Research and evaluation of ruts in the asphalt pavement on Lithuanian highways.
Sivilevicius, Henrikas ; Vansauskas, Vidmantas
Introduction
During the last decades, there have been dramatic changes in
traffic volumes, traffic weights and tyre pressures, which have resulted
in a significant increase in a permanent deformation of hot mix asphalt
(HMA) pavements. Permanent deformation is a major mode of failure in
flexible pavements consisting of both rutting and shoving (Hajj et al.
2011a).
Evaluation methods and tools used for assessing pavement conditions
provide an invaluable service to infrastructure engineers, technicians,
budget planners and decision makers. These tools provide information
relevant to the maintenance and rehabilitation of national
infrastructure (Thodesen et al. 2012).
According to ASTM E 867-02a (2004), a rut is a contiguous
longitudinal depression deviating from a surface plane defined by a
transverse cross slope and longitudinal profile. Rut depth is the
maximum measured perpendicular distance between the bottom surface of
the straightedge and the contact area of the gauge with the pavement
surface at a specific location.
As time passes, pavement sections start deteriorating due to
traffic and environmental effects (Haryanto, Takahashi 2007; Hu et al.
2011; Sivilevicius, Sukevicius 2007; Xia, Wang 2010; Wang et al. 2009;
Yavuzturk et al. 2005; Petkevicius et al. 2010; Al-Suleiman et al. 2000;
Sivilevicius 2011a; Chandra 2004; Yang et al. 2009; Zhang et al. 2002;
Xia 2010).
Road surface profile is an important factor that affects dynamic
responses of the vehicle, which in turn affects pavement responses (Wang
et al. 2012). The study has developed a complete two-dimensional
axle-tyre-pavement interaction finite-element model to investigate the
effects of the rutted surface on near-surface pavement responses.
In general, pavement sections subjected to higher traffic volumes
have a higher rate of deterioration. Consequently, thicker pavements
with higher-quality materials are required for high traffic facilities
(Zaghloul, Holland 2008). Therefore, it is not possible to compare the
structural capacity of two pavement sections such as high traffic main
interstate highways and low-traffic rural roads subjected to different
traffic intensity without taking into consideration traffic effects.
Pavement surface deflections have been successfully used as an
indicator of airport pavement life (Gopalakrishnan 2008). In this study,
pavement surface deflections measured prior to trafficking have been
related to the rutting performance of four flexible pavement test
sections at the FAA's National Airport Pavement Test Facility
(NAPTF). While a number of load repetitions N increases, the rut depth
of airport runways is also growing regardless of the number of wheels in
the airplane chassis.
The procedure for designing an asphalt mix specifies a range in air
void content from 3% to 5%. However, actual variability in the air void
content of the road surface varies more because of differences in
temperature and compacting. With reference to Michigan transport
department, the tolerance of air void content in the compacted asphalt
mixture is 91% from the target air void content of 3% to 5%. Therefore,
practical and permissible variability in air void content is 2-6%. In
practice, the in-place air void content of the existing pavements varies
across the lane (in the transverse direction) because of additional
compaction in wheel paths due to traffic. This leads to differences in
percent air voids across the asphalt mat. Such differences are
independent of segregation (Chang et al. 2002). Therefore, ruts appear
in the wheel rolling strips of compressed asphalt.
Rut parameters are affected by aggregate structure (Khedr, Breakah
2011; Lin, Cao 2009; Nukuhya et al. 2002), angularity (Souza et al.
2012; Topal, Sengoz 2005), moisture (Hajj et al. 2011b) and HMA density
(Mogawer et al. 2011).
The Georgia department of Transportation typically uses relatively
large maximum-size aggregates to ensure that base and binder course
mixtures are resistant to rutting (Brown et al. 1989).
Latvian scientists (Haritonovs et al. 2010) described the asphalt
coating mixture and their resistance to load after assessing the actual
characteristics of road surface operation.
de Freitas et al. (2005) present the findings of a study seeking to
quantify the effect of those factors on top-down cracking (TDC). The
study consists of a laboratory component involving an accelerated
wheel-tracking device and a modelling component involving a 3D
non-linear viscoelastic finite element model.
Apeagyei (2011) study was conducted to investigate the rutting
resistance of asphalt concrete (AC) mixtures as a function of dynamic
modulus ([absolute value of [E.sup.*]]) and gradation. Rutting was
simulated using a flow number (FN) test. FN tests conducted at
54.4[degrees]C were used for rutting simulation in 16AC mixtures in the
laboratory. The possibility of predicting rutting resistance to asphalt
mixtures from dynamic modulus and gradation has many potential practical
implications and requires further investigation. Dynamic modulus
([absolute value of [E.sup.*]]) is one of the fundamental properties
defining the response of hot-mix asphalt (HMA) mixtures to flexible
pavement systems (Ceylan et al. 2009; Salama et al. 2007).
Said et al. (2011) evaluate an approach to predicting rut formation
in AC layers. The approach is based on a viscoelastic model for
predicting permanent vertical strain in AC layers subjected to a moving
load. The approach is capable of calculating rutting profiles including
the upheaval important for estimating rut depth.
Ali et al. (2009) concern the analysis of rutting urban pavements
using finite-element modelling, which takes into account the non-linear
behaviour of pavement materials and complex traffic conditions. The
model is used for the examination of rutting in the urban pavement and
for studying rehabilitation methods. The performed analysis shows that
urban traffic conditions are detrimental for urban pavements and the use
of high resistance AC constitutes an efficient alternative for urban
pavement rehabilitation.
Coleri et al. (2008) demonstrate the applicability of the
integrated Weibull approach to simulating the in situ rutting
performance of AC mixes by applying appropriate correction factors to
laboratory models. Correction factors were used for calibrating
laboratory equations according to deflection data from four test
sections of a heavy vehicle simulator to estimate in situ rutting
performance. The results indicate that phase separation occurs at higher
repetition values with increasing shear stress.
The dependence of rutting evolution on stress state was verified,
and a model relating rut depth to load repetition was derived (Malysz et
al. 2012). A laboratory study was carried out to verify if pavement
rutting could be estimated by permanent strain laboratory testing.
Collop et al. (2006) investigate the use of discrete element
modelling to simulate the behaviour of a highly idealised bituminous
mixture under uniaxial and triaxial compressive creep tests. The
idealised mixture compresses single-sized spherical (sand-sized)
particles mixed with bitumen and has been chosen so that packing
characteristics are known (dense random packing) and the behaviour of
the mixture will be dominated by the bitumen and complex aggregate
interlock effects will be minimised. An elastic contact has been assumed
for compressive normal contact stiffness and a viscoelastic contact for
shear and tensile normal contact stiffness to respect contact behaviour
in the idealised mixture. The models of different binders not assembled
by multi-sphere and elliptical particle contact (inter-particle contact)
were created by Markauskas et al. (2010).
