This study aims to develop an analytical approach for assessing the 3D active stability and failure probability of the tunnel face in spatially variable and anisotropic soils. An advanced failure mechanism based on discrete failure boundaries is first developed using the rigorous discretization technique. By taking the soil strata inclination as a priori condition, a non-stationary random field is proposed to represent the soil spatial variation. Comprehensive mathematical formulations are derived to denote the soil anisotropy. By incorporating spatially variable and anisotropic soils into the advanced failure mechanism, the critical support pressure and critical failure surface are determined to check the face stability using the limit analysis method. The proposed approach is validated through comparative analyses with analytical and numerical solutions. A systematic parametric investigation is then performed to discuss the effects of anisotropic and random field parameters on the face stability. Subsequently, the failure probability is derived under a specified supporting pressure, and a series of charts are provided to discuss the influence of random field parameters on the failure probability. The analysis results reveal that the proposed approach can be served as a reference methodology for the stability and probabilistic analysis of tunnel face under complex geotechnical scenarios.

Soil nail is an extensively adopted reinforcement measure to improve the slope stability and prevent landslides, yet few studies have explicitly assessed the stability of inclined nailed slopes with simultaneous consideration of earthquakes and pore water pressures. The aim of this study is to propose an analytical approach to fill this research gap. In the proposed method, the 3D discretization failure model is adopted to describe the 3D failure characteristic of slopes, the modified pseudo-dynamic (MPD) approach is adopted to describe the spatial and temporal variations of seismic loads in the slope, and a simplified approach is adopted to calculate the pore water pressure. Then, based on the upper-bound limit analysis (UBLA) method, the 3D limit surcharge and the 3D limit failure surface are determined to check the slope stability with the aid of a hybrid optimization algorithm. Comparisons with existing analytical values and numerical results show that the developed method is an effective approach to study the 3D stability of inclined nailed slopes subjected to earthquakes and pore water pressures. The parametric analysis is finally conducted to analyze the influence of slope geometries, earthquake and soil parameters, pore water pressure, and nail reinforcements on the slope stability.

This study develops a theoretical framework for the three-dimensional (3D) stability and failure probability analysis of seismic slopes, incorporating both the spatial variability of soil shear strength properties and the amplification effect of seismic loads within the slope. Four types of random fields are generated via the Karhunen-Loève expansion method to characterize the spatial variability of soil shear strength properties, with the depth-dependent trends of soil properties incorporated as prior constraints. The modified pseudo-dynamic approach is adopted to capture the amplification of seismic loads along the slope height. Within the upper-bound limit analysis framework, a 3D discretized slope failure model that integrates spatially variable soil properties and depth-dependent seismic forces is established, allowing the critical horizontal seismic acceleration coefficient and the time-dependent failure probability under a given seismic event to be determined for assessing the 3D stability and reliability of the slope. The effectiveness and superiority of the developed method are validated through comparisons with numerical simulations. Finally, a comprehensive parametric analysis is performed to investigate the influences of slope angle, seismic parameters, random field parameters on the critical horizontal seismic acceleration coefficient, the time-dependent failure probability, and the geometry of the slope instability surface.

Previous analytical models for the passive stability analysis of the shield tunnel face always assumed the global failure at the excavation face. However, recent experimental and numerical results have refuted this hypothesis and found that partial failure is more likely to occur at the excavation face when the passive failure happens. To better explore the passive stability of excavation faces, two improved three-dimensional (3D) failure models were developed considering the possibility of the partial failure at the excavation face. To check the passive stability, the limit passive pressure and the corresponding failure surface were derived using a combination of the upper-bound limit analysis method (UBLAM) and a hybrid optimization method. Validations illustrate that the 3D transition circular partial failure model is preferable for the passive stability analysis. The parametric and sensitive analysis shows that the importance sequence of the analytical variables on the stability issue is friction angle > relative cover depth > ground surcharge > cohesion > soil gravity. The extension of the developed method in nonhomogeneous soils shows that, for these selected cases, the passive failure is more likely to occur from the layered interface or above the layered interface, and larger limit passive pressure triggers smaller upper partial failure as the layered interface rises. The application to a practical tunnel case further validates the effectiveness of the developed method. (c) 2025 American Society of Civil Engineers.

