CAPITULO 2 MARCO TEORICO
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2-1 DEFINICIONES Definiciones. Los términos contenidos en estas especificaciones, o en el Contrato, o en cualquier documento o instrumento relacionado con trabajos de Construcción donde rijan estas normas, en lo que respecta a su espíritu y significado deberán interpretarse como sigue. Agregado: Un material granular duro de composición mineralógica como la arena, la grava, la escoria, 0 la roca triturada, usado para ser mezclado en diferente tamaños.2 Alineamiento Horizontal: Es la proyección sobre un plano horizontal del eje de
una obra vial, a partir de este se trazan las dimensiones de la sección transversal sobre el mismo plano. Sus elementos son tangentes y curvas horizontales. La posición de los puntos y elementos de un proyecto geométrico, tanto en planta como elevación, está ligada a los datos geodésicos del banco más más cercano a la nueva nueva obra. obra. Alineamiento vertical: El Alineamiento Vertical es proyección del eje de una vía
terrestre sobre un plano vertical, depende principalmente de la configuración topográfica del terreno en el que se localiza el proyecto, y está compuesto por tangentes verticales con diferentes pendientes enlazadas por medio de curvas verticales. Alcantarilla. Cualquier estructura, no clasificada como puente, que permite el paso de agua de un lado al otro bajo la calzada. Base. La capa o capas de material colocado sobre una sub-base o subrasante para soportar la superficie de rodamiento. Bombeo: Es la pendiente que se da a ambos lados del eje de la corona, para
facilitar el drenaje drenaje trasversal trasversal del camino. camino. Según Según el Manual Cent Centroam roamericano ericano de
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Normas para para el Diseño Diseño Geométr Geométrico ico de las C Carret arreteras eras Regionales, Regionales, la pendiente pendiente transversal de los carriles varía entre el 1.5% a 3.0% Base Granular: Material constituido por piedra de buena calidad, triturada y mezclada con material de relleno o bien por una combinación de piedra o grava, con arena y suelo, en su estado natural. Todos los materiales deben ser calificados para formar una base integrante de la estructura del pavimento. Calzada. La porción de la carretera o calle comprendida entre las cunetas, bordillos y orillas de los espaldones, reservada para el uso de los vehículos. Canaleta. Las cunetas son los elementos más habituales del desagüe longitudinal del agua procedente de la plataforma y de sus márgenes Capa. Cualquier riego continúo de material que recibe, en las operaciones de colocación y compactación de suelos o agregados, el mismo esfuerzo de compactación en toda su extensión. Cuando se instalan tubos de alcantarilla menores o iguales a 1200 milímetros de diámetro, se considera que el material de relleno colocado a ambos lados del tubo está contenido en la misma capa, cuando el material es acomodado a la misma elevación y el esfuerzo de compactación aplicado a un lado es el mismo que el aplicado al otro, en una operación continua. Carpeta o superficie de rodamiento o rodadura: La parte superior de un pavimento, por lo general de pavimento bituminoso o rígido, que sostiene directamente la circulación vehicular.
Toda el área área co com mpren prendi dida da dent entro del derec erecho ho de vía, Carretera o calle. Toda incluyendo el área adicional requerida para taludes, como se ordene, especifique o indique en los planos de construcción aprobados. Carriles de tránsito. La parte de la carretera asignada al movimiento de los vehículos, excluyendo los espaldones.
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Colectores. Los colectores se disponen para recoger el agua captada por los sumideros normalmente son prefabricados de hormigón y suelen colocarse bajo las canaletas canaletas
curvas circulares del alineamiento horizontal estarán las Curvas circulares.- las definidas por su grado de curvatura y por su longitud, los elementos que la caracterizan están de transición.- Las curvas espirales de transición se utilizan Curvas espirales para unir las tangentes con las curvas circulares formando una curva compuesta por una transición de entrada, una curva circular central y una transición de salida de longitud igual a la de entrada. Deflexión: El desplazamiento vertical temporal de un pavimento proveniente de la aplicación de cargas de las ruedas de los vehículos. Densidad. Es la masa por unidad de volumen de un material, o sea, la gravedad específica multiplicada por la unidad de masa del agua. Derecho de vía. Es la propiedad requerida para ser utilizada en la construcción de una vía de transporte.
Espaldón. La parte de la carretera contigua a los carriles de tráfico, necesarias para el acomodo de los vehículos que se detienen, para uso en emergencias y para el soporte lateral de la estructura del pavimento. Especificaciones. El vocablo general aplicado a todas las normativas, disposiciones y requisitos, relativos a la ejecución de la obra. Especificaciones Especiales. Complemento y/o revisión de las Especificaciones Generales, que abarcan las condiciones peculiares de una obra individual. Estación. La medida de distancia utilizada en carreteras y ferrocarriles.
