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Nota tŽcnica / Technical note =
An‡lisis de
esfuerzos en pavimentos de concreto tipo
whitetopping=
:
caso de estudio v’a Bibli‡n-Zhud
<=
i
style=3D'mso-bidi-font-style:normal'>Stress
analysis in whitetopping concrete pavements: Case study the Bibli‡n-Zhud
highway
Jaime
Bojorque-I–eguez
Profesor Facultad de Ingenier’a, Departame=
nto
de Ingenier’a Civil, Universidad de Cuenca, Av. 12 de Abril y Agust’n Cuenca=
,
Cuenca, Ecuador, 01.01.168.
Aut=
or de
correspondencia: jaime.bojorque@ucuenca.edu.ec
Fecha de recepci—n: 19 de octubre de 2021 - Fecha de aceptaci—n: 1 de=
noviembre
de 2021
=
=
RESUMEN
En este documento se presenta los resultados =
del
an‡lisis retrospectivo para determinar las posibles causas del deterioro
prematuro del pavimento r’gido de la v’a Bibli‡n-Zhud, arteria principal que
conecta la zona austral con el norte del pa’s. En base a las caracter’sticas=
de
la v’a y cargas de tr‡fico se realiza un an‡lisis de los esfuerzos que se
generan en las losas de pavimento. Los esfuerzos son determinados a travŽs d=
e
ecuaciones anal’ticas y mŽtodos de elementos finitos. Se estableci— que los
resultados por ambos mŽtodos son muy similares. Mediante el empleo de elemen=
tos
finitos se analiz—, adicionalmente, el efecto de las variaciones en las carg=
as
y del espesor del pavimento en los esfuerzos. Se determin— que bajo las carg=
as
actuales y por las variaciones del espesor, el pavimento r’gido de la v’a no
soporta los esfuerzos a los que est‡ sometido, identific‡ndose claramente el
desarrollo de diferentes mecanismos de falla siendo los m‡s concurrentes las
grietas de esquina, las grietas transversales y las longitudinales.
Pal=
abras
clave : Pavimento r’gido, deterioro, refuerzo delgado, esfuerzos.
ABSTRACT
This article p=
resents
the results of a retrospective analysis to explain the probable causes of th=
e
premature deterioration of the rigid pavement of the Bibli‡n-Zhud highway, m=
ain
artery connecting the southern with the northern zone of the country. Based =
on
the characteristics of the road and traffic loads, an analysis of the stress=
es
generated in the pavement slabs is conducted. Stresses are determined throug=
h
analytical equations and finite element methods. The results by both methods
are remarkably similar. In addition, by using finite elements, the effect of
variations in loads and pavement thickness on stress was also analyzed. The
analysis reveals that under the current loads and due to the variations in
thickness, the rigid pavement of the road does not support the stresses to
which it is subjected, clearly identifying the development of different fail=
ure
mechanisms, the most concurrent being corner cracks, transversal and
longitudinal cracks.
Keywords : Rigid pavement, deteriorat=
ion,
whitetopping, stresses.
1.  =
; INTRODUCCIîN =
span>
Considerando la gran inversi—n econ—mica que la construcci—n de una =
v’a
representa, es necesario mantenerla y rehabilitarla adecuadamente para
garantizar su buen desempe–o durante su vida œtil. Garantizando adicionalmen=
te
la seguridad y confort a los usuarios. Existen varias alternativas de
rehabilitaci—n para las v’as segœn el grado de deterioro y tipo de superfici=
e
de rodadura. Una alternativa de rehabilitaci—n para un pavimento flexible
deteriorado es el empleo de una capa de refuerzo con hormig—n adherida o no
adherida, a este tipo de rehabilitaci—n se la denomina ÒwhitetoppingÓ
(Harrington & Fick, 2014).
El œnico acceso, mediante una v’a interprovincial, que tiene la
provincia del Azuay, Ecuador, con el norte del pa’s es a travŽs la v’a
Bibli‡n-Zhud que cruza la provincia del Ca–ar. Con la finalidad de rehabilit=
ar
esta v’a de pavimento flexible, en el a–o 2008, se consider— el empleo de un=
a
capa de rodadura constituida por losas de concreto de cemento Portland
(whitetopping) dise–adas para ser colocadas sobre el pavimento flexible, con=
un
periodo de dise–o de 20 a–os. Sin embargo, la v’a en menos de cinco a–os ha
presentado deterioros en varias losas, causando inconvenientes a los usuario=
s.