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.

The face stability analysis of a longitudinally inclined shield tunnel using an analytical approach in water-rich areas is still a research gap. To solve this face stability problem, a numerical simulation based on the FLAC3D is first conducted to calculate the seepage field behind the inclined tunnel face. An improved rotational failure mechanism is developed to make it possible to investigate the face stability of inclined tunnels using analytical approaches. In the framework of the kinematic approach of limit analysis, the limit support pressures and corresponding failure surfaces of the inclined tunnel face are determined to analyze the face stability issue. The interpolation tool (griddata) in MATLAB is adopted to involve the obtained numerical values of pore water pressures into the analysis of the stability issue. The analytical solutions obtained from the proposed method are validated by comparisons with existing results from published literatures and numerical results. For a quick estimation of the inclined tunnel face stability in water-rich areas, a series of design charts are then presented for various soil strength parameters, water tables, and inclined angles. Finally, an application of the proposed method to a practical tunneling case is provided, which further illustrates the effectiveness of the proposed method.

Comprehensive assessment of the active/passive seismic stability of shallow tunnel faces is an urgent and complex task. This work establishes a promising three-dimensional (3D) approach using upper-bound limit analysis to evaluate the active and passive seismic stability of shallow shield tunnel faces. The outcrop failure model and inside failure model are provided for active failure analysis. To capture the spatiotemporal variations of seismic loading, the pseudodynamic approach is employed to assess the limit active and passive support pressures. Comparisons with published studies and numerical simulations demonstrate that the proposed 3D approach greatly improves existing 2D results for limit active and passive support pressures. A detailed investigation is then conducted to analyze the effects of pseudodynamic parameters, surface surcharge, and buried depth on face stability of shallow tunnels. Finally, the proposed approach is further tested by conducting the seismic face stability analysis of Changsha Metro 2 tunnel based on actual seismic response. The results indicate that the surface surcharge has a greater influence on limit passive support pressure than limit active support pressure, and increasing of buried depth leads to a larger safety range of limit support pressure. Active and passive face failure of shallow tunnels under earthquakes can endanger the safety of tunnels and ground surfaces, leading to severe casualties and property losses. Determination of limit support pressures under seismic forces is a critical task in shield tunnel construction. This work establishes an approach to assess 3D active and passive seismic stability of shallow shield tunnel faces. Time-space variations of seismic loading are incorporated to accurately determine limit active and passive support pressures using pseudodynamic approach. Effects of seismic parameters, surface surcharge, and buried depth on face stability of shallow tunnels are then presented and discussed. Finally, the proposed approach is tested by conducting the seismic face stability analysis of Changsha Metro 2 tunnel based on actual seismic response. The results indicate that surface surcharge has a greater influence on limit passive support pressure compared with limit active support pressure, and increasing buried depth leads to a larger safety range of limit support pressure. The proposed approach determines a safety range of limit support pressures more accurately for shallow shield tunnels during earthquakes.

In this study, an analytical model for the three-dimensional (3D) dynamic stability analysis of vegetation-rooted slopes is first developed under steady-state unsaturated flow conditions. Root reinforcement, defined as the increase in the soil shear strength produced by the mechanical and hydrological effects of vegetation roots, is included in the proposed analytical model. By combining the modified pseudo-dynamic approach (MPDA) and the kinematic theory of limit analysis to the 3D discretized failure model, the most critical failure surface and the corresponding factor of safety (FS) are derived to examine the stability of vegetation-rooted slopes with the aid of the optimization algorithm of particle swarm. The proposed approach is verified by comparing with published analytical solutions and numerical results. A series of parametric analysis are then conducted to examine the influence of seismic-related parameters, vegetation properties, possible surcharge and slope geometry parameters on the slope stability. Finally, a comparison between the slope stability under different root architectures is provided and discussed. The results show that, for these selected cases, the stability of vegetation-rooted slopes is significantly improved by approximately 45

