Abstract
The failure modes of rockburst in catastrophe theory play an essential role in both theoretical analysis and practical applications. The tensile cracking and sliding rockburst is studied by analyzing the stability of the simplified mechanical model based on the fold catastrophe model. Moreover, the theory of mechanical system stability, together with an engineering example, is introduced to verify the analysis accuracy. Additionally, the results of the fold catastrophe model are compared with that of the cusp catastrophe model, and the applicability of two catastrophe models is discussed. The results show that the analytical results of the fold catastrophe model are consistent with the solutions of the mechanical systems stability theory. Moreover, the critical loads calculated by two catastrophe models are both less than the sliding force, which conforms to the actual situations. Nevertheless, the critical loads calculated from the cusp catastrophe model are bigger than those obtained by the fold catastrophe model. In conclusion, a reasonable result of the critical load can be obtained by the fold catastrophe model rather than the cusp catastrophe model. Moreover, the fold catastrophe model has a much wider application. However, when the potential function of the system is a high-order function of the state variable, the fold catastrophe model can only be used to analyze local parts of the system, and using a more complex catastrophe model such as the cusp catastrophe model is recommended.
Highlights
Rockburst is a common geological disaster encountered during underground engineering excavations in high-stress areas
The critical loads and the instability of the tensile cracking and sliding rockburst have been investigated by applying two rockburst models based on the catastrophe theory
The applicability of these two models, including the fold and the cusp catastrophe model, has been analyzed. e following conclusions can be obtained: (1) e critical load of instability has been obtained by applying the fold catastrophe model to analyze the simplified mechanical model of the tensile cracking and sliding rockburst. e results are consistent with the theoretical solutions from the theory of mechanical system stability, demonstrating that the proposed method is reliable
Summary
Rockburst is a common geological disaster encountered during underground engineering excavations in high-stress areas. Through detailed field investigation, the failure modes of rockburst were summarized, simplified mechanical models were established, and the critical conditions of stability were reached at last [21]. According to the damage mechanism, researchers have identified failure models for different types of rockburst. E tensile cracking and sliding rockburst often occurs in brittle layered or massive rock bodies with microcracks, and the rockburst area is generally located at the tunnel sidewall. Based on a brief overview of the known rockburst failure modes and the principle of catastrophe theory, this paper applied the catastrophe theory to calculate the critical loads of the tensile cracking and sliding rockburst. According to the theory of mechanical system stability, the critical loads of the tensile cracking and sliding rockburst are calculated and compared with those calculated by the two catastrophe models to verify the application of these two models. An engineering example is introduced to verify the correctness as well
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