Bulking instability analysis of the horizontally stratified rock reinforced with bolts based on cusp catastrophe model

The sedimentary rock masses are commonly seen in underground engineering, and it is a threat to the safety of underground constructions greatly. Bolt supporting reinforcement works effectively in enhancing the rock in underground engineering. In this study, the roofs made of the horizontally layered rock were simplified to the rock plate structure with two different constrains, and a cusp catastrophe model was established based on the structural mechanics. With the application of the developed cusp catastrophe model, the influences of ratio of span to thickness, the amounts, and the preload of the bolts on the stability of the stratified rock were studied. Findings show that the installation of bolts can increase the anti-bulking capacity of the layered rock. The bolts can change the failure of the layered rock from bulking failure to shear failure. Improving the integrity of the layered rock is also helpful for enhancing the resistance to the bulking instability.

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A cusp catastrophe model for alluvial channel regime and classification of channel patterns

Geoscientific Model Development Discussions ◽

10.5194/gmdd-7-1477-2014 ◽

2014 ◽

Vol 7 (1) ◽

pp. 1477-1497

Author(s):

Y. Xiao ◽

X. J. Shao ◽

Y. Yang

Keyword(s):

Three Dimensional ◽

Cusp Catastrophe ◽

Channel Stability ◽

Catastrophe Model ◽

Cusp Catastrophe Model ◽

Alluvial Channel ◽

The Stability ◽

Three Dimensional Coordinate ◽

Channel Patterns ◽

Natural Rivers

Abstract. A cusp catastrophe model for alluvial channel regime is established by selecting suitable parameters to reflect channel stability. An equation is obtained from the equilibrium state of channel regime, which is a cusp catastrophe surface in a translated three dimensional coordinate. The stability of channel patterns can be identified by such a model in a direct way, and the 2-D projection of the cusp catastrophe surface can be used to classify alluvial channel patterns. Predictions based on this model are consistent with field observations involving about 100 natural rivers. The results indicate that this method may be applied to study the regime of natural rivers and to assist decision making in river engineering.

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A Cusp Catastrophe Model for Alluvial Channel Pattern and Stability

Water ◽

10.3390/w12030780 ◽

2020 ◽

Vol 12 (3) ◽

pp. 780

Author(s):

Yi Xiao ◽

Shengfa Yang ◽

Mi Li

Keyword(s):

Cusp Catastrophe ◽

New Approach ◽

Channel Pattern ◽

Catastrophe Model ◽

Cusp Catastrophe Model ◽

Complicated Process ◽

Alluvial Channel ◽

The Stability ◽

Channel Patterns ◽

Natural Rivers

The self-adjustment of an alluvial channel is a complicated process with various factors influencing the stability and transformation of channel patterns. A cusp catastrophe model for the alluvial channel regime is established by selecting suitable parameters to quantify the channel pattern and stability. The channel patterns can be identified by such a model in a direct way with a quantified index, which is a 2D projection of the cusp catastrophe surface, and the discriminant function is obtained from the model to distinguish the river state. Predictions based on this model are consistent with the field observations involving about 150 natural rivers of small or medium sizes. This new approach enables us to classify the channel pattern and determine a river stability state, and it paves the way toward a better understanding of the regime of natural rivers to assist decision-making in river management.

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Comparison of the Fold and Cusp Catastrophe Models for Tensile Cracking and Sliding Rockburst

Mathematical Problems in Engineering ◽

10.1155/2021/6682999 ◽

2021 ◽

Vol 2021 ◽

pp. 1-10

Author(s):

Xinjiang Wei ◽

Xiao Wang ◽

Taotao Chen ◽

Zhi Ding ◽

Xi Wu

Keyword(s):

Critical Loads ◽

Failure Modes ◽

System Stability ◽

Cusp Catastrophe ◽

Practical Applications ◽

Catastrophe Model ◽

Cusp Catastrophe Model ◽

The Stability ◽

Catastrophe Models ◽

Fold Catastrophe

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.

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