The dynamic evolution characteristic of the bond strength at the interface of a bolt and a rock mass under an axial tensile load and the mechanical behavior of fully grouted bolts in situ were ...investigated considering the non-uniform stress of the surrounding rock along the bolts. A new dynamic bond-slip model was first proposed to describe the dynamic evolution characteristic of the bond strength at bolt-rock interfaces. Based on the proposed dynamic bond-slip model, analytical solutions of the shear stress distribution along the bolts, load-displacement relationship, and relative displacement considering the slip of the free end were developed. Then, incorporating the non-uniform normal stress of the surrounding rock along the bolts, the shear stress distribution and load-displacement behavior of the fully grouted bolts were presented. Moreover, analytical approaches were also proposed for determining the stress distribution along the bolt and rock deformation in cases of in situ prestressed and non-prestressed bolts. The proposed model and analytical solution were validated by published results from laboratory model tests and in situ tests, respectively. The new analytical solution completes the theoretical framework for addressing the fundamental problem of fully grouted bolts in pull-out tests and in situ rock masses and provides a useful theoretical tool that can potentially be applied to bolt design and laboratory and in situ testing.
A new procedure for the ground response curve (GRC) is investigated in strain-softening surrounding rock for a circular opening. The procedure started each step with a radius increment and the ...analytical solutions of stress and strain in each annulus were presented. The plastic region is divided into a finite number of concentric annuli, whose thickness is uniformly determined by a small radius increment. Combining the equilibrium equation and failure criterion, stress for each annulus can be obtained analytically. The displacement for each step can be calculated analytically through solving the differential equation by invoking flow rule and Hooke’s law. The strains for each annulus can be obtained by the strain-displacement relationship. In the successive manner, the distributions of stress and displacement can be found. It should be noted that the finial stress and displacement at radial direction are the internal support pressure and deformation at the excavation surface, respectively. By assuming different plastic radii (using a plastic radius increment), GRC, the evolution curve of plastic radii and internal support pressure can be obtained analytically. Some numerical and engineering examples are performed to demonstrate the validity of the proposed procedure. It is shown that the results of the proposed procedure at the tunnel crown are basically consistent with field measuring data. The influence of the annulus number, plastic radius increment and dilation on the accuracy of the proposed approach is investigated. Results show that the solutions are more accurate and the calculation efficiency is higher.
•Elasto-plastic solution for shallow tunnel in a semi-infinite space was proposed.•The gravitational effect on stress in the elastic surrounding rocks is notable.•The influence of gravity on the ...elasto-plastic model is limited.•Calculations of plastic zone shape are consistent with the results generated by Midas-GTS.
This study focuses on a novel approach to develop an elasto-plastic solution for surrounding rocks around a shallow tunnel in an elasto-plastic semi-infinite space that incorporates the gravitational effect based on the bipolar coordinate system. A shallow circular tunnel was excavated in continuous, isotropic, and homogeneous rock masses. The solution for the surrounding rock in semi-infinite space was regarded as a semi-infinite plane problem, and the semi-infinite plane was partitioned along the curve trajectories of the bipolar coordinate. Based on the Mohr-Coulomb failure criterion and considering the gravitational effect, the closed-form solutions for the stress distribution of the surrounding rock were proposed. Furthermore, novel approaches for the calculation of the shape of the plastic zone around the tunnel and the critical internal support pressure were obtained. These presented approaches were validated by comparing the results of finite element method and the published literature. Using the numerical method, the sensitivity of gravity and the influences of the geological strength index, internal support pressure, surface loading, and buried depth of the tunnel on the plastic radius, shape of the plastic zone, and stress distribution of the surrounding rocks around the shallow circular tunnel were discussed.
AbstractIn this study, using the kinematic approach of limit analysis, a new numerical model was developed to investigate the effect of the coupled flow deformation on tunnel face stability. By ...incorporating the innovative mesh-dividing optimization technology with the principle of generating a three-dimensional (3D) rotational failure mechanism into a customized program of linear interpolation, the pore-water distribution in the stage of the global failure ahead of the tunnel face determined by FLAC3D was interpolated on the 3D rotational failure mechanism. The support pressures predicted by the developed model improved the existing upper-bound solutions by at least 14.2% for the case of slight cohesion soils but made little difference with the existing upper-bound solutions for high cohesion soils. The support pressures predicted by the developed analytical method were in close agreement with those from numerical simulations and in situ data. The results showed that the critical face pressures increased linearly with increasing water table elevation. Several design charts are provided for parametric analysis, which can be directly used by tunnel engineers in the evaluation of face stability.
