Shear strength and crack characteristics are crucial factors in determining the engineering properties of expansive soils. In this study, direct shear tests, triaxial shear tests, and crack development tests were implemented to assess the impacts of cement content and dry-wet cycles on the mechanical behavior of expansive soil. The full-surface fracture indices of the triaxial specimens were extracted, and a comprehensive fracture index was calculated. Subsequently, a Support Vector Machine (SVM) model was established to analyze the development of cohesion. The findings indicated that the shear strength and its parameters decrease as the frequency of dry-wet cycles increases, and they initially rise and then fall with the increase in cement content. The maximum shear strength occurs at a cement content of 6%-8%. The correlation between comprehensive fracture index and strength index is better than that of single fracture index, and the correlation between average crack width is the strongest. The support vector machine model is established by replacing the average width of cracks with dry-wet cycle frequency. The model has a small prediction accuracy error, strong adaptability, and high potential. It can provide theoretical support and technical guidance for predicting strength indices using fracture parameters or for construction in expansive soil regions in engineering practice.