Dawson (2008) studied the applicability and limits of applicability
of the fourth-law to typical low-volume road pavements with no or only
thin seals that obtain their structural performance primarily from the
aggregate base (or equivalent) layer and for which pavement
deterioration is overwhelmingly due to rutting. Rutting does not develop
linearly with the number of contact axle loads; thus, it cannot be
expected to increase linearly with ESALs. In this way, the frequent
implicit use of power law approaches is deprecated (Dawson 2008).
The approach (Lottoman, Frith 1989) to predicting moisture
sensitivity of AC pavements is based on the acceleration of fatigue
cracking and field distress of wheel path rutting. Prediction methods
incorporate the mechanical properties of the specimen, derived physical
property rations with field time and environmental effects. In this
case, moisture effects on wheel path rutting as changes in the permanent
deformation of AC due to plastic flow are defined.
Styrene butadiene styrene and starch have been used by many to
modify asphalt cement and to improve the properties of AC. The basic
properties of modified asphalt binders and stone mastic asphalt concrete
(SMAC) containing the above-introduced asphalt binders were studied and
compared with those of asphalt cement (Al-Hadidy, Yi-qiu 2010). SMAC was
tested carrying out experiments on Marshall stability, Marshall
Quotient, tensile strength, tensile strength ratio, rutting resistance,
flexural strength and resilient modulus.
Gokhale et al. (2005) presents a description of the testing
program, data collection effort and subsequent analyses and findings
focusing primarily on the initiation mechanisms of rutting in asphalt
mixtures as generated and observed under accelerated pavement testing.
The analysis of data on rutting indicates that unmodified AC mixtures
are rutted significantly more than modified mixtures under similar
loading and temperature conditions.
The content, structure and characteristics of a HMA mixture used
for constructing a pavement layer designed under deterministic
(Sivilevicius et al. 2011) or stochastic (Sivilevicius, Vislavicius
2008) methods depend on HMA manufacture in asphalt-mixing plant
tolerance (Braziunas, Sivilevicius 2010; Sivilevicius 2011b).
After a scale of pavement damage to road asphalt has reached an
intolerable limit, a surface or binder course is recycled in a hot
manner using an in-place or in-plant method adding new minerals and old
asphalt properties rejuvenating binders (Cygas et al. 2011; Mucinis et
al. 2009). For the purposes of the current analysis (Zaghloul, Holland
2008), a pavement section is assumed to be reconstructed when its
structural adequacy index reaches a value of 0.5.
Apeagyei et al. (2011) evaluated the rutting resistance of
plant-produced AC mixtures in the laboratory. Nineteen plant-produced AC
mixtures were used; the mixtures contained reclaimed asphalt pavement
(RAP) the amounts of which ranged from 0% to 25%. The mixtures that
contained no RAP showed dynamic modulus ([absolute value of [E.sup.*]])
values comparable to those that contained 25% of RAP in most cases. For
most of tested 19 mixtures, those having a lower FN contained no RAP,
25% of RAP or had PG 64-22 as the design binder grade. Statistical
analysis showed that the amount of RAP was the most significant factor
in affecting rutting resistance in the studied mixtures
Capuruco et al. (2005) present a new statistic term--full-car
roughness index used for calculating pavement roughness from
longitudinal pavement profiles. The index has been developed to better
simulate the interaction between the vehicle and the road.
Solowczuk (2011) presents the findings of the impact of rut depth
on 85% of speed quantile, [v.sub.85] along with information about
average speeds for vehicles carrying passengers and goods as well as
speeds reached at various available stopping sight distances.
Fwa et al. (2012) introduce an analytical procedure for assessing
the severity of rutting based on vehicle skidding and hydroplaning
analysis. For the given rut depth filled with water, the computer model
computes a hydroplaning speed of a typical passenger car and the
required braking distance of the car travelling at the known speed. Fwa
et al. (2012) have presented an approach to determining the threshold of
a critical rut depth of pavement maintenance based on the consideration
of hydroplaning risk and safety requirements for braking distance.
Vehicle manufacturers place a major focus on improving the design
of vehicle components to better respond to changes in road surface
profiles (Zaabar, Chatti 2011). Nevertheless, changes in the surface
profile still directly affect user costs, including repair and
maintenance costs and damage to goods.
The permissible depth of the rut and the assessment of the pavement
based on this indicator (rut depth) are very important. These
requirements and indicators fundamentally differ in separate countries,
where in some of which only the mean [h.sub.m] of rut depth is assessed
and some estimate a standard deviation of depth [s.sub.h].
The average depth of asphalt cover tracks started to be limited in
the Netherlands a few decades ago (Elsenaar, van de Fliert 1977)--they
were not to be deeper than 20 mm. Permissible rut depth in Norway,
depending on the category of the road, ranges from 20 to 35 mm. The
permissible rut depth of highways in Germany is 7 mm. Moreover, it
cannot exceed 2 mm during their first 2 years of operation. Fifteen
millimetre rut depth is considered critical in the UK and 20 mm depth is
deemed unacceptable in all cases (Vasiliev 1999).
In Switzerland, the condition of the surface is measured not only
by rut depth h but also by the depth of water level inside it [h.sub.v].
In France, water level in the rut is also standardised and, depending on
traffic, ranges from 6 to 12 mm. In Poland, the depth of the rut is
assessed according to its effect on traffic safety. All ruts are divided
into four separate categories: 0, I, II and III for different road
classes. Unfortunately, there is a lack of literature (publications)
about requirements for permissible rut depth and justification
principles and methods of road condition assessment indicators according
to this parameter (Vasiliev 1999). Lithuania has established 20 mm
permissible rut depth without specifying whether it is the mean, or one
single value. There are also no requirements for the standard deviation
[s.sub.h] of rut depth. When verifying the condition of operating roads
covered with the asphalt pavement, the total percentage of road sections
having deeper than 20 mm ruts is counted. The article presents one of
the first attempts to measure rut depth on Lithuanian roads and display
the obtained statistics (Getautis, Sivilevicius 2009).
Using a variety of multi-criteria evaluation methods, the risk of
construction projects is determined thus selecting the best alternatives
and maximum benefit (Zavadskas, Turskis 2011; Zavadskas et al. 2010).
The given methods can be adjusted to analysing the factors affecting the
ruts that appear in the asphalt pavement on the road and to finding the
most appropriate solution.
1. Factors determining and assessing rutting
The roughness of the road surface, assessed by IRI, depends on the
size of fatigue cracks and the average depth of ruts (Caliendo 2012;
Loizos, Plati 2008). When input data are implemented and a distress
model is calibrated for local conditions, the Mechanistic-Empirical
Pavement Design Guide (MEPDG) automatically predicts the corresponding
IRI over time (Rajbongshi, Das 2008). The equation used is as follows:
IRI = [IRI.sub.0] + 0.015(SF)+ 0.400([FC.sub.total]) +
0.008(TC)+40.0(RD), (1)
where: [IRI.sub.0]--initial IRI after construction; SF - site
factor; [FC.sub.total]--the area of fatigue-cracking (combined
alligator, longitudinal and reflection cracking in the wheel path);
TC--the length of transverse cracking; RD--average rut depth.
