Segmented Liner Research Articles

Analytical seismic model for a tunnel with segmental liner buried in the half-space soil

In this paper, by using the wave function expansion (WFE) and the expansion of the cylindrical wave into plane wave (ECPW) methods, an analytical method for the dynamic response of a circular tunnel with segmental liner buried in the half-space soil to harmonic elastic waves is developed. The liner of the tunnel is supposed to consist of several segments and joints. Both the segments and joints are treated as open cylindrical shells, and the segment and joint shells together thus form an equivalent continuous shell (ECS) liner, and the thin shell theory is utilized to describe its vibration. The scattered wave field due to the presence of the tunnel and boundary of the half-space soil is divided into two parts, namely, the direct scattered wave field and secondary scattered wave field. The expressions for the direct scattered cylindrical waves in the soil is determined via the WFE method, while the secondary scattered waves form the boundary of the half-space soil are obtained by the ECPW method together with the application of the boundary condition along the soil surface. Applying the cylindrical shell theory on the ECS liner and using the Fourier series expansions for the variables and parameters of the ECS liner along the azimuthal direction together with introducing the Fourier component constitutive relation for the ECS liner, a system of equations for the Fourier component ECS displacements are derived with the differential equations for the ECS liner displacements. By using the system of equations, the expressions for the free and scattered wave fields and the continuity conditions at the interface between the liner and soil, the system of equations for the ECS liner coupled with the soil are derived. By using the developed analytical method for the tunnel, some results of the ECS tunnel under different incident waves are given.

Acoustic scattering mechanism and noise attenuation of circumferentially non-uniform liner with spectral-wave guide method

In this paper, a model is established with application of the spectral-wave guide method, which has higher accuracy and can serve as a rapid calculation tool for sound transmission calculations. Based on this calculation model, some numerical results of circumferentially non-uniform lined annular/circular ducts are carried out, and some physical mechanisms can be discovered. The numerical results show that periodical impedance distributions along the circumferential direction will lead to discontinuous scattered modes with regular spacing; and mirror-symmetric structure liner will converge the energy of opposite modes. Relying on this mechanism, the potential of acoustic scattering can be further developed by suppressing lower or enhancing higher order modes with expressly designed segmented liner configurations. In particular, the intrinsic mechanism of mode redistribution brought about by the non-uniform liner can be subtly utilized to attenuate broadband noise. The present work indeed shows that circumferentially non-uniform liner is conducive to the reduction of the practical broadband sound source. Furthermore, the effects of non-uniform flow are considered in the model, then distinction of noise attenuation and scattered modes energy in different flows is shown. A possible mechanism is proposed that refraction effects in complex flows lead to the distinction. These works show that the current model has profound potential and availability for the research and designs of circumferentially non-uniform liner.

Modeling analysis of combustion instability in an annular combustor equipped with circumferentially segmented perforated liner

Hazardous azimuthal thermoacoustic modes often occur in lean-premixed annular combustors. One practical control method is the application of perforated liners with bias flow. However, circumferentially uniform perforated liners are not competent to control them, because the perforated plate covered by a single azimuthally uniform backing cavity cannot provide sufficient acoustic pressure difference across the perforated plate to bring in adequate acoustic damping. In this work, we developed a three-dimensional thermoacoustic model to consider the effects of a novel passive control damper of the circumferentially segmented perforated liner. Emphasis is placed on the effects of the segmented liner on controlling the azimuthal modes. It is found that the azimuthal mode in the premixed annular combustor can be either plenum-dominant or combustor-dominant, with the frequency of the latter one larger than the former. The stabilities of the two kinds of modes behave differently with the change of time delay. The results of the lined combustor cases indicate that the circumferentially segmented perforated liner generally improves the control effectiveness compared with the circumferentially uniform perforated liner thanks to the rigid plates inserted in the backing cavity. At the locally inserted position, the rigid plate enforces a rigid boundary condition that changes the azimuthal pressure mode shape in the backing cavity. As a result, more acoustic damping through the pressure difference across the plate is produced. Symmetry-breaking effects are found if the segmentation is asymmetric or two-fold symmetric. The behavior of the splitting frequencies caused by the segmented liner is also studied, and the symmetric segmented liner turns out to be a better choice because the resulting azimuthal mode is degenerate with two equivalent suppressed growth rates. In order to further enhance the control effect, one significant effective measure is to increase the depth of the backing cavity.

