# A New Shear Strength Model with Structural Damage for Red Clay in the Qinghai-Tibetan Plateau
###### Abstract  
Under the background of climate warming in the Qinghai-Tibetan Plateau (QTP), frequent freeze-thaw cycling (FTC) brings about great geological disasters such as subgrade failure, landslides, and mudslides, which is closely related to the strength reduction caused by the structural damage of soils. In this study, to explore the association between macro shear strength and microstructure evolution of soils subjected to FTC, the red clay distributed widely in the QTP was chosen and used to conduct a series of triaxial shear and nuclear magnetic resonance (NMR) tests in the range of 1 to 7 FTCs. Triaxial shear test results reveal that the shear strength reduction of specimens mainly occurs within five FTCs, and the trend of peak deviator stress with increasing FTCs can be described in three stages: rapid descent (FTCs less than three), slow descent (FTCs between three and five), and stabilization (FTCs greater than five). NMR tests show that the \(T_{2}\) spectrum curves exhibit a distinct bimodal distribution characteristic, corresponding to macropores and micropores. Part of the micropores gradually develop into macropores with increasing FTCs, especially within five FTCs. The increase in macropores proportion leads to a loose soil structure, which is consistent with the deterioration of the shear strength of specimens. Finally, based on the experimental results and classical Mohr-Coulomb theory, a new shear strength model with structural damage for red clay has been proposed by introducing a damage factor expressed by \(T_{2}\) spectral area. fontsize  
Nowadays, the studies on the soil engineering properties after FTCs are mostly concerned with the change in the soil mechanical properties [10; 11; 12; 13], soil permeability and hydraulic properties [14; 15; 16; 17], dynamic properties and strength evolution of soil after FTCs [18; 19], and the freeze-thaw resistance characteristics of modified soil [20; 21; 22]. Previous studies have informed that the FTCs reduce the shear strength of soil [23]. However, the influence mechanisms of FTCs on soil strength failed to be completely unified due to different test materials and conditions [24]. Furthermore, there are few studies concerning the shear strength of red clay after FTCs. Understanding the variation of the shear strength of red clay is very important for the ecological and environmental protection of the QTP. In essence, the FTC affects the strength properties by changing the structure of the soil, and the changes in the strength of the soil can be explained by quantitative changes in the microstructure. Therefore, numerous scholars endeavor to explain the effect of FTCs on soil strength from the microstructure level. [PERSON] et al. [25] conducted mercury intrusion porosimetry (MIP) and scanning electron microscope (SEM) tests on silty clay. They found that repeated FTC processes altered the distribution of pores inside specimens, with the increase in penetration pores and cracks, resulting in a decline in the strength of specimens. However, both MIP and SEM tests have a size effect, and the test specimens need to be freeze-dried, which leads to the distortion of pore data to a certain extent. Moreover, the utilization of computer tomography (CT) technology in geotechnical research is increasingly mature. The structural damage of soil induced by FTCs was analyzed quantitatively using CT scanning technology [26; 27; 28]. [PERSON] et al. [29] attempted to uncover the change mechanism of the silty clay strength in the QTP under the influence of FTCs through SEM and CT tests. The findings revealed that when the number of FTCs increased, the structure of silty clay became loose, causing the bond between soil particles to weaken. After five FTCs, the porosity of silty clay and the content of large aperture pores increased significantly. However, CT detection is expensive, and the post-processing of image results is complex. Nuclear magnetic resonance (NMR) can carry out nondestructive detection of the pore distribution of objects.