Rut depth caused by flow rutting is modelled as a function of
elastic strain, temperature and the number of loadings, as shown in the
MEPDG equation (NCHRP 2004; Oscarsson 2011):
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]; (2)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (3)
where: [[epsilon].sub.p] is accumulated plastic strain at N load
repetitions; [[epsilon].sub.r] is the resilient strain of the asphalt
material; [k.sub.1] is the variable confining pressure factor as a
function of depth; [a.sub.1] is laboratory-determined nonlinear
regression coefficients; [[beta].sub.r1] is laboratory to field
calibration factors; N is the number of loaded repetitions, T is
temperature ([degrees]F); RD is rut depth (in.); n is the number of AC
sub-layers; and hi is the thickness of a sub-layer (in.).
The latest development of predicting rutting within the HMA layer
calls for determining plastic vertical compressive strain within the HMA
layer. The total rutting within the HMA layer is then calculated by
multiplying the permanent strain times the thickness of the HMA layer
(Hajj et al. 2011a; Shukla, Das 2008):
[RD.sub.HMA] = [[epsilon].sub.p] x [h.sub.AC]; (4)
where: [RD.sub.HMA] is rutting generated in the HMA layer;
[[epsilon].sub.p] is permanent strain within the HMA layer; and
[h.sub.AC] is the thickness of the HMA layer.
With reference to available literature (Kannemeyer 2003), the
majority of the developed models of the ruts observed in asphalt base
pavements evaluate materials not acceptable producing such types of
pavements within the existing HDM-III models. The following rut
development model is employed for predicting the expected rut depth:
RD = a + b x T, (5)
where: RD--predicted rut depth, mm; a, b parameters the value of
which depends on the type of the road base; T--cumulative traffic
carried in million standard axles and equal to YE4 used in HDM-III,
assuming a load equivalency factor of 4.
Malysz et al. (2012) discuss the permanent deformation behaviour of
unbound aggregates used in accelerated pavement test (APT) sections. The
dependence of rutting evolution on stress state was verified, and a
model relating rut depth to load repetition was derived. Rut depth in
APT test sections was noticeably greater than that expected from
permanent deformation in the specimens of the triaxial apparatus.
The subgrade showed almost no contribution on rutting, and the
surface treatment is too thin to cause any effects:
RD = a + b x [square root of N], (6)
where: RD--rutting depth; N--the number of cycles; a and
b--statistical regression parameters.
The theoretical pavement life of rutting resistance (known as the
theoretical pavement rutting life index) was calculated using the Eqn.
(7) below (Goh et al. 2011):
The theoretical pavement rutting life index (TPRLI)
= [Rutting.sub.Allow]/[Rutting.sub.Actual], (7)
where: TPRLL is the theoretical pavement rutting life index, an
index value that indicates the theoretical pavement rutting life in the
field (year); [Rutting.sub.Allow]--allowable maximum rutting (0.25 in);
[Rutting.sub.Actual]--actual rutting in the field per year (in/year).
According to the HDM-4 programme drawn up by an order of the World
Bank, one of the main pavement quality indicators is average rut depth
[h.sub.m] and the standard deviation [s.sub.h] of rut depth (Kannemeyer
2003) determining the condition of the surface (Table 1).
Taniguchi and Yoshida (2003) mention the calibration of the HDM-4
rutting model on Japanese national highways and compare the HDM-4
rutting model with the rutting prediction model included in the Pavement
Management System developed by the Ministry of Land, Infrastructure
Transportation of Japan (MLIT-PMS). The maintenance control index (MCI)
of MLIT-PMS is given by the following expression:
MCI = 10 - 1.48[C.sup.0.3] - 0.29[D.sup.0.7] -
0.47[[sigma].sup.0.2], (8)
where: C--the amount of cracking, %; D--rut depth, mm;
[sigma]--longitudinal roughness, mm.
The management criteria of the MCI in actual road management are
provided in Table 2. In order to evaluate the road and automobile
stability in motion on the uneven surface with ruts, the following
criterion is suggested (Vansauskas, Bogdevicius 2009):
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (9)
where: [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is the
summary moment of cohesion forces around body axis z; T is general
movement time; [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is
the overall automobile mass moment of inertia around axis z; g is
gravity acceleration.
The performed analysis shows that ruts on the asphalt pavement are
formed by heavy vehicles (Perera, Kohn 2004), and, because of their
large and frequently changing depth, mainly suffer fast travelling
private cars. Therefore, not only the average rut depth is important but
also its variation causing the driver surprise and confusion effect. The
statistical parameters of rut depth have been improperly investigated
and still remain interesting to science and the field of study.
2. Methodology for rut measurement and data processing
The problem of rutting has been relevant and yet unresolved in
Lithuania as well as in other countries. Ruts become deeper as heavy
vehicles drive on highways and other country roads. With no timely
corrections to the pavement in a few years' time rutting would
exceed the limit depth of 20 mm and reach a critical depth of 40 mm,
which would inevitably increase the number of traffic accidents.
The staff of the Transport and Road Research Institute (TKTI)
annually monitors the rut depth of the roads of national significance
(18 highways and 132 regional) every 20 m. The obtained data have been
used for assessing the condition of country roads. Mobile Road Research
Laboratory RST 28 is used for performing measurements.
Rut depth on roads is measured in both travel directions of each
lane, including the left and right wheel. Rut distribution in transverse
road direction schemes (Fig. 1) for highways Vilnius-Kaunas with a
dividing strip and Vilnius-Minsk are presented as an example. While
driving the mobile laboratory at a speed of [v.sub.RST28] = 80 km/h,
only the ruts deeper than surface texture depth have been measured.
[FIGURE 1 OMITTED]
According to geometrical data on TKTI rut measurement, calculations
were made and statistical indicators showing the rut depth of highways
were obtained (Table 3). A rut number in Table 3 fits the numbers
presented in the schemes of Figure 1.
The mean of rut depth [h.sub.m] (position indicator) and standard
deviation [s.sub.h] (dispersion indicator) of each longitudinal
direction of the road were measured.
Every 20 m of measurement, unit data [h.sub.i] was used for
calculating mean [h.sub.m] of every separate rut of the road:
[h.sub.m] = [n.summation over (i=1)][h.sub.i]/n, (10)
where: [h.sub.i]--the rut depth of the i-th measurement, mm; n--the
number of measurements (i = 1, 2, ..., n).
Each standard deviation of rut [s.sub.h] was measured using similar
data:
[s.sub.h] = [square root of ([[n.summation over (i=1)][([h.sub.i] -
[h.sub.m]).sup.2]]/[n - 1])] (11)
where: [h.sub.i]--the rut depth of the i-th measurement, mm; n--the
number of measurements; [h.sub.m]--mean.