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Estructura del pavimento. La combinación de la sub-base, base y superficie de rodamiento, colocadas sobre una subrasante para soportar y distribuir las cargas del tránsito a la subrasante de la carretera. Estructuras. Los puentes, alcantarillas, tomas y cabezales, muros de retención, pozos de inspección, casetas, cloacas, tuberías de servicio, sub drenajes, drenajes y otros elementos similares que pueden ser necesarios en el trabajo. Formaleta. Las estructuras de encofrado temporales o moldes, utilizados para retener al hormigón fluido con la forma en que fue diseñado hasta que se endurezca. Los encofrados deben tener suficiente resistencia para resistir la presión ejercida por el concreto plástico y las presiones adicionales generadas por la vibración. Hombro (Berma): Las áreas de la carretera, contiguas y paralelas a la carpeta o superficie de rodadura, que sirven de confinamiento a la capa de base y de zona de estacionamiento accidental de vehículos. Ingeniero. El representante, debidamente autorizado, en quien se ha delegado la responsabilidad de la supervisión de ingeniería sobre la construcción. Se denomina también como Contratante cuando actúa como su representante. Laboratorio. Un laboratorio de materiales de capacidad reconocida, aprobado por el Contratante. Lavaderos.- Son pequeños encauzamientos a través de cubiertas de concreto, lamina, piedra con mortero o piedra acomodada que se colocan en las salidas de las alcantarillas o terrenos erosionables, eliminando los daños que originaria la velocidad del agua. Material. Cualquier sustancia especificada o necesaria para completar Satisfactoriamente el trabajo objeto del contrato. Medición. El proceso de identificar las dimensiones, cantidades o tonelaje de
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Todos llos os pla plano nos, s, o rep repro rodu ducci cción ón de ello ellos, s, rel relat ativ ivos os a la con const stru rucci cción ón Planos. Todos de la obra. Planos estándar. Los planos de detalles aprobados para uso repetitivo e Incluidos como parte del conjunto de planos. Prisma de la carretera. El volumen definido por el área comprendida entre la sección transversal del terreno original y la sección transversal final, multiplicada por la distancia horizontal a lo largo de la línea de centro de la carretera. Proyecto. La sección específica de la carretera o calle, incluyendo sus obras de arte, taludes, zanjas, canales y cauces, necesarios para la construcción satisfactoria, y que deban ejecutarse bajo los términos del contrato y contratos Subsidiarios. Puente. Una estructura mayor de 6 metros de longitud, incluyendo todos sus Tram Tramos y apoy apoyos, os, que que facil facilit ita a el paso paso sobr sobre una una depr epresi esión ón,, ca cauc uce, e, línea línea férrea, Carretera u otra obra que signifique obstrucción. Rugosidad: La desviación vertical del perfil de un pavimento de su forma tal como fue diseñado y que resulta en incomodidades en el manejo del vehículo. Por lo general, la rugosidad se mide para fines de mantenimiento vial por medio de IRI.3 Roca: Se entiende por roca el material que contiene 25 por ciento o más, en volumen, de pedazos de roca mayores de 100mm de diámetro. Relleno. El material usado para reemplazar, o el acto de reemplazar material Removido durante la construcción. Material colocado o el acto de colocar material adyacente a las estructuras.
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Sección transversal. La sección vertical del terreno o estructura en ángulo recto respecto a la línea de centro o línea base del firme u otro elemento de la obra. Sub-base. La capa o capas de material colocado sobre una subrasante para soportar la base. Sub-rasante: Capa de terreno de una carretera, que soporta la estructura del pavimento y que se extiende hasta una profundidad en que no le afecte la carga de diseño que corresponde al transito previsto. Superficie de rodamiento. La capa superior de la estructura de un pavimento, diseñada para soportar las cargas del tránsito y resistir el deslizamiento de los vehículos y la abrasión que ellos producen, así como el intemperismo. Transito (Trafico): Acción de desplazarse de personas, vehículos y animales por vías públicas. Transito promedio diario: Se define el volumen de tránsito promedio diario (TPDA) como el número total de vehículos que pasan durante un período dado, en este caso una semana de acuerdo a esto se presenta el siguiente volumen de tránsito promedio diario, dado en vehículos por día. Vehículo: Artefacto de libre operación que sirve para transportar personas o bienes.4 Velocidad de marcha: Se define la velocidad como la relación entre el espacio recorrido y el tiempo que se tarda en recorrerlo, o sea, una relación de movimiento que queda expresada, para velocidad constante, por la formula: V =
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2-2 LEVANTAMIENTO TOPOGRAFÍCO 2-2-1 GENERALIDADES
En el estudio, elaboración y ejecución de cualquier proyecto de Ingeniería de obras que tengan como asiento la superficie de la tierra, es necesario el uso de la Topografía. En la elaboración del área destinada para la obra. Las características del terreno son la guía del Ingeniero para la mejor distribución y ubicación de la obra, en sus aspectos funcionales y ornamentales y para conseguir la mayor rigidez, estabilidad y seguridad de ésta. Se refiere al levantamiento topográfico de la zona. TOPOGRAFÍA. E s la ciencia que estudia el conjunto conjunto de de procedim procedimientos ientos para determinar las posiciones de puntos sobre la superficie de la tierra, por medio de medidas según los 3 elementos del espacio. Estos elementos pueden ser: dos distancias y una elevación, o una distancia, una dirección y una elevación.
