Numerical study on transverse deformation characteristics of shield tunnel subject to local soil loosening

In this study,a refined numerical model for segmental lining of a shield tunnel,which contains detailed models of reinforcement and connecting bolts,is established using finite element software.The model is first validated by the results from a full-scale model test.Then,based on the load-structure method,this numerical model is adopted to investigate the internal force distribution and the transverse deformation characteristics of the shield tunnel when it is subject to local soil loosening.The influence of loosening position,loosening range,and loosening extent on the mechanical response is extensively studied through comprehensive numerical analyses.The results show that the main influence of local soil loosening on the ring is to disturb the force balance and change the constraint conditions,thus changing the deformation pattern and force state.After the loosening occurs,the bending moment of the ring in the loosening range increases and the axial force decreases.The vertical convergence of the ring is the largest and the equivalent stiffness of the ring is the smallest when the local soil loosened at the haunch and the loosening range a is 90°.The vertical convergence of the ring increases with increasing of the loosening extent,and the equivalent stiffness decreases linearly with increasing of the loosening extent.The results can enhance our understanding of mechanical behaviors of segmental lining associated soil loosening,and will show a possible way for detecting soil loosening based on the measured deformation and internal forces.

DIFFERENTIAL QUADRATURE METHOD FOR BENDING OF ORTHOTROPIC PLATES WITH FINITE DEFORMATION AND TRANSVERSE SHEAR EFFECTS

Based on the Reddy's theory of plates with the effect of higher-order shear deformations, the governing equations for bending of orthotropic plates with finite deformations were established. The differential quadrature (DQ) method of nonlinear analysis to the problem was presented. New DQ approach, presented by Wang and Bert (DQWB), is extended to handle the multiple boundary conditions of plates. The techniques were also further extended to simplify nonlinear computations. The numerical convergence and comparison of solutions were studied. The results show that the DQ method presented is very reliable and valid. Moreover, the influences of geometric and material parameters as well as the transverse shear deformations on nonlinear bending were investigated. Numerical results show the influence of the shear deformation on the static bending of orthotropic moderately thick plate is significant.

DYNAMIC RESPONSE OF LAMINATED ORTHOTROPIC SPHERICAL SHELLSINCLUDING TRANSVERSE SHEAR DEFORMATION AND ROTATORY INERTIA

In this paper.the equations of motion of axisymmetrically laminated cylindrical orthotropic spherical shells are derived.Theeffects of transverse shear deformation and rotatory inertia are considered.On this basis,the dynamic response of spherical shells under axisymmetric dynamic load is calculated using the finite difference method The effects of material parameters.structural parameters and transverse shear dgformation are discussed.

THE EFFECT OF TRANSVERSE SHEAR DEFORMATION ON STRESS CONCENTRATION FACTORS FOR SHALLOW SHELLS WITH A SMALL CIRCULAR HOLE

Simplified equations are derived for the analysis of stress concentration for shear-deformable shallow shells with a small hole. General solutions of the equations are obtained, in terms of series, for shallow spherical shells and shallow circular cylindrical shells with a small circular hole. Approximate explicit solutions and numerical results are obtianed for the stress concentration factors of shallow circular cylindrical shells with a small hole on which uniform pressure is acting.

Differential Quadrature Method for Bending Problem of Plates with Transverse Shear Effects

A differential quadrature (DQ) method for orthotropic plates was proposed based on Reddy' s theory of plates with the effects of the higher-order transverse shear deformations. Wang-Bert's DQ approach was also further extended to handle the boundary conditions of plates. The computational convergence was studied, and the numerical results were obtained for different grid spacings and compared with the existing results. The results show that the DQ method is fairly reliable and effective.

APPROXIMATE VIBRATION ANALYSIS OF LAMINATED CURVED PANEL USING HIGHER-ORDER SHEAR DEFORMATION THEORY

An approximate analysis for free vibration of a laminated curved panel(shell)with four edges simply supported(SS2),is presented in this paper.The transverse shear deformation is considered by using a higher-order shear deformation theory.For solving the highly coupled partial differential governing equations and associated boundary conditions,a set of solution functions in the form of double trigonometric Fourier series,which are required to satisfy the geometry part of the considered boundary conditions,is assumed in advance.By applying the Galerkin procedure both to the governing equations and to the natural boundary conditions not satisfied by the assumed solution functions,an approximate solution,capable of providing a reliable prediction for the global response of the panel,is obtained.Numerical results of antisymmetric angle-ply as well as symmetric cross-ply and angle-ply laminated curved panels are presented and discussed.

