Isogeometric Analysis of Longitudinal Displacement of a Simplified Tunnel Model Based on Elastic Foundation Beam

Serious uneven settlement of the tunnel may directly cause safety problems.At this stage,the deformation of the tunnel is predicted and analyzed mainly by numerical simulation,while the commonly used finite element method(FEM)uses low-order continuous elements.Therefore,the accuracy of tunnel settlement prediction is not enough.In this paper,a method is proposed to study the vertical deformation of the tunnel by using the combination of isogeometric analysis(IGA)and Bézier extraction operator.Compared with the traditional IGA method,this method can be easily integrated into the existing FEM framework,and ensure the same accuracy.A numerical example of an elastic foundation beam subjected to uniformly distributed load and an engineering example of an equivalent elastic foundation beamof the tunnel are given.The results show that the solution of the IGA method is closer to the theoretical solution of the initial-parameter method than the FEM,and the accuracy and reliability of the proposedmodel are verified.Moreover,it not only provides some theoretical support for the longitudinal design of the tunnel,but also provides a new way for the application and popularization of IGA in tunnel engineering.

Bending the Foundation Beam on Elastic Base by Two Reaction Coefficient of Winkler’s Subgrade

A new method for analysis of counter beams is presented in the paper. The analysis has taken into account their stiffness EI, Winkler’s space with modulus of subgrade reaction k and equality deformities of the foundation beam with the ground. The solution is found by using the numerical analysis of the Winkler’s model, with variation of different moduli of the subgrade reaction k2 outside the force zone r, while under the force P exists the modulus of the subgrade reaction k, up to the definition of minimum bending moments. The exponential function k2(r), as the geometric position of the minimum moments is approximately assumed. From the potential energy conditions of the reciprocity of displacement and reaction, the width of the zone r and the modulus of the subgrade reaction k2 are explicitly determined, introducing in the calculation initial and calculation soil displacement wsi successively. At the end of the paper, it presented numerical example in which the influence of k and k2 values on bending moments of the counter beam is analyzed. The essential idea of this paper is to decrease the quantity of the reinforcement in the foundations, beams, i.e. to obtain a cost-efficient foundation construction.

DYNAMIC ANALYSIS OF ARREST OF BUCKLE PROPAGATION ON A BEAM ON A NONLINEAR ELASTIC FOUNDATION BY FEM

Based on the dynamic governing equation of propagating buckle on a beam on a nonlinear elastic foundation, this paper deals with an important problem of buckle arrest by combining the FEM with a time integration technique. A new conclusion completely different from that by the quasi-static analysis about the buckle arrestor design is drawn. This shows that the inertia of the beam cannot be ignored in the analysis under consideration, especially when the buckle propagation is suddenly stopped by the arrestors.

A method to Estimate Dynamic Responses of VLFS Based on Multi-Floating-Module Model Connected by Elastic Hinges

Based on the elastic foundation beam theory and the multi-floating-module hydrodynamic theory,a novel method is proposed to estimate the dynamic responses of VLFS(Very Large Floating Structure).In still water,a VLFS can be simplified as an elastic foundation beam model or a multi-floating-module model connected by elastic hinges.According to equivalent displacement of the two models in static analysis,the problem of rotation stiffness of elastic hinges can be solved.Then,based on the potential flow theory,the dynamic responding analysis of multi-floatingmodule model under wave loads can be computed in ANSYS-AQWA software.By assembling the time domain analysis results of each module,the dynamic responses of the VLFS can be obtained.Validation of the method is conducted through a series of comparison calculations,which mainly includes a continuous structure and a three-part structure connected by hinges in regular waves.The results of this paper method show a satisfactory agreement with the experiment and calculation data given in relative references.

Seismic response evaluation of the impact of corrosion on buried pipelines based on the Markov process

Water distribution and gas supply systems are among the infrastructure systems that have many buried steel pipelines. Corrosion gradually appears inside and outside of the pipe walls over the service life of these pipelines, the corrosion is primarily caused by the surrounding soil and the materials that flow through the pipelines. However, due to the uncertainty of the characteristics of the soil and materials, the size of the corrosion region is a stochastic variable. In this paper, using a homogeneous Markov process, a model is presented to simulate the occurrence of corrosion. Then, in combinations with a linear corrosion development model, the probability density function of the pipeline area corrosion percentage is derived. Based on the corrosion model, the pipeline seismic displacements and stresses are predicted. Furthermore, using the random perturbation approach, the mean and variance of the pipeline seismic response are given. To illustrate the validity of the proposed approach, a 200-meter long pipeline is numerically investigated and its random seismic response is obtained.

A Numerical Method for Cavity Identification in Beams on an Elastic Foundation

An analytical solution for the natural frequencies of a beam containing a cavity on an elastic foundation is presented. Based on the analytical solution, a numerical method for identifying cavities in the foundation is developed. The position and size of the cavities are identified by minimizing an objective function, which is formulated according to the difference between the computed and measured natural frequencies of the system. The conjugate gradient algorithm is adopted for minimizing the objective function. Some numerical examples are presented to demonstrate the applicability of the presented cavity determination method. The results show that the presented method can be used to identify the cavity position and size conveniently and efficiently.

