimate the force

acting on the top slab of an embankment installation culvert, as well as Eq. (2) for the

contribution of the lateral fills:

𝑊 = 𝐹 ∗ 𝛾 ∗ 𝐵 ∗ 𝐻 (1)

with:

𝐹 = 1 + 0.20 ∗𝐻𝐵

(2)

where W is the earth total weight (in kN/m), F is the soil-structure interaction factor for

embankments, is the unit weight of the embankment soil, B is the outside culvert width and H is

the embankment height.

The factor F, which was determined based on the Marston-Spangler theory, should be ≤ 1.15,

when the fill on the sides of the culvert section is compacted, or ≤ 1.40, if these side fills have no

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compaction. The reason for the F value being higher when the lateral soil is not compacted is

related with the larger deformation that such soil will suffer, which will then produce a heavier

downward load on the central soil, above the BC. However, it fails to properly reproduce the arch

effects that will develop in the soil around a rectangular cross section, as well as the subsequent

stress redistribution (Abolmaali and Garg 2008; Lawson et al. 2010). This is due to an inadequate

interpretation of the complex soil-structure interaction and to some difficulty in characterising

and controlling the factors that rule the mentioned phenomena, namely the soil properties and the

geometry and stiffness of the structure (Kang et al. 2008; Liu et al. 2008; Oshati et al. 2012; Chen

et al. 2016).

It is important to notice that the AASHTO specifications assume a rectangular distributed force

acting on the top slab, disregarding its variation along the width of the culvert. According to the

literature review, this variation is of significant importance in the present case, due to the

development of the mentioned arch-effect.

The installation method is also relevant, since a pipe buried in a narrow trench represents a

completely different situation, in terms of soil-structure interaction, of a culvert founded on the

natural ground surface, and covered with soil afterwards. Also, metal and concrete circular

culverts have significantly different flexibility properties than quadrilateral cross-section concrete

culverts (Yang 2000). Therefore, stress distribution on the top slab of the quadrilateral geometry

cannot be calculated with the same formulations. Furthermore, the width-to-height ratio and

concrete thickness of the quadrilateral culvert are also very influential on the top slab deflection

and steel reinforcement required (Shatnawi et al. 2017). Most of these factors can only be

thoroughly defined using very robust numerical models – which are not as popular in regular

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engineering practice as they might be among researchers – and even those need some validation,

which can only be achieved through monitoring of live-scale structures.

Other authors (Kim and Yoo 2005), aiming to increase the effectiveness of the analytical models,

proposed a different set of equations for determining the factor F, to be used when computing the

earth pressures acting on the top slab (Eqs. 3 and 4). These equations can be considered an

improvement of the original method, since it includes the foundation stiffness. However, they

still don’t consider such factors as the frictional forces on the walls of the BC, or the earth

pressure on its bottom slab.

𝐹 = 1.047 ∗ 𝐻0.055 (for yielding foundation soils) (3)

𝐹 = 1.200 ∗ 𝐻0.059 (for unyielding foundation soils) (4)

Arch effects can be both global – related with the culvert installation method – and local – which

is a function of the soil response to the culvert deflection. Therefore, another form of stress

redistribution occurs when the top slab is sufficiently flexible for a significant differential

deformation between the centre of the slab and the areas near the vertical walls of the BC,

creating three distinctive areas of soil above the structure (Figure 2). The two lateral soil blocks

have a relative settlement (cb1) and vertical stresses smaller than the one experienced by the

central block (cb2). These differential settlements between the middle and lateral blocks generate

shear stresses (2) which, in turn, impose additional loads on the lateral blocks. The higher

deflection of the central section significantly decreases the corresponding acting load, and

increases the loads on the lateral sections, where the deformation is practically inexistent (Figure

2).

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Figure 2: Relative displacement on a flexible top slab of an embankment installation BC

The aim of this research work was to contribute to the insufficient knowledge regarding the

complex stress distribution around a BC. For better understand the complex interaction between

all the intervenient factors, an extensive monitoring programme was designed and implemented

on a live-scale concrete BC, from the start of the construction. The data was then compared with

the results yielded by one of the most worldwide used analytical models, proposed by the

American Association of State Highway and Transportation Officials.

2. Case study

2.1 Structure description

The monitored live-scale structure was a concrete BC under a 15m embankment (Figure 3). It

was built for the “Transmontana” highway, which connects the cities of Vila Real and Bragança,

located in the north region of Portugal.

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Four different soils were considered (Table 1), based on their origin and relative location. Soil 1

is the embankment soil, which was thoroughly and previously studied, and its application on site

monitored with care, mostly using the nuclear apparatus. Soil 2 was fabricated on-site by

stabilizing a nearby gravelly soil with cement, to create an adequate foundation bed (Chen and

Sun 2013) with 5 m width and 2 m thick. Soil 3 was a drained coluvionar soil, also 2 m thick and,

finally, Soil 4 was the natural bedrock, classified as a W3-4.

Figure 3: General view of the embankment approximately at mid-height

Top and bottom slabs are 3.77 m width, with a thickness of 0.275 m, while vertical walls are 5.55

m high, with a thickness of 0.385 m (Figure 4). Horizontal slabs have a slenderness ratio of =

47.5, very similar to that of the vertical walls ( = 49.9).

The reinforced concrete BC (C40/50 and S500) was precast between 6 to 9 months prior

installation, in just one element, with a length of 1.25 m, instead of a more traditional solution of

two symmetric ‘U’ shape elements, therefore avoiding any kind of problems resulting from the

interface between the top and bottom halves. According to the AASHTO specifications

(AASHTO 2010), precast BC with a span-to-thickness ratio lower than 18 have shown a

significantly higher strength than estimated by this specification. This is a relevant aspect, since

both the slabs and the walls have span-to-thickness ratios well below 18 (13.7 and 14.4,

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respectively). However, Kim and Yoo (2005) state that, based on several numerical analysis, the

thickness of the culvert has only a small effect (approximately 1%) on the total load acting on the

top slab.