SNAP－THROUGH OF LAMINATED ORTHOTROPIC SHALLOW SPHERICAL IMPERFECT SHELLS WITH TRANSVERSE SHEAR

The equations of large deformations of laminated orthotropic spherical shellsare derived. The effects of transverse shear deformation and initial imperfection are considered. on this basis. the semi-analytical solution of the axisymrnetric snap-throughbuckling of laminated orthotropic shallow spherical shells under uniform pressure is obtained using orthogonal collocation method. The effects of material parameters, structuralparameters, initial imperfection and transverse shear deformation are discussed.

Investigation of mechanical failure performance of a large-diameter shield tunnel segmental ring

The control criteria for structural deformation and the evaluation of operational safety performance for large-diameter shield tunnel segments are not yet clearly defined.To address this issue,a refined 3D finite element model was established to analyze the transverse deformation response of a large-diameter segmental ring.By analyzing the stress,deformation,and crack distribution of large-diameter segments under overload conditions,the transverse deformation of the segmental ring could be divided into four stages.The main reasons for the decrease in segmental ring stiffness were found to be the extensive development of cracks and the complete formation of four plastic hinges.The deformation control value for the large-diameter shield tunnel segment is chosen as 8%o of the segment's outer diameter,representing the transverse deformation during the formation of the first semi-plastic hinge(i.e.,the first yield point)in the structure.This control value can serve as a reinforcement standard for preventing the failure of large-diameter shield tunnel segments.The flexural bearing capacity characteristic curve of segments was used to evaluate the structural strength of a large-diameter segmental ring.It was discovered that the maximum internal force combination of the segment did not exceed the segment ultimate bearing capacity curve(SUBC).However,the combination of internal force at 9°,85°,and 161°of the joints,and their symmetrical locations about the 0°-180°axis exceeded the joint ultimate bearing capacity curve(JUBC).The results indicate that the failure of the large-diameter segment lining was mainly due to insufficient joint strength,leading to an instability failure.The findings from this study can be used to develop more effective maintenance strategies for large-diameter shield tunnel segments to ensure their long-term performance.

Weakening behavior of waterproof performance in joints of shield tunnels under adjacent constructions

Groundwater leakage in shield tunnels poses a threat to the safety and durability of tunnel structures. Disturbance of adjacent constructions during the operation of shield tunnels frequently occurs in China, leading to deformation of tunnel lining and leakage in joints. Understanding the impact of adjacent constructions on the waterproofing performance of the lining is critical for the protection of shield tunnels. In this study, the weakening behavior of waterproof performance was investigated in the joints of shield tunnels under transverse deformation induced by adjacent construction. First, the relationship between the joint opening and transverse deformation under three typical adjacent constructions (upper loading, upper excavation, and side excavation) was investigated via elaborate numerical simulations. Subsequently, the evolution of the waterproof performance of a common gasket with a joint opening was examined by establishing a coupled Eulerian-Lagrangian model of joint seepage, and a formula describing the relationship between waterproof performance and joint opening was proposed. Finally, the weakening law of waterproofing performance was investigated based on the results of the aforementioned studies. It was determined that the joints with the greatest decline in waterproof performance were located at the tunnel shoulder in the upper loading case, tunnel crown in the upper excavation case, and tunnel shoulder in the side excavation case. When the waterproof performance of these joints decreased to 50% and 30%, the transverse deformations were 60 and 90 mm under upper loading, 90 and 140 mm under upper excavation, and 45 and 70 mm under side excavation, respectively. The results provide a straightforward reference for setting a controlled deformation standard considering the waterproof performance.

Geometrically exact nonlinear analysis of pre-twisted composite rotor blades

Modeling of pre-twisted composite rotor blades is very complicated not only because of the geometric non-linearity, but also because of the cross-sectional warping and the transverse shear deformation caused by the anisotropic material properties. In this paper, the geometrically exact nonlinear modeling of a generalized Timoshenko beam with arbitrary cross-sectional shape,generally anisotropic material behavior and large deflections has been presented based on Hodges＇ method. The concept of decomposition of rotation tensor was used to express the strain in the beam. The variational asymptotic method was used to determine the arbitrary warping of the beam cross section. The generalized Timoshenko strain energy was derived from the equilibrium equations and the second-order asymptotically correct strain energy. The geometrically exact nonlinear equations of motion were established by Hamilton＇s principle. The established modeling was used for the static and dynamic analysis of pre-twisted composite rotor blades, and the analytical results were validated based on experimental data. The influences of the transverse shear deformation on the pre-twisted composite rotor blade were investigated. The results indicate that the influences of the transverse shear deformation on the static deformation and the natural frequencies of the pre-twisted composite rotor blade are related to the length to chord ratio of the blade.