-4 -at, °c

Fig. 8.9. Temperature dependence of the modulus of elasticity of frozen soils (according to N.A. Tsytovich): 1 - sand; 2 - silty sandy-clay material; 3 - clay at 0.2 MPa load.

modulus of elasticity of ice is less than that of ground with a rigid mineral skeleton (sand), but is much higher than that of frozen clays which have a greater amount of unfrozen water.

Upon axial deformation of a frozen soil specimen there is a change of cross-sectional area: at compression it increases, on stretching it narrows. Therefore, in order to describe the stress-deformational state of the frozen soil in the elastic region Hooke's law is not sufficient. One more relationship is necessary by which the ratio of transverse and longitudinal deformations can be expressed: according to Poisson's law, e2 = e3 = — pe1, where e1 is the relative longitudinal deformation, while e2 and e3 are transverse deformations; p is the proportionality factor or Poisson's ratio. The latter serves as a second important characteristic of elastic material (Table 8.4).

Transverse deformation under the effect of longitudinal force arises owing to bonds existing between particles of the frozen soil, therefore the coefficient is also an index characterizing volumetric deformation of the frozen soil.

The data presented in Table 8.4 show the substantial influence of temperature on Poisson's ratio for frozen soils, which with higher temperature tends to a maximum value of 0.5 (as for ideally plastic bodies), while with lowering of temperature, to the values typical of a rigid body.

Among indices of deformability of frozen soils are the coefficients of viscosity and compressibility.

Viscosity represents one of the main rheologic properties of frozen soils. It is represented by the coefficient of effective viscosity t] (hereafter viscosity coefficient) which is equal to the ratio of the stress value acting, a, to the resulting rate of flow e, that is, t] = p/§. The viscosity coefficient or simply viscosity is measured in N s m " 2 (Pa s).

With respect to the two straight parts of the rheologic curve for the frozen

Table 8.4. Poisson's ratio for frozen soils (after N.A. Tsytovich)


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