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Hub AI
Ice road AI simulator
(@Ice road_simulator)
Hub AI
Ice road AI simulator
(@Ice road_simulator)
Ice road
An ice road or ice bridge is a human-made structure that runs on a frozen water surface (a river, a lake or a sea water expanse). Ice roads are typically part of a winter road, but they can also be simple stand-alone structures, connecting two shorelines. Ice roads may be planned, built and maintained so as to remain safe and effective, and a number of guidelines have been published with information in these regards. An ice road may be constructed year after year, for instance to service community needs during the winter. It could also be for a single year or two, so as to supply particular operations, such as a hydroelectric project or offshore drill sites.
The ability of an ice road to safely support the weight of a vehicle, or any other loads applied onto it, referred to as bearing capacity, is the primary concern when designing, building and using that structure. Generally speaking, a vertically loaded ice cover will react in two ways: 1) it will sink, and 2) it will bend in flexure. In order to meet the ice bearing criteria, the top surface should not sink below the water line and the applied flexural stress should not exceed the ice's flexural strength. Three loading regimes have to be considered: a) maximum weight for standard usage or for parking during a short duration; b) a load that remains stationary during an extensive time period; and c) dynamic loading of the ice cover, from a traveling vehicle.
For standard traffic activities, guidelines typically use a simple empirical formula to determine the maximum vehicle weight that should be allowed on an ice road. This formula, which was initially proposed in 1971, is often referred to as Gold's formula:
where P is the load, h is the thickness and A is a constant with a unit of pressure. It may be linked with an idealized elastic response of the ice cover:
where σmax is the maximum tensile strength at the bottom of an infinite ice plate resting on an elastic foundation. The parameter C is based on the theory of thick plates. Hence, with this idealized formulation, A is representative of the ice cover tensile strength. Although recommended values for A range from 3.5 to 10 kg/cm2 (50 to 142 psi), lower bound values are generally those that are used for safety purposes. This level of conservatism is justified because, unlike human-made materials such as steel or concrete, natural ice covers inherently contain a large amount of structural flaws (fractures, water and air pockets). Moreover, for a public road, which is relatively uncontrolled, such an approach introduces a high safety factor against breakthroughs and is therefore desirable. For industrial roads, the design may be less conservative so as to handle their functional requirements, i.e. higher A values can be used, but under the close supervision of a professional engineer.
When using Gold's formula, a purely elastic response is assumed, which is, by definition, instantaneous and independent of loading time. Ice, however, naturally exists at a high homologous temperature, i.e. near its melting point. As is the case for any other material under these conditions, response to loading is not only elastic, but incorporates other components, namely:
Thus, an ice cover may be able to safely support a vehicle, but if it remains on the ice for too long, deformation will continue via microcracking, leading to the collapse of the ice cover below the vehicle. Recommendations vary as to how this can be avoided. Some sources prescribe a maximum of two hours for a stationary load, which is also what Gold recommended. Others advise to use the freeboard of the ice as an indicator, which can be done by drilling a hole in it and monitoring the distance between the water in the hole and the ice surface. The vehicle should be removed before the water reaches the surface in that hole. Another reason why the amount of freeboard matters is that if the water makes its way onto the ice surface (through cracks and fissures), the ice cover's bearing capacity diminishes rapidly, which can accelerate breakthrough. For long-term loads, a professional engineer may have to be consulted.
As a vehicle travels on the road, a dynamic loading regime is exerted onto the ice cover. Below a specific speed, referred to as critical, the ice cover beneath the vehicle will assume the shape of a bowl moving with the vehicle, pushing away the water around it, as the keel of a boat does. At (and above) the critical speed, a series of waves will form behind and in front of the vehicle. "If the celerity of these waves is the same as the vehicle speed, the deflection and the stresses in the ice sheet are amplified, similar to resonance in an oscillating system" (pp. 8–10). The critical speed depends on ice thickness and water depth. Another issue that arises is the reflection of these waves from the shoreline back toward the vehicle. This can induce additional stresses on the ice – one way to mitigate this issue is to avoid approaching shorelines at 90 degrees. The critical speed is what determines the speed limit for vehicles traveling on ice roads. That limit can be as low as 10 to 35 km/h (6 to 22 mph). Dynamic loading of the ice cover may also dictate a minimum distance between vehicles.