Para distancias y elevaciones se emplean unidades de longitud (en sistema métrico étrico decimal) y para direcciones direcciones se s e emplean emplean unidades unidades de arco. (Grados (Grados sexagesimales) El conjunto de operaciones necesarias para determinar las posiciones de puntos y posteriormente se representación en un plano es lo se que llama comúnmente “Levantamiento”. La mayor parte de los levantamientos, tienen por objeto el calculo de superficies y volúmenes, y la representación de las medidas tomadas en el
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Por Ruta se entiende la faja de terreno, de ancho variable, que se extiende entre los puntos terminales e intermedios por donde la carretera debe obligatoriamente pasar, y dentro de la cual podrá localizarse el trazado de la vía. Como quiera que las rutas, puedan ser numerosas, el estudio de las mismas tiene como finalidad seleccionar aquella que reúna las condiciones óptimas para el desenvolvimiento del trazado. El estudio es por consiguiente un proceso altamente influenciado por los mismos factores que afectan el trazado, y abarca actividades que van desde la obtención de la información relativa a dichos factores hasta la evaluación de la ruta, pasando por los reconocimientos reconocimientos preliminares. preliminares. 2-2-3 CLASES DE LEVANTAMIENTOS: ESTOS PUEDEN SER TOPOGRÁFICOS O GEODÉSICOS. Topográficos: Son aquellos que por abarcar superficies reducidas pueden hacerse despreciando la curvatura de la tierra, sin error apreciable. Geodésicos: Son levantamientos en grandes extensiones que hacen necesario considerar la curvatura de la tierra.
Los levantamientos topográficos son los más comunes y los que más interesan en este curso. Los Geodésicos son motivo de estudio especial al cual se dedica la Geodesia. Dentro de los levantamientos Topográficos se encuentran: 1-Levantamiento de Terrenos en General: Tienen por objeto marcar linderos o localizarlos, medir y dividir superficies, ubicar terrenos en planos
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4- Levantamientos Catastrales: Son los que se hacen en ciudades, zonas urbanas y municipios, para fijar linderos o estudiar las obras urbanas. 5- Levantamientos Aéreos: Son los que se hacen por medio de la fotografía, generalmente desde aviones, y se usan como auxiliares muy valiosos de todas las otras clases de levantamientos. La Fotogrametría se dedica especialmente al estudio de estos trabajos. La teoría de la Topografía se basa esencialmente en la Geometría Plana, Geometría del Espacio, Trigonometría y Matemáticas en general. Además del conocimiento de estas materias, se hacen necesarias algunas cualidades personales, como por ejemplo: Iniciativa, habilidad para manejar los aparatos, habilidad para tratar a las personas, confianza en si mismo y buen criterio general. 2-2-4 ASPECTOS IMPORTANTES EN UN LEVANTAMIENTO PRECISIÓN: Todas Todas las oper operaci acion ones es en Topogr Topograf afía ía están están sujet sujetas a las impe imperf rfecci eccion ones es propias de los aparatos y a las imperfecciones en el manejo de ellos; por lo tanto ninguna medida en Topografía es exacta, y es por eso que la naturaleza y magnitud de los errores deben ser comprendidas para obtener buenos resultados. Las equivocaciones, a diferencia de los errores, son producidas por la falta de cuidado, distracciones o falta de conocimientos, y no pueden controlarse y estudiarse. En la preescisión hay muchos grados, según sea el objeto del trabajo, y las medidas deben hacerse tan aproximadas como sea necesario únicamente. COMPROBACIONES:
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toda claridad para evitar el tener que pasarlas posteriormente, es decir, se toman en limpio, y consecuentemente no se pasan en limpio. Deben incluirse la mayor cantidad de datos complementarios posibles para evitar confusiones o malas interpretaciones, ya que es muy común que los cálculos o dibujos los hagan personas diferentes a las encargadas del trabajo de campo. ESTUDIO DEL TRAZADO
El proceso de estudio del trazado de una carretera implica una búsqueda continua, una evaluación y selección de las posibles líneas que se pueden localizar en cada una de las fajas de terreno que han quedado como merecedoras de un estudio más detallado después de haber practicado los reconocimientos preliminares y la evaluación de las rutas. La finalidad de este estudio es la de establecer en dichas fajas la línea o líneas correspondientes a posibles trazados de la carretera. Para ello es necesario llevar a efecto un minucioso reconocimiento adicional sobre las rutas seleccionadas. Dos enfoques posibles para efectuar los reconocimientos de campo; el aéreo y el terrestre, utilizados por separado o conjuntamente. E l método método terrestre terrestre es aconsejable acons ejable cuando, después de haber llevado a término los reconocimientos preliminares los posibles alineamientos del trazado han quedado bien definidos; asimismo, cuando el ancho de la faja de derecho de vía es reducido y cuando el uso de la tierra es escaso. El método aéreo, en cambio, es preferible cuando durante dichos reconocimientos no ha sido posible precisar los alineamientos del trazado; cuando el terreno es muy accidentado y cuando el uso de la tierra, es muy intenso.
