Research On The Criterion Of The Stability Assessment System Of Underground Caverns Based On Catastrophe Theory

As the highlight of water resources industry in China transferred to the southwest of alpine valleysgradually, underground powerhouse has become a vital component of the water conservancy constructionin recent years.Owe to the concerns of the feature and security of hydropower engineering, research on the stability of surrounding rock of underground powerhouse system is generally indispensable. However, its analysis methodshavenot yet reach an agreement for the fieldin consequence of the specific nonlinearity and complexity of geotechnical engineering. This studyis committed to provide a quantitative criterion forthe stability of surrounding rock of underground caverns conditionsbased on catastrophe theoryand finite element numerical analysis method.The contents of this paper are mainly focused on the following four aspects.Firstly, according to the equilibrium surface and plane form of the cusp catastrophe, the paperparticularlyexpoundedhow the continuous motion of control variable give rise tocatastrophepoint in the state variables. Catastrophe characteristic value is the main index for judging catastrophes. Once the catastrophe characteristic value changing from positive to negative and afterwards to positive, that is to say the projection of the equilibrium point get through the bifurcation set, the equilibrium point jumped from upper leafvia the bifurcation set to the lowerleaf, state variablesoccurred in catastrophe point. Through the analysis of the trajectory of the equilibrium pointprojection, catastrophe process can be easy to access.Secondly, in the case of potential function could not be expressedaccurately, the approximate form ofthe potential functioncan be obtained by the inversion of the computedspecific solutions.A generalized nonlinear inversion method was used for inverting the specific solution sequenceto achieve the nonlinear dynamics equation of thestate variables and to deduce the expression of potential functions. Through the linear change method, the cusp catastrophewas turned into the standard form. The corresponding potential function was the averagepotential function to a certain stage.Thirdly, through the analysis of the change of state of surrounding rock during the process of excavation, the four most representative state variables( the average displacement, strain energy, the plastic dissipation energy and entropy) of the amount of the overall change of state of surrounding rock were picked as the criterion of instability. By the calculation of the mentioned four state variables in each excavation step, the potential functionswere fitted and the catastrophepoints were distinguished. Meanwhile, through the analysis of trajectory of the equilibrium point projection and thecatastrophe characteristic value, the step of the instability of surrounding rock excavation was finally determined.Lastly, the strength subtraction method was used while systemswere stable after excavationto calculate the corresponding displacementof arch,strain energy and the yield area under different reduction factor.The potential functions and standard form of cusp catastrophe wereinvertedby these three criteria.The characteristic values of catastrophe analysis were calculated for obtaining the reduction factor when the catastrophe emerged in, which also signify the safety factor of the system.