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The impacts of multiple reflection within the interlayer on wave propagation across layered rock masses have remained unclear. To address this, we first derive the governing equations for the wave propagation in time domain based on an equivalent layer model. These equations are validated by comparing them with a previously used method in an idealized case. Subsequently, a systematic investigation is carried out, progressing from idealized to generalized cases, to explore the frequency-dependent characteristics of the transmission and reflection coefficients, as well as energy dissipation rate. The mechanisms behind these frequency-dependent features are thoroughly analyzed, in conjunction with the evolution of waveforms and the effects of multiple reflections. The results indicate that the proposed model and derived equations effectively simulate the multiple reflection effects in the wave propagation behavior of layered rock masses. Multiple reflections within the interlayer result in an oscillatory decay of the transmission coefficient in layered rock masses as wave frequency increases. Interestingly, stress waves with frequencies that are even multiples of the ratio of wave speed to interlayer thickness demonstrate a robust capability to propagate across the interlayer. This phenomenon arises from the superposition of multiple reflected waves in phase within the interlayer, and gradually disappears with a decrease in quality factor of interlayer or an increase in wave frequency. The underlying mechanisms of these features are convincingly explained by combining the effects of multiple wave reflections. Highlights: A wave propagation equation accounting for multiple reflections in layered rock masses was derived. A non-monotonic relationship was revealed between transmission coefficient and wave frequency. A comprehensive analysis was conducted for the underlying mechanisms in frequency dependence. [ABSTRACT FROM AUTHOR]

Face stability is an essential issue in tunnel design and construction. Layered rock masses are typical and ubiquitous; uncertainties in rock properties always exist. In view of this, a comprehensive method, which combines the Upper bound Limit analysis of Tunnel face stability, the Polynomial Chaos Kriging, the Monte-Carlo Simulation and Analysis of Covariance method (ULT-PCK-MA), is proposed to investigate the seismic stability of tunnel faces. A two-dimensional analytical model of ULT is developed to evaluate the virtual support force based on the upper bound limit analysis. An efficient probabilistic analysis method PCK-MA based on the adaptive Polynomial Chaos Kriging metamodel is then implemented to investigate the parameter uncertainty effects. Ten input parameters, including geological strength indices, uniaxial compressive strengths and constants for three rock formations, and the horizontal seismic coefficients, are treated as random variables. The effects of these parameter uncertainties on the failure probability and sensitivity indices are discussed. In addition, the effects of weak layer position, the middle layer thickness and quality, the tunnel diameter, the parameters correlation, and the seismic loadings are investigated, respectively. The results show that the layer distributions significantly influence the tunnel face probabilistic stability, particularly when the weak rock is present in the bottom layer. The efficiency of the proposed ULT-PCK-MA is validated, which is expected to facilitate the engineering design and construction.

The aim of this study is to assess the three-dimensional (3D) stability of the tunnel face with considering the possibility of the upper partial failure in layered rock masses. The failure characteristic of the rock material is denoted by the nonlinear Hoek–Brown failure criterion, and a multi-tangent method is introduced and adopted to determine the equivalent Mohr–Coulomb parameters. Based on the traditional 3D rotational failure model, the whole failure model and the upper partial failure model are developed with considering layered rock masses and possibility of upper partial failure at the tunnel face. The upper-bound limit analysis approach is adopted to determine the limit support pressure and failure surface. The proposed method is validated by comparison with existing solutions and numerical results. Parametrical analysis is then conducted to investigate the influence of analytical parameters on the face stability. Finally, the effect of seepage forces on the tunnel face stability is presented. The results show that, the upper partial failure is likely to happen when a soft layer in the upper section of tunnel face. This possibility increases as properties of lower layer increase, the tunnel diameter decreases, and the layered position moves down. The presence of underground water delays the occurrence of upper partial failure at the tunnel face. [ABSTRACT FROM AUTHOR]

An analysis of tunnel face stability generally assumes a single homogeneous rock mass. However, most rock tunnel projects are excavated in stratified rock masses. This paper presents a two-dimensional (2D) analytical model for estimating the face stability of a rock tunnel in the presence of rock mass stratification. The model uses the kinematical limit analysis approach combined with the block calculation technique. A virtual support force is applied to the tunnel face, and then solved using an optimization method based on the upper limit theorem of limit analysis and the nonlinear Hoek–Brown yield criterion. Several design charts are provided to analyze the effects of rock layer thickness on tunnel face stability, tunnel diameter, the arrangement sequence of weak and strong rock layers, and the variation in rock layer parameters at different positions. The results indicate that the thickness of the rock layer, tunnel diameter, and arrangement sequence of weak and strong rock layers significantly affect the tunnel face stability. Variations in the parameters of the lower layer of the tunnel face have a greater effect on tunnel stability than those of the upper layer.