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El levantamiento de esta poligonal consiste en la medición de los ángulos y los lados, en la nivelación de todos sus vértices y en la toma de las secciones transver transversales. sales. Estas poligonales son abiertas, por que comienzan y terminan en puntos diferentes, pero deben tener controles en su trayectoria, según esto se pueden presentar dos casos: a) Poligonales que comienzan y terminan en puntos de coordenadas conocidas, las cuales tendrán control azimutal y métrico. b) Poligonales que comienzan y terminan en puntos de coordenadas desconocidas, las cuales tendrán control azimutal a través de acimutes determinados por medio de observaciones solares y que se aconsejan realizar cada 5 kilómetros. Los instrumentos utilizados en el levantamiento de esta poligonal deben garantizar la precisión exigida, los mismos deben ser tales como teodolitos, niveles automáticos, cinta métricas, estadía invar., etc. 2-3 ESTUDIO HIDROLOGICO 2-3-1 GENERALIDADES El objetivo de los estudios Hidrológicos es determinar el caudal que debe evacuar cada elemento del desagüe superficial, ya sea longitudinal o transversal. Este caudal se debe determinar para cada una de las cuencas
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2-3-3 CARACTERÍSTICAS FÍSICAS DE UNA CUENCA.
Entre las características más trascendentes que podemos mencionar tenemos: Área: Se define como la superficie en proyección horizontal delimitada por el parte agua y se puede medir directamente del mapa topográfico. Perímetro: Es la longitud del limite exterior de la cuenca y depende de la superficie y la forma de la cuenca. Elevaciones máximas y mínimas: la influencia de la respuesta hidrológica de la cuenca es importante, puesto que a mayores pendientes corresponden mayores velocidades del agua en las corrientes y menor será el tiempo de concentración de la cuenca. Longitud del cauce principal: Es la longitud del canal natura o artificial más largo dentro de la cuenca. 2-3-4 CRITERIOS PARA EL TRAZO DEL PARTEAGUAS.
Seleccionar los puntos más elevados del entorno físico de la cuenca. Definición Definición del del sis sistem tema a de drenaje drenaje superficial y el cauce más más largo. Determinación del punto de interés.
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las estimaciones del volumen del escurrimiento a estimaciones de las cantidades de caudales (gastos) o descargas. Existen al menos tres métodos para la evaluación de la escorrentía superficial, a partir de la obtención de datos de precipitación o lluvia: el primer método, está basado en la utilización de la fórmula racional; el segundo, utiliza el hidrograma unitario de la cuenca en estudio; y el tercero, se hace valer de fórmulas empíricas propuestas por diferentes autores. A continuación se describe desc ribe los primeros primeros dos métodos, métodos, ya que que el tercero tercero es poco recomendable, por el hecho de que posee muchas limitaciones respecto a la deducción de las ecuaciones o fórmulas. MÉTODO RACIONAL Consiste únicamente en la aplicación de una fórmula, la cual expresa que la descarga es igual a un porcentaje de la precipitación multiplicada por el área de la cuenca. La duración mínima de la lluvia es el Tiempo de Concentración (Tc). Esta es la base del método o fórmula racional. Se enuncia enuncia así: Q= K C i A Donde:
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Este método se basa fundamentalmente en una virtual determinación del caudal de escorrentía a partir de las precipitaciones, y está restringido a cuencas pequeñas. Se le llama formula racional, porque las unidades de las variables que intervienen posee una consistencia numérica aproximada los parámetros que implica la ecuación se trabajan de forma independiente convirtiéndolos en una variable, para cada cuenta consiste en la aplicación de dicha ecuación La hidrogeología trata específicamente la descripción de la capacidad que tiene las formaciones geológicas de infiltrar aguas para el enriquecimiento de los mantos acuíferos. El objetivo de un estudio hidrológico en zonas de estudio para esta investigación, es realizar los análisis correspondientes a fin de establecer el caudal de diseño para el período de retorno adecuado, cota topográfica que alcanzará la lámina de agua correspondiente a dicho caudal, así como las medidas estructurales y no estructurales a implementar para la prevención y mitigación de impactos por eventos de crecida. Los Estudios Hidrológicos e Hidráulicos deben llevarse a cabo a partir de información hidroclimatológica y topográfica de la zona de interés, y deben determinar la amenaza que puede generar el proyecto o a la que puede verse expuesto, de acuerdo a los niveles de inundación. De acuerdo a los resultados se
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b)
Métodos estadísticos de carácter regional de los valores máximos de
lluvia o de crecida según metodologías de regionalización de precipitación o caudales. c)
Aplicación de un modelo de simulación hidrometeorológico lluvia –