Statistic indicators ofeach rut (4 or 8) from all 18 highways are
presented in Table 3. They show that the deepest ruts of the road having
a dividing strip equal [h.sub.m] =8.69 mm and standard deviation makes
[s.sub.h=] 5.81 mm (rut 1 on the A12 road) and the situation on the
roads without a dividing strip--[h.sub.m] = 12.10 mm and [s.sub.h] =
5.38 mm (rut 2 on the A8 road). An average depth of the smallest ruts of
the least rutted roads having a dividing strip equal [h.sub.m] = 1.81 mm
and standard deviation makes [s.sub.h] = 1.18 mm (rut 7 on the road A13)
while the roads without a dividing strip--[h.sub.m] = 2.98 mm and
[s.sub.h] = 1.93 mm.
A part of measurement data that shows the texture depth of the
pavement surface is rejected and does not affect the pavement layer due
to rutting. Therefore, the first interval (class) of histograms (Fig. 2)
does not start from [h.sub.imin] =0 (zero) but from [h.sub.imin] having
the values 0.3, 0.4, 0.5 or 0.6 mm.
After calculating [h.sub.m], [s.sub.h], the percentage coefficient
of variation [V.sub.h], the characteristics of the form of frequency
distributions considering data grouped in the intervals of histograms
were calculated: skewness sk and kurtosis--ku.
Since all empirical values of histogram (Fig. 2) skewness sk are
higher than zero (sk varies from 1.08 to 6.94), the asymmetry of
histograms is positive (right) and differs from the normal section. An
empirical value of kurtosis ku is also higher than zero (ku varies from
1.32 to 97.1), thus, the peaks of the histograms are sharper than that
of normal distribution (positive kurtosis).
Empirical skewness and kurtosis of the histograms were compared
with critical values depending on the size of sample n only. For that
reason, standard deviations of skewness and kurtosis were calculated:
[s.sub.sk] = [square root of ([6n(n - 1)]/[(n - 2)(n + 1)(n + 3)])]
(12)
and
[s.sub.ku] = [square root of ([24n[(n - 1).sup.2]]/[(n - 3)(n -
2)(n + 3)(n + 5)])] (13)
When [absolute value of sk] [less than or equal to] 3[s.sub.sk] and
[absolute value of ku] [less than or equal to] 5[s.sub.ku], it can be
considered that the normality hypothesis of empirical data is accepted.
Otherwise, the raised hypothesis is rejected or accepted as doubtful.
Considering sample sizes n = 11.669 and n = 14.569 of the
Vilnius-Kaunas-Klaipeda highway shown in Table 3 and Fig. 2, the values
of standard deviations were calculated according to Eqns (12) and (13):
[s.sub.sk] = 0.0002099 and [s.sub.sk] =0.0001681, [s.sub.ku] = 0.0453
and [s.sub.ku] = 0.0406. The values of skewness [s.sub.sk] multiplied by
3, which are 0.00063 and 0.0050, respectively, are much lower than sk
values calculated from measurement data given in the histograms (Fig.
2). The values of kurtosis [s.sub.ku] multiplied by 5, which are 0.227
and 0.203 respectively, are much lower than ku values calculated from
measurement data given in the histograms (Fig. 2). These data reasonably
lead to the conclusion that the depth of the ruts distributes not
according to the normal law.
With an increase in rut depth [h.sub.m], average skewness and
kurtosis decrease (Fig. 3). This correlation implies that the deeper is
the road rut, the closer to the individual sections of rut depth is the
dissemination of normal distribution.
According to the calculated values of skewness and kurtosis, Uddin
et al. (2012) assessed the non-normality of data on highway
construction.
[FIGURE 2 OMITTED]
The value of the variation coefficient of a quite large sample
taken from normal general wholeness should not be higher than 33%. A
high percentage of variation coefficient V of rut depth (from 58.2% to
80.4%) shows that data (Fig. 2) are not distributed according to normal
distribution.
The analysis of the histograms of the grouped study data discloses
they are close to lognormal or exponential distribution. Lognormal
distribution (Billot et al. 2009) has the probability density function:
f(x, [mu], [sigma]) = [1/x[sigma][square root of 2[pi]]]exp[-[(ln x
- [mu]).sup.2]/2[[sigma].sup.2]], (14)
where [mu] and [sigma] are the mean and standard deviation of the
logarithm of variable x, respective y.
[FIGURE 3 OMITTED]
The curves of the probability density function of norma
distribution and lognormal distribution (Fig. 2) drawn from histogram
data differ fundamental y indicating that rut depth is closer to
lognormal distribution.
A eight parameters of depth positioning ([h.sub.m]) and dispersion
([s.sub.h]) of the ruts on the roads with a separating strip indicate
that the right ane has the deepest ruts as main y heavy vehicles drive a
long them. Figure 4a indicates that each lane has a deeper rut on the
right. The ruts of the reconstructed road (Road A13) are deeper because
at the beginning it had no separating strip, and following many years,
the second new two-lane carriageway was built (5-8 ruts). The rutting
depth of the second lane is lower as mainly passenger cars drive there.
The average depth [h.sub.m] of the investigated road rutting (the
number of them N = 100) is growing along with its standard deviation
[s.sub.h] (Figs 4 and 5). A positive linear correlation (Fig. 5) between
the above-introduced statistical indicators has been found, and the
received regression equations [s.sub.h] = f([h.sub.m]) and
[s.sup.2.sub.h] = f([h.sub.m]) show a sufficiently strong link between
these indicators (determination coefficients [R.sup.2] are 0.74 and
0.61, respectively).
Permissible rut depth after performing more statistical studies and
the dynamic parameters of the cars travelling at a different speed after
calculating the influence of rut depth can be determined. While defining
permissible and critical rut depth, national economic opportunities and
a strategy for reducing accidents must be evaluated.
[FIGURE 4 OMITTED]
Conclusions
1) After measuring the rut depth of each 18 Lithuanian highways
every 20 m applying the mobile laboratory RST 28, large samples (n=
454-14.567) were used for calculating arithmetical mean [h.sub.m],
standard deviation [s.sub.h] and variation coefficient V of rut depth.
Skewness (sk) and kurtosis (ku) were calculated, histograms were drawn,
normal and lognormal theoretical curves of the probability density of
distribution were grouped into intervals considering the obtained
information. Statistical data show that:
--[h.sub.m], [s.sub.h] and V of the right and left rut of each lane
differ: the roads having a dividing strip in the first lane, which is
mainly driven by heavy vehicles, have deeper rutting, and deeper ruts
can be noticed on the right side of the first lane;
--rut depth is not distributed according to normal distribution;
--without measuring and evaluating ruts, the depth of which is less
than the depth of the pavement surface texture, the depth of deeper
(real) ruts distributes according to lognormal distribution;
--the bigger is the mean of rut depth, the closer its depth
distribution gets to normal distribution;
--while the mean [h.sub.m] of the rut depth of the road pavement is
linearly increasing, the standard deviation [s.sub.h] of its depth is
also increasing (coefficient of determination [R.sup.2] = 0.74);
[h.sub.m] and a linear positive correlation of variance [s.sup.2.sub.h]
are weaker ([R.sup.2] = 0.61).