Un refuerzo de hormig—n whitetopping sobre un pavimento de mezcla asf‡ltica
existente, puede clasificarse por su espesor y por el tipo de enlace con la
capa de asfalto subyacente (Rasmussen & Rozycki, 2004). Los refuerzos
convencionales, tienen un espesor de m‡s de 20.5 cm (8 in) y son dise–ados y=
construidos
sin considerar la posible fuerza de uni—n entre la capa de hormig—n y la cap=
a
de asfalto. El refuerzo de hormig—n est‡ destinado a corregir el deterioro
estructural
y funcional en un pavimento asf‡ltico existente a un costo adecuado. =
La
superficie del hormig—n tiene buena durabilidad y rendimiento a largo plazo,=
y
disminuye el tiempo de mantenimiento y el costo del ciclo de vida del pavime=
nto
(Tarr, Sheehan, & Ardani, 2000; Rea & Jensen, 2005). Sin embargo, pa=
ra
un buen desempe–o se debe tener, muy en cuenta, el espesor de la capa de
refuerzo a colocar, el espaciamiento de las juntas y la calidad del paviment=
o
asf‡ltico existente. No considerar adecuadamente estas caracter’sticas puede
resultar en fallas prematuras del pavimento (Rasmussen, McCullough, Ruiz, Ma=
ck,
& Sherwood, 2002; Lin & Wang, 2005). La American Concrete Pavement
Association (ACPA, 2011), recomienda, entre otros aspectos, las siguientes
acciones para asegurar un proyecto exitoso; i) fresar el pavimento asf‡ltico
existente para eliminar o reducir las distorsiones superficiales de 50 mm (2
in) o mayores; ii) un menor espaciamiento entre las juntas para reducir los
esfuerzos por alabeo y deformaciones; y iii) las juntas deben aserrarse tan
pronto como sea posible debido a que la ventana de tiempo para aserrar es me=
nor
que en el caso de los pavimentos convencionales.
El desempe–o del refuerzo de concreto es sensible a las dimensiones d=
e
la losa, que es relativamente delgada. Cuando se compara con un pavimento de
concreto convencional, los pavimentos whitetopping, generalmente, deben tene=
r
un espaciado de junta m‡s corto, especialmente los refuerzos muy delgados. E=
l
prop—sito de esto es tener las grietas formadas solo en las juntas (Lin &=
;
Wang, 2005). De lo contrario, podr’an producirse grietas longitudinales en e=
l
medio de la losa, debido a esfuerzos de tracci—n excesivos (Eacker, 2004). L=
a
regla general para el espaciamiento entre juntas en losas de whitetopping
consiste en seleccionar un espaciado de 12 a 18 veces el espesor de la losa.=
La mezcla de concreto para los whitetopping no es diferente de la mez=
cla
de concreto para un pavimento convencional. La gu’a de dise–o de ACPA (2002)
recomienda que la mezcla de concreto tenga una resistencia a la compresi—n
m’nima, a los de 28 d’as, de 280 kg/cm2 (4,000 psi). Las propieda=
des
tŽrmicas del agregado (coeficiente tŽrmico de expansi—n CTE, conductividad
tŽrmica y calor espec’fico) y la granulometr’a del agregado deben considerar=
se
en el dise–o de la mezcla. El CTE es de interŽs teniendo en cuenta que la
literatura muestra que hay un aumento significativo en los esfuerzos en la c=
apa
de whitetopping debido a los gradientes tŽrmicos (Roesler, Harvey, Farver,
& Long, 1998; Wu, & Tia, 2007).
Para el dise–o de refuerzos whitetopping los mŽtodos generalmente
empleados son el de la ACPA (2002) y AASHTO (1993). Estos mŽtodos, para la d=
efinici—n
del espesor de la losa, consideran el tr‡fico de veh’culos pesados, la
resistencia a la flexi—n del concreto y el valor de soporte de la cimentaci—=
n.
Para carreteras primarias y autopistas interestatales, la gu’a de dise–o
recomienda un espesor que van desde 20.5 cm (8 in) a 30.5 cm (12 in).=
o:p>
Los principales tipos de deterioros observados en los pavimentos de
refuerzo tipo whitetopping son (Rasmussen & Rozycki, 2004; Rasmussen &am=
p;
Ayers, 2003; Silfwerbrand. 1997): grietas de esquina, grietas longitudinales=
,
grietas transversales y fallas en las juntas. Causas de falla, t’picas, que =
se
producen en los pavimentos r’gidos son presentadas en la Norma ASTM D6433, e=
l
Manual de Identificaci—n de Deterioros del U.S. Department of Transportation
(Miller & Bellinger, 2014), el Cat‡logo de Deterioros de Pavimentos
R’gidos, DIRCAIBEA (DIRCAIBEA, 2002), entre los documentos m‡s relevantes pa=
ra
el presente estudio.