escorrentía. Las técnicas de modelación pueden ser aplicadas cuando los datos hidrométricos y de crecidas encontrados no sean suficientemente extensos para poder aplicar las técnicas estadísticas de carácter regional mencionadas anteriormente. La utilización de métodos aproximados debe limitarse únicamente a los casos en que no haya información hidrométrica disponible o suficiente para la aplicación de los mismos. Dado que el método racional tiene sus limitaciones en cuanto a área de aplicación y a que es un método empírico y no hidrometeorológico, no debe usarse para el análisis hidrológico en zonas de inundación. Para esta investigación se utilizara el método racional La información mínima requerida para el diseño de una obra hidráulica es:
El volumen de agua.
Velocidad.
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CARTOGRAFÍA
En nuestro país El Centro Nacional de Registro (CNR) es la institución encargada de proporcionar los planos cartográficos a escalas de 1:25,000, 1:50,000, 1:100000, etc. sobre estas se trazan los parte aguas de las diferentes áreas que influyen en el drenaje de la cuenca o proyecto, así como permite definir los puntos más favorables para el encauzamiento de los drenajes interceptados.
INTENSIDAD DE LLUVIA
La intensidad de lluvia es la tasa promedio de lluvia en milímetros por minutos para una cuenca o subcuenca de drenaje particular. La intensidad se selecciona
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A.
Bajo potencial de escorrentía. Suelos que tienen altas tasa de infiltración aún cuando se encuentran muy húmedos. Son suelos compuestos de arena o grava profundas bien o excesivamente drenados.
B.
Moderadamente bajo potencial de escorrentía. Suelos con una tasa de infiltración moderada cuando están muy húmedos. Suelos con textura moderadamente finas a moderadamente gruesa y permeabilidad moderadamente rápida rápida..
C.
Moderadamente alto potencial de escorrentía. Suelos con infiltración lenta cuando se encuentra muy húmedos. Consisten de suelos con un estrato que impide el movimiento del agua hacia abajo.
D.
Alto potencial de escorrentía. Suelos con infiltración muy lenta cuando están muy húmedos. Consisten de suelos arcillosos con alto potencial de exposición.
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dichas variables a partir de los mapas o el levantamiento de campo de dichas variables, en la tabla 4.7.1 se presentan algunos coeficientes de escorrentía. Tabla 1 Coeficientes de Escorrentía usados en el Método Racional. Característica de la superficie
Período de retorno (Años)
Áreas desarrolladas 2 5 10 25 50 Asfáltico 0.73 0.77 0.81 0.86 0.90 Concreto/techo 0.75 0.8 0.83 0.88 0.92 Zonas verdes (jardines, parques, etc.) Condición pobre(cubierta de pasto menor del 50% del área) plano,0-2% plano,0-2% 0.32 0.34 0.37 0.4 0.44 promedio, promedio, 2-7% 0.37 0.4 0.43 0.46 0.49 P endiente, endiente, superior a 7% 0.4 0.43 0.45 0.49 0.52 Condición promedio(cubierta promedio(cubierta de pasto del 50 al 75% del área) P lano,0-2% 0.25 0.28 0.3 0.34 0.37 P edio, 2-7% 0.33 0.36 0.38 0.42 0.45
100 0.95 0.97
500 1 1
0.47 0.58 0.53 0.61 0.55 0.62 0.41 0.53 0.49 0.58
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2-3-8 MÉTODOS DE CÁLCULO
Para la estimación de los caudales máximos instantáneos, se utiliza un modelo basado en el comportamiento de la precipitación. Se requiere realizar un análisis sistemático de lluvia, tomando en consideración los parámetros siguientes: intensidad de lluvia, duración y período del evento estudiado. Para esto se necesita el registro de intensidades máximas, que están constituidas por los valores más altos observados en cada año (series anuales) o por los n valores mayores observados en el período total de observación (series parciales), parciales), siendo n el número de años en el período considerado. Las curvas de Intensidad-Duración-Frecuencia se derivan del análisis estadístico de largos períodos de los registros de lluvia. Cada curva representa la relación intensidad vrs tiempo para un determinado período de retorno, de una
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LA FRECUENCIA
En cuanto mayor es la intensidad de las tormentas, más rara es su ocurrencia o menor su frecuencia. En forma aproximada, a una intensidad más alta de duración específica, tiene una frecuencia de una vez en n años. Dicha tormenta es llamada tormenta de n años consignada en el período de registro de x años. Metodología para la determinación de las curvas intensidad-duración frecuencia (IDF)
El comportamiento de la lluvia que cae en un determinado territorio en cantidad y en un tiempo determinado es necesario para definir los diseños de las obras de conservación de suelo, puentes, daños por acumulación de agua y
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d) Se grafica en papel probabilí probabilístico stico Gumbel, Gumbel, los datos de intensidad intensidad (I) contra la Probabilidad de Ocurrencia (f) para cada duración, de acuerdo a las siguientes coordenadas: En el Eje X: Probabilidad de ocurrencia (f); En el Eje Y: In Intensi ensid dad de P rec ecip ipit itac ació ión n (I). I). e) Luego se traza una recta promedio que se ajuste lo mejor posible a la nube de puntos plateados para cada duración.
