Universidad Nacional del Santa
INTEGRANTES: ESQUIVEL SAAVEDRA EDITH GAMEZ VELÁSQUEZ MILAGROS GAMARRA ABAD JHEANCARLOS HUAMAYALLÍ FLORES JOEL QUINCHO CHAUCA CARLOS VILLANUEVA LINO KEVIN DOCENTE:
CURSO:
ING. JULIO CESAR TIVASPLATA DIAZ
MECANICA DE SUELOS I
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RESUMEN
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INDICE
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INTRODUCCIÓN
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TENSION SUPERFICIAL Las moléculas de un líquido se atraen entre sí, de ahí que el líquido esté "cohesionado". Cuando hay una superficie, las moléculas que están justo debajo de la superficie sienten fuerzas hacia los lados, horizontalmente, y hacia abajo, pero no hacia arriba, porque no hay moléculas encima de la superficie. El resultado es que las moléculas que se encuentran en la superficie son atraídas hacia el interior de éste. Para algunos efectos, esta película de moléculas superficiales se comporta en forma similar a una membrana elástica tirante (la goma de un globo, por ejemplo). De este modo, es la tensión superficial la que cierra una gota y es capaz de sostenerla contra la gravedad mientras cuelga desde un gotario. Ella explica también la formación de burbujas. Algunos valores de la tensión superficial son: TABLA N° 01: VALORES DE LA TENCION TEN CION SUPERFICIAL
Líquido
Temperatura (ºC)
líquido Tensión (N/m)
Petróleo
0º
0,0289
Mercurio
20º
0,465
Agua
0º
0,0756
20º
0,0727
50º
0,0678
100º
0,0588
superficial
Con moléculas de otras sustancias puede haber atracción o repulsión. La dirección de resultante (sólidolíquido + líquido-líquido) hace que el líquido se eleve o hunda levemente muy cerca de paredes sólidas verticales, según haya atracción o repulsión. Para diferentes combinaciones de líquidos y sólidos se tabulan los ángulos de contacto. Ángulos menores de 90º corresponden a atracción y mayores de 90º a repulsión. Esto también explica la formación de meniscos en tubos angostos y el ascenso o descenso de líquido por tubos capilares.
ASCENCION CAPILAR Los continuos espacios vacíos del suelo pueden comportarse en conjunto como tubos capilares con secciones transversales diferentes. En contraste con lo que ocurre en los tubos, los vacíos continuos del suelo se comunican entre si en toda dirección, constituyendo un enrejado de vacíos. v acíos.
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FIGURA N° 01: TEORÍA DEL TUBO CAPILAR Donde: P: Es el peso de la columna de agua F: Fuerza de ascensión capilar: Ts: tensión superficial del agua por unidad de línea de contacto entre el agua y el tubo ( ≅0,0764 g/cm para agua pura y vidrio limpio). hc: altura de la ascensión capilar; d: diámetro del tubo γa = peso específico del agua
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En la FIGURA N°02 se N°02 se ha colocado suelo en un cilindro transparente. La parte inferior ha sido protegida para evitar que el suelo salga pero permitir el contacto con el agua, mientras que el extremo superior queda expuesto a la atmósfera. Algún tiempo después de poner en contacto la parte inferior del tubo con el agua, la FIGURA N°02 muestra N°02 muestra que el agua asciende capilarmente hasta una altura máxima hc. A una altura hcs, la FIGURA N°02 B muestra que el suelo está completamente saturado, mientras la región de suelo comprendida entre hcs y hc según la Figura N°02 B, B, está parcialmente saturada de agua. La FIGURA N°02 C, muestra que el ascenso capilar resulta ser más rápido mientras el grado de saturación disminuya. Hazen (1930) obtuvo una ecuación que permite determinar el máximo ascenso capilar de agua en el suelo, que es:
…….. FORMULA N°
Donde: hc = Máximo ascenso capilar en el suelo. e = Índice de vacíos. D10 = Tamaño efectivo. C = Constante que depende de la forma de las partículas.
01
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TABLA N° 03: VALORES DE COEFICIENTES DE C
La FIGURA N° 03 muestra 03 muestra dos curvas que han sido determinadas experimentalmente de la observación del ascenso capilar en diversos suelos. A la altura hcs, se la llama altura de saturación capilar y puede ser determinada con la Figura 4.7. En un perfil de suelo, el agua ascenderá capilarmente a partir del nivel freático y saturará todos los espacios vacíos hasta una altura hcs con respecto al nivel freático. El máximo ascenso capilar se registrará a una altura hc. Al igual que en los tubos, mientras más pequeñas sean las partículas del suelo, mayor será el ascenso capilar.
