Reliability Analysis Of Tunnels Research Articles

Dimension-Reduction Spectral Representation of Soil Spatial Variability and Its Application in the Efficient Reliability Analysis of Seismic Response in Tunnels

Reliability analysis of tunnels considering soil spatial variability was traditionally carried out using Monte Carlo simulations, which are computationally expensive. This study proposes a dimension-reduction spectral representation method (SRM) for simulating parameter stochastic fields to capture uncertainties in soil properties, which can be coupled with the probability density evolution method (PDEM). Additionally, the PDEM is employed to conduct seismic reliability assessments of tunnels in a more efficient manner. By integrating a non-intrusive dynamic random finite element method (FEM), this study explores the horizontal drift angle and vertical relative settlement of tunnel dynamic response under different coefficient of variations (COVs) and horizontal autocorrelation lengths of elastic modulus (E). Results show the changes in COVs have more pronounced effects on the mean and standard deviation of horizontal drift angle and vertical relative settlement of tunnel than alterations in horizontal autocorrelation lengths. A limit state pertaining to the horizontal drift angle and vertical relative settlement is established through the use of a probability density function (PDF) and cumulative distribution function (CDF). The results suggest that the combination of soil spatial variability and PDEM can serve as an effective approach for practical tunnel design.

Reliability analysis considering spatial variability by combining spectral representation method and support vector machine

Spatial variability is an essential characteristic of soil properties, particularly in performing reliability analysis of tunnels, as these properties exhibit marked differences depending on the soil surrounding. This set of parameters can be a multidimensional–multivariate random field with various distributions. However, the disadvantage of spectral representation method (SRM) is that it is less accurate when simulating cross-correlation of small samples. Thus, a new approach that combines SRM and support vector machine (SVM) is proposed to accurately describe uncertain soil parameters. The proposed method considers both the auto-correlation and the cross-correlation of a multidimensional–multivariate random field under a small size of samples. In addition, SVM can facilitate the effective identification of small samples. Numerical cases demonstrate that spatial variability significantly influences the reliability of tunnels, and that ignoring the spatial variability of soil properties overestimates the probability of failure. These findings indicate that the combined method is an effective approach for random field simulation and reliability analysis in tunnel engineering.

High Dimension Model Representation-Based Response Surface for Reliability Analysis of Tunnel

Uncertainty is an important prosperity to rock tunnel. Reliability analysis is widely used to deal with the uncertainty. But it is difficult to be adopted in rock tunnel using the traditional reliability method because the limit state function is an implicit function. High dimension model representation (HDMR) can approximate the high dimensional, nonlinear, and implicit function using the low dimensional function. In this study, the HDMR method was adapted to approximate the limit state function through combining with response surface method (RSM). A new reliability analysis approach of HDMR-based response surface method, combined with the first-order reliability method (FORM), is developed to calculate the reliability index of tunnel, and implementation of the method is explained briefly. A circular tunnel with analytical solution and horseshoe tunnel with numerical solution are used to demonstrate the proposed method. The obtained reliability index is in excellent agreement with Low and Tang’s (2007) method and traditional RSM. It shows that HDMR-based response surface can approximate well the limit state function, and the proposed method is an efficient and effective approach for reliability analysis in tunnel engineering. It is very useful for reliability analysis of practical large-scale rock engineering.

Analytical and Reliability Study of the Tunnel with Rockbolts in Rock Masses

Rockbolts are a critical reinforcement ways which widely used in tunnel engineering. In this paper, an analytical solution of circular tunnel with rockbolts was proposed based on homogenization method, and then the stability of a circular tunnel was investigated by considering the uncertainty based on the proposed analytical solution. Elastoplastic analytical solution for unsupported circular tunnel was presented briefly in hydrostatic stress field with a linear Mohr-Coulomb yield criterion and a non-associated flow rule. An analytical solution of circular tunnel with rockbolts was proposed through considering rock mass and rockbolts as a new homogeneous, isotropic, parameters strengthened equivalent composite material. A numerical example is used to verify the proposed analytical solution. The results show that the proposed solution can effectively characterize the mechanical behavior of rock mass and rockbolts in tunnel. Then, the proposed solution is adopted to calculate reliability index and failure probability of tunnel. The results show that the proposed method can also be effectively used to perform the stability and reliability analysis of tunnel and rockbolts have an important effect on plastic zone size and displacement of tunnel.

