Study of the compressive strength and damage constitutive model of frozen sand has an important significance for construction design and prevention-control of soil destabilization damage in frozen soil engineering. In this paper, a new triaxial apparatus was used to carry out a series of triaxial compression tests of frozen sand under different confining pressure and strain rate, based on which a segmental strength criterion is established to describe the damage of microelement strength of frozen sand. Assuming that the microelement strength of frozen sand obeys the Weibull distribution, a statistical damage constitutive model of frozen sand is established by statistics and continuous medium mechanics. Based on the test data, the model parameters were calculated and the relationship between the strength distribution parameters, the strain rate, and the confining pressure was obtained. Finally, the calculated values of the damage constitutive model are compared with the experimental values, and it is found that the model can simulate the stress-strain process curve of frozen sand well and can reflect the transition of the curve from elasto-plasticity to strain-hardening when the strain rate increases from low to high. The results of this study have an important significance in engineering construction of cold regions and artificial ground freezing projects.

In order to reveal the influence law of freezing pressure and confining pressure on the strength characteristics of frozen sand, with the self-developed high-pressure frozen soil triaxial instrument, the triaxial compression tests of frozen sand under different freezing pressures and confining pressures were carried out. The test results show that the freezing pressure will not change the stress–strain curve of the frozen sand. Similar to the confining pressure, the freezing pressure influences the strength of the frozen soil in two ways: strengthening and weakening. The threshold confining pressure resulting from the test was about 45 MPa. Through comparison of the initial elastic modulus with the secant elastic modulus at 0.5 times the strength, it is found that the initial elastic modulus is more appropriate to use in engineering calculations. The internal friction angle is greatly affected by the freezing pressure, and cohesion shows little change with the freezing pressure. Compared with the test results and other constitutive equations, it is found that the constitutive equation established in this paper considering the effect of freezing pressure can better describe the stress–strain relationship of the pressurised frozen sand.