Undrained semi-analytical solution for cylindrical cavity expansion in anisotropic soils under biaxial stress conditions

This paper presents an undrained semi-analytical elastoplastic solution for cylindrical cavity expansion in anisotropic soil under the biaxial stress conditions.The advanced simplified SANICLAY model is used to simulate the elastoplastic behavior of soil.The cavity expansion is treated as an initial value problem and solved as a system of eight first-order ordinary differential equations including four stress components and four anisotropic parameters.The results are validated by comparing the new solutions with existing ones.The distributions of stress components and anisotropic parameters around the cavity wall,the expansion process,the stress yield trajectory of a soil element and the shape and size of elastoplastic boundary are further investigated to explore the cavity expansion response of soils under biaxial in situ stresses.The results of extensive parameters analysis demonstrate that the circumferential position of the soil element and the anisotropy of the soils have noticeable impacts on the expansion response under biaxial in situ stresses.Since the present solution not only considers the anisotropy and anisotropy evolution of natural soil,but also eliminates the conventional assumption of uniform radial pressure,the solution is better than other theoretical solutions to explain the pressure test and pile installation effect of shallow saturated soil.

ANALYTICAL SOLUTIONS TO EXPANSION OF CYLINDRICAL CAVITY IN LINEAR SOFTENING SOIL

Based on the results of conventional triaxial compression tests for a soil, a trilinear elasto-plastic model is proposed to simulate the stress-strain softening curve. According to this curve, the constitutive relation between the bulk strain and two principal strains is established. By using Mohr-Coulomb’s yield criterion as the initial yield function with plastic ?ow phases stage and constructing the rational yield function for the strain softening phase stage, the analytical solutions to the stress, strain, and displacement ?elds for the expansion of cylindrical cavity are presented. Finally, a computational example is used to show the radii of di?erent stress zones and the corresponding internal pressure.

SOLUTIONS FOR CYLINDRICAL CAVITY IN SATURATED THERMOPOROELASTIC MEDIUM

Based on the thermodynamics of irreversible processes, the mass conservation equation and heat energy balance equation are established. The governing equations of thermal consolidation for homogeneous isotropic materials are presented, accounting for the coupling effects of the temperature, stress and displacement fields. The case of a saturated medium with a long cylindrical cavity subjected to a variable thermal loading and a variable hydrostatic pressure （or a variable radial water flux） with time is considered. The analytical solutions are derived in the Laplace transform space. Then, the time domain solutions are obtained by a numerical inversion scheme. The results of a typical example indicate that thermodynamically coupled effects have considerable influences on thermal responses.

Cylindrical cavity expansion responses in anisotropic unsaturated soils under plane stress condition

In this paper,an anisotropic critical state model for saturated soils was extended to unsaturated conditions by introducing suction into its yield function.Combining this model with soil-water characteristic curves related to porosity ratio was employed to characterize the coupled hydromechanical behavior of unsaturated anisotropic soil.Based on the plane stress condition,the problem of the cylindrical cavity expansion in unsaturated anisotropic soils was transformed into first-order differential equations using the Lagrangian description.The equations were solved as an initial value problem using the Runge-Kutta algorithm,which can reflect the soil-water retention behavior during cavity expansion.Parametric analyses were conducted to investigate the influences of overconsolidation ratio(OCR),suction,and degree of saturation on the expansion responses of a cylindrical cavity in unsaturated anisotropic soil under plane stress condition.The results show that the above factors have obvious influences on the cavity responses,and the plane strain solution tends to overestimate expansion pressure and degree of saturation but underestimates suction around the cavity compared to the proposed plane stress solution.The theoretical model proposed in this paper provides a reasonable and effective method for simulating pile installation and soil pressure gauge tests near the ground surface of the unsaturated soils.

Numerical Study of Convective and Radiation Heat Transfer Characteristics in an Upward-Facing Cylindrical Cavity under Back-Side Windy Condition

Under the back-side windy condition,the convection and radiation heat transfer characteristics in an iso-flux upward-facing cylindrical cavity were studied by three-dimensional numerical simulation.The impacts of cavity tilt angle,wind incident angle and wind speed on convection and radiation heat transfer Nusselt number Nuc and Nur were analyzed,and the possible explanations for their impacts were presented.Results show that due to the disturbance of wind,the influence of cavity tilt angle becomes more complicated and is related to wind incident angle and wind speed.The variation of Nuc or Nur with wind incident angle is different for different cavity tilt angles.Despite of the changes of cavity tilt angle or wind incident angle,the Nuc increases with the wind speed while the Nur presents a declination with the increasing of wind speed.Hence,compared with cavity tilt angle and wind incident angle,wind speed may be the dominant factor affecting or controlling the convective and radiation heat transfer of cavity.