Las grietas de esquina ocurren cuando se excede el l’mite de fatiga d=
el
material de hormig—n, que depende de la relaci—n esfuerzo-resistencia y la
magnitud de las aplicaciones de carga. Esto enfatiza aœn m‡s la necesidad de=
un
buen pavimento asf‡ltico subyacente como capa de soporte para el refuerzo de
concreto. Las causas del deterioro de las grietas de esquina, grietas
transversales y longitudinales son la repetici—n de las cargas pesadas del
tr‡nsito en combinaci—n con la acci—n del bombeo a travŽs de bordes y juntas=
,
que debilita y erosiona el apoyo de la cimentaci—n; con deficiente transmis=
i—n
de cargas entre las juntas, provocando la sobrecarga. El alabeo de las losas
por variaciones tŽrmicas o de contenido de humedad, tambiŽn, generan este ti=
po
de agrietamiento. En el caso de grietas transversales y longitudinales,
adicional a las causas indicadas, una inadecuada ejecuci—n de la junta;
aserrado tard’o de la junta; y losas con una relaci—n longitud/ancho excesiv=
a,
contribuyen al agrietamiento. Es importante indicar que la severidad del
agrietamiento longitudinal y transversal es sensible al espesor de la losa y=
al
tipo de terreno de cimentaci—n.
Los pavimentos r’gidos responden a las cargas de varias maneras. Las
cargas generadas afectan el desempe–o de la estructura tanto a corto como a
largo plazo. Los tres esfuerzos principales que se generan en un pavimento
r’gido son (Huang, 2012): i) esfuerzos por alabeo (curling), ii) esfuerzos d=
e
contracci—n y expansi—n (warping), y iii) esfuerzos por cargas (loading). Lo=
s
esfuerzos por alabeo se producen por las diferencias de temperatura entre la
superficie superior e inferior de la losa de hormig—n hidr‡ulico, haciendo q=
ue
la losa se curve. Dado que el peso de las losas y el contacto con la base
restringen su movimiento, se generan esfuerzos. Durante condiciones de clima
c‡lido (por lo general, durante el d’a), la parte superior de la losa puede
estar m‡s caliente que la inferior, lo que produce un curvado en la direcci—=
n
opuesta. Durante un clima m‡s fr’o (por ejemplo, de noche o cuando se produc=
e
un frente fr’o), la superficie se enfr’a m‡s r‡pidamente que la parte inferi=
or,
haciendo que la parte superior de la losa se contraiga m‡s r‡pido que la
inferior, lo que hace que la losa se curve en los bordes. Adem‡s del alabeo,
las temperaturas ambientales y humedades hacen que las losas de cemento se
expandan, cuando est‡n calientes y se contraigan cuando est‡n fr’as, lo que
causa el movimiento en las juntas, fen—meno conocido como deformaci—n por
humedad (warping). Sin embargo, estos esfuerzos son muy peque–os en comparac=
i—n
con los generados por cambios de temperatura y/o tr‡fico, por lo que
generalmente no se los determina (Huang, 2012).
Los esfuerzos generados por las cargas del tr‡fico, en general, son l=
os
mayores en el dise–o de las v’as. Estas cargas provocan esfuerzos de compres=
i—n
y de tracci—n dentro de la losa y cualquier otra losa adyacente, cuando exis=
ta
transferencia de carga entre losas. A lo largo de las juntas, los bordes del
pavimento tienden a curvarse hacia arriba cuando la superficie del concreto =
es
m‡s seca y fr’a que la inferior. Los bordes curvados se convierten en
voladizos, lo que genera que el tr‡fico que pasa sobre las juntas causa una
desviaci—n vertical repetitiva que crea agrietamiento por fatiga en el
hormig—n. Los cambios de esfuerzos que se generan deben ser compensados por =
la
resistencia del hormig—n. Dado que el concreto de cemento Portland es mucho =
m‡s
resistente en compresi—n que en tracci—n, los esfuerzos por tracci—n tienden=
a
controlar el dise–o del pavimento. En general, para la determinaci—n de los
esfuerzos se cuenta con ecuaciones anal’ticas y programas numŽricos. Las
ecuaciones empleadas para estimar los esfuerzos de deformaci—n fueron
desarrolladas por Westergaard (Huang, 2012), adicionalmente se tienen progra=
mas
computacionales en base a elementos finitos como EverFE (Davids et al. ,
2003).