[FIGURE 5 OMITTED]
2) While rut depth is increasing, its dispersion (variance) is also
rising, which causes not only greater dynamics of the vehicle but also
driving inconveniences, greater emotional stress and fatigue for the
driver, which increases the number of accidents. The variation of rut
depth rises the surprise appearance of a dangerous road section, the
necessity of decreasing speed, the probability of driver's
confusion (disorder), especially when the rut is filled with water. Rut
depth is limited and must not exceed permissible and critical values
that may differ in separate countries due to set employed different
principles and methods. It is only possible to standardise maximum
permissible rut depth after thorough additional tests based on the
influence of geometrical rut parameters determining the dynamics of
driving a car.
http://dx.doi.org/ 10.3846/13923730.2013.817481
References
Al-Hadidy, A. I.; Yi-qiu, T. 2010. Comparative performance of the
SMAC made with the SBS- and ST-modified binders, Journal of Materials in
Civil Engineering ASCE 22(6): 580-587.
http://dx.doi.org/10.1061/(ASCE)MT.1943-5533.0000057
Ali, B.; Sadek, M.; Shahrour, I. 2009. Finite-element model for
urban pavement rutting: analysis of pavement rehabilitation methods,
Journal of Transportation Engineering ASCE 135(4): 235-239.
http://dx.doi.org/10.1061/(ASCE)0733-947X(2009)135: 4(235)
Al-Suleiman, T. I.; Obaidat, M. T.; Abdul-Jabbar, G. T.; Khedaywi,
T. S. 2000. Field inspection and laboratory testing of highway pavement
rutting, Canadian Journal of Civil Engineering 27(6): 1109-1119.
http://dx.doi.org/10.1139/cjce-27-6-1109
Apeagyei, A. K. 2011. Rutting as a function of dynamic modulus and
gradation, Journal of Materials in Civil Engineering ASCE 23(9):
1302-1310. http://dx.doi.org/10.1061/(ASCE)MT.1943-5533.0000309
Apeagyei, A. K.; Diefenderfer, B. K.; Diefenderfer, S. D. 2011.
Rutting resistance of asphalt concrete mixtures that contain recycled
asphalt pavement, Transportation Research Record 2208: 9-16.
http://dx.doi.org/10.3141/2208-02.
ASTM E 867-02a. 2004. Terminology Relating to Vehicle Pavement
Systems. Annual Book of ASTM Standards. Section four Construction Volume
04 03 Road and Paving Materials; Vehicle-Pavement Systems, 969-976.
Billot, R.; El Fanazi, N. E.; De Vuyst, F. 2009. Multilevel
assessment of the impact of rain on drivers' behavior. Standartized
methodology and empirical analysis, Transportation Research Record 2107:
134-142. http://dx.doi.org/10.3141/2107-14
Braziunas, J.; Sivilevicius, H. 2010. The bitumen batching
system's modernization and its effective analysis at the asphalt
mixing plant, Transport 25(3): 325-335.
http://dx.doi.org/10.3846/transport.2010.40
Brown, E. R.; Collins, R.; Brownfield, J. R. 1989. Investigation of
segregation of asphalt mixtures in the state of Georgia, Transportation
Research Record 1217: 1-8.
Caliendo, C. 2012. Local calibration and implementation of the
Mechanistic-Empirical Pavement Design Guide for flexible pavement
design, Journal of Transportation Engineering ASCE 138(3): 348-360.
http://dx.doi.org/10.1061/(ASCE)TE.1943-5436.0000328
Capuruco, R. A. C.; Hegazy, T.; Tighe, S. L.; Zaghloul, S. 2005.
Full-car roughness index as summary roughness statistic, Transportation
Research Record 1905: 148156. http://dx.doi.org/10.3141/1905-17
Ceylan, H.; Schwartz, C. W.; Kim, S.; Gopalakrishnan, K. 2009.
Accuracy of predictive models for dynamic modulus of hot-mix asphalt,
Journal of Materials in Civil Engineering ASCE 21(6): 286-293.
http://dx.doi.org/10.1061/(ASCE)0899-1561(2009)21:6 (286)
Chandra, S. 2004. Effect of road roughness on capacity of two-lane
roads, Journal of Transportation Engineering ASCE 130(3): 360-364.
http://dx.doi.org/10.1061/(ASCE)0733-947X(2004)130: 3(360)
Chang, C.-M.; Baladi, G. Y.; Wolff, T. F. 2002. Detecting
segregation in bituminous pavements, Transportation Research Record
1813: 77-86. http://dx.doi.org/10.3141/1813-10
Coleri, E.; Tsai, B. W.; Monismith, C. L. 2008. Pavement rutting
performance prediction by integrated Weibull approach, Transportation
Research Record 2087: 120-130. http://dx.doi.org/10.3141/2087-13
Collop, A. C.; McDowell, G. R.; Lee, Y. W. 2006. Modeling dilation
in an idealized asphalt mixture using discrete element modeling,
Granular Matter 8: 175-184. http://dx.doi.org/10.1007/s10035-006-0013-3
Cygas, D.; Mucinis, D.; Sivilevicius, H.; Abukauskas, N. 2011.
Dependence of the recycled asphalt mixture physical and mechanical
properties on the grade and amount of rejuvenating bitumen, The Baltic
Journal of Road and Bridge Engineering 6(2): 124-134.
http://dx.doi.org/10.3846/bjrbe.2011.17
Dawson, A. R. 2008. Rut accumulation and power low models for
low-volume pavements under mixed traffic, Transportation Research Record
2068: 78-86. http://dx.doi.org/10.3141/2068-09
de Freitas, E. F.; Pereira, P.; Picado-Santos, L.; Papagiarnakis,
A. T. 2005. Effect of construction quality, temperature, and rutting on
initiation of top-down cracking, Transportation Research Record 1929:
174-182. http://dx.doi.org/10.3141/1929-21
Elsenaar, P. M.W; vandeFliert, C. 1977. Quality criteria for
maintenance and reinforcement of pavements in the Netherlands,
Transportation Research Record 652: 65-70.
