Stability Analysis Method Of The Surrounding Rock In Tunnel Engineering Based On The Reliability Theory

Complex geological and geotechnical conditions,limited and costly site investigation and insufficient information are encountered in tunnel engineering,which brings inevitable uncertainties.Conventional deterministic factor of safety method deals with these uncertainties simply,but it could not depict the actual reliability of the tunnel support systems including the surrounding rock and the supporting structures.Reliability theory,which can address the uncertainties rationally and explicitly and could play a supplementary and useful role,is gett ing more and more attention in tunnelling engineering.From the point that the function of the supporting structures is to strengthen the surrounding rock to improve its safety and stability,a factor of safety of the surrounding rock stability is developed based on the convergence confinement method(CCM)and the critical strain in this paper,combining the reliability based design(RBD)and the factor of safety.On this basis,the optimization of the uncertainty characterization of the rock mass variables,the tunnel preliminary support design calculation and trial,and the reliability checking calculations of the surrounding rock and the support structures based on the critical strain and the confining displacement respectively are studied,forming a tunnel preliminary support design calculation method based on the factor of safety of the surrounding rock stability.The main contents are as following:Firstly,based on the geometric meaning of the reliability index,a practical reliability optimization model is constructed,including the supplement of a judgment formula to the sign modification of the reliability index and the consideration of the non-negativity of the rock mass parameters.By using the optimal functions nested in the numerical software,this reliability model can simply address the transformation problems of the performance function and the partial derivatives and the algorithm problem,which avoids the complicated computations and improves the convergence.Furthermore,it can obtain an actual s ign of the reliability index.Based on this,more accurate reliability methods are constructed combining the finite difference method and importance sampling,respectively.Based on these reliability methods,the reliability based design problems are translated into the solutions to the nonlinear function through mathematical modelling,and a direct and simple solution is established using line search methods.Numerical and tunnel support des ign examples are presented to validate the convergence,accuracy of the proposed RBD methods.In addition,different line search methods for the outer loop calculations,the initial iteration values,and the tolerance errors are investigated.Secondly,taking a tunnel support design case as an example,a potential desig n model is constructed for global sensitivity analysis(GSA),and the first-order sensitivity index and the total effect index of the rock mass parameters under different conditions are calculated by the variance-based GSA method.Verification of these calculation results shows that the GSA can identify the non-influential parameters and select the most sensitive parameters under different conditions,which can optimize the uncertainty characterization of the input parameters.On the one hand,identifying the non-influential parameters can reduce the costs of the RBD calculations and the project-specific site investigation.On the other hand,allocating more resources to investigate the sensitivity parameters for project-specific site observations can improve the accuracy of its statistical properties.Additionally,results show that if a sensitivity factor is detected by the GSA,whether the RBD results with the target failure probability of 1% and 0.1% could cover the relative extreme deterministic results should be checked for the purpose of safety and accuracy.Thirdly,the CCM is expounded in the view of the internal support pressure,and different factors of safety under the framework of the CCM are investigated and studied.The factor of safety considering material properties of supporting structures is firstly introduced,and then the factor of safety of the surrounding rock is defined as the ratio of its maximum self-supporting capacity to its final support pressur e when the support systems are finally in equilibrium.Then,from the point that the function of the supporting structures is to strengthen the surrounding rock to improve its safety and stability,the support pressure required to ensure the probability of failure that the train of the surrounding rock is greater than the critical strain is lower than the target probability of failure is derived by the proposed RBD method.Then the factor of safety of the surrounding rock stability is developed based on that the maximum capacity of the support structures should be greater than this required support pressure.Based on Hoek's classical weak rock parameters,the influence of the critical s train,the coefficient of the variation(Co V)of the support pressure,the in situ stress and the closed-form functions of the ground response curve(GRC)on the factor of safety of the surrounding rock stability are investigated,and the corresponding val ues of this factor of safety under different conditions are summarized in tables for reference.Subsequently,the numerical GRC functions of different positions are calculated combining the numerical simulation and the stress relief method,acting as the supplementary role to the closed-from GRC functions by considering deficient factors such as the rock mass density.And the simulation of tunnel support design in terms of the CCM is developed,considering factors such as the installation positions of the supporting structures.On this basis,taking the circular tunnel as an example,the tunnel preliminary support design computation method based on the factor of safety of the surrounding rock stability is developed,which includes calculation,trial and error and checking steps.The calculation step is to calculate the support design pressures of different parts based on the factor of safety and the numerical GRC functions.The trial and error step aims to estimate the detailed parameters of the supporting structures using the corresponding material formulae,making sure t hat the strains of the support systems are lower than the allowable values under unfavorable situations with three-sigma rule through trial and error.The checking step is to check the reliability of the surrounding rock and the supporting structures in terms of their critical strain or displacement.Eventually,taking the horseshoe shaped section of Luoyixi tunnel as an example,the tunnel preliminary support design computation approach for the complex conditions and non-circular tunnels is investigated based on t he factor of safety of the surrounding rock stability.The GSA is used to select the input parameters.And then the circular and horseshoe shaped tunnel are compared from the aspects of the strains of surrounding rock,numerical GRC functions and the suppo rt design schemes.Based on this,the support design of the horseshoe shaped sect ion is conducted based on the proposed approach and the parameter analysis is presented.The results show that the proposed method could reach the target reliability level.Parametric analysis reveals that the cost of the shotcreting lining increases sharp ly as the target reliability index increases,due to the marginal effect of the reliability index caused by the stiffness of the supporting structure.It is suggested to adjus t the stiffness of supporting structures or adjust the footage of one excavation cycle for the cases with strict reliability requirements to improve the reliability level of surrounding rock economicall y and reasonably.Based on the examples of the circular and horseshoe shaped tunnels,the detailed procedures of the proposed method are outlined,forming a complete tunnel preliminary support design computation method based on the factor of safety of the surrounding rock stability.