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Tabla 2Períodos de Retorno Recomendados Recomendados Para Algunas Estructuras. Tipo de Estructura Alcantarillas de carreteras Volumen de trafico bajos Volumen de trafico intermedio Volúmenes Volúmenes de trafico altos Puentes de carreteras Sistema Secundario
Periodos de Retorno
Elv
5-10 10-25 50-100
( - ) ( - ) ( - )
10-50
( - )
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2-3-10 TIEMPO DE CONCENTRACIÓN
Se define el tiempo de concentración (Tc) como el tiempo requerido por una gota de agua para fluir desde el punto más remoto en la cuenca hasta el punto de interés de tal forma que el inicio de la tormenta la escorrentía parte desde el punto más alejados de la cuenca al sitio de control, para luego suponer que se establece una corriente permanente lo que nos permite conocer el caudal máximo
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L: Longitud máxima del canal (o río) desde aguas arriba hasta la salida, metros. S: Pendiente de la cuenca o H/L (adimensional), donde H es la diferencia de elevación entre el punto mas remoto de la cuenca y el punto de interés. 3) Ecuación de Giandot Giandotti: ti:
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dos sustancias que son importantes en las propiedades y en el comportamiento de un suelo: el agua y los gases ( en general, el aire), así, puede decirse que un suelo es un material formado por predominantemente por partículas de rocas y minerales derivados de las rocas sin material cementante, pero con unas ciertas proporciones de aire, de agua y de material orgánico. La necesidad de realizar ensayos sobre los suelos, como cualquier otro material, esta originada por el deseo de su caracterización cuantificando sus propiedades,
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Tabla No 3 Coeficientes de variación normalmente aceptados en los
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maneras, de las conocidas son la oxidación con agua oxigenada y el método del
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Grupo A-1: A-1: Comprende Comprende las mezcl mezcla a bien graduadas, graduadas, compuestas compuestas de fragm fragment entos os
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Subgrupos A-7-6: Comprende aquellos suelos cuyos índices de plasticidad son
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S = Arena o suelo arenoso.
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Las cargas de Diseño son estimadas estimadas mediante la siguiente Ecuación: ESAL´s =TPDA x F.crec x D x FE x LD x LC.
En donde: TPDA =promed omedio io diar iario de transit sito para ara el vehícu ehículo lo al primer imer año de se serrvicio icio.. F.crec = Factor de crecimiento crecimiento al periodo Total de Diseño (Año 2004-2031). 2004-2031). D = numero de días por Ano (365). FE =Factor actor de Equiv E quivalencia. alencia. LD = Factor de distribución en el canal de diseño = 0.5 LC = Factor de distribución por carril = 1.0 Es import importante ante señalar que el Factor de Equivalencia para los vehí vehículos del tipo tipo C2, C3, T3-S1y T3-S 1y T3-S2 T3-S 2 ha sido estim estimado ado bajo la hipót hipótesis esis de que que el 100% 100% de ellos circulan circulan con el 100% de su carga máxim máxima a legal. Cargas equivalentes Totales en el Periodo de Diseño ( ESAL´S)
La combinación de los valores de las tablas anteriores permite la determinación de la “Repetición de ejes equivalentes en el periodo de Diseño” para el pavimento de tipo Flexible y de tipo Rígido, y cuyo valor final, se presentara en tablas donde se interrelacionan las variables que intervienen para el calculo de este termino. 2-6-8-1 Calidad del material de fundación (MR)
La segunda variable de diseño corresponde a la calidad del material de fundación, para lo cual se diseño un programa de muestreo y ensayos de los materiales. El resultado de esta investigación investigación es presentada y detallada en el apartado de Suelos y Materiales”. Y cuy cuyos valo alores se res esu umen en la tabla abla jun junto co con n su
representación grafica en el cual se observara la tendencia y comportamiento de los materiales a lo largo del trazado.
