The mechanical behavior of frozen soils is governed by intrinsic material properties such as moisture content in the frozen and unfrozen state, air entrapment, salt content, grain size, etc., and by externally imposed conditions such as strain-rate, temperature and confining pressure. Several authors, notably Andersland and Ainouri (1970), Alkire and Andersland (1973), Sayles (1974), Parameswaran and Jones (1981) have studied the strength and deformation of various frozen soils at various temperatures and strain-rates. Findings, reported by Chamberlain et al. (1972) and Zhu and Carbee (1987), showed the deformation characteristics and stress–strain relationships of frozen soils, as well as the strength and creep behavior under high confining pressures. Francis and David (1981) measured the strength of frozen silt as a function of water content, or dry unit weight of the soil, with uniaxial compression tests. Parameswaran and Jones (1981) and Baker et al. (1982) found that the strength of frozen soil increased to a peak value with increasing confining pressure, but with a further increase in confining pressure, the strength declined. Based on their data from creep tests and uniaxial compression tests, Zhu et al. (1991) put forward a relationship between thermal stress and strain of frozen ground, and classified the stress–strain behavior of frozen soils into nine types: 1) viscoelastic–plastic-I (initial tangential modulus or quasi-elastic modulus depends on strain ratio, with constant failure strain); 2) viscoelastic–plastic-II (initial tangential modulus is independent on strain ratio, while failure strain depends on it); 3) elastic–continuous, nonlinear stain hardening; 4) elastic nonlinear stain hardening–softening; 5) elastic linear stain hardening; 6) elastic linear stain hardening–softening; 7) elastic stain hardening with yield; 8) elastic–ideal plasticity; and 9) elastic strain softening. Zhu et al. (1991) also gave the corresponding stress–strain relation.

The studies mentioned above assumed that, for analytical purposes, frozen soils exhibit zero volume change (Ladanyi and Johnston, 1973). However, as frozen ground which is rheologically sensitive, its volumetric deformation is a key factor. As part of the development of permafrost engineering, researchers sought more information on strain behavior. Experimental procedures were thus devised to measure volume changes of the samples during testing. However, they were not widely used due to the technical difficulties in being able to do so. For example, the equipment described by Vyalov et al. (1966) was not capable of measuring very small volume changes. These changes could not be measured either using the equipment of Goughnour and Andersland, 1968 R.R. Goughnour and O.B. Andersland, Mechanical properties of a sand–ice system, Journal of the Soil Mechanics and Foundation Division. American Society of Civil Engineers 94 (1968) (SM4), pp. 923–950.Goughnour and Andersland (1968) under confining pressure. Chamberlain et al. (1972) used a hand operated volume compensating device to measure volume changes in samples of frozen soil deformed under very high confining pressure and strain-rates, but it was doubtful whether the constant monitoring of volume changes during longer tests involving much slower strain-rates would be realistic. Moreover, the equipment described by Baker (1976) gave accurate results only when the permafrost samples tended to uniformly deform and when the test temperature was within the range of 0 to − 10 °C, with the confining pressures ranging from 0 to 0.25 MPa. O'Connor and Mitchell (1978) assembled an inexpensive system, adapted from conventional equipment and capable of measuring total volume changes during triaxial tests on permafrost specimens. This system, however, was not suited for tests in which large volumetric strains occurred rapidly. To address this issue, Zhu et al. (1996) introduced a new approach by modifying a commercial MTS-810 triaxial testing machine to measure the sample volume change, which could be used from room temperature down to − 30 °C and with confining pressures of 0–24 MPa.

When testing unfrozen soils, it is customary to correct for the height and cross-section of a specimen as a result of both consolidation and shear. For frozen soils, however, deformation after applying the confining pressure is minimal since there is no water drainage. It is also a current practice to consider the initial height, H0, and cross-sectional area, A0, as being equal to those after applying the confining pressure (Hc and Ac, respectively). That is, the differences between H0 and Hc, and A0 and Ac are normally overlooked when testing with frozen soils. This should not be the case, however. It was found that, although change of the specimen's cross-section and height was very small after application of the confining pressure for over 2 h, but it was significant during shearing, hence, that change must be considered. During shear the average cross-section of the specimen, At, gradually increases with the axial deformation (l), and the volume of the specimen (Vt) also changes. The present research was better undertaken the volumetric variations of frozen soils, and their influence on the average cross-section of the specimen, as well as its stress–strain behavior and compressive strength. This will be helpful in clarifying the behavior of frozen soil under static loading, and guide the design and the evaluation of foundations in permafrost regions.