## 4 Analysis and Discussion  
### Analysis of the Micro-Deformation Mechanism of Rock  
At different stages of the experiment, a digital microscope was used to observe the microstructures of cracked red sandstone in the dry state, water-saturated state, and after 40 freeze-thaw cycles from two fixed angles, as shown in Figure 13. These microscopic images provide an intuitive representation of the changes in rock skeleton particles during freeze-thaw cycles, highlighting the deformation and damage caused by freeze-thaw action. Additionally, the deformation results revealed by the microscopic images effectively validate the strain data obtained from monitoring experiments.  
Figure 12: (**a**) Comparison of strain characteristic values for the 20 mm depth cracked rock specimen; (**b**) comparison of strain characteristic values for the 30 mm depth cracked rock specimen; (**c**) comparison of strain characteristic values for the 40 mm depth cracked rock specimen.  
The red sandstone specimens in the dry state, water-saturated state, and after 40 freeze-thaw cycles exhibit an overall reddish-brown color with uniform particle distribution. In the dry state, the bonding between particles via white debris-like cementing material is clearly visible, with small intergranular pores forming a porous structure. In the water-saturated state, the rock pores are fully filled with water molecules. Comparing microscopic images after 40 freeze-thaw cycles with the initial dried state reveals significant changes. Under the effects of frost heaving forces and thermal expansion and contraction of skeleton particles, the debris-like cementing material sustained considerable damage, leading to a reduction in cementing material. The original pores expanded, the newly formed pores became more numerous, and the remaining skeleton particles were more clearly revealed.  
Rock, as a porous medium composed of solid skeleton grains and intergranular pores, has a structure formed by interconnected solid skeleton grains. The pores are usually filled with one or more fluids. The previous literature has clarified that rock deformation is caused by the deformation of skeleton grains and changes in their arrangement [33]. This manifests in two forms, \"body deformation\" and \"structural deformation\", as shown in  
Figure 13: Comparison of (**a**) 300\(\times\) magnified image of angle 1 in the dry state; (**b**) 300\(\times\) magnified image of angle 2 in the dry state; (**c**) 300\(\times\) magnified image of angle 1 in the water-saturated state; (**d**) 300\(\times\) magnified image of angle 2 in the water-saturated state; (**e**) 300\(\times\) magnified image of angle 1 after 40 freeze–thaw cycles; and (**f**) 300\(\times\) magnified image of angle 2 after 40 freeze–thaw cycles.  
Figure 14. The actual deformation of the rock is a combination of these two basic types of deformation, and the total strain is the algebraic sum of the body strain and structural strain. The descriptions of body and structural deformation in rocks are as follows:  
1. Body Deformation: This refers to the overall deformation caused by the deformation of the skeleton grains themselves, which is classified as elastic deformation. During this process, changes in the stress within the skeleton grains lead to changes in their volume, but the arrangement of the skeleton grains remains unchanged. Therefore, the body stress (\(\sigma_{c}\)) determines the body deformation of the rock.
2. Structural Deformation: This refers to the overall deformation caused by changes in the arrangement of the skeleton grains, which is classified as plastic deformation. During this process, changes in the contact stress between the skeleton grains result in relative displacement between them, altering the arrangement of the skeleton grains, though the volume of the grains themselves does not change. Therefore, the contact stress (\(\sigma_{c}\)) between the skeleton grains determines the structural deformation of the rock.  
Rock skeleton particles