Analytical modelling of segmental liner joints for close-proximity tunnelling in soft ground

Close-proximity tunnellng seriously threatens the safety of existing tunnels and, therefore, leads a pressing need of enhancing our understanding of the role and mechanical properties of liner joints in tunnel construction. This study conducted an investigation into the moment-joint opening and load–displacement relationships of the liner joints under the effect of shield approaching, reaching, and passing the existing tunnel using the proposed analytical calculation that takes into account the concrete tensile strength and the real moment of inertia. The most affected liner joints for different tunnelling stages were recognised. The findings of this study indicated that the moment-joint opening relationship of the joints shows a good correspondence with the distance to the new tunnel excavation. The liner joint behaviour can be affected not only by the distance to the new tunnel excavation but also by the jack-arch mechanism. The findings also stand out the importance of the structural capacity available in the liner joints as they may operate completely in different manners, depending on tunnelling stages.

The influence of face and shield annulus pressure on tunnel liner load development

Three dimensional (3D) finite-difference analysis simulations together with rare field data from strain gauges installed in segmental lining rings at the Seattle Sound Transit Northgate Link tunnel project are examined to provide a better understanding of segmental liner loading developed during earth pressure balance shield tunneling. A simplified 3D numerical model is presented for pressure balanced mechanized tunneling, where the annulus between the shield and excavated ground is full of pressurized material, simplifying the shield shape, and the modeling of the annular gap. This simplified model is based on the assumption that the shield annulus pressure controls the tunnel convergence prior to lining installation. While the presented model simplifies the modeling of the TBM shield, it captures the important components in shield tunneling, including the jointed segmental lining, grout injection pressure, time-dependent grout hardening, and the non-liner soil behavior using the hardening soil constitutive model. The results of this study show that the final lining loads are controlled by the chamber pressure for pressure balance TBMs with pressurized material in the shield annulus. In the case study presented here, pressure drops of the chamber pressure (common in EPB tunneling due to excavation standstill), result in a significant influence on tunnel lining loads.

A generalized compliance model for study of acoustic damping behavior of mixed porosity segmented perforated liner

Acoustic liners play a vital role in the reduction of aero-engine noise and combustion instabilities. In the present work, acoustic damping behavior of perforated cylindrical liners of mixed porosities is investigated both analytically and experimentally. The aim of the paper is to propose a generalized analytical model for the compliance of mixed porosity liners. The analytical results are obtained by considering the compliance of each segment of distinct porosities. Experimental results are compared with the analytical predictions to validate the proposed generalized compliance expression. Predicted results are in reasonable good agreement with the experimental results. A parametric study is carried out for different flow with variably segmented liner configurations. The effect of number of liner segments is studied. Liners with higher number of segments are shown to perform better than the liners having lesser number of segments.

IFAR liner benchmark challenge #1 – DLR impedance eduction of uniform and axially segmented liners and comparison with NASA results

This paper presents the contribution from the German Aerospace Center (DLR) to the first liner benchmark challenge under the framework of the International Forum for Aviation Research (IFAR). Therefore, two sets of acoustically damping wall treatments, called ‘liner samples’, have been produced by additive manufacturing based on the design data provided by NASA coordinating this benchmark. These liner samples have been integrated and acoustically characterized in the liner flow test facility DUCT-R at DLR Berlin as well as in the liner flow test facility GFIT at NASA Langley. Besides the dissipation coefficients and the axial pressure profiles, the liner wall impedance was educed by first determining the axial wave numbers and then applying a straightforward method based on the one-dimensional Convected Helmholtz Equation. Finally, the comparison of the liner impedance values to the NASA results show a fairly good agreement.

Preliminary Design for Segmental Joint of Precast Tunnel Liner

Abstract Responses of the segmental tunnel liner to external forces are primarily dependent on complicated interactions among construction process, soil structural interactions, segmental (longitudinal) joint characteristic etc. However, most proposed liner’s design procedures and recommendations are basically empirical and experience based, especially when the roles of tunnel joint are concerned. In the present study, a preliminary design calculation for the segmental joint with consideration of three practical conditions was proposed. The method adopts two main assumptions; the stiffness reduction factor and simplified pre-stressed concrete blocks, so that the flexural capacity of the segmental joint and its interactions to the main reinforced concrete segment body can be designated. Calculation examples are given for three most probable cases, namely, 1) the unbolted joint without joint opening, 2) the bolted joint without joint opening and 3) the unbolted segmental joint with allowing joint opening. Based on these calculations, the required compressive strength of concrete, thickness of liner, steel reinforcement, bolts and number of segments of the liner could be specified. The proposed method could well provide an engineer a tool to determine the initial joint configuration and its interaction to the overall tunnel lining.