El presente estudio se centra en establecer las posibles causas del
deterioro prematuro del pavimento tipo whitetopping de la v’a Bibli‡n-Zhud,
ello en base a un extenso an‡lisis de esfuerzos generados por las cargas de
tr‡fico y cambios de temperatura. Se emplean tanto ecuaciones anal’ticas com=
o
mŽtodos numŽricos para realizar una comparaci—n entre ambos mŽtodos y
seleccionar el —ptimo para analizar factores adicionales como el incremento =
de
cargas y la reducci—n de espesor de las losas.
2. &n=
bsp; MATERIALES
Y MƒTODOS
2.1. Zona de estudio y
caracter’sticas de la v’a
La v’a Bibli‡n-Zhud tiene una longitud
aproximada de 53 km, de los cuales 36 km, en tres tramos: Zhud (0+000) - El
Juncal (9+124); Ca–ar (24+609) - Campo Alegre (46+069); y Campo Alegre (47+5=
09)
- Bibli‡n (53+019), tienen una capa de rodadura con pavimento r’gido tipo
whitetopping y los restantes con pavimento flexible. En la Fig. 1 se present=
a
la ubicaci—n de la v’a dentro de Ecuador. Las losas para la capa de rodadura
fueron dise–adas en 22 cm de espesor con el empleo de pasadores en las junta=
s
transversales y varillas de uni—n en las longitudinales. La calzada de v’a e=
s
de dos carriles, uno en cada direcci—n, con espaldones. Las losas de concret=
o
tienen una longitud de 4.5 m por 4.0 m de ancho, por carril, emple‡ndose
pasadores de 25 mm en las juntas transversales. Las losas fueron dise–adas c=
on
una resistencia a la flexi—n (m—dulo de rotura) de 4.41 MPa (45 kg/cm2<=
/sup>).
Actualmente, a lo largo de toda la v’a se observan varios deterioros,
especialmente, grietas de esquina, grietas longitudinales y grietas
transversales. Como hip—tesis de partida se considera que el espesor de la
losa, las cargas de los veh’culos y la resistencia de los materiales
contribuyeron al deterioro prematuro del pavimento r’gido. Vale la pena
mencionar que, factores adicionales como el clima y el bombeo (lavado de fin=
os)
aceleran los procesos de deterioro del pavimento. Estos factores deber’an
considerarse si se requiere entender la evoluci—n en el tiempo del proceso d=
e
deterioro, lo que va fuera del alcance del presente estudio.
Los par‡metros de partida para el an‡lisis=
de
esfuerzos corresponden a los siguientes: espesor de la losa 22 cm, coeficien=
te
de Poisson de 0.15, m—dulo de elasticidad del concreto 3Õ725,000 psi (para u=
n
fÕc=3D360 kg/cm2 ), coeficiente tŽrmico del concreto 6x10-6=
sup>¡F.
El m—dulo de reacci—n del soporte es de 209 pci; este valor fue determinado =
en
base a ensayos de deflectometr’a FWD. Las cargas consideradas son las m‡xima=
s
estipuladas para buses y camiones segœn el Ministerio de Transportes y Obras
Pœblicas del Ecuador MTOP (Tabla Nacional de Pesos y Dimensiones). Para eje
simple rueda doble es de 11 ton (108 kN) y para eje t‡ndem es de 20 ton (196
kN). Para la determinaci—n del diferencial de temperatura en la losa, se
consider— el registro de temperatura ambiente en la estaci—n Ca–ar del 2012
(Estaci—n Ca–ar M0031, INAMHI, 2015) en donde la m‡xima temperatura llega a =
los
29¼C (febrero) y la m’nima a -2¼C (diciembre). Considerando estas temperatur=
as
ambientales, se asume una diferencia de temperatura en las losas de 15¼C.
2.2. &nb=
sp; Esfuerzos
en las losas
Los c‡lculos mediante ecuaciones anal’ticas representan una aproximac=
i—n
de los esfuerzos que se esperan en los pavimentos, con fines de dise–o.
Programas m‡s avanzados como los basados en elementos finitos proporcionan
informaci—n adicional que es de utilidad para el an‡lisis del comportamiento
del pavimento. El paquete
computacional EverFE proporciona una
Figura 1. <=
/b> Ub=
icaci—n
geogr‡fica de la v’a Bibli‡n-Zhud en la provincia del Ca–ar, Ecuador.=
o:p>
plataforma simple y f‡cil de usar para el an‡lisis de esfuerzos de pavimento
r’gidos de configuraciones variables y en diferentes condiciones de carga,
incluidas cargas tŽrmicas inducidas por gradientes de temperatura. Detalles =
m‡s
espec’ficos del programa de elementos finitos EverFe, empleado en este estud=
io,
se pueden obtener en Davids (2003). Maske et al. (2013) analiz— el
dise–o de pavimentos r’gidos mediante mŽtodos emp’ricos y mŽtodos basados en
elementos finitos para comparar los resultados de los esfuerzos del paviment=
o.