Seismic stability of slopes reinforced with soil nails has been traditionally investigated by two-dimensional limit equilibrium method. In this paper, the strength reduction method in combination ...with the kinematic approach of limit analysis is employed to assess the factor of safety (Fos) of slopes reinforced by soil nails using the three-dimensional rotational failure mechanism. The pseudo static approach is used to represent the seismic effects. Both the tensile failure and pull-out failure of soil nails are considered in the computations of internal energy dissipations. Comparisons are made to validate the proposed approach, which shows that the implemented approach is an efficient design tool for evaluating the factor of safety of slopes reinforced by soil nails. Parametric analysis is conducted to discuss the influence of model parameters, including nail length, nail density, soil shear strength and seismic forces, on slope stability. A set of stability charts is finally provided for fast assessments of slope safety.
Most subways excavated in nonhomogeneous and water-bearing soils but few existing analytical models focus on the combined effect of soil nonhomogeneity and pore water pressures. To address this ...issue, a three-dimensional (3D) rotational collapse mechanism is improved to investigate the effect of vertical variability of soil strength on the face stability of a circular tunnel excavated in saturated nonhomogeneous soils by means of the kinematical approach of limit analysis. The pore water pressure distribution obtained numerically is interpolated on the 3D improved collapse mechanism by a linear interpolation technology. The effectiveness of the developed model is verified by comparing the required face pressures with the existing solutions, the numerical simulations and the monitoring data of the Shenzhen urban rail transit line 9 project. The effects of nonhomogeneous friction angles and cohesion and water table elevation on the face stability are investigated.
Abstract
Conducting soil stability assessments around tunnels has always been a concern. However, most existing studies have regarded soil as an isotropic and homogeneous material. To overcome this ...limitation, within the framework of upper bound theory, this paper proposes a novel rotational–translational failure mechanism where the velocity discontinuity surfaces are derived numerically. This theoretical mechanism includes two cases according to the positions of the velocity discontinuity surfaces. An analytical solution for pore water pressure is obtained using the conformal mapping method, which involves solving the two-dimensional (2D) Laplace equation and considering the soil and shotcrete permeability. Then, upper bound expressions for the limit supporting pressure are derived by computing work equations with and without pore water pressure. Comparisons with previous work and numerical results illustrate that the presented approach offers improvements and could be applicable for stability analyses of shallow rectangular tunnels in anisotropic and nonhomogeneous soils. Finally, this paper discusses the effects of the anisotropy and nonhomogeneity of soil properties on the normalized limit supporting pressure and the collapsing domains of rectangular tunnels with different geometric shapes. In addition, the impact of pore water pressure on the changed water levels is assessed. The results demonstrate that for rectangular tunnels that are excavated in water-bearing zones, the width-to-height ratio plays a significant role in the stability of the surrounding soils.
An improved approach for the face stability analysis of shallow tunnels in non-homogeneous and anisotropic soil is developed in this study. Based on the discretization technique, an advanced passive ...failure mechanism is proposed to determine the critical support pressure of the tunnel face in the framework of the upper bound theorem. To better estimate the tunnel face stability, the effects of the pore water pressure and nonuniform ground surcharge on the critical support pressure of the tunnel face are also incorporated in the non-homogeneous and anisotropic soil properties. Then the optimal supporting forces obtained from the proposed failure mechanism are validated by those from the conventional limit analysis model in homogeneous soil and finite element limit analysis in homogeneous and non-homogeneous soils.
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.
•A radius-iterative-approach was proposed for shallow tunnels.•Plastic radius and elastic-plastic solution for shallow tunnels were proposed.•The corrected technique for plastic radius was proposed ...for shallow tunnels.
This study presents a semi-analytical elastic-plastic solution for a shallow tunnel subjected to ground loss in the strain-softening surrounding rock. The most important contribution is the radius-iterative-approach in which the initial plastic radius is first determined by the strain continuity boundary condition on the elastic-plastic interface and then corrected to the precise one. The corrected approach follows three steps: (1) Applying the radius increment technique to semi-infinite space (2) Carrying out the plastic radius correction by using iteration method from the elastic-plastic interface to the tunnel wall. (3) If the calculated convergence value is equal to the convergence value on the tunnel wall, the accurate determination of the plastic region, stresses, and displacements, of the whole half plane, can be derived consequently. All the results compare favorably with numerical simulation results. The study completes the theoretical framework for addressing the fundamental problem of shallow tunnels excavated in the semi-infinite space and also provides a useful theoretical tool for potential application on the tunnel and underground engineering problems.
