Strength distributions of warm frozen clay and its stochastic damage constitutive model

There are many defects, such as fissures and cavities, in warm frozen clay and in warm ice-rich frozen clay. These defects are distributed randomly, which make some mechanical properties of these clays exhibit great uncertainty. Thus it is unreasonable to take some deterministic values as the mechanics parameters of these frozen clays. Furthermore, warm frozen clay and warm ice-rich frozen clay are less stable than clays at colder temperatures. Therefore, it is necessary to determine the strength and constitutive relationship of these clays using probabilistic methods. In this paper, based on the characteristics of the random distribution of defects in the warm frozen clay and warm ice-rich frozen clay, the strength distribution laws for both clays are investigated at − 0.5 °C, − 1.0 °C and − 2.0 °C through a series of experimental data, respectively. The investigated results show that the Weibull distribution can more closely reflect the strength distribution law than other probability distributions. Based on the results mentioned above, a stochastic damage model for the warm frozen clay and warm ice-rich frozen clay was developed using the continuous damage theory and probability, as well as statistic theory. Comparing theoretical results of the model with experimental data at these three temperatures, respectively, it is found that the stress-strain relationships of the two kinds of frozen clays, especially their deformation characteristics after failures, could be described by the model very well. Since the range of strength variation for both kinds of frozen clays is very large, it is unsafe and unreasonable for engineering design to use the average strengths of frozen clay soils. The reliability of the strength of these two clays was investigated and discussed on the basis of the fact that the strength of warm frozen clay and warm ice-rich frozen clay satisfy the Weibull distribution.