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Determinación del CBR de diseño
La determinación del CBR de diseño se fundamenta en una recomendación específica de la Guía AASHTO-93, la cual se cita a continuación: “Es importante notar que el diseño de la estructura del pavimento según esta Guía se basa en el Valor promedio aritmético del MR(Modulo de Resilencia). El proyectista no debe seleccionar un MR que se base en algún mínimo o un criterio conservador, ya que ello resultaría en un diseño mayor que el proveniente de la aplicación del factor de Confiabilidad10”
Retomando la anterior cita el CBR de diseño será calculado mediante la siguiente Ecuación Aritmética.
Aplicando Aplicando la form formula ula obtenem obtenemos os un Resultado donde donde se presentara presentara el CBR CBR que predomina. Sin embargo y con el fin de garantizar que estos CBR puedan ser alcanzados durante la etapa de construcción de la subrasante, sin tener que recurrir a acarrear a distancias largas los mejores materiales, lo que pudiera significar un costo adicional en obra. Es conveniente resaltar, sin embargo, que esta decisión significa la introducción de un “factor de seguridad” adicional, lo cual pudiese resultar en un diseño conservador, con el resultado de espesores mayores a los realmente requeridos. Tabla No 16 CALIFICACIÓN MB B R M MM SUB-CORONA CBR, CBR, 20% 10%, CBR, CBR, 20% 5%, CBR, CBR, 10% CBR, CBR, 10% CBR, CBR, 5% SUB-BASE CBR, 50 50% 30%, CBR, 50 50% 20%, CBR, 30 30% CBR, 30 30% CBR, CBR , 20% 20% BASE CBR, 80% 50%, CBR, CBR, 80 80% 40%, CBR, CBR, 50 50% CBR, 40% CBR,0 CBR,0.0% .0% CAPA
Clasificación de un suelo para pavimentos, en base a su valor de C.B.R. Fuente:
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2-6-9 VARIABLES DEL PAVIMENTO FLEXIBLE. Potencia (SN) requerida del pavimento.
En los pavimentos de mezclas asfálticas por medio de la formula de diseño se obtiene el numero estructural (SN) y en función del mismo se determinan los distintos espesores de las capas que conforman el paquete estructural. La Ecuación ASSHTO-93 para pavimentos flexibles resuelve, para las variables independientes independientes de cargas equivalentes equivalentes La formula general que relaciona el número estructural (SN) con los espesores de capa es la siguiente: SN = a1 x D1 +a2 x m2 x D2 +a3 x m3 x D3
En donde: •
a1, a2, a3
son coeficientes Estructurales o de capa que indican la
resistencia relativa de los materiales de la superficie de rodadura, base y sub-base respectivamente. Los cuales son establecidos por medio de ensayos conocidos como prueba Marshall de la mezcla y CBR de una base granular granular sin trat tratam amiento, iento, dichos dichos valores son obtenidos obtenidos mediante mediante
ala
interpolación de la siguiente figura. •
m2, m3 son los coeficientes de drenaje para la base y sub-base.
•
D1, D2, D3 son los Espesores de capa en pulgadas para la superficie de
rodadura, base y sub-base. Esta formula tiene muchas soluciones, en función de las diferentes combinaciones De espesores; no obstante existen normativas que tienden a dar espesores de capa que deben ser construidas y protegidas de deformaciones permanentes, por efecto de las capas superiores de mayor resistencia.
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Grafica No 3: Valores del coeficiente a1, para capas de rodamiento de mezcla asfáltica cuya estabilidad Marshsall varia de 0 a 2,400 lb.
Grafica No 4: Valores del coeficiente a2 para bases granulares sin tratamiento alguno, con diferentes CBR.
Además de estos nomogramas existen otros los cuales brindan la misma ayuda ver anexo 7. En la siguiente tabla se dan valores de espesores mínimos sugeridos para capas asfálticas y base granular en función del transito.
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Espesores minimos sugeridos Numero de ESAL´s Capas Asfalticas Base Granular Menos de 50,000 3,0 cm 10 cm 50,000 - 150,000 5,0 cm 10 cm 150,000 - 500,000 6,5 cm 10 cm 5000,000 - 2,000,000 7,5 cm 15 cm 2,000,000 - 7,000,000 9,0 cm 15 cm Mas de 7,000,000 10,0 cm 15 cm Fuente uente:: Guia Guia para para diseño de de Estructu Estructuras ras de Pav P aviment imentos, AAS A ASHT HTO, O, 1993.