The face stability assessments of seismic tunnels have been complicated and crucial problems. To solve this issue, an advanced three-dimensional (3D) rotational failure mechanism with considering seismic effects is developed to assess the seismic face stability of shield tunnels in weak rock masses. The Hoek-Brown (HB) failure criteria is employed to characterize rock masses with weak strength. The corresponding Mohr-Coulomb (MC) parameters are determined using the tangential line method. The modified pseudo-dynamic (MPD) approach is utilized to accurately involve damping property of geomaterials, realistic surface boundary conditions and dynamic properties of seismic waves in face stability assessments. The upper limit analysis approach is utilized for the determination of critical face pressures of seismic tunnels. Comparisons against numerical and analytical solutions demonstrate the efficacy of proposed approach for evaluating the seismic face stability. Subsequently, the impacts of seismic actions and weak rock parameters on face stability are analyzed and a design table is provided for practical use. Finally, the proposed approach is tested by conducting seismic face stability assessments of the JinXiu tunnel with actual seismic response.

Due to the complexity and untraceability of the grouting process and the underpinning of the slurry diffusion law, the current study on the grouting properties of alluvial filler soil lags behind the engineering application. Therefore, grouting model tests, including a laboratory soil test and a dynamic penetration test, are developed in this study to investigate the diffusion law of slurry and strength characteristics in alluvial filler soil. Through the excavation of the grouting model, the diffusion pattern of the grouting slurry can be observed precisely. Then an approach proposed in this study for estimating the shear strength growth of the grouting soil is verified by the grouting model tests. In addition, to assess the grouting volume, an analytical model considering the shrinkage coefficient of the slurry is developed. The good agreement between the test data and analytical results shows that the proposed method can effectively estimate the increase in shear strength and grouting amount. The excavation results show that the slurry is generally first filled and fractured along the interface between rock and soil and mainly fractured horizontally, with widths between 0.3~6.0 cm. The curves for the diffusion radius versus the distance from the grouting hole show a wavelike relationship in all directions (i.e., horizontal, up, and down).

Semianalytical solutions for circular tunnels under biaxial in situ stress fields are developed in this study. The surrounding rock is assumed to behave as an elastic-brittle-plastic model and is characterized by the unified strength criterion. For the stress analysis, the perturbation solutions for arbitrary-orders plastic radius for deep-buried tunnels are presented with a newly developed numerical iterative method. Furthermore, a stress renewal algorithm is provided for determining the stress function in elastic zones more accurately. In accordance with the small deformation assumption and nonassociated flow rule, the analytical expressions for radial and circumference displacement in a plastic zone are presented for the first time. Subsequently, the undetermined coefficients in plastic displacement can be solved numerically with the least square method. Based on the proposed semianalytical solutions for circular tunnels, an improved equivalent circular method is developed for estimating the plastic radius and convergence of tunnels with arbitrary shaped cross sections approximately. The reliabilities of the proposed semianalytical solutions and the improved equivalent circular method are verified by comparing with numerical simulation and field data. Meanwhile, the whole calculating process is illustrated in a flow chart for the convenience of programming. From the perspective of practicality, the provided solutions can be employed for predicting plastic radius and ground response curves in tunnel excavation, which can supply important references for the tunnel stability assessment and support design.

This study aims to evaluate the stability of the soil-nailed slope using an improved discretisation-based failure model in the framework of the upper-bound limit analysis theorem and the homogenisation approach. The improved discretisation-based failure model generated from the slope crest is first proposed by using the discretisation technique. Based on the homogenisation approach, a failure criterion for reinforced soils is established with considering the possible tensile failure and pull-out failure of soil nails. The proposed failure criterion is then incorporated into the improved slope failure model to determine the factor of safety (FoS) of the reinforced slope by using a method integrated the upper-bound limit analysis theorem and the strength reduction technique. The proposed method is validated by comparing with existing solutions and numerical results, showing that the proposed method is an effective approach to investigate the stability of reinforced slopes, especially for the cases with high reinforcement density. The effects of model parameters on the slope stability are finally presented.

