Solving Method for Soil Spring Stiffness of Shallow Shield Tunneling

Based on complex variable theory in plane elasticity, the equivalent spring stiffness is derived from the analytical solution by means of simplifying shallow shield tunneling to semi-infinite plane with hole, which is applied to response displacement method. The performances of the analytical solution are evaluated and compared with that of the deep shield tunneling through a series of selected various tunnel depths and soil Poisson's ratios. The relation of compression and shear spring stiffness is discussed. Meanwhile, two factors affected soil spring stiffness, tunnel depth and soil Poisson's ratio, are also analyzed. It is shown that soil spring stiffness of shallow shield tunneling is different from that of deep shield tunneling, and the ratio of compression and shear spring stiffness varies along shallow shield tunneling. It is also found that the value and distribution law of soil spring stiffness of shallow shield tunneling greatly depend on tunnel depth and soil Poisson's ratio.     

Progress of Study in Elasticity Problem with Different Moduli

This paper briefly describes elasticity theory with different moduli and research progress in recent twenty years,analyzes computational results respectively from these two theories to all kinds of engineering structures and concludes that applying different moduli theory to solve some engineering components conforms to the real mechanics performance.This paper also deals with the differences between analytical solution and numerical one.Though finite element method is an effective measure to solve these nonlinear problems,seeking analytical solutions is still a difficulty and goal for some problems.     

Elastic-Perfectly Plastic Solution of Tunnel Surrounding Rocks Using Mogi-Coulomb Strength Criterion

Reasonable choice of rock strength criteria is crucial for stress and displacement prediction and support design in tunnel engineering. Based on Mogi-Coulomb strength criterion and elastic-perfectly plastic model, analytical solutions of stress and displacement for surrounding rocks around a circular tunnel were derived The intermediate principal stress coefficient was used to present the intermediate principal stress effect. The results in this study were compared with the current solutions in the literatures and the influence of intermediate principal stress and shear strength parameters of surrounding rocks was discussed. The results showed extensive applicability and the Mohr-Coulomb strength criterion and Matsuoka-Nakai criterion are two special cases; when the intermediate principal stress coefficient b was equals to 0.5, the results indicated that the intermediate principal stress effect and its range for rock strength; the influence of cohesion and internal friction angle on the plastic radius and tunnel wall displacement was significant; Care should be taken to the effects of intermediate principal stress and shear strength parameter variations of surrounding rocks on tunnel design and construction.     

落锤冲击气囊施加均布动荷载的试验方法

在结构构件上施加均布冲击(爆炸)荷载一直是动力试验领域的难题。提出了一种落锤冲击气囊施加均布动荷载的试验装置,和一个双自由度弹簧阻尼冲击加载简化分析模型;给出了该模型的基本力学方程、边界条件和求解方法,并进行了有限元验证;建立了所提出冲击加载试验装置的精细化有限元模型,分析了构件上各受荷区域的荷载均布情况,验证了所提出装置的可行性。基于所建立的简化分析模型,讨论了刚度、荷载作用时间和阻尼比等关键参数,对构件上动荷载的影响,并给出了基本规律。计算结果表明,在选定合适的参数后,落锤冲击气囊试验装置能够较好地模拟构件上的均布动荷载,为实验室中进行爆炸冲击试验提供了一种可能。     

Galerkin Approximate Solutions of Displacement Including the Effect of Dead Loads for Two Kinds of Rectangular Plates

Based on the strain energy considering the effect of dead loads, the general form static equilibrium differential equations were formulated by means of the potential energy principle. The approximate solutions of live load or later load displacement including the effect of dead loads for the clamped rectangular plate and the simply supported rectangular plate were generated by the Galerkin method. These formulas are simple and clear, and their physical concepts are explicit. The correctness of these formulas was verified by the finite element method. The dead loads and other factors that influence the effect of dead loads are shown by these formulas. The effect of dead loads on the two different boundary condition rectangular plate were analyzed by these approximate solutions. The effect of dead loads improves the bending stiffness of plate and minimizes the displacement of live loads or later loads. The key physical factors governing the effects of dead loads on plates are the dead load, the ration of span to thickness and boundary condition etc. This effect of dead loads is not negligible, especial in thinner plates or plates with smaller stiffness, more attention should be paid to the effect of dead load in the calculation and analysis for plates.     

