Analysis Of Tunnel Excavation Response And Deformation Reliability Under Spatial Variability Condition

In the process of formation,rock and soil strata in geological formations are influenced by various factors such as stress history,environmental conditions,and geological structural movements.The physical-mechanical properties of surrounding rock often exhibit noticeable randomness and spatial autocorrelation,known as spatial variability distribution characteristics.This directly affects the mechanical behavior of the surrounding rock after tunnel excavation,which in turn relates to support load calculations,surrounding rock deformation predictions,and the formulation of safety control strategies.However,current tunnel designs often employ engineering analogies and deterministic calculation methods,all of which neglect the spatial variability of surrounding rock parameters.Related spatial variability studies are often based on a few distribution types of independent random fields,without fully considering the randomness and correlation characteristics among surrounding rock parameters.In tunnel excavation processes under complex geological conditions,the spatial variability of surrounding rock parameters becomes more pronounced and can have a more significant impact on tunnel excavation responses.Ignoring the randomness and intercorrelation characteristics of surrounding rock parameters can sometimes lead to unreasonable or even contradictory designs.Therefore,it is an urgent scientific problem to conduct in-depth research on tunnel excavation response patterns and reliability analysis under multi-distribution type surrounding rock parameter cross-correlated random fields.This research has important theoretical significance and engineering practical value for ensuring the safety of tunnel construction.Based on the above issues,this paper uses a combination of mathematical statistics,theoretical analysis,numerical simulation,and sampling calculations to complete the uncertainty characterization of edge distributions and joint distributions of small-sample rock and soil parameters.It constructs a multi-distribution type multivariate surrounding rock parameter cross-correlated random field,conducts research on tunnel excavation response patterns under spatial variability conditions,and achieves efficient calculation of tunnel deformation reliability.This research is applied to the engineering of the Huangjiagou tunnel on the Zhengwan high-speed railway.The specific research content and main results are as follows:(1)Research on uncertainty characterization of rock and soil parameters in small samples based on the Bootstrap method.Six traditional probability distributions(Gamma distribution,Normal distribution,Half-Normal distribution,Log-Normal distribution,Weibull distribution,Extreme Value Type Ⅰ distribution)and four kernel density estimation methods(Gaussian,Uniform,Triangular,Epanechnikov)were used to fit the probability density of surrounding rock parameters,and the marginal distributions were selected through KS tests.Multivariate Gaussian Copula and multivariate t Copula functions were used to describe the joint distribution of multivariate surrounding rock parameters,and the best joint distribution model was selected based on criteria such as AIC and BIC.Within the framework of the Bootstrap method,the best distribution results of multivariate surrounding rock parameters were presented in a probabilistic form,effectively characterizing the distribution characteristics of small-sample rock and soil parameters.By comparing simulated data with sample data,the rationality of the selected optimal distribution model was validated,effectively addressing the challenge of characterizing the uncertainty of small-sample rock and soil parameter distributions,and providing a solid theoretical foundation for constructing diverse distribution cross-correlation random fields.(2)Research on multivariate rock mass parameters cross-correlation random field simulation based on Copula theory.Building upon the characterization of parameter distribution uncertainties,and combining stochastic field theory,a multivariate rock mass parameters cross-correlation random field model encompassing multiple distribution types was successfully constructed using Cholesky decomposition techniques.This model more accurately captures the dependencies among parameters and realistically simulates the spatial distribution characteristics of rock mass parameters.With the aid of MATLAB and FLAC3D platforms,a comprehensive program for stochastic finite difference simulation of multivariate rock mass parameters cross-correlation random field was developed.Based on this program framework,the accuracy of the cross-correlation random field was validated through engineering examples and extreme condition cases,achieving satisfactory results.This provides a novel research and analysis approach for the spatial variability analysis of tunnel engineering.(3)Research on tunnel excavation response patterns under the conditions of multivariate rock mass parameters with cross-correlated random fields.Building upon the foundations laid in Chapter 2 for characterizing parameter distribution uncertainties and in Chapter 3 for the framework of cross-correlated random field-based stochastic finite difference simulations,a research system for tunnel excavation response based on cross-correlated random field theory was established.Through extensive numerical computations,the study systematically investigates the effects of different probability distribution types,variability coefficients,and different ranges of fluctuation of rock mass parameters on tunnel excavation.It analyzes the probability statistical characteristics of important indicators such as rock mass deformation,plastic zone area,and surface settlement.Based on the statistical results,four typical engineering effects caused by the spatial variability of rock mass parameters during tunnel excavation are summarized.These typical engineering effects encompass various mechanisms that influence rock mass deformation during the tunnel excavation process,providing substantial insights into the impact of spatial variability of random field characteristic parameters on tunnel excavation deformation.(4)Efficient calculation strategy for tunnel deformation reliability under spatial variability conditions.This research focuses on the reliability of tunnel deformation under the conditions of cross-correlated random fields for multiple surrounding rock parameters.It introduces the calculation methods of traditional Monte Carlo simulation and subset simulation.Building upon subset simulation,the Hamiltonian Monte Carlo method is introduced to construct a Markov chain,establishing a tunnel deformation reliability calculation method based on subset simulation optimized by Hamiltonian Monte Carlo-.This method optimizes the sampling strategy in Markov chain Monte Carlo simulation within subset simulation,achieving a more efficient search for target samples.It addresses the issues of low computational efficiency or difficulty in computation encountered by traditional methods under spatial variability conditions,providing a more efficient analytical tool for accurately and efficiently assessing tunnel deformation reliability.(5)Based on the Zhengwan high-speed railway,research on tunnel excavation deformation under spatial variability conditions was conducted at the Huangjiagou tunnel.Field geological investigations were conducted to determine the engineering geological conditions of the tunnel site area,including topography,lithology,geological structures,and hydrogeology.Using a small-sample rock and soil parameter distribution characterization method,the distribution characteristics of the collected small-sample data in the tunnel site area were described.A crosscorrelated random field model of surrounding rock parameters was established,taking into account the randomness and correlation of rock mechanics parameters,and the settlement distribution characteristics of the tunnel face were analyzed.Through the cross-correlated random field model and the Hamiltonian Monte Carlo optimization subset simulation method,the reliability of tunnel settlement deformation under spatial variability conditions was further analyzed,providing important theoretical support for the study of deformation reliability of the Huangjiagou tunnel of the Zhengwan high-speed railway under spatial variability conditions.