Circular Lining Research Articles

Technical feasibility of lined mining tunnels in closed coal mines as underground reservoirs of compressed air energy storage systems

In this paper, four mining levels in a closed coal mine in the Asturian Central Coal Basin (NW Spain) have been selected as a case study to investigate the technical feasibility of underground compressed air energy storage systems. First, in order to determine the suitable level and type of concrete lining, a numerical model has been established to analyze the geomechanical performance considering air pressures of 6, 10, 20 and 25 MPa and three different embodiments of concrete lining. Then, another numerical model is used to study the coupled thermo-mechanical performance at level 3, considering 100 operation cycles between 6 and 10 MPa air pressure using a circular concrete lining with a 20 mm thick sealing layer. The results obtained indicate that the deformations are lower at levels 1 and 3, where the shales are located at the top of the coal seam. Deformations and tensile stresses are significantly reduced when a circular concrete lining is used. As the thermal analysis shows, temperature fluctuations are restricted to sealing layer and concrete lining and do not reach the rock mass itself. Therefore, negligible deformations are produced by the effect of temperature compared to the effect of air pressure. Maximum tensile stress and total displacements during the operation occur at the top of the mining drift and reach 9.5 MPa and 3.6 mm, respectively. A technical feasibility can be achieved using a circular concrete lining with a suitable reinforcement system.

Numerical study of seismic resistance of prefabricated circular tunnel linings

Prefabricated circular tunnel linings are used in the construction of tunnels using the shield method, which significantly increases the speed and reduces the cost of building highways. Many methods have been developed for designing seismic resistant tunnel linings. Due to simplicity, analytical methods are usually used for preliminary design. In this case, the presence of joints between the blocks of the ring and between the rings is not taken into account. Compared to analytical methods, numerical methods, especially three-dimensional (3D), allow the most explicit consideration of the problem being solved. However, due to their complexity and time-consuming nature, 3D numerical models are only rarely used. In most reinforced concrete prefabricated linings, the deformation at the joints has a significant effect on the deformation of the rings. Thus, the magnitude and distribution of internal forces largely depend on the distribution and characteristics of the joints. Therefore, one of the most important factors in the design of a circular tunnel lining is the effect of segment connections on its overall behavior. This paper compares the internal forces that occur in the tunnel lining, determined using analytical analysis and numerical simulation in a three-dimensional formulation. When using numerical analysis methods, seismic loads are considered as quasi-static. However, almost all quasi-static analyzes presented in the literature include the same assumptions as closed form solutions and therefore have the same limited applicability. The main disadvantage of quasi-static models is that they do not take into account changes in the behavior of the structure over time.

A spring-like interface between saturated frozen soil and circular tunnel lining under the moving load in cold regions without considering frost heave

The vibration of underground or buried piping during construction and long-term operation causes secondary disasters, and becomes more complex when tubes are buried in cold regions. The interface between saturated frozen soil and lining is regarded as a thin spring-like layer whose thickness could be negligible. In this paper, the dynamic response of saturated frozen soil is studied in frequency domain by using the Helmholtz composition and Fourier transform to obtain analytical solutions of the radial and axial displacement, as well as expressions of the stiffness coefficient (Kr) and damping coefficient (Cr) of the spring-like interface. Numerical results indicate that Kr and Cr are related to physical properties of the lining and its surrounding soil, and the coefficients of the spring-like model could be changed by adjusting lining parameters to improve structure stability under the same load conditions. Also, the viscoelastic contact surface of the spring-like model is considered to have less effect on the surrounding soil than that when the lining has complete contact with the soil under load. The degree of soil freezing significantly affects the axial and radial displacement of the soil when the interface between lining and unsaturated frozen soil is taken into consideration.

Study on the Influence of Internal Water Pressure on the Internal Force of Circular Hydraulic Tunnel Lining

The internal water pressure condition influences the internal force of the circular hydraulic tunnel lining. However, calculating the lining’s internal force of this type of tunnel still lacks practical theory. Based on the modified routine method and the theory of structural mechanics, the internal stress model of the tunnel section is established in this paper. The general calculation formula of lining internal force is deduced by considering arbitrary water level height and different water conveyance pressures. The formula is used to calculate the internal force of the lining under the action of internal water pressure and the influence laws of water level height and water conveyance pressure are explored, respectively. In addition, case analysis was carried out for several typical projects. The results show that the maximum internal force of the lining increases with the increase of water pressure and inner radius and the maximum internal force is in a fixed special position when the water is conveyed under pressure. When the water is conveyed without pressure, the internal force of the lining will increase with the increased water level. However, the maximum bending moment and axial force will reduce at the special water level. This calculation theory considering different working conditions of internal water pressure solves the calculation problem of the internal force of a circular hydraulic tunnel. It improves the design theory of tunnel structure and provides a theoretical basis for this type of tunnel’s structural design and safe operation.