Las conclusiones extra’das del estudio son que los mŽtodos de elementos fini=
tos
pueden proporcionar un dise–o —ptimo y econ—mico. Adicionalmente, los mŽtodo=
s
de elementos finitos proporcionan una estimaci—n m‡s precisa del comportamie=
nto
de las secciones cr’ticas del pavimento r’gido bajo cargas aplicadas.=
o:p>
Debido a la dificultad de contar con datos adecuados de la disposici—=
n
de los pasadores y su desempe–o en la estructura, y al no contar con las
caracter’sticas geomec‡nicas de los materiales capa por capa, se realiza el
an‡lisis con un modelo de losa simple asentada sobre una estructura que
comprende la cimentaci—n. Adicionalmente, el modelo propuesto concuerda muy
bien con los resultados de las ecuaciones anal’ticas, valid‡ndose el empleo =
del
mismo. Para todos los an‡lisis, cada losa fue dividida en una ret’cula de
32x32x4 elementos (en sus ejes X, Y y Z, respectivamente). Esta ret’cula
permite una buena aproximaci—n en el c‡lculo, a la vez que la capacidad
computacional requerida y el tiempo de cada corrida permanecen a niveles
razonables.
Se evalœan las cargas considerando, primero, un eje simple de neum‡ti=
co
doble y luego el efecto de un eje t‡ndem. Con la configuraci—n empleada se
verifican los esfuerzos en el interior, en la esquina y en los bordes de la
losa. En el caso de los gradientes positivos (parte superior m‡s caliente qu=
e la
inferior), las cargas de tr‡nsito son aplicadas en el borde de las losas,
produciŽndose esfuerzos m‡ximos en la cara inferior de la losa. En el caso d=
e
los gradientes negativos (parte superior m‡s fr’a que la inferior), las carg=
as
de tr‡nsito son aplicadas en la esquina de las losas, produciŽndose esfuerzo=
s
m‡ximos en la cara superior.
3.  =
; RESULTADOS
Y DISCUSIONES
En base a los par‡metros indicados, ecuaciones anal’ticas y mŽtodos d=
e
elementos finitos, se evalœa el efecto de los esfuerzos en el interior, bord=
e y
esquina de las losas. Los resultados de la acci—n combinada de los esfuerzos
por temperatura y carga vehicular, segœn las ecuaciones anal’ticas dan que e=
l
esfuerzo en el interior es de 3.17 MPa, en el borde 4.38 MPa, y en la esquin=
a
2.52 MPa. El esfuerzo combinado en el borde de la losa representa el m‡s
cr’tico equivalente al 99% de la resistencia de dise–o del concreto de 4.41
MPa. Un aumento en la carga provocar’a que se sobrepase la resistencia del
concreto generando fallas en la losa. As’ tambiŽn, una disminuci—n en la
resistencia del hormig—n iniciar’a de igual manera el fallo.
3.1. &n=
bsp; Resultados
de esfuerzos en la losa por elementos finitos
En la Fig. 2 se proporciona los resultados generados en EverFE, donde=
se
presentan los esfuerzos en los bordes, centro y esquina de la losa para la
carga de eje simple de 11 ton. El esfuerzo que se produce en el borde
longitudinal (Fig. 2a) es de 4.38 MPa, lo que corresponde al 99% de la
resistencia del material. Cualquier cambio en el espesor de la losa,
resistencia del material o carga superior a la establecida, producir’a el
agrietamiento y falla de la losa. En la Fig. 2b se muestra el an‡lisis para
esfuerzos en la esquina y borde lateral, para la carga de 11 ton y gradiente
tŽrmico positivo. En este caso, los esfuerzos m‡ximos se producen en el bord=
e
transversal de la losa y en la parte inferior de la misma, alcanzando un val=
or
de 2.60 MPa, es decir, un 59% de la resistencia del concreto. Para el caso d=
e
los esfuerzos en la esquina y gradiente tŽrmico negativo, estos esfuerzos se
producen en la parte superior de la losa cerca de la esquina con un valor de
3.02 MPa, siendo el 68% de la resistencia del material, los esfuerzos genera=
dos
en esta zona son los que generan grietas de esquina.
