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This behavior, critical state soil mechanics simply assumes as a given. For these reasons, critical-state and elasto-plastic soil mechanics have been subject to charges of scholasticism; the tests to demonstrated its validity are usually "conformation tests" where only simple stress-strain curves are demonstrated to be modeled satisfactorily.
However, the liquid–vapor boundary terminates in an endpoint at some critical temperature T c and critical pressure p c. This is the critical point. The critical point of water occurs at 647.096 K (373.946 °C; 705.103 °F) and 22.064 megapascals (3,200.1 psi; 217.75 atm; 220.64 bar). [3]
A more advanced understanding of the behaviour of soil undergoing shearing led to the development of the critical state theory of soil mechanics (Roscoe, Schofield & Wroth 1958). In critical state soil mechanics, a distinct shear strength is identified where the soil undergoing shear does so at a constant volume, also called the 'critical state'.
Contractive soils become denser as they shear, and their rate of contraction decreases until they reach a critical void ratio. A critical state line separates the dilatant and contractive states for soil. The tendency for a soil to dilate or contract depends primarily on the confining pressure and the void ratio of the soil.
In thermodynamics, a critical line is the higher-dimensional equivalent of a critical point. [1] It is the locus of contiguous critical points in a phase diagram . These lines cannot occur for a single substance due to the phase rule , but they can be observed in systems with more variables, such as mixtures.
Angle of repose of a heap of sand Sandpile from the Matemateca collection. The angle of repose, or critical angle of repose, [1] of a granular material is the steepest angle of descent or dip relative to the horizontal plane on which the material can be piled without slumping. At this angle, the material on the slope face is on the verge of ...
This is because a loose sand has a tendency to compress when a load is applied. Dense sands, by contrast, tend to expand in volume or 'dilate'. If the soil is saturated by water, a condition that often exists when the soil is below the water table or sea level, then water fills the gaps
Anisimov et al. (2004), [11] without referring to Frenkel, Fisher, or Widom, reviewed thermodynamic derivatives (specific heat, expansion coefficient, compressibility) and transport coefficients (viscosity, speed of sound) in supercritical water, and found pronounced extrema as a function of pressure up to 100 K above the critical temperature.