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PERMEABILIDAD
FLUJOS LAMINAR Y TURBULENTO
Un flujo se define como laminar cuando las líneas dé flujo permanecen sin juntarse entre sí en toda su longitud, excepción hecha del efecto microscópico de mezcla molecular.
FIGURA N° 04: DISTINCIÓN EXPERIMENTAL OBJETIVA ENTRE EL FLUJO LAMINAR Y EL TURBULENTO. El flujo turbulento ocurre cuando la condición anterior no se cumple. Una línea de flujo se define como la línea ideal que en cada punto tiene la dirección del flujo, en el instante de que se trate; en todo punto el vector velocidad y la línea de flujo que pasa por él, serán tangentes. Si en un tubo se inserta una fuente puntual de tintura, como se muestra en la Fig. anterior, se tiene una distinción objetiva de los dos tipos de flujo mencionados observando la trayectoria trazada por la tintura, que puede asimilarse a una línea de dibujo, si éste está establecido. Se sabe que a velocidades bajas un flujo ocurre en forma laminar, mientras que al aumentar aquéllas se llega a un límite en que se transforma en turbulento; si en ese punto la, velocidad se reduce, el flujo volverá a ser laminar, pero la nueva transición ocurre, genera1mente, a menor velocidad que la primera. Esto indica la existencia de un intervalo de, velocidades en el cual el flujo puede ser laminar o turbulento. Reynolds encontró que la velocidad crítica del agua puede expresarse por la ecuación:
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En la figura siguiente se muestra la variación de la velocidad con el gradiente hidráulico en flujo laminar y turbulento. La diferencia principal entre ambos estriba en que en el flujo laminar, la energía disponible se pierde por resistencias viscosas entre las diversas láminas líquidas en deslizamiento relativo.
FIGURA N°05: VARIACIÓN DE LA VELOCIDAD CON EL GRADIENTE HIDRÁULICO EN EL FLUJO LAMINAR Y TURBULENTO. En el caso .del flujo turbulento, por otra parte, existe una pérdida continua de energía debido a las velocidades diferentes de las partículas adyacentes de líquido aun cuando la masa fluya a velocidad constante.
FIGURA N° 06: DISTRIBUCIÓN DE VELOCIDADES EN UN CONDUCTO CON FLUJO LAMINAR. El flujo turbulento es de por sí, no establecido y no uniforme, ya que existen en él movimientos irrestrictos de
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COEFICIENTE DE PERMEABILIDAD DEFINICIÓN LEY DE DARCY El coeficiente de permeabilidad permeabilidad k de un suelo se define por medio de la ley de Darcy, Dar cy, que relaciona las magnitudes características de una corriente.
v = ki o
q = A ki
…….. FORMULA N°03
LEY DE DARCY
En la figura: A
es una sección perpendicular a las líneas de corriente,
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De donde: v1
A
v
…….. FORMULA N° 05
Av
Considerando al filtro un espesor unitario normal al papel, se tiene:
A Av
1
n
1 e
…….. FORMULA N° 06
e
Por lo tanto: v
1
1 e
v
…….. FORMULA N° 07
e
La velocidad v que que se deduce directamente de la ley de Darcy, se llama velocidad de descarga o, simplemente, velocidad. La velocidad v 1 que toma en cuenta la existencia de una fase s{olida impermeable, se llama velocidad de filtración y es la velocidad media de avance del agua en la dirección del flujo. Sin embargo, en la obtención de la velocidad de filtración se supuso que el agua tenía trayectoria recta al pasar a o largo del filtro, por lo cual no representa la velocidad con la que el agua ag ua se está moviendo. El agua no recorre la longitud L al atravesar el suelo, sino una línea sinuosa o irregular de longitud de longitud Lm. Entonces si v 2 es la velocidad media real, podrá escribirse:
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a)
Directos: Permeámetro de carga constante. Permeámetro de carga variable. Prueba directa de los suelos en el lugar.
-
b)
Indirectos:
-
Cálculo a partir de la curva granulométrica. Cálculo a partir de la curva granulométrica. Cálculo con la prueba horizontal de capilaridad. PERMEÁMETRO DE CARGA CONSTANTE:
Ofrece el método más simple para determinar el coeficiente de permeabilidad de ese suelo. Una muestra de suelo de área transversal A y longitud L, confinada en un tubo, se somete a una carga hidráulica h. El agua fluye a través de la muestra, midiéndose la cantidad que pasa en el tiempo t . Aplicando la ley de Darcy: V = kAit
…….. FORMULA N° 09
V es es la mencionada cantidad de agua.