La comparaci—n de resultados entre
las ecuaciones anal’ticas y el programa de elementos finitos se incluyen en =
la
Tabla 1. Se puede apreciar que los par‡metros ingresados en el programa
representan adecuadamente los resultados anal’ticos, valid‡ndose el empleo d=
el programa
EverFE. Esta validaci—n sirve para posteriores an‡lisis de los par‡metros de=
la
estructura del pavimento y cargas con ejes t‡ndem y gradientes tŽrmicos
positivos y negativos. .
Com=
o se
indic— anteriormente, los esfuerzos generados en el borde de la losa est‡n m=
uy
cercanos a los valores de dise–o. Para la carga de 11 ton en un eje simple
neum‡tico doble, espesor de 22 cm y resistencia del concreto a la flexi—n de
4.41 MPa, las losas est‡n a l’mite de su resistencia, pero deber’an funciona=
r
segœn el an‡lisis de esfuerzos. Sin embargo, un incremento en las cargas del
tr‡fico o una disminuci—n en resistencia del concreto o en el espesor del
pavimento, provocar’a el deterioro del pavimento. =
span>
Un
incremento de 20% de la carga prevista de 11 ton (factor 1.2 recomendado por=
la
PCA, 1984), a 13.2 ton, provoca que el esfuerzo llegue a los 4.71 MPa valor
superior al de dise–o de 4.41 MPa. En la Fig. 3a se incluyen los esfuerzos
generados con un aumento de carga a 13.2 ton y en la Fig. 3b se indica una
imagen del tipo de deterioro encontrado en la v’a en el kil—metro 48+800. De=
la
Fig. 3 se observa que la zona de esfuerzos mayores se produce en el borde y
centro de la losa lo que puede provocar la aparici—n y generaci—n de grietas
transversales y el deterioro del pavimento, como se observa in situ en algun=
os
sitios de la v’a, por ejemplo, en la abscisa 48+800.
<=
span
lang=3Des-419 style=3D'mso-bidi-font-size:9.0pt;mso-ansi-language:#580A'>En =
la Fig.
4 se puede apreciar el mecanismo que se desarrolla en la generaci—n de griet=
as
de esquinas. Si bien, los esfuerzos no llegan a l’mite de la resistencia, se
puede
a)
Esfuerzos en la losa, m‡ximo 4.38 MPa borde=
,
3.28 MPa interior centro
b)
Esfuerzos en la losa, m‡ximo 2.60 MPa en el
borde.
Fig=
ura 2. Es=
fuerzos
en: a) bordes y centro; b) esquina, carga 11 ton.
<=
o:p>
=
a) Es=
fuerzos
por Elementos Finitos, zonas de esfuerzos m‡ximos
b) Agrietamiento e=
n la v’a
abscisa 48+800 =
p>
Figura 3. Esfuerzos en el borde de la losa para carga de 13.2 ton. <=
/span>
=
a) Esfue=
rzos
por Elementos Finitos, zonas de esfuerzos m‡ximos
b)
Agrietamiento en la v’a abscisa 50+766
Figura 4. Esfuerzos en la esquina de la losa, carga 13.2 ton.
<=
v:shape
id=3D"Picture_x0020_75" o:spid=3D"_x0000_i1031" type=3D"#_x0000_t75" alt=
=3D"A picture containing graphical user interface
Description autom=
atically generated"
style=3D'width:146pt;height:113pt;visibility:visible;mso-wrap-style:squar=
e'>
a)
Esfuerzos en losa 22 cm. =
Esfue=
rzo
m‡ximo 4.38 MPa
<=
v:shape
id=3D"Picture_x0020_76" o:spid=3D"_x0000_i1030" type=3D"#_x0000_t75" alt=
=3D"A picture containing application
Description automatically gene=
rated"
style=3D'width:119pt;height:113pt;visibility:visible;mso-wrap-style:squar=
e'>
b)
Esfuerzos en losa 21 cm. Esfuerzo m‡ximo 4.=
71
MPa
<=
v:shape
id=3D"Picture_x0020_77" o:spid=3D"_x0000_i1029" type=3D"#_x0000_t75" alt=
=3D"Graphical user interface
Description automatically generated wi=
th low confidence"
style=3D'width:116pt;height:113pt;visibility:visible;mso-wrap-style:squar=
e'>
c)
Esfuerzos en losa 20 cm. Esfuerzo m‡ximo 5.=
08
MPa
Figura 5. Efecto del espesor de losa en esfuerzos en el bord=
e.
observar la concentraci—n de esfuerzos. Las grietas de esquina son
deterioros frecuentemente encontrados a lo largo de la v’a Bibli‡n-Zhud
(ejemplo Fig. 4b), indicando con ello que se ha excedido el l’mite de fatiga
del hormig—n.
