Metodo Grafico de Estabilidad Para El Dimensionamiento de Tajeos
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Metodo Grafico de Estabilidad para el Dimensionamiento de Tajeos...
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Montenegro Pérez, Manuel Reynaldo
U.N.M.S.M. FIGMMG Montenegro Pérez, Manuel E.A.P. Ingeniería deReynaldo Minas
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INDICE 1. Resumen Ejecutivo ………………………………………………………. 11 2. Marco Teórico …………..………………………………………………... 22 2.1.
Introducción……………………………………………………….. 2
2.2.
Radio Hidráulico………………………………………………….. 2 2
2.3.
Número de Estabilidad …………………………………………….88
2.4.
Gráficos de Estabilidad …………………………………………….17 17
2.5.
Diseño con cablebolt……………………………………………… . 22 22
2.6.
Estimación de dilución…………………………………………….. 24 24
2.7.
Curvas de isoprobabilidad …………………………………………26 26
3. Limitaciones del Método………………………………………………….. 28 28 4. Metodología de trabajo …………………………………………………… 28 . 28 5. Aplicación ………………………………………………………………… 31 31 5.1.
Aplicación del método para valoración de la estabilidad en la 31 mina CSA, Cobar, Australia ………………………………………… 31
6. Recomendaciones ………………………………………………………… . 44 44 7. Conclusiones ………………………………………………………………. 44 44 8. Bibliografía …………………………………………………………………45 45
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MÉTODO GRÁFICO DE ESTABILIDAD PARA EL DIMESIONAMIENTO DE TAJEOS
1. Resumen Ejecutivo Uno de los problemas más comunes para desarrollar ingeniería ingeni ería en excavaciones mineras es determinar la estabilidad de las aberturas diseñadas para las paredes de los tajeos abiertos, o diseñar las paredes del tajeo pero obteniendo un factor de seguridad que garantice el no el colapso de las l as paredes del tajeo. El método gráfico de Estabilidad fue desarrollado en el siglo pasado por Mathews, pero debido a que la data para lo consideración co nsideración de sus ábacos fue de carácter limitado, estos gráficos han sufrido varias modificaciones y actualizaciones. Estas actualizaciones se dieron tomando to mando en cuenta muchos más casos prácticos y tomando más zonas de estabilidad que las planteadas al inicio por Mathews. Algunos de los investigadores que aportaron con este método luego de su creación por Mathews (1980) fueron: Potvin (1988), quien estableció un área de transición no vista antes en el gráfico de Mathews; Nickson (1992), quien agrego el termino de estabilidad con soportes; posteriormente tenemos a Stewart & Forsyth (1995), quienes en vez de acotar los gráficos con zonas con soporte, delimitaron zonas potencialmente propensas a estabilidad, falla, hundimiento; luego de estos investigadores, se encuentra a Hadjigeorgius (1995), quien demostró que para tajeos que poseen radios hidráulicos mayores a 15, la curva se hacía mucho más plana; continuando cont inuando con estas actualizaciones está el investigador Pascoe (1998); y finalmente tenemos a Trueman (2000).
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El diseño de estos gráficos se basa esencialmente en dos factores; el número de estabilidad, que representa la capacidad del macizo rocoso para permanecer estable bajo ciertas condiciones dadas de esfuerzos, estructura de la roca y orientación de los planos de la roca, y el otro factor es el Radio hidráulico o factor de forma, el cual considera la geometría de las paredes del tajeo.
2. Marco Teórico 2.1.
Introducción Continuando con los trabajos previos realizados por Mathews (1981), Potvin y Milne (1992), Nickson (1992), Stewart y Forsyth (1995), Hadjigeorgious (1995), Pascoe (1998) y Trueman (2000), han desarrollado el Método Gráfico de Estabilidad. La versión actual del método cuenta con una data de más de 400 casos recolectados en minas de Canadá, toma en cuenta los principales factores de influencia inf luencia del diseño de tajeos abiertos. Información sobre la resistencia y estructura de la masa rocosa, los esfuerzos alrededor de la excavación, y el tamaño, forma y orientación de la excavación, es utilizada para determinar si el tajeo será estable sin sostenimiento, o inestable aún con sostenimiento. El método también sugiere rangos de densidad de cablebolt , cuando el diseño está en el rango de “estable con sostenimiento”.
2.2.
Radio Hidráulico Muchas técnicas empíricas de diseño están basadas en lo que se conoce como radio hidráulico o span de la abertura. El soporte de la carga fue relacionada al span de los túneles desde 1946 (Terzagui). El término span fue usado como un parámetro para determinar la carga efectiva para los techos de los túneles. Para ciertas condiciones condiciones del
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arco era linealmente relacionado a la abertura máxima. En muchos métodos empíricos de diseño civil de túneles, la abertura del túnel es solo un factor que puede ser relacionado a la carga sobre el macizo rocoso. El termino span puede ser efectivamente relacionado con la estabilidad porque la abertura máxima define la distancia entre el elemento de mayor soporte del techo del túnel que son los hastiales del túnel. El término span también puede ser utilizado para evaluar la geometría de los túneles porque los extremos de los túneles son normalmente bastante alejados que no ofrecen soporte a la mayoría de la longitud del túnel.