Mining engineering with layered structures often obtains extensive geological data to ensure reliability of mining operations. Effectively utilizing these data to characterize the spatial distribution of mechanical parameters in layered rock mass is crucial for slope stability analysis. This study focuses on the Heishan open-pit mine as a case study, leveraging the distinctive characteristics of mining engineering geological data. A three-dimensional fracture network was then generated based on the distribution of fractures in the rocks, and the representative elementary volume of the rock mass was determined by calculating the volumetric joint count (Jv). Statistical characteristics of various geological data are analyzed, and a geological statistical method combining the Kriging method and inverse distance power method is applied to establish a spatial distribution block model for geological strength index (GSI) and rock mechanical properties. Subsequently, a spatial variability model of the mechanical parameters of the layered rock mass was generated based on the Hoek–Brown criterion. Furthermore, the heterogeneous mechanical model is implemented in numerical software for stability analysis and slope angle optimization. The findings indicate that each engineering zone of layered slopes exhibits unique mechanical parameters while demonstrating significant layered distribution patterns at a macro level. Considering spatial variability, the mechanical model significantly impacts slope stability and slope angle optimization outcomes. Our research methodology facilitates accurate quantification of the heterogeneity of mechanical parameters in layered slopes without incurring excessive additional survey costs, enabling more rational explanations of slope landslides and the provision of suitable slope angle optimization designs. [ABSTRACT FROM AUTHOR]

Flexural toppling failure is one of the most common instabilities in large underground caverns and occurs when the steeply inclined rock layers form a small angle to the cavern axis. This study investigates a typical flexural toppling failure in the underground powerhouse at the Wudongde hydropower station, Southwest China, using in situ tests and numerical tools. The characteristics of flexural toppling failure in the large underground caverns were initially analysed by field observations and conventional testing methods, including the use of multipoint extensometers, acoustic wave tests and borehole television images. A high-resolution microseismic monitoring system was installed in the right main powerhouse to reveal new and important insights into the mechanisms of typical failures that occur in bedded rock masses. The fracturing processes of the rock mass associated with the flexural toppling failure were analysed based on microseismic monitoring data, and the development of flexural toppling failure was related to shear failure. Then, the discrete element method was used to further investigate the effect of geological planes on the formation of flexural toppling failure. Finally, the complex mechanism of flexural toppling failure was evaluated by incorporating field observations, in situ monitoring and numerical modelling. An effective method of preventing this type of failure in underground caverns was analysed. The results can improve our understanding of flexural toppling failure in the underground caverns of the Wudongde hydropower station, and the proposed method can be adopted to study similar large underground caverns. [ABSTRACT FROM AUTHOR]

In nature, rock masses often present non-horizontal layered characteristics due to geological tectonics. Tunnelling in such rock formations threatens and reduces the stability of the tunnel face. In addition, the existence of weak interlayer poses a potential threat to stability. In this study, an analytical model is established to comprehensively consider the influence of rock layer inclination and weak interlayer on the stability of the tunnel face. Then the virtual supporting force is obtained using the upper limit theorem of kinematic limit analysis with the nonlinear Hoek-Brown yield criterion. The optimal upper-bound solution is examined by the Genetic Algorithm. Several design charts are provided to analyze the effects of the tunnel diameter, inclination angle and weak interlayer on the stability of a tunnel face. The obtained results show that the instability of the tunnel face increases significantly due to the container of the weak interlayer. And the parameters of the lower-layer play a crucial role in the collapse of the tunnel face. Moreover, the effects of the position and thickness of the weak interlayer on the stability of tunnel face are discussed. The critical angle for the inclination of the rock layer leading to the most unstable state is remarked. [ABSTRACT FROM AUTHOR]

• Distinguished differences of large cavern displacements in various geo-stresses. • Revealed different deformation mechanisms of two zones for underground powerhouse. • Deduced mechanism of overall deformation profile of underground powerhouse cavern. • Effects of bedding thickness and intersecting chamber on cavern deformations. In low to moderate stress regions, deformations of the high sidewall dominated by bedding planes dipping against the cavern space, often pose an unpredictable threat to local stability of underground powerhouse. In this study, detailed field surveys, in-situ tests, beam theory, and the discrete element method (DEM) are used to critically investigate the deformation mechanisms of high sidewall in layered rock strata steeply inclined against the inner space of the underground powerhouse cavern. First, an approach integrating in-situ surveys, deformation monitoring and acoustic wave tests, is adopted to analyse the evolutionary features of displacements of a high sidewall in layered strata steeply dipping against cavern space. Differences of deformation behaviours and their relationships with excavating activities in low to moderate and high geo-stress regions, were distinguished. Second, two zones with different deformation mechanisms in layered strata involved are presented, which could be evidenced by the presence of various displacement modes near the top area of a high sidewall. Then, based on the conceptual beam models, mechanisms of displacements controlled by bedding planes in two zones are investigated. Synergistic effects arising from two zones promoting the overall deformation profile are presented. Third, combining with DEM simulations, the mechanical influences of bedding thickness on the excessive deformation modes near the top of sidewall, are revealed. Displacements of a sidewall partly affected by an intersecting chamber are described in detail. Finally, suggestions for applicable supports of the high sidewall with bedding planes dipping steeply toward the internal area of surrounding rocks during cavern excavation are presented. The aforementioned investigations can provide valuable guidelines for the construction of similar underground powerhouse caverns. [ABSTRACT FROM AUTHOR]