Symmetrical global sensitivity analysis (SGSA) can help practitioners focusing on the symmetrical terms of inputs whose uncertainties have an impact on the model output, which allows reducing the complexity of the model. However, there remains the challenging problem of finding an efficient method to get symmetrical global sensitivity indices (SGSI) when the functional form of the symmetrical terms is unknown, including numerical and non-parametric situations. In this study, we propose a novel sampling plan, called symmetrical design, for SGSA. As a preliminary experiment for model feature extracting, such plan offers the virtue of run-size economy due to its closure respective to the given group. Using the design, we give estimation methods of SGSI as well as their asymptotic properties respectively for numerical model and non-parametrical model directly by the model outputs, and further propose a significance test for SGSI in non-parametric situation. A case study for a benchmark of GSA and a real data analysis show the effectiveness of the proposed design.

The mechanical response characteristics of rocks under cyclic loading conditions are crucial factors for evaluating and analyzing the stability of rock mass during underground excavation. In this study, based on fractal theory and a series of tests using the MTS815.02 rock mechanics test system, the classification and fractal characteristics of limestone specimen fragments are investigated. The results show that limestone specimens subjected to cyclic loading can generate more small‐sized fragments than conventional compression, but the large‐fragment‐producing abilities of the two tests exhibit small difference. The mass fraction of the fragments in the cyclic loading test is obviously greater than that in the conventional test when the fragment size is less than 4.75 mm; however, only a small difference is observed between the cyclic loading tests with frequencies of 0.25 and 0.5 Hz. In the same type of test, a confining pressure is helpful in reducing the fragmentation of limestone specimen. As the size interval decreases, the shapes of limestone fragment transition from rectangular to long slice and then to square. The results also indicate that the confining pressure has a significant influence on the size‐quantity and size‐mass fractal dimensions of limestone fragments. The former has a positive correlation with the confining pressure, whereas the latter decreases with confining pressure. The conclusions obtained in this investigation can enrich the theoretical research on the failure response and mechanism of rock under cyclic loading conditions.