Reliability based optimization of steel-fibre segmental tunnel linings subjected to thrust jack loadings

The circular lining in mechanized tunnelling consists of concrete segments, which are exposed to different loading cases during tunnel construction. One of the most critical loading condition is the thrust jack force, which is induced to the lining segments by the Tunnel Boring Machine (TBM) during construction. Experimental campaigns showed that steel fibre reinforced concrete is suitable for bearing such loads and could replace conventional reinforcement schemes. In this contribution, a numerical model is presented, which allows to directly track the influence of important design parameters such as fibre type, fibre orientation, fibre content and concrete strength on the structural response of steel-fibre reinforced segments. For this purpose, submodels on the single fibre level are combined into a crack bridging model considering the fibre orientation and the fibre content. The submodels are integrated into a finite element model to perform numerical structural analyses. Two validation examples demonstrate that the modelling approach is capable to predict the failure loads as well as the crack development of fibre reinforced specimens subjected to localized loads. Finally, an optimization procedure is carried out to determine a robust and cost-effective design of a fibre reinforced segmental linings. A hybrid reinforcement scheme consisting of two layers of fibre reinforced concrete is employed in order to provide an improved material utilization. The thickness of the segment and the fibre content are optimized taking uncertainties of the material parameters and construction tolerances as uncertain a priori parameters into account. A sufficient load bearing capacity and serviceability performance under all possible conditions is ensured by the consideration of accepted failure probabilities as constraints in the optimization task.

Study on Dynamic Characteristics of Circular Tunnel Lining in Fractional Derivative Viscoelastic Radially Inhomogeneous Soil

Considering the heterogeneous and viscoelastic characteristics of the soil around the tunnel, the dynamic characteristics of circular tunnel lining in fractional derivative viscoelastic radially inhomogeneous soil are studied. To accurately describe the viscoelasticity of the soil around the circular tunnel, the fractional derivative viscoelastic model is used to describe the stress‐strain relationship of the soil. To consider the heterogeneous characteristics of the soil around the circular tunnel caused by construction and in situ stress, the soil around the tunnel lining is divided into undisturbed area and disturbed area, and the disturbed area is divided into multiple thin concentric rings. A dynamic interaction model of fractional derivative viscoelastic radially inhomogeneous soil‐circular tunnel lining is established. By solving the vibration of the soil in undisturbed area and each circle and considering the continuity conditions of the radial displacement and radial stress of the soil at the junction of each circle, the transfer matrix of the radial displacement and radial stress of the soil at the outer and inner boundaries of disturbed area is obtained. Based on the transfer matrix of the radial displacement and radial stress of soil in the disturbed area and considering the boundary conditions and continuity conditions of the problem, the solution of the dynamic response of circular tunnel lining in fractional derivative viscoelastic radially inhomogeneous soil is obtained in the frequency domain. The results show that the fractional derivative viscoelastic inhomogeneous soil‐circular tunnel lining system also has resonance under the action of simple harmonic internal pressure, and the curves of the radial displacement and radial stress of soil varying with frequency obtained by the fractional derivative viscoelastic model fluctuate greatly. When studying the dynamic response of circular tunnel lining in inhomogeneous soil, the influence of viscoelasticity of the soil around the tunnel should not be ignored. The shear modulus ratio of soil in the affected area around the tunnel has a great influence on the dynamic characteristics of circular tunnel lining in fractional derivative viscoelastic radial inhomogeneous soil, and the inhomogeneous characteristics of soil should not be ignored. The greater the thickness and shear modulus of the tunnel lining, the greater the stiffness of tunnel lining and the smaller the radial stress and radial displacement of the soil.