Ice road
An ice road or ice bridge is a human-made structure that runs on a frozen water surface (a river, a lake or a sea water expanse). Ice roads are typically part of a winter road, but they can also be simple stand-alone structures, connecting two shorelines. Ice roads may be planned, built and maintained so as to remain safe and effective, and a number of guidelines have been published with information in these regards. An ice road may be constructed year after year, for instance to service community needs during the winter. It could also be for a single year or two, so as to supply particular operations, such as a hydroelectric project or offshore drill sites.
The ability of an ice road to safely support the weight of a vehicle, or any other loads applied onto it, referred to as bearing capacity, is the primary concern when designing, building and using that structure. Generally speaking, a vertically loaded ice cover will react in two ways: 1) it will sink, and 2) it will bend in flexure. In order to meet the ice bearing criteria, the top surface should not sink below the water line and the applied flexural stress should not exceed the ice's flexural strength. Three loading regimes have to be considered: a) maximum weight for standard usage or for parking during a short duration; b) a load that remains stationary during an extensive time period; and c) dynamic loading of the ice cover, from a traveling vehicle.
For standard traffic activities, guidelines typically use a simple empirical formula to determine the maximum vehicle weight that should be allowed on an ice road. This formula, which was initially proposed in 1971, is often referred to as Gold's formula:
where P is the load, h is the thickness and A is a constant with a unit of pressure. It may be linked with an idealized elastic response of the ice cover:
where σmax is the maximum tensile strength at the bottom of an infinite ice plate resting on an elastic foundation. The parameter C is based on the theory of thick plates. Hence, with this idealized formulation, A is representative of the ice cover tensile strength. Although recommended values for A range from 3.5 to 10 kg/cm2 (50 to 142 psi), lower bound values are generally those that are used for safety purposes. This level of conservatism is justified because, unlike human-made materials such as steel or concrete, natural ice covers inherently contain a large amount of structural flaws (fractures, water and air pockets). Moreover, for a public road, which is relatively uncontrolled, such an approach introduces a high safety factor against breakthroughs and is therefore desirable. For industrial roads, the design may be less conservative so as to handle their functional requirements, i.e. higher A values can be used, but under the close supervision of a professional engineer.
When using Gold's formula, a purely elastic response is assumed, which is, by definition, instantaneous and independent of loading time. Ice, however, naturally exists at a high homologous temperature, i.e. near its melting point. As is the case for any other material under these conditions, response to loading is not only elastic, but incorporates other components, namely:
Thus, an ice cover may be able to safely support a vehicle, but if it remains on the ice for too long, deformation will continue via microcracking, leading to the collapse of the ice cover below the vehicle. Recommendations vary as to how this can be avoided. Some sources prescribe a maximum of two hours for a stationary load, which is also what Gold recommended. Others advise to use the freeboard of the ice as an indicator, which can be done by drilling a hole in it and monitoring the distance between the water in the hole and the ice surface. The vehicle should be removed before the water reaches the surface in that hole. Another reason why the amount of freeboard matters is that if the water makes its way onto the ice surface (through cracks and fissures), the ice cover's bearing capacity diminishes rapidly, which can accelerate breakthrough. For long-term loads, a professional engineer may have to be consulted.
As a vehicle travels on the road, a dynamic loading regime is exerted onto the ice cover. Below a specific speed, referred to as critical, the ice cover beneath the vehicle will assume the shape of a bowl moving with the vehicle, pushing away the water around it, as the keel of a boat does. At (and above) the critical speed, a series of waves will form behind and in front of the vehicle. "If the celerity of these waves is the same as the vehicle speed, the deflection and the stresses in the ice sheet are amplified, similar to resonance in an oscillating system" (pp. 8–10). The critical speed depends on ice thickness and water depth. Another issue that arises is the reflection of these waves from the shoreline back toward the vehicle. This can induce additional stresses on the ice – one way to mitigate this issue is to avoid approaching shorelines at 90 degrees. The critical speed is what determines the speed limit for vehicles traveling on ice roads. That limit can be as low as 10 to 35 km/h (6 to 22 mph). Dynamic loading of the ice cover may also dictate a minimum distance between vehicles.
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