###### Abstract
To estimate the strength loss of rocks after freeze-thaw cycles, [PERSON] [32] developed a multiple regression model consisting of uniaxial compressive strength, dry density, number of cycles, and porosity based on multiple linear regression analysis to predict with high accuracy the uniaxial compressive strength of rocks (similar to the present test) after 25 freeze-thaw cycles. [PERSON] [33] used an exponential decay model for the first time to describe the loss of freeze-thaw strength of rocks and verified the validity of the model by freeze-thaw tests on 10 different lithologies. [PERSON] [34], [PERSON] [35], [PERSON] [36], and [PERSON] [37] studied the relationship between the physical and mechanical properties of rocks after freeze-thaw cycles and the number of freeze-thaw cycles using an exponential function model and evaluated the disintegration rate of rocks under the action of freeze-thaw cycles using decay constants and the half-life of each mechanical parameter. [PERSON] [38] and [PERSON] [39] theoretically established a rock strength deterioration model and verified its rationality based on the trends of the expansion of pores or microfractures after freeze-thaw cycles. [PERSON] [40], [PERSON] [41], and [PERSON] [42] studied the freeze-thaw deterioration characteristics of rocks using fine structure testing techniques (optical microscopy, X-ray diffraction analysis, nuclear magnetic resonance, and CT investigation) and found that the number and size of pores increased after the freeze-thaw cycling of rocks and that medium-sized and small-sized pores increased significantly in size. In summary, the current research on indoor freeze-thaw tests and strength decay models of rock in cold regions has achieved some results, but there are still some shortcomings, which are mainly reflected in the following two aspects. 1. The study of freeze-thaw degradation characteristics of excavated unloaded rock masses on steep and high slopes in cold regions is inadequate. The excavation unloading relaxation phenomenon on steep and high slopes is significant, and the damage and rupture of rock masses in a certain range in the excavation face provides a means of intervening in freeze-thaw erosion. Therefore, it is necessary to investigate the freeze-thaw erosion and deterioration of excavated and unloaded rock masses of steep and high slopes in regions with seasonal freezing by considering the indoor test program of the interaction between excavation disturbance and freeze-thaw cycles;
2. Most of the studies on freeze-thaw strength decay models are based on the attenuation of uniaxial peak strength deterioration, while the rock body of the reservoir bank of the excavation and unloaded zone is still in a three-way stress state and has an inhibitory effect on freeze-thaw cycle erosion. Therefore, the established freeze-thaw strength decay model should be realistic and reflect the decay of freeze-thaw strength under the stress state of the rock body of the reservoir bank of the excavation and unloaded zone. In this paper, based on the freeze-thaw cycle erosion of an excavation unloaded rock mass of a steep and high bank slope in hydropower projects in cold regions, the unloaded-damaged sample is prepared for the typical sandstone of a reservoir bank slope of a hydropower station in a cold region through a triaxial unloading confining pressure test. A freeze-thaw mechanics test is then carried out to study the freeze-thaw deterioration characteristics of the unloaded-damaged sample. A freeze-thaw strength decay model is established, and the model parameters are identified by combining the test results and subsequent validation. The results of the study are useful for the prediction of freeze-thaw hazards and the design of support schemes for excavated slopes in cold regions.