Due to the emission of carbon dioxide and other greenhouse gases, the global climate is warming. As the world’s biggest emitter of carbon emissions, China faces a more severe challenge in reducing carbon emissions than developed countries. A reasonable prediction of the carbon peak in China will help the government to formulate effective emission reduction paths. This paper analyzes the changes in carbon emissions in China from 2004 to 2020, uses the STIRPAT model and scenario analysis method to predict carbon emissions from 2021 to 2030, and then calculates the carbon efficiency during carbon peaking to select the most effective carbon peak path for China. The results show that China’s carbon emissions increased year by year from 2004 to 2020. Under the baseline scenario, China is unlikely to reach its carbon peak before 2030. Under the regulatory scenarios, China can reach its carbon peak before 2030. The peak values from high to low are seen with the rapid development-weak carbon control scenario, rapid development-intensified carbon control scenario, slow development-weak carbon control scenario and slow development-intensified carbon control scenario, respectively. Correspondingly, China will peak its carbon emissions in 2029, 2028, 2028 and 2028, respectively, according to these scenarios. The carbon efficiency under the rapid development-weak carbon control scenario is the highest, which means that accelerating the growth rate of population, GDP and urbanization while moderately carrying out the transformation of industrial structure and energy structure is an effective way to achieve the goal of “carbon peak by 2030”.

In the process of roadway excavation, the rock mass around the roadway is often subjected to cyclic loads, and the rock mechanical properties and strain energy evolution under cyclic loads are obviously different from those under compression, so it is urgent to carry out research on rock mechanical properties and strain energy evolution under cyclic loads. This study aims to investigate the evolution of residual strain and strain energy in rocks under uniaxial cyclic loading-unloading experiments (UCLUE). Four types of rocks, namely coal, white sandstone, red sandstone, and granite, were subjected to uniaxial compression experiments (UCE) and various uniaxial cyclic loading-unloading experiments (UEACLUE). The findings are as follows: analysis of UEACLUE revealed a gradual decrease in residual strain with an increasing number of cycles, leading to its eventual disappearance. However, if the cyclic loading-unloading (CLU) was continued beyond this point, the rocks displayed a reappearance of residual strain. The number of cycles required to eliminate residual strain was found to be inversely proportional to the peak strength of the rocks, while directly proportional to the upper limit value of UCLUE. Among the different stages of the uniaxial cyclic loading and unloading test, the plastic stage of white sandstone exhibited the largest disparity in dissipated strain energy, followed by the plastic stage of red sandstone, with coal displaying the smallest difference. Analysis of dissipated strain energy in the four types of uniaxial cyclic loading and unloading tests revealed differences of 0.00348 mJ▪mm⁻³, 0.03488 mJ▪mm⁻³, 0.02763 mJ▪mm⁻³, and 0.01619 mJ▪mm⁻³ in the plastic stage for the respective rock types. Furthermore, examination of the input strain energy density (ISED) and dissipated strain energy density (DSED) during the CLU process showed a linear relationship between these variables. Additionally, the investigation of ISED and DSED in other types of UCLUE demonstrated adherence to the cyclic-linear dissipation law (CLDL). The study of mechanical properties and strain energy evolution under CLU is of positive significance for the development of rock fatigue damage and rock damage mechanics.

To investigate the influence of the length-to-diameter (L/D) ratio and strain rate on the evolution of strain energy of sandstone under uniaxial compression, experimental tests were conducted using the RMT-150B rock mechanics test system. Specifically, uniaxial compression experiments (UCE), uniaxial loading-unloading experiment(ULUE) and uniaxial cyclic loading-unloading experiments (UCLUE) were performed. The results show that: 1) Based on an investigation of the Kaiser effect in UCLUE, it is postulated that a small degree of loading-unloading has negligible impact on the storage of strain energy in rock masses. The hypothesis regarding the limited influence of loading-unloading on the elastic strain energy storage of rocks is confirmed through a comparative analysis between the elastic strain energy storage in UCLUE and ULUE. 2) By analyzing the ESED and ISED of sandstone under different L/D ratios and strain rates, it is found that it follows the linear energy storage law. The evolution of elastic strain energy is not affected by strain rate. Therefore, the UCLUE at any strain rate can analyze the elastic strain energy of uniaxial compression experiment with the same size at any strain rate, and provide a new method for strain energy analysis at different length-diameter ratios and strain rates. 3) When the stress of sandstone samples of equal size is equal, the smaller the strain rate, the longer the loading experiment of sandstone, the more time the friction development and interconnection of cracks in sandstone are, and the more dissipated strain energy and input strain energy are generated. 4) Smaller L/D ratios are associated with larger ESED and DSED values in sandstone. As the stress intensifies, the ESED and DSED of certain sandstones with larger L/D ratios experience a sharp increase when approaching the failure stress. Under equal stress levels, it is possible for sandstones with larger L/D ratios to exhibit higher ESED and DSED values compared to those with smaller L/D ratios.