Many published experimental tests and field observations have shown that blow-out failure is potentially more likely to happen during the excavation of shallowly buried tunnels. However, limited research has been con-ducted to assess the three-dimensional (3D) blow-out stability analysis of shield tunnel faces, especially in anisotropic and heterogeneous soils. To resolve this shortcoming, a 3D blow-out failure mechanism is developed to make it possible to incorporate the influences of the anisotropies and heterogeneities of the soil properties into the determination of the limit blow-out pressure and the limit failure surface in the framework of upper-bound limit analysis theory. For verification purposes, the proposed method is tested through comparisons with existing analytical solutions and numerical results for some special cases. Then, the effects of the anisotropic and het-erogeneous soil properties on the normalized limit blow-out pressure and the limit failure surface are presented and discussed. Finally, applications of the proposed method to blow-out stability analyses considering spatially variable soil properties and inclined ground surfaces are performed to illustrate that the proposed method has the potential to serve as a benchmark for the blow-out stability of tunnel faces under complex geological and geometrical conditions.

This study aims to propose an effective approach to evaluate the seismic stability of heterogeneous slopes reinforced by inclined soil nails. The modified pseudo dynamic approach is applied to properly describe the characteristics of seismic loads with time and space. The discretization-based failure mechanism generated from the slope crest is divided horizontally into many blocks to incorporate the heterogeneous soil properties and depth-dependent seismic accelerations into the analysis of the stability issue. The critical seismic acceleration coefficient is then determined to assess the slope stability using the kinematic approach of limit analysis. The proposed method is validated by comparisons with existing solutions and numerical results for some available cases. A systematic parametric analysis is conducted to discuss the effects of model parameters on the slope stability. Results show that there exist optimal relative nail lengths and optimal incline angles of soil nails to obtain the maximum critical seismic acceleration coefficient for reinforced slopes. Finally, an application of the proposed model to spatially variable soil strength properties is performed to illustrate that the proposed method has the potential to serve as a benchmark for the slope stability under complex geological conditions.

In this work, the stability of a shield tunnel face under pore water pressures is examined by combining the non-linear Mohr-Coulomb failure criterion in the framework of the kinematic approach of limit analysis. The non-linear Mohr-Coulomb failure criterion represented by the tangent technique in combination of the pore water pressure distribution calculated by the mesh dividing optimization technology are incorporated into the 3D rotational failure mechanism to assess the critical support pressure of a tunnel face for the first time. Based on the proposed method, parametric studies are performed by giving design charts to study the effect of model parameters on the calculated critical support pressure. In these charts, comparisons with results from the linear Mohr-Coulomb failure criterion are used to verify the proposed method. Finally, the influence of the non-linear coefficient on the feature of the 3D rotational failure mechanism is presented.

Accurately estimating the stability of horseshoe tunnel faces remains a challenge, especially when excavating in rock masses. This study aims to propose an analytical model to analyze the stability of the horseshoe tunnel face in rock masses. Based on discretization and “point-by-point” techniques, a rotational failure model for horseshoe tunnel faces is first proposed. Based on the proposed failure model, the upper-bound limit analysis method is then adopted to determine the limit support pressure of the tunnel face under the nonlinear Hoek–Brown failure criterion, and the calculated results are validated by comparisons with the numerical results. Finally, the effects of the rock properties on the limit support pressure and the 3D failure surface are discussed. The results show that (1) compared with the numerical simulation method, the proposed method is an efficient and accurate approach to evaluating the face stability of the horseshoe tunnel; (2) from the parametric analysis, it can be seen that the normalized limit support pressure of the tunnel face decreases with the increasing of geological strength index, GSI, Hoek–Brown coefficient, mi, and uniaxial compressive strength, σci, and with the decreasing of the disturbance coefficient of rock, Di; and (3) a larger 3D failure surface is associated with a high value of the normalized limit support pressure.