An Unsteady Flow Analysis in Gas Transmission Pipeline Based on Theory of Functional Analysis

Branch -like pipeline is a common structure in gas transmission pipeline. In the light of the constituent properties of natural gas branch - like pipeline system, the system can be divided into fundamental constituent units. This paper presents a realistic unsteady flow model consisting of simple models of pipeline units and connecting conditions, boundary conditions and initial condition associated with units by using system analysis method. The solutions in wide sense are obtained by theory of functional analysis and operator series method, Such a method has the properties of both analytical solution and numerical solution methods. When the divided pipeline unit is larger, an intuitive approximate analytical solution may be obtained; while the one is smaller, a more accurate numerical solution may be acquired. Based on this, a general computer program has been developed for this model and solutions have been used successfully in a local natural gas transmission network in Sichuan. It is proved that the model and algorithm proposed in this paper are of the advantages of convenient calculation, high precision, time saving and wide application range by way of analysis and application.     

Behavior Analysis of Laterally Loaded Single Pile under Large Deflection

Based on the simplified elastoplastic constitutive model of soil, the calculation method for the laterally loaded single pile with large deflection was submitted. The coefficient of subgrade reaction was presumed to increase linearly with depth, which simulates the soil resistance close to ground well. The relevant program was then developed using FORTRAN language. The examples show that (1)the displacement and bending moment increase nonlinearly when the lateral load and the moment load increase. (2)The pile displacement decreases with depth. (3)The pile displacement at the point which is over ten times pile diameter from ground is so small that can be neglected. (4)The pile head condition is the key factor, which influences the distributions of pile responses along depth. (5)By improving the mechanical properties of soil around pile, the maximum lateral displacement and bending moment can be decreased efficiently. The calculation results are in good agreement with the field test results and are better than those obtained using the pre existing solutions, which shows the presented solutions are reliable.     

Analytical Solution for One Dimensional Contaminant DiffusionThrough Unsaturated Soils Beneath Landfills

A one-dimensional diffusion model was developed to investigate contaminant distributions in unsaturated soils beneath a landfill. On the basis of the assumption that the volume water content is a linear function of depth, the analytical solution of the model was obtained by using the method of separation of variables combined with generalized orthogonal theory. The results obtained by the proposed analytical solution agree well with those obtained by the finite element software COMSOL Multiphysics 4.2. The proposed analytical solution can be degraded to the steady-state solution. When the maximum volume water content of 0.6 and minimum volume water content of 0.3 is assumed for an unsaturated soil, the 100-year contaminant flux at the bottom of unsaturated soil was 91 g/ha/a, which is 1.4 times greater than that of the case assuming porosity of 0.3 for the saturated and 0.7 times less than that with a saturated volume water content of 0.6. When the sum of the top and bottom volume water content of the unsaturated soil remains constant, the relative concentration at the bottom of the soil will decrease with increase of the volume water content at the top of the soil. The bottom contaminant flux was not greatly affected by the variation of the distribution of volume water content when the sum of the top and bottom volume water content remains constant. The proposed analytical solution is relatively simple, and can be used for verification of complicated numerical models, experimental data fitting, and preliminary design of landfill liner systems.     

Deflection and Stress Analysis of a Pavement Slab under Temperature Gradient and Axial Loading Coupling

It has been established that a pavement slab will curl up if a temperature gradient exists across the depth of a slab. A negative temperature gradient causes the slab edge to curl up while a positive temperature gradient curls up the slab center. Temperature stress in slabs is induced by self-weight and other slab constraints. At present in P. R. China, the total stress considered in cement concrete pavement design includes the load stress plus the temperature stress, and only transverse cracking from bottom to top is considered for concrete pavement. Slab responses under axial loads and temperature gradient coupling are not included. We modeled a single slab with a frictionless interface between the slab and foundation using the finite element method. Slab deflection and stress were calculated under axial loads at different slab positions and negative or positive temperature gradient coupling. The calculated results show that the different conditions of axial loads and temperature gradient coupling will change the maximum tension and cause various types of cracks in a slab.     