Imaging ahead of a tunnel boring machine with DC resistivity: A laboratory and numerical study

Tunnel Boring Machines (TBMs) are used for tunneling and underground construction, by excavating material and subsequently installing a segmental concrete tunnel liner for support. However, unknown ground conditions pose a significant risk to tunneling operations and any damage to the machine can be disastrous to a project. There is a need for tools which look ahead of the TBM for potential hazards during tunneling, such as water saturated zones, faults, boulders and metal pipes. Geophysical methods offer the capability to image unexcavated material in order to avoid such hazards and thus improve tunneling operations. In particular, the DC resistivity method is useful because it is sensitive to a large range of conductivity variations in geological and man-made materials.The research presented in our paper consists of three parts: (1) a laboratory study of a DC resistivity system mounted on a scale model TBM within a simulated tunneling environment, (2) a series of forward models studying different DC resistivity survey designs, and (3) the inversion and imaging of synthetic DC resistivity data under different constraints. We introduce several new survey designs that attach electrodes on a probe (or probes), which are then pushed into the earth in front of the machine each time excavation stops. Our laboratory data and forward modeling results show that using probes reduces interference caused by the metallic TBM body, and increases the distance ahead of the machine at which a target may be detected. The TBM influence on the data is significantly reduced once the probe is pushed 25% of the TBM diameter ahead of the machine and negligible once the probes are pushed 50% ahead of the machine. Depending on the specific survey design, targets can be detected from up to 70% of the TBM diameter away. Finally, we invert synthetic data to produce ahead-of-tunneling images using different amounts of prior information (e.g. TBM geometry and host resistivity) and also study time-lapse inversion. Numerical results show the target can be imaged with these methods from distances up to 45% TBM diameter.

Void detection in two-component annulus grout behind a pre-cast segmental tunnel liner using Ground Penetrating Radar

Ground Penetrating Radar (GPR) is being considered as a potential non-destructive technique for ensuring complete annulus grout backfill behind pre-cast segmental tunnel liners. Current methods for ensuring grout backfill involve drilled verification holes through the waterproof liner. The Rondout bypass tunnel, in Newburgh, NY, where void formation behind the tunnel liner is possible due to high groundwater pressures, provided an example project to evaluate GPR capabilities. While the application of GPR for void detection in one component grouts behind tunnel liners has been well-documented, site specific calibration of the GPR equipment and the application to two-component grouts is necessary. Experiments were conducted on actual tunnel segments to determine the most appropriate antenna frequency that can penetrate through the steel-reinforced segments and produce the best resolution. Mock air and water voids were embedded within areas of complete grout behind the segment to demonstrate the GPR signatures. Steel reflectors buried within the grout provided indirect measurements of the electromagnetic (EM) properties of the two-component grout. All field results were compared against analytical evaluation and numerical models to validate void detection. The findings of this research allow for direct implementation of the GPR technique for detection of voids behind segmental tunnel liners with two-component grout backfill.

Analysis of the behaviour of a novel support system in an anisotropically jointed rock mass

When constructing an excavation, the segmental lining installed in an anisotropic rock mass is susceptible to asymmetrical pressure and substantial local instabilities. To promote liner stability in such cases, a support system that combines a segmental lining with a highly deformable expanded clay and rock bolts is proposed. A series of physical model tests were performed to study the effect of this support system. In the tests, different dip angles of the primary rock mass jointing, different thicknesses of the expanded clay and different lengths and spacings of rock bolts were considered. Variations in the internal forces and deformation of the segmental lining were recorded in each case. The distribution of the internal forces and deformation of the segmental lining were anisotropic due to the rock mass anisotropy; the maximum positive bending moment and positive deformation on the liner mainly developed in the direction normal to the stratification. By using a sufficiently thick deformable clay layer, the anisotropy of the load transferred to the segmental liner can be minimized. By adding rock bolts, the combined support system can take full advantage of the reinforcement effect of the rock bolts and the yielding effect of the deformable clay layer, and the effect of the rock bolts plus the yielding layer is greater than the sum of the two individual effects. Such a system can change the internal force and deformation distribution of the segmental lining to improve liner stability.

