Study on the Generalized Displacement Boundary and Its Analytical Prediction for Ground Movements Induced by Shield Tunneling

The process of shield tunnel excavation would inevitably cause surrounding ground movement, and excessive displacement in the soil could lead to large deformation and even collapse of the tunnel. The methods estimating convergence deformation around tunnel opening is summarized. Then, a universal pattern of displacement boundary condition around the tunnel cavity is originally introduced, which is solved as the combination of three fundamental deformation modes, namely, uniform convergence, vertical translation, and ovalization. The expression for the above-mentioned displacement boundary condition is derived, by imposing which the analytical solution for ground movements, based on the stress function method, is proposed. The reliability and applicability of this proposed solution are verified by comparing the observed data in terms of surface settlement, underground settlement, and horizontal displacement. Further parametric analyses indicate the following: (1) the maximum settlement increases linearly with the gap parameter and the tunnel radius, while it is negatively related to the tunnel depth; (2) the trough width parameter is independent of the gap parameter and the radius, while it is proportional to the tunnel depth. This study provides a new simple and reliable method for predicting ground movements induced by shield tunneling.

Guaranteed Lower Bounds for the Elastic Eigenvalues by Using the Nonconforming Crouzeix–Raviart Finite Element

This paper uses a locking-free nonconforming Crouzeix–Raviart finite element to solve the planar linear elastic eigenvalue problem with homogeneous pure displacement boundary condition. Making full use of the Poincaré inequality, we obtain the guaranteed lower bounds for eigenvalues. Besides, we also use the nonconforming Crouzeix–Raviart finite element to the planar linear elastic eigenvalue problem with the pure traction boundary condition, and obtain the guaranteed lower eigenvalue bounds. Finally, numerical experiments with MATLAB program are reported.

Study on Properties Prediction and Braiding Optimization of Axial Braided Carbon/Carbon Composite

It is well established that the microstructure has significant effects on the properties of axial braided C/C composites. In this study, a method coupling the homogenization method and finite element method (FEM) was proposed to predict the relationship between the microstructure characteristics and macroscopic properties. Based on the representative volume element (RVE) model, the periodic displacement boundary condition was introduced to predict the equivalent elastic properties of the RVE and component of C/C composite material, and the coefficient of thermal expansion (CTE) of the material was predicted by the energy prediction method. The predicted results were in good agreement with experimental results. By predicting the thermal and mechanical properties of the materials with different braiding spacing and fiber rod diameter, the variation of the properties with braiding spacing and fiber rod diameter was obtained. The research methods and results in this paper could provide important references for the optimization and rational application of composite materials.

On a boundary value problem for a third-order parabolic-hyperbolic type equation with a displacement boundary condition in its hyperbolicity domain

Исследована краевая задача со смещением для неоднородного уравнения параболо-гиперболического типа третьего порядка с волновым оператором в области гиперболичности, когда в качестве одного из граничных условий задана линейная комбинация с переменными коэффициентами производных от значений искомой функции на независимых характеристиках, а также на линии изменения типа и порядка. Найдены необходимые и достаточные условия существования и единственности регулярного решения задачи. В некоторых частных случаях представление решения исследуемой задачи выписано в явном виде.

Estimation Modal Parameter Variation with Respect to Internal Energy Variation Based on the Iwan Model

Typical factors that cause nonlinear behavior in structures are geometric nonlinearity, force and displacement boundary condition nonlinearities, and material nonlinearity. The nonlinearity caused by an increase of the internal energy in built-up structures is mostly due to the displacement boundary condition induced by the contact interface region. This study proposes an experimental mode analysis technique that predicts changes in natural frequencies and damping ratios when the external excitation force increases in a structure’s contact surfaces. Specifically, the nonlinearity of the dynamic characteristics induced by the contact region is described by the constitutive Iwan model. Next, an estimation method was developed for two parameters among the four of the Iwan model. This study used a modal analysis method. As an extension of a previous study, the approximate form of the harmonic excitation-induced force was determined in closed form. The configuration of the numerical model for the full structure was introduced from this resultant form. By using these numerical results, responses in the full structure, according to the harmonic excitation, have been represented in mode summation form. This research proposes an estimation method for two parameters among the four of the constitutive model. The proposed method was verified by simulations conducted with the lumped model and by experiments conducted on a partially connected double beam.

Similarity Solution for the Synchronous Grouting of Shield Tunnel Under the Vertical Non-Axisymmetric Displacement Boundary Condition

Similarity solution is investigated for the synchronous grouting of shield tunnel under the vertical non-axisymmetric displacement boundary condition in the paper. The synchronous grouting process of shield tunnel was simplified as the cylindrical expansion problem, which was based on the mechanism between the slurry and stratum of the synchronous grouting. The stress harmonic function on the horizontal and vertical ground surfaces is improved. Based on the virtual image technique, stress function solutions and Boussinesq's solution, elastic solution under the vertical non-axisymmetric displacement boundary condition on the vertical surface was proposed for synchronous grouting problems of shield tunnel. In addition, the maximum grouting pressure was also obtained to control the vertical displacement of horizontal ground surface. The validity of the proposed approach was proved by the numerical method. It can be known from the parameter analysis that larger vertical displacement of the horizontal ground surface was induced by smaller tunnel depth, smaller tunnel excavation radius, shorter limb distance, larger expansion pressure and smaller elastic modulus of soils.

Interaction of Multiple Cylindrical Cavities and Fixed Surface in Elastic Semi-Space

In natural medium, engineering materials and structures, it can be found that there are cavities everywhere. Sometimes the surface of the structure is fixed, and it could be seen as a rigid line. When structure is impacted by dynamic load, the scattering field will be produced because of the cavities and the fixed surface, and it could cause dynamic stress concentration at the edge of the cavities. In this paper, the solution of displacement field for elastic semi-space with fixed surface and multiple cylindrical cavities by anti-plane SH-wave is constructed. In complex plane, considering the displacement boundary condition of the fixed surface, the displacement field aroused by the anti-plane SH-wave and the scattering displacement field impacted by the cylindrical cavities comprised of Fourier-Bessel series with undetermined coefficients are constructed. Through applying the method of multi-polar coordinate system, the equations with unknown coefficients can be obtained by using the stress free condition of the cylindrical cavities in the radial direction. According to orthogonality condition for trigonometric function, these equations can be reduced to a series of algebraic equations. Then the value of the unknown coefficients can be obtained by solving these algebraic equations. The total wave displacement field is the superposition of the displacement field aroused by the anti-plane SH-wave and the scattering displacement field. By using the expressions, an example is provided to show the effect of the change of relative location of the cylindrical cavities. Based on this solution, the problem of interaction of multiple cylindrical cavities and a linear crack in semi-space with fixed surface can be investigated further.