Based on Mohr-Coulomb criterion, the generalized perturbation solutions for elastic brittle-plastic rock surrounding deep-buried non-circular tunnels are presented in this study. The asymptotic expansions and a novel equivalent elliptical method adaptable for arbitrary shaped tunnel are provided for the perturbation analysis. Concerning the plastic analysis, the recurrence formulas and a simplified semi-analytical approach are developed for solving arbitrary-order approximations of stress functions conveniently. Subsequently, a novel undetermined coefficient method incorporating the stress continuity on elastoplastic interface is presented for determining the plastic radius and stress functions in elastic zone. On the basis of the preceding solutions, the extended solutions with equivalent elliptical method are developed for further expanding the applicable range of solutions. Besides, the perturbation analysis based on generalized Hoek-Brown criterion can be implemented in terms of the equivalent angles of friction and cohesive strengths. The whole computing process is provided in flow chart for the convenience of programming. The reliability of the solutions has been verified by comparing with the calculating results of numerical simulation. Significant improvements can be noticed for the predicted plastic radius compared with the results by the existing equivalent circular method. From a theoretical point of view, the developed perturbation solutions with equivalent section method complete the framework of the elastoplastic analysis for non-circular tunnels. From the perspective of practicality, the proposed solutions can provide preliminary insight for the rapid stability evaluation, plastic radius prediction, and tunnel outline design in practical engineering. (c) 2022 Elsevier Inc. All rights reserved.

This study aims to develop an effective approach to conduct the three-dimensional (3D) modified pseudo-dynamic stability analysis of slopes reinforced using inclined soil nails. Based on the 3D discrete failure mechanism, the factor of safety (FoS) for the soil nailed slope is determined using a method that integrates the upper-bound limit analysis approach and the strength reduction technique. The incline angle of soil nails that is neglected in previous literature for 3D seismic stability analysis of slopes using analytical methods is also considered in the calculation of the FoS. The modified pseudo-dynamic approach is introduced to properly incorporate the impact of seismic loads into the analysis of slope stability. The proposed method is validated by comparisons with existing analytical solutions and numerical results, showing that the proposed method is an effective approach to assess the seismic stability of soil nailed slopes. Finally, the effect of model parameters on the calculated FoS of the soil nailed slope is presented. The parametric analysis shows that the effects of seismic actions on the slope stability are greatly influenced by the ratios of seismic acceleration for the slope crest to the slope toe, and there exists an optimal incline angle of the soil nail to achieve the best reinforcement.

This study proposed an effective approach to accurately evaluate the three-dimensional (3D) seismic bearing capacity of heterogeneous and anisotropic slopes in the framework of the upper-bound limit analysis theorem. An improved discretized horn mechanism was first developed so that the properties of heterogeneous and anisotropic soils could be involved in the slope stability analysis. To incorporate the impact of seismic forces, the modified pseudo dynamic approach was adopted, which ensured that the complete time-history of the seismic-induced ground movement, the soil-damping properties, and the amplification effect could be considered in this study. The seismic bearing capacity of slopes was then calculated by using a method that integrated the upper-bound limit analysis theorem and the modified pseudo dynamic approach. The proposed method was validated by comparisons with previous analytical solutions for some available cases, showing that the proposed method is an effective approach to determine the 3D seismic bearing capacity of heterogeneous and anisotropic slopes. The effects of model parameters on the ultimate bearing capacity and the critical failure surface are then presented. Finally, the influence of pore-water pressure on the seismic slope stability is discussed.

Many analytical methods have been adopted to estimate the slope stability by providing various stability numbers, e.g. static safety of factor (static FoS) or the critical seismic acceleration coefficient, while little attention has been given to the relationship between the slope stability numbers and the critical seismic acceleration coefficient. This study aims to investigate the relationship between the static FoS and the critical seismic acceleration coefficient of soil slopes in the framework of the upper-bound limit analysis. Based on the 3D rotational failure mechanism, the critical seismic acceleration coefficient using the pseudo-static method and the static FoS using the strength reduction technique are first determined. Then, the relationship between the static FoS and the critical seismic acceleration coefficient is presented under considering the slope angle β, the fractional angle φ, and the dimensionless coefficients B/H and c/γH. Finally, a fitting formula between the static FoS and the critical seismic acceleration coefficient is proposed and validated by analytical and numerical results.