Soil-Structure Interaction Analysis of Jack-up Platforms Subjected to Monochrome and Irregular Waves

As jack-up platforms have recently been used in deeper and harsher waters, there has been an increasing demand to understand their behaviour more accurately to develop more sophisticated analysis techniques. One of the areas of significant development has been the modelling of spudean performance, where the load-displacement behaviour of the foundation is required to be included in any numerical model of the structure. In this study, beam on nonlinear winkler foundation （BNWF） modeling--which is based on using nonlinear springs and dampers instead of a continuum soil media--is employed for this purpose. A regular monochrome design wave and an irregular wave representing a design sea state are applied to the platform as lateral loading. By using the BNWF model and assuming a granular soil under spudcans, properties such as soil nonlinear behaviour near the structure, contact phenomena at the interface of soil and spudcan （such as uplifting and rocking）, and geometrical nonlinear behaviour of the structure are studied. Results of this study show that inelastic behaviour of the soil causes an increase in the lateral displacement at the hull elevation and permanent unequal settlement in soil below the spudcans, which are increased by decreasing the friction angle of the sandy soil. In fact, spudeans and the underlying soil cause a relative fixity at the platform support, which changes the dynamic response of the structure compared with the case where the structure is assumed to have a fixed support or pinned support. For simulating this behaviour without explicit modelling of soil-structure interaction （SSI）, moment- rotation curves at the end of platform legs, which are dependent on foundation dimensions and soil characteristics, are obtained. These curves can be used in a simplified model of the platform for considering the relative fixity at the soil- foundation interface.

Closed-form solution of beam on Pasternak foundation under inclined dynamic load

The dynamic response of an infinite Euler–Bernoulli beam resting on Pasternak foundation under inclined harmonic line loads is developed in this study in a closed-form solution.The conventional Pasternak foundation is modeled by two parameters wherein the second parameter can account for the actual shearing effect of soils in the vertical direction.Thus,it is more realistic than the Winkler model,which only represents compressive soil resistance.However,the Pasternak model does not consider the tangential interaction between the bottom of the beam and the foundation;hence,the beam under inclined loads cannot be considered in the model.In this study,a series of horizontal springs is diverted to the face between the bottom of the beam and the foundation to address the limitation of the Pasternak model,which tends to disregard the tangential interaction between the beam and the foundation.The horizontal spring reaction is assumed to be proportional to the relative tangential displacement.The governing equation can be deduced by theory of elasticity and Newton’s laws,combined with the linearly elastic constitutive relation and the geometric equation of the beam body under small deformation condition.Double Fourier transformation is used to simplify the geometric equation into an algebraic equation,thereby conveniently obtaining the analytical solution in the frequency domain for the dynamic response of the beam.Double Fourier inverse transform and residue theorem are also adopted to derive the closed-form solution.The proposed solution is verified by comparing the degraded solution with the known results and comparing the analytical results with numerical results using ANSYS.Numerical computations of distinct cases are provided to investigate the effects of the angle of incidence and shear stiffness on the dynamic response of the beam.Results are realistic and can be used as reference for future engineering designs.

JUMPING INSTABILITIES IN THE POST-BUCKLING OF A BEAM ON A PARTIAL NONLINEAR FOUNDATION

Mode jumping is an instability phenomenon in the post-buckling region, which causes a sudden change in the equilibrium configuration and is thus harmful to structure. The con- figuration of a partial elastic foundation can directly induce mode coupling from the buckling stage and through the whole post-buckling region. The mode coupling effect due to the configuration of partial foundation on mode jumping is investigated and demonstrated to be an important factor of determining mode jumping. By properly choosing the partial elastic foundation configuration, mode jumping can be avoided.

Enhanced elastic beam model with BADS integrated for settlement assessment of immersed tunnels

Excessive settlement may induce structural damage and water leakage in immersed tunnels,seriously threatening the tunnels’safety.However,making accurate assessment of the settlement in immersed tunnels is difficult due to the incomplete knowledge of the geotechnical parameters and the inadequacy of the model itself.This paper proposes an effective method to accurately assess the settlement in immersed tunnels.An enhanced beam on elastic foundation model(E-BEFM)is developed for the settlement assessment,with the Bayesian adaptive direct search algorithm adopted to estimate unknown model parameters based on previous observations.The proposed method is applied to a field case of the Hong Kong–Zhuhai–Macao immersed tunnel.The original BEFM is used for comparison to highlight the better assessment performance of E-BEFM,particularly for joints’differential settlement.Results show that the proposed method can provide accurate predictions of the total settlement,angular distortion(a representation of tubes’relatively differential settlement),and joints’differential settlement,which consequently supports the associated maintenance decision-making and potential risk prevention for immersed tunnels in service.

ADOMIAN POLYNOMIALS FOR NONLINEAR RESPONSE OF SUPPORTED TIMOSHENKO BEAMS SUBJECTED TO A MOVING HARMONIC LOAD

This paper investigates the steady-state responses of a Timoshenko beam of infinite length supported by a nonlinear viscoelastic Pasternak foundation subjected to a moving harmonic load. The nonlinear viscoelastic foundation is assumed to be a Pasternak foundation with linear-plus-cubic stiffness and viscous damping. Based on Timoshenko beam theory, the nonlinear equations of motion are derived by considering the effects of the shear deformable beams and the shear modulus of foundations at the same time. For the first time, the modified Adomian decomposition method（ADM） is used for solving the response of the beam resting on a nonlinear foundation. By employing the standard ADM and the modified ADM, the nonlinear term is decomposed, respectively. Based on the Green＇s function and the theorem of residues presented,the closed form solutions for those linear iterative equations have been determined via complex Fourier transform. Numerical results indicate that two kinds of ADM predict qualitatively identical tendencies of the dynamic response with variable parameters, but the deflection of beam predicted by the modified ADM is smaller than that by the standard ADM. The influence of the shear modulus of beams and foundation is investigated. The numerical results show that the deflection of Timoshenko beams decrease with an increase of the shear modulus of beams and that of foundations.