SHIP RESISTANCE IN THICK BRASH ICE

Abstract The mechanical properties of thick brash ice are considered, with special emphasis on the friction angle ф for a linear Mohr-Coulomb failure criterion. The static equilibrium of a uniform brash layer is discussed, and the internal stresses are given for neutral, active, and passive stress states. Horizontal displacement of brash by a smooth vertical plate is analyzed, and the crushing forces for plastic yielding in the passive stress state are deduced for cohesionless brash and for ice that has finite internal cohesion. Propagation of a crushing disturbance is treated, and the condition for localization of crushing is derived from consideration of mass and momentum conservation. Formation of pressure ridges by localized crushing against a plate is analyzed, and estimates are obtained for the limiting thickness of ice crushed against a plate. Horizontal thrusting of brash by a plate inclined from the vertical is dealt with by graphical derivations of initial passive pressure using the Poncelet construction, and it is argued that for large displacements the crushing forces against an inclined plate are the same as those for a vertical plate because of pressure ridge formation. In the analysis of low speed ship resistance, the emphasis is on resistance at the bow. Starting from analysis of penetration by a slender smooth wedge and taking account of interface friction in an approximate way, an expression is obtained for the resistance of “sharp” conventional bows, and comparisons are made with plasticity results for plane-strain penetration of wedges into semi-infinite media. Formation of a “false nose” of brash in front of a blunt bow is considered for Mohr-Coulomb and Von Mises failure criteria, and an expression for the resistance of blunt bows is derived. Frictional resistance aft of the bow section is controlled largely by the normal pressure of ice against the hull. After consideration of neurtral and active stress for the thickened ice alongside the hull, the normal force is expressed as a fraction of the passive state crushing force. Bow resistance and hull friction can be combined into a single expression of the form ABR, where A is a dimensionless function, B is the ship's width and R is the passive state crushing force (per unit width) for the brash layer. The limiting ice resistance for ship movement can be related to the ship's thrust, which in turn can be estimated from readily available data such as shaft power and thrust per unit power. Equating the theoretical expression for ship resistance to a suitable expression for limiting propeller thrust at an appropriate hull speed, an estimate of limiting ice thickness is obtained. For ships of a given type, which tend to have shaft power proportional to the cube of the beam, the limiting ice thickness is directly proportional to the beam. Using the very limited data on mechanical properties of brash ice and assuming that the propellers continue to function well, the estimates indicate that a Great Lakes bulk carrier would be near its limit of movement when the brash thickness in a wide channel is about 10% of the beam, while an icebreaker in saltwater brash could perhaps keep moving until the brash thickness reached about 20% of the ship's beam.