Probabilidad de excedencia de la fricción de diseño en curvas horizontales.
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Date
2025
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Publisher
Universidad de Concepción
Abstract
El diseño de carreteras busca cumplir con criterios técnicos que garanticen condiciones adecuadas de seguridad y confort. Esto exige comprender la respuesta de los conductores frente a los elementos geométricos del alineamiento, considerando las características del conductor, del vehículo y del terreno. Uno de los factores más relevantes en el diseño de curvas horizontales es el coeficiente de fricción, el cual se relaciona directamente con la velocidad a la que los conductores abordan una curva. Para analizar este aspecto, se utilizó el modelo de tres zonas, representado mediante un diagrama fricción–velocidad que incorpora tres niveles de fricción: la fricción operativa, que corresponde a la fricción demandada por los conductores en condiciones normales de circulación asociado a su percepción de confort; la fricción de diseño, establecida por el proyectista según criterios normativos; y la fricción del pavimento, que representa la fricción disponible entre el neumático y la superficie.
Los márgenes de seguridad se definen como la diferencia entre estos niveles de fricción y suelen abordarse de forma determinística. Sin embargo, al estar influenciadas por variables como la velocidad de operación, la percepción de confort, las condiciones del pavimento o la decisión del proyectista, estas fricciones presentan incertidumbre en su estimación.
Con el fin de incorporar dicha incertidumbre, se aplicaron principios de confiabilidad para estimar la probabilidad de que la fricción operativa supere la fricción de diseño en distintas configuraciones geométricas. Las funciones de fricción utilizadas en las funciones de estado límite fueron generadas mediante simulación de Montecarlo, lo que permitió obtener distribuciones de probabilidad lognormal. El análisis se llevó a cabo en curvas con velocidades de diseño de 50 y 70 kilómetros por hora, seleccionando tres radios representativos para cada caso. A cada uno se le asignaron niveles de desviación estándar bajo, medio y alto, con el objetivo de incorporar la variabilidad geométrica propia del proceso de diseño.
Los resultados muestran que, las probabilidades de excedencia en curvas horizontales asociadas a velocidades de diseño de 50 km/h son cercanas al 100%, dado que la fricción de operación supera sistemáticamente a la fricción de diseño, lo que evidencia una disminución efectiva en el margen de seguridad disponible asociado al confort.
Roadway design aims to meet technical criteria that ensure appropriate safety and comfort conditions. This requires understanding driver responses to the geometric elements of the alignment, considering driver, vehicle, and terrain characteristics. One of the most relevant factors in horizontal curve design is the coefficient of friction, which is directly related to the speed at which drivers approach a curve. To analyze this aspect, the three-zone model was used, represented through a friction–speed diagram that incorporates three levels of friction: operational friction, which corresponds to the friction demanded by drivers under normal driving conditions and is associated with their perception of comfort; design friction, established by the designer based on regulatory criteria; and pavement friction, which represents the available friction between the tire and the surface. Safety margins are defined as the difference between these friction levels and are typically addressed in a deterministic manner. However, since they are influenced by variables such as operating speed, comfort perception, pavement conditions, or the designer’s decisions, these friction values present uncertainty in their estimation. To incorporate this uncertainty, reliability principles were applied to estimate the probability that the operational friction exceeds the design friction under different geometric configurations. The friction functions used in the limit state functions were generated using Monte Carlo simulation, which allowed for obtaining lognormal probability distributions. The analysis was carried out on curves with design speeds of 50 and 70 kilometers per hour, selecting three representative radii for each case. Each was assigned low, medium, and high standard deviation levels to incorporate the geometric variability inherent to the design process. The results show that the probabilities of exceedance in horizontal curves associated with design speeds of 50 km/h are close to 100%, as the operational friction consistently exceeds the design friction. This indicates an effective reduction in the available safety margin associated with comfort.
Roadway design aims to meet technical criteria that ensure appropriate safety and comfort conditions. This requires understanding driver responses to the geometric elements of the alignment, considering driver, vehicle, and terrain characteristics. One of the most relevant factors in horizontal curve design is the coefficient of friction, which is directly related to the speed at which drivers approach a curve. To analyze this aspect, the three-zone model was used, represented through a friction–speed diagram that incorporates three levels of friction: operational friction, which corresponds to the friction demanded by drivers under normal driving conditions and is associated with their perception of comfort; design friction, established by the designer based on regulatory criteria; and pavement friction, which represents the available friction between the tire and the surface. Safety margins are defined as the difference between these friction levels and are typically addressed in a deterministic manner. However, since they are influenced by variables such as operating speed, comfort perception, pavement conditions, or the designer’s decisions, these friction values present uncertainty in their estimation. To incorporate this uncertainty, reliability principles were applied to estimate the probability that the operational friction exceeds the design friction under different geometric configurations. The friction functions used in the limit state functions were generated using Monte Carlo simulation, which allowed for obtaining lognormal probability distributions. The analysis was carried out on curves with design speeds of 50 and 70 kilometers per hour, selecting three representative radii for each case. Each was assigned low, medium, and high standard deviation levels to incorporate the geometric variability inherent to the design process. The results show that the probabilities of exceedance in horizontal curves associated with design speeds of 50 km/h are close to 100%, as the operational friction consistently exceeds the design friction. This indicates an effective reduction in the available safety margin associated with comfort.
Description
Tesis presentada para optar al título de Ingeniero/a Civil.
Keywords
Construcción de carreteras, Fricción, Curvas