The Taylor series multipole boundary element method (TSM BEM)and its applications in rolling engineering

Rainfall is the main input for probabilistic analysis and prediction of rainfall-triggered landslide. The joint probabilistic structure of daily rainfall (DR) and cumulative rainfall (CR), which are dominant parameters of rainfall related on landslide in Chongqing region, was analyzed. Following the traditional technology, daily rainfall was translated into discrete variable by rainfall grade and cumulative rainfall became continuous variable if records with very small cumulative rainfall were ignored. Then joint probabilistic model of discrete variable and continuous one was derived, and transiting solution of conditional density function was put forward, together with its approximation via a family of Dirac δ sequences. Naturally, the proposed method was used to analyze conditional density function of cumulative rainfall in Chongqing region, and the numerical results were verified by comparison. However, most of the conditional density functions were irregular and not modeled by simple probability density function, thus the finite mixture distribution was introduced, which is of uncomplicated format and relatively high precision. At last, the joint probabilistic model of daily rainfall and cumulative rainfall was built up by combining frequency function of grade of daily rainfall with conditional density model of cumulative rainfall.     

Non-linear finite element analysis based on the spatial catenary cables

According to the elastic catenary theory,this paper derives the spatial catenary cable element from the exact analytical expression,which is used for finite element analysis of the structure.It deduces the precise expression of two-node cable element tangent stiffness matrix and the tension of cable end.The equivalent node load of cable element is expressed by the total load algorithm,and the non-linear equation is solved by double Newdon-rapson method.The proposed non-linear semi-analytical finite element method based on spatial catenary cable element can take full account of the impact of non-linear geometry.The initial configuration and the internal forces on any directional spatial loads can be solved.The example shows that the calculation method is accurate and effective.     

AN IMPLICIT ENTHALPY SOLUTION OF CONDUCTION-CONTROLLED PHASE CHANGE PROBLEMS

An implicit enthalpy solution is developed for analysis of one-dimensional conduction controlled phase change problems. The solution is based on separating the sensible and latent heat terms in an enthalpy formulation. By making the assumption of equal volume node-jumping,a variable time together with a fixed space grid is used to ensure that the phase boundary is always on a node point,so that the nonlinearity associated with the latent heat can be effectively dealt with via the source term. A freezing problem around a pipe with analytical solution is applied to demonstrate the effect of the present method.     

Corrected extended finite element method for two phase flow

An extended finite element method based on SUPG/PSPG is proposed to simulate the two phase flow problems. A corrected XFEM is introduced to ensure the blending element to satisfy the Partition of Unity in processing the discontinuity of the interface. Level set method is adopted to track the kinetic phase interface as the fluid flow. Free oscillation is numerically simulated with the presented method. The obtained numerical results are in consistent with the analytical and experimental results. Additionally, breaking dam problem is considered, the numerical solutions agree well with experimental results which illustrate the correctness and efficiency of the proposed method. No re-meshing is needed during the simulation of the two phase fluid flow and the moving interface can be accurately tracked by means of the presented method.     

Calculating Critical Loads of Thin Plates With Method of Weighted Residuals

In elastic mechanics, it is common practice to calculate critical loads in buckle of thin plates by means of double triangle series. The calculation process is more complex, this method has not facility in engineering application. In many cases critical loads of thin plates can not obtain precise analytic solutions. It is very important to solve approximate resolutions of critical loads of plates in engineering. The method of weighted residuals is an available measure to solve proximal resolutions of differential equations and has extensive application in egineering. In order to simplify calculation process and obtain profitble result, by means of method of weighted residuals and Cantorovich variational principle, taking the second Tchebychev's polynomials as trial functions, it was calculated, critical loads of rectangle thin plates in different supporting conditions. Calculation results indicate that this calculation method is simple and has some precision, it is applied conveniently in engineering.     

Galerkin Boundary Element Method for Direct Boundary Integral Eqution for Dirichlet Problem of 2-D Laplace Eqation

The direct boundary integral equation of two-dimensional Laplace equation for Dirichlet problem is(con-sidered).It is deduced by Green's formula and the fundamental solution.The most-used numerical method for solving(direct) boundary integral equation is collocation method,and seldom have been used the Galerkin scheme in this case.The direct boundary integral eqution is changed into the variational eqution.Using linear element,it is solved by Galerkin boundary method.In the variational eqution double integrations shall be carried out.The paper presents the analytical formula to calculate the inner integration and the Gaussian quadrature is used for the outer integration. The numerical experimentation proved thefaesibility and the efficiency.     