En la Fig. 5 se presenta de forma gr‡fica el efecto de la disminuci—n
del espesor del pavimento en los esfuerzos en el borde de la losa. En base a=
la
extracci—n de nœcleos, se determin— que algunas losas tienen espesores menor=
es
a los 22 cm, de aqu’ que se consider— el an‡lisis de otros espesores para
analizar el efecto de la disminuci—n del mismo en los esfuerzos. En caso de =
la
losa de 22 cm, el esfuerzo m‡ximo est‡ al l’mite de la resistencia (Fig. 5a)=
,
para una losa de 21 cm, el esfuerzo de 4.71 MPa sobrepasa la resistencia del
material (Fig. 5b), y para una losa de 20 cm, el esfuerzo m‡ximo que se gene=
ra
es de 5.08 MPa sobrepasando la resistencia de dise–o del concreto en un 15%
(Fig. 5c).
De la Fig. 5 se observa que hay una concentraci—n de esfuerzos en la
parte central de la losa lo que generar’a el inicio de grietas transversales=
.
Al considerar la carga de 11 ton actuante en la esquina, los esfuerzos debid=
o
al cambio de espesor no aumentan en mayor medida, para una losa de 22 cm, el
esfuerzo en la esquina es de 3.02 MPa, para 21 cm de 3.16 MPa y para 20 cm d=
e
3.31 MPa. Al aumentar la carga, a 13.2 ton, el esfuerzo m‡ximo que se genera=
en
la losa de 20 cm es de 3.72 MPa lo que equivale al 84% de la resistencia del
concreto. Aqu’ se aprecia la generaci—n de esfuerzos que pueden conducir a l=
a
formaci—n de grietas de esquina. Para que se sobrepase la resistencia del
hormig—n, la carga del eje debe ser del orden de 17.5 ton. =
Al considerar el efecto de un eje t‡ndem, los esfuerzos no son tan al=
tos
como en el eje simple, sin embargo, estos camiones con frecuencia llevan
sobrepeso. Aunque los esfuerzos no superan a la resistencia del concreto, se
presenta una concentraci—n de esfuerzos que pueden generar grietas
transversales y/o longitudinales en el caso de un incremento en las cargas d=
el
tr‡fico o una disminuci—n en resistencia del concreto o en el espesor del
pavimento, o una combinaci—n de Žstas. Al analizar los esfuerzos que se gene=
ran
en el borde transversal de la losa por eje t‡ndem se aprecia el desarrollo d=
e
una zona de concentraci—n de esfuerzos que pueden generar el desarrollo del
agrietamiento longitudinal, iniciando en la junta y prolong‡ndose
longitudinalmente.
Considerando que el aumento de la carga por eje afecta directamente a
los esfuerzos en la losa, durante el mes de febrero 2018, el MTOP realiz— el
conteo y pesaje de los veh’culos que circulan en la v’a Bibli‡n-Zhud, sector
San JosŽ de Inganilla. En el Informe de Tr‡fico (MTOP, 2018) se incluye el
reporte de pesaje de cada eje segœn el tipo de veh’culo. Los tipos de veh’cu=
los
considerados en el reporte, en los cuales se realiz— el pesaje, son: 2D, 2DA=
,
2DB, V2DB, 3A, V3A, 3S2 y 3S3 (Tabla Nacional de Pesos y Dimensiones). Las
cargas medidas y m‡ximas permitidas en los ejes de los diferentes veh’culos =
se
presentan en la Tabla 2.
Se observa que, en casi todos los casos, excepto para el tipo 2DA, lo=
s
pesos medidos sobrepasan los estipulados por el MTOP. Los camiones 2DB (eje
simple neum‡tico doble) y 3A (eje t‡ndem), se los toma como referencia para =
el
an‡lisis de esfuerzos, al ser los m‡s cr’ticos en cuanto a la carga. La carg=
a
del cami—n 2DB de 19.56 ton es 77.8% m‡s que la permitida. Para el cami—n 3A
(30.46 ton) la carga es 52.3% mayor.