Fwa, T. F.; Pasindu, H. R.; Ong, G. P. 2012. Critical rut depth for
pavement maintenance based on vehicle skidding and hydroplaning
consideration, Journal of Transportation Engineering ASCE 138(4):
423-430. http://dx.doi.org/10.1061/(ASCE)TE.1943-5436.0000336
Getautis, E.; Sivilevicius, H. 2009. Lietuvos valstybines reiksmes
keliu asfalto dangos provezuu gylio statistinis tyrimas ir vertinimas
[Statistical analysis and evaluation of the depth of the ruts on
Lithuanian state significance roads], Mokslas--Lietuvos ateitis
[Science--future of Lithuania] 1(6): 14-19.
http://dx.doi.org/10.3846/mla.2009.6.03
Goh, S. W.; You, Z.; Williams, R. C.; Li, X. 2011. Preliminary
dynamic modulus criteria of HMA for field rutting of asphalt pavements:
Michigan's experience, Journal of Transportation Engineering ASCE
137(1): 37-45. http://dx.doi.org/10.1061/(ASCE)TE.1943-5436.0000191
Gokhale, S.; Choubane, B.; Byron, T.; Tia, M. 2005. Rut initiation
mechanisms in asphalt mixtures as generated under accelerated pavement
testing, Transportation Research Record 1940: 136-145.
http://dx.doi.org/10.3141/1940-15
Gopalakrishnan, K. 2008. Predicting capacities of runways serving
new large aircraft, Transport 23(1): 44-50.
http://dx.doi.org/10.3846/1648-4142.2008.23.44-50
Hajj, E.Y.; Morian, N.; El Tannoury, G. A.; Manoharan, S.; Sebaaly,
P. E. 2011b. Impact of lime application method on ravelling and moisture
sensitivity in HMA mixtures, International Journal of Pavement
Engineering 12(2): 149-160.
http://dx.doi.org/10.1080/10298436.2010.535539
Hajj, E. Y.; Tannoury, G.; Sebaaly, P. E. 2011a. Evaluation of rut
resistance asphalt mixtures for intersection, Road Materials and
Pavement Design 12(2): 263-292.
http://dx.doi.org/10.1080/14680629.2011.9695246
Haritonovs, V.; Smirnovs, J.; Naudzsuns, J. 2010. Prediction of
rutting formation in asphalt concrete pavement, The Baltic Journal of
Road and Bridge Engineering 5(1): 38-42.
http://dx.doi.org/10.3846/bjrbe.2010.05
Haryanto, I.; Takahashi, O. 2007. Use of secant shear modulus for
rutting potential assessment of Indonesian wearing course mixtures, The
Baltic Journal of Road and Bridge Engineering 2(3): 95-100.
Hu, S.; Zhou, F.; Scullion, T. 2011. Development, calibration, and
validation of new M-E rutting model for HMA overlay design and analysis,
Journal of Materials in Civil Engineering ASCE 23(2): 89-99.
http://dx.doi.org/http://dx.doi.org/10.1061/(ASCE)MT. 1943-5533.0000130
Kannemeyer, L. 2003. Modelling rutting in flexible pavements in
HDM-4 [online], [cited 12 May 2013], Available from Internet:
http://www.lpcb.org/index.php/component/docman/doc_
view/459-1995-rut-depth-modelling-rut-depths-in-flex
ible-pavements?Itemid =
Khedr, A. S.; Breakah, T. M. 2011. Rutting parameters for asphalt
concrete for different aggregate structures, International Journal of
Pavement Engineering 12(1): 13-23.
http://dx.doi.org/10.1080/10298430903578960
Lin, Q.; Cao, D. 2009. Research on material composition and
performance of porous asphalt pavement, Journal of Materials in Civil
Engineering ASCE 21(4): 135-140.
http://dx.doi.org/10.1061/(ASCE)0899-1561(2009)21:4 (135)
Loizos, A.; Plati, C. 2008. An alternative approach to pavement
roughness evaluation, International Journal ofPavement Engineering 9(1):
69-78. http://dx.doi.org/10.1080/10298430600949894
Lottoman, R. P.; Frith, D. J. 1989. Predicting the effects of
moisture on wheelpath rutting in asphalt concrete, Transportation
Research Record 1228: 63-72.
Malysz, R.; Nunez, W. P.; Bica, A. V. D.; Ceratti, J. A. P.; de
Azevedo Bernardes, J. 2012. Investigation of thin pavements rutting
based on accelerated pavement testing and repeated loading triaxial
tests, Journal of Transportation Engineering ASCE 138(2): 141-148.
http://dx.doi.org/10.1061(ASCE)TE.1943-5436.0000298
Markauskas, D.; Kacsianauskas, R.; Dzsiugys, A.; Navakas, R. 2010.
Investigation of adequacy of multi-sphere apprimoximation of elliptical
particles for DEM simulations, Granular Matter 12: 107-123.
http://dx.doi.org/10.1007/s10035-009-0158-y
Mogawer, W. S.; Austerman, A. J.; Daniel, J. S.; Zhou, F.; Bennert,
T. 2011. Evaluation of the effects of hot mix asphalt density on mixture
fatigue performance, rutting performance and MEPDG distress predictions,
International Journal of Pavement Engineering 12(2): 161-175.
http://dx.doi.org/10.1080/10298436.2010.546857
Mucsinis, D.; Sivilevicsius, H.; Oginskas, R. 2009. Factors
determining the inhomogeneity of reclaimed asphalt pavement and
estimation of its components content variation parameters, The Baltic
Journal of Road and Bridge Engineering 4(2): 69-79.
http://dx.doi.org/10.3846/1822-427X.2009.4.69-79
NCHRP. 2004. Guide for the mechanistic-empirical design of new and
rehabilitated pavement structures. Report 1 37A. Washington, DC:
Transportation Research Board. 93 p.
Nukuhya, B.; Roque, R.; Tia, M.; Mehta, Y. A. 2002. Effect of
aggregate structure on rutting potential of densegraged asphalt
mixtures, Transportation Research Record 1789: 136-145.
http://dx.doi.org/10.3141/1789-15
Oscarsson, E. 2011. Evaluation of the mechanistic-empirical
pavement design guide model for permanent deformations in asphalt
concrete, International Journal of Pavement Engineering 12(1): 1-12.
http://dx.doi.org/10.1080/10298430903578952
Perera, R.; Kohn, S. 2004. Effects of variation in quarter-car
simulation speed on international roughness index algorithm,
Transportation Research Record 1889: 144151.
http://dx.doi.org/10.3141/1889-16
Petkevicsius, K.; Zilionienee, D.; Vorobjovas, V. 2010. Funkcional
conditions and state of hot mix asphalt pavement and its structure of
Lithuanian motor roads, The Baltic Journal of Roads and Bridge
Engineering 5(1): 43-49. http://dx.doi.org/10.3846/bjrbe.2010.06
Rajbongshi, P.; Das, A. 2008. Optimal asphalt pavement design
considering cost and reliability, Journal of Transportation Engineering
ASCE 134(6): 255-261.
