The Research On Analysis Method Of Reliability Calculations For Stability Of Tunnel Engineering

The reliability evaluation of tunnel stability is invariably one of the significant issues encountered in the domain of tunnel engineering. Throughout the whole evaluation process, as an indispensable element of the reliability theory, as well as an essential procedure in performing reliability optimization designs and risk predictions, the investigation on the analysis method of reliability calculations plays a paramount role for the stability of tunnels, in which the rationality and precision of the calculated results are not only directly related to the level of safety and reliability of tunnels, but also have marked influences on the corresponding decision-making in such a field. For that reason, based on the consideration of associated engineering properties residing in the tunnel itself, the explorations of analysis method and theory of reliability calculations for tunnel stability are implemented from the probabilistic and non-probabilistic viewpoint, respectively, aiming at the two critical problems involved in the reliability analysis (i.e., the development of performance functions and the description of uncertainty factors). These outcomes could then have possible applications in tunnel engineering.Firstly, in the context of probabilistic methods, when developing the performance function, a difference approximation-based technique used to calculate the derivatives is proposed according to the limitations in reliability calculations for implicit performance functions. Taking the conventional primary support installed by rockbolts and shotcrete lining as an example, a corresponding performance function is built via the shear failure theory, the thin-walled cylinder formula and the consistent deformation theory of the ground-support interaction analysis. Within a framework of the first-order reliability method, a difference approximation is thereby introduced to estimate the partial derivatives of the implicit performance function. On this basis, such a performance function can be transformed into an expression involving a single unknown described as the reliability index with the aid of Taylor’s formula, and then the resulting approximate iterative procedure for determining the reliability index can be rendered by incorporating the derivation rule of compound function. A straightforward and practical algorithm for the non-explicit performance functions in tunnel engineering is hence presented.Subsequently, in view of the complexity of the implicit performance function in tunnelling, the exploration is carried out in order to circumvent the difficulties still encountered in reliability analysis by introducing the function modelling of the response surface. In conformity with the performance function provided by the deformation principle of the surrounding rock, the sampling strategy of the classical response surface method (RSM) is analyzed. By consideration of the relationships between the statistical moments and the probability distributions of stochastic variables, and according to those various distributions exhibited actually in tunnel engineering, one key limitation of the classical RSM is that the sampling strategy can be incapable of reflecting the actual characteristics of distribution curves, but be only applicable to those curves behaved symmetrically. It is therefore recommended to use the Rosenblueth method to account for the effects of skewness coefficient on the configuration of distribution curves, whose skewness is rectified through certain coefficients. The resulting RSM that has the applicability in practical situations for various distributions of random variables is then presented, the example analysis shows that such a method can, to a certain extent, ameliorate and enhance the accuracy of computational results.Thirdly, much effort continues to direct towards the investigation on the sequential response surface technique, as the major representative of the classical RSM, by combining the engineering properties related to the coupling actions between variables (or interactions between factors) and different levels of the importance among those variables. According to the difficulties arising in the prerequisites for the sequential response surface method, a complete quadratic polynomial including the cross terms is employed to consider the coupling action between those variables. By integrating the regression analysis of orthogonal composite design with the statistical significance testing, a discriminant tool serving to the delineation of the effect of various factors on tunnel stability is provided, and a resulting optimum approach is then proposed for the response surface model to identify the importance level of basic variables. On this basis, the reliability index can be obtained through its geometrical meaning when knowing the actual interval of various variables. Consequently, a more reasonable quadratic RSM for reliability computations of tunnels is established, whose effectiveness and reasonableness are then validated using the illustrative example.For the purpose of performing further discussion on the applicability of the response surface modelling treated for the reliability problem, two fundamental issues posed in the RSM, viz., the function expression and the sampling strategy, are both taken into account according to the highly complicated mechanical state in tunnelling. For the expression of the response surface, the support vector regression approach is offered, which is much stricter in theory and more effective for complex nonlinear problems than the quadratic polynomial and some other existing functions. As regards the sampling strategy associated to the experimental design, the uniform design method is introduced, which is more applicable to the nonlinear model estimation and more efficient in computations than other design approaches. Such a combination of the two above devices tends to perfect the response surface technique, thus widening its applicability in solving the tunnel reliability problems of complicated performance functions. The correctness and referential value of the suggested method are demonstrated by the example analysis and verification.Eventually, on the basis of the probabilistic treatments in the above chapters, a special attention is devoted to enriching and improving the analysis method of reliability calculations for tunnel stability. Owing to the fact that the data on the uncertainties are quite limited and the uncertainty information is rather unavailable in tunnel engineering, the essential prerequisite in the probabilistic concept is not fulfilled. In this environment, the investigation on the reliability method is performed based on the set model of uncertainties from the non-probabilistic perspective. By introducing the concept of robust reliability, the Information-Gap (Info-Gap) robust theory is provided to handle the uncertain variables quantitatively with the Info-Gap set model. According to the mechanical mode in tunnelling, the robustness function is formulated by correlating the response value with the critical value of the output model. It is then followed by the definition of the robust reliability index, indicating that the tunnel performance could suffer the greatest horizon of the fluctuation of uncertain variables before failure. Therefore, a novel non-probabilistic evaluation methodology is developed based on the Info-Gap robustness model. The example analyses and discussions are presented to demostrate the proposed model with relatively favorable feasibility and a certain perspective of practical applications.