Diffusion Behavior of Chloride Ions in Concrete Pipe Piles

Concrete pipe piles, whose internal surface is usually closed and external one is exposed to chloride environment, are widely used in marine environment. Based on Fick second law and the boundary condition of pipe pile, the analytical solution to chloride diffusion equation was deduced with the method of separation of variables. The solution comprises two parts: a stationary solution consisting of Bessel functions, and a transient solution. This is different from the traditional analytical solution that is based on semi-infinite boundary condition. Applying this result to a typical PHC pipe pile, the diffusion of chloride concentration was analyzed. Furthermore, the effects of the ratio of outer radius and inner radius, diffusion coefficient and protective concrete cover thickness on diffusion of chloride concentration were also discussed. When the ratio of outer radius and inner radius equals 1.5, the decay rate of secondary segment of transient solution is 4 times larger than that of the primary part. This example provides a computational basis for the corrosion of steel bar and some reference for durability design of pipe piles as well.     

Deformation Monitoring and Its Control in a Shallow buried Large span Tunnel Constructed Using the Pile Beam Arch Method

Deformation monitoring and control measures of a shallow buried large span tunnel constructed using the pile beam arch (PBA) method are described, taking the North Gongti Road Station of Beijing Metro line 10 as an example. Based on the monitoring datum, the crown settlement, convergence, ground settlement of the tunnel and the bridge foundation settlement are analyzed. The results show that (1) the PBA tunneling method can restrain the ground settlement and deformation of a shallow buried large span tunnel; (2) the depth, tunnel span and pilot tunnel construction may influence the deformation of a shallow buried large section tunnel significantly; and, (3) advanced conduit grouting, timely preliminary support and permanent lining construction can reduce the deformation effectively.     

An Elastic Theory Approach and Parametric Analysis of Pile Group in Layered Soils

Based on the technique proposed by Muki & Sternberg, a rigorous analytical method for calculating the interaction factor between two piles with different lengths, diameters and properties is presented. The pile group in layered soils is calculated by using the principle of superposition. The validity of the presented method has been verified through comparing with those from other existing solutions. A parametric analysis is made to study the pile group settlement and the loads shared by the individual pile. The proposed interaction factors of pile-pile can consider the strengthening effect of intervening piles. The proposed method can be used to analyze the large pile group.     

Comparision of Theoritical Solutions and Ultimate Span-Length between FRP Cables and Steel Cables

As the self weight of cable affects mechanical behavior obviously with the inerease of span length.FRP (fiber reinforced polymer) cable that has the lighter weight than the conventional cables has advantage for long span structures.The analysis of single cable is the fundamental theory for the design of cable structures.Based on different considerations of gravity loads.the solutions of the single cable on gravity loads have three sets of solutions: parabola solution.catenary solution and elastic catenary solution.And the equations for the three sets of solutions are derived by taking the end tension force of cable as the control parameter.The comparison between FRP cables and steel cables is conducted by elastic catenary solution.and the results show that the lager span structure can be realized by FRP cables.The precision for the parabola solution and catenary solution is compared for stay cables and horizontal cables.and the proper ranges of both approximate methods are proposed.Based on the above methods.the ultimate span length of FRP cable and steel cable are analyzed.It is concluded that the ultimate span of FRP cable is 4.4 times larger than that of steel cable.     

A Calculating Method of Non Linear Earth Pressure Behind Retaining Walls

Based on equilibrium analysis of forces and moment with inclined soil element, an analytical solution of earth pressure with inclined surface of fill and rough retaining wall was proposed, and the influence of slope angle of fill on earth pressure also was discussed. It is shown that the classical Rankine's earth pressure theory is a special case of the analytical solution with horizontal surface of fill and a smooth retaining wall. The results also show that the limiting rupture angle of a sliding wedge behind a retaining wall decreased with increasing slope angle of fill or friction angle between soil and a retaining wall, with the settled value of the internal friction angle of fill. The non linear character of earth pressure exhibited distinctly for the earth pressure along a retaining wall was obtained by an analytical solution. The value of earth pressure is 0 at the toe of retaining wall, consistent with the testing results. In addition, the value of earth pressure at the toe of the retaining wall will increase rapidly with increasing slope angle of fill. The analytical solution of earth pressure behind a retaining wall with fill of clay soils can be further studied with the investigative method we developed.