Analytical solution for longitudinal bending stiffness of shield tunnels

The longitudinal bending stiffness of tunnels is one of the most important parameters for the structural design of the tunnel longitudinal deformations during seismic loading. The aim of the paper is to derive an analytical solution for the longitudinal bending stiffness of a segmental liner, typically used on tunnels built with a shield. For the derivation, it is assumed that the tunnel liner includes bolts, segments and rubber gaskets. All the elements are considered as linear elastic. The bolts are assumed to work only in tension and the rubber gaskets are assumed to work only in compression. The deformation of any tunnel cross section complies with the assumption that normals to the neutral axis remain normal and thus the neutral axis does not change along the tunnel during deflection. Based on these assumptions, a longitudinal equivalent model for shield tunnels is developed and the governing equations are obtained. A closed-form analytical solution for the longitudinal bending stiffness is developed and verified by providing comparisons between its results and those from the Finite Element program ABAQUS. A parametric analysis, using the new analytical solution, is included to investigate the influence of key parameters such as the thickness of the rubber gaskets, the ratio of the liner thickness to the internal tunnel diameter, and the transverse bending stiffness of the tunnel cross section on the longitudinal bending stiffness of the tunnel.

Evaluation of liner responses due to non-uniform tail void grouting pressure

ABSTRACTTail void grouting initially does facilitate the action of ground loads around the lower half of the liner and no excess pressure being accumulated. However, at a later stage (almost at the completion of grouting), grout pressure becomes non-uniformly distributed around grout injection holes especially on the upper half of the liner. In the present study, the boundary and loading conditions were simulated by using a series of finite element analyses. It aimed to explore the effects of such temporary non-uniform loading conditions on development of the liner internal forces. The results obtained for tunnel with diameter of 6.0 m were presented. It was found that there were critical locations where application of non-uniform grouting pressure could result in large amounts of bending moment and deformation. Those critical locations; about ±30° to ±50° from crown of the tunnel, were about the locations where actual grouting was injected in the field. The stiffness of sub-soil beneath the tunnel invert had minor effect on the amount of induced structural forces. However, ground coverage was more important. The results, though cannot fully represent complicated tail grouting behaviours, provided a simple analytical procedure for exploring the effects of tail void grouting on the segmental liner.

Seismic Design of a Single Bored Tunnel: Longitudinal Deformations and Seismic Joints

The large diameter bored tunnel passing through rock and alluvial deposits subjected to seismic loading is analyzed for estimating longitudinal deformations and member forces on the segmental tunnel liners. The project site has challenges including high hydrostatic pressure, variable ground profile and high seismic loading. To ensure the safety of segmental tunnel liner from the seismic demands, the performance-based two-level design earthquake approach, Functional Evaluation Earthquake and Safety Evaluation Earthquake, has been adopted. The longitudinal tunnel and ground response seismic analyses are performed using a three-dimensional quasi-static linear elastic and nonlinear elastic discrete beam–spring elements to represent segmental liner and ground spring, respectively. Three components (longitudinal, transverse and vertical) of free-field ground displacement–time histories evaluated from site response analyses considering wave passage effects have been applied at the end support of the strain-compatible ground springs. The result of the longitudinal seismic analyses suggests that seismic joint for the mitigation measure requiring the design deflection capacity of 5–7.5 cm is to be furnished at the transition zone between hard and soft ground condition where the maximum member forces on the segmental liner (i.e., axial, shear forces and bending moments) are induced. The paper illustrates how detailed numerical analyses can be practically applied to evaluate the axial and curvature deformations along the tunnel alignment under difficult ground conditions and to provide the seismic joints at proper locations to effectively reduce the seismic demands below the allowable levels.

Influence of consolidation settlement on the stability of inclined TBM tunnels in a coal mine

The Xinjie Coalfields in China plan to construct two inclined mine access tunnels using a tunnel boring machine. These tunnels will be supported by a segmented concrete liner and will penetrate 50m of Quaternary silty clay before they enter the sedimentary bedrock hosting the coal seams. Dewatering associated with future coal mining activities are expected to reduce the pore pressures within the silty clay resulting in approximately 0.3m of consolidation-induced settlement that may affect the mine tunnels. Consolidation settlement of thick soil deposits has damaged shafts at other coal mines in China and thus it was important to evaluate the impact of consolidation settlement on the planned tunnels, which will be the first inclined tunnels excavated by TBM in a coal mine in China. The consolidation deformation ratio obtained from 1-D consolidation tests on core samples of the silty clay was used to estimate the consolidation settlement. By regarding the inclined mine tunnel as a cantilever beam, a method is proposed to analyse the influence of consolidation settlement on the stability of the tunnel. An equivalent continuous model was used to study the mechanical behaviour of the segmented liner. Using the proposed new method, the consolidation settlements are predicted to not adversely affect the inclined tunnels because the lateral stiffness of the tunnel liner is relatively soft. The bending of the tunnel liner caused by the ground settlement does not induce high stresses in the liner.