Figure 4: Schematic distribution of the soil layers surrounding the BC (all dimensions in meters)

Table 1: Parameters estimated for the four types of soil considered

2.2 Monitoring system

The instrumentation setup, shown in Figure 5, was designed based on the information, available

in the literature (Yang 2000; Abolmaali and Garg 2008; Liu et al. 2008; Pimentel et al. 2009),

regarding typical deformation modes and expected earth pressure distribution. The instrumented

section was located approximately at the middle of the longitudinal length of the structure, and

the whole setup, including the data logging and energy systems, was installed on a purposely

built steel platform, located at the mid-height of the BC (Figure 5). The data presented was

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acquired over a total period of 257 days, counted from the beginning of the construction of the

embankment, and includes temperature variation on the outer (TS1) and inner (TS2) surface of

the concrete mass, as well as inside the BC (TS3); rotations of the top nodes of the structure

(RR1 and RR2); strains, through strain gages embedded in the concrete (EX1 to EX8); horizontal

relative displacement between the walls (RD1) and vertical relative displacement between the top

slab and the middle height of the box (RD2); and soil pressures on the top slab (PC2, PC3 and

PC4) and side walls (PC1 and PC5). The redundant instrumentation level was intentional since,

based on the authors experience, malfunction or loss of one or more instruments during

construction of the BC or the embankment is possible.

Figure 5: Instrumentation setup of the concrete BC (left) and general view of the logging system (right)

The influence of environmental temperature on concrete structures, namely on their deformation

patterns, is well-known. Such influence is also significant on the transducers and, therefore, a

total of three PT100 temperature sensors were installed – two sensors on the inside of the casted

concrete, near the interior and exterior surfaces of the BC (approximately 40 mm from the

surfaces); and one sensor inside the BC environment, to monitor ambient temperature.

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After setting the concrete BC, and prior to the start of the embankment construction, 2

inclinometers were installed near the interior top corners (Figure 6a). These inclinometers

(LSOC-1 type, 4-20mA output, produced by Level Developments, Ltd) are uniaxial transducers

that measure the inclination relatively to the horizontal plane, ranging from -1º to +1º, with a

precision above 0.5º/1000. As with all the remaining transducers, each value obtained is the

difference between the actual electrical signal and a reference signal, registered as soon as the

transducers were connected. Each transducer then has its own calibration factor, which enables

the final result to be obtained in the correct units (e.g. the results from inclinometers are thus

transposed to thousands of degree).

A total of eight strain gage were embedded before the concrete casting (Figure 6b). Each strain

gage was aligned and glued to a 500 mm long smooth stainless-steel bar, with 10 mm in

diameter, with an anchorage in each extremity. It was positioned at mid-length of the bar and

covered with a special varnish (for humidity protection) and an epoxy resin layer (for mechanical

protection). The bar was then coated by a rubber membrane, to avoid any bonding with the

surrounding concrete, thus assuring that only the relative distance between the anchorages was

indeed measured. Experimental results evidenced the capacity of these transducers to effectively

assess axial deformations, over a given length, with a resolution of 1x10-6 mm/mm. This is

achieved with controlled rebar/concrete slipping, thus keeping the steel bar in its constitutive

elastic domain and accommodating the eventual formation of cracks wider than 1.0 mm

(Rodrigues 2011).

The displacements were monitored with 2 linear variable differential transformers, or LVDT

(Figure 6c), model DCTH1000, 4-20mA output, produced by RDP Electronics, Ltd, with a full

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range of 50 mm and an error less than ± 0.25%FS. They were installed at mid-height of the

interior cross-section of the BC, to measure the horizontal relative displacement between the

walls, and at mid-width, to measure the vertical displacement of the top slab relatively to the

medium horizontal plane. The horizontal LVDT was tied to a steel bar, which in turn had its tips

fixed to the walls. The vertical LVDT was also tied to a steel bar, which connected the top slab to

the floor of the platform where the monitoring setup was installed.

Five single faced vibrating wire pressure cells (Figure 6d), produced by Soil Instruments, Ltd,

with a pressure range between 0 and 300 kPa (PC1 and PC5), and between 0 and 700 kPa (PC2,

PC3 and PC4). These cells are able to measure pressures with an error lower than 1%FS. A

temperature sensor is included in each PC, in order to compensate for thermic effects. The cells

were thoroughly applied on the concrete surface, over a thin layer of grout, aiming a perfect

adhesion to the concrete surface and thus avoiding any kind of arching effect. The described

procedure guarantees a uniform pressure on the cell.

Figure 6: General view of the transducers after installation: (a) inclinometers; (b) extensometers; (c) LVDTs; (d)

pressure cells

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3. Data analysis

Installation of the equipment on the BC structure, and subsequent data logging, started almost

two weeks before the beginning of the embankment construction, which was used to check the

correct functioning of the sensors. The values here presented were not filtered or smoothed, and

the outliers were not removed. The plotted values correspond to the difference between a specific

reading and the values logged on the first day of construction. The embankment reached the

upper slab of the box and the final surface level after 24 and 92 days, respectively. The

construction progress rate was approximately constant throughout these 92 days, except for the

period between days 27 and 46, during which the construction rate was significantly lower. The

BC was monitored until day 257. The fact that the monitoring started before the beginning of the

construction and was maintained until several months after it was terminated, allowed for a

complete assessment of the structural behaviour during the initial phase of its service life span.

3.1 Inclinometers

The values registered by both inclinometers (Figure 7) show that the upper corners assumed a

positive rotation (based on the adopted convention presented in the diagram) immediately after

the construction of the embankment. However, such rotation didn’t progress until the

embankment height levelled the top slab, which is probably due to the higher influence of the

load when at low-to-middle height of the walls, i.e. as the load advances towards the top of the

BC, its effect on the rotation of the upper corners diminishes. It is also important to consider the

difficulty in compacting the soil near the walls, which probably influenced the lateral loads and,

consequently, all the data collected during this stage.