Influence of water pressure on deep subsea tunnel buried within sandy seabed

For a subsea tunnel, the changeable high water pressure is of great significance in the soil-water-tunnel interaction. In this study, a series of parametric studies were conducted to investigate the effect of high water pressures on the seabed settlement and the earth pressures as well as the axial forces and bending moment of a tunnel lining during excavation. The simulation results disclose that the seabed settlement along the transversal tunnel direction increased linearly with the rising water level and the ranges of settlement troughs can be up to around 5 D (D, tunnel diameter) in width. Similarly, the settlement along the longitudinal tunnel direction featuring a semi-trough shape also shows a linear increase with the rising water level, and the maximum influence zone could reach a length of 3 D in front of the excavation face. With the increase of water pressure during tunneling, the total earth pressures along the perimeter of a circular tunnel lining increased significantly and their distributions were prone to be more uniform around the tunnel perimeter. As a result, the deep sea tunnel lining has a typical feature of large axial force and relatively smaller bending moment.

Benchmark solutions of large-strain cavity contraction for deep tunnel convergence in geomaterials

To provide precise prediction of tunnelling-induced deformation of the surrounding geomaterials, a framework for derivation of rigorous large-strain solutions of unified spherical and cylindrical cavity contraction is presented for description of confinement-convergence responses for deep tunnels in geomaterials. Considering the tunnelling-induced large deformation, logarithmic strains are adopted for cavity contraction analyses in linearly elastic, non-associated Mohr–Coulomb, and brittle Hoek–Brown media. Compared with approximate solutions, the approximation error indicates the importance of release of small-strain restrictions for estimating tunnel convergence profiles, especially in terms of the scenarios with high stress condition and stiffness degradation under large deformation. The ground reaction curve is therefore predicted to describe the volume loss and stress relaxation around the tunnel walls. The stiffness of circular lining is calculated from the geometry and equivalent modulus of the supporting structure, and a lining installation factor is thus introduced to indicate the time of lining installation based on the prediction of spherical cavity contraction around the tunnel opening face. This study also provides a general approach for solutions using other sophisticated geomaterial models, and serves as benchmarks for analytical developments in consideration of nonlinear large-deformation behaviour and for numerical analyses of underground excavation.

Application of coupled XFEM-BCQO in the structural optimization of a circular tunnel lining subjected to a ground motion

A new structural optimization method of coupled extended finite element method and bound constrained quadratic optimization method (XFEM-BCQO) is adopted to quantify the optimum values of four design parameters for a circular tunnel lining when it is subjected to earthquakes. The parameters are: tunnel lining thickness, tunnel diameter, tunnel lining concrete modulus of elasticity and tunnel lining concrete density. Monte-Carlo sampling method is dedicated to construct the meta models so that to be used for the BCQO method using matlab codes. Numerical simulations of the tensile damage in the tunnel lining due to a real earthquake in the literature are created for three design cases. XFEM approach is used to show the cracks for the mentioned design cases. The results of the BCQO method for the maximum design case for the tunnel tensile damage was matching the results obtained from XFEM approach to a fair extent. The new coupled approach manifested a significant capability to predict the cracks and spalling of the tunnel lining concrete under the effects of dynamic earthquakes.

Elastoplastic Analysis of Two-Layered Circular Lining Based on the Unified Strength Theory

Based on the Unified Strength Theory (UST), elastoplastic analysis of the two-layered circular lining is carried out. The stresses, displacements, and the elastic and plastic zones in both layers are discussed under different values of Young’s moduli of the inner and outer layers. The results reveal that, compared to the single-layered lining, the tangential stress distributions in the two-layered linings are more reasonable along the radial direction, which is beneficial to enhance the overall elastic and plastic ultimate bearing capacities. When considering the intermediate stress (i.e., the axial load), the elastic ultimate bearing capacity will be higher. However, the plastic ultimate bearing capacity remains unchanged. Moreover, a comparison between the Unified Strength Theory and Tresca Criterion is analyzed as well.

Numerical Investigation of Closed-Form Solutions for Seismic Design of a Circular Tunnel Lining (by Quasi-Static Method)