El inconveniente del permeámetro es que, en suelos poco permeables, el tiempo de prueba se hace tan largo que deja de ser práctico, usando gradientes g radientes hidráulicos razonables.
PERMEÁMETRO DE CARGA VARIABLE
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PRUEBA HORIZONTAL DE CAPILARIDAD
La rapidez con la que se eleva el agua, por acción capilar, en un suelo, es una medida indirecta de la permeabilidad de éste. Este hecho permitió a Terzaghi desarrollar un método práctico para estimaciones de la permeabilidad en el campo. El método de Terzaghi, sirvió de antecedente para una prueba más adecuada, conocida hoy como prueba horizontal de capilaridad. El método de Terzaghi consiste en colocar una muestra de suelo en un tubo vertical transparente, detenida por una malla apropiada colocada en el extremo inferior de aquél. El tubo se fija de tal modo que su base quede justamente bajo el nivel nivel del agua. Se hacen observaciones del progreso de la superficie de avance ascendente del agua a partir del instante en que comenzó el experimento. Haciendo una gráfica del valor de h, contra los correspondientes tiempos, se obtiene una curva. Si se preparan varias de estas curvas maestras para suelos de permeabilidades conocidas, la permeabilidad de cualquier otro suelo puede estimarse observando la posición relativa de la curva correspondiente en la carta de las curvas preparadas.
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INFLUENCIA DE LA ESTRATIFICACIÓN DE SUELOS De forma general, la permeabilidad es mayor cuando la corriente es paralela a las capas de un suelo que cuando es perpendicular. Esta propiedad es evidente según los dos ejemplos de la figura.
FIGURA N°08: INFLUENCIA DE LA ESTRATIFICACIÓN EN LAS CORRIENTES. Figura a: Capa de grava comprendida entre dos capas de arcilla: el caudal será muy pequeño en el sentido 11’, al estar limitado por la posibilidad de atravesar las capas de arcilla, y será elevado en el sentido 22’, ya que la capa
de grava funciona por sí sola como un dren. Figura b: Pantalla impermeable (tablestacas, muro de hormigón, lámina de inyección o simple hoja de plástico) en un macizo de arena: la pantalla no presentará ningún obstáculo a la corriente en el sentido 11’, y la impedirá totalmente en el sentido 22’ .
Se puede expresar cualitativamente esta propiedad diciendo que la corriente está condicionada:
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MACIZO ESTRATIFICADO Este macizo puede estar sometido sucesivamente: a una corriente paralela a las capas, de gradiente hidráulico i 0, de caudal q0, a partir del cual se puede definir un coeficiente medio de permeabilidad k 0: q k 0 90 …….. FORMULA N° 10 Z i0
-
A una corriente perpendicular a las capas, de gradiente hidráulico i 90 90, de caudal q90, a partir del cual se puede definir un coeficiente medio de permeabilidad k 90 90:
-
k
q0
…….. FORMULA N°11
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hi
q90 L k i
z i
…….. FORMULA N° 15
Observando que: Z hi = = h = Zi 90 90
…….. FORMULA N° 16
Se puede calcular el caudal q90:
q90
LZi90 n z i
…….. FORMULA N°17
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b) Anisotropía de los suelos aluviales En los macizo de origen aluvial, incluso de apariencia homogénea el mismo fenómeno de deposito favorece la creación de capas muy delgadas horizontales de limos, que corresponden a los períodos de decrecida. De aquí es inferior a la permeabilidad horizontal. Esta noción se verifica por la experiencia y se la define como la anisotropía del suelo. Más adelante veremos su influencia en las redes de corriente.
MEDIDA DEL COEFICIENTE DE PERMEABILIDAD 1. Medida de k en laboratorio El principio consiste en medir, por medio de un aparato análogo al que hemos representado en la figura, las
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notación Q y no q para recordar que se trata de tJn caudal total).
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c)
Capa permeable en corriente libre
1)
Medida con dos piezómetros.
Llamamos: z
a la cota de la línea de saturación por encima del fondo
impermeable, en el punto M, x
a la distancia de este punto al eje del pozo,
Q
al caudal del pozo tras estabilización.
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H
nivel de la capa fuera de la zona de acción del pozo, y
R
radio de acción, y por 10 tanto radio de la depresión.
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Según Post y Londe, para la construcción de presas y diques de tierra, se pueden clasificar los materiales en: -
permeables
2.10-3 > k > 2.10 -7 m/s
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d 10 10 expresa en centímetros la abertura del tamiz a través del cual pasa el 10% del peso de los materiales sólidos
(llamado diámetro eficaz del material).
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EJERCICIOS
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