2.2.1. Propiedades geométricas del radio hidráulico: El radio hidráulico tiene una interesante propiedad matemática que se relaciona al span. Si se considera una abertura con un span de S metros y un largo de L metros. A medida que el largo se incrementa hacia el infinito, para un span constante, el radio hidráulico converge a la mitad del span, como se muestra en la ecuación 2.1. cando
La figura 2.1 muestra como el radio hidráulico hidrául ico de una superficie se aproxima a la mitad del span a medida que el ratio de aspecto se incrementa (ratio entre longitud y span). Cuando la longitud de una abertura es nueve veces el span, el radio hidráulico esta entre el 90% del su máximo valor de la mitad del span. Esto indica que los finales de una abertura están ejerciendo una influencia significativa en el diseño de la estabilidad de la abertura cuando la longitud es nueve veces el span.
cacin .
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Influencia del ratio de aspecto sobre el RH
El radio hidráulico también puede ser expresado como la distancia a los pilares de soporte, calculado del centro de la superf icie. icie. Considerando na abertra rectanglar de “a” metros de span y “b” metros de longitud. Desde el centro del rectángulo, la distancia a cada uno de los pilares pi lares es a/2 y b/2 metros. La Figura 2.2 muestra la derivación derivación de la ecuación 2.2 que expresa el radio hidráulico como una función de la distancia a los pilares de soporte. Esta forma de expresar expresar el radio hidráulico muestra intuitivamente porque este puede ser relacionado relacion ado con la estabilidad de la superficie, mucho más claro que q ue expresar el área dividido entre el perímetro.
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Figura 2.2 RH expresado como la distancia a los pilares de soporte
Uno de los principales propósitos del radio hidráulico es permitir la comparación entre varias formas de excavaciones. La ecuación 2.3 puede ser expresada de manera general para permitir un factor por el número de lados que tenga la superficie.
∑
La figura 2.3 muestra el radio hidráulico calculado para varios tipos de formas de aberturas, calculadas basando en área sobre
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intuitivamente pensar que la superficie extra del d el cuadrado sobre el círculo, o del rectángulo sobre la elipse, podría ser perjudicial para la estabilidad. Para aberturas rectangulares con un span dado, la longitud es 9 veces el span antes de que el radio hidráulico hi dráulico sea igual al 90% de su máximo. Esto implica el fin de la galería aplica soporte significativo hacia el centro, a una distancia de 4.5 veces el span.
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Determinar el radio hidráulico para una geometría irregular de minería presenta algunas dificultades. En general, las aberturas mineras sin representadas por la geometría más larga posible de cuatro lados que no cruza los pilares de la roca. En algunos casos la abertura minera puede ser representada por una forma de más de cuatro lados, a pesar de que generalmente una figura de cuatro lados será el resultado más representativo del radio hidráulico. Más de una figura puede ser probada como en la figura 2.4. El radio hidráulico representa un mejoramiento sobre el término span para evaluar geometrías mineras. Las geometrías irregulares
mineras con presencia de pestañas, chimeneas, post pilares e irregular geometría de paredes; no pueden ser efectivamente representadas.
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Número de Estabilidad El número de estabilidad es uno de los dos parámetros que utiliza el método grafico para determinar las diferentes zonas de estabilidad estabili dad determinadas en las gráficas. Uno de los factores que se usan para hallar el número de estabilidad (N) es la forma modificada de clasificación ingenieril del Instituto Geotécnico de Noruega (NGI), el sistema Q, para caracterizar la calidad del macizo rocoso. l valor modificado de Q Q’ es calclado de los resltados de
mapeo estructural o logeo geotecnia de los testigos t estigos del macizo rocoso de acuerdo a la clasificación del sistema Q, pero asumiendo que el parámetro de reducción de agua en las juntas y el factor de reducción reducción de esfuerzos (SRF) son ambos iguales a cero. La calidad del macizo rocoso se define por:
Donde el RQD es el índice de designación de la calidad de la roca desarrollado por Deere en 1964 y está basado en un porcentaje modificado de recuperación de testigos, el número de sistemas de juntas (Jn), el número de rugosidad de las juntas (J r ) y el número de alteración de las juntas (Ja). El número de estabilidad desarrollado por Mathews es determinado mediante el ajuste del valor de Q’ a los esferzos indcidos
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desarrollados en las siguientes secciones con más detalle, dando su método de cálculo y la explicación de cada uno un o de estos.
2.3.1. Factor A El factor A, también llamado el factor de esfuerzos en la roca, refleja los esfuerzos actuantes sobre las caras libres del tajeo abierto en profundidad. Este factor es determinado a partir de la resistencia compresiva no confinada de la roca intacta y el esfuerzo actuante paralelo a la cara expuesta del tajeo bajo consideración. La resistencia de la roca intacta puede ser determinada mediante ensayos de laboratorio de la roca. El esfuerzo compresivo inducido se establece a partir del modelamiento numérico o se estima a partir de distribuciones de esfuerzos, usando valores de esfuerzos insitu medidas o asumidas. El factor de esfuerzo en la roca, A, es por lo tanto determinado a
partir de la relación , resistencia de la roca intacta a esfuerzo
compresivo inducido, sobre el borde de la abertura:
( ( )
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paralelo a la superficie libre, y es más pequeña pe queña cuando los planos son perpendiculares entre sí. El factor B, que depende de la diferencia entre la orientación de la junta crítica y cada cara del tajeo, puede ser determinado a partir del diagrama reproducido en la Figura 2.7.
