Misplaced Pages

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39-621: A consortium of seven mining companies sponsored environmental impact studies to construct a deep-water port in Bathurst Inlet. Their plans included building a 211 km (131 mi) road connecting the port to their mines. The port would serve vessels of up to 25,000 tonnes. A plan referred to the Nunavut Impact Review Board in May 2004 projected a capacity to moor vessels of up to 50,000 tonnes. In this earlier plan

78-491: A blizzard. If the ice road is part of a winter road, then closure can also be due to an over-land segment that has become unserviceable. Ice crossings can be made to support higher loads if they are reinforced, and there are a number of ways this has been done in the past. Also, because these structures are vulnerable to a warming climate, which reduces their operational lifespan, they may benefit from reinforcement along problematic segments, such as creek crossings and where

117-435: A floating ice sheet has been investigated via field testing. The most compelling evidence of such wave patterns, however, was captured by satellite imagery. When an ice road is part of a winter road , as is commonly the case, its design and construction is comprised within the overall road planning, i.e. in conjunction with the over-land segments. Either way, factors that need to be addressed before construction include

156-421: 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,

195-437: 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

234-433: 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

273-419: 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

312-500: 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

351-412: Is an effective shear force. The stress–strain relations for a linear elastic Kirchhoff plate are given by Since σ α 3 {\displaystyle \sigma _{\alpha 3}} and σ 33 {\displaystyle \sigma _{33}} do not appear in the equilibrium equations it is implicitly assumed that these quantities do not have any effect on

390-499: 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

429-578: Is normal to the mid-surface and directed in the positive x 3 {\displaystyle x_{3}} direction, the principle of virtual work then leads to the equilibrium equations N α β , α = 0 M α β , α β − q = 0 {\displaystyle {\begin{aligned}N_{\alpha \beta ,\alpha }&=0\\M_{\alpha \beta ,\alpha \beta }-q&=0\end{aligned}}} For moderate rotations,

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468-539: Is the displacement of the mid-surface in the x 3 {\displaystyle x_{3}} direction. If φ α {\displaystyle \varphi _{\alpha }} are the angles of rotation of the normal to the mid-surface, then in the Kirchhoff–Love theory φ α = w , α 0 . {\displaystyle \varphi _{\alpha }=w_{,\alpha }^{0}\,.} For

507-405: Is to pack the snow layer with tracked vehicles into a thin layer, thereby increasing its density and reducing its insulating properties. The other is to remove it altogether, typically with vehicles fitted with a snowplow . Once the ice has reached the target thickness (via accelerated growth after removing the insulating effects of the snow), road construction per se may commence. At that point,

546-557: The Bathurst Inlet Road would be an ice road , like that from Yellowknife , not an all-weather road as in post-2005 proposals, following the failure of the ice road to freeze early enough to allow transport of a whole year's worth of supplies. In 2008 several of the companies dropped out. In August 2013 Bathurst Inlet Port & Road (BIPR) Project , a joint venture composed of GlencoreXstrata , Sabina Gold and Silver Corporation, presented continued plans for facilities at

585-464: The Cartesian coordinates on the mid-surface of the undeformed plate, x 3 {\displaystyle x_{3}} is the coordinate for the thickness direction, u 1 0 , u 2 0 {\displaystyle u_{1}^{0},u_{2}^{0}} are the in-plane displacements of the mid-surface, and w 0 {\displaystyle w^{0}}

624-655: The Grays Bay Port that would "include a dock, concentration storage shed, fuel storage facilities and a camp. These facilities will support storage of concentrate, loading of bulk-carrier ships, and re-supply of fuel and goods for the Project." The project that was first proposed in 2003 has been subject to changes in demands made by the Nunavut Impact Review Board regarding Environmental Impact Study. Environmental groups have raised concerns over

663-485: 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

702-399: The dynamics of a Kirchhoff–Love plate are where, for a plate with density ρ = ρ ( x ) {\displaystyle \rho =\rho (x)} , and The figures below show some vibrational modes of a circular plate. The governing equations simplify considerably for isotropic and homogeneous plates for which the in-plane deformations can be neglected and have

741-484: The following: Factors that need to be considered in route selection include the following: Before first access to the ice, the following factors need to be considered: Snow cover removal is the first major operation in an ice road construction scheme. It may only begin once the ice thickness is safe to support the machinery used for that operation. There are two ways of doing it, depending on available equipment and state of practice for that particular road. One

780-441: The full three-dimensional solid mechanics problem to a two-dimensional problem. The aim of plate theory is to calculate the deformation and stresses in a plate subjected to loads . Of the numerous plate theories that have been developed since the late 19th century, two are widely accepted and used in engineering. These are The Kirchhoff – Love theory is an extension of Euler–Bernoulli beam theory to thin plates. The theory

819-410: The governing equation is For an orthotropic plate Therefore, and The governing equation of an orthotropic Kirchhoff plate loaded transversely by a distributed load q {\displaystyle q} per unit area is where The dynamic theory of plates determines the propagation of waves in the plates, and the study of standing waves and vibration modes. The governing equations for

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858-603: The governing equation is In index notation, In direct tensor notation, the governing equation is ∇ 2 ∇ 2 w = 0 . {\displaystyle \nabla ^{2}\nabla ^{2}w=0\,.} For a transversely loaded plate without axial deformations, the governing equation has the form where for a plate with thickness 2 h {\displaystyle 2h} . In index notation, and in direct notation In cylindrical coordinates ( r , θ , z ) {\displaystyle (r,\theta ,z)} ,

