In order to study the ductile deformation characteristics and failure process of plain concrete under uniaxial compression, this paper proposes a new constitutive model. The new model was used to fit and analyze the constitutive curve of concrete under uniaxial compressive under various degradation forms and was compared with the traditional constitutive models. Finally, the new model was used to quantitatively analyze and predict the stress–strain curve of concrete in different degradation periods of a set of freeze–thaw measured data. The results show that, compared with the traditional constitutive model, the new model is simple in form and has few parameters, and the numerical value of the parameter can reflect the ductile deformation capacity of concrete. The fitting curve of the new model has the highest fitting degree with the measured stress–strain curve of concrete, and the goodness of fit (R²) is also the largest. The new model is suitable for fitting the stress–strain curve of concrete under uniaxial compression under various deteriorating forms, and the degree of fit between the constitutive prediction curve and the measured curve is high. It can be seen from the fitting results of the new model parameters that the ductile deformation capacity of concrete decreases first and then increases slightly, which is inconsistent with the law of gradual deterioration of strength. There is a minimum moment of ductility deformation capacity of concrete (MDC). The MDC of O-C40 concrete is about 114 freeze–thaw cycles, and the MDC of O-C50 concrete is about 116 freeze–thaw cycles; the degree of fit between the constitutive prediction curve and the measured curve is high. We hope that the improvement mentioned offers valid reference to the study of ductile deformation characteristics and failure process of compressed concrete under different deterioration forms.

Deformation rate analysis utilizes deformation memory effect (DME) that is one of the fundamental properties of rock, to estimate in situ stress underground. It could be influenced by the stress history which has been subjected to in the past. To understand the influence under the cyclic loading path, in the experimental study, different stress levels were applied on sandstone samples and two types of granite samples. In the theoretical investigation, the sliding friction model consisting of multiple microstructure surfaces is considered in this paper. Both experiments and the theoretical model show that when the number of cyclic loading times keeps increasing, (1) the stress read at the DRA inflection is getting closer to the previously cyclic stress; (2) the angle at the DRA inflection becomes sharper, which gives clearer inflection point; and (3) the strain differential amplitude in the DRA curve gradually decreases and then toward a stable value. An upper limit exists for influence, indicating that the best cyclic loading times occur when the pulse amplitude of the strain differential stops changing. It is confirmed that the multiple cyclic loading method provides a better outcome for experiment using artificial preload when DME is utilized for stress reconstruction. Without other factors disturbing, the memory information of the in situ stress would hardly lose under the history of cyclic loading.