Study of the Damage Mechanics and Dewatering Recovery Programs for the Shield Tunnel under the Yangtze River

A case is presented about damages due to leakage and inrushing water that developed in the segmented pre-casted concrete liner of a shield tunnel under the Yangtze River. Various possible causes were considered to explain the damage mechanism. The opening and distribution due to differential settlement caused by the leakage of biogas or water in the shield tunnel were analyzed. The damage mechanism of the aquifuge, which occurred under the tunnel through exertion of a high piezometric head in the lower confined aquifer, was analyzed. The tensile-shear damage mechanism of the aquifuge was studied, and the judgment formulas, which were used to determine whether surface water bursting occurred, were derived. Two dewatering recovery programs were simulated by the finite difference method in conjunction with MODFLOW software. From the simulation results, the hydraulic gradient and settlements caused by decreased pore pressure were calculated. The optimal dewatering scheme and protection measurements are suggested.

Investigation of friction characteristics in segmented piston ring liner assembly of IC engine

Summary The friction at the piston ring cylinder liner assembly (PRLA) is a major contributor in the total friction losses in the I.C. engine. New materials, coatings and high-tech machining processes that previously were considered to be too expensive and therefore only used in complex applications are today becoming more affordable. A significant amount of the total power loss in a modern automotive engine is due to the Friction interaction between the top compression ring and the cylinder liner, especially at the TDC and BDC where boundary lubrication exists. The change in piston speed is accompanied with change the lubrication regime in the cylinder, which results change in friction between the ring and the liner during the entire stroke of the piston. Theoretical modelling of friction force from the various sources of friction will be compared to experimental results for analysing the tribological characteristics. The appropriate sample of piston ring and cylinder liner pair is developed for studying the different tribological parameters on Reciprocating Tribometer. The variable parameters are engine speed, oil viscosity, and load. The experimental results and observations are studied under different operating conditions in speed ranges from 300 rpm to 1500 rpm with constant load of 60 N. It can be seen that as speed increases, the friction force and friction coefficient also decreases.

Study on the damage mechanics and dewatering recovery programs for shield tunnel

A case is presented about damages due to leakage and inrushing water that developed in the segmented precasted concrete liner of a shield tunnel under the Yangtze River. Various possible causes were considered to explain the damage mechanism. The opening and distribution due to differential settlement caused by the leakage of biogas or water in the shield tunnel were analyzed. The damage mechanism of the aquifuge, which occurred under the tunnel through exertion of a high piezometric head in the lower confined aquifer, was analyzed. The tensile-shear damage mechanism of the aquifuge was studied, and the judgment formulas, which were used to determine whether surface water bursting occurred, were derived. Two dewatering recovery programs were simulated by the finite difference method (FDM) in conjunction with MODFLOW software. From the simulation results, the hydraulic gradient and settlements caused by decreased pore pressure were calculated. The optimal dewatering scheme and protection measurements are suggested.

Investigation on the Cause of Damages of a Deep Tunnel

A study is presented on the damages that developed in the segmented precasted concrete liner of a deep tunnel excavated by means of a tunnel boring machine (TBM). Various possible causes are considered i.e., the pore-water pressure acting on the liner; the excessive mountain pressure; the anisotropic in situ stress field; and the incomplete filling of the rock-lining gap. The in situ investigation, carried out to quantitatively assess the level and the extent of the damages, ruled out the pore pressure as the main source. In fact, minor water leakages were observed at the fractured sections. The remaining alternatives were analyzed through a series of nonlinear finite-element calculations in the plane strain regime. They account for the strain softening behavior of the lining and for the lack of tensile stresses at the rock-lining interface. The results give insight into the rock-liner interaction and show that the observed damages are likely to depend on the incomplete filling of the gap. On this basis some conclusions are drawn on the stresses developing within the liner and on the procedures suitable for its structural rehabilitation.

Optimisation of axially segmented liners for aeroengine broadband noise

A practical two-stage method for optimising an acoustic liner divided into axial segments for aeroengine broadband noise is presented. The principles are explained based on a three segment design but extension to more segments is straightforward. Initially, the optimisation focuses on the material properties of the individual segments. The second stage determines the optimum axial segment lengths and the optimum permutation of segments along the duct by evaluating the fully scattered acoustic field. This method is deployed to optimise an absorber for a broadband source noise of bandwidth 900 Hz–1.8 kHz. The axial order of the segments is found to have a dramatic influence on the optimum axial segment lengths. In the case study, comparisons with optimised uniform liners over this frequency range demonstrate only a small noise reduction. A simple optimisation that neglects scattering between axial segments significantly overestimates the available attenuation and provides a poor estimate of the optimum segment lengths.