897-410: 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

936-493: The ice cover: where σ max 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/cm (~ 50–150 lbs/in ), lower bound values are generally those that are used for safety purposes. This level of conservatism

975-476: The ice is able to safely support the heavier equipment required for that phase, which mostly consists of artificial thickening using a pump or a spraying system. The aim is to bring the thickness up to what is required for the heaviest vehicles that are anticipated when the ice road opens. Vehicles traveling on an ice road include ordinary automobiles and trucks of various sizes and weights. Standard winter tires are sufficient, i.e. cleats and tire chains can damage

1014-401: 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 km/h (6.2 mph) to 35 km/h (22 mph). Dynamic loading of the ice cover may also dictate a minimum distance between vehicles. The effects of dynamic loading on

1053-594: The impact the road would have on the annual migration of the Bathurst Caribou herd . There are four barren-ground caribou herds in the Northwest Territories—Cape Bathurst, Bluenose West, Bluenose East and Bathurst caribou herd. The Bluenose East caribou herd began a recovery with a population of approximately 122,000 in 2010, which is being credited to the establishment of Tuktut Nogait National Park . According to T. Davison 2010, CARMA 2011,

1092-437: The kinematic assumptions of Kirchhoff-Love theory lead to the following strain-displacement relations This theory is nonlinear because of the quadratic terms in the strain-displacement relations. The equilibrium equations for the plate can be derived from the principle of virtual work . For the situation where the strains and rotations of the plate are small, the equilibrium equations for an unloaded plate are given by where

1131-729: The momentum balance and are neglected. It is more convenient to work with the stress and moment resultants that enter the equilibrium equations. These are related to the displacements by and The extensional stiffnesses are the quantities The bending stiffnesses (also called flexural rigidity ) are the quantities For an isotropic and homogeneous plate, the stress–strain relations are The moments corresponding to these stresses are The displacements u 1 0 {\displaystyle u_{1}^{0}} and u 2 0 {\displaystyle u_{2}^{0}} are zero under pure bending conditions. For an isotropic, homogeneous plate under pure bending

1170-564: The risks of damage to the ice cover, which would compromise its ability to support the weight it has been designed for. Maintenance comprises two main tasks: An ice road will typically be closed as a result of deterioration of the running or operating surface, before there is any risk of ice cover failure. Surface deterioration can happen when the ice surface becomes too soft, or because of an excessive amount of meltwater on its surface. Mid-season road closures can also happen for similar reasons, and also because of inclement weather, such as

1209-456: The road surface. However, tire chains may be stored in the vehicle for emergency purposes; they can also come in handy when traveling on a winter road with grades steeper than 8% on over-land segments. Signage may indicate speed limits, for instance a maximum of 25 km/h (16 mph), and spacing between vehicles, for instance 500 m (1,600 ft) for loads more than 12,500 kg (27,600 lb). These restrictions are to decrease

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1248-414: The situation where the strains in the plate are infinitesimal and the rotations of the mid-surface normals are less than 10° the strains-displacement relations are Therefore, the only non-zero strains are in the in-plane directions. If the rotations of the normals to the mid-surface are in the range of 10° to 15°, the strain-displacement relations can be approximated using the von Kármán strains. Then

1287-530: The strain-displacement relations take the von Karman form and the equilibrium equations can be expressed as The boundary conditions that are needed to solve the equilibrium equations of plate theory can be obtained from the boundary terms in the principle of virtual work. For small strains and small rotations, the boundary conditions are Note that the quantity n α   M α β , β {\displaystyle n_{\alpha }~M_{\alpha \beta ,\beta }}

1326-424: The stress resultants and stress moment resultants are defined as and the thickness of the plate is 2 h {\displaystyle 2h} . The quantities σ α β {\displaystyle \sigma _{\alpha \beta }} are the stresses. If the plate is loaded by an external distributed load q ( x ) {\displaystyle q(x)} that

1365-571: The three other herds "declined 84-93% from peak sizes in the mid-1980s and 1990s. The proposed deep-water port serves as the basis of location in Don Bassingthwaite's short story, "Too Much Is Never Enough" from the science fiction anthology, Foreshadows: The Ghosts of Zero . 67°39′15″N 108°28′09″W  /  67.65417°N 108.46917°W  / 67.65417; -108.46917  ( Kiluhiqtuq formerly Bathurst Inlet ) Ice road An ice road or ice bridge

1404-410: 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

1443-469: The winter road crosses a shoreline. Plate theory In continuum mechanics , plate theories are mathematical descriptions of the mechanics of flat plates that draw on the theory of beams . Plates are defined as plane structural elements with a small thickness compared to the planar dimensions. The typical thickness to width ratio of a plate structure is less than 0.1. A plate theory takes advantage of this disparity in length scale to reduce

1482-514: 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

1521-472: Was developed in 1888 by Love using assumptions proposed by Kirchhoff. It is assumed that a mid-surface plane can be used to represent the three-dimensional plate in two-dimensional form. The following kinematic assumptions are made in this theory: The Kirchhoff hypothesis implies that the displacement field has the form where x 1 {\displaystyle x_{1}} and x 2 {\displaystyle x_{2}} are

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