Figura 2.6 Orientación de la junta crítica con respecto a la superficie de la excavación, según Potvin (1988)
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Aunque la forma de calcular el factor B fue cambiada por Potvin, algunos investigadores (Trueman, Stewart & Forsyth) Fors yth) decidieron investigar acerca de esta modificación al método original, y llegaron a la conclusión el número de estabilidad resulta en una no apreciable diferencia en la capacidad predictiva de la técnica para excavaciones sin soporte. Por lo que muchos empiristas prefieren calcular el factor de B de la manera manera original propuesta por Mathews.
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2.3.3. Factor C El factor C es el factor de ajuste por el efecto de la gravedad. La falla puede ocurrir desde el techo debido a caídas inducidas por la gravedad o, desde las paredes del tajeo, debido a lajamientos o deslizamientos. Potvin (1988) sugirió que tanto las fallas inducidas por gravedad y como las fallas por lajamiento, dependen de la inclinación de la superficie del tajeo α. l factor C para estos casos pede ser calculado a partir de la relación C = 8 – 6 – 6 Cos α o determinado a partir del diagrama graficado en la Figura 2.9. Este factor tiene un valor máximo de 8 para paredes verticales y un valor mínimo de 2 para techos horizontales de tajeos.
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La falla por deslizamiento dependerá de la inclinación β de la junta crítica, y el factor de ajuste C, es dado en la Figura 2.10.
Figura 2.10 Factor C para deslizamiento, según Potvin (1988). (1988 ).
Aunque la forma modificada del factor C tampoco es muy mu y aceptada por algunos usuarios del método, por lo que prefieren el método original que se ve en la Figura 2.11.
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2.3.4. Discusión de los factores Como resultado de una amplia discriminación en varios libros (Hoek, Kaiser and Bawden 1995, Hutchison and Diederichs 1996), los factores descritos usados para el cálculo de N han ganado una gran aceptación entre investigadores y usuarios del método. La aplicabilidad de la metodología metodologí a de entrada en un análisis de caso a caso fue revisada y, con la excepción de las pequeñas modificaciones mostradas en la figura 2.12, fueron consideradas apropiadas (Hadjigeorgius, Leclair, and Potvin 1995). Por otro lado, algunos autores auto res (Stewart y Forsyth 1995, Trueman et al. 2000) han indicado su preferencia por la formulación propuesta originalmente por Mathews, mostradas en
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Varias modificaciones se han propuesto al gráfico e estabilidad durante la última década. Aunque, debe ser notado que la mayoría de estas propuestas no han sido probadas extensivamente en casos de estudio, ni tampoco son ampliamente empleado por los usuarios del método. Scoble y Moss (1994) sugirieron que se s e debía aumentar dos factores de ajuste más, D para voladura y E para pa ra clasificación de intervalos en subniveles con algunos factores tentativamente propuestos. Un factor por falla fue desarrollado para que pueda incorporarse al factor de estabilidad (Suorineni, Tannant, and Kaiser 1999). Este factor de falla considera los ángulos entre la falla y la superficie del tajeo y la posición donde la falla
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macizo rocoso fue cuantificada como la perdida de la resistencia del macizo rocoso.
2.4.
Gráficos de Estabilidad El método gráfico de estabilidad de Mathews (1981) para el diseño de tajeos abiertos fue inicialmente propuesto para profundidades de 1000 metros, tomando como data inicial 26 casos estudiados en 3 minas.
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termino caved utilizado en el gráfico de Potvin no tiene un significado literal, si no que se refiere a una zona inestable inesta ble y no a un hundimiento, hun dimiento, como normalmente significaría.
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Potvin et al. (1989) notaron que hay un gran problema dirección en la data usada para hacer el grafico 2.18, reflejando la prueba pru eba y error natural del diseño de cablebolt. Ellos también dijeron que los cablebolts no son muy efectivos cuando el factor de tamaño ta maño relativo de los bloques, es menos de 0.75 y cuando la densidad del d el cablebolt es menos de 1 perno por diez metros cuadrados en los límites de la abertura.
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Estimación de dilución El uso de CSM (cavity monitoring survey) su rvey) (Miller, Potvin et al., 1992) presentan un método practico para recolectar data para la variable de estabilidad de tajeos continuos, el Equivalent Linear Overbreak/Slough, ELOS (Clark y Pakalnis, 1997). Clark y Pakalnis (1997) definen el ELOS como el equivalente a la sobre rotura linear a lo
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“UNIVERSIDAD
NACIONAL MAYOR
[Escriba texto]
DE
Como paso siguiente se debe usar una software para evaluar el
SAN MARCOS”
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