0http://dx.doi.org/10.1061/(ASCE)0733-947X(2008)134: 6(255)
Said, S. F; Oscarsson, E.; Hjort, M. 2011. Prediction of flow
rutting in asphalt concrete layers, International Journal of Pavement
Engineering 12(6): 519-532.
http://dx.doi.org/10.1080/10298436.2011.559549
Salama, H. K.; Haider, S. W.; Chatti, K. 2007. Evaluation of new
mechanistic-empirical pavement design guide rutting models for
multiple-axle loads, Transportation Research Record 2005: 112-123.
http://dx.doi.org/10.3141/2005-13
Shukla, P. K.; Das, A. 2008. A re-visit to the development of
fatigue and rutting equations used for asphalt pavement design,
International Journal of Pavement Engineering 9(5): 355-364.
http://dx.doi.org/10.1080/10298430701690462
Sivilevicsius, H. 2011a. Modelling the interaction of transport
system elements, Transport 26(1): 20-34.
http://dx.doi.org/10.3846/16484142.2011.560366
Sivilevicsius, H. 2011b. Application of expert evaluation method to
determine the importance of operating asphalt mixing plant quality
criteria and rank correlation, The Baltic Journal of Road and Bridge
Engineering 6(1): 48-58. http://dx.doi.org/10.3846/bjrbe.2011.07
Sivilevicsius, H.; Podvezko, V.; Vakrinienee, S. 2011. The use of
constrained and unconstrained optimization modes in gradation design of
hot mix asphalt mixture, Construction and Building Materials 25(1):
115-122. http://dx.doi.org/10.1016/j.conbuildmat.2010.06.050
Sivilevicsius, H.; Ssukevicsius, Ss. 2007. Dynamics of vehicle
loads on the asphalt pavement of European roads which cross Lithuania,
The Baltic Journal of Road and Bridge Engineering 2(4): 147-154.
Sivilevicsius, H.; Vislavicsius, K. 2008. Stochastic simulation of
the influence of variation of mineral material gradin and dose weight on
the homogeneity in hot-mix asphalt, Construction and Building Materials
22(9): 2007-2014. http://dx.doi.org/10.1016/j.conbuildmat.2007.07.001
Solowczuk, A. 2011. Estimation of free-flow speeds on rutted
asphalt two-way, two-lane roads with the soft shoulders, The Baltic
Journal of Road and Bridge Engineering 6(3): 201-209.
http://dx.doi.org/10.3846/bjrbe.2011.26
Souza, L. T.; Kim, Y.-R.; Souza, F. V.; Castro, L. S. 2012.
Experimental testing and finite-element modeling to evaluate the effects
of aggregate angularity on bituminous mixture performance, Journal of
Materials in Civil Engineering ASCE 24(3): 249-258.
http://dx.doi.org/10.1061/(ASCE)MT.1943-5533.0000 386
Taniguchi, S.; Yochida, T. 2003. Calibrating HDM-4 rutting model on
national highways in Japan, in The 22nd PIARC World Road Congress, 19-25
October, 2003, Durban, South Africa, 10 p.
Thodesen, C. C.; Lerfald, B. O.; Hoff, I. 2012. Review of asphalt
pavement evaluation methods and current applications in Norway, The
Baltic Journal of Road and Bridge Engineering 7(4): 246-252.
http://dx.doi.org/10.3846/bjrbe.2012.33
Topal, A.; Sengoz, B. 2005. Determination of fine aggregate
angularity in relation with the resistance to rutting of hot-mix
asphalt, Construction and Building Materials 19(2): 155-163.
http://dx.doi.org/10.1016/j.conbuildmat.2004.05.004
Uddin, M.; Goodrum, P. M.; Mahboub, K. C.; Stromberg, A. 2012.
Solution to nonnormality in quality assurance and acceptance quality
characteristics data, Transportation Research Record 2268: 50-58.
http://dx.doi.org/10.3141/2268-07
Vansauskas, V.; Bogdevicsius, M. 2009. Investigation into the
stability of driving an automobile on the road pavement with ruts,
Transport 24(2): 170-179.
http://dx.doi.org/10.3846/1648-4142.2009.24.170-179
Vasiliev, A. P. 1999. Prichiny obrazovaniia kolei i puti ikh
ustraneniia, Nauka i tekhnika v dorozhnoj otrasli 2(9): 6-9.
Wang, H.; Zhang, Q.; Tan, J. 2009. Investigation of layer
contributions to asphalt pavement rutting, Journal of Materials in Civil
Engineering ASCE 21(4): 181-185.
http://dx.doi.org/10.1061/(ASCE)0899-1561(2009)21:4 (181).
Wang, G.; Roque, R.; Morian, D. 2012. Effects of surface rutting on
near-surface pavement responses based on a two-dimensional
axle-tire-pavement interaction finite-element model, Journal of
Materials in Civil Engineering ASCE 24(11): 1388-1395.
http://dx.doi.org/10.1061/(ASCE)MT.1943-5533.0000526
Xia, K. 2010. A finite element model for tire/pavement interaction:
application to predicting pavement damage, International Journal of
Pavement Research and Technology 3(3): 135-141.
Xia, K.; Wang, L. 2010. Polishing mechanism and its numerical
modeling for flexible pavement, International Journal of Pavement
Research and Technology 3(1): 43-50.
Yang, J.; Lu, H.; Zhu, H. 2009. Approaches to rut depth prediction
in semirigid asphalt pavements, Journal of Engineering Mechanics ASCE
135(6): 510-516. http://dx.doi.org/10.1061/(ASCE)0733-9399(2009)135:
6(510)
Yavuzturk, C.; Ksaibati, K.; Chiasson, A. D. 2005. Assessment of
temperature fluctuations in asphalt pavements due to thermal
environmental conditions using a two-dimensional, transient
finite-difference approach, Journal of Materials in Civil Engineering
17(4): 465-475.
Zaabar, I.; Chatti, K. 2011. New mechanistic-empirical approach for
estimating the effect of roughness on vehicle durability, Transportation
Research Record 2227: 180-188. http://dx.doi.org/10.3141/2227-20.
Zaghloul, S.; Holland, J. T. 2008. Comparative analysis of
long-term field performance of recycled asphalt in California
environmental zones, Transportation Research Record 2084: 83-99.
http://dx.doi.org/10.3141/2084-10
Zavadskas, E. K.; Turskis, Z. 2011. Multiple criteria decision
making (MCDM) methods in economics: an overview, Technological and
Economic Development of Economy 17(2): 397-427.
http://dx.doi.org/10.3846/20294913.2011.593291
Zavadskas, E. K.; Turskis, Z.; Tamossaitienee, J. 2010. Risk
assessment of construction projects, Journal of Civil Engineering and
Management 16(1): 33-46. http://dx.doi.org/10.3846/jcem.2010.03
Zhang, J.; Cooley, L. A.; Kandhal, P. S. 2002. Comparison of
fundamental and simulative test methods for evaluating permanent
deformation of hot-mix asphalt, Transportation Research Record 1789:
91-100. http://dx.doi.org/10.3141/1789-10
Henrikas SIVILEVICIUS, Vidmantas VANSAUSKAS
Department of Transport Technological Equipment, Vilnius Gediminas
Technical University, Plytinesg. 27, LT-10105 Vilnius, Lithuania
Received 1 Sep. 2012; accepted 8 Apr. 2013
Henrikas SIVILEVICIUS. Prof Dr Habil at the Department of Transport
Technological Equipment, Faculty of Transport Engineering, Vilnius
Gediminas Technical University, Lithuania. PhD in the construction of
automobile roads (1984). DrSc (2003) in civil engineering. Research
interests: hot mix asphalt (HMA) production quality and development of
the quality control method, stochastic modelling and the application of
statistical methods on the roads of flexible pavement construction,
improvement in asphalt recycling technology, multi-criteria decision
making (MCDM) in the transport system.