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After the embankment reached the top slab, the upper corners progressively assumed a negative

rotation, due to the increasing loads acting on the top slab, which continued to evolve until the

end of the embankment construction, after which some further deformation still occurs,

essentially due to creep of the concrete. The recorded data shows, very clearly, that the

construction progress was slower between days 27 and 46 and increased afterwards. This is also

very clear in the data recorded from the remaining sensors.

Although the horizontal load on the walls is also increasing (due to Poisson’s effect), thus

creating a progressive resistance to the outward rotation of the walls, it is less influent than the

vertical load acting on the top slab. The average rotation, at the end of embankment construction,

is 0.150 degrees, which would result in mid-span horizontal and vertical displacements of 7.26

mm (walls) and 4.93 mm (top slab), respectively. Since the real rotation of the walls is not free,

due to the lateral soil, the estimated value of 7.26 mm is higher than the value obtained by the

RD1 transducer (Figure 8) which, for the same date, measured a distance increase, between the

two walls, of approximately 10.0 mm, resulting in a mid-span horizontal displacement of 5.0

mm. However, the rotation of the top slab, not affected by the attached soil, produced an

estimated mid-span vertical displacement very similar to that obtained by the RD2 sensor (Figure

8).

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Figure 7: Data logged by the inclinometers installed near the top of the BC walls

3.2 Vertical and horizontal mid-span displacements

The initial inward rotation of the walls was, once again, confirmed by the data recorded by the

RD1 sensor (Figure 8). Until the embankment reached the top slab, the lateral earth pressure

produced a reduction of the internal free width of the BC, measured at mid-span. In accordance,

the internal height increased, due to the rigidity of the nodes of the BC and to the lack of any load

on the top slab that could counteract this behaviour. When the embankment reached the top slab

the overall deformation pattern rapidly changed, with the inversion of the top slab mid-span

displacement to the interior of the box, while the walls displacement was now towards the outside

of the box. This was due to the vertical load increase on the top slab. Although the lateral earth

pressures were increasing with the embankment height, not only because of the increased

pressure originated by the embankment, but also because the outward deformation of the walls

progressively compacted the soil adjacent to the BC, such increase was less influential than the

vertical load on the top slab, and thus incapable of stopping the overall bulking of the box.

Nevertheless, the low compaction of the soil in this region, combined with the length of the mid-

span movement of the wall, didn’t allow the mobilisation of an earth pressure coefficient k = h /

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v above unity (this is later corroborated, when analysing Figure 9). If one, or both, of these

factors would have been more influential, the k value would increase to a value higher than 1.0

(somewhere between its at-rest value and its passive limit state value), representative of a lateral

earth pressure higher than the corresponding vertical pressure.

Based on the data presented in Figure 8, the horizontal distance between the two walls increased

by 2Yw = 10.5 mm, during the construction of the embankment, resulting in a value of Yw = 5.25

mm. Considering the effective length of these walls to be half of the total height, i.e. Hw = 5.55/2

= 2.775 m, the rotation of the walls, expressed as a percentage of their effective length, was

(Y/H)w = 0.00189 radians. The vertical LVDT registered a deflection of the top slab, at the time

of the end of the embankment construction, of approximately Ys = 4.5 mm. This value is similar

to the displacement registered for the walls. However, the top slab has a significantly smaller

effective length (Hs = 3.77/2 = 1.885 m) than the walls, for the same flexural stiffness, resulting

in a rotation of (Y/H)s = 0.00239 radians.

Figure 8: Vertical and horizontal displacements of the walls and top slab, measured at the respective mid-spans

3.3 Soil pressures

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The pressure cells installed on the walls of the BC (PC1 and PC5) started registering pressure

variations almost immediately after the start of the embankment construction (Figure 9). The

pressure cells on the top slab, as expected, only started to register significant values by day 24,

when the embankment height reached the top slab. Until then, the erratic variations of the

readings in PC2, PC3 and PC4 were due to temperature changes, since these sensors, as the

inclinometers and extensometers, are temperature-sensitive. The time interval between days 27

and 46, during which the embankment construction was stopped or very slow, is very clear in the

data registered by the pressure cells. After that, the construction progression is well defined by

the increase in pressure registered by all the cells, especially PC2 and PC4.

At the end of the construction phase, the pressure cells on the top slab registered values of

approximately 708 kPa (PC2), 106 kPa (PC3) and 660 kPa (PC4). An average value of

(708+660)/2 = 684 kPa was assumed to be acting on both ends of the top slab, when the

construction was terminated. After that, additional variations were registered by these

transducers, which agrees with the variations in the data collected by the extensometers.

Although the pressure registered by the PC2, at the end of the embankment construction, was

slightly higher than the upper limit of the measuring range (700 kPa), indicated by the supplier,

the results were still considered valid, not only because there is always some slack regarding the

lower and upper limits, but also because the response of this pressure cell was very similar to the

sister PC4.

The value registered by the PC1 sensor was, at the end of the construction, significantly higher

than the PC5 value (64 to 39 kPa). After that it decreased until day 206, at which point it

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stabilised at approximately 45 kPa. Since the difference between the two sensors, when the

construction was terminated, is probably related with a secondary reason (e.g. the soil near PC1

was, during the construction phase, slightly more compacted than the soil near PC5), and,

especially, because at the end of the monitoring period the PC1 value dropped to 45, a value

much closer to the one obtained by the PC5, the value considered for the lateral earth pressure

acting on the left-hand wall was 45 kPa, resulting in an average value for the two sensors of

(39+45)/2 = 42 kPa.

The values registered by pressure cells PC2, PC3 and PC4 were in accordance with the stress

distribution on the top slab mentioned in the literature, particularly for those culverts which are

wide enough to allow more significant flexural movements of the top slab (Figure 2). As soon as

the construction reached the top slab, the stress increase on the central area of the top slab (PC3)

was significantly lower than in the lateral areas, directly above the walls, where the walls provide

a strong point due to their high axial stiffness. The fact that the differential stress between the

central and the lateral cells started right from the start of the loading process, when the soil load is

still relatively small, reinforces the importance of taking such behaviour in consideration while

designing the BC.