In this paper, four known analytical methods including Wang (1993), Penzien (2000), Park et al. (2009), and Bobet (2010) were Evaluated based on seismic design of circular tunnel in Tehran Metro Line 6. For this purpose, a quasi-static numerical method was applied in the framework of finite difference method (FDM) under the same assumptions. In both numerical and analytical methods, to consider the nonlinear behavior of soil, linear equivalent properties of soil derived from ground analysis were incorporated in EERA software. obtained results shown that the Park’s analytical solution under various conditions of interaction between the tunnel lining and soil provides very close results to the of numerical modeling. Afterward, a comprehensive validation was performed to assess the impact of the rigidity of the surrounding ground and the maximum shear strain value. In this regard, several earthquake scenarios with different shear wave rates were used to achieve a wide range of flexibility ratio (F) and maximum shear strain. The results showed a significant difference between the results of Penzine’s and Bobet’s methods under the no-slip conditions and those of numerical analyses for a certain range of flexibility and shear strain ratios. In the final part of the paper, a quasi-static seismic numerical study was performed under realistic soil-structure interaction conditions to illustrate the importance of the actual interaction between the tunnel lining and surrounding soil. The results showed that the actual interaction conditions governing estimation of the axial force play a very important role. Also, it was found that Park’s solution, because of the ability to consider the slip at the interface provides results very close to those of the numerical modeling. In contrast, one of the serious limitations of the other analytical methods is their inability to simulate the slip interface between the tunnel lining and soil.

The ultimate limit state of the underground circular tunnel segment lining

Circular tunnel segment lining with staggered joints in track tunnels of Prague Underground was found to be on the ultimate limit state; static analysis (mathematical modeling) is used to determine the causes which led to such situation. This situation is signalized by cracks and related deformations; lining load-limit coefficient can be used to determine the cause. Analysis is performed in the form of parametric study, where the variables are the values of geotechnical figures, the rigidity of the lining with staggered joints and the load of the lining. This paper focuses on analysis of reinforced concrete segmental lining Ø5.3 / 5.8 m (5 + 1 element) and cast iron Ø5.1 / 5.5 m (9 + 1 element). Parametric study using coefficient of loading limit for both of these cases in the Prague Underground leads to fast and relatively easy determination of the cause of the reaching of the ultimate limit state.

Influence of Pipe Ramming on Stress State of Surrounding Soil and Nearby Tunnel Lining

ANNOTATIONThis article proposes an approach to the prediction of stress state and assessing the strength of a circular tunnel lining and the surrounding rock mass under construction near the production used by the micro-tunneling technology of pipe ramming. The basis of this method is an analytical solution of the corresponding plane problem of elasticity theory.

Durability of crystalline phase in concrete microstructure modified by the mineral powders: evaluation by nanoindentation tests

Abstract This paper presents the nanoindentation investigation of the evolution of concrete microstructure modified by the Internal Crystallization Technology mineral powders. The samples under study were retrieved from a fragment of a circular concrete lining of the vertical mine shaft at a depth of approximately 1,000 m. Due to the aggressive environment and exposure to contaminated water, the internal surface of the structure was deteriorated, decreasing its strength significantly. The mineral powders were applied directly on the surface lining. The specimens were investigated one month, three months and one year after the application of the aforementioned substance in order to verify the time dependence of the strengthening processes and durability of the crystalline phase. The microstructural changes of concrete were assessed with the use of nanoindentation technique. The testing procedure involved including the previously cut specimens in the epoxy resin and grinding and polishing in order to reduce the surface roughness. As a result of the nanoindentation tests the hardness as well as Young’s modulus of the material were evaluated. The results were then compared and statistically analyzed. As a consequence, the disintegration time of the crystalline network in the pores of concrete was identified.

A Green Function of Vertical Interfacial Point Source SH Wave Scattering by a Circular Lining in an Elastic Quarter Space

An anti-plane Green function is formulated for steady state solution of a circular lining impacted by a vertical interfacial point source in an elastic quarter space. Series forms of scattering and stationary wave of the circular lining are constructed with Fourier wave function expansion method. Basic solution of the anti-plane point source is employed to represent displacement fields of incident wave. Stress-free conditions on the quarter bounds are satisfied by using image method. Displacement and stress continuity conditions of the lining are expanded as Fourier series to determine definite equations of unknown coefficients of wave function series.

Three-dimensional orthotropic equivalent modelling method of large-scale circular jointed lining

Due to the large spatial scale differences between the structure details and the global tunnel, the large-scale shield tunnels were usually modeled as continuous ‘pipes’ in the 3-D numerical analyses. The details (e.g. joints) that greatly affect the integral stiffness of the continuous 3-D tunnel models have seldom been discussed in literatures. This paper presents an idea of orthotropic equivalence for the modeling of the large-scale circular shield tunnel and the optimization procedure for the identification of the nominal material constants. Considering the tunnel’s structural characteristic in its radial, circumferential and axial directions and its periodicity, the segmentally erected lining is equivalently modeled as an orthotropic continuous structure. An optimization procedure based on the idea of inverse analysis and FE method which can quickly identify the equivalent constants is also proposed. Validation example shows that a reasonable consistency between results predicted by the equivalent/segmental models and the analytical formulas is achieved.