Vidmantas VANSAUSKAS. PhD student at the Department of Transport
Technological Equipment, Faculty of Transport Engineering, Vilnius
Gediminas Technical University, Lithuania. MSc in transport engineering
(2007). Research interests: vehicle dynamics, evaluation of pavement
surface condition, modelling road roughness.
Corresponding author: Henrikas Sivilevicius
E-mail:
[email protected]
Table 1. Permissible parameters of rut depth (mm)
Statistical Condition of the pavement surface
indicator
New Good Satisfactory Unsatisfactory Bad
Mean rut 0 2 5 15 25
depth
([h.sub.m])
Standard 0 1 2 5 8
deviation
of rut
depth
([s.sub.h])
Table 2. The dependence of maintenance
levels on the MCI (Taniguchi, Yoschida
2003)
MCI Management level
More than 5 Not needing repair
(desirable
management level)
3-5 Needing repair
Less than 3 Needing immediate
repair
Table 3. Statistical indicators of the rut depth of the highway
asphalt layer
Name and number of the Rutting measured every 20 m, number of
road readings n, mean [h.sub.m], standard
deviation [s.sub.h]
Rut No. 1 2 3 4
A1 (Vilnius-Kaunas- n 14567 14596
Klaipeda) [h.sub.m] 6.07 6.93 2.52 3.12
[s.sub.h] 4.88 4.77 1.71 1.97
A2 (Vilnius-Panevezys) n 6245 6041
[h.sub.m] 6.24 7.08 1.94 2.21
[s.sub.h] 5.09 5.33 1.17 1.42
A3 (Vilnius-Minskas) n 1318 1323
[h.sub.m] 4.40 3.97 3.47 3.59
[s.sub.h] 3.50 3.02 2.56 2.43
A4 (Vilnius-Varena- n 6079 6079
Gardinas) [h.sub.m] 4.75 4.63 4.79 4.45
[s.sub.h] 3.47 3.68 3.47 3.46
A5 (Kaunas- n 4058 1260
Marijampole-Suvalkai) [h.sub.m] 6.83 6.82 3.17 5.13
[s.sub.h] 8.56 7.39 2.47 3.61
A6 (Kaunas-Zarasai- n 8966 1107
Daugpilis) [h.sub.m] 8.58 8.02 4.94 6.77
[s.sub.h] 6.27 5.44 2.81 3.94
A7 (Marijampolee- n 1997 1997
Kybartai- [h.sub.m] 3.24 3.41 2.98 3.38
Kaliningradas) [s.sub.h] 2.10 1.95 1.93 1.80
A8 (Panevezys- n 3991 3983
Aristava-Sitkunai) [h.sub.m] 9.07 12.1 8.34 12.27
[s.sub.h] 6.36 5.38 6.51 5.73
A9 (Panevezys-Siauliai) n 3533 3533
[h.sub.m] 6.98 7.86 6.58 8.09
[s.sub.h] 5.12 4.50 4.62 4.67
A10 (Panevezys- n 3084 3084
Pasvalys-Bauska) [h.sub.m] 9.59 9.10 9.34 9.43
[s.sub.h] 8.56 8.40 8.22 8.77
A11 (Siauliai-Palanga) n 7179 870
[h.sub.m] 6.13 5.04 1.66 3.02
[s.sub.h] 4.98 3.53 1.02 1.31
A12 (Ryga-Siauliai- n 8794 454
Taurage-Kaliningradas) [h.sub.m] 8.69 8.53 1.14 2.03
[s.sub.h] 5.81 4.87 1.29 2.24
A13 (Klaipeeda-Liepoja) n 2148 862
[h.sub.m] 6.12 5.25 2.14 5.01
[s.sub.h] 5.34 3.47 1.86 5.40
A14 (Vilnius-Utena) n 4279 4277
[h.sub.m] 5.49 5.22 4.78 4.13
[s.sub.h] 2.57 3.35 2.72 3.20
A15 (Vilnius-Lyda) n 2057 2057
[h.sub.m] 4.80 5.12 4.40 4.71
[s.sub.h] 3.82 3.79 3.38 3.45
A16 (Vilnius-Prienai- n 5996 5995
Marijampolee) [h.sub.m] 4.78 3.80 3.85 3.32
[s.sub.h] 4.34 3.06 3.44 2.90
A17 (bypass of n 1115 1115
Panevezys) [h.sub.m] 6.20 8.47 6.03 8.50
[s.sub.h] 5.24 4.44 5.11 4.37
A18 (bypass of n 854 853
Siauliai) [h.sub.m] 4.60 3.99 4.23 3.43
[s.sub.h] 2.94 2.90 2.77 2.55
Name and number of the Rutting measured every 20 m,
road number of readings n, mean
[h.sub.m], standard deviation
[s.sub.h]
5 6 7 8
A1 (Vilnius-Kaunas- 11669 11969
Klaipeda) 7.72 7.53 2.64 3.29
5.47 4.95 1.54 2.07
A2 (Vilnius-Panevezys) 6245 6246
6.37 6.89 2.04 2.70
4.27 5.06 1.92 2.15
A3 (Vilnius-Minskas) -- --
-- -- -- --
-- -- -- --
A4 (Vilnius-Varena- -- --
Gardinas) -- -- -- --
-- -- -- --
A5 (Kaunas- 4787 1099
Marijampole-Suvalkai) 4.01 4.79 2.75 4.30
4.33 3.85 2.28 3.03
A6 (Kaunas-Zarasai- 8966 1104
Daugpilis) 7.94 7.17 2.63 2.91
6.45 5.49 2.14 2.31
A7 (Marijampolee- -- --
Kybartai- -- -- -- --
Kaliningradas) -- -- -- --
A8 (Panevezys- -- --
Aristava-Sitkunai) -- -- -- --
-- -- -- --
A9 (Panevezys-Siauliai) -- --
-- -- -- --
-- -- -- --
A10 (Panevezys- -- --
Pasvalys-Bauska) -- -- -- --
-- -- -- --
A11 (Siauliai-Palanga) 7176 863
5.57 5.03 3.36 3.20
4.37 3.45 2.56 2.66
A12 (Ryga-Siauliai- 8794 454
Taurage-Kaliningradas) 7.14 7.86 2.21 3.04
5.04 4.36 1.39 1.67
A13 (Klaipeeda-Liepoja) 2147 860
4.04 4.74 1.81 3.16
2.30 3.22 1.18 1.43
A14 (Vilnius-Utena) -- --
-- -- -- --
-- -- -- --
A15 (Vilnius-Lyda) -- --
-- -- -- --
-- -- -- --
A16 (Vilnius-Prienai- -- --
Marijampolee) -- -- -- --
-- -- -- --
A17 (bypass of -- --
Panevezys) -- -- -- --
-- -- -- --
A18 (bypass of -- --
Siauliai) -- -- -- --
-- -- -- --