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Figure 9: Soil pressures on the walls and top slab

3.4 Concrete strains

The extensometers showed a similar pattern to that already presented by the inclinometers: as

soon as the soil reached the top slab, the strains reveal a deflection of the top and bottom slabs to

the inside of the BC (Figure 10) and a deflection of the walls to the outside of the BC (Figure 11).

In both figures there are some outliers, particularly at days 163 and 193, that were not removed

from the plots. Data from the EX3 and EX4 extensometers shows a progressive contraction and

extension, respectively, of the upper and lower surface of the top slab, after the embankment

construction reached this height. The data recorded by the extensometers on the bottom slab

(EX7 and EX8) shows a strain trend similar to the extensometers on the top slab, although with

slightly higher values. This is due to the fact the former responded to the self-weight of the BC,

as soon as it was installed on site, while the latter were still submitted only to temperature

variations. An explanation for this relative behaviour might be the lower stiffness of the

foundation soil, which enables both ends of the bottom slab (below the walls) to puncture the

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soil, due to the load concentration on these areas, and therefore producing the flexion of the

bottom slab. A stiffer foundation soil would probably reduce this flexural deformation.

Figure 10: Strain measurements on the horizontal reinforcements of the top and bottom slabs

Regarding the strain pattern on the walls, Figure 11 shows that after the embankment

construction was finished, the extensometers registered some additional increments, which might

be attributed to creep effects on the concrete, but also to some additional load increase, as

discussed further ahead. Temperature variations were influential on the recorded data, even more

so than in the case of the inclinometers. One of the internal extensometers (EX6) suffered a

malfunction after installation and could not retrieve any valuable information. Similarly, the

inside extensometer EX2 started to record only on day 73, and thus this first value was used as

reference.

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Figure 11: Strain measurements on the vertical reinforcements of the BC walls

3.5 Visual inspection of the inside of the BC

A visual inspection of the BC was developed, 12 months after the construction of embankment,

and crack patterns and respective widths were registered. Cracks were observed on both slabs,

within a central area of approximately 1.0 m (Figure 12), in several of the BC modules that form

the entire length of the structure.

The average spacing of the cracks on the top and bottom slabs was 250 mm and 200 mm,

respectively (the widths were not directly measured since the cracks were filled with dust). Based

on these values, and on the maximum strain values obtained by the extensometers EX4 (840 x10-

6 mm/mm, top slab) and EX8 (1000 x10-6 mm/mm, bottom slab), width values of 0.21 mm and

0.20 mm were estimated, following the contents of the current European standard for structural

concrete, i.e. Eurocode 2 (BSi EN 1992-1-1 2004). The same standard (Part 1-1) imposes, for

structures susceptible to ‘corrosion induce by carbonation’, class XC2, a maximum crack width

of 0.3 mm. Therefore, the present structure fulfils the requirements regarding the serviceability

limit state of cracking.

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Figure 12: Cracks on the bottom (a) and top (b) slabs, observed 1 year after embankment construction

4. Numerical models

Two different numerical models were developed for the present study, namely a linear elastic

(LEM) model and a finite element model (FEM). The LEM model was then used to study the

response of the structure when submitted to two different load schemes, which were obtained

using either the AASHTO or the experimental data registered by the pressure cells. The FEM is

clearly more appropriate to simulate the structural complexity formed by the box and the

surrounding soil. However, the LEM, although less sensitive, constitutes a faster and more “user-

friendly” approach, thus justifying a thorough assessment of its adequacy to act as a BC analysis

tool. In short, the idea behind the development and comparison between the two models was to

evaluate the difference, in data quality, that a finite element code could eventually guarantee.

4.1 Linear elastic model

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A linear elastic model, with beam-type elements, was used to test the relative influence of the

AASHTO and experimental loads. Although this type of model is the most common when

designing concrete box culverts, the cracks observed on the inside surface of the top and bottom

slabs, imply that a simple linear-elastic model has limitations regarding the accurate prediction of

the stresses and strains installed in the BC. Nevertheless, a Poisson’s Coefficient of 0.0 was used

to mitigate this deficiency (BSi EN 1992-1-1 2004). A unit weight of 25 kN/m3 and Young’s

Module of 35 GPa were also considered for the concrete BC.

As previously mentioned, the LEM was used to observe the structural behaviour corresponding to

two different load schemes, i.e. AASHTO and experimental. However, the load scheme based on

the experimental data was further divided in two different schemes, one with both the vertical and

horizontal loads estimated from the pressure cells, and a second scheme with only the vertical

load applied. The idea behind the elimination of the horizontal load is the fact that, due to

difficulties in compacting the lateral soil, it would only become influential after a significant

lateral deformation of the BC. Therefore, and since this evolution in the magnitude of the

horizontal load is impossible to simulate in such a simple model, the two situations were tested

(i.e. with and without the horizontal load).

4.2 Elasto-plastic model (Mohr-Coulomb)

A 2D numerical model was simultaneously developed using the open-access code ADONIS. The

BC was represented by 3-node beam elements, with 3 degrees of freedom per node, with bending

and axial stiffness, and considering elastic behaviour. Interface elements, with 2 pairs of nodes

and almost-zero thickness, were used to model the soil-structure interaction. All soil clusters were

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discretised into 6-node triangular elements, assuming plane strain conditions. The total width of

the fill modelled was 50 m, with a symmetry vertical axis. Classic boundary conditions were

considered, i.e. fixed horizontal and vertical displacement at the bottom boundary and fixed

horizontal displacement at the lateral boundaries. The soil parameters were already summarised

in Table 1.