Dynamic Response of Underground Circular Lining Tunnels Subjected to Incident P Waves

Dynamic stress concentration in tunnels and underground structures during earthquakes often leads to serious structural damage. A series solution of wave equation for dynamic response of underground circular lining tunnels subjected to incident plane P waves is presented by Fourier-Bessel series expansion method in this paper. The deformation and stress fields of the whole medium of surrounding rock and tunnel were obtained by solving the equations of seismic wave propagation in an elastic half space. Based on the assumption of a large circular arc, a series of solutions for dynamic stress were deduced by using a wave function expansion approach for a circular lining tunnel in an elastic half space rock medium subjected to incident plane P waves. Then, the dynamic response of the circular lining tunnel was obtained by solving a series of algebraic equations after imposing its boundary conditions for displacement and stress of the circular lining tunnel. The effects of different factors on circular lining rock tunnels, including incident frequency, incident angle, buried depth, rock conditions, and lining stiffness, were derived and several application examples are presented. The results may provide a good reference for studies on the dynamic response and aseismic design of tunnels and underground structures.

Response of Shallow-Buried Circular Lining Tunnel to Incident PWave

Taking the circular lining tunnel in half-space as prototype, this paper investigates the dynamic responses of this tunnel. A series solution for the scatting waves in half-space and the lining is derived by wave expansion method under the assumption of the large circular arc. And then, combining the boundary conditions, the tunnel dynamic response is shift to seeking the solution of series of algebraic equations. Finally, the effects of buried depth, lining rigidity and incident frequency upon the dynamic hoop stress in the inner lining surface caused by incident plane Pwave is quantitatively analyzed from the view of theory in a typical case.

Large Extrusion Deflection Control Technology for Tunnel in Active Fault Zone

The Wushaoling tunnel passes the active engineering fault 7(simply called F7 below), where the surrounding rock is broken, mainly composed of fault boulder clay and rubble with very low strength/geostress ratio, resulting in remarkable deflection. Measures have been taken to control the large deflection of the primary support effectively and to ensure safety of the lining structure so that the F7 can be passed as early as possible . Two small-section roundabout drifts for left and right line each, affected less by the high geostress, are excavated in order to continue the construction ahead, to release partial geostress and to conduct experimental study guiding the design &construction of the main tunnels. At the same time, in-situ experiments are carried on against different pattern and parameters of support structure. Based on the above study, the measures are finally determined such as adopting circular multiple-support composite lining, setting deformation joints per segment to absorb the movement of the active fault, adhering the construction principle of “rapid excavation, rapid support, rapid closure and timely lining”, etc. As a result, the large deflection is controlled effectively in subsequent construction and the large-scale active fault rarely encountered domestic and abroad has been passed successively.

Research on Dynamic Response of Underground Circular Lining Tunnel under the Action of P Waves

Dynamic stress concentration of tunnels and underground engineers under the action of earthquake waves is a fundamental problem. Selecting circular lining tunnel in semi-infinite space under the action of P waves as prototype, based on the assumption of large circular arc, a set of dynamic stress series solution in semi-infinite space and lining is deduced by wave function expansion method. With specific examples, the influences on shallow-buried depth rock tunnels of different factors which include incident frequency, incident angle, buried depth, rock conditions and lining rigidity are studied. The results show that low-frequency P waves are more dangerous to tunnel lining than high-frequency P waves; When P waves is incident from the bottom of the vertical tunnel or small angle (θα = 0° ~ 30°), the damage of tunnel lining is more seriously; Under the hard rock conditions, when the tunnel buried depth reaches more than 100m, the thickness of overlying rock is not a major factor effecting the dynamic stress and earthquake damages of tunnel structure lining; Under the soft surrounding rock condition, the value of dynamic stress concentration coefficient of lining is still up to 6.5 when the buried depth of tunnels is more than 100m, and what’s more the tunnel lining may still be caused seriously earthquake damage; With the increasing of lining stiffness, the dynamic stress concentration of lining is more uneven, and the value span is greater; so under the premise of meeting bearing capacity and deformation of lining, soft lining is recommended to adapt in the tunnel structure to decrease earthquake damage of tunnels.