Tabla No 17
Taless mín Tale mínim imo os de dependen de la las pr practic ctica as lo loca cale less y es estta co condicio icion nado el el usa usarrlos; los; diseñadores pueden encontrar necesario modificar hacia arriba los espesores mínimos por su experiencia obtenida; estos valores son sugeridos y se considera su uso considerando que son capas asfálticas sobre bases granulares sin tratar 11. 2-6-10 VARIABLES DEL PAVIMENTO RÍGIDO
La ecuación de diseño AASHT AAS HTOO-93 93 para pavimentos pavimentos Rígidos contem contempla pla al igual que el pavimento flexible otras variables independientes cuyo valor se asigna en función de recomendaciones precisas del método. •
Servisiabilidad Final Pt se considero de igual manera que en el pavimento flexible Retomando el mismo concepto el cual de manera general dice: El índice de serviciabilidad es la manera en que un pavimento cumple su función de ser cómoda, fácil, rápida y segura la circulación de los vehículos. En consideración al concepto anterior se considero tomar un valor de 2.25.
•
Servisiabilidad inicial Po este valor será calculado al igual que en el pavimento de tipo Flexible. Utilizando la siguiente Ecuación. Pó = 7.10 – 2.19 x (IRI) 0.5 para pavimentos Rígidos12.
En el cual fijando un Índice de Regularidad Internacional de 2.00 m/Km. (1.5 a 2.5) se obtiene un índice de serviciabilidad inicial Po de 4.0 manteniendo se ambos valores dentro de los rangos permisibles. •
Coeficiente de drenaje (Cd). Será retomado siguiendo el mismo concepto utilizado en el cálculo del pavimento flexible 1.15
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Coeficiente de transferencia de carga(J) Este factor se utiliza para tomar en cuenta la capacidad del pavimento de concreto de transmitir las cargas a través de los extremos de las losas (juntas o grietas), su valor depende de varios factores, tales como: Tipo de pavimento (en masa reforzando en las juntas, de armadura continua, etc.); el tipo de borde ù hombro (de asfalto o de concreto unida al pavimento principal). La colocación de elementos de transmisión de carga (pasadores en los pavimentos con juntas, acero en los armados continuos, etc.). En función de estos parámetros, se indican en la siguiente tabla los valores del coeficien coeficientte J : Coeficiente de Transferencia de Carga
Con pasajuntas y Reforzado con malla. Millones de Ejes Equivalentes
No
Si
J unt untas sin sin pasajuntas (Friccion (F riccion entre entre Agregados). No
Si
Con R efuerzo efuerzo continuo
No
Si Calles y Caminos vecinales
Hasta 0,3 0,3-1 1-3 1-3 3-10 10-30 Mas de 30
3.32 3.2 3.2 3.2 3.2 3.2
2.7 2.7 2.7 2.7 2.7 2.7
3.2 3.4 3.6 3.8 4.1 4.3
2.8 3 3.1 3.2 3.4 3.6
Tipo de P aviment avimento o
2.9 3 3.1
2.5 2.3 2.6
Caminos P rincipale rincipales sy Autopistas.
Tabla No 18
Tom To mando lla a an anterio eriorr in inform ormación ción co con nsid sideram eramo os la se selecc lecció ión n de de de de un un coe coefficie icien nte de 2.8 considerando que se el hombro se construirá de concreto y que la transmisión de carga se realizara a través de la fricción entre agregados (juntas sin pasa juntas). Calidad del concreto en losa de pavimento (S´c Ec)
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catedráticos en esta área. La ecuación de correlación incorporada al método AASHTO-93 Ec = 6,750 Mr sugiere un valor de Modulo Elástico del concreto (Ec) igual a 3,550,500 psi. Modulo de reacción de la subrasante (K)
La última independiente considerada en la ecuación de diseño del Método AASHTO-93, corresponde al Modulo de Reacción de la subrasante (k), y el cual depende de: •
Espesor y calidad de la base sobre la cual se construirá la losa del pavimento
En nuestro caso se ha seleccionado el empleo de los materiales existentes a lo largo del trazado vial, donde se tratara predomine la misma calidad de suelo en la mayor parte del tramo. En el cual debe de utilizarse el material existente que contenga un CBR del 14% como mínimo.
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Constructivo • Permite el movimiento y alabeo de las losas por efecto de las Cargas de tránsito • Permite transferencia de cargas entre losas Considerando que en el Diseño de espesores la transferencia de carga (fricción entre agregados) a través de las juntas es una variable independiente se procede al diseño de la separación entre las juntas transversales, para lo cual nos auxiliamos de las tablas del Manual Centro Americano para Diseño de Pavimentos las cuales citamos a continuación. Tabla No 20