Reliability analysis of tunnels using an adaptive RBF and a first-order reliability method

A new reliability analysis method for tunnels was developed by integrating an adaptive Radial Basis Function (RBF) metamodeling technique with a First-Order Reliability Method (FORM). In each iteration of the adaptive RBF (A-RBF) technique, an explicit metamodel of the performance function was constructed using an augmented RBF, before an alternate FORM was applied. Additional sample points were then added in the neighborhood of the design point in order to improve the accuracy of the metamodel. Three examples were solved and the proposed approach worked well. This work provides an efficient and effective reliability analysis method for practical tunnel engineering problems.

Nonlinear response and reliability analysis of tunnels under strong earthquakes

The damages of tunnels under earthquakes showed that soil–rock deposits around a tunnel have significant effects on its response to earthquake excitations, caused by the spatial variability and correlation of the soil properties, which may properly be modelled as a random field. This paper studied these effects through modelling the surrounding soil as a random field on the response of a tunnel and made some comparisons with the corresponding deterministic analysis. A two-dimensional finite element model of the tunnel-soil system was examined, and the corresponding random field was simulated by the spectral representation method. The results revealed that the corners of the tunnel are the critical locations for the axial force and bending moment. The comparisons showed that the results of the deterministic analysis usually yield higher results than the corresponding random field results. The reliabilities of a tunnel for two limit-state functions were considered: one is defined as exceeding the design limit according to the Chinese design code, whereas the other is exceeding the ultimate strength of the reinforced concrete tunnel lining. The equivalent extreme events were formulated for the respective limit-state functions, from which the tunnel system reliability can be evaluated. The probability density evolution method was used to calculate the stochastic response and reliability of the tunnel under a strong earthquake.

Reliability analysis of tunnel using least square support vector machine

In the reliability analysis of tunnels, the limited state function is implicit and nonlinear, and is difficult to apply based on the traditional reliability method, especially for large-scale projects. Least squares support vector machines (LS-SVM) are capable of approximating the limited state function without the need for additional assumptions regarding the function form, in comparison to traditional polynomial response surfaces. In the present work, the LS-SVM method was adapted to obtain the limited state function. An LS-SVM-based response surface method (RSM), combined with the first-order reliability method (FORM), is proposed for use in tunnel reliability analysis and implementation of the method is described. The reliability index obtained from the proposed method applied to particular tunnel configurations under different conditions shows excellent agreement with Low and Tang’s (2007) method and traditional RSM results, and indicates that the LS-SVM-based RSM is an efficient and effective approach for reliability analysis in tunnel engineering.

Experimental Research on Mechanical Properties of the early-Age Shotcrete

Abstract. The compressive strength and elastic modulus of early-age shotcrete have important influence on the safety of tunnel during construction period. In order to investigate the laws of the mechanical properties of early-age shotcrete, experiments on the compressive strength and elastic modulus of early-age shotcrete with two different mixes used frequently on construction sites were carried out. The results show that the compressive strength and elastic modulus of shotcrete develop fairly rapidly and especially the development of elastic modulus of shotcrete is faster than that of ordinary concrete. There is an exponential relationship between the compressive strength and time as well as the elastic modulus development and time. Simultaneously their formulas were derived. The research results of this paper are not only helpful to understand the laws of the mechanical properties of early-age shotcrete, but also provide some reference for the reliability analysis of tunnel under construction.

Reliability analysis of tunnel surrounding rock stability by Monte-Carlo method

Discussed advantages of improved Monte-Carlo method and feasibility about proposed approach applying in reliability analysis for tunnel surrounding rock stability. On the basis of deterministic parsing for tunnel surrounding rock, reliability computing method of surrounding rock stability was derived from improved Monte-Carlo method. The computing method considered random of related parameters, and therefore satisfies relativity among parameters. The proposed method can reasonably determine reliability of surrounding rock stability. Calculation results show that this method is a scientific method in discriminating and checking surrounding rock stability.