Los esfuerzos generados por la carga de 19.56 ton, en el bode y centr=
o
de la losa, sobrepasan la resistencia del concreto lo que producir’a la fall=
a
del pavimento. En el borde de la losa se generan esfuerzos del orden de 6.38
MPa, lo que corresponde a 145% de la resistencia de dise–o de 4.41 MPa. Los
esfuerzos en la esquina y borde de la losa tambiŽn son importantes, llegando=
a
valores iguales que la resistencia del pavimento, cualquier cambio en
resistencia y/o espesor, provocar’a la falla de esquina. Estas cargas que
superan los valores estipulados por el MTOP, en cuanto a pesos m‡ximos, gene=
ran
esfuerzos de fatiga en el pavimento, sin embargo, debido a otros aspectos co=
mo
la calidad de la subrasante, la calidad de la estructura del pavimento, la t=
rabaz—n
del agregado o transferencia de carga en los pasadores, aœn no han fallado
todas las losas.
En el caso del veh’culo tipo 3A, al igual que el veh’culo 2DB, los
esfuerzos en los bordes superan la resistencia del pavimento lo que provoca=
r’a
la formaci—n de grietas transversales y longitudinales. Si bien, en la esqui=
na
los esfuerzos aœn no superan la resistencia del concreto, estos representan =
el
84% de la resistencia de dise–o. Se puede indicar que los camiones que
transitan por la v’a Bibli‡n-Zhud est‡n provocando grandes esfuerzos que
superan la resistencia del pavimento, generando el deterioro del pavimento e=
n
ciertas zonas.
4.  =
; CONCLUSIONES =
span>
En la actualidad, la v’a Bibli‡n-Zhud presenta diferentes fallas como
grietas de esquina, grietas longitudinales y grietas transversales, entre la=
s
m‡s frecuentes y severas. Los esfuerzos generados en las losas debido a los
cambios tŽrmicos y cargas de los camiones han provocado el fallo de algunas
losas de la v’a. En base al presente estudio se puede indicar que el deterio=
ro
prematuro del pavimento r’gido tipo whitetopping de la v’a Bibli‡n-Zhud no e=
s
atribuible a una sola causa, sino a la acci—n de varios factores, entre los =
que
constan las cargas de tr‡fico que sobrepasan a las de dise–o, la variaci—n e=
n
el espesor de la losa y la resistencia del concreto.
Se ha identificado que existen tramos en condiciones de excelentes a
buenos que, debido a otros aspectos, que no son posibles valorar en la
actualidad, como la calidad de la estructura del pavimento asf‡ltico al mome=
nto
de la construcci—n y la transferencia de carga en los pasadores, entre otras=
,
aœn mantienen un desempe–o adecuado. La heterogeneidad de la estructura actu=
al
hace que el desempe–o del pavimento losa por losa sea variable. El deterioro=
en
el carril derecho en el tramo Zhud-Juncal es m‡s severo que en el resto de l=
a
v’a. Esto podr’a deberse a que los camiones van desde las provincias del Gua=
yas
y Chimborazo hacia Ca–ar con mayores cargas de mercader’a. =
De los an‡lisis de esfuerzos realizados se observ— que, para cargas
mayores a las de dise–o, los esfuerzos en el borde y centro de la losa
sobrepasan la resistencia del concreto lo que produce el agrietamiento del
pavimento. Empleando los pesos de los camiones medidos in situ, en el borde =
de
la losa se generan esfuerzos del orden de 6.38 MPa, lo que corresponde a 145=
%
de la resistencia de dise–o de 4.41 MPa. Los esfuerzos en la esquina de la l=
osa
tambiŽn son significativos, representando el 100% de la resistencia del
pavimento. Estas cargas superan los valores estipulados por el MTOP, en cuan=
to
a pesos m‡ximos, generando esfuerzos de fatiga en el pavimento, lo que provo=
ca
el fallo de las losas.
Para prevenir el deterioro acelerado de la v’a es fundamental realiza=
r
un control de los pesos m‡ximos de los camiones que circulan por la carreter=
a,
debiendo cumplirse lo estipulado por el MTOP. Es necesario realizar una
rehabilitaci—n a la v’a, considerado un dise–o adecuado que englobe el desem=
pe–o
de la estructura actual. As’ tambiŽn, es conveniente para proyectos futuros,=
en
la zona o en otras del pa’s, realizar estudios de tr‡fico y proyecciones
adecuadas para estimar correctamente las tasas de crecimiento del parque
automotor, en especial de los camiones al ser los m‡s agresivos referente a =
la
generaci—n de esfuerzos en la v’a.
AGRADECIM=
IENTO
El autor desea agradecer al Ministerio de Transporte y Obras Pœblicas
del Ca–ar y a la Empresa Pœblica de la Universidad de Cuenca (UCuencaEP), en=
tidad
contratante y contratista, respectivamente, del estudio de la v’a Zhud-Bibl=
i‡n.
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