Application Research Of Catastrophe Theory In The Surrounding Rock Stability Analysis

Geotechnical and geological engineering systems show highly non-linear characteristics,the deformation、destruction and instability fully reflect the complexity of the system dynamics process. Starting from the non-linear characteristics of the systems, exploring its inherent universal law furtherly and developing scientific and rational theories and analytical methods which can reflect the system changing from gradual change to mutation and from the continuous to discontinuous will be an important developing direction. In this context, the catastrophe theory has been more widely used in the field of geotechnical engineering as a nonlinear theory.Current applications of catastrophe theory in geotechnical engineering mainly focus on the following two directions:(1) Simplify the engineering systems and create a simple physical model,then create the mathematical expression in line with the catastrophe model based on these work. This method can only be used to study a simple system which limits the application of catastrophe theory in geotechnical engineering.(2) Select a variable as the potential of a system, get the potential change sequence by means of numerical simulation, and then fit the potential function in line with the catastrophe model to study, but there is no uniform way of interpolation and lack research on the specific solution process in current applications.What is more, whether the criterion value is negative is the only criterion to judge a system status, and only a few sets of variables are calculated,which can not reflect the true change regulation of the criterion value from the overall in the process of catastrophe theory application.The main content of this thesis is to inquiry the application method of catastrophe theory in tunnel surrounding rock stability on the basis of numerical simulation. For the existing problems in current study, the paper has mainly done the following work:(1)Based on a large number of simulations, this thesis makes a comparison of the difference between middle point interpolation and end point interpolation and analyses the accuracy and reliability of the two interpolation methods.(2)Taking rock sample compression test as an example, sum up the change regulation of the criterion value, propose the comprehensive mutation standard based on the combination of the criterion variable curve trend and whether the criterion value is negative and work out the mutation threshold of rock sample mechanical system by changing the material parameters. (3) On the basis of the above work, study the impact of tunnel diameter and buried depth on the stability of the tunnel, analyse the tunnel status changes at different hole diameters and different buried depths using the catastrophe theory, get the defining depth of shallow tunnels and deep tunnels at different hole diameters.(4) In the interpretation of the criterion variable curve,this paper draws on the idea of "giant fluctuation" from dissipative structure theory, makes a scientific explanation for the trend of the criterion variable curve, points out that "giant fluctuation" is the cause of the system state mutation.