## 3 Results
### Analysis of Strain Characteristic Values of Cracked Red Sandstone Under Multiple Freeze-Thaw Cycles
#### 3.3.3 Thermal Expansion Amplitude  
1. Measurement Points on the Short Edge and Long Edge of the Crack  
As shown in Figure 10, with the increase in the number of freeze-thaw cycles, the thermal expansion amplitudes on both the short and long sides of the cracks in the rock specimens with three different crack depths remained relatively stable. The average thermal expansion amplitudes for the short edge of the cracks with depths of 20 mm, 30 mm, and 40 mm were 937 \(\mu\varepsilon\), 1057 \(\mu\varepsilon\), and 1568 \(\mu\varepsilon\), respectively. The average thermal expansion amplitude on the short edge of the 40 mm deep crack was 1.67 times that of the 20 mm deep crack and 1.48 times that of the 30 mm deep crack. The average thermal expansion amplitudes for the long edge of the cracks with depths of 20 mm, 30 mm, and 40 mm were 873 \(\mu\varepsilon\), 1035 \(\mu\varepsilon\), and 1437 \(\mu\varepsilon\), respectively. The average thermal expansion amplitude on the long edge of the 40 mm deep crack was 1.65 times that of the 20 mm deep crack and 1.39 times that of the 30 mm deep crack. The deeper the crack, the larger the average thermal expansion amplitude for both the short and long edges. This phenomenon is primarily due to the greater cold contraction deformation in rocks with deeper pre-existing cracks, which leads to a larger recovery deformation when the rock temperature returns to room temperature.  
Figure 10: (**a**) Thermal expansion amplitude of the crack’s short edge; (**b**) thermal expansion amplitude of the crack’s long edge.  
Figure 9: (**a**) Cold contraction amplitude at the symmetric point of the crack’s short edge; (**b**) cold contraction amplitude at the symmetric point of the crack’s long edge.  
Symmetric Measurement Points on the Short Edge and Long Edge of the Crack  
As shown in Figure 11, with the increase in the number of freeze-thaw cycles, the thermal expansion amplitudes of both the short edge and long edge of the cracks in the rock specimens with three different crack depths show minimal changes. The average thermal expansion amplitudes for the short edge of the cracks with depths of 20 mm, 30 mm, and 40 mm are 1022 \(\mu\varepsilon\), 1379 \(\mu\varepsilon\), and 900 \(\mu\varepsilon\), respectively. The 30 mm depth cracked rock specimen exhibits the largest average thermal expansion amplitude for the short edge, followed by the 20 mm depth specimen, with the 40 mm depth specimen showing the smallest amplitude. This indicates that the thermal expansion amplitude variation pattern at the symmetric points of non-penetrating cracks differs from that of the surface points but is generally consistent with the cold contraction amplitude variation pattern. For the long edge, the average thermal expansion amplitudes for the cracks with depths of 20 mm, 30 mm, and 40 mm are 1055 \(\mu\varepsilon\), 937 \(\mu\varepsilon\), and 1287 \(\mu\varepsilon\), respectively. The 40 mm depth cracked rock specimen has the largest average thermal expansion amplitude at the symmetric point on the long edge, followed by the 20 mm  
In summary, as the depth of the pre-existing crack increases and the depth of the rock matrix at the symmetric points decreases, the average cold contraction and thermal expansion amplitudes of both the short and long edges transition from initially being smaller than those at the symmetric points to ultimately becoming larger than those at the symmetric points. The main reason for this phenomenon may be that as the crack depth increases, the surface points of the pre-existing crack experience less constraint from the surrounding rock matrix. This allows for more pronounced deformation during freeze-thaw cycles. Compared to the constraints at the symmetric points, the degree of freedom at the surface points of the pre-existing crack increases significantly, resulting in the deformation amplitude gradually exceeding that of the symmetric points.