To investigate the failure effects of critical fissures in rock specimens subjected to plane strain compression (PSC), five types of internal fissures in rock specimens were designed and twelve PSC tests were conducted for two lithologies based on the discrete element method (DEM). The results were analyzed in terms of the fracture mode, data characteristics, and crack evolution. The results indicated the following. (1) The rock samples with a critical fissure under PSC showed a weak face shear fracture mode, which was influenced by lithology, fissure angle, and fissure surface direction. (2) There were four critical expansion points (CEPs) of axial stress of the rocks under PSC, which were the stage signs of rock materials from local damage to complete fracture. The rock-bearing capacity index (RockBCI) was further proposed. (3) The bearing capacity of rock samples with horizontal fissures, fissures whose angles coincided with the fracture surface, and fissures whose surface was perpendicular to the lateral confine direction was the worst; their BCI² values were found to be 80.6%, 70.8%, and 56.9% of the rock samples without any fissures, respectively. The delayed fracture situation under PSC was identified and analyzed. (4) The crack evolution followed the unified law of localization, and the fissures in the rocks changed the mode of crack development and the path of the deepening and connecting of crack clusters, as well as affecting the time process from damage to collapse. This research innovatively investigated the behavior characteristics of rock samples with a fissure under PSC, and it qualitatively and quantitatively analyzed the bearing capacity of rock mass from local damage to fracture.

Energy sustainability and the establishment of the ‘national water network’ are all inseparable from the construction of underground engineering. Monitoring indices for the surrounding rock are vital for the safety management of underground engineering construction, which determines the actual state of the surrounding rock. The complexity of deep underground engineering construction leads to many situations that cannot be predicted and explained by existing experience. Therefore, it is necessary to identify which monitoring index best represents the surrounding rock damage. Currently, there are no advanced and convenient effectiveness evaluation schemes for surrounding rock monitoring information. To fill the technical gap, this study introduces the volume expansion rate (VER) index for surrounding rock and proposes a machine learning (ML)-based evaluation scheme for the effectiveness of monitoring indices. First, six conditions with different in situ stresses are designed, and tunnel excavation monitoring tests are conducted. Second, the surrounding rock damage determination experiments using the ML classification algorithm are performed, and the accuracy matrix and index significance scores are obtained. The evaluation results show that: (1) The multi-class logistic regression algorithm is more suitable for determining surrounding rock damage with high accuracy and more appropriate significance evaluation outcomes. (2) Under the higher in situ stress condition, the tangential stress is more sensitive to the surrounding rock damage. (3) As the in situ stress increases, the significant monitoring indices demonstrate a transition ‘from shallow to deep, from regional damage to point failure’, describing the instability of the surrounding rock and inspiring a new instability criterion for surrounding rock.

Accurate identification of building structure frequencies forms the basis for damage detection. The structural dynamic response signal, under ambient excitation, can be transformed into a superposition of multiple single-frequency exponentially damped sinusoids combined with random white noise. However, the peak power spectrum of the response signal tends to exhibit line splitting, compromising the precision of frequency identification. This study examines the accuracy characteristics of the single-frequency free damping vibration signal (SFFDVS) and derives the Cramer–Rao lower bound for the frequency estimator. It thoroughly analyzes the factors influencing the accuracy of SFFDVS frequency identification. The study reveals that the primary cause of spectral line splitting is the random delay inherent in SFFDVS. Based on the maximum likelihood method (MLM), this research introduces the MLM algorithm for SFFDVS and provides a simulation analysis. The findings indicate that the MLM estimation algorithm for frequency parameters effectively addresses spectral line splitting and offers robust noise resistance and recognition accuracy.