Forced and Natural Vibrations of an Orthotropic Pre-Stressed Rectangular Plate with Neighboring Two Cylindrical Cavities

Forced and natural vibrations of a rectangular pre-stressed orthotropic compositeplate containing two neighboring cylindrical cavities whose cross sections are rectangularwith rounded-off corners are investigated numerically. It is assumed that all the end surfacesof the rectangular pre-stressed composite plate are simply supported and subjected to auniformly distributed normal time-harmonic force on the upper face plane. The consideredproblem is formulated within the Three-Dimensional Linearized Theory of Elastic Waves inInitially Stressed Bodies (TDLTEWISB). The influence of mechanical and geometricalparameters as well as the initial stresses and the effect of cylindrical cavities on the dynamicalcharacteristics of the rectangular orthotropic composite plate are analyzed and discussed.

Different optical properties in different periodic slot cavity geometrical morphologies

In this paper,optical properties of two-dimensional periodic annular slot cavity arrays in hexagonal close-packing on a silica substrate are theoretically characterized by finite difference time domain（FDTD） simulation method.By simulating reflectance spectra,electric field distribution,and charge distribution,we confirm that multiple cylindrical surface plasmon resonances can be excited in annular inclined slot cavities by linearly polarized light,in which the four reflectance dips are attributed to Fabry–Perot cavity resonances in the coaxial cavity.A coaxial waveguide mode TE11 will exist in these annular cavities,and the wavelengths of these reflectance dips are effectively tailored by changing the geometrical pattern of slot cavity and the dielectric materials filled in the cavities.These resonant wavelengths are localized in annular cavities with large electric field enhancement and dissipate gradually due to metal loss.The formation of an absorption peak can be explained from the aspect of phase matching conditions.We observed that the proposed structure can be tuned over the broad spectral range of 600–4000 nm by changing the outer and inner radii of the annular gaps,gap surface topography.Meanwhile,different lengths of the cavity may cause the shift of resonance dips.Also,we study the field enhancement at different vertical locations of the slit.In addition,dielectric materials filling in the annular gaps will result in a shift of the resonance wavelengths,which make the annular cavities good candidates for refractive index sensors.The refractive index sensitivity of annular cavities can also be tuned by the geometry size and the media around the cavity.Annular cavities with novel applications can be implied as surface enhanced Raman spectra substrates,refractive index sensors,nano-lasers,and optical trappers.

An engineering analysis of penetration of metal ball into fibre-reinforced composite targets

An engineering analysis of computing the penetration problem of a steel ball penetrating into fibre-reinforced composite targets is presented. Assume the metal ball is a rigid body, and the composite target is a transversely isotropic elasto-plastic material. In the analysis, a spherical cavity dilatation model is incorporated in the cylindrical cavity penetration method. Simulation results based on the modified model are in good agreement with the results for 3-D Kevlar woven （3DKW） composite anti-penetration experiments. Effects of the target material parameters and impact parameters on the penetration problem are also studied.

The Scattering of SH Wave in a Nano Hole Embedded the Infinite Inhomogeneous Medium

Scattering of the shear waves by a nano-sized cylindrical hole embedded the inhomogeneous is investigated in this study. The Helmholtz equation with a variable coefficient is transformed the standard Helmholtz equation by the complex function method and the conformal mapping method. By wave function expanding method, the analytical expressions of the displacement field and stress field in the inhomogeneous medium are obtained. Considering the surface effect and using the generalized Young-Laplace equation, we obtain the boundary conditions at nano arbitrary-shaped hole, then the field equations satisfying boundary conditions are attributed to solving a set of infinite algebraic equations. Numerical results show that when the radius of the cylindrical cavity shrinks to nanometers, surface energy becomes a dominant factor that affects the dynamic stress concentration factor (DSCF) around the cylindrical cavity. The influence the density variation of the inhomogeneity on the DSCF is discussed at the same time.

Nonstationary plane contact problem in theory of elasticity for conformal cylindrical surfaces

A numerical–analytical approach is described to investigate the process of impact interaction between a long smooth rigid body and the surface of a circular cylindrical cavity in elastic space. A non-stationary mixed initial boundary value problem is formulated with a priori unknown boundaries moving with variable velocity. The problem is solved using the methods of the theory of integral transforms, expansion of desired variables into a Fourier series, and the quadrature method to reduce the problem to solving a system of linear algebraic equations at each time step. Some concrete numerical computations are presented.The cylindrical body mass and radius impact on the proile of the transient process of contact interaction has been analysed.

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

Abstract.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 fromthe 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.