An isotropic linear elastic behaviour was assumed for the BC. The elastic perfectly plastic Mohr-

Coulomb model was used for the soils, with an associated flow rule. No softening or hardening

post-yielding behaviour was defined, and a linear elastic response was considered before

yielding. Therefore, the model requires a total of 5 parameters, namely the cohesion and friction

angle, the Young’s module, the Poisson’s ratio and the dilatancy angle. As with the elastic model,

a Poisson’s ratio of 0.0 was used for the BC concrete. Interface nodes were attached to each other

by normal and shear springs, using Coulomb friction law.

5. Experimental vs numerical results

5.1 Loads acting on the BC

The mechanical behaviour of buried structures is highly influenced by the soil-structure

interaction. If it is true that the stresses on the structure depend on the soil pressures, it is also true

that these pressures depend on the deformation of the structure. Moreover, the pressure pattern on

the structure depends not only on the geotechnical properties of the embankment material, but

also on the construction sequence and on the relative stiffness between soil and structure. This

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complex set of constrains increases the difficulty in estimating the soil loads acting on the

culvert.

In this section, the loads estimated through the AASHTO model are compared with the loads

estimated from the values obtained by the pressure cells. Only permanent loads, namely the self-

weight of the structure and soil and the lateral earth pressures, were considered in the analysis.

The inclusion of an imposed surface load of 10 kPa was contemplated, but the idea was

abandoned since its effect on the structure, 15 m below, would be minimum. The load schemes

considered are presented in Figure 13, obtained either from the AASHTO recommendations (M1)

and from the experimental data (M2 and M3). Also shown in Figure 13 are the loads on the top

slab and walls of the BC, obtained with the FEM.

Regarding the M1 scheme, the vertical load corresponds to the soil weight above the structure

(Eq. 1), majorated by a factor F (Eq. 2), to account for the weight of the lateral fills. Therefore,

assuming a culvert width of 3.77 m and an embankment height of 15 m, a value F = 1.80 was

obtained. Since the side fills were thoroughly compacted (there is no reason to think otherwise), a

maximum value of 1.15 was used, as proposed by the AASHTO specifications (AASHTO 2002).

Considering an embankment unit weight of 18.8 kN/m3, a total vertical load of 1223 kN/m was

obtained, corresponding to a distributed load of 324 kPa. The lateral pressures indicated, which

were assumed rectangular, were obtained from the vertical pressure at mid-height of the BC (at a

total depth of 15+5.55/2 = 17.78 m), affected by the earth pressure coefficient ‘at rest’, estimated

from the well-known Jaky’s expression (Eq. 5), resulting in a horizontal distributed load of 127

kPa.

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𝑘 = 1 ‒ sinϕ' = 1 ‒ sin38 = 0.38 (5)

The loads indicated for the M2 scheme were obtained from the values registered by the pressure

cells installed on the BC. The load considered on the ends of the top slab, where PC2 and PC4

were installed, is the average (684 kPa) of the values registered by these two transducers (708

kPa and 660 kPa); while the load at mid-span is the value registered by PC3 (106 kPa). The

lateral load, which, similarly to the M1 case, was also admitted being rectangular, is the average

(42 kPa) of the values obtained by PC1 (39 kPa) and PC5 (45 kPa). Finally, the M3 scheme is

very similar to the M2, with the only difference residing on the removal of the horizontal load.

Figure 13: Distributed loads obtained from the AASHTO (M1) model and from the experimental data (M2 and M3)

and comparison with the loads resulting from the FEM simulation

The vertical load of 324 kPa on the top slab, obtained with the M1 model, corresponds to 306%

of the pressure registered at mid-span of the slab (106 kPa), and to only 47% of the average

pressure registered at the ends (684 kPa). On the other hand, the vertical pressures obtained with

the FEM model are very similar to the experimental values, the exception being the mid-span

value. This is noteworthy since, on the FEM simulation, the box culvert was modelled

considering elastic constitutive behaviour, while the experimental model is notoriously nonlinear

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(based on the evident cracking patterns developed). Also important is that the FEM load values

on both extremes of the top slab were not obtained at points 0.0 and 3.77, but, instead,

approximately 25 cm to the interior of the top slab surface, where the centres of the circular

pressure cells were located.

Regarding the lateral pressure, and assuming an ‘at-rest’ state, the 127 kPa load predicted by the

M1 model corresponds to 302% of the average value registered by the lateral pressure cells (42

kPa). The FEM value shows a significant variation with height, which is in accordance with the

data obtained from a field installation (Oshati et al. 2012). Although it is always between the

AASHTO and the experimental values, its average is exactly 100 kPa, which is significantly

closer to the AASHTO value than the experimental value. Still, the AASHTO value is 127% of

the average FEM value.

5.2 Displacements of the BC

The displacement of the slabs and walls are presented in Figure 14, together with the

displacements registered by the respective transducers (RD1 and RD2). The values presented

were obtained using the load schemes shown in Figure 13. The values presented for the top and

bottom slabs are relative to the corner nodes, since the foundation was modelled as an elastic

mean, which resulted in a translation movement of the whole structure, in the vertical direction.

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Figure 14: Displacements of the walls and top slab, obtained with the load schemes shown in Figure 11

The results presented show that the horizontal load obtained with the AASHTO proposal, which

is 3x higher than the experimental value and 1.3x higher than the average FEM value, was

responsible for a flexural deformation of the walls to the inside of the BC, while the experimental

flexural deformation was clearly to the outside. Accordingly, the flexural deformation of the top

slab produced by the AASHTO-based load was clearly different from the deformation originated

by the remaining load possibilities. Even the fact that this is the highest load acting at mid-span

(where its effect is more relevant) changed the overall behaviour of the structure. Not

surprisingly, the elastic model with no horizontal load (see Section 4.1) presented the horizontal

deformation closest to the experimental value. A similar situation happened for the vertical

deformation, although in this case the FEM model was also capable to predict an even slightly

higher value (and, therefore, closer to the experimental vertical deformation). Finally, the fact

that no model included the effect of the concrete cracking is certainly responsible (at least,

partially) to the lower horizontal and vertical deformations registered, relatively to the

experimental values.

6. Discussion

6.1 Soil pressure on the top slab

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The vertical load acting on the top slab, throughout the construction sequence, was calculated

using AASHTO’s standard specifications for highway bridges (AASHTO 2002) and bridge

design specifications (AASHTO 2010), and presented in Figure 15. These specifications assume

a soil-structure interaction factor (Fi), given by Eq. (6), as a function of the increasing

embankment height (Hi). This factor is used in the calculation of the vertical force (Wi) acting on

the top slab, given by Eq. (7). The Wi value was then divided by the culvert width (B) to obtain

the vertical pressure acting on the top slab (pvi) (Eq. 8). Note that, after the embankment reached

the 3 m mark, the soil-structure interaction factor (F) was higher than the limit of 1.15 (assumed

for compacted fills), and therefore this value was adopted for the remaining construction.

𝐹𝑖 = 1 + 0.20 ∗𝐻𝑖

𝐵 = 1 + 0.20 ∗𝐻𝑖

3.77 = 1 + 0.053 ∗ 𝐻𝑖 (6)

𝑊𝑖 = 𝐹𝑖 ∗ 𝛾 ∗ 𝐵 ∗ 𝐻𝑖 = 18.8 ∗ 𝐵 ∗ 𝐻𝑖 + 0.9964 ∗ 𝐵 ∗ 𝐻𝑖2 (7)

𝑝𝑣𝑖𝐴𝐴𝑆𝐻𝑇𝑂

𝑠𝑙𝑎𝑏 =𝑊𝑖

𝐵 = 18.8 ∗ 𝐻𝑖 + 0.9964 ∗ 𝐻𝑖2 (8)

Figure 15 also includes the vertical pressures registered by the cells installed on the top slab

(PC2, PC3 and PC4), as well as their equivalent total value. This total value was estimated

assuming a trapezoidal distribution of the load (with the area of each trapezoid calculated through

the data registered by the three PC), which was then divided by the culvert width (Eq. 9).

𝑝𝑣𝑖𝑒𝑥𝑝𝑒𝑟,𝑡𝑜𝑡𝑎𝑙

𝑠𝑙𝑎𝑏 =𝑃𝐶𝑖2 + 𝑃𝐶𝑖4 + 2 ∗ 𝑃𝐶𝑖3

4(9)

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From Figure 15 it is possible to conclude that AASHTO specifications, in fact, underestimate the

total pressure on the top slab, corresponding to only 82% of the total experimental pressure,

obtained from the values registered by the three pressure cells. However, it is important to notice

that, although the total AASHTO pressure acting on the top slab is lower than the real value, the

fact that no guidance is given regarding the distribution of this force, makes the use of AASHTO

specifications more conservative than necessary, since the load divided by the BC width results

in a value at mid-span (which is the most significant, in terms of the flexural design of the slab),

approximately 3 times higher than the experimental value at mid-span, given by PC3.

Figure 15: Evolution of vertical pressure on the top slab throughout the embankment construction (experimental data

and AASTHO proposal)

6.2 Soil pressure on the walls

The outward inclination of the walls registered by the sensors indicates that the structure was

progressively pushed against the soil after the embankment construction reached the top slab, as

previously discussed. In a natural soil deposit, this would mean that the horizontal stress would

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be higher than that given by the at-rest state, since the earth pressure coefficient value would be

somewhere between the at-rest state and the passive limit state. However, the rotation of the

walls was estimated (Section 3.3) to be 0.00189 radians. Since, in the case of a medium dense

cohesionless soil, the Rankine passive state is reached after a rotation of approximately 0.02

radians (Canadian Geotechnical Society 1992; AASHTO 2010), it can be concluded that, indeed,

the lateral earth pressure coefficient k was far from its passive limit. AASHTO specifications

suggest that Eq. (5) should be used for the estimation of the earth pressure coefficient at-rest. In

this case, and considering a nominal friction angle of 38º, a value k = 0.38 is obtained.

To study the evolution of the real ratio between horizontal and vertical pressures, an experimental

k was estimated as a function of the embankment height (Eq. 10), dividing the medium value of

the lateral pressure cells (Eq. 11), by the total soil weight above these cells (Eq. 12). The

evolution of this parameter is presented in Figure 16.

𝑘𝑖𝑒𝑥𝑝𝑒𝑟 =

𝑝ℎ𝑖𝑒𝑥𝑝𝑒𝑟𝑤𝑎𝑙𝑙

𝑝𝑣𝑖𝑒𝑥𝑝𝑒𝑟𝑠𝑙𝑎𝑏

(10)

𝑝ℎ𝑖𝑒𝑥𝑝𝑒𝑟𝑤𝑎𝑙𝑙 =

(𝑃𝐶𝑖1 + 𝑃𝐶𝑖5)2

(11)

𝑝𝑣𝑖𝑒𝑥𝑝𝑒𝑟𝑠𝑙𝑎𝑏 = 𝛾 ∗ (5.55

2 + 𝐻𝑖) = 18.8 ∗ (5.552 + 𝐻𝑖) (12)

An initial experimental value of k = 0.232 was estimated considering the average horizontal

pressure registered by both lateral PC (when the embankment height reached the top slab), and

the nominal vertical soil pressure (obtained by multiplying the unit weight of the soil by the

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distance between the lateral PC and the top slab). This value is significantly lower than the

theoretical value proposed by AASHTO (k = 0.38). One possible explanation is the fact that the

soil near the walls was only mildly compacted, especially when compared with the soil located

further away from the structure (due to the use of small rollers, instead of the heavier compactors,

near these sensitive areas). Therefore, instead of having an experimental initial k value higher

than the theoretical k0, due to the compaction energy (Lirer et al. 2010), a lower value was

obtained instead. Nevertheless, there is another possible reasonable explanation for this lower

value of the earth pressure coefficient, which is the deformability of the geomembrane, that was

installed between the soil and the concrete, which absorbed part of the lateral soil load.

It is also possible to observe a reduction of the k parameter with the evolution of the embankment

height. This is most likely explained by the fact that the vertical pressure on the lateral areas of

the BC are significantly lower than the vertical pressures registered by the cells installed on the

top slab, which are being used for estimating the mentioned k values. These differences in the

vertical pressure values are due to the ‘suspension’ of the lateral soil on the soil located above the

top slab, as seen in Section 1, thus decreasing the vertical load on the soil on the side of the walls

and, consequently, the respective horizontal loads.

Both the initial difference, between the theoretical and experimental k, and the subsequent

reduction of the experimental value as the embankment height increases, are not taken in

consideration by the AASHTO specifications. To include the effect of both these factors on the

calculation of the horizontal pressures acting on the walls, a modification to Eq. (5) is proposed

in Eq. (13), obtained by curve fitting to the experimental data. The last two members of the

equation were obtained by curve fitting: first, a curve was adjusted to the variation of the

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experimental k with the inverse of the embankment height (1/H); the results obtained were

subtracted to the theoretical initial k (obtained using Jaky’s equation), and a second curve was

adjusted to the variation of these values with H. The results obtained with this modification are

included in Figure 16.

k = (1 ‒ sinϕ') ‒ 0.0309 ∗ ln(Hi) ‒ 0.3266 (13)

Figure 16: Comparison between the experimental earth pressure coefficient (Eq. 10) and the value obtained using the

proposed correction (Eq. 13)

This reduction of the k value with the embankment height should be taken in consideration in the

structural analysis, when estimating the horizontal pressures (ph) on the BC walls. However, the

proposed adjustment to Jaky’s equation is specific to the present soil-structure combination and is

only useful for different situations as a general guidance in terms of the magnitude of the

differences that can be obtained, between theoretical and live scale values.

To analyse these horizontal pressures at mid-height of the walls, the experimental values obtained

using Eq. (11) were compared (Figure 17) with the values obtained using AASHTO

specifications for the vertical pressures (Eq. 8), multiplied by an earth pressure coefficient k (the

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Hi value did not include the soil between the top of the BC and the lateral PC). Three different

origins were considered for the earth pressure coefficient k: AASHTO proposal (Eq. 5), the

experimental values obtained from Eq. (10) and the proposed values from Eq. (13). It is

interesting to notice that the lateral pressures obtained with the k values estimated from Eq. (13)

are significantly closer to the experimental values from Eq. (10) than those obtained using

AASHTO’s Eq. (5). This seems to indicate that the correct estimation of the pressure coefficient

k is more relevant than any possible modification of the equation used by the AASHTO

specifications, which seems to be sufficiently accurate, as long as the k value is accurately

estimated.

Figure 17: Lateral earth pressures at mid-height of the box (where PC1 and PC5 were installed), obtained from the

experimental data (Eq. 11) and from the AASHTO’s Eq. (5) using the following k values: (i) Jaky’s (Eq. 5); (ii)

experimental value (Eq. 10); (iii) proposed values (Eq. 13)

7. Conclusions

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The present work describes the structural evolution of a precast reinforced concrete box culvert,

from its installation throughout the end of the embankment construction, over a period of more

than 250 days, using a wide variety of sensors. The data registered confirmed the theoretical

interpretation associated with this type of structures, i.e. the flexion of the top slab produces a

pressure decrease due to an arch effect that develops in the soil above it.

The field results were confirmed with a finite element numerical model and proved to be

significantly different from the values obtained by the well-know AASHTO analytical model.

Further analysis of these results points to the poor estimation of the soil pressures, on both the top

slab and walls, and the coefficient of earth pressure at rest, as the main reasons behind this

inaccuracy. Both cases could be optimised by increasing the accuracy of the earth pressure

coefficient, since this would result in lower horizontal earth pressures on the walls, thus

increasing their flexion and, consequently, the flexion of the top slab. The higher deformation of

the structure would reduce the soil pressures in the centre area of the slab, and transfer them to

the sides, above the walls.

References

AASHTO. 2002. Standard Specifications for Highway Bridges, 17th Edition. American Association of State Highway and Transportation Officials.

AASHTO. 2010. LRFD Bridge Design Specifications (5th Edition). American Association of State Highway and Transportation Officials.

Abolmaali, A., and Garg, A. 2008. Shear Behavior and Mode of Failure for ASTM C1433 Precast Box Culverts. Engineering, (August): 331–338.

BSi EN 1992-1-1. 2004. BS EN 1992: 2004 - Eurocode 2: Design of concrete structures, Part 1-1: General rules and rules for buildings. British Standards Institution, London.

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Canadian Geotechnical Society. 1992. Canadian Foundation Engineering Manual. 3rd Edition. Canadian Geotechnical Society.

Chaloulos, Y.K., Bouckovalas, G.D., Zervos, S.D., and Zampas, A.L. 2015. Lateral soil-pipeline interaction in sand backfill: Effect of trench dimensions. Computers and Geotechnics, 69: 442–451.

Chen, B., Song, D., Mao, X., Chen, E.J., and Zhang, J. 2016. Model test and numerical simulation on rigid load shedding culvert backfilled with sand. Computers and Geotechnics, 79: 31–40.

Chen, B., and Sun, L. 2013. The impact of soil properties on the structural integrity of high-fill reinforced concrete culverts. Computers and Geotechnics, 52: 46–53.

Chen, B., Zheng, J., and Han, J. 2010. Experimental Study and Numerical Simulation on Concrete Box Culverts in Trenches. Journal of Performance of Constructed Facilities, 24(3): 223–234.

Ebeling, R., and Mosher, R. 1996. Red River U-frame lock No. 1 Backfill-structure-foundation interaction. Journal of geotechnical engineering, 122(3): 216–225.

Hansen, P., Miller, L., Valsangkar, A., Bourque, S., and MacLeod, T. 2007. Performance of induced trench culverts in New Brunswick. In Proceedings of the Annual Conference and Exhibition of the Transportation Association of Canada. Transportation Association of Canada, Ottawa, Ont., Saskatoon, Saskatchewan, 14-17 October 2007. pp. 14p.

Kang, J., Parker, F., Kang, Y.J., and Yoo, C.H. 2008. Effects of frictional forces acting on sidewalls of buried box culverts. International Journal for Numerical and Analytical Methods in Geomechanics, 32(3): 289–306.

Kim, K., and Yoo, C.H. 2005. Design Loading on Deeply Buried Box Culverts. Journal of Geotechnical and Geoenvironmental Engineering, 131(1): 20–27.

Lawson, W., Wood, T., Newhouse, C., and Jayawickrama, P. 2010. Evaluating Existing Culverts for Load Capacity Allowing for Soil Structure Interaction. Report No. 0-5849-1. Texas Department of Transportation, Austin, TX,.

Lirer, S., Flora, A., and Nicotera, M. V. 2010. Some remarks on the coefficient of earth pressure at rest in compacted sandy gravel. Acta Geotechnica, 6(1): 1–12.

Liu, H., Zou, D., and Liu, J. 2008. Particle Shape Effect on Macro and Micro Behaviours of Monodisperse Ellipsoids. International Journal for Numerical and Analytical Methods in Geomechanics, 32(3): 189–213.

Marston, A., and Anderson, A.O. 1913. The Theory of Loads on Pipes in Ditches and Tests of Cement and Clay Drain Tile and Sewer Pipe. Iowa State College of Agriculture and Mechanic Arts, 11(31).

Marston, M.G. 1930. The Theory of External Loads on Closed Conduits in the Light of the Latest Experiments. Highway Research Board Proceeding, 6(96).

O’Neal, T.S., and Hagerty, D.J. 2011. Earth pressures in confined cohesionless backfill against tall rigid walls — a case history. Canadian Geotechnical Journal, 48(8): 1188–1197.

Oshati, O.S., Valsangkar, A.J., and Schriver, A.B. 2012. Performance of two cast-in-place box culverts under high embankments. Canadian Geotechnical Journal, 49(12): 1331–1346.

Pimentel, M., Costa, P., Félix, C., and Figueiras, J. 2009. Behavior of Reinforced Concrete Box

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Culverts under High Embankments. Journal of Structural Engineering, 135(4): 366.Rodrigues, C. 2011. Monitoring of civil engineering structures based on optical fibre solutions (in

Portuguese). Faculty of Engineering of the University of Porto.Shatnawi, A., Almasabha, G., and Tarawneh, B. 2017. Structural behavior of concrete box

culverts under deep burial. Journal of Pipeline Systems Engineering and Practice, 8(4): 4–8.Yang, M. 2000. Evaluation of Factors Affecting Earth Pressures on Buried Box Culverts. PhD

thesis. University of Tennessee, Knoxville.

Figure captions






Figure 6: General view of the transducers after installation: (a) inclinometers; (b) extensometers; (c) LVDTs; (d)

pressure cells







Figure 13: Distributed loads obtained from the AASHTO (M1) model and from the experimental data (M2 and M3)

and comparison with the loads resulting from the FEM simulation


Figure 15: Evolution of vertical pressure on the top slab throughout the embankment construction (experimental data

and AASTHO proposal)

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Figure 16: Comparison between the experimental earth pressure coefficient (Eq. 10) and the value obtained using the

proposed correction (Eq. 13)

Figure 17: Lateral earth pressures at mid-height of the box (where PC1 and PC5 were installed), obtained from the

experimental data (Eq. 11) and from the AASHTO’s Eq. (5) using the following k values: (i) Jaky’s (Eq. 5); (ii)

experimental value (Eq. 10); (iii) proposed values (Eq. 13)

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202x102mm (300 x 300 DPI)

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197x182mm (300 x 300 DPI)

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308x231mm (300 x 300 DPI)

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190x242mm (300 x 300 DPI)

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368x246mm (300 x 300 DPI)

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Figure 6: General view of the transducers after installation: (a) inclinometers; (b) extensometers; (c) LVDTs; (d) pressure cells

200x134mm (300 x 300 DPI)

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176x106mm (300 x 300 DPI)

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176x140mm (300 x 300 DPI)

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176x118mm (300 x 300 DPI)

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174x140mm (300 x 300 DPI)

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176x216mm (300 x 300 DPI)

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200x74mm (300 x 300 DPI)

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Figure 13: Distributed loads obtained from the AASHTO (M1) model and from the experimental data (M2 and M3) and comparison with the loads resulting from the FEM simulation

235x118mm (300 x 300 DPI)

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240x118mm (300 x 300 DPI)

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Figure 15: Evolution of vertical pressure on the top slab throughout the embankment construction (experimental data and AASTHO proposal)

94x132mm (300 x 300 DPI)

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Figure 16: Comparison between the experimental earth pressure coefficient (Eq. 10) and the value obtained using the proposed correction (Eq. 13)

94x132mm (300 x 300 DPI)

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Figure 17: Lateral earth pressures at mid-height of the box (where PC1 and PC5 were installed), obtained from the experimental data (Eq. 11) and from the AASHTO’s Eq. (5) using the following k values: (i) Jaky’s

(Eq. 5); (ii) experimental value (Eq. 10); (iii) proposed values (Eq. 13)

94x132mm (300 x 300 DPI)

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Table 1: Parameters estimated for the four types of soil considered

Reference Soil

S1

Soil

S2

Soil

S3

Soil

S4

γ (unit weight, kN/m3) 18.8 22.0 20.0 24.0

c’ (cohesion, kPa) 10 45 35 45

φ’ (friction angle, degrees) 30 45 40 45

E (Young’s modulus, MPa ) 100 1000 100 1000

ν (Poisson’s ratio) 0.3 0.3 0.3 0.3

ψ (dilation angle